BJ Services’ Frac Manual
Contents
BJ SERVICES COMPANY
HYDRAULIC FRACTURING
MA N U A L
Version 1.0
(A4-Sized)
June 2005
Page i
Version 1.0 June 2005
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Tony Martin
Region Engineer
Singapore
BJ Services’ Frac Manual
Contents
Contents
Contents .....................................................................................................................................ii
List of Figures ............................................................................................................................ v
1.
Introduction ................................................................................................................... 1
2.
Basics of Hydraulic Fracturing...................................................................................... 4
2.1
2.2
2.3
2.4
2.5
3.
Types of Fracturing..................................................................................................... 12
3.1
3.2
3.3
3.4
3.5
3.6
4.
Stress........................................................................................................................................53
Strain ........................................................................................................................................53
Young’s Modulus.......................................................................................................................54
Poisson’s Ratio .........................................................................................................................55
Other Rock Mechanical Properties ............................................................................................56
In-Situ Stresses.........................................................................................................................58
Stresses Around a Wellbore......................................................................................................59
Fracture Orientation ..................................................................................................................60
Breakdown Pressure and Frac Gradient....................................................................................61
Rock Mechanical Properties from Wireline Logs........................................................................63
2-D Fracture Models ................................................................................................... 68
8.1
8.2
8.3
Page ii
Proppant Pack Permeability and Fracture Conductivity .............................................................45
Proppant Selection....................................................................................................................48
BJ Services FlexSand and LiteProp .........................................................................................50
Rock Mechanics ......................................................................................................... 53
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
8.
Water-Based Linear Systems....................................................................................................29
Water-Based Crosslinked Systems ...........................................................................................30
Oil-Based Systems....................................................................................................................33
Emulsions .................................................................................................................................35
Energised Fracturing Fluids.......................................................................................................35
Visco-Elastic Surfactant Fluids ..................................................................................................36
Additives ...................................................................................................................................40
Proppants ................................................................................................................... 45
6.1
6.2
6.3
7.
Fundamental Fluid Properties ...................................................................................................19
Shear Stress and Shear Rate....................................................................................................19
Types of Fluid ...........................................................................................................................20
Measuring Viscosity ..................................................................................................................23
Apparent Viscosity ....................................................................................................................25
Flow Regimes and Reynold’s Number.......................................................................................26
Friction Pressure .......................................................................................................................27
Fluid Systems ............................................................................................................. 29
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.
Low Permeability Fracturing ......................................................................................................12
High Permeability Fracturing .....................................................................................................12
Frac and Pack Treatments ........................................................................................................13
Skin Bypass Fracturing .............................................................................................................15
Coal Bed Methane Fracturing....................................................................................................16
Fracturing Through Coiled Tubing .............................................................................................16
Fluid Mechanics.......................................................................................................... 19
4.1
4.2
4.3
4.4
4.5
4.6
4.7
5.
The Basic Process ......................................................................................................................4
Pressure .....................................................................................................................................5
Basic Fracture Characteristics.....................................................................................................6
Fluid Leakoff ...............................................................................................................................8
Near Wellbore Damage and Skin Factor ....................................................................................9
Radial or Penny-Shaped ...........................................................................................................68
Kristianovich and Zheltov - Daneshy (KZD) ...............................................................................69
Perkins and Kern – Nordgren (PKN)..........................................................................................70
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9.
Fracture Mechanics .................................................................................................... 72
9.1
9.2
9.3
10.
Advanced Concepts.................................................................................................... 80
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.
Planning and Execution...........................................................................................................121
Anatomy of a Minifrac..............................................................................................................124
Decline Curve Analysis ...........................................................................................................125
Pressure Matching ..................................................................................................................131
Near Wellbore Effects and Multiple Fractures..........................................................................132
Minifrac Example 1 - 2D Minifrac Analysis...............................................................................134
Minifrac Example 2 - 3D Pressure Matching with FracProPT...................................................139
Minifrac Example 3 – Problems with Tortuosity .......................................................................147
Minifrac Example 4 – Perforation Problems.............................................................................153
Designing the Treatment .......................................................................................... 164
17.1
17.2
17.3
17.4
17.5
17.6
17.7
Page iii
The Step Up Test ....................................................................................................................115
The Step Down Test ...............................................................................................................116
Step Rate Test Example – Step Up/Step Down Test ...............................................................117
The Minifrac .............................................................................................................. 121
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17.
Controlling Fracture Initiation...................................................................................................109
Controlling Tortuosity ..............................................................................................................111
Perforating for Skin Bypass Fracturing ....................................................................................112
The Step Rate Test .................................................................................................. 115
15.1
15.2
15.3
16.
Economic Justification for Fracturing .......................................................................................101
Completion Limitations ............................................................................................................104
Things to Look For ..................................................................................................................106
Perforating for Fracturing.......................................................................................... 109
14.1
14.2
14.3
15.
Steady State Production Increase .............................................................................................95
Pseudo-Steady State Production Increase ................................................................................96
Nodal Analysis ..........................................................................................................................99
Candidate Selection.................................................................................................. 101
13.1
13.2
13.3
14.
RES’s FracPro and Pinnacle Technology’s FracproPT..............................................................91
Meyers & Associates’ MFrac .....................................................................................................92
Other Simulators .......................................................................................................................93
Predicting Production Increase................................................................................... 95
12.1
12.2
12.3
13.
Tortuosity ..................................................................................................................................80
Nolte Analysis ...........................................................................................................................82
Dimensionless Fracture Conductivity.........................................................................................82
Tip Screen Out ..........................................................................................................................83
Multiple Fractures and Limited Entry .........................................................................................84
Proppant Convection and Settling .............................................................................................85
Proppant Flowback ...................................................................................................................86
Forced Closure..........................................................................................................................88
Non-Darcy Flow ........................................................................................................................88
3-D Fracture Simulators ............................................................................................. 91
11.1
11.2
11.3
12.
LEFM and Fracture Toughness .................................................................................................72
Non-Linear and Non-Elastic Effects...........................................................................................75
The Energy Balance..................................................................................................................77
General ...................................................................................................................................164
Designing for Skin Bypass.......................................................................................................165
Designing for Tip Screen Out ..................................................................................................166
Designing for Frac and Pack ...................................................................................................167
Designing for Tight Formations ...............................................................................................168
Designing for Injection Wells ...................................................................................................170
Designing for CBM Treatments ...............................................................................................170
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17.8
17.9
17.10
18.
Real-Time Monitoring and On-Site Re-Design......................................................... 176
18.1
18.2
18.3
19.
Horsepower Requirements......................................................................................................209
Flow Lines...............................................................................................................................210
High Pressure Pumps .............................................................................................................211
Intensifiers...............................................................................................................................214
Blenders, Gel Hydration and Liquid Additives..........................................................................216
Proppant Storage and Handling ..............................................................................................218
Treatment Monitoring ..............................................................................................................220
Wellhead Isolation Tool ...........................................................................................................221
The Frac Spread – How it Fits Together. .................................................................................224
Designing Wells for Fracturing ................................................................................. 228
21.1
21.2
21.3
22.
Pressure Matching ..................................................................................................................186
Well Testing for Fracture Evaluation........................................................................................193
Other Diagnostic Techniques .................................................................................................205
Equipment................................................................................................................. 209
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
21.
Real-Time Data Gathering.......................................................................................................176
On-Site Redesign....................................................................................................................181
Real-Time Fracture Modeling ..................................................................................................183
Post Treatment Evaluation ....................................................................................... 186
19.1
19.2
19.3
20.
Designing for Coiled Tubing Fracturing ...................................................................................172
Unified Fracture Theory and Proppant Number .......................................................................173
Net Present Value Analysis .....................................................................................................174
How Many Wells do I Need to Drill? ........................................................................................228
The Best Wells are the Best Candidates for Fracturing ...........................................................229
Designing Wells for Fracturing ................................................................................................229
The Fracture Treatment: From Start to Finish.......................................................... 232
22.1
22.2
Frac Job Flow Chart ................................................................................................................232
Example Treatment Schedules ...............................................................................................238
Nomenclature ........................................................................................................................ 241
Index
Page iv
.................................................................................................................................. 245
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List of Figures
Section 2
2.1a
2.3a
2.5a
Typical hydraulic fracture treatment job plot.
Diagram showing fracture half Length xf, fracture height H, and fracture width W.
Illustration of the reduction in permeability around the wellbore.
Section 3
3.3a
3.3b
3.4a
Diagram illustrating the components of the frac-pack completion.
Diagram illustrating two of the four positions in which a standard gravel pack or frac
pack tool can be set. The left hand side shows the squeeze position, in which fluids
flow down the tubing, through the crossover, out into the annulus below the GP
packer and into the formation. The right hand side shows the lower circulating
position. Fluid flows down to the perforations, as for the squeeze position. However,
because the setting tool has been shifted upwards, the fluid can flow either into the
formation, or back through the screens, up the washpipe (inside the screens) through
the crossover, and out into the annulus above the tubing (shown in blue). By closing
the annulus at surface, the fluid can be squeezed into the formation, whilst
maintaining a dead string on the annulus, to monitor BHP.
Diagram illustrating how the skin bypass fracture penetrates the skin to allow
undamaged communication between the reservoir and the wellbore.
Section 4
4.2a
4.3a
4.3b
4.3c
4.4a
4.4b
4.4c
4.4d
4.5a
4.6a
Graph illustrating Newton’s law of fluids
Relationship between shear rate and shear stress for a Bingham plastic fluid.
Relationship between shear rate and shear stress for a power law fluid. Note that the
graph shows the relationship in its most common form. However, in certain fluids the
line can also curve upwards.
Power law fluid log-log plot.
Chandler 35 viscometer. The position of the rotor is indicated (A), whilst the bob is
hidden inside this. The cup (B) holds the test fluid, and is mounted on a support (C)
that can move up and down as required.
Cross-section through the rotor and bob on a model 35 viscometer.
Schematic diagram showing the model 35 viscometer bob assembly.
Fann 50 high pressure, high temperature rheometer. This model is fully computer
controlled, whereas earlier models had manual controls and were twice the size of the
model shown.
Graph illustrating the change in apparent viscosity for a power law fluid at two
different shear rates.
Diagram illustrating the three flow regimes.
Section 5
5.1a
5.2a
5.2b
5.2c
5.3a
5.6a
Page v
Hydration of polymer gels in water. A shows a polymer molecule before hydration in
water, whilst B shows a polymer molecule after hydration in water.
A crosslinked polymer. A shows the hydrated polymer prior to addition of the
crosslinker. B shows the crosslink chemical bonds between the polymer molecules.
pH ranges for crosslinkers (after SPE 37359).
Temperature range for crosslinkers (after SPE 37359).
Aluminium phosphate association polymer.
Proppant transport as a function of foam quality. This graph is a combination of the
work performed by several individuals and organisations. It is intended as a
qualitative illustration of the effect foam quality has on the ability of the fracturing
foam to transport and suspend proppant.
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Section 6
6.1a
6.1b
6.1c
6.1d
6.3a
The effect of uniform and natural grain size distribution on porosity.
Diagram illustrating how larger grains have larger pore spaces and hence greater
permeability.
Diagram illustrating the difference between a proppant with good sphericity and
roundness (left), and a proppant with poor sphericity and roundness (right).
Three SEM micrographs showing the effects of frac fluid residue. The micrograph on
the left shows undamaged proppant before the addition of the frac fluid. The center
micrograph shows the residue left by a poorly designed crosslinked system. The final
micrograph shows the same proppant pack after an enzyme breaker has been used.
SEM micrograph of FlexSand grain clearly showing the indentations caused by the
closure of the surrounding proppant grains.
Section 7
7.1a
7.2a
7.4a
7.5a
7.5b
7.7a
7.8a
A block of material subjected to a force F.
Strain produced by the application of force F.
Application of force F also produces a deformation in the y direction.
Force F applied to produce a shear stress.
Volume changes from V1 to V2 as pressure increases from P1 to P2.
Three dimensional stresses around a wellbore.
Changes in stress regime due to erosion.
Section 8
8.1a
8.2a
8.3a
Propagation of a radial or penny-shaped fracture.
Schematic showing the general shape of the KZD fracture.
The Perkins and Kern - Nordgren fracture.
Section 9
9.1a
9.1b
9.1c
9.2a
9.2b
9.2c
9.3a
The Griffith crack.
Failure modes in Linear Elastic Fracture Mechanics.
Coordinate system for stress intensity factor.
The Cleary et al approach.
Crack tip diameter and the plastic zone. Note that rp is the radius of the plastic zone.
The shape of the plastic zone, for a Poisson’s ratio of 0.25.
Sources of Energy Gains and Losses for the fracturing fluid. Energy Gains + Energy
Losses = 0.
Section 10
10.1a. Diagram illustrating the effects of horizontal stress contrast on tortuosity (after GRIAST 1996).
10.2a The Nolte plot.
10.4a The Tip Screen Out.
10.6a Proppant convection. As the heavier slurry enters the fracture it sinks and displaces
the lighter slurry upwards.
10.7a Illustration of the “Pipelining” effect.
Section 12
12.2a
12.2b
12.2c
12.3a
Page vi
Transient production. The red lines illustrate the variation of pressure with distance
from the wellbore, as time increases. The radius of the disturbed formation is
continually increasing.
Pseudo-steady state production. The radius of the disturbed formation has reached
the reservoir boundary, re, and now the reservoir pressure is decreasing.
The McGuire-Sikora Curves.
Nodal analysis IPR curves for a gas well with a fracture of varying propped fracture
width.
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Section 13
13.3a
The effect of skin factor upon production rate. Note that this Figure is based purely on
skin factor effects. No fracture stimulation is included.
Section 14
14.1a
14.1b
14.2a
14.2b
14.3a
14.3b
The Effect of perforations on fracture initiation.
Perforating for zonal coverage.
Perforation strategy for vertical wells.
Perforation strategy for horizontal wells.
The Effect of fracture initiation point on skin bypass fracs.
Multiple skin bypass fracs over a long interval.
Section 15
15.1a
15.2a
15.3a
15.3b
15.3c
The step up test.
The step down test.
Step up pressure-rate crossplot using the example data. This plot shows the fracture
extension pressure to be at +/- 6570 psi.
Step down pressure-rate crossplot for the example data. The convex shape of the
curve indicates near wellbore friction dominated by tortuosity.
Step down pressure-rate crossplot for the example data, using surface treating
pressure (STP). This graph illustrates the danger of using STP for step rate test
analysis, as in this case, the near wellbore friction would have been incorrectly
diagnosed as being perforation dominated.
Section 16
16.2a
16.2b
16.3a
16.3b
16.3c
16.3d
16.4e
16.4f
16.6a
16.6b
16.6c
16.6d
16.6e
16.7a
16.7b
16.7c
16.7d
16.7e
16.7f
16.7g
16.7h
Page vii
Typical minifrac job plot, showing BHTP, STP and rate.
Expanded plot showing BHTP.
Typical minifrac pressure decline curve.
Use of a square root time plot to determine closure pressure.
Typical minifrac pressure decline Horner plot.
Graph showing the variation of g(∆tD) with ∆tD.
Typical Nolte G time pressure decline plot.
Example derivative plot based on a Horner Plot.
Minifrac example 1 job plot.
BH gauge pressure decline against elapsed time. Possible closure pressure at +/2770 psi (where the two red lines cross, marking a change in gradient). Note the
sudden drop of about 50 psi as the pumps shut down at t = +/- 13 mins.
BH gauge pressure decline against the square root of elapsed time. Possible closure
pressure at +/- 2790 psi (where the two red lines cross, marking a change from
straight line to curve).
G function plot. The “true” ISIP is at +/- 3150 psi, whilst the closure pressure appears
to be at +/- 2780 psi (where the two red lines cross). This gives a Gc of 1.30.
Horner plot. The results from this plot are ambiguous and do not help in the analysis.
Minifrac example 2 step rate test job plot.
Step rate test crossplot for minifrac example 2, step rate test, showing fracture
extension at +/- 8700 psi.
Minifrac example 2 job plot.
Comparison between gauge and calculated BHTP for minifrac example 2. Note that
whilst the calculated BHTP follows the same general trend as the gauge BHTP, the
actual value is quite different. Short term variations in the trend of the calculated
BHTP are caused by the variations in rate. The general offset of the data is probably
caused by incorrect input data in the fracture monitoring package (in this case
FracRT).
Minifrac example 2 pressure decline with derivative.
Minifrac example 2 pressure decline square root time plot, with derivative.
Initial pressure match for minifrac example 2.
Interim pressure match after the stresses have had a first approximate adjustment. In
this case, the stress gradient for the sandstone was increased from 0.62 to 0.68 psi/ft,
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and then 1300 psi was added to each stress. Note that the pressures are on a larger
vertical scale than in Figure 16.7g.
16.7i Minifrac example 2 final pressure match.
16.7j FracProPT estimated fracture dimensions for minifrac example 2.
16.8a Minifrac example 3 treatment plot.
16.8b Minifrac example 3, detail of post-treatment pressure decline.
16.8c Minifrac example 3, square root time pressure decline plot.
16.8d Horner plot for minifrac example 3. Note that several lines may be fitted to the final
slope on the LHS of this plot. In fact, the reservoir pressure is substantially lower than
that indicated on the plot (as the well is produced by ESP’s), so all of these lines may
be unreliable.
16.8e G Function plot for minifrac example 3. Note the true ISIP of +/- 2730 psi, and the
closure pressure of +/- 2320. These values are in agreement with the value obtained
from other plots, such as the pressure decline and the square root time plots.
16.8f MFrac output showing the initial pressure match before any adjustments were made.
There is very little agreement between the predicted and actual BHTP’s.
16.8g Final MFrac output, after the model has been adjusted.
16.9a Job plot for Minifrac Example 4, Step Rate Test 1
16.9b Step up crossplot for Step Rate Test 1. Fracture extension seems to be at
approximately 9100 psi.
16.9c Step down crossplot. Note the concave shape of the best fit curve, indicating that the
near wellbore friction is dominated by the perforations.
16.9d Minifrac Example 4 job plot.
16.9e Detail of job plot showing bottom hole proppant concentration, gauge BHTP and
slurry rate, as the proppant slug enters the formation. Note the +/- 400 psi rise in
pressure.
16.9f Minifrac pressure decline, showing +/- 650 psi near wellbore friction and a closure
pressure of +/- 8350 psi.
16.9g Square root of time plot for the minifrac pressure decline. This gives a slightly lower
closure pressure than Figure 16.9f, at +/- 8230 psi.
16.9h Job plot for second step rate test.
16.9i Step down crossplot for the second step rate test.
16.9j Minifrac Example 4 BHTP plot before pressure matching.
16.9k Minifrac Example 4 pressure match using MFrac.
16.9l Job plot for the main treatment for Minifrac Example 4. Note the proppant
concentration is measured at the surface.
16.9m Detail of the main treatment for Minifrac Example 4, showing the formation’s response
to the proppant slugs. Proppant concentration is bottom hole.
Section 17
17.4a
17.9a
The diagram on the LHS illustrates the position of the slurry and the ‘pack’ at
screenout – with the top of the ‘packed’ proppant at the top of perforations, and the
annular space between the completion and the wellbore full of slurry, up until the
crossover ports. The RHS shows the position of the pack after all the proppant has
been allowed to settle.
Optimum dimensionless fracture conductivity against dimensionless proppant number
(after Economides et al, 2002).
Section 18
18.1a
18.1b
18.1c
18.2a
Process loop for real-time fracture modeling and redesign.
Inside of a typical frac control van, showing the numerical display and some of the
displays being run by JobMaster.
Remote data transmission schematic.
On-site redesign process flowchart.
Section 19
19.1a
19.2a
Pressure matching. The variables in the simulator are adjusted to make the
calculated net pressure match the actual net pressure.
Anatomy of a drawdown / build-up well test (after Agarwal, 1980)
Page viii
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19.2b
19.2c
19.2d
19.2e
19.2f
19.2g
19.2h
19.2i
19.2j
19.2k
19.2l
19.3a
19.3b
Graphs illustrating the deviation from transient flow caused by a reservoir boundary
(i.e. pseudo-steady state flow).
Constant rate drawdown semi-log plot. The straight line section can be used to
evaluate the permeability. The deviation from the straight line at late time, is due to
boundary effects of the reservoir, as the transient flow changes to pseudo-steady
state flow.
Example Horner plot, showing the extrapolation of the straight line portion to obtain
the reservoir pressure, Pi. Once again, deviation from the straight line is caused by a
change from transient flow to pseudo-steady state flow.
Log-log diagnostic plot with derivative for the pressure build-up of an infinite-acting
reservoir (i.e. no boundaries and no pseudo-steady state flow).
Log-log diagnostic plot with derivative for the pressure build-up of reservoir with a
partial boundary (e.g. a sealing fault).
Log-log diagnostic plot with derivative for the pressure build-up of an infinite
conductivity fracture.
Log-log diagnostic plot with derivative for the pressure build-up of a finite conductivity
fracture.
Type curves for a single well in an infinite reservoir, with wellbore storage and skin
damage (after Agarwal, Al-Hussainy and Ramey, 1970).
Example of a log-log plot of ∆t against ∆P, used for type curve matching.
Post-treatment log-log plot of well test data for a gas well.
Type curves for a well with a finite conductivity, vertical fracture (after Agarwal et al,
1979 and Economides et al, 1987).
The principle of tiltmeter fracture diagnostics (after Cipolla and Wright, 2000).
Generic temperature log illustrating that the treating fluid has entered only a small
portion of the perforated interval. The fracture will have initiated in the smaller interval.
However, this does not necessarily mean that this is the center of the fracture.
Section 20
20.1a
20.2a
20.3a
20.3b
20.3c
20.3d
20.3e
20.3f
20.3g
20.4a
20.4b
20.4c
20.4d
20.5a
20.5b
20.5c
20.5d
20.5e
Page ix
Typical pump curves. This set is for a 30-16-6 frac skid, with a 16V92TA engine, a
CLBT8962 transmission and a pacemaker pump with a 4.5 inch fluid end. Nominal
rating of the pump skid is 700 HHP.
Chart showing fluid velocity against fluid rate for various nominal diameters of Figure
1502 high pressure iron.
Schematic diagram of a generic frac pump.
Generic frac pump, suction stroke.
Generic frac pump, discharge stroke.
Skid mounted 16V 92T pump unit (700 HHP). Skid splits into two parts.
Two views of a trailer-mounted Gorilla pump unit (2700 HHP).
Body-load Kodiak pump unit (2200 HHP).
Skid-mounted 1300 HHP pump unit.
Schematic diagram of a generic intensifier.
Schematic diagram of the intensifier hook-up.
Intensifier worksite. Each intensifier (A) is hooked up to three frac pumpers (B), which
are pumping the power fluid. Power fluid is handled by the power fluid unit (C).
Intensifiers are rigged into a manifold (D). Note that whilst there are three intensifiers
and 9 power fluid pumpers on location, there are also an additional two frac pumpers
(E) rigged up to the downhole line to provide extra horsepower.
Detail of an intensifier. In the foreground, on the RHS, is the downhole fluid end. In
the background, on the LHS, is the power end, complete with high pressure iron
rigging it to the frac pumpers.
Generic flow diagram for a frac blender. Note that on a blender fitted with a Condor
tub (such as BJ’s Cyclone blenders), the functions of the blender tub and the
discharge pump are combined.
125D Frac blender, capable of 125 bpm and 35,000 lbs/min proppant rate.
Body-load mounted Cyclone II blender, capable of 25 bpm.
Skid mounted Cyclone blender.
LFC hydration unit.
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20.6a
Frac sand being delivered from a Sand King to the hopper of a blender. Note that
there are two blenders in this picture – one is on standby as a backup in case of
equipment failure.
20.6b Vertically mounted, gravity feed proppant bins.
20.6c Trailer mounted sand dumper.
20.6d BJ Services Sand King.
20.6e Sand belt conveyor.
20.7a External view of BJ’s Stimulation Van 1800.
20.7b External view of a treatment monitoring container.
20.7c Two internal views of a treatment monitoring van.
20.8a Generic wellhead isolation tool rigged up to wellhead. The WIT is connected to the
wellhead via the wellhead’s top flange. At this point the wellhead master valve and
sub master valves are closed, maintaining control of the well and allowing the frac
lines and WIT to be pressure tested.
20.8b+c Once the WIT has been connected to the wellhead and pressure tested (Fig 20.8a),
the next stage is to close the valves of the frac lines (not shown – note that some
WIT’s have their own master valves) and open the master and sub master valves on
the wellhead. One the wellhead is open, the stinger is stroked down into the top of the
tubing by pumping hydraulic fluid into the master cylinder.
20.8d Wellhead isolation tool rigged up on location. Note the two 3” frac lines connected to
either side, plus the remote actuated 4” plug valve.
20.9a Schematic diagram of a frac spread.
20.9b Large scale treatment, carried out on several low permeability zones simultaneously.
Note the number of Sand Kings and frac tanks on location, as well as the use of two
blenders (one for backup in case of equipment failure). This frac spread features a
separate mobile field lab (bottom left) and a third blender, just for gelling up the tanks
and for pumping fluid from the tanks that are located a significant distance from the
blender (located just above the bottom left hand row of frac tanks).
20.9c The MV Blue Ray, a Gulf of Mexico frac boat, designed primarily for high
permeability, frac and pack treatments.
20.9d Skin Bypass Frac spread, using the “batch” frac method. The two frac pumps are
positioned opposite each other, just below the wireline mast (the small read and
yellow derrick). A third pump (with “BJ” painted on its roof) is being used as an
annulus pump. The two vertical stainless steel tanks on the RHS are for fluid storage.
The two batch mixers (each with two round batch tanks - the blue batch mixer is 2 x
50 bbls, whilst the red one is 2 x 40 bbls), used to batch mix the proppant into the gel,
are located at the bottom of the picture.
20.9e Coiled tubing frac spread. The wellhead is positioned directly below the CT injector
(center of picture), with the reel on the RHS. On the LHS are two nitrogen tankers.
The main part of the frac spread is positioned behind the injector, with the sand dump
truck being the most prominent feature.
20.9f The MV Thanh Long. This was a boat put together for a single fracturing treatment,
for a customer operating offshore Vietnam. The aft deck holds the following
equipment:- 4 x 1200 HHP frac pumps, Cyclone II blender, 2 x 640 cu ft proppant
bins, treatment monitoring container c/w field lab, 4 x 165 bbls tanks and a 100 bbl
vertical tank.
Section 22
22.1a
Page x
Frac job process flow diagram.
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1. Introduction
1.
Introduction
History
The first attempts at fracturing formations were not hydraulic in nature – they involved the use
of high explosives to break the formation apart and provide “flow channels” from the reservoir
to the wellbore. There are records indicating that this took place as early as 1890. Indeed,
one of the predecessor companies of BJ Services, the Independent Torpedo Company
(founded in 1905), used nitroglycerine to explosively stimulate formations in Ohio. This type of
reservoir stimulation reached its ultimate conclusion with the experimental use of nuclear
devices to fracture relatively shallow, low permeability formations in the late 1950’s and early
1960’s.
In the late 1930’s, acidising had become an accepted well development technique. Several
practitioners observed that above a certain “breakdown” pressure, injectivity would increase
dramatically. It is probable that many of these early acid treatments were in fact acid
fractures.
In 1940, Torrey recognized the pressureinduced fracturing of formations for what it was.
His observations were based on squeeze
cementing operations. He presented data to
show that the pressures generated during these
operations could part the rocks along bedding
planes or other lines of “sedimentary
weakness”. Similar observations were made for
water injection wells by Yuster and Calhoun in
1945.
The first intentional hydraulic fracturing process for stimulation was performed in the Hugoton
gas field in western Kansas, in 1947. The Klepper No 1 well was completed with 4 gas
producing limestone intervals, one of which had been previously treated with acid. Four
separate treatments were pumped, one for each zone, with a primitive packer being
employed for isolation. The fluid used for the treatment was war-surplus napalm, surely an
extremely hazardous operation. However, 3000 gals of fluid were pumped into each
formation.
Although post treatment tests showed that the gas injectivity of some zones had been
increased relative to others, the overall deliverability from the well was not increased. It was
therefore concluded that fracturing would not replace acidising for limestone formations.
However, by the mid-1960’s, propped hydraulic fracturing had replaced acidising as the
preferred stimulation method in the Hugoton field. Early treatments were pumped at 1 to 2
bpm with sand concentrations of 1 to 2 ppa.
Today, thousands of these treatments are
pumped every year, ranging from small skin
bypass fracs at $20,000, to massive fracturing
treatments that end up costing well over $1
million. Many fields only produce because of
the hydraulic fracturing process. In spite of this,
many industry practitioners remain ignorant of
the processes involved and of what can be
achieved.
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1. Introduction
The Process
Hydraulic fracturing occurs as a result of the phenomenon described by Darcy’s law for radial
flow:kh∆P
...................................................................... (1.1)
q
=
µ ln(re/rw)
Where q is the flow rate, k the formation permeability, h the net height, ∆P the pressure
differential (or drawdown), µ the fluid viscosity, re the drainage radius and rw the wellbore
radius. This Equation describes the flow rate for a given reservoir-wellbore configuration, for
an applied pressure differential. Re-arranging this Equation gives a different emphasis:
∆P
=
q µ ln(re/rw)
................................................................... (1.2)
kh
This Equation describes the pressure differential produced by a given flow rate.
Remembering that Darcy’s Equation applies equally to injection and to production, Equation
1.2 tells us the pressure differential needed to pump a fluid of viscosity µ into a given
formation at a given rate q.
As the flow rate increases, the pressure differential also increases. Pressure and stress are
essentially the same thing (see Section 2.2), so that as the fluid flow generates a pressure
differential, it also creates a stress in the formation. As flow rate (or viscosity) increases, so
does the stress. If we are able to keep increasing the rate, eventually a point will be reached
were the stress becomes greater than maximum stress that can be sustained by the
formation – and the rock physically splits apart.
This is how we frac, by pumping a fluid into a formation at high rate and – consequently –
high pressure. However, it is important to remember that it is pressure – not rate – that
creates fractures (although we often use rate to create the pressure).
Pressure – and stress – is stored energy, or more
accurately stored energy per unit volume. Energy
is what hydraulic fracturing is all about. In order to
create and propagate a fracture to useful
proportions, we have to transfer energy to the
formation. Producing width and physically tearing
the rock apart both require energy. Overcoming the
often highly viscous frac fluid’s resistance to being
pumped also takes energy. So the key to
understanding the hydraulic fracturing process is to
understand the sources of energy gain, such as the
frac pumps and the well’s hydrostatic head, and the sources of energy loss and use. The sum
of these is always equal to zero.
As pressure is energy, a great deal can be learned about a formation by studying the
pressures produced by a treatment. The product of the pressure and the flow rate gives us
the rate at which energy is being used, i.e. work. This is usually expressed as hydraulic
horsepower. The analysis of the behaviour of fracturing pressures is probably the most
complex aspect of the process that most Frac Engineers will become involved in.
Once a fracture has been created, proppant is placed inside it. If the treatment has been
designed effectively and pumped without any problems, then this proppant should form a
highly conductive path from the reservoir to the wellbore. This is what makes the well produce
more.
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1. Introduction
Using this Manual
This manual is not intended as an all-inclusive work on
the science of hydraulic fracturing. Instead, it is intended
to be a practical introduction to the science and art
involved in these processes. It is intended to be used by
junior Engineers who wish to gain some knowledge of
the fracturing process, and by experienced Engineers
who wish to gain a deeper insight into specific areas.
This manual has been written with the intent that anyone
with a technical background can come to understand
fracturing.
Readers are invited to consult the references at the end of each section for more detailed
information on any specific subject.
The author of this manual welcomes any comments that the reader may have – whether it is
about something which is unclear, an omission or something that is just simply incorrect. I
welcome any constructive comments that the reader may have.
Throughout this manual, the author has used United Kingdom English, rather than American
English. Consequently, some readers may find the occasional word that seems to be spelled
in a manner somewhat different from that which they are used to. Examples include
programme (instead of program), acidise (instead of acidize), grey (instead of gray),
aluminium (instead of aluminum) and sulphate (instead of sulfate). The author makes no
apologies for this.
Acknowledgements
This manual has taken five years to complete, on and off (two to write and three to get proof
read.....). Over this period, I have received assistance from a number of persons who deserve
my thanks. Todd Gilmore, for continually reviewing each section as it was written; Antonio
Moreira for correcting the mistakes and omissions in the equipment section; Phil Rae for his
continuing help, support and encouragement; and finally Dave Cramer, Ron Matson, Harold
Hudson and Kieran O’Driscoll, for the vital but tedious and time consuming process of proof
reading. Thanks to you all.
Tony Martin, Singapore, June 2005.
References
Torrey, P.D.: “Progress in Squeeze Cementing Applications and Technique”, Oil Weekly, July
29, 1940.
Yuster, S.T. and Calhoun, J.C., Jr.: “Pressure Parting of Formations in Water Flood
Operations – Part I”, Oil Weekly, March 12, 1945.
Yuster, S.T. and Calhoun, J.C., Jr.: “Pressure Parting of Formations in Water Flood
Operations – Part II”, Oil Weekly, March 19, 1945.
Farris, R.F. : “Hydraulic fracturing, a method for increasing well productivity by fracturing the
producing formation and thus increasing the well drainage area”, US Patent reissued Nov 10,
1953. Re. 23733.
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas, USA (1970).
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2. Basics of Hydraulic Fracturing
2.
Basics of Hydraulic Fracturing
Hydraulic fracturing is the process of providing a conductive path from the reservoir to the
wellbore. How this is achieved depends upon the objectives, the reservoir and the well.
2.1
The Basic Process
As fluid is pumped into a permeable formation, a pressure differential is generated that is
proportional to the permeability of the formation, kf . As the rate increases, this pressure
differential between the wellbore pressure and the original reservoir pressure also increases.
This pressure differential causes additional stress around the wellbore. Eventually, as the rate
is increased, this pressure differential will cause stresses that will exceed the stress needed
to break the rock apart, and a fracture is formed. At this point, if the pumps are shut down or
the pressure is bleed off, the fracture will close again. Eventually, depending on how hard the
rock is and the magnitude of the force acting to close the fracture, it will be as if the rock had
never been fractured. By itself, this would not necessarily produce any increase in production.
However, if we pump some propping agent, or proppant, into the fracture and then release
the pressure, the fracture will stay propped open, providing the proppant is stronger than the
forces trying to close the fracture. If this proppant also has significant porosity, then under the
right circumstances a path of increased permeability has been created from the reservoir to
the wellbore. If the treatment has been designed correctly, this will produce an increase in
production.
Generally, the process requires that a highly viscous fluid is pumped into the well at high rate
and pressure, although this is not always the case (see Skin Bypass Fracturing, below). High
rate and high pressure mean horsepower, and this is why the process generally involves
large trucks or skids with huge diesel engines and massive pumps. A typical frac pump will be
rated at 700 to 2700 hydraulic horsepower (HHP) – to put this in perspective, the average car
engine (outside North America, that is) has a maximum power output of 80 to 100 HP.
Pressure, Rate, Proppant Concentration
In order to create the fracture, a fluid stage known as the pad is generally pumped first. This
is then followed by several stages of proppant-laden fluid, which actually caries the proppant
into the fracture. Finally, the whole treatment is displaced to the perforations. These stages
are pumped consecutively, without any pauses. Once the displacement has finished, the
pumps are shut down and the fracture is allowed to close on the proppant. The Frac Engineer
can vary the pad size, proppant stage sizes, number of proppant stages, proppant
concentration within the stages, the overall pump rate and the fluid type in order to produce
the required fracture characteristics. Typically, the treatment will look like Figure 2.1a:-
BHTP
Rate
STP
Prop Conc
Time
Figure 2.1a – Typical hydraulic fracture treatment job plot
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2. Basics of Hydraulic Fracturing
2.2
Pressure
Everybody understands what pressure is. Or at least, everyone thinks they understand what
pressure is. If you ask someone to define pressure, then they will usually say “force divided
by area”, or something similar. This is not what pressure is - it is merely how we measure,
create and use pressure.
The simple fact is that pressure is stored energy, and we use that energy to perform work on
the formation during the fracturing process. Everything we do in fracturing can be thought of
in terms of energy. For instance, when we pump a fluid into a fracture we start out with
chemical energy – in the form of diesel fuel. This is converted to mechanical energy by the
diesel engine. The high pressure pump then transfers this mechanical energy into pressure in
the fracturing fluid. As the fluid moves into the formation, the pressure is transformed into
stress in the formation (see below), which is another form of stored energy, and so the walls
of the fracture are pushed back, creating fracture width and forcing the fracture to propagate.
Work is defined as the rate at which energy is used – in the SI system, one watt is defined as
a joule per second. Therefore, by observing the way the pressure is changing, or not
changing, with respect to time, we can tell how much work we are performing on the
formation (see Section 10.2 – Nolte Analysis).
Pressure and stress are essentially the same thing. The only difference is that stresses act in
solids and pressures act in liquids and gases. Because liquids and gases easily deform away
from any applied force, pressures tend to act equally in all directions. Stresses, however, tend
to act along planes, so that a solid experiencing a stress will always have a plane where the
stresses are a maximum, and a plane perpendicular to this where the stresses are at a
minimum.
In fracturing, we refer to several different pressures. These names merely refer to where and
when we are measuring (or calculating) the pressure;
Surface Treating Pressure, STP – also referred to as wellhead pressure, injection pressure,
tubing pressure (if we are pumping down the tubing), PSTP, Pwellhead, Ptubing and so on. The
name speaks for itself – it is the pressure that the pumps have to act against at the surface.
Hydrostatic Pressure – also referred to as hydrostatic head, PH, HH and Phydro. This is the
pressure downhole due to the weight of the column of fluid in the well. This pressure is a
function of the density of the fluid and the vertical depth:
HH
= 0.433 γ TVD .................................................................. (2.1)
where HH is the hydrostatic head in psi, γ is the specific gravity of the fluid and TVD is the
true vertical depth at which the pressure is acting. This looks relatively easy to calculate, but
can get quite complicated in a dynamic system in a deviated well with fluids of several
different densities actually in the well – which is the usual situation during a frac job. We use
computers to keep track of this.
Tubing Friction Pressure – also known simply as friction pressure, Pfrict or ∆Pfrict. This
pressure will be covered in more detail in later sections of this manual (see Section 4). For
now, we can define it qualitatively as the pressure caused by the resistance of the fluid to flow
down the tubing. Friction pressure decreases with increasing tubular diameter and increases
with rate.
Bottom Hole Treating Pressure – BHTP or PBHT. This is the pressure inside the well, by the
formation being treated. Generally, at is calculated at the center of the perforated interval. At
this point, the fluid has not passed through the perforations or into the fracture. Unless there
are gauges in the well, or there is a static column, this pressure is usually calculated:-
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2. Basics of Hydraulic Fracturing
BHTP
= STP + HH - ∆Pfrict ........................................................ (2.2)
As there are always uncertainties with the calculation of ∆Pfrict (unless fluid rate is zero), there
will always be uncertainties in calculated BHTP.
Perforation Friction Pressure – also known as perforation friction or ∆Pperf. This is the
pressure drop experienced by the fluid as it passes through narrow restrictions generally
referred to as perforations:∆Pperf
2
=
2.93 SG (q/n)
4
.............................................................. (2.3)
d
where ∆Pperf is in psi, SG is the specific gravity of the fluid, q is the slurry rate in bpm, d is the
perforation diameter in inches and n is the number of perforations.
Near Wellbore Friction Pressure – a.k.a. near wellbore friction or ∆Pnwb. This is the sum of
the perforation friction and any pressure losses caused by tortuosity, which will be covered in
greater detail in Section 10.
Closure Pressure – Pc or Pclosure. This is the force acting to close the fracture. Below this
pressure the fracture is closed, above this pressure the fracture is open. This value is very
important in fracturing and is usually determined from a minifrac, by careful examination of the
pressure decline after the pumps have been shut down.
Extension Pressure – or Pext. This is the pressure required in the frac fluid in the fracture in
order to make the fracture propagate. It is usually 100 to 200 psi greater than the closure
pressure, and this pressure differential represents the energy required to actually make the
fracture propagate, as opposed to merely keeping it open (i.e. Pclosure). In hard formations,
fracture extension pressure is close to the closure pressure. In softer formations, where
significant quantities of energy can be absorbed by plastic deformation at the fracture tip,
extension pressure can be significantly higher than closure pressure (see Section 9). The
fracture extension pressure can be obtained from a step rate test.
Net Pressure – or Pnet. This is a fundamental value used in fracturing and the analysis of this
variable forms a whole branch of frac theory by itself. This will be discussed in detail later on
in this manual. For now, Pnet is the difference between the fluid pressure in the fracture and
the closure pressure, such that:Pnet
= BHTP – ∆Pnwb - Pclosure .................................................. (2.4)
= STP + HH – ∆Pfrcit – ∆Pnwb - Pclosure ............................... (2.5)
Pnet is a measure of how much work is being performed on the formation. By analysing the
trends in Pnet a great deal can be determined about how the fracture is growing – or shrinking.
Instantaneous Shut in Pressure – or ISIP or ISDP. This is the pressure, which can be
determined either at surface or bottom hole, which is obtained just after the pumps are shut
down, at the start of a pressure decline. If measured at bottom hole, the ISIP should be equal
to the BHTP, provided Pnwb is zero. One of the methods for determining if the Pnwb is
significant is to compare the ISIP and the BHTP from a minifrac (provided the BHTP is
reliable).
2.3
Basic Fracture Characteristics
Every fracture, regardless of how it was pumped or what it is designed to achieve, has certain
basic characteristics, as shown in Figure 2.3a (below).
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2. Basics of Hydraulic Fracturing
All fracture modeling is designed around determining these three characteristics, height H,
half length xf and width W. Once these three characteristics have been determined, other
quantities such as proppant volume, fracture conductivity and ultimately production increase
can be determined. It is usually assumed that the two wings of the fracture are identical and
180 º apart (i.e. on opposite sides of the wellbore. This is not necessarily the case. It is also
normal to model the fracture wings as being elipitcal in shape - however, the reality is that the
geometry is probably quite a bit more complex. However, based on the three characteristics
of width, half length and height, we can define a few simple parameters, which will be used
frequently in this manual:-
W
xf
H
Figure 2.3a – Diagram showing fracture half Length xf, fracture height H, and fracture width W.
Aspect ratio;
AR
H
= x .................................................................................. (2.6)
f
So a radial frac, which is perfectly circular and has a height equal to twice the fracture half
length, has an AR of 0.5
Fracture conductivity;
Fc
= w̄ .kp .............................................................................. (2.7)
where w̄ is the average fracture width and kp is the permeability of the proppant pack.
Remember that the width in Equation 2.7 is the propped width, which is usually less than the
width actually created during the treatment. The propped width is a function of the volume of
proppant pumped into the fracture, expressed in terms of the mass of proppant per unit area
of the fracture face. This areal proppant concentration is expressed in terms of lbs/sq ft, and
is not to be confused with the slurry proppant concentration, that is expressed in lbs/gal (or
ppg). This is a measure of how much proppant is added by the surface mixing equipment to a
gallon of frac fluid. Another way of expressing slurry proppant concentration, which is used
less often but is clearer and easier to understand, is ppa, or lbs of proppant added. This
clearly illustrates the quantity of proppant being added to a gallon of clean fluid.
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2. Basics of Hydraulic Fracturing
2.4
Fluid Leakoff
Hydraulic fracture treatments are pumped into permeable formations – there is little point in
carrying out the process in a formation with zero permeability. This means that as the
fracturing fluid is being pumped into the formation, a certain proportion of this fluid is being
lost into the formation as fluid leakoff.
The leakoff coefficient is a function of the formation permeability kf, the fracture area A, the
pressure differential between the fracturing fluid and the formation ∆P, the formation
compressibility, viscosity and the fluid characteristics. Often, this coefficient is set as a
constant throughout the treatment, which means that the fluid loss rate varies with time and
fracture area only, and does not vary with pressure differential or fluid type. The effect of the
formation permeability and the fluid characteristics are often combined together into a single
leakoff coefficient, variously called CT, CL or Ceff. We shall use Ceff. This coefficient defines the
volume of fluid leaked off into the formation VL, as follows:VL
= π Ceff A
t ................................................................... (2.8)
½
where t is the time that the fracture has been open. The units of Ceff are generally ft/min , so
in Equation 2.8 if the area is in square feet, the leakoff volume is in cubic feet. Remember that
the area A is the surface area of the whole fracture, including both sides of both wings of the
fracture. A fracture geometry model must be used to determine the value for A. In a multilayer reservoir, with different values of Ceff for each zone, the total leakoff will be the sum of
the leakoff for each zone.
The leakoff coefficient is usually determined from minifrac tests and from analysis of previous
treatments.
A more accurate method for calculating fluid loss is to use a dynamic leakoff model, in which
variations in the pressure differential and the fluid composition are taken into account. In
dynamic leakoff, the overall leakoff coefficient is generally assumed to have three
components; the viscosity controlled coefficient CV or CI, the compressibility controlled
coefficient CC or CII and the wall-building coefficient Cw or CIII.
The viscosity controlled coefficient is the effect of the fracture fluid filtrate moving into the
formation under Darcy linear flow conditions, and is defined as (in field units):CI
= 0.0469
kf φ ∆P
...................................................... (2.9)
2µf
where kf is the permeability of the formation to the frac fluid filtrate, φ is the formation porosity
and µf is the frac fluid filtrate viscosity in cp.
The compressibility controlled coefficient defines the leakoff which is due to the formation
compressing, and allowing volume into which the frac fluid filtrate can move. It is defined, in
field units, as:CII
= 0.0374 ∆P
kr cf φ
µr
................................................. (2.10)
where kr is the permeability of the formation to the reservoir fluid, cf is the compressibility of
-1
the formation in psi and µr is the reservoir fluid viscosity in cp.
The wall building coefficient is usually determined experimentally using a standard fluid loss
test. The volume of filtrate is plotted against the square root of time, to give a slope m. The
wall building coefficient is then defined as (in field units):-
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2. Basics of Hydraulic Fracturing
CIII
=
0.0164 m
.................................................................... (2.11)
Af
where Af is the area of the filter cake in the fluid loss cell. Generally, modern fracture
simulator will have wall-building coefficients for a wide range of fracturing fluids, so that all the
Engineer has to do is select the fluid type.
The three components can then be combined to produce Ceff as follows:Ceff
=
1+
2 ClClICllI
............................ (2.12)
2
2
2
(ClClll) +(4 CII ( CI + CIII ))
2
This is for dynamic fluid leakoff. The components can be arranged in a different form for
harmonic fluid leakoff:Ceff
(ClCllClll)
= (C C + C C + C C ) .................................................. (2.13)
l ll
ll lll
l lll
This process of deducing the theoretical leakoff coefficient looks to be rather intimidating, and
in practice is only used in fracture simulators. During minifrac analysis, the permeability of the
formation and the wall building coefficient are varied to produce the required leakoff rate.
Generally, the dynamic model is better than the harmonic, although under most
circumstances there will not be much difference between the two. This is especially true for a
non-wall-building fluid, or for gas reservoirs.
Another form of fluid loss into the formation is called spurt loss. This is the fluid loss which
occurs on “new” parts of the fracture, before the fluid has a chance to build up a filter cake.
Usually, the fracture models take a simplistic approach to spurt loss and use a spurt loss
coefficient, Sp , such that:Vs
= A Sp ............................................................................. (2.14)
where Vs is the volume of fluid lost due to spurt loss and A is the total area of the fracture
(both wings). A more detailed approach to spurt loss (and fluid loss in general) can be found
in SPE Monograph Volume 12, Recent Advances in Hydraulic Fracturing, Chapter 8 (see
references).
2.5
Near Wellbore Damage and Skin Factor
Darcy’s Equation for radial flow defines the rate at which oil is produced from the reservoir
into the wellbore, under steady state flow conditions. In field units for an oil well, Darcy’s
Equation becomes:q
=
0.00708 k h ∆P
.......................................................... (2.15)
µ ln (re/rw)
where q is the downhole flow rate in bbls/day. We can see that the wellbore radius, rw has a
huge impact on the flow rate. This is easily visualised, as the closer the fluid comes to the
wellbore, the more congested the flow paths become and the faster the fluid has to move.
Therefore, the final few inches by the wellbore are the most critical part of the reservoir.
Unfortunately, this is also the part of the reservoir most susceptible to damage. This damage
can come from a variety of sources, but most often comes from the process of drilling the well
in the first place.
A full discussion on sources of formation damage is beyond the scope of this manual.
However, the major sources are; particulates in the drilling fluid (barite, calcium carbonate
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2. Basics of Hydraulic Fracturing
etc), filtrate invasion, whole fluid invasion, pH of drilling fluid and surfactants in the drilling
fluid.
What this results in, is a region around the wellbore of reduced permeability, as illustrated in
Figure 2.5a.
This reduction in permeability around the wellbore is generally referred to as the Skin, which
was first rationalised by van Everdingen and Hurst (1949). The skin factor, S, is a variable
that is used to describe the difference between the ideal production given in Equation 2.15,
and the actual production through the damaged area. Generally, the skin is measured using a
pressure build up test. The API has defined the skin factor for an oil well as follows (see
Section 19):S
= 1.151
P1hr - Pwf
k
- log10
+ 3.23 ....................... (2.16)
m
φµcrw2
where Pwf is the bottom hole stabilised flowing pressure (psi), P1hr is the bottom hole pressure
after one hour of static pressure build up (psi), k is the formation permeability, m is the slope
of the graph of P against log10[(t + ∆t)/∆t ] (in psi per log10 cycle), φ is the porosity (fraction), µ
-1
is the fluid viscosity (cp), c is the average reservoir compressibility (psi ) and rw is the
wellbore radius (feet).
Wellbore
Damage
Permeability
low
high
Figure 2.5a – Illustration of the reduction in permeability around the wellbore
To help matters, m can be found from the following (in field units):m
=
162.6 q µ
.................................................................... (2.17)
kh
Note that both q and µ are at bottom hole conditions. A completely undamaged reservoir will
have a skin factor of zero. Damaged reservoirs will have skins in the ranging from 0 to 50 or
even higher. Under certain circumstances, stimulation can result in a negative skin factor,
which means that the well is producing more than predicted by ideal Darcy flow.
Once the skin factor has been obtained, it can be used in Darcy’s Equation to give the
modified flow from a skin damaged reservoir:q
Page 10
=
0.00708 k h ∆P
......................................................... (2.18)
µ [ln (re/rw) + S]
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2. Basics of Hydraulic Fracturing
This means that as S increases, flow rate decreases, and vice versa.
Another way of employing the skin factor is to use an effective wellbore radius, as given in
Equation 2.19:rw ’
-S
= rw e ............................................................................ (2.19)
This means that in a damaged wellbore, the well is behaving as if it had a smaller wellbore
radius, whilst a stimulated reservoir behaves as if it had a larger wellbore radius.
References
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Archer, J.S. and Wall, C.G.: Petroleum Engineering – Principles and Practices, Graham and
Trotman, London (1986).
van Everdingen, A.F. and Hurst, W.: “The Application of the Laplace Transformation to Flow
Problems in Reservoirs”, 1949, Trans., AIME, 186, 305-324.
Meyer and Associates, MFrac version 5.10 on-line Help section, 2003.
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3. Types of Hydraulic Fracturing
3.
Types of Hydraulic Fracturing
There are various different types of hydraulic fracturing, which have evolved around the basic
process of creating a fracture and then propping it open. The type of treatment selected
depends upon the formation characteristics (permeability, skin damage, fluid sensitivity,
formation strength), the objectives of the treatment (stimulation, sand control, skin bypass or a
combination) and the constraints we have to work within (cost, logistics, equipment etc).
3.1
Low Permeability Fracturing
There are various different types of hydraulic fracturing, which have evolved around the basic
process of creating a fracture and then propping it open. The type of treatment selected
depends upon the formation characteristics (permeability, skin damage, fluid sensitivity,
formation strength), the objectives of the treatment (stimulation, sand control, skin bypass or a
combination) and the constraints we have to work within (cost, logistics, equipment etc).
This type of fracturing is often carried out in tight gas formations, found in areas such as the
Rocky Mountains, Algeria, Western Germany, parts of Australia and many other places worldwide. Permeabilities for such formations range 1 md right down to 1 µd and less. This type of
treatment is also applicable to low permeability oil formations, although permeabilities tend to
be 1 or 2 orders of magnitude greater.
In order for hydrocarbons to flow down the fracture, rather than through the adjacent
formation, the fracture must be more conductive than the formation. Given that the kp for
20/40 Colorado Silica frac sand is 275 darcies (provided closure pressure is below 3,000 psi),
we can see that even a very narrow fracture will have a much higher conductivity than the
formation itself. This does not allow for the effects of non-Darcy flow (see Section 10).
Therefore, the limiting factor defining how much the reservoir production has increased is not
how conductive the fracture is (as any propped fracture will be significantly more conductive
than the formation), but instead is how fast the formation can get the hydrocarbon to the
fracture. Therefore, when treating low permeability reservoirs, fractures should be designed
with a specific minimum fracture conductivity, but a large surface area - which means,
because formations are usually limited in height, designing for maximum fracture half length,
xf. See Section 17.9 for a detailed discussion of how to determine the required fracture
conductivity.
Because formation permeability is low, fluid leakoff also tends to be low. This has two
consequences. First, pad volumes tend to be very low, relative to the rest of the job volumes.
In some cases, a pad is hardly needed at all – the proppant-laden fluid can be used to create
the fracture. The second consequence is that fracture closure time – the length of time taken
for the fracture to close on the proppant after the treatment has finished – tends to be long.
This means that the fracturing fluid has to suspend the proppant for a relatively long period of
time at bottom hole temperature.
Therefore, hydraulic fracture treatments in low permeability formations tend to have fairly
large fluid and proppant volumes, although the overall proppant concentration in the fluid is
relatively low. Pad volumes are small. Treatment fluids are usually fairly robust, capable of
maintaining viscosity for extended periods of time. The process of designing for low
permeability formations is discussed in greater detail in Section 17.5.
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3. Types of Hydraulic Fracturing
3.2
High Permeability Fracturing
High permeability fracturing is, not unexpectedly, the opposite of low permeability fracturing.
In high permeability formations, moving the fluid through the rock to the fracture is easy. The
hardest part is creating a fracture that is more conductive than the formation in the near
wellbore region.
In Equation 2.7, the concept of fracture conductivity was introduced. The next step is to define
relative or dimensionless conductivity, CfD (often referred to as FcD in many previous
publications):
CfD =
Fc
xf kf ................................................................................. (3.1)
where xf is the fracture half length and kf is the permeability of the formation. CfD is a measure
of how conductive a fracture is compared to the formation and compares the ability of the
fracture to deliver fluids to the wellbore with the ability of the formation to deliver fluids to the
fracture. A CfD of greater than one means that the fracture is more conductive than the
formation, whereas a CfD of less than one means that the fracture is less conductive than the
formation and the reservoir fluids flow more easily through the formation. This does not
account for the effects of the skin factor – in reality all the fracture needs to be in order to
increase production, is more conductive than the skin (see Section 3.4 – Skin Bypass
Fracturing).
From Equation 2.7, which stated that Fc = w̄ .kp, we can see that two parts of the definition of
CfD are fixed; kf and kp (although kp can be increased to a certain extent by using a better
quality proppant). Therefore, in order to increase dimensionless conductivity, we have to
maximise w̄ and minimise xf. This means that we need a very short, wide fracture. In order to
achieve this, a technique known as the Tip Screen Out (TSO) is often used. This will be
discussed in more detail in Section 17.3.
Because the formations have high permeability, fluid leakoff tends to be very high. Therefore,
pad volumes tend to be a significant part of the treatment. This high leakoff is used by the
technique of TSO fracturing. Young’s modulus tends to be very low, which means that
creating fracture width is relatively easy.
Formations with very high permeability also tend to have two other characteristics. First, they
are often weak or unconsolidated, so that the fracturing process is often combined with gravel
packing techniques to produce a frac pack treatment (see below, Section 3.3). Second, the
formations also tend to have large skin factors, so that a significant production increase can
be obtained simply by providing a conductive path through the skin (see Section 3.4, below).
The processes involved in designing treatments for high permeability are discussed in greater
detail in Section 17.3
3.3
Frac and Pack Treatments
The frac and pack (or simply frac-pack) treatment is a combination of a high permeability
fracture treatment and a gravel pack treatment. Technically, the process of designing the
actual treatment is the same as for a high permeability frac. Operationally, however, the
process is much more complex, due the presence in the wellbore of the gravel pack
completion. Figure 3.3a illustrates this.
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GP/Prod. Packer
Fluid Control Valve
Blank Pipe
Screen
Sump Packer
Figure 3.3a – Diagram illustrating the components of the frac-pack completion. Setting tool is
shown in the squeeze position.
Figure 3.3b – Diagram illustrating two of the three positions in which a standard gravel pack or
frac pack tool can be set. The left hand side shows the squeeze position, in which fluids flow
down the tubing, through the crossover, out into the annulus below the GP packer and into the
formation. The right hand side shows the lower circulating position. Fluid flows down to the
perforations, as for the squeeze position. However, because the setting tool has been shifted
upwards, the fluid can flow either into the formation, or back through the screens, up the
washpipe (inside the screens) through the crossover, and out into the annulus above the tubing
(shown in blue). By closing the annulus at surface, the fluid can be squeezed into the formation,
whilst maintaining a dead string on the annulus, to monitor BHP.
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3. Types of Hydraulic Fracturing
The treatment is normally pumped with the setting tool in the squeeze position, although
sometimes the tool is in the lower circulating position (see Figure 3.3b). In either case,
fracturing fluids are pumped down the tubing, through the setting tools, through the crossover,
out into the annulus and into the perforations.
As stated before, the pumping schedule is designed as if the completion did not exist, and a
normal high permeability fracture treatment was being performed. With one exception – extra
proppant (or gravel) is pumped on the final stage, in order to fill the annulus space between
the screen and the casing, producing the gravel pack. The process of designing a frac and
pack treatment will be discussed in more detail in Sections 17.3 and 17.4.
3.4
Skin Bypass Treatments
Skin bypass treatments are designed to do exactly what the name describes – bypass skin
damage. These treatments are not necessarily designed to be the absolute optimum
stimulation treatment for the well. Instead, these treatments are designed to be small, cost
effective and easy to run operationally. Often these treatments are pumped in places where
space or equipment weight is a limiting factor – such as offshore. In many cases, if the frac
engineer was given a technical free hand to design the optimum treatment, the job itself
would be much larger. However, given the restraints of cost and space that are often placed
upon frac engineers, the skin bypass frac is an attempt (often highly successful) to produce
effective stimulation.
The skin bypass frac can also be considered as a more effective alternative to matrix
acidising, when factors such as mineralogy, temperature, logistics and cost prevent the use of
acid.
Figure 3.4a – Diagram illustrating how the skin bypass fracture penetrates the skin to allow
undamaged communication between the reservoir and the wellbore.
Figure 3.4a shows the basic concept behind the skin bypass frac. Although the formation has
considerable damage (dark-shaded area), this is effectively bypassed by the more conductive
path created by the fracture. In order for the fracture to produce a production increase, it does
not have to be more conductive than the formation (i.e. CfD > 1.0). It merely has to be more
conductive than the damaged area. Of course, usually we are usually aiming for considerably
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3. Types of Hydraulic Fracturing
more than just the production increase due to skin bypass. Given that Skin Bypass Fracs are
normally carried out on marginal wells (wells that cannot justify the expense of a major
stimulation treatment), often the economics dictates that significant production increase must
be obtained. Equation 3.1 gave the definition of dimensionless conductivity, which has to be
greater than 1.0 for the fracture to provide stimulation of the formation. Equation 3.2 shows
the condition, for a fracture which has HD ≤ 1.0, under which the skin bypass fracture is more
conductive than the formation:
Fc
H kf
>
ln (re/rw)
ln(re/rw + S) .................................................. (3.2)
Where Fc is the fracture conductivity (mdft), H is the fracture height (ft), re is the radial extent
(ft), rw is the wellbore radius and S is the skin factor. So if S = 0, the RHS of Equation 3.2
goes to 1, so that then Fc has to be greater than H.kf , which is another way of saying that the
CfD has to be greater than one. This Equation takes into account the fact that the fracture
does not cover the entire zone vertically. However, it is an approximation, as it does not
account for vertical flow or non-Darcy effects (Section 10).
HD is the dimensionless height and is equal to the fracture height divided by the formation
height.
3.5
Coal Bed Methane Fracturing
It is estimated that for every tonne of coal that is generated underground - by the process of
coalification - up to 45 mscf of gas (mostly methane) is generated. In areas such as the
Southern North Sea, this gas migrates upwards until it reaches an impermeable layer, so that
the coal itself contains very little gas. In other cases, nearly all the gas remains in place,
waiting to be produced.
Coal itself usually has very low matrix permeability, with the gas being produced through
natural fractures (called cleats) and through desorption from the coal itself. The objective of
coal bed methane fracturing is to connect up the cleats with a propped fracture, allowing the
gas to be produced both from the cleats and from the coal
CBM fracturing is more of an art than a science. Because of the unusual characteristics of the
formations, most fracture simulators are unable to accurately model these treatments.
Engineers usually have to rely on experience and trial and error.
These treatments usually consist of large volumes of proppant, pumped at low
concentrations, at high rates. Various fluid systems have been used, but recent work has
demonstrated that crosslinked fluids, especially guar-based gels, can be very damaging to the
formation. The trend has been towards HEC, foams and even just water as the carrier fluid.
Proppant concentrations tend to be in the 3 to 4 ppg range. Because wells are relatively low
rate, large fracture conductivities are not required – what is needed is a conductive path from
cleat to cleat. As formations are usually shallow, sand is generally selected as the proppant.
CBM wells often tend to be marginal. They will not produce economically without a frac
treatment, but even after a frac can be very low rate. Therefore, fracturing treatments tend to
be fairly low tech, no frills operations, using minimal fluids technology and often eliminating
the need for modern, sophisticated, computerised blending and pumping equipment. CBM
fracturing will be covered in more detail in Section 17.7.
Gas production from a CBM reservoir relies on different mechanisms than production from
conventional reservoirs. The main production mechanism is not expansion of gas in pore
spaces - coals generally have little or no primary porosity. Instead, as stated above, the gas is
adsorbed into the coal itself. In order to produce the gas, the pressure has to be reduced
below a specific critical pressure, at which point the gas starts to desorb. Some CBM
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reservoirs are naturally below this critical pressure. Most, however, are significantly above this
pressure. In such cases, considerable quantities of water have to be rapidly produced in order
to get the reservoir pressure low enough to initiate gas desorption. Often, a propped fracture
plays a critical role in this de-watering process.
3.6
Fracturing Through Coiled Tubing
Fracturing through coiled tubing has been around since the early 1990’s, and was first carried
out through a string of coiled tubing that was left in the well after the treatment, becoming the
production tubing. However, as the industry began to perceive the advantages of this process
– and as Engineers began to leave their preconceived coiled tubing ideas behind – the
concept has become more widely accepted.
The advantage of coiled tubing fracturing does not lie with the design or type of fracture that is
placed in the ground, as most types of fracture can be performed this way. The benefits of CT
fracturing lie in the operational aspects of how the treatments are placed.
The obvious limitation for coiled tubing fracturing is the diameter of the coil and the maximum
pressure it can be taken to. However, this restriction is not nearly as bad as it initially seems.
With modern fluid systems, friction pressure down the coiled tubing can be dramatically
reduced, allowing treatments to be pumped at quite high rates. Also, as the coiled tubing is
static during the treatment (i.e. the tubing is not being plastically deformed on a continuous
basis), the maximum allowable pressure is far higher than is normal for CT operations.
Advantages
1.
2.
3.
4.
The coiled tubing can be used to isolate the completion from the fracturing process.
By setting a squeeze packer at the end of the tubing, the hole tubing string is
protected from the pressure and temperature changes normally experienced by the
completion. This means that completions that are pressure-limited (due to sliding
sleeves, packer ratings, poor quality tubing, wellhead size etc) can be fractured.
Completions which cannot be cooled down too much (due to risk of stinging the
tubing out if the PBR on the packer), can also be fractured.
Coiled tubing fracturing is particularly effective when working on monobore
completions, or on wells that have not yet been completed. By using an opposing cup
tool, the coiled tubing can be used to easily isolate one zone from another. An
extension of this, is that the tool can be very easily moved from one zone to another,
allowing multiple fracs to be performed in rapid succession.
If required, the coiled tubing can be used to gas lift the well on to production after the
treatment(s).
Coiled tubing can often be used as an alternative to a workover. This can mean
significant cost saving, especially offshore.
Disadvantages
1.
2.
3.
4.
The extra cost of the coiled tubing unit, over and above the cost of the frac spread.
However, often this extra cost can produce savings in other areas (rig time, frac crew
time etc). The operating company must also be prepared to pay for some or all of the
cost of the coiled tubing string.
The extra space needed, due to the extra equipment required as compared to the
frac spread by itself. Of course, if the CT unit is being used as an alternative to a
workover rig, this may not be as significant.
Rate limitations. In general, for a given fluid system, higher rates can be achieved
through completions than through coiled tubing. However, it should be remembered
that it is usually possible to take the static coiled tubing to higher pressures than the
completion/wellhead assembly.
Although it is possible to frac through coiled tubing with standard fluid systems, as the
depth increases and/or the coiled tubing diameter decreases, it may be necessary to
use more exotic and expensive fluid systems.
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3. Types of Hydraulic Fracturing
References
Product Catalogue, Colorado Silica Sand, 1994
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Gidley, J.L., et al: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Bradley, H.B. (Ed): Petroleum Engineers Handbook, SPE, Richardson, Texas (1987)
Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,
SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, Houston,
October 1999.
O’Driscoll, K.: Middle-East Region Coal Bed Methane Fracturing Manual, BJ Services, 1995.
Gavin, W.G.: “Fracturing Through Coiled Tubing – Recent Developments and Case
Histories”, SPE 60690, presented at the 2000 SPE/ICoTA Coiled Tubing Roundtable,
Houston, April 2000.
Wong, G.K., Fors, R.R., Casassa, J.S., Hite, R.H., and Shlyapobersky, J.: “Design, Execution
and Evaluation of Frac and Pack (F and P) Treatments in Unconsolidated Sand Formations in
the Gulf of Mexico”, SPE 26563, presented at the SPE Annual Technical Conference and
Exhibition, Houston TX, Oct 1993.
Tiner, R.L., Ely, J.W. and Schraufnagel, R.: “Frac Packs – State of the Art”, SPE 36456,
presented at the SPE Annual Technical Conference and Exhibition, Denver CO, Oct 1996.
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4. Fluid Mechanics
4.
Fluid Mechanics
Fluid Mechanics is the study of the behaviour of fluids. In the oil field, this means that fluid
mechanics is used to predict fluid friction pressures and the forces due to the dynamics of
fluid flow. Rheology is the study of the deformation and flow of matter, and in the oil field is
used to predict the resistance of a fluid to the application of a force or pressure.
4.1
Fundamental Fluid Properties
Density (ρ) -
A measure of how much matter a material contains within a unit of
volume. The denser a material is, the heavier a given volume.
Provided the liquid composition remains constant, we can think of
fluid density (especially for water-based fluid systems) as a constant
– although it will actually decrease slightly with increasing
temperature and increase slightly with increasing pressure.
Hydrocarbon-based
fluid
systems
are
significantly
more
compressible, and assuming a constant density can result in
inaccuracies (see references for diesel data).
Viscosity (µ) -
Viscosity is a measure of how much a fluid resists deformation as a
result of an applied force or pressure. It is a measure of how “thick”
the fluid is. Viscosity is only very rarely a constant value, as it can
change dramatically with temperature, applied shear stress and fluid
composition. Viscosity is defined as the relationship between shear
stress and shear rate.
Temperature (T) -
A measure of how much energy a material contains – the hotter the
material, the more energy. Although strictly speaking temperature is
not a fundamental property, in the oil field it an important parameter
that needs to quantified. Most fluid properties are affected to a
greater or lesser extent by temperature.
4.2
Shear Stress and Shear Rate
Shear Rate (γ). In fluid mechanics, shear rate is a measure of how fast a fluid is flowing past
a fixed surface. Shear rate can be thought of as a measure of how much agitation a fluid is
receiving.
Causes of Shear Rate:-
Spinning centrifugal pump
Flow through a pipe
Fann 35 Test
Jet mixer
Tank agitators
Shear Stress (τ). Shear stress is the resistance the fluid produces to an applied shear rate.
For instance, it requires more force (pressure) to pump water at 20 bpm than at 10 bpm.
Viscosity (µ). The fluid property that defines how much shear stress is produced by a shear
rate, is called viscosity. The greater the viscosity, the greater the resistance of a fluid to shear
agitation.
Newton’s Law of Fluids
µ
Page 19
=
τ
γ ........................................................................................... (4.1)
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Shear Stress, τ
This is known as Newton’s law of fluids, and is illustrated in Figure 4.2a:-
0
Slope = µ
0
Shear Rate, γ
Figure 4.2a – Graph illustrating Newton’s law of fluids
In oil field units, Newton’s law can be expressed as follows:-
µ
= 47,879
τ
γ .............................................................................. (4.2)
2
-1
with µ measured in cp (centipoise), τ in lbf/ft and γ in sec . Newton was the first to realise the
relationship in fluids between an applied force and the resistance to that force. His
experiments were carried out on simple fluids such as water and brine, and not on more
complex fluids, such as those used in stimulation activities.
4.3
Types of Fluid
In the oil field, we generally deal with three different types of fluids, according to how the
relationship between shear stress and shear rate develops. These fluid types are defined
below.
Newtonian Fluids
As illustrated in Figure 4.2a, these are fluids for which Newton’s law is valid. Newtonian fluids
have a straight line (linear) relationship between shear rate and shear stress until turbulence
occurs. Equations 4.1 and 4.2 are valid. Examples of Newtonian fluids include:Fresh Water
Sea Water
Most Acids (ungelled)
Diesel
Alcohols
Gases
Bingham Plastic Fluids
Bingham plastic fluids require an initial shear stress to be induced before they will deform. Put
another way, they have a yield point or gel strength that must be broken before the fluid can
move (although some fluids have a gel strength that is nothing to do with yielding). This type
of fluid is not Newtonian, although they usually have a constant viscosity once the initial gel
strength has been overcome.
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4. Fluid Mechanics
τ
= Yp + Pvγ ......................................................................... (4.3)
2
Yp is the yield point, and in the oil field has units of lbf/100 ft (note that in the oil field, τ has
2
the units lbf/ft , so the value for Yp has to be converted before it is used), whilst Pv is the
plastic viscosity, with cp as its units.
Shear Stress, τ
Figure 4.3a illustrates the behaviour of a Bingham plastic fluid Examples of Bingham plastic
fluids include some cement slurries and some drilling muds.
Slope = Pv
Yp
0
0
Shear Rate, γ
Figure 4.3a – Relationship between shear rate and shear stress for a Bingham plastic fluid.
Power Law Fluids
The third group of fluids is generally referred to as power law fluids, although there are other
names which have been used to describe them. In general, there is no linear relationship
between shear rate and shear stress, so that apparent viscosity (the viscosity which the fluid
appears to have, at a specific shear rate) changes with shear rate. The following Equation
describes the behaviour of the power law fluid, and this is illustrated in Figure 4.3b.
n’
= K’γ .............................................................................. (4.4)
Shear Stress, τ
τ
0
0
Shear Rate, γ
Figure 4.3b – Relationship between shear rate and shear stress for a power law fluid. Note that
the graph shows the relationship in its most common form - “shear thinning”. However, in
certain fluids the line can also curve upward - “shear thickening”.
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4. Fluid Mechanics
K’ is referred to as the power law consistency index, and in order to be coherent has the
n’ 2
rather awkward units of lbf sec /ft . n’ is the power law index and is dimensionless.
In order to determine n’ and K’, the log of Equation 4.4 is taken;
log τ
= log K’ + n’ log γ .......................................................... (4.5)
On a plot of logτ against logγ, the intercept of the vertical axis is log K’ and the gradient of the
line is n’, as shown in Figure 4.3c;
log τ
Slope = n’
log K’
0
0
log γ
Figure 4.3c – Power law fluid log-log plot
Power law fluids can be divided into 3 major categories;
Shear-thinning fluids. In these fluids, n’ is less than 1, so that the fluids experience a
decrease in apparent viscosity as the shear rate increases. Most of the fluids used for
fracturing fall within this category.
Newtonian fluids. Newtonian fluids are a special case of power law fluids in which n’ is
equal to one, i.e. the viscosity is constant and equal to K’.
Shear-thickening fluids. These fluids have an n’ greater than one, and so exhibit an
increase in apparent viscosity as shear rate increases. Extreme examples of these fluids can
behave as it they were solids when exposed to even moderate shear forces.
Another example of a power law fluid is the Herschel-Buckley fluid, which is often used to
model the flow behaviour of foams;
τ
= τ’o + K’’ γ
n’’
.................................................................... (4.6)
where τ’o is the threshold shear stress, K’’ is the Herschel-Buckley consistency index and n’’
the Herschel-Buckley exponent.
Herschel-Buckley fluids are basically a combination of the Bingham plastic fluid and the
power law fluid. An initial threshold shear stress has to be overcome before the fluid will flow.
Once this has happened, the viscosity is not constant, and will vary according to the shear
rate.
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4. Fluid Mechanics
4.4
Measuring Viscosity
In order to measure viscosity, two variables need to be determined. First, the shear rate of
some moving device within the fluid, needs to be determined. Second, the resistance to this
shear rate needs to be evaluated. This can be done either by measuring the amount of force
required to move the source of shear rate, or by measuring the deflection on an object placed
in the fluid, close to the source of shear rate.
If the fluid being analysed is not Newtonian, then the apparatus will have to perform these
tasks at several different shear rates.
Once the resistance to the shear rate (i.e. the shear stress) has been determined at one or
more known shear rates, the viscosity (or the components required to determine the apparent
viscosity) can be derived.
Model 35 Viscometer
The model 35 viscometer, produced either by Fann or Chandler, is the most common device
used in the oil industry for determining viscosity and rheological properties. It is robust, easy
to use and reliable. It can also be fairly easily calibrated, provided the user is familiar with the
process. Figure 4.4a shows a photograph of a model 35 viscometer, whilst Figures 4.4b and
4.4c illustrate how it works;
Figure 4.4a – Chandler 35 viscometer.
The position of the rotor is indicated
(A), whilst the bob is hidden inside
this. The cup (B) holds the test fluid,
and is mounted on a support (C) that
can move up and down as required.
A
B
C
Torsion
Spring
Bob
Shaft
Rotor
Fluid
Bob
Bob Shaft
Bob
Figure 4.4b – Cross-section through the rotor
and bob on a model 35 viscometer
Page 23
Figure 4.4c – Schematic diagram showing
the model 35 viscometer bob assembly
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4. Fluid Mechanics
The model 35 viscometer works by rotating the rotor (see Figure 4.4b) around the bob. The
fluid is positioned in a narrow gap between the rotor and the bob. As the rotor spins, it
produces a shear on the fluid, which in turn produces a drag force on the bob. The bob is
mounted on a spring loaded bob shaft (see Figure 4.4c), so that as it experiences a drag
force, it will rotate slightly. The greater the drag force, then more the bob rotates. Attached to
the top end of the bob shaft is a dial indicator, allowing the operator to read how much the
bob has rotated. As the bob deflection is directly related to the shear stress being
experienced by the fluid, it is possible to use the dial reading as a measure of viscosity.
Generally, the model 35 viscometer can spin the rotor at the following speeds, although these
vary slightly from model to model. The speeds are 1, 2, 3, 6, 12, 20, 30, 60, 100, 200, 300
and 600 rpm.
By plotting the rpm’s of the rotor (shear rate) against the dial reading (shear stress) it is
possible to determine what type of fluid is being measured, by analysing the shape of the
curve.
τ
= 0.01066 N θ .................................................................. (4.7)
γ
= 1.703 ω ......................................................................... (4.8)
where N is the spring factor of the torsion spring fitted to the model 35 viscometer (usually
equal to 1), θ is the dial reading and ω is the speed of the rotor in rpm’s. It should be noted
that Equation 4.8 is valid only for the R1 rotor and B1 bob combination – for other
combinations refer to the manufacturer’s manual.
By using Equations 4.7 and 4.8, a plot of shear rate against shear stress can be produced, or
if necessary, a log-log plot. From these, the viscosity defining parameters can be derived.
Other Methods for Measuring Viscosity
Various other methods for measuring viscosity are available;
i)
Helical Screw Rheometer. Uses a helical screw inside a sleeve. The screw rotates
and fluid flows up the inside of the sleeve and out of the top. The amount of force
taken to rotate the screw is measured to produce the shear stress. The shear rate is
derived from the speed of the screw. Used by some service companies for in-line
real-time viscosity measurement during frac jobs.
ii)
Fann 50 HPHT Viscometer. Works on the same principle as the model 35
viscometer, but is designed so that the analysis can be carried out at high
temperature and pressure. These viscometers are also usually remote controlled by a
PC, allowing shear rate and temperature schedules to be used, as well as the
recording of all data. Although quite expensive, these machines are commonly used
for designing frac fluid systems. Figure 4.4d shows a Fann 50.
Figure 4.4d – Fann 50 high
pressure, high temperature
rheometer. This model is fully
computer controlled, whereas
earlier models had manual
controls and were twice the
size of the model shown.
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4. Fluid Mechanics
iii)
Brookfield In-Line Viscometer. Viscometer designed to provide real time viscosity
measurement for fluids flowing down a process line. This viscometer works on a
similar principle to the model 35, although the rotor and bob are of a different size and
shape.
iv)
Funnel Viscometer. A simple device for determining apparent viscosity. It consists of
a funnel with a hole in the end. A specific volume of the fluid is placed in the funnel,
and the time taken for it to drain out of the small hole in the bottom of the funnel is
measured. A chart then provides a quick conversion from time to apparent viscosity.
The above are the most commonly used varieties in the oil industry, although it should be
remembered that a wide variety of devices and methods are available.
4.5
Apparent Viscosity
The apparent viscosity of a fluid is the viscosity of the fluid at a specific shear rate. For a
Newtonian fluid, the apparent viscosity is the same as the actual viscosity. For all other fluids,
the apparent viscosity is the slope of a line on a shear rate vs shear stress curve, from the
origin to the line, at a specific shear rate, as shown in Figure 4.5a:-
Shear Stress, τ
2
1
0
a
0
Shear Rate, γ
b
Figure 4.5a – Graph illustrating the change in apparent viscosity for a power law fluid at two
different shear rates.
As can been seen in Figure 4.5a, for a shear thinning power law fluid, the apparent viscosity
of the fluid (the slope of the two lines) decreases as the shear rate increases. At shear rate
"a" the slope of line 1 (and hence the apparent viscosity) is greater than the slope of line 2 at
the greater shear rate "b". Hence the fluid is said to be shear thinning.
In practice, it is the apparent viscosity that is usually measured. The model 35 viscometer is
set up so that at 300 rpm (with an R1 rotor, B1 bob and spring factor = 1), the apparatus
reads apparent viscosity directly – no additional calculations are required.
The apparent viscosity can be calculated as follows, for a power law fluid:-
µapp
Page 25
=
47879 K'
...................................................................... (4.9)
1-n'
γ
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4.6
Flow Regimes and Reynold’s Number
Figure 4.6a illustrates the three different flow regimes that a fluid can experience, with plug
flow being at the lowest fluid velocity, and turbulent flow being at the highest.
Plug
Laminar
Turbulent
Figure 4.6a – Diagram illustrating the three flow regimes
i)
Plug Flow. At low flow rates, the fluid flows with an almost uniform velocity profile.
The fluid moves with a uniform front across almost the entire flow area.
ii)
Laminar Flow. As the flow rate increases, the velocity profile begins to change. Fluid
close to the walls of the pipe (or duct, or fracture) flows slowest, whilst fluid in the
center of the pipe flows fastest. Fluid velocity is a function of distance from the pipe
wall. Also known as streamline flow.
iii)
Turbulent Flow. As the flow rate continues to increase, the contrast in velocity
across the flow area becomes unsustainable, and the fluid breaks down into turbulent
flow. This is characterised by a series of small scale eddies and whirls, all moving in
the same overall direction.
The friction pressure produced by the fluid flow is highly dependent upon the flow regime.
Therefore, it is important to be able to determine the flow regime.
Reynold’s Number
The flow regime is found by using the Reynold’s number (NRe), as follows;
100 <
NRe
NRe
NRe
< 100
< 2000
> 2000
Plug Flow
Laminar Flow
Turbulent Flow
It should be remembered that these are very generalised numbers. The actual numbers can
vary significantly, depending upon the circumstances. The Reynold’s number itself can be
found from the following formula:NRe
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=
ρdv
........................................................................... (4.10)
µ
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where ρ is the fluid density, d is the inside diameter of the pipe, v is the “bulk” fluid velocity
along the pipe and µ is the viscosity. Equation 4.10 is for SI units, whilst Equation 4.11 is for
field units;
NRe
= 132,624
SG q
........................................................... (4.11)
dµ
where SG is the specific gravity, q is the flow rate in bpm, d is the inside diameter in inches
and µ is the viscosity in cp.
Obviously Equations 4.10 and 4.11 only apply to Newtonian fluids, i.e. fluids with a constant
viscosity. As stated before, Frac Engineers only rarely deal with Newtonian fluids, so below is
Equation 4.11 converted for power law fluids;
2-n'
NRe
SG v
= 15.49 K'(96/d)n' ......................................................... (4.12)
where v is the velocity in ft/sec. To make things easier, v can be easily found from the flow
rate, q:v
q
= 17.157 d2 .................................................................. (4.13)
with q in bpm and d in inches.
Usually, when fracturing, it is best to keep abrasive fluids at flow rates below that needed for
turbulent flow. This is to prevent the erosion of flow lines and the washing out of seals,
caused by the action of the proppant. BJ Services'Standard Practices states that for abrasive
fluids, the fluid velocity must be kept below 40 ft/sec.
4.7
Friction Pressure
One of the ultimate objectives of fluid mechanics - as far as the Frac Engineer is concerned,
anyway – is to be able to predict the friction pressure (∆Pfrict) of the fluids that are being
pumped. This is often very difficult, as fluid composition and temperature is constantly
changing as the treatment progresses. In addition, two-phase (liquid and proppant) and even
three-phase (liquid, proppant and gas) flow is common.
Predicting fluid friction pressure is therefore an unreliable process and there really is no
substitute for reliable bottom hole pressure data. Failing that, the next best option is to use
friction pressure tables, such as BJ’s Fracturing Fluids – Friction Pressure Data. These tables
are usually based on data generated by actually pumping the fluid around a flow loop, and so
are based on a situation similar to the actual treatment process. Most modern fracture
simulators incorporate data from these tests in their fluid models, so friction pressures
predicted by these are also reasonably reliable (although not perfect, as the temperature of
the wellbore is constantly changing) unless there is proppant in the fluid.
Finally, when the three methods outlined above are not possible, the friction pressure may be
calculated from fluid data, using the one of several available methods. The method outlined
below, based on the use of Fanning friction factors, is fairly reliable (i.e. it is just as good as
the data used as inputs), but is not intended for use in narrow diameter pipes at higher than
normal flow rates (such as for coiled tubing treatments).
∆Pfrict
2
= 0.325
SG L v f
......................................................... (4.14)
d
where L is the length of pipe in feet and f is the friction factor (dimensionless).
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4. Fluid Mechanics
The friction factor is determined by using the Reynold’s number. For plug and laminar flow:f
16
= N ............................................................................. (4.15)
Re
whilst for turbulent flow:f
0.0303
= N 0.1612 .................................................................... (4.16)
Re
So the first step in the process of finding ∆Pfrict is to determine the Reynold’s number. Once
that has been found, the friction factor can be determined, which in turn leads to the friction
pressure.
References
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Economides, M.J.: A Practical Companion to Reservoir Stimulation, Elsevier, 1992
FracRT Version 4.6 User’s Manual, BJ Services, 1995 onwards
Friction Pressure Manual, The Western Company, 1989 onwards
Fracturing Fluids – Friction Pressure Data, BJ Services, 1983 onwards
API Recommended Practice 39, Measuring the Properties of a Cross-Linked Water-Based
rd
Fracturing Fluid, 3 Edition, American Petroleum Institute, May 1998
Stimulation Engineering Support Manual, BJ Services, October 1996 onwards
Standard Practices, BJ Services, 2000 onwards
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5. Fluid Systems
5.
Fluid Systems
The fracturing fluid is a vital part of the fracturing process. It is used to create the fracture, to
carry the proppant into the fracture, and to suspend the proppant until the fracture closes. On
a more basic level, the fluid system is the vehicle that allows us to transfer mechanical energy
(in the frac pumps) into work performed on the formation.
In order to carry out these tasks efficiently, the ideal fluid must have a combination of the
following properties.
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
Low cost.
Ease of use.
Low tubing friction pressure.
High viscosity in the fracture, to suspend the proppant.
Low viscosity after the treatment, to allow easy recovery.
Compatibility with the formation, the reservoir fluids and the proppant.
Safe to use.
Environmentally friendly.
Some of these properties are not easy to combine in the same fluid. Usually, the process of
selecting a fracturing fluid is a trade off. It is up to the Engineers to decide which properties
are most important and which properties can be sacrificed. In order to make this choice
easier, there are a number of fluid systems available for fracturing.
5.1
Water-Based Linear Systems
The first fracturing fluid, used in Kansas in 1947, was gasoline gelled with war surplus
napalm. Obviously this was a highly dangerous fluid, and it wasn’t long before water based
systems were available. The first of these systems used starch as the gelling agent, but by
the early 1960’s guar was introduced and soon became the most common polymer for
fracturing. Today, polymers derived from the guar bean are used in most fracturing treatments
- the other main source of polymers being cellulose and it'
s derivatives.
Before the dry polymer is added to the water, the individual molecules are tightly curled up on
themselves. As the polymer molecule hydrates in water, it straightens out – which is why
these fluids are referred to as linear gels – as illustrated in Figure 5.1a:-
A
B
Figure 5.1a – Hydration of polymer gels in water. 'A'shows a polymer molecule before hydration
in water, whilst 'B'shows a polymer molecule after hydration in water.
It is these long, linear molecules that produce the increase in viscosity. However, it should be
remembered that this hydration only occurs at a specific pH range. Outside this range, the
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5. Fluid Systems
hydration rate can be very slow and sometimes almost non-existent. Different polymers have
different pH ranges, and buffers may have to be used to make the polymer hydrate. If a
polymer that hydrates at a neutral pH is added to water, it may start to hydrate very rapidly.
This leads to the formation of “clumps” of non-hydrated polymer, surrounded by partially
hydrated polymer, surrounded in turn by hydrated polymer. These are known as fish-eyes and
are a sign that the gel has been poorly mixed.
Several techniques can be employed to prevent the formation of fish-eyes.
i)
ii)
iii)
iv)
Buffer the water so that the pH will prevent hydration. Once the polymer powder is
thoroughly dispersed in the water, a different buffer is used to change the pH to a
point where the polymer will hydrate.
Add the polymer through a high shear device (such as a jet mixer) to ensure that the
polymer does not form clumps.
Circulate the hydrating gel through a high shear device, such as a choke, to break up
any fish eyes.
Slurry the polymer into a hydrocarbon-based fluid (such as diesel, kerosene or even
methanol). The slurry is then added to the water, allowing the polymer to disperse
before it hydrates.
A combination of these methods can also be used.
Common polymers used for linear gels include:Starch
Guar
Hydroxypropyl Guar (HPG)
Carboxymethyl Hydroxypropyl Guar (CMHPG)
Carboxymethyl Guar (CMG)
Cellulose
Hydroxyethyl Cellulose (HEC)
Carboxymethyl Hydroxyethyl Cellulose (CMHEC)
Xanthan
®
®
®
Xanthan derivatives (e.g. Bioxan , Xanvis , XC Polymer etc)
The most commonly used polymers for fracturing are Guar, HPG and CMHPG, mostly as the
basis for crosslinked systems (see below). HEC is probably the most widely used polymer for
linear gel fracturing, due to its popularity for fracturing low temperature, high permeability
formations.
BJ’s range of water-based linear gel frac fluids includes the Aqua Frac system, which is
based on guar and its derivatives. Gelling agents are GW-3, GW-4 & GW-27 (guar), GW-32
(HPG), GW-38 (CMHPG) and GW-45 (CMG). Also in BJ’s product range is the Terra Pack
system, which is primarily designed for gravel packing, but can also be used for fracturing.
The gelling agent for Terra Pack II is GW-21 (HEC) and for Terra Pack III is GW-22
(Xanthan).
5.2
Water-Based Crosslinked Systems
The majority of hydraulic fracturing treatments are carried out using water based crosslinked
gels. These systems offer the best combination of low cost, ease of use, high viscosity and
ease of fluid recovery. Generally, water based crosslinked gels will be used unless there is a
specific reason not to use them – they are the default option.
The starting point for a crosslinked system is a linear gel, as described above in Section 5.1.
When used for crosslinked systems, linear gels are often referred to as base gels. The most
commonly used linear gels are guar and its derivatives; HPG, CMG and CMHPG.
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A crosslinked gel, as illustrated in Figure 5.2a, consists of a number of hydrated polymer
molecules, which have been joined together by the crosslinking chemical. This series of
chemical bonds between the polymer molecules greatly increases the viscosity of the system,
sometimes by as much as 100 times.
In order for an efficient crosslink to occur, two separate things need to happen. First, the base
gel needs to be buffered to a pH which will allow the crosslinking chemical to work. Usually,
this is at a different pH to that required for polymer hydration, so a different pH buffer has to
be used. Secondly, the crosslinking radical needs to be present at sufficient concentration. If
both these conditions occur, the gel will experience a dramatic increase in viscosity.
A
B
Figure 5.2a – A crosslinked polymer. ‘A’ shows the hydrated polymer prior to addition of the
crosslinker. ‘B’ shows the crosslink chemical bonds between the polymer molecules.
Obviously, a fully crosslinked polymer is extremely viscous, and can result - under the wrong
conditions - in a high level of fluid friction as it is pumped downhole. To counter this, it is quite
common to use a delayed crosslinker. A delayed crosslinker can take anything up to 10
minutes before the gel is fully hydrated, depending upon the temperature, initial pH and shear
that the fluid experiences. The ideal crosslink delay system would delay the onset of crosslink
as long as possible, but would still have the fluid fully crosslinked by the time it reaches the
perforations.
The most commonly used crosslinking systems are as follows:Borates
“Exotic” Borates
Zirconates
Aluminates
Titanates
Zirconates
Aluminates
Organic Titanates
Borates
0
1
2
3
4
5
6
7
8
9
10
Figure 5.2b – pH ranges for crosslinkers (after SPE 37359)
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11
12
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5. Fluid Systems
Of these, the borates and “exotic” borates are by far the most commonly used, followed by
the zirconates. Figure 5.2b illustrates the pH ranges of these crosslinkers, whilst Figure 5.2c
shows their temperature ranges:Zirconates
Aluminates
Titanates
High Temperature Borates
Conventional Borates
100
150
200
250
Temperature,
300
350
400
oF
Figure 5.2c – Temperature range for crosslinkers (after SPE 37359)
All crosslinked gels tend to be shear thinning, which means that the apparent viscosity of the
fluid decreases with shear rate. This is because the shear acts to break the crosslink bonds
between the hydrated polymer molecules. Borate crosslink bonds will reconnect and produce
a good quality gel after the shearing has taken place. However, zirconate bonds are much
more shear sensitive and may not reconnect. Therefore, it is essential to consider the level of
shear that a fluid will experience when selecting a crosslinker.
Like most fracturing companies, BJ Services tends to classify its crosslinked fluids systems by
the type of crosslinker used:Viking™ is a guar-based system that uses conventional borates for the crosslink. It is a
cheap, easy to use fluid intended for low temperature applications. There is no crosslink
delay. Crosslinkers used are XLW-4, XLW-32 or XLW-10.
Viking D is the delayed crosslink version of Viking, and uses the crosslinkers XLW-30 or
XLW-30A.
®
Spectra Frac G is probably the most commonly used of all BJ’s borate frac fluid systems. It
is guar based, and uses an organo-borate crosslinker for a much greater temperature range
than the Viking systems. The system is a premium system at lower temperatures, typically
providing more viscosity. The crosslinker can be delayed, and the length of time for the delay
can be varied over a significant range. The crosslinker for the system is XLW-24.
®
®
Spectra Frac G HT is the high temperature version of Spectra Frac G . It is guar based,
and uses an organo-borate crosslinker for a much greater temperature range than the Viking
systems. The crosslinker also employs a self-breaking mechanism, which helps to reduce the
viscosity over a period of time above +/- 230°F. The crosslinker can be delayed, and the
length of time for the delay can be varied over a significant range. The crosslinker for the
system is XLW-56.
Lightning™ is a new fracturing fluid system that uses a newly developed low-residue guar
polymer, GW-3. The system uses the same borate crosslinkers as Viking™.
®
Medallion Frac is a CMHPG based system that uses a zirconate crosslinker. Unlike the
®
borate systems, which operate at a pH above +/- 9.0, Medallion Frac operates at a pH
below neutral, usually around 4.5 to 5.5. Because of its low pH, it is the fluid of choice for CO2
foam fracs, pads for acid fracs, and for formations which are sensitive to high pH’s.
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5. Fluid Systems
Crosslinkers for the system are XLW-41, XLW-53 or XLW-60. XLW-60 is a delayed crosslink,
whilst XLW-41 and XLW-53 are designed for a rapid crosslink. The crosslinkers can be used
together in varying proportions to adjust the crosslink time as desired.
®
®
Medallion Frac HT is a high pH version of Medallion Frac . It uses a different buffer to
achieve the required pH (usually around 8.0 to 9.0), but otherwise is the same as Medallion
®
Frac . The high pH zirconate system is more temperature stable than the low pH. Generally,
the high pH system uses XLW-60 as the crosslinker.
Vistar™ is a low or high pH, zirconate crosslinked system, designed so that only very low
polymer loading is needed, as compared to other fluid systems. The base gel is a guarderivative (GW-45). Crosslinkers for the system are XLW-63 (lower temperatures) and XLW14 (high temperatures).
Crosslinked systems are also characterized by the quantity of polymer used in the base gel.
For instance, a “35 lb” system has the base gel mixed with 35 lbs of polymer in every 1000
®
gals of water. If this base gel were to be used in Spectra Frac G , the fluid system would be
®
known as Spectra Frac G HT 3500.
LFC, XLFC, VSP and GLFC
LFC (which stands for Liquid Frac Concentrate) and XLFC are slurried polymer systems,
usually designed to carry 4 lbs of polymer in every gallon of slurry. Simply add the slurry to
water and the base gel will form. Slurrying the polymer in an oil-based system helps disperse
the polymer in the water (preventing fish-eyes) and is much easier to meter when hydrating
gel on-the-fly. The liquid base for the slurry is usually diesel or a low toxicity diesel-derivative.
However, LFC and XLFC systems have been developed that use vegetable or fish oil as the
base liquid, although these hold reduced amounts of polymer per gallon. In addition to the
base oil and polymer, LFC and XLFC also contain suspending agents to prevent settling
during storage, dispersants to help mix the slurry and wetting agents to help the polymer
hydrate quickly once the LFC or XLFC is added to water. A pH buffer can also be
incorporated to help the polymer hydrate more quickly, especially at low temperatures.
LFC-1, GLFC-1 and XLFC-1 contain guar (GW-27)
LFC-2, GLFC-2 and XLFC-2 contain HPG (GW-32)
LFC-3, GLFC-3 and XLFC-3 contain CMHPG (GW-38)
XLFC-5 contains GW-3
XLFC is the updated version of LFC. VSP (or Vistar Slurried Polymer) is a version of XLFC
developed for the Vistar™ system and contains CMG (GW-45).
GLFC systems, which can be mixed with guar, HPG or CMHPG, use an organically-derived
base oil in order to meet increasingly tight environmental regulations in many areas of the
world.
5.3
Oil-Based Systems
As stated previously, the very first hydraulic fracture treatment was carried out using gasoline
gelled with war surplus napalm. The operation was performed on Pan American Petroleum’s
Klepper No 1 well, Grant county, Kansas, (part of the Hugoton gas field) in 1947. The
treatment was aimed at 4 gas bearing limestone formations, at about 2500 ft. The gasolinebased fluid was selected, as it was perceived to be more compatible with the formation. This
continues to be the primary reason for selecting an oil-based fluid.
For the record, the treatment on Klepper No 1 failed to produce a significant production
increase, and it was decided that the "Hydrafrac” process would never compete successfully
with acidising in this type of formation.
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The first widely-used oil-based fluid system, was based on the reaction of an acidic material
(tallow fatty acid) and basic material (caustic) to form a polymeric salt, in a process similar to
the manufacture of soap. These fluids provided viscosity, but where very unstable at elevated
temperatures. As time progressed, this system was replaced by others based on the use of
aluminium phosphates, which were able to provide significantly increased viscosity and more
stability at elevated temperatures.
In the early 70’s, the aluminium phosphate systems were replaced by the aluminium ester
systems. The association of aluminium and phosphate esters is illustrated in Figure 5.3a.
These systems used a combination of two products to produce the required viscosity. The
relative ratio of these two products was extremely critical – so critical that it was difficult to mix
these systems on the fly. Consequently, a great deal of time and effort was spent in pregelling tanks full of hydrocarbons, resulting in considerable spillage and waste of chemicals.
R
R
O
P
O
O
P
O
O
O
H
Al
H
O
O
O
R
P
O
O
Al
O
O
R
O
O
Al
H
R
O
P
O
O
H
R
Figure 5.3a – Aluminium phosphate association polymer
More recently, BJ Services has introduced a much more user-friendly system known as
Super RheoGel. The ratios of the various components of the system are not nearly as
critical, so that the gel can now be mixed on the fly. The following products are used in Super
RheoGel:GO-64 (gelling agent) and XLO-5 (activator) are the main components of the system. They
are added in equal quantities, at different stages of the blending procedure, to produce the
required viscosity and stability.
NE-110W is a critical surfactant blend used in the continuous mix gelled oil system. This
material aids in fluid recovery by acting as a hydrotropic material in the system. It helps to
reduce emulsion tendencies of oils and also acts as a long-term breaker for the system. NE110W also helps to counteract the oil-wetting surfactants contained in products such as
diesel.
GBO-5L, GBO-6 and GBO-9L are the breakers for the system.
Most gelled oil systems can be prepared with a wide variety of hydrocarbon based fluids,
including diesel, kerosene, “frac oil”, condensate and many lease crudes. Because the fluid
used to fracture the well is itself hydrocarbon based, the well can be put straight on to
production after the treatment is over. This makes the fluid recovery phase of the operations
much easier.
The Super RheoGel system does not work like a conventional water-based crosslink system.
There is no base gel viscosity when the GO-64 is added, as it does not react with the base
hydrocarbon. Instead, the GO-64 disperses in the hydrocarbon. When the XLO-5 is added,
the crosslinker joins up the GO-64 molecules, trapping the hydrocarbon molecules within the
GO-64/XLO-5 matrix and producing viscosity. Because the GO-64 does not react with the
base hydrocarbon, it is possible to gel any fluid system in which this product can be
dispersed, hence the ability of the system to be used in a wide variety of hydrocarbon-based
fluids.
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Methanol can also be used as the base for fracturing fluids, although the systems designed
for oil-based fluids (such as Super RheoGel) are not suitable. Instead, a polymer is used to
produce a base gel and a specialised crosslinker is used to provide the viscosity necessary
for proppant transport.
Methanol-based fracturing fluids are used in water- and fluid-sensitive reservoirs where fluid
recovery after the treatment is critical. The methanol reduces interfacial tension between the
fracturing fluid and the connate water and also helps remove and prevent capillary water
blocks. This allows for much easier recovery of the fracturing fluid from dry gas and watersensitive reservoirs.
BJ Services'methanol-based fracturing fluid is called Methofrac XL. The system is designed
for continuous or batch-mixed applications. GM-55 is the guar-derivative polymer powder,
whilst XLFCM-1 is the slurried polymer concentrate. The crosslinker is XLW-40, which is a
titanium-based, is usually diluted before use. The diluted versions (XLW-40B, -41A and -41B)
are mixed by adding 2.5 to 10% of XLW-40 by volume to methanol or iso-propyl alcohol, as
appropriate (see BJ Services'Mixing Manual instructions). The breaker for the Methofrac XL
system is GBW-5.
When mixing with lease crude or condensate, obtain fresh samples of the hydrocarbon and
test to make sure that the system performs as required. This practice should also be followed
when mixing with fluids such as kerosene or diesel, as local variations in product quality can
have a significant effect on fluid performance. Additionally, be aware that BJ Services has
strict safety and operations standards for the use of hydrocarbon based fluids, and for the
handling of low flash point liquids. These standards can be found in BJ’s Standard Practices
Manual and BJ’s Corporate Safety Standards and Procedures Manual.
5.4
Emulsions
In general, emulsions are only rarely used in fracturing operations, but in some parts of the
world they have been found to have an ideal combination of fluid loss characteristics,
formation compatibility and downhole viscosity. As a result, in these areas their use is
common.
Most of these systems are oil-in-water emulsions and operate in a similar fashion. Water is
gelled with a standard gelling agent and held in a tank(s). During the job, water and oil are
mixed together at the ratio of 2 parts oil to one part gel. An emulsifier is either pre-blended in
the water phase (the gel) or added on the fly. The fluids very quickly form a brown emulsion,
the viscosity of which is largely proportional to the initial viscosity of the water phase.
Some systems require an external breaker in order to destroy the emulsion and allow the
fluids to be recovered. However, in most systems, the emulsion quickly falls apart after
exposure to the formation.
BJ Services emulsion-based fluid system is known as Polyemulsion for which the
emulsifying agent is E-2.
5.5
Visco-Elastic Surfactant Fluids
Visco-elastic surfactant (VES) systems are water-based fluids that employ a completely
different method from all other water-based fluid systems for obtaining viscosity. They do not
rely upon the hydration of a polymer. Instead, they use the unique properties of certain
surfactants when mixed at certain concentrations in brine-based fluids.
In aqueous fluids, surfactants will tend to expel their lipophilic (water-repelling) tails out from
the surface of the fluid. As the concentration of the surfactant increases, close packing occurs
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and no more surfactant molecules can expel their tails. At this point, the surfactant molecules
will start to form spherical aggregates (or micelles) with the lipophilic tail facing inwards, and
the hydrophilic head facing outwards. The concentration at which these micelles start to form
is called the critical micellar concentration (CMC), and is often around 0.5% by volume of
surfactant. The CMC will decrease as the molecular weight of the surfactant increases.
As the surfactant concentration increases further, and in the presence of a suitable counter
ion (such as those produced by brines), these micelles can come together to form worm- or
rod-shaped aggregates or micelles. It is these rod-shaped micelles that impart viscosity to the
water.
VES fluids have some rather unique properties, as follows:1.
2.
3.
4.
5.
VES fluids are extremely shear thinning, with the property to quickly re-heal after the
shear is removed. This means that the fluids have an extremely low friction pressure,
whilst at the same time retaining excellent proppant transport characteristics.
VES fluids are very easy to mix. Simply start with the base brine and add the
surfactant on the fly.
VES fluids can be made to be very environmentally friendly, depending upon the
combination of surfactant and brine used.
VES fluids often require no breaker system, as micelles can be disrupted by changes
in pH, high temperatures, dispersion in formation waters or by contact with
hydrocarbons.
The VES system is as formation and proppant pack friendly as the base brine used to
mix it. The systems contain no polymers, and therefore produce no polymer residue.
Therefore, these fluids are capable of providing zero formation damage and 100%
regained proppant pack permeability.
The two main disadvantages of VES fluids are that they are relatively expensive and that they
are limited by temperature. Proppant transport characteristics are rapidly lost above
temperatures of +/- 230°F. Development work continues, however. Another problem with VES
fluids is leakoff. Because they contain no polymers, they do not have any wall-building
characteristics, and so leakoff control is entirely dependent upon the fluid’s viscosity and/or
additives used in the system.
BJ Services’ has two VES fluid systems, called ElastraFrac and AquaClear.
ElastraFrac uses the surfactant MA-1. The system uses potassium, ammonium or
magnesium chloride as the base brine, although more exotic phosphate-based brines are
used at temperatures above +/- 200°F. The surfactant used is anionic (unlike competitor’s
products that use cationics and hence risk oil-wetting the formation).
AquaClear is also a surfactant-based fracturing fluid. The system uses either a combination
of FAC-1W and FAC-2, or the single surfactant FAC-3W as the VES. It is designed for mixing
on-the-fly and is suitable for use up to +/- 250 °F. The system is easily used as an energised
fluid and does not need an additional foaming agent).
5.6
Energised Fracturing Fluids
Energised fluids consist of a liquid phase – usually a water-based linear or crosslinked gel –
and a gaseous phase, which is typically N2, CO2 or a combination of these. Such treatments
involve large amounts of equipment and personnel. Consequently, they are relatively
expensive. These treatments are also referred to a foam fracs, as foam is generally what is
arriving at the formation. Because of the safety implications of working with both cryogenic
fluids and energised fluids, the procedures detailed in BJ’s Standard Practices Manual and
BJ’s Corporate Safety Standards and Procedures Manual, should be closely followed at all
times.
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Foamed fluids have several unique properties that make them advantageous under certain
circumstances:i)
ii)
iii)
iv)
Viscosity and proppant transport. Stable foams have a comparatively high viscosity
and make excellent fluids for carrying and suspending proppant.
Foams have very good leakoff properties. This is due to the multi-phase flow effects
as the foam tries to move through the formation'
s porosity.
Because foams are typically only 30 to 40% liquid, they are more compatible with
water sensitive formations than frac systems which are 100% liquid.
The extra energy stored in the fluid, coupled with the low hydrostatic head of the
foam, makes fluid recovery relatively easy.
Foam Quality
Proppant Transport
The foam quality, often expressed as a percentage or just simply as a quality (i.e. “70 quality”
or even “70Q”) is the percentage of foam or energized fluid that is gas, at the anticipated
bottom hole conditions. In order to design a foam treatment, an Engineer must have a
reasonable idea of the expected bottom hole treating pressure and temperature, as the
volume occupied by the gas phase will vary depending on both of these (although the
temperature is much less significant than the pressure). As illustrated by Figure 5.6a, foam
viscosity (and hence it’s ability to transport proppant) is heavily influenced by the quality. If the
bottom hole pressure is significantly less than anticipated, the foam quality will be too high,
and the gas phase will expand to make a mist, rather than foam.
STABLE
FOAM
0
20
40
60
80
100
Foam Quality
Figure 5.6a – Proppant transport as a function of foam quality. This graph is a combination of the
work performed by several individuals and organisations. It is intended as a qualitative
illustration of the effect foam quality has on the ability of the fracturing foam to transport and
suspend proppant.
Gas assisted fluids use lower gas quality (typically 20 to 40%) than foamed fluids. The main
purpose of the gas phase is to reduce hydrostatic head and hence aid fluid recovery. In such
treatments, the proppant transport and fluid leakoff properties for a fully foamed fluid system
are not required.
Proppant Concentration
Because proppant is added to the liquid phase of the foamed frac fluid, there is a limit to the
overall proppant concentration that can be achieved downhole. Because it is not possible to
blend and pump proppant at more than 18 or 19 ppg in the liquid phase, by the time the liquid
phase has been mixed with the gaseous phase, the overall proppant concentration has been
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reduced to 7 or 8 ppg. For this reason, it is not possible to place the very high proppant
concentrations required for fracturing high permeability formations. This means that foam
fracturing is limited to medium and low permeability reservoirs, for skin bypass fracturing
(although the extra cost can defeat the low cost objectives of this type of treatment) and for
coal bed methane fracturing.
Constant Internal Phase vs Constant External Phase
Foams can be thought of as being a multi-phase fluid, with a gas-internal phase, and a liquid
external phase. The difficulty comes in deciding whether or not the proppant is part of internal
phase or the external phase.
The traditional method of modeling foams and designing treatment schedules uses the
constant external phase method. This assumes that the proppant is part of the external
phase. It is easier to operate on location, as both the slurry rate and the gas rate remain
constant. However, under constant external phase, the actual fraction of the foam that is
liquid can be severely reduced as higher proppant concentrations are reached. Obviously, the
proppant has no properties that act to hold the foam together, so foams can become very
unstable as the proppant concentration increases.
The modern way of modeling foam is to use the constant internal phase method. This models
the proppant as being part of the gas phase. Therefore, in order to keep foam quality
constant, the gas rate has to go down as the proppant concentration rises, and then increase
rapidly as the treatment goes to flush. This method is harder operationally, but provides much
more stable foam.
Foam Stability
The stability of foam is its ability to remain as foam, rather than separating out into two or
even three phases. Ideally, the fluid should remain as foam long enough for the fluid to be
recovered as foam after the treatment. Obviously, temperature and fluid contamination will act
to reduce foam stability. There are three main methods for maximising foam stability:i)
ii)
iii)
Mixing the liquid and gas phases at high shear, such as with a foam generator, or by
passing the mixed phases through a high shear device, such as a choke. The greater
the shear that the foam experiences, the more stable it becomes. High shear acts to
reduce the average size of the gas bubbles, which in turn makes it harder for then to
separate out.
Crosslinking the fracturing fluid after the foam has been formed. By using a delayed
crosslinker, the onset of crosslink can be timed to take place after the foam has been
generated, so that the gas bubbles are literally crosslinked into position.
Foaming agents. These surfactants act to increase the surface tension of a material,
so that the gas bubbles are much more stable.
Often a combination of these methods is used.
Foam Viscosity
The viscosity, proppant transport characteristics, fluid leakoff and stability of the foam are all
influenced by the same foam characteristics - the liquid phase viscosity, the average gas
bubble size, the foam quality and the surface tension properties of the liquid phase. All of
these are affected by temperature and two of these are significantly affected by pressure.
This means that calculating the viscosity – and hence the friction pressure and fluid leakoff –
of the foam is very difficult.
Consequently, calculated bottom hole treating pressures for foam fracs are extremely
unreliable and should not be used for analysis unless there is absolutely no alternative
whatsoever. The results from such an analysis should be considered as educated guesswork
only.
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N2 Foam Fracs
N2 foamed fracs are the most straightforward of all the types of energized fluid fracs
performed. Nitrogen is stored as a cryogenic liquid, in specialised, highly insulated tanks on
location. Prior to the treatments, each tank uses a heat exchanger to vapourise a small
amount of the liquid into gas. This has the effect of pressuring up the tank, so that liquid
nitrogen is forced from the tank to the N2 pumpers.
Before liquid N2 can be pumped, the pump itself has to be cooled down. This is done by
flowing liquid N2 though the pump and out of a vent. Initially gas will bleed out if the vent.
Eventually, as the unit cools down, liquid will be seen coming out of then vent, indicating to
the operator that the unit is now ready to pump. Therefore, when designing N2 foam fracs,
sufficient liquid nitrogen should be on location for cooling the N2 pumpers down at least 3
times (once for the minifrac, once for the main treatment and one spare).
It is much easier to convert a liquid from low to high pressure, than it is to convert a gas from
low to high pressure. Consequently, the N2 pumpers will be working on liquid N2 that is stored
and pumped at around –320°F. This means that specialised equipment is required for
pumping this cryogenic liquid. These pumpers also include a vapouriser, which will heat the
high pressure liquid and convert it into a gas (for this reason, N2 pumpers are often referred to
as “converters”). These vapourisers can be diesel fired or run from the engine coolant.
As N2 is chemically inert, there are no limitations on the fluid systems it can be used with.
CO2 Foam Fracs
CO2 has a number of properties that make its use significantly different from N2. To start with,
liquid CO2 is stored at –20°F. The much higher temperature means that the liquid can be
pumped with a standard frac pumper (provided they have been specially prepared – see BJ’s
Standard Practices Manual). It also means that the liquid CO2 does not have to be converted
into a gas before it is mixed with the liquid phase – this will happen automatically as the CO2
heats up.
The second major property difference of CO2 is its tendency to form a solid (“dry ice”) if stored
or pumped under the wrong conditions. Obviously, this must be avoided. Dry ice will only form
below +/- 80 psi. So at every stage, the liquid CO2 is kept well above this pressure. Typically,
CO2 is stored at between 150 to 300 psi. There are several different methods for pumping the
liquid CO2 from the tanks to the pumpers. One method involves forcing it out with N2 pressure
applied above the fluid level in the CO2 tank. Another method employs specialised boost
pumps. Yet another method employs a combination of these two systems. Once again, BJ’s
Standard Practices Manual should be consulted before designing any treatments.
The third major difference is that unlike N2, CO2 is not chemically inert. Specifically, on
contact with water based fluids, some of the CO2 will dissolve into the water to form an acid.
This has the effect of lowering the pH of the system. This means that CO2 is not compatible
with high pH fracturing fluids, such as borate crosslinked gels.
Binary Fracs
Binary Fracs involve the use of a mixture of both CO2 and N2 to provide the foam. They were
originally developed as a method of getting around one service company’s patent on CO2
foam fracturing. Since then, the method has been extensively developed and is now the
preferred method of foam fracturing for many operating companies.
Binary fracs are the most complicated stimulation operations performed, requiring the use of
no less than three service supervisors (one for the CO2, one for the N2 and one for the liquid
phase, who is in overall control). Consequently, these are relatively uncommon.
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Poly CO2
Poly CO2 is a highly specialised fluid developed by Nowsco in Canada. In this fluid, a
specialised additive is mixed into the water-based liquid phase, which causes the waterbased gel and the liquid CO2 to form an emulsion, rather than foam. The emulsion is not
particularly stable, and will break down after the fluid contacts the formation.
This fluid system has only ever been used in low temperature applications, and it is unclear
as to whether the stimulation benefits come from the placing of proppant, or from the thermal
shock experienced by the formation. However, in certain formations it has proved to be highly
successful.
5.7
Additives
There are an enormous number of additives used in the preparation of the various types of
fracturing fluids, and an exhaustive list is beyond the scope of this manual. However, below is
a description of the general types of additive, together with the most commonly used
examples from BJ’s product range.
Gelling Agents
Water-based gelling agents are designed to increase the viscosity of water. This water can
be fresh (rarely), 2% KCl, 3% NH4Cl, seawater or any of a myriad of different kinds of brines.
Nearly all the gelling agents are some kind of polymer. A wide range is available, depending
upon hydration pH, temperature stability and polymer residue:Guar
High-yield guar
Hydroxypropyl Guar (HPG)
Carboxymethyl Hydroxypropyl Guar (CMHPG)
Carboxymethyl Guar (CMG)
Hydroxyethyl Cellulose (HEC)
Carboxymethyl Hydroxyethyl Cellulose (CMHEC)
Xanthan
Polysaccharide
GW-4, GW-27
GW-3
GW-32
GW-38
GW-45
GW-21, GW-24L, AG-21R
GW-28
GW-22, GW-22L, GW-37
GW-23
Oil-based gelling agents are designed to increase the viscosity of oil-based fluids. These
gelling agents work on a wide variety of hydrocarbons, but are primarily designed for diesel
and kerosene. Any other hydrocarbon fluid should be tested prior to application.
GO-64
GM-55
Gelling agent for Super Rheo Gel
Gelling agent for Metho Frac XL
Crosslinkers and Complexers
Crosslinkers and complexers are designed to dramatically increase the viscosity of an already
gelled fluid, so that high viscosity can be maintained for extended periods of time at high
temperatures. For many fluid systems, the crosslinker is the chemical that really defines its
characteristics.
XLW-4, XLW-32, XLW-10
XLW-30, XLW-30A
XLW-14, XLW-63
XLW-24
XLW-56
XLW-60
XLW-40B, XLW-41A, -41B
XLO-5
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Crosslinkers for Viking and Lightning
Crosslinkers for Viking D
Crosslinkers for Vistar
Crosslinker for SpectraFrac G
Crosslinker for SpectraFrac G HT
Crosslinker for Medallion Frac & Medallion Frac HT
Crosslinker for Metho Frac XL
Complexer for Super RheoGel
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Breakers
Breakers are designed to reduce the viscosity of the fracturing fluid to a minimum, so that the
fluid can be easily recovered after the treatment. They are also designed to minimise polymer
residues, so that damage to the proppant pack is minimised.
GBW-5, GBW-7, GBW-41L
GBW-23, GBW-24
GBW-26C
GBW-12CD
GBW-14C
High Perm CRB
GBO-5L, GBO-6, GBO-9L
Oxidizing breakers
Delayed oxidizers
Enzyme breakers for cellulose + derivatives
Enzyme breaker for guar + derivatives
Enzyme breaker for xanthan + derivatives
Encapsulated oxidizing breaker
Breakers for Super RheoGel
Buffers
Buffers are designed to either raise the pH or lower the pH, as required.
Low pH buffers
High pH buffers
BF-1, BF-10L, BF-10LE
BF-7, BF-7L, BF-8L, BF-9L, caustic soda
Surfactants
The word Surfactant comes from the phrase SURFace ACTive AgeNT, and includes any
chemical that affects the interface properties between materials. Because this covers such a
wide range of materials, it is necessary to discuss this group of products in more detail.
Surfactants can also be grouped according to the type of charge they possess, so that some
surfactants are anionic (negative charge), some are cationic (positive charge), some are
amphoteric (cationic at low pH and anionic at high pH), some are Zwitterionic (both cationic
and anionic simultaneously) and some are non-ionic. Generally speaking, it is best not to mix
anionic and cationic products together, as they might form viscous deposits. Details of this
can be found in BJ’s Mixing Manual.
Most of BJ’s surfactant products are designed to leave the formation water wet. This means
that the relative permeability of the formation to water has been lowered, and the relative
permeability of the formation to oil has been raised. However, it is important to note the
following:Cationic surfactants will leave sandstones oil wet and carbonates water wet
Anionic surfactants will leave sandstones water wet and carbonates oil wet.
Amphoteric surfactants can behave either way depending upon the pH. At acidic pH’s (less
than 7), amphoteric surfactants show cationic properties, whilst at alkaline pH’s (greater than
7), they display anionic properties. At neutral pH, they behave like non-ionic surfactants.
Non-emulsifying surfactants are designed to prevent the formation of emulsions between
the crude oil in the formation and the treatment fluid. All water-based treatments should have
a non-emulsifying surfactant added to them, unless they are being pumped into a water
injection well or dry gas reservoir with no trace of condensate.
Inflo 100, Inflo 102
NE-13
NE-110W
NE-118
NE-940
Blend of cationic and nonionic
Blend of cationic and nonionic
Anionic
Nonionic
Nonionic
Note that some non-emulsifiers will also act to break existing emulsions.
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Foaming agents work by increasing the surface tension of the fluid. This helps increase foam
stability. Most foaming agents also acts as detergents and dispersants
FAW-4
FAW-18W
FAW-20
FAW-21
FAO-25
Anionic
Anionic
Anionic
Amphoteric
Nonionic – foaming agent for oil-based fluids
Note that FAW-4, FAW-18W and FAW-20 will leave carbonate formations oil wet.
Low surface tension modifiers act to reduce the surface tension of the fluid. This helps the
fluid penetrate into very small places, such as the pore spaces in low permeability reservoirs.
These products also help the treatment fluid flow back out of the well after the treatment is
finished.
Flo-Back-20, Flo-Back-30
Inflo-100
Inflo-150
Nonionic
Blend of cationic and nonionic
Nonionic
Mutual solvents will dissolve hydrocarbon based deposits and allow them to disperse water
based fluids.
US-2, US-40
Inflo-40
Nonionic
Nonionic
Emulsifiers are used to deliberately create emulsions. They only should be used as part of
an emulsion-based fluid system
AE-7
E-2
Cationic
Cationic
Biocides
Biocides, also known as Bactericides, are designed to kill bacteria. Any bacteria – especially
sulphate reducing bacteria – will eat the polymer used in frac fluids. A colony of bacteria can
reduce a tank of good quality gel into foul-smelling slick water in less than an hour. Biocides
are used to prevent this. Initially, all tanks used for frac fluids should be as clean as possible.
This will help reduce the risk of bacterial contamination. However, the water used to mix the
gel can still contain these bacteria, especially if the climate is hot or seawater is being used.
The biocide should be added either directly to the tank before the water is added, or it should
be thoroughly mixed into the water prior to the addition of any polymer. Once the biocide has
been added, it will quickly kill any bacteria that are present in the water.
It is recommended that a biocide is used on any treatment with involves pre-gelling the fluid.
It should be remembered that biocides are designed to prevent a colony of bacteria from
developing in the first place, rather than for killing an existing colony - any gel that is
suspected of being contaminated should be discarded, and its tank thoroughly cleaned. In
order to break down the gel, bacteria secrete enzymes (similar enzymes to the breakers
described above). These enzymes will cause a tank of gel to degrade, so that even if all the
bacteria in a tank have been killed, their enzymes are still present in the tank. This is why
contaminated tanks of gel need to be discarded, and not used again.
It should also be noted that in their concentrated form, biocides are very dangerous materials
(after all, they are designed for killing living things) and should be handled with extreme care.
Magnacide 575
XCide 102, 207
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Gel Stabilisers
Gel stabilisers are used to prolong the viscosity of crosslinked gels at high temperatures.
They work by one of two methods:- they can scavenge the oxygen in the fluid; or they can
chelate cations which can contribute to the degradation of the gel.
GS-1, GS-1L, GS-9
Methanol
Clay Control Additives
Clay control additives are used to prevent the swelling, migration and disintegration of clay
minerals such as illite, smectite, chlorite and montmorillonite. Fresh water by itself will cause
these problems. The addition of chloride ions to fresh water will prevent these problems in
most formations, so that most treatments carried out with seawater do not need any additional
clay stabilisers. However, exceptionally water sensitive formations may need additional
protection, which is where BJ’s range of synthetic clay control additives is applied.
KCl, NH4Cl, NaCl etc
CaBr2, ZnBr2, etc
Clay Treat 3C
Clatrol
Claymaster 5C, FSP
standard salts for brines
specialised salts for high density completion
brines (some of these may be incompatible
with BJ’s crosslinked fluids).
KCl substitute, recommended for Vistar.
Note that any salts containing calcium or magnesium should not be mixed with frac fluids, as
these are incompatible with some crosslinkers. Also note that some of the synthetic clay
control additives are cationic in nature and should not be mixed with any anionic products.
Fluid Loss Control
Fluid loss control additives can be used for two main reasons; firstly, to lower a very high
matrix leak off rate; and secondly, to prevent fluid loss down natural fractures. The use of fluid
loss additives is becoming less and less common, as the understanding of fluid leakoff
increases. Most Engineers also believe that pumping more fluid is preferable to using
additives that can potentially produce permanent damage.
Silica flour, 100 mesh sand
5% diesel
®
Adomite Regain
Used for blocking natural fractures
References
BJ Services’ Mixing Manual
BJ Services’ Stimulation Engineering Support Manual
BJ Services’ Products and Services Manual
BJ Services’ Product Bulletins
BJ Services’ Standard Practices Manual
BJ Services’ Corporate Safety Standards and Procedures Manual
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Rae, P., and Di Lullo, G.: “Fracturing Fluids and Breaker Systems – A Review of State-of-theArt”, paper SPE 37359, presented at the SPE Eastern Regional Meeting, Colombus OH, Oct
1996.
Brannon, H.D., and Ault, M.C.: “New, Delayed Borate-Crosslinked Fluid Provides Improved
Conductivity in High Temperature Applications”, paper SPE 22838, presented at the SPE
Annual Technical Conference and Exhibition, Dallas TX, Oct 1991.
Cramer, D.D., Dawson, J., and Ouabdesselam, M.: “An Improved Gelled Oil System for High
Temperature Fracturing Applications”, paper SPE 21859, presented at the Rocky Mountain
Regional Meeting and Low-Permeability Reservoirs Symposium, Denver CO, Apr 1991.
Blauer, R.E., and Kohlhaas, C.A.: “Formation Fracturing with Foam”, paper SPE 5003,
th
presented at the 49 Annual Fall Meeting of the SPE, Houston TX, Oct 1974.
Grundman, S.R., and Lord, D.L.: “Foam Stimulation”, paper SPE 9754, JPT pp 597 – 602,
Mar 1983
Valkó, P., and Economides, M.J.: “Foam Proppant Transport”, paper SPE 27897, presented
at the SPE Western Regional Meeting, Long Beach CA, Mar 1994.
Tjon-Joe-Pin, R, DeVine, C.S., and Carr, M.: “Cost Effective Method for Improving
Permeability in Damaged Wells”, paper SPE 39784, presented at the SPE Permian Basin Oil
and Gas Recovery Conference, Mar 1998.
Di Lullo, G., Ahmad, A., and Rae, P.: “Towards Zero Damage: New Fluid Points the Way”,
paper SPE 69453, presented at the SPE 2001 Latin American and Caribbean Petroleum
Engineering Conference, Buenos Aires, Argentina, March 2001.
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6. Proppants
6.
Proppants
The word proppant comes from the abbreviation of two words - “propping agent”. Proppants
are granular materials, which are placed inside the fracture in order to “prop” the fracture
open as the pressure falls below closure. The conductivity of the fracture is directly related to
the quantity of proppant within the fracture, the type of proppant, the producing conditions and
the size of the proppant grains.
The purpose of hydraulic fracturing is to place the right amount of the right kind of proppant in
the right place. When this is done correctly, the well is effectively stimulated.
6.1
Proppant Pack Permeability and Fracture Conductivity
As discussed in Section 2, one of the major factors affecting post-treatment well performance
is the fracture conductivity. This is the product of the proppant pack permeability and the
width of the fracture. In other words, the fracture conductivity is a function of the type of
material holding the fracture open and the amount of this material within the fracture.
The permeability of the proppant pack is controlled by several factors:i)
Proppant Substrate. The material that the proppant is made from obviously has a
big effect on the permeability of the proppant pack. Some materials are stronger than
others and are better able to withstand the enormous forces trying to crush the
proppant as the fracture closes. The weaker the material, the more the proppant grain
will deform. Proppant deformation reduces the porosity of the pack and reduces the
overall fracture width. The more brittle the proppant is, the more likely it is that the
proppant will produce fines as the grains are pushed together in a series of point to
point contacts. Any fines will significantly reduce the proppant pack permeability.
ii)
Proppant Grain Size Distribution. A normal sedimentary formation has a wide
variety of grain sizes, depending upon how well “sorted” the individual rock grains are.
In general, any sandstone will be a mixture of small, medium and large grains. The
mixture of grain sizes acts to reduce the formation'
s permeability and porosity, as the
smaller grains will occupy the pore spaces between the larger grains and will also
tend to plug up the pore throats. However, if a set of particles are of almost identical
size, then there will be no fines to block up the pore spaces and pore throats, so that
the porosity (and hence the permeability) are maximised.
This is why proppants are generally produced within a specific grain size distribution.
This uniformity of grain size is one of the main reasons why proppant is usually
several orders of magnitude more permeable than the formation, and also one of the
main reasons why so much effort is spent in ensuring this uniformity of size. This is
illustrated in Figure 6.1a, below;
Uniform
Natural
Figure 6.1a – The effect of uniform and natural grain size distribution on porosity
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6. Proppants
Proppants are supplied within a specific grain size range. This grain size refers to the
size of sieve used to sort the proppant. For instance, 20/40 size means that the vast
majority of the proppant will fit through a size 20 sieve (20 holes per square inch), but
will not fit through a size 40 sieve (40 holes per square inch). This is sometimes
confusing, as larger grain sizes correspond to smaller mesh numbers. Common
proppant sizes are 8/12, 12/20, 16/30, 20/40 and 40/60, although theoretically any
combination of sizes can be produced.
iii)
Average Proppant Grain Size. Generally, the larger the average proppant grain size
is, the higher the permeability of the proppant (provided the grain size distribution is
reasonably uniform). This is because larger grains produce larger pore spaces and
pore throats, allowing an increased flow rate for a similar porosity. However, the
larger grains are more susceptible to producing permeability reducing fines than are
the smaller grain sizes. This is because larger grains distribute the closure pressure
across fewer grain-to-grain points of contact and so the point contact loads tend to be
greater. This is illustrated in Figure 6.1b;
Figure 6.1b – Diagram illustrating how larger grains have larger pore spaces and hence greater
permeability.
iv)
Sphericity and Roundness. These quantities define how spherical the proppant
grains are and how many sudden, sharp edges the grains have. Obviously, the
smoother and more spherical the proppant grain is, the higher the pack permeability.
There are standard API procedures for checking these quantities, but unfortunately
they rely on some subjective analysis. Consequently, it is often difficult to see a clear
trend between one proppant type and another. However, in general, artificial
proppants will have better sphericity and roundness than naturally occurring types.
This is illustrated in Figure 6.1c;
Figure 6.1c – Diagram illustrating the difference between a proppant with good sphericity and
roundness (left), and a proppant with poor sphericity and roundness (right).
Coarse, angular grains also tend to produce more fines, as corners and edges tend to
get broken off as compressive stress is applied. Therefore, proppants with good
sphericity and roundness also tend to retain greater permeability at high stresses. In
addition, because proppant with low sphericity and roundness will produce a more
convoluted flow path for the produced fluids, non-Darcy pressure losses tend to be
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6. Proppants
greater in these materials (see Section 10.9), leading to decreased effective proppant
pack permeability.
iv)
Frac Fluid Quality. The amount of residue left by the fracturing fluid can also have a
big influence on the permeability of the proppant pack. In order to assess the effect of
these fluids, a quantity called Regained Permeability is measured. Put simply, a
sample of the proppant is put into a load sell and is subjected to a closure pressure,
at an elevated temperature. A standard, non-damaging fluid is then flowed through
the test cell. By analysing the pressure drop and flow rate, the permeability of the
pack can be calculated. Next, the frac fluid is flowed through the test cell, and allowed
to remain there for a specific time, during which it is designed to break. Once the fluid
has broken, the permeability of the pack is measured again, by the same method as
before. The two permeabilities are compared and the result (the regained
permeability) is given as the percentage of the original permeability that remains after
the test.
Figure 6.1d, below, illustrates the difference between fluids with a high and low
regained permeability;
Figure 6.1d – Three SEM micrographs showing the effects of frac fluid residue. The micrograph
on the left shows undamaged proppant before the addition of the frac fluid. The center
micrograph shows the residue left by a poorly designed crosslinked system. The final
micrograph shows the same proppant pack after an enzyme breaker has been used.
Proppant packs can lose significant proportions of their permeability to fluid damage.
Cheap, poorly designed fluids can cause regained permeabilities to be as low as only
30% or even less, whereas the state-of-the-art fluids can produce values in excess of
90%.
v)
Closure Stress. As the proppant is crushed by the closure of the formation, it will
start to produce fines. As discussed above, these fines will reduce the permeability of
the pack. The stronger the proppant, the fewer fines are produced - nevertheless, all
proppant types experience a decrease in permeability as closure stress increases, to
a greater or lesser extent. In addition, most proppants also have a “maximum” stress,
above which whole-scale disintegration of the proppant substrate starts to occur,
rather than simple fines production. At this point, pack permeability falls dramatically.
It should be noted that the reservoir pressure has an influence on the closure stress
experienced by the proppant. This phenomenon is discussed in greater detail later in
this manual (see Section 7.6). The relationship between reservoir pressure and
closure pressure is dependent upon a number of factors - there are circumstances
under which a decrease in reservoir pressure can result in an increase in closure
stress. Additionally, there can be localised areas of low reservoir pressure (such as
near the wellbore during drawdown) where once again the proppant experiences
higher closure pressure. This potential increase in stress with the life of the well must
be allowed for when selecting a proppant.
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6. Proppants
vi)
Non-Darcy Flow. This effect will be discussed on more detail in Section 10.9.
However, as the flow rate through the proppant pack increases, the pressure drop will
increase at a rate faster than that predicted by Darcy’s law. This is due to the effects
of inertial energy loses, as the fluid rapidly changes direction as it moves through the
pore spaces. As the fluid velocity increases, the pressure drop due to inertial flow
effects increases with the square of the velocity. So at low flow rates, (such as in a
reservoir rock), non-Darcy effects can safely be ignored, whilst at high rates (such as
in a proppant pack), the effective proppant permeability has to be reduced to reflect
this effect. The phenomenon is particularly significant in high rate gas completions.
vii)
Multi-Phase Flow. Multi-phase flow has a similar effect upon proppant pack
permeability as it does on formation permeability. It reduces it, by an amount that is
dependent upon the absolute permeability, and the relative saturation of each phase.
As it is very rare for a reservoir to produce a single phase (with the exception of some
gas reservoirs), it is also very rare for proppant to conduct only a single phase.
Therefore, the actual effective permeability of the proppant pack may be significantly
less than the published data, which is generally produced for single-phase flow only
(although this situation is improving).
6.2
Proppant Selection
As illustrated in Section 6.1, there are a substantial number of variables that must be taken
into account when selecting proppant. However, in many cases the selection process has
been simplified.
All proppant suppliers and manufactures publish data for pack permeability against closure
stress, for all their proppant types and grain size distributions. Provided the closure stress is
known (taking into account any subsequent loss in reservoir pressure), the absolute
permeability of the proppant pack can be easily found. This eliminates the need for the Frac
Engineer to hold data on sphericity, roundness, crush resistance, grain size distribution,
substrate material etc. Simply look up the proppant you are interested in, and see what the
permeability is for a given closure stress.
Most fracture simulators already have this data for most major proppant types. This allows the
simulator to predict the fracture conductivity for most given proppant/closure stress
combinations. Usually, there is also a “proppant damage factor”, which allows the user to
simulate the regained permeability effects of the fracturing fluids.
Some - but not all - fracture simulators will also model the effects of non-Darcy flow, showing
a decrease in effective permeability as production rate rises.
However, no current fracture simulators allow for the effects of multi-phase flow. Data on this
has been published by a few sources, the most notable of these being the Stim-Lab
Consortium’s PredictK software and Carboceramics' FracFlow proppant permeability
simulator.
Table 6.2a gives guidelines as the maximum closure stress each of the major proppant types
can withstand, before substrate failure begins to occur. Obviously, these limits are very
generalised, and are highly dependent upon factors such as grain size and the quality of the
manufacturing process and/or source of sand. More detailed information is available from the
manufacturers or in the references;
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6. Proppants
Type
Frac Sand
Low Density Ceramics
Intermediate Density Ceramics
Sintered Bauxite
Maximum
Closure
Stress, psi
5,000
9,000
12,000
14,000
Product
Example
Brady, Ottawa, Colorado
CarboEconoprop, CarboLite,
ValueProp
CarboProp, InterProp
Carbo HSP, Bauxite
Table 6.2a – Generalised maximum closure stresses for the main proppant types.
Important Note
The quality of the proppant, and the subsequent conductivity of the fracture, has a bigger
effect on post treatment production than virtually anything else under the Frac Engineer’s
control. In most cases, an economy made on proppant selection is a false economy. For
instance, although low-density ceramics cost two to three times as much as frac sand, they
have four to five times the pack permeability - even at low closure stresses - due to their high
sphericity and roundness.
Resin-Coated Proppant
Many operating companies prefer to use resin-coated proppant or sand for some or all of their
fracture treatments. There are many different types of resin coat and the manufacturers are
continually improving and updating their products. Therefore, the reader is advised to consult
the manufacturer’s specifications for details of any specific product. However, broadly
speaking, resin-coated proppant can be divided into two main categories as follows:Curable
Curable resin-coated sand or proppant is coated with a resin designed to harden when
exposed to temperature and/or closure stress. This allows the resin-coated grains to adhere
to each other, and hence dramatically reduce the effects of proppant flowback (see Section
10.7 for more details). At low temperatures, an activator is added to the fracturing fluid in
order to improve the adhesion.
Tempered or Pre-Cured
Tempered or Pre-cured resin coatings are harder than curable resin coats. They rely more on
closure pressure than temperature in order to make the sand or proppant grains adhere to
each other. These resin-coatings also have a secondary effect. Because the resin coat acts to
reduce the localised contact stresses between proppant or sand grains and because any
fines produced by this process are kept within the resin coat, these materials tend to have a
higher closure pressure resistance than the same material without the resin coat. This means
that they retain permeability under higher crush loadings and so can – for instance – extend
the range over which a cheaper material, such as frac sand, can be used.
Resin coated proppant or sand has a number of significant drawbacks, however:1. Cost. Coating the grains with resin can substantially increase the cost of the
proppant, especially when coatings designed for high pressure and temperature are
used.
2. Resin coats tend to affect the properties of the fracturing fluid. The exact variation in
properties depends upon the pH of the frac fluid and the type of resin coat. However,
it is common for resin-coated proppant to make frac fluids much harder to break. It is
recommended that when resin-coated proppant or frac sand is being used, testing is
performed on the frac fluids with the proppant in the fluid.
3. Resin coat tail-in. Many operators like to save money on a treatment by only using
resin coated sand or proppant for the last 20 or 30% of the treatment. The theory
being that only the part of the proppant close to the wellbore actually needs to
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6. Proppants
adhere together to prevent proppant flowback. However, due to the effects of
proppant convection and settling (see Section 10.6), there is no guarantee that the
proppant pumped last in the treatment will be the proppant that ends up right by the
wellbore. In fact, the only way to guarantee this is to pump 100% resin coated
material.
6.3
BJ Services’ FlexSand and LiteProp
BJ Services’ has two proprietary products that have significant technological advantages over
conventional proppant systems
FlexSandTM
FlexSand™ is designed to prevent proppant flowback by dramatically increasing the internal
friction of the grains inside the proppant pack. Put simply, in order for proppant flowback to
occur, individual proppant grains have to be able to move relative to each other. FlexSand
acts to prevent this by introducing deformable particles into the proppant pack.
The FlexSand grains are designed to be slightly
deformable relative to the proppant itself. The theory,
as illustrated in Figure 6.3a, is that as the formation
closes on the proppant, the proppant causes the
FlexSand to deform slightly, allowing the proppant
grains to “key into” the FlexSand and as a result
making it much harder for the grains to move relative to
each other. Typically, FlexSand is mixed into the sand
or proppant at between 10 and 15% by weight. The
material can be either added on the fly – using a
process controlled FlexSand “Bazooka” – or can be dry
blended into the proppant or frac sand prior to the
treatment.
Figure 6.3a – SEM micrograph of
FlexSand grain clearly showing
the indentations caused by the
closure of the surrounding
proppant grains.
Because the FlexSand has to be only slightly
deformable relative to the proppant, there are three
different types supplied, for different sand or proppant
types; FlexSand™ LS, FlexSand™ MSE and FlexSand™ HS. These are made of different
materials and – in the case of the FlexSand™ HS material – different shapes. BJ Services’
patent for FlexSand™ describes the method of preventing proppant flowback, and does not
limit BJ to any specific material, nor to any grain size or shape.
FlexSand also has a secondary effect. Because the FlexSand grains deform slightly, they act
to “cushion” the sand or proppant grains, reducing the localised point contact stresses
between grains. The reduces the quantity of fines produced, particularly by frac sand, and
helps to preserve proppant or sand permeability at higher closure stresses. Thus using
FlexSand can also lead to improved fracture conductivity in addition to preventing proppant
flowback.
LitePropTM
LiteProp™ is a proprietary low-density proppant system, designed to be neutrally buoyant in
the fracturing fluid. Currently, it comes in two versions, LiteProp™ 125 and LiteProp™ 175,
with SG’s of 1.25 and 1.75 respectively. Table 6.3a illustrates how this compares to other
types of proppant.
Because the LiteProp is designed to be neutrally buoyant, there is no need to use an
expensive crosslinked fracturing fluid. Instead, any brine with the same SG as the LiteProp
can be used. This in turn significantly reduces the cost and complexity of fracturing
operations. However, there are a few points to be aware of when using LiteProp:Page 50
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6. Proppants
Proppant
Type
LiteProp 125
LiteProp 175
Frac Sand
Carbolite
Carbprop
Carbo HSP
Specific
Gravity
1.25
1.75
2.65
2.71
3.27
3.56
Table 6.3a – Specific gravity of selected proppant types
1. Although expensive fracturing fluids do not have to be used, heavy-weight brines will
still have to be mixed, if neutral density is required. For instance, 1.25 SG calcium
chloride brine requires 2860 lbs of CaCl2 per 1000 gals of brine – mixing this quantity
of material on location could present a logistical challenge in itself.
2. Although the proppant does not require fluid viscosity in order to stay in position
within the fracture, this is not the only reason for having viscosity in the fluid. If the
fracture is experiencing significant tortuosity (see Section 10.1), viscosity will be
required to transport the proppant through the near wellbore region. A system without
viscosity may experience premature screenouts.
3. Fracturing fluids are also designed to reduce leakoff. The polymer in a typical
crosslinked gel will form a filter cake against the wall of the fracture, reducing the rate
at which fluids leave the fracture. Brines will not have this polymer and so will leak off
into the formation much more quickly. Therefore, significantly higher fluid volumes
may be required.
4. At the time of preparation of this manual, LiteProp is limited to fairly shallow
formations, as the maximum closure stress that can be sustained by the material is
about 5,000 psi (for LiteProp™ 125).
Nevertheless, in spite of these limitations LiteProp has the potential to revolutionise the way
fracturing treatments are performed.
References
Technical Data Interactive CD ROM, Carbo Ceramics Inc, 2000 onwards.
www.carboceramics.com, Carboceramics Inc. website, 2001 onwards
PredictK software, Stim-Lab Consortium, 1999 onwards
BJ Services’ Mixing Manual
BJ Services’ Stimulation Engineering Support Manual
Vincent, M.C., Pearson, C.M., and Kullman, J.: “Non-Darcy and Multiphase Flow in Propped
Hydraulic Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity”, paper
SPE 54630, presented at the SPE Annual Technical Conference and Exhibition, Houston, Oct
1999.
nd
API Recommended Practice 56 Testing Sand Used in Hydraulic Fracturing Operations, 2
Edition, American Petroleum Institute, December 1995.
API Recommended Practice 60 Recommended Practices for Testing High Strength
nd
Proppants Used in Hydraulic Fracturing Operations, 2 Edition, American Petroleum Institute,
December 1995.
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6. Proppants
Rickards, A., Lacy, L., Brannon, H., Stephenson, C. and Bilden, D.: “Need Stress Relief? A
New Approach to Reducing Stress Cycling Induced Proppant Pack Failure”, paper SPE
49247 presented at the 1998 SPE Annual Technical Conference and Exhibition, New
Orleans, Louisiana, Oct 1998.
Wood, W.D., Brannon, H.D., Rickards, A.R. and Stephenson, C.: “Ultra-Lightweight Proppant
Development Yields Exciting New Opportunities in Hydraulic Fracturing Design”, paper SPE
84309, presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver,
Colorado, Oct 2003.
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7. Rock Mechanics
7.
Rock Mechanics
Rock mechanics is the study of the mechanical properties of a rock, especially those
properties which are of significance to Engineers. It includes the determination and effects of
physical properties such as bending strength, crushing strength, shear strength, moduli of
elasticity, porosity and density, and their interrelationships.
7.1
Stress
Consider the situation illustrated in Figure 7.1a, in which a block of material is subjected to a
force F:-
F
Area = A
Figure 7.1a – A block of material subjected to a force F.
The block of material has an area A, on the plane at right angles to the line of action of the
force. Therefore the stress, σ, is given by:-
σ
F
= A .................................................................................. (7.1)
Note that this is very similar to the formula for calculating pressure. Stress and pressure have
the same units and are essentially the same thing – stored energy. The main difference
between the two is that in liquids and gases, the material will flow away from an applied force,
until the force and stress (or pressure) is the same in all directions (i.e. an equilibrium has
been reached). However, solids cannot deform in such a manner, so these materials will
always have a plane across which the stresses are at a maximum. They will also have a
plane perpendicular to this, across which the stresses are at a minimum.
Properties such as mass and volume are said to be scalars – they require only a magnitude
to define them. Quantities such as force and velocity are vectors – they require not only a
magnitude, but also a direction in which they are acting in order to be fully defined. Stress
takes this one step further, and is a tensor property – it can only be fully defined by a
magnitude and an area across which it is acting.
7.2
Strain
Strain is measure of how much the material has been deformed when a stress is applied to it.
Figure 7.2a illustrates how the block of material is compressed by the force F:-
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7. Rock Mechanics
F
x1
x2
Figure 7.2a – Strain produced by the application of force F
As the force is applied, the height of the block of material changes from x1 to x2. The strain, ε,
is given by:-
ε
=
x1 - x2
x1 ........................................................................... (7.2)
Note that the strain is defined in the same direction as the applied force F and perpendicular
to the plane across which the stress acts.
Strain is important as this is the way we measure stress – by observing the deformation of a
known piece of material. Strain is dimensionless.
7.3
Young’s Modulus
Young’s modulus, E, (also known as modulus of elasticity or elastic modulus) is defined as
follows:E
=
σ
ε ................................................................................... (7.3)
E is the ratio of stress over strain. As strain is dimensionless, E has the same units as stress.
Young’s modulus is a measure of how much a material will elastically deform when a load is
applied to it. This is another term for hardness.
On a more fundamental level, if stress and pressure are closely related (apply a pressure to a
surface and it will induce a stress), then in fracturing, we can think of Young’s modulus as a
measure of how much a material (i.e. rock) will elastically deform when a pressure is applied
to it. As pressure is stored energy, E is also a measure of how much energy it takes to make
the rock deform.
Materials with a high Young’s modulus, such as glass, tungsten carbide, diamond and
granite, tend to be very hard and brittle (susceptible to brittle fracture). Conversely, materials
with a low E, such as rubber, Styrofoam and wax, tend to be soft and ductile (resistant to
brittle fracture).
Caution – Elastic vs Plastic. Elastic deformation is reversible – if the force (or pressure, or
stress) is removed, the material returns back to its original size and shape. If so much force is
applied to a material that it passes beyond its elastic limit then the material will start to
plastically deform. This is permanent. A good illustration of this is the small spring from a ball
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7. Rock Mechanics
point pen. When the spring is lightly stretched, it will return to its original shape. However, if
the spring is stretched too far, it will be permanently, or plastically, deformed. Young’s
Modulus only applies to elastic deformation. As a group of materials, rocks tend not to
plastically deform very much. Instead they will elastically deform and then fracture if the stress
gets too high. Notable exceptions to this are salt beds, soft carbonates (e.g. chalk) and young
coals.
Static Young’s Modulus is the standard measure of E and is applicable to hydraulic
fracturing. The material is being deformed slowly and in only one direction.
Dynamic Young’s Modulus is the rock property measured by special sonic logging tools.
The material is no longer static – it is being continually stretched and then compressed
rapidly. There is often a significant variation between static and dynamic values for E due to a
process known as hysteresis. Hysteresis is a retardation of the effects of forces, when the
forces acting upon a body are changed (as if from viscosity or internal friction). In this
situation, it represents the history dependence of the physical systems. In a perfectly elastic
material, elastic stress and strain is infinitely repeatable. In a system exhibiting hysteresis, the
strain produced by a force is dependent upon not only the magnitude of that force, but also
the previous strain history (see Section 7.10)
Plane Strain Young’s Modulus. In hydraulic fracturing, the strain in the direction
perpendicular to the fracture plane (i.e. the direction in which fracture width is produced) is
effectively zero. This is because in this situation the denominator in Equation 7.2 (the “x1”) is
so large that the strain is effectively zero, even though there has been measurable material
deformation. This is known as “plane strain”, which implies that strain only exists in a
directions perpendicular to the direction in which strain is zero. To account for this anomaly,
fracture simulators use the plane strain Young’s modulus, E’, to calculate the fracture width:E’
=
E
2 ............................................................................. (7.4)
(1 - ν )
In fracturing, Young’s modulus will typically have values ranging from as low as 50,000 psi
(for a shallow, very soft chalk or weak sandstone) to as high as 6,000,000 psi for deep, tight,
shaley sandstone. It should be noted that Young’s modulus may not be constant in weak or
unconsolidated formations.
7.4
Poisson’s Ratio
Poisson’s ratio, ν, is a measure of how much a material will deform in a direction
perpendicular to the direction of the applied force, parallel to the plane on which the stress
induced by the strain is acting. This is illustrated by Figure 7.4a:F
x1
x2
y1
y2
Figure 7.4a – Application of force F also produces a deformation in the y direction
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7. Rock Mechanics
The strain in the x direction, εx, is given by Equation 7.2 (see Section 7.2). The strain in the y
direction is given by the following:-
εy
=
y1 - y2
y1 ........................................................................... (7.5)
Note that this value is negative – this is a result of the way the forces and the direction the
forces act in are defined. Compressive strain is positive and tensile strain is negative.
Poisson’s ratio is defined by Equation 7.6:-
ν
=-
εy
................................................................................. (7.6)
εx
Poisson’s ratio is an important factor in determining the stress gradient of the formation, but is
less important in defining fracture dimensions, although it does have some effect. Typical
values for ν for rocks are between 0.2 and 0.35 (ν is dimensionless).
7.5
Other Rock Mechanical Properties
Tensile Strength. The tensile strength of a material is the level of tensile stress that is
required in order to make the material fail. Usually, as stress is applied the material will
elastically deform (reversible), plastically deform and then fail. In most rocks this amount of
plastic deformation is negligible and the material will, for all practical purposes, elastically
deform and then fail.
This property is important in hydraulic fracturing, as this stress level has to be overcome in
order to split the rock. Usually, the frac gradient (which is the pressure – a.k.a. the stress –
needed to make the rock fracture) has two components – the stresses induced by the
overburden, and the tensile strength of the rock. See Section 7.6 below for a more detailed
explanation of in-situ stresses.
It should be noted that materials also have a Compressive Strength, which is the compression
load, beyond which a material will fail. Failure mechanisms are more complex, as the material
is often compressed in several directions at once. Generally, rocks are much stronger in
compression than in tension, a fact which we take advantage of during fracturing.
Shear Modulus. The shear modulus is similar to the Young’s modulus, except that it refers to
the material being in shear, rather than in compression or tension. It defines how much
energy is required to elastically deform a material in shear:-
x
F
h
a
b
Figure 7.5a – Force F applied to produce a shear stress
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7. Rock Mechanics
With reference to Figure 7.5a, the shear stress, τ, is given by:-
τ
F
= A .................................................................................. (7.7)
where A is the area of the block of material parallel to the line of action of the force F, (this is
the plane along which the shear stress acts) and is equal to a × b.
The shear strain, γ, is defined as follows:-
γ
x
= h ................................................................................... (7.8)
Therefore, the shear modulus, G, is equal to the shear stress divided by the shear strain:G
Fh
t
= g = x A ....................................................................... (7.9)
Bulk Modulus. This is another elastic constant, which defines how much energy is required
to deform a material by the application of external pressure. This is a special form of
compressive stress, in which the applied compressive stress is equal in all directions.
Suppose we have a block of material, which originally has a pressure P1, applied to it, and
has a volume V1. This pressure is increased to P2, which causes the volume to decrease to
V2, as illustrated below in Figure 7.5b. The increase in bulk stress is the same as the increase
in pressure, P2 – P1. The bulk strain is equal to the change in volume, V2 – V1 divided by the
original volume, V1. Thus, the bulk modulus, K, is given by:K
V1(P2 - P1)
P2 - P1
= - (V - V )/V = - V - V
....................................... (7.10)
2
1
1
2
1
Figure 7.5b – Volume changes from V1 to V2 as pressure increases from P1 to P2.
K
dP
= - V dV ......................................................................... (7.11)
The minus sign is introduced into the equation due to the fact that the term V2 – V1 will always
be of the opposite sign to the term P2 – P1.
The bulk modulus is therefore a measure of how much energy it takes to compress a material
using externally applied pressure.
Relationships Between the Four Elastic Constants. The four main elastic constants –
Young’s modulus, shear modulus, bulk modulus and Poisson’s ratio - are all related to each
other. If two of these material properties are known, the other two can be deduced:-
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E
= 3K (1 – 2ν ) ................................................................. (7.12)
K
=
E
......................................................................... (7.13)
3 - 6ν
G
=
E
........................................................................ (7.14)
2 + 2ν
ν
=
3K - E
6K ......................................................................... (7.15)
Therefore, if the Young’s modulus and the Poisson’s ratio are known, the shear modulus and
the bulk modulus can be deduced. Thus, fracture simulators only require the input of E and ν.
7.6
In-Situ Stresses
In situ stresses are the stresses within the formation which act as a load (usually
compressive) on the formation. They come mainly from the overburden, and these stresses
are relatively easy to predict. However, factors such as tectonics, volcanism and plastic flow
in underlying formations can significantly affect the in-situ stresses – these factors are much
harder to predict. In addition, the act of producing a localised anomaly – such as an oil well –
can also significantly affect the stresses in a specific area.
The stresses due to the overburden are simply the sum of all the pressures induced by all the
different rock layers. Therefore, if there has been no external influences – such as tectonics –
and the rocks are behaving elastically, the vertical stress, σv, at any given depth, H is given
by:-
σv
=
H
0
ρnghn ....................................................................... (7.16)
where ρn is the density of rock layer n, g is the acceleration due to gravity and hn is the
vertical height of zone n, such that h1 + h2 + ..... + hn = H.
This is usually modified (after Biot et al) to allow for the effects of pore (or reservoir) pressure,
such that:-
σv
= γob H - αPres ............................................................... (7.17)
where γob is the overburden pressure gradient (usually between 1.0 and 1.1 psi/ft) and α is
Biot’s poroelastic constant, and is a measure of how effectively the fluid transmits the pore
pressure to the rock grains. α depends upon variables such as the uniformity and sphericity of
the rock grains. By definition α is always between 0 and 1, usually it is taken to be between
0.7 and 1.0 for petroleum reservoirs.
Stresses under the ground do not just act on a single plane. There is a complex three
dimensional stress regime. To simplify things, stresses are usually resolved into three
mutually perpendicular stress components; the vertical stress, σV, and two horizontal
stresses, σH, min and σH, max.
Additionally, as the stresses are three dimensional, so are the strains. The elastic relationship
between these stresses and strains in three mutually perpendicular directions, x, y and z, is
governed by Hooke’s law:-
εx
Page 58
1
= E [σx - ν(σy + σz)] ........................................................ (7.18)
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Now, for the case of elastic deformation with no outside influences (such as tectonics) in
subterranean rock strata, there are two important things to note. First, σH,min = σH, max, as the
stresses will be symmetrical on the horizontal plane. Secondly, as each individual unit of rock
is pushing against another identical unit of rock with the same force, εH, min = εH, max = 0 (i.e. no
deformation on the horizontal plane).
Therefore:-
σH
=
σv ν
1-ν
............................................................................ (7.19)
As a result of the work of Terzaghi, Biot and Handin et al., this Equation is generally modified
to allow for the effects of the pore pressure:-
σH
=
ν(σv - 2αP)
+ αP ........................................................ (7.20)
1-ν
From Equation 7.20 we can see that the Poisson’s ratio can have a considerable influence on
the horizontal in-situ stresses.
7.7
Stresses Around a Wellbore
A wellbore is essentially a pressure vessel with a very thick wall. Consequently, the same
theories that are applied to thick walled pressure vessels can also be applied to wellbores,
providing that the in-situ stresses and reservoir pressure are accounted for. Figure 7.7a
illustrates how the stresses at any given point near the wellbore can be resolved into three
principle stresses. Once again, these are perpendicular to each other.
σv
σt
σr
σr
σt
σv
Figure 7.7a – Three dimensional stresses around a wellbore
From Deily and Owens (1961) we can get expressions for the radial and tangential stresses
induced by a pressure in the wellbore, Pwb, at a radius r, from the centre of the well. The
vertical stress is as given in Equation 7.17;
σt
Page 59
= -[Pwb - α(Pres + Pwb - Pr)]
2
2
rw
rw
2
2
r + 1 + r σv .............. (7.21)
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σr
2
rw
= (Pwb – Pres) r2
+
ν
1-ν
2
rw
1 - r2 (Pob – Pres) ......... (7.22)
where Pob is the pressure due to the overburden (see reference for more details).
At the wellbore face, the stresses due to wellbore pressure will be at a maximum. Also, this is
by definition the point at which the fracture initiates. Therefore, these are the stresses which
interest us most. At the wellbore r → rw and Pr → Pwb so that:2ν
(γ H - αPres) – (Pwb – αPres) .......................... (7.23)
1 - ν ob
σt
=
σr
= Pwb - Pres ..................................................................... (7.24)
Furthermore, Barree et al (1996) went on to show that provided the rock does not have any
significant tensile strength and no significant plastic deformation, failure of the rock (i.e.
breakdown) occurred when the tangential stresses were reduced to zero;
Pb
7.8
=
2ν
(γ H - αPres) + αPres ...................................... (7.25)
1 - ν ob
Fracture Orientation
Fractures will always propagate along the line of least resistance. In a three dimensional
stress regime, a fracture will propagate so as to avoid the greatest stress. This means that a
fracture will propagate parallel to the greatest principal stress, and perpendicular to the plane
of the greatest principle stress. This is a fundamental principle – therefore the key to
understanding fracture orientation is to understand the stress regime itself.
Propagation parallel to the greatest principle stress usually means that the fracture will
propagate on a vertical plane. We can see from Equations 7.16 to 7.20 that the horizontal
stresses in an undisturbed elastic formation will always be less than the vertical stress.
However, there are some exceptions to this.
Magnitude of In-Situ Stress
Magnitude of In-Situ Stress
σV
Depth
Depth
Formation lost
due to erosion
σV
σH
Original Stress Regime
σH
Stress Regime After Loss
of Height by Erosion
Figure 7.8a – Changes in stress regime due to erosion
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7. Rock Mechanics
Equations 7.17 and 7.20 define the magnitude of horizontal and vertical stresses in
undisturbed formations. The horizontal stresses are induced by the vertical stresses. There is
evidence to suggest that these horizontal stresses somehow get “locked” into place
(Economides, et al), and remain relatively constant, regardless of what later happens to the
vertical stress. Figure 7.8a illustrates what happens when the vertical stress is reduced.
If formation is lost due to erosion, then the overburden stresses are reduced. However,
because the horizontal stresses are “locked-in”, they have not been reduced. Therefore, there
is a region, close to the new surface, where the horizontal stresses are greater than the
vertical stresses. This means that the fracture will propagate horizontally – a “pancake frac”.
Thus, in shallow formations in areas with a history of surface erosion, horizontal fracs are not
only possible, they are in fact likely. This does not apply to formations which are very weak or
unconsolidated, as stresses cannot be “locked in” if the rock strata have no strength.
Another consequence of this phenomenon is that in formations where the σV and the σH are
approximately equal, it can be very hard to predict fracture orientation.
The action of outside forces, such as tectonics and volcanism, can also significantly affect
fracture orientation. The extra stresses imposed by the movement of the Earth’s crust, which
does not usually alter the overburden stress, but can significantly alter the horizontal stresses.
In addition, formations can sometimes be bent and buckled. In Barbados, there is a formation
that has experienced so much tectonic stress that it now runs vertically. Its stresses have
been locked into place, so now the original vertical stress is horizontal, and vice versa. So the
fractures propagate horizontally.
Influence of Wellbore Orientation. Drilling a well can significantly alter the stress regime in
an area around the well. The distance away from the wellbore that is affected by this change
is dependent upon the Young’s modulus of the formation. Hard formations (high E) tend to
transmit stress more easily than soft formations (which will deform to reduce the stress).
Therefore hard formations are affected more than soft formations.
In the area around the wellbore – the area affected by the new stress regime – fractures may
propagate parallel to the wellbore, even if the wellbore is highly deviated or even horizontal.
As the fracture propagates away from the wellbore, it will eventually reach a point at which the
normal stress regime of the formation becomes more significant than the near wellbore stress
regime. At this point, the fracture will change orientation. Sometimes this re-orientation can be
quite sudden, resulting in sharp corners in the fracture, which can cause premature screen
outs.
7.9
Breakdown Pressure and Frac Gradient
The breakdown pressure is the pressure it takes to initiate a fracture from the wellbore. Due
to the effects of the stresses induced by the presence of the wellbore, the breakdown
pressure is usually significantly greater than the fracture - or frac – gradient, which is a
measure of how much pressure it takes propagate the fracture through the formation, away
from the influence of wellbore effects. Both are usually expressed as pressure gradients (i.e.
in psi/ft or kPa/m) so that similar formations in different wells at different depths can be more
easily compared. The frac gradient is a very important quantity in fracturing, as it is the most
significant contributor to the bottom hole treating pressure, which in turn helps to define the
surface treating pressure, the loading on the completion and the proppant selection.
In order to produce a fracture in the formation, two forces have to be overcome. The first force
is the in-situ stress, which is defined in Equations 7.19 and 7.20 when there are no external
influences such as tectonics etc. The second force that has to be overcome is the tensile
strength of the rock, which is usually in the region of 100 to 500 psi. Roegiers, in his chapter
on Rock Mechanics in Economides and Nolte’s excellent Reservoir Stimulation, defined the
breakdown pressure in the following Equations:Pb, upper
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= 3 σH,min - σH,max – P + T ............................................... (7.26)
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Pb, lower
=
3σHmin - σHmax - 2ηP + T
............................................. (7.27)
2(1 - η)
where η is a parameter defined by the Poisson’s ratio and Biot’s constant, as follows:-
η
=
α(1 - 2ν)
..................................................................... (7.28)
2(1 - ν)
Pb, upper is the breakdown pressure assuming no fluid invasion into the formation (and hence
the maximum possible theoretical breakdown pressure), Pb, lower is the lower boundary for
breakdown pressure, assuming significant alteration of the near wellbore pore pressure due
to fluid invasion, σH,min is the minimum horizontal stress, σH,max is the maximum horizontal
stress, P is the reservoir pressure and T is the tensile strength of the rock. From this we can
see that the higher the reservoir pressure, the easier it is to fracture the rock, so that depleted
reservoirs tend to have higher breakdown pressures than undepleted reservoirs. In addition,
we can see that when we have fluid invasion, the breakdown pressure can be significantly
reduced, which implies that lower viscosity fluids provide lower breakdown pressures. In the
case where there are no significant external influences on the stress regime, the two
horizontal stresses are equal and the Equations can be simplified to:and
Pb, upper
= 2 σH – P + T ................................................................ (7.29)
Pb, lower
=
2σH - 2ηP + T
............................................................ (7.30)
2(1 - η)
The breakdown gradient is simply the breakdown pressure, Pb, divided by the TVD.
The frac gradient is the pressure required to make the fracture propagate, outside of the
influences of the wellbore (the region referred to as “far-field”). As stated above, this is often
significantly lower than the breakdown pressure, depending upon the viscosity of the frac
fluid, the reservoir pressure and the contrast between maximum and minimum horizontal
stresses.
In general, the far field fracturing pressure is equal to the minimum horizontal stress, modified
to allow for the effects of pore pressure. In general, any external effects such as tectonics or
faulting, will only act to increase the stresses. Therefore Equation 7.18 defines the frac
gradient, gf, as follows:gf
=
1
TVD
ν(σv - 2αP)
+ αP ....................................... (7.31)
1-ν
Important Note. The best way to get the frac gradient for a formation is to pump some fluids
into it and measure the response. There are many influences on the formation that Equations
7.26 and 7.27 do not account for, such as tectonics (there are very few areas of the world that
are completely free of tectonics), and the only way to account for these is to actually measure
them. The second best way to get the frac gradient is to look at data from offset wells. Make
sure that you are looking at data from the same formation. Compare values for Poisson’s ratio
and reservoir pressure. If these values are similar (provided they come from the same
formation), then the frac gradient will probably be similar as well. Once these two methods
have been rejected, the remaining way to get the frac gradient is to use the Equations above.
This method should only be used if attempts at carrying out the other two methods have
failed.
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7. Rock Mechanics
7.10
Rock Mechanical Properties from Wireline Logs
Certain types of open hole wireline logs can be used to provide useful information about the
mechanic properties of the formations involved in the fracturing process. The dipole sonic or
sonic array is the main tool used to do this. This is a special tool, and is different from the
sonic logging tool used to generate the sonic transit time seen on most logs.
In order to be able to quantify the rock mechanical properties, the logging tool must be able to
generate and measure two completely different types of sonic waveform, the shear or s-wave
and the compression or p-wave, as illustrated in Figure 7.10a, below:-
Figure 7.10a – The left hand side shows the shear or s-wave, whilst the right hand side shows
the compression or p-wave. In both diagrams, the blue arrows illustrate the overall movement of
the sonic waveform, whilst the red arrows indicate the movement of individual particles.
For the shear wave, the material is continually sheared in one direction and then the opposite
direction, back and forth. The plane across which the material is being sheared is
perpendicular to the direction the shear wave is travelling. For the compression wave, the
material is subject to alternating compression and tension, on a plane that is again
perpendicular to the direction of wave travel.
The dipole sonic tools measures the transit time of both the shear wave, ts and compression
wave, tp. These values are usually expressed in units of µsec/ft, so that the transit time is the
reciprocal of the wave velocity. The transit time of the sonic waves through the formation can
be used to derive dynamic rock mechanical properties as follows:2
νd
0.5(ts/tp) - 1
= (t /t )2 - 1 ............................................................... (7.32)
s p
Ed
= 2 t 2 (1 + νd) ............................................................ (7.33)
s
ρb
ρb
= 26,950 t 2 (1 + νd) (in field units)............................. (7.34)
s
Where νd is the dynamic Poisson’s ratio, Ed is the dynamic Young’s modulus (see below for
an explanation of dynamic and static properties) and ρb is the bulk density, usually taken from
the corrected bulk density log. For Equation 7.34 in field units, ρb is in g/cc and ts is in µsec/ft
6
– the units most commonly used on logs - whilst Ed is in psi x 10 .
Other rock mechanical properties can also be found (in “log” field units):-
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7. Rock Mechanics
Ed
..................................................................... (7.35)
2(1 + νd)
Gd
=
Kd
1
1
= 26,950 ρb t 2 - 3t 2 ..................................................... (7.36)
p
s
cb
1
= K ............................................................................... (7.37)
cr
=
α
cr
= 1 - c .......................................................................... (7.39)
d
1
............................................... (7.38)
1
4
26950 ρb t 2 - 3t 2
ma
sma
b
Where Gd is the dynamic shear modulus, Kd is the dynamic bulk modulus, cb is the bulk
compressibility of the formation, cr is the rock, or zero porosity, compressibility tma is the rock
matrix compression wave transit time (see below), tsma is the rock matrix shear wave transit
time (see below) and α is Biot’s poroelastic constant. Table 7.10a lists commonly used values
for tma and tsma:-
Rock
Matrix
Commonly used values for sonic wave
rock matrix transit times, µsec/ft
Compression Wave
tma
Shear Wave
tsma
Quartz
55.5 or 51.0
83.3
Calcite
49.7
90.0
Dolomite
43.5
78.7
Anhydrite
50.0
87.7
Granite
50.8
89.3
Salt
66.7
125.0
Table 7.10a – Commonly used values for compression and shear wave rock matrix sonic transit
times (after Schlumberger, 1989)
Figure 7.10b shows an example dipole sonic log with interpreted values for Poisson’s ratio,
Young’s modulus and horizontal stress.
Stress can be derived by using the dynamic Poisson’s ratio and the density log (to give the
vertical stress) using Equation 7.19. However, it should be remembered that these “stress
logs” are based on dynamic properties (see below) and do not take poroelastic effects into
account. Nevertheless, whilst the absolute values for these logs cannot be trusted, they can
be useful for determining stress contrasts.
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7. Rock Mechanics
Dynamic and Static Rock Mechanical Properties
In most applications, including hydraulic fracturing, we are using values for rock mechanical
properties that are based on static material properties. However, because of the conditions
that sonic-based rock mechanical properties are measured under, they are said to be
dynamic, and there is often a significant difference between the static properties that the Frac
Engineer needs and the dynamic properties that are measured by open hole logs.
0
0
GR
200
4
HCA L
14
PR
1
50
DTCO
250 1
YO UNGS
3.5
50
DTSM
250 500 0
HSTRES S
750 0
9, 050
9, 100
9, 150
9, 200
Figure 7.10b – Example interpreted dipole sonic log. The left track shows gamma ray (GR) and
caliper (HCAL) logs. The center track shows compression (DTCO) and shear (DTSM) wave transit
times. The right track shows interpreted values for Poisson’s ratio (PR), Young’s modulus
(YOUNGS) and horizontal stress (HSTRESS).
To put things simply, when a stress related event happens to a material, the changes that
occur to the stresses in the material to not occur instantly. Instead, any change to the stress
will spread through the material at the speed of sound in that material. Usually, the time taken
for this to happen is so small compared for the time taken for the applied stresses to change
(as in fracturing) that it does not affect the process. However, when the stresses applied to a
material alter at a speed that is a significant fraction of the speed of sound of that material,
then the time taken for the change in stress to propagate can significantly affect the stresses
themselves. For instance, when a compression wave is passing through a material, any given
portion of that material is constantly being subjected to alternating tensile and compression
loads. The speed at which the load changes is directly proportional to the frequency of the
sound wave, whilst the speed that the compression wave moves through the material is the
speed of sound for that material. At low frequencies, the length of time taken for a piece of the
material to undergo one full stress cycle is much less than the length of time it takes one
sound wave to travel past that piece of material. However, as the frequency increases, the
length of time between stress cycles decreases, whilst the wave transit time stays constant,
and it becomes increasingly difficult for the material to return to it’s original state before the
next wave passes through. This causes a deviation away from linear elastic behaviour, as
illustrated by Figure 7.10c.
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7. Rock Mechanics
Stress
Stress
TENSION
TENSION
Strain
COMPRESSION
Strain
COMPRESSION
Figure 7.10c – Static (left) and dynamic (right) cyclic stress loading.
The left side of Figure 7.10c shows cyclic loading under static conditions. As the load is
alternated between tension and compression, the relationship between stress and strain is
linear (proportional to the Young’s modulus) and follows the same path on the stress strain
plot every time, provided the elastic limit is not exceeded and the material is not plastically
deformed. This relationship between stress and strain is referred to as linear elastic.
The right side of Figure 7.10c shows the dynamic case. The behaviour of the material under
loading is now dependent upon the stress history of the material. The relationship between
stress and strain is different depending upon whether the loading is being applied or removed
and whether it is tensile or compression. This deviation away from linear behaviour becomes
more pronounced as the frequency of the sound waves (i.e. the frequency of the stress
cycling) increases. When an alternating stress is applied to a material the induced alternating
strain moves through this material at the speed of sound, for that material. However, as the
frequency of the changes gets closer to the speed of sound in that material, the material has
insufficient time to return to its original state, before the next deformation occurs. Thus the
subsequent deformation is influenced by the previous deformation.
This deviation from linear elastic behaviour under high frequency stress cycling is often
referred to as hysteresis. Hysteresis is a general term used throughout science and
engineering to denote when the behaviour of a material under certain conditions is dependent
upon the historical application of these conditions. The behaviour of a material that does not
exhibit hysteresis (such as that shown on the left hand side of Figure 7.10c), is the same
every time, regardless of what has happened previously.
In order to convert from dynamic to static properties, several correlations are available.
Usually these are based on empirical data derived from tests on core samples and then
extrapolated back to BH conditions. As such, there is a degree of inaccuracy associated with
them. Lacy’s method (1997) is recommended for Young’s modulus:E
2
= 0.018 Ed + 0.422 Ed ................................................... (7.40)
However, there is no such correlation for Poisson’s ratio.
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7. Rock Mechanics
Frac Gradient
The horizontal stresses (assumed to be equal) can be calculated using the log data and
Equation 7.20. To use this Equation, three important pieces of information must be acquired:•
•
•
Vertical stress. Usually found by taking the bulk density back to the surface and using
Equation 7.16.
Pore pressure.
Biot’s poroelastic constant, usually found using Equation 7.37 – 7.39 and table 7.10a.
Otherwise use 0.8 for a poorly consolidated formation and 1.0 for a consolidated
formation
References
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Economides, M.J.: A Practical Companion to Reservoir Stimulation, Elsevier, 1992
Biot, M.A.: “General Theory of Three-Dimensional Consolidation,” Journal of Applied Physics ,
1941, 12, p155-164.
Biot, M.A.: “General Solutions of the Equations of Elasticity and Consolidation for a Porous
Material,” Journal of Applied Mechanics, 1956, 23, p91-96.
Deily, F.H., and Owens, T.C.: “Stress Around a Wellbore”, paper SPE 2557, presented at the
Annual Fall Meeting of the SPE, October 1969.
Barree, R.D., Rogers, B.A., and Chu, W.C.: “Use of Frac-Pack Pressure Data to Determine
Breakdown Conditions and Reservoir Properties”, paper SPE 36423, presented at the SPE
Annual Technical Conference and Exhibition, Denver, October 1996.
Handin J., Hager, R. V. Jr, Friedman, M., and Feather, J. N.: “Experimental Deformation of
Sedimentary Rocks Under Confining Pressure: Pore Pressure Tests,” Bulletin AAPG, 1963,
47, p717-755.
Terzaghi, K. van: “Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der
Hydrodynamischen Spannungserscheinungrn,” Sber. Akad. Wiss, Vienna, 1923, 123, p105
(in German)
Bradley, H.B. (Editor), Petroleum Engineering Handbook, Society of Petroleum Engineers,
Richardson, Texas, 1987, 51.
Log Interpretation Principles/Practices, Schlumberger Educational Services, Houston, Texas,
1989, 5.
Lacy, L.L.: “Dynamic Rock Mechanics Testing for Optimized Fracture Design”, paper SPE
38716, presented at the 1997 SPE Annual Technical Conference and Exhibition, San
Antonio, Texas, Oct 1997
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8. 2-D Fracture Models
8.
2-D Fracture Models
2-D fracture models were the industry’s first attempt at mathematically modelling the process
of fracture propagation. By today’s standards, they are crude approximations. However, there
are two important points to note. First, in order to understand how the modern 3-D models
work, it is first necessary to understand the 2-D models. Second, there are some
circumstances in which certain 2-D models can be valid. These include coal bed methane
fracturing (KZD) and fracturing in massive, uniform formations (radial).
8.1
Radial or Penny-Shaped
R
H
Wmax
Figure 8.1a – Propagation of a radial or penny-shaped fracture
Figure 8.1a shows the propagation of a radial or penny-shaped fracture. In this model, the
height, H, is a function of the radius or half-length of the fracture, R, such that H = 2R. This
produces a fracture, which is circular in shape. The width of the fracture is given by:2
Wmax
=
8 ( 1 - ν ) ∆P R
............................................................ (8.1)
πE
Where ∆P is the net pressure, ν is the Poisson’s ratio and E is the Young’s modulus.
In this model, the width at any part of the fracture is a function of the distance between the
center and the edge of the frac such that:w(r)
w̄
= Wmax
1-
r
R .......................................................... (8.2)
8
= 15 Wmax ........................................................................ (8.3)
Note the following points, which are applicable to all the 2-D fracture models:i)
Wmax is inversely proportional to the Young’s modulus. This means that as the
formation gets harder (i.e. the Young’s modulus increases), the net pressure required
to produce a given width increases. So it takes more energy to produce width in a
hard formation than it does in a soft formation.
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8. 2-D Fracture Models
ii)
Wmax is directly proportional to the half-length of the fracture – if the half-length is
doubled, the width is doubled. Note that this is the created width, not the final
propped width, which is what the post treatment production increase will be partially
dependent upon. The propped width will always be equal to or less than the created
width, and is a function of the volume of proppant placed per unit area of the fracture.
iii)
Wmax is relatively insensitive to changes in Poisson’s ratio. An increase in ν from 0.2
2
to 0.25 (an increase of 25%) will change the term (1 - ν ) from 0.96 to 0.9375, a
decrease of only 2.34%. Therefore, it is pointless to spend too much time trying to get
accurate values for ν. However, as seen in Chapter 6, ν can have a significant effect
on the magnitude of the horizontal stresses – if the frac gradient is unknown, then
finding accurate values for ν can be important.
The radial model has no limits to height growth. As long as the fracture is growing outwards
(i.e. R is increasing), then it will also be growing up and down the wellbore (i.e. an increase in
H). This type of propagation can be found in a massive uniform formation with no vertical
variations in rock properties and hence no “barriers” to height growth. It can also be found for
small fractures that have not contacted any “barriers”, such as in skin bypass fracturing.
The volume of the fracture is obtained from the volume of fluid pumped into the fracture, less
the volume of fluid leaked off. The volume of fluid leaked off is a function of the leakoff area of
2
the fracture (which is equal to 2πR ), so that if the fluid efficiency (η), injected volume of fluid,
E, ν and ∆P are known, R can be easily obtained:R
=
3
3ηQtE
....................................................... (8.4)
2
16 ( 1 - ν ) ∆P
where Q is the average pump rate and t is the pump time.
8.2
Kristianovich and Zheltov - Daneshy (KZD)
This model was originally developed by two Russians, Kristianovich and Zheltov, and was
later modified by Daneshy, Geertsma and de Klerk , and also by Le Tirant and Dupuy. Often,
this model is referred to as GDK, after Geertsma and de Klerk. In this model, the height is
fixed, and remains constant throughout. It is usually set as the gross height of the formation:Wmax
L
H
Figure 8.2a – Schematic showing the general shape of the KZD fracture
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8. 2-D Fracture Models
As we can see from Figure 8.2a, the KZD model produces a fracture with a constant height.
This means that there must be slippage between the formation being fractured and the
formations above and below. This is unlikely (but not unknown) in most situations, but can
happen when fracturing coal beds. The maximum width is related to the half length L by the
following Equation:2
Wmax
=
4 ( 1 - ν ) ∆P L
............................................................ (8.5)
E
Note that for a given net pressure and half length, the maximum width of a KZD fracture is
greater than the maximum width of a radial fracture by a factor of π/ 2.
The average width is given by:w̄
π
= 4 Wmax .......................................................................... (8.6)
Therefore, for two “wings”, the length of the fracture is given by
L
=
2
ηQtE
.................................................. (8.7)
2
2 π ( 1 - ν ) ∆P H
where η is the fluid efficiency, Q is the average pump rate and t is the pump time.
8.3
Perkins and Kern - Nordgren (PKN)
This fracture model was originally conceived by Sneddon and later developed by Perkins and
Kern, with further work by Nordgren, Nolte and Advanti et al. In this model, the maximum
width is related to the height of the fracture, such that:2
Wmax =
2 ( 1 - ν ) ∆P H
............................................................... (8.8)
E
whilst the average width, w̄ , is given by:w̄
=
π
5 Wmax ............................................................................. (8.9)
Wmax
H
L
Figure 8.3a – The Perkins and Kern - Nordgren fracture
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8. 2-D Fracture Models
Thus, both fracture height and width are constant down the length of the fracture. Figure 8.3a
illustrates the shape of this fracture.
The length of the fracture can be determined by a method similar to those used for the radial
and KZD fractures:L
=
5ηQtE
2
2 ........................................................ (8.10)
4 π ( 1 - ν ) ∆P H
The PKN fracture geometry was used for many years by the industry as the standard, until
the advent of pseudo-3D fracture simulators and an improved understanding of fracture
propagation and fracture mechanics (see Sections 9 and 11).
References
Abé, H., Mura, T., and Keer, L.M.: “Growth Rate of a Penny-Shaped Crack in Hydraulic
Fracturing of Rocks”, J. Geophys. Res. (1976) 81, 5335.
Zheltov, Y.P., and Kristianovitch, S.A.: “On the Mechanism of Hydraulic Fracturing of an OilBearing Stratum”, Izvest. Akad. Nauk SSR, OTN (1955) 5, 3-41 (in Russian)
Daneshy, A.A.: ”On the Design of Vertical Hydraulic Fractures”, JPT, Jan 1973, 83-93.
Geerstma, J., and de Klerk, F.A.: “Rapid Method of Predicting Width and Extent of
Hydaulically Induced Fractures”, JPT, Dec 1969, 1571-81
Le Tirant, P., and Dupuy, M.: “Fracture Dimensions Obtained During Hydraulic Fracturing
Treatments of Oil Reservoirs”, Rev. Inst. Français du Pétrole (1967) 44-98 (in French).
Sneddon, I.N.: “The Distribution of Stress in the Neighbourhood of a Crack in an Elastic
Solid”, Proc. Royal Society of London, (1946) 187, 229.
Perkins, T.K., and Kern, L.R.: “Widths of Hydraulic Fractures”, JPT, Sept 1961, 937-949.
Nordgren, R.P.: “Propagation of a Vertical Hydraulic Fracture”, SPEJ, Aug 1972, 306-314.
Nolte, K.G.: “Determination of Proppant and Fluid Schedules From Fracturing Pressure
Decline”, SPEPE, July 1986, 255-265.
Advanti, S.H., Khattib, H., and Lee, J.K.: “Hydraulic Fracture Geometry Modeling, Prediction
and Comparisons”, paper SPE 13863, presented at the SPE/DOE Low-Permeability Gas
Reservoirs Symposium, Denver, May 1985.
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
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9. Fracture Mechanics
9.
Fracture Mechanics
Fracture mechanics is the study of how fractures propagate through a material. The aim of
fracture mechanics is to predict how fast a crack will grow, and at what point the fracture
becomes “critical” – i.e. the fracture will suddenly spread across the entire material causing
catastrophic failure. In hydraulic fracturing we use fracture mechanics to predict how far our
fracture will grow – both horizontally and vertically.
When reading this section, it should be remembered that stress and pressure are essentially
the same thing. This means that a pressure in a fracture puts a stress of equal magnitude in
the formation at the fracture face, in a direction perpendicular to the fracture face. Therefore,
when the fracture is propagating, the critical stress (the stress needed to make the fracture
grow) has to be equal to the net pressure.
9.1
Linear Elastic Fracture Mechanics and Fracture Toughness
Linear Elastic Fracture Mechanics (LEFM) is all about the prediction of how much stress (i.e.
energy) it takes to make a fracture propagate. LEFM assumes linear elastic deformation
(constant Young’s modulus) followed by brittle fracture – it is assumed that no significant
energy is absorbed by non-linear or non-elastic effects. That is to say, energy stored as stress
in the material is transferred directly to fracturing the material, and no energy is lost to plastic
deformation. LEFM was used almost exclusively in the earlier fracture models (see Section
8), and is still used – to a greater or lesser extent - in a number of fracture models currently
available in the industry (e.g. MFrac, StimPlan – see Section 11).
The Griffith Crack
The first person to adopt a meaningful analytical approach to studying the mechanics of
fracture propagation was Griffith, in the 1920’s. Figure 9.1a illustrates the concept of the
Griffith crack, which can be expressed with the following Equation;
δU
δa
2
=
2πσ a
E ..............................................................................9.1
σ
2a
σ
Figure 9.1a – The Griffith crack
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9. Fracture Mechanics
where U is the elastic energy (i.e. the energy used to produce elastic stress on the material),
a is the characteristic fracture length, σ is the far field stress (i.e. the “bulk” stress away from
the influence of the fracture) and E is the Young’s modulus. Therefore, Equation 1 describes
the amount of additional energy (δU) required to make the fracture grow from length a to
length a + δa.
Usually, δU/δa is replaced by 2G. G is referred to as the “elastic energy release rate” and also
the “crack driving force”, such that;
G
πσ2a
= E
............................................................................. (9.2)
In order to reach this relationship, Griffith makes a significant assumption – that there is no
energy lost at the fracture tip and not used to propagate the fracture. Energy is used either to
elastically deform the material or to rupture the material. Therefore, there can be no plastic
deformation at the tip, and the Griffith model is only applicable to materials liable to elastic
deformation followed by brittle fracture.
Griffith Failure Criterion
Given that for a uniform material with constant geometry δU/δa is a constant, there is a critical
value of stress, σc, at which the material will experience catastrophic failure, i.e. the fracture
propagates at high velocity across the material causing failure. This critical stress is defined
as follows;
σc
=
2
EGIc
....................................................................... (9.3)
πa
The critical energy release rate, Glc, is determined experimentally and is a material property,
although it will vary with both temperature and the overall geometry of the test specimen.
Equation 9.3 also defines - for a given stress - a critical fracture length. If the fracture is less
than this critical length, the material will not fail. However, if the fracture grows above this
critical length, the material will fail.
The subscript "I" refers to the failure mode, as illustrated in Figure 9.1b. Failure mode I is the
"opening mode", mode II is the "sliding mode" and mode III is the "tearing mode". In hydraulic
fracturing, we are usually only concerned with failure mode I.
Mode I
Opening
Mode II
Sliding
Mode III
Tearing
Figure 9.1b – Failure modes in Linear Elastic Fracture Mechanics
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9. Fracture Mechanics
Stress Intensity Factor
With reference to Figure 9.1c, the stresses in the principal directions, at some point away
from the fracture tip, can be expressed as follows;
σxx
=
K
3θ
θ
θ
cos 2 1 - sin 2 sin 2 ...................................... (9.4)
2πr
σyy
=
K
θ
θ
3θ
cos 2 1 + sin 2 sin 2 ...................................... (9.5)
2πr
and
where K is the stress intensity factor.
σ
y
r
Fracture
θ
x
a
σ
Figure 9.1c – Coordinate system for stress intensity factor
Considering the plane strain situation (i.e. εzz = 0, an object with a thickness large enough to
make strain on the z-axis negligible), and the case that a >> r, then the stress in the ydirection – “across” the line of the fracture (i.e. θ = 0) – can be expressed as follows;
σyy
=
K
........................................................................... (9.6)
2πr
Obviously in Equation 9.6, as r tends to 0, σyy tends to . This represents a fundamental flaw
in this approach to modelling fractures – it fails close to the fracture tip.
Using this approach, K is the only factor that affects the magnitude of the stress at a given
distance from the fracture tip. Whilst K is a material property, it is also a variable, depending
upon the gross geometry of the fracture and its surroundings, as well as temperature.
Assuming a constant temperature in any given instance, relationships linking K, a and σ for
most situations have been solved, either analytically or numerically. At material failure, σc can
be described in terms of a critical stress intensity factor, KIc, which is more commonly referred
to as the fracture toughness;
σc
=
KIc
........................................................................... (9.7)
β πa
This is the fundamental Equation of Linear Elastic Fracture Mechanics, where β is a
geometrical factor and is equal to 0.4 for a radial fracture. KIc is related to GIc as follows;
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9. Fracture Mechanics
2
GIc
2 KIc
= (1 - ν ) E ................................................................... (9.8)
For a given geometry, the fracture toughness is a material property. Equation 9.8 shows that
it represents the amount of mechanical energy a material can absorb before it fails by brittle
fracture. Put simply, a material with a low KIc is brittle and a material with a high KIc is tough.
2
The term E/(1 - ν ) is often referred to as the plane strain Young'
s modulus or E'
, so that Glc is
equal to Klc divided by E'
.
9.2
Non-Linear and Non-Elastic Effects
From the extensive work done in this field, it is clear that LEFM alone does not adequately
account for the pressure needed to make the fracture grow. There is a tip over pressure
effect, which means that more pressure (energy) is required than is predicted by LEFM. Two
possible – and not necessarily mutually exclusive – theories for this are described below.
Crack Tip Dilatency
The theory of crack tip dilatency was first put forward by Cleary et al, and has been used
extensively by them in the FracPro model. This approach has almost entirely done away with
the concept of fracture toughness, which means that users of simulators based on this model
find that changes to input fracture toughness values have little or no effect on fracture
geometry. Instead the theory states that deep underground, the effect of the confining stress
is much more significant than the effect of the fracture toughness. Thus KIc can be ignored if
the following condition is satisfied;
σ π R >> KIc ..................................................................................... (9.9)
where R is the radius of the fracture and is analogous to the LEFM characteristic fracture
length. Equation 9.9 shows us that fracture toughness is more significant for small fractures in
shallow formations, such as during skin bypass fracturing.
The fracturing fluid does not penetrate to the very end of the fracture. This means that there is
a very rapid change in net pressure at a distance ω from the tip of the fracture, as illustrated in
Figure 9.2a.
Pnet
Dilation Contribution
ω
r
Figure 9.2a – The Cleary et al approach.
If the condition described in Equation 9.9 is satisfied, then ω can be found as follows;
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9. Fracture Mechanics
ω
R
≈ 2
2
Pnet
...................................................... (9.10)
Pnet + Pc
Because the fluid does not penetrate into the tip of the fracture, energy is lost as the tip of the
fracture deforms. It is postulated that this deformation occurs in a non-linear or dilatent
fashion. This crack tip dilatency reduces the energy left for the fracturing fluid to propagate
the fracture, and hence reduces the size of the fracture, for a given Pnet.
Crack Tip Plasticity
The crack tip plasticity theory allows for a significant region of plastic deformation at the
fracture tip. All materials exhibit some level of plastic deformation prior to failure – it is
assumed in LEFM, and most of the other approaches to modeling hydraulic fracturing, that
this is not significant. This may be true in some formations. However, there may be a wide
range of circumstances under which significant plastic deformation is not only possible, but
probable.
Even so-called brittle materials can experience plastic deformation when exposed to extreme
tri-axial stresses.
As the load on a material containing a fracture increases, the stresses around the fracture tip
also increase. Because of the geometry of the area of the fracture tip, these stresses are
usually far in excess of the overall stress on the material - as illustrated in Equation 9.6. As
the overall stress increases, the stress around the fracture increases to a point where it
exceeds the yield point of the material (σy). The material then starts to plastically deform, and
to move in a direction that will relieve the stress – away from the crack tip. This produces a
crack tip of finite radius, as opposed to the infinitely small fracture tip modeled in LEFM. The
diameter of the fracture tip, d, is given by the following Equation:
2
d
=
2
KI (1 - ν )
.................................................................... (9.11)
Eσy
For a long, narrow fracture, having a tip of finite radius can significantly reduce the overall
length of the fracture. This is illustrated in Figure 9.2b:-
σyy
σy
rp
Fracture
r
d
The plastic zone
Figure 9.2b – Crack tip diameter and the plastic zone. Note that rp is the radius of the plastic
zone.
Figure 9.2b shows the plastic zone as a circle around the fracture tip. However, this is not
necessarily the case. By using the principle stresses given by Equations 9.4 and 9.5, and
assuming plane strain (εzz = 0), the von Mises yield criterion gives the following result:
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9. Fracture Mechanics
σy2πrp
1
=4
2
KI
3
2
2
2 sin θ + (1 - 2ν) (1 + cosθ ) ............................ (9.12)
2
By plotting, in polar coordinates, σy2πrp/KI (dimensionless plastic radius) against θ, we can
see the shape of the plastic zone at the fracture tip, as illustrated in Figure 9.2c. This
produces two plastic “ellipses” either side of the fracture plane.
0.5
σy2 π r p
ν = 0.25
2
KI
θ
-0.5
0.5
-0.5
Figure 9.2c – The shape of the plastic zone, for a Poisson’s ratio of 0.25 (after Martin, 2000)
In hard rocks, the actual size of the plastic zone is quite small, compared to the volume of the
fracture. However, as Young’s modulus and yield stress decrease, the relative size of the
plastic zone increases until it reaches a relatively large volume. At this point, the energy
absorbed by the plastic deformation of this volume becomes a significant fraction of the
energy contained in the fracturing fluid.
This means that in a formation liable to significant plastic deformation, it requires significantly
more energy to propagate the fracture than is predicted by LEFM. As discussed below, if the
fracture tip takes more energy, the fracture will be smaller and will have less width.
9.3
The Energy Balance
The process of propagating a fracture through a formation is all about the transfer of energy
from the frac pumps to the formation. Energy transfer occurs as shown in Figure 9.3a.
Reducing all the processes occurring in the creation of a fracture to energy, allows them to be
related to each other in the most fundamental fashion. To start with, we must remember that
pressure and stress are essentially energy per unit volume.
Therefore, the total energy per unit time (a.k.a. power) in the fluid available for creating a
fracture is:U̇
= BHTP.Q ...................................................................... (9.13)
Not forgetting that:BHTP
= STP + HH – Pfrict ....................................................... (9.14)
Therefore, the total energy available to the fracturing fluid is given by:-
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Page 78
The Frac Fluid
At the Wellhead
STP
Energy from
Hydrostatic Head
By the Perforations
BHTP
Friction Pressure in the Surface
Lines and W ellbore
In the Near W ellbore
Region, P net
Perforation Friction & Tortuosity
Moving Down the
Fracture, P net
Fluid Leakoff
Ufluid
=
Overcoming the Closure
Stress of the Formation
Compression of Formation
to Produce Frac W idth
Fluid Friction in Fracture
At the Fracture Tip
P net- Fluid Friction
in Fracture
Propagation of
Fracture
tp U̇ dt.................................................................... (9.15)
0
Figure 9.3a – Sources of Energy Gains and Losses for the fracturing fluid.
Energy Gains + Energy Losses = 0.
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Chemical Energy from the Diesel
Fuel is Changed into Mechanical
Energy by the Engine, which is
Changed into Pressure and
Kinetic Energy by the Frac Pump
BJ Services’ Frac Manual
9. Fracture Mechanics
Energy Losses
Energy Gains
BJ Services’ Frac Manual
9. Fracture Mechanics
Where tp is the total pumping time. Equation 9.15 looks intimidating, but it is simply the area
under the graph of (bottom hole) horsepower against time.
A substantial portion of the energy is used up, simply by overcoming the in-situ stresses of
the formation. Another portion of the energy is used up in overcoming friction in the near
wellbore area. Therefore, the final amount of energy available for fracturing the formation is
given by:= tp P Q dt................................................................ (9.16)
U
fluid
0
net
Given that in most cases the rate is relatively constant, a plot showing Pnet versus time can
show a great deal about how much energy is being used to create the fracture. This is the
basis of Nolte analysis (see Section 10.2).
Most fracture simulators spend a great deal of time quantifying these energy loses and gains,
so that the amount of energy left in the fracturing fluid for propagation and the production of
width can be a found. If the Young’s modulus is known, the fracture width – for a given Pnet –
can be easily determined. This then leaves the amount of energy available for the
propagation of the fracture, which in turn defines how big the fracture gets. This is the ultimate
goal of the fracture simulator.
References
Griffith, A.A.: “The phenomena of rupture and flow in solids”, Phil. Trans. Roy. Soc. of
London, A 221 (1921), pp. 163 – 167
th
Broek, D.: Elementary Engineering Fracture Mechanics, Kluwer Academic Publishers, 4 Ed.
(rev), 1986.
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Cleary, M.P., Wright, C.A., and Wright, T.B.: “Experimental and Modeling Evidence for Major
Changes in Hydraulic Fracturing Design and Field Procedures”, paper SPE 21494, presented
at the SPE Gas Technology Symposium, Houston TX, Jan 1991.
de Pater, C.J., Weijers, L., Savi , M., Wolf, K.H.A.A., van den Hoek, P.J., and Barr, D.T.:
“Experimental Study of Nonlinear Effects in Hydraulic Fracture Propagation”, paper SPE
25893, SPEPF, Nov. 1994, pp. 239 – 246.
Dugdale, D.S.: “Yielding of steel sheets containing slits”, J. Mech. Phys. Sol., 8, 1960, pp. 100
– 108.
Martin, A.N.: “Crack Tip Plasticity: A Different Approach to Modeling Fracture Propagation in
Soft Formations”, paper SPE 63171 (revised), presented at the SPE Annual Technical
Conference and Exhibition, Dallas TX, Oct 2000.
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10. Advanced Concepts
10.
Advanced Concepts
In this section we shall deal with some of the more advanced concepts used in the process of
designing hydraulic fracture treatments, as well as in diagnosing what may (or may not) have
happened during a frac or minifrac treatment.
10.1
Tortuosity
Hydraulic fractures are created by pressure, not rate. Often we use rate to help generate the
required pressure, but we shouldn’t loose sight of the fact that it’s pressure that splits the
rock. Over a long perforated interval, fractures can form anywhere that the fluid pressure
exceeds the local frac gradient. Generally, the rock will have one point that is weaker than the
rest and the initial fracture will form here. However, if the pressure continues to rise, additional
fractures may be formed. Potentially, every single perforation is a source of fracture initiation.
Many of these fractures will be very small – but some may be large enough to take a
significant proportion of the treatment fluid.
Away from the artificial stress environment around the wellbore, treatments tend to produce a
relatively small number of larger fractures. Normally, fractures do not tend to join together –
the stress regime around the fracture tip tends to keep fractures apart. However, under the
influence of the complex stresses around the wellbore and perforations, fractures can join
together, sometimes giving several narrow paths towards a single, large fracture. So the
treating fluid has to travel from a region containing a large number of small fractures to a
region containing a small number of large fractures. In doing so, the fluid has to move through
a series of convoluted, narrow fractures – or put another way, through a tortuous path. This
tortuosity can produce a significant loss in pressure, resulting in a smaller than expected
fracture and possible early screenouts. Screenouts can also be caused by tortuosity for
another reason – the width of these channels through the rock is often not large enough to
carry the proppant concentration passing through it. This causes the proppant to bridge off,
preventing any further flow of proppant.
Tortuosity manifests itself as a pressure drop through the near wellbore region. There are
also other phenomenon that can result in a near wellbore pressure loss (such as poor quality
perforations). However, the important point is that there is a loss of pressure, which can be a
substantial proportion of the observed net pressure (i.e. the total energy available to
propagate the fracture). Because the pressures inside the fracture drive the pressures at the
surface, the pressure loss due to the tortuosity actually produces a higher BHTP and hence
higher STP. This gives the surface observer the impression that the net pressure is higher
than it really is. For instance, for a well with 200 psi net pressure and 300 psi pressure loss
due to tortuosity, it appears, to an Engineer who is unaware of the tortuosity, that the net
pressure is 500 psi. This means that Engineer thinks that the frac fluid has much more energy
for creating fracture volume than it has in reality, potentially resulting in a treatment design
that contains more proppant than can physically fit into the fracture. It is therefore important to
understand the magnitude of the near wellbore pressure loss, so that this can be allowed for
when designing the treatment.
Hard Rocks (that is, rocks with a high Young’s modulus and low fracture toughness) tend to
be more susceptible to tortuosity than soft rocks. In this type of brittle formation, there is
already a fracture formed at each perforation by the explosive action of the perforating
charges – all we are doing when we pump fluid is making these fractures extend, through a
medium that allows easy fracture extension. Because of the high Young’s modulus, the stress
concentrations at the fracture tip are more intense and so these smaller fractures are less
likely to link up. This means that hard rocks are more likely to produce a large number of
small fractures than soft rocks.
Deviated Wellbores tend to be more susceptible to tortuosity than vertical wells. As fractures
propagate, they compress the rock either side of them. This makes it harder for other
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10. Advanced Concepts
fractures to propagate in this region. As discussed in section 7, fractures tend to propagate on
a vertical plane. This means that the more deviated the wellbore, the less each fracture
interferes with its neighbour, and so they propagate more easily. Additionally, as each fracture
is further apart, there is less joining together of fractures. Finally, there is some evidence to
suggest that on some deviated wells, the fracture can initiate along the wellbore. At some
point not too far from the wellbore, the fracture grows out far enough so that the influence of
the wellbore is less significant than the influence of the in-situ stresses. At this point the
fracture has to change its orientation, rapidly if the rock is very hard. This produces a “corner”
around which the fluid and proppant has to flow, which causes further loss of pressure.
Thus, highly deviated wells in hard rocks are more likely to experience tortuosity problems
than vertical wells in soft formations. This does not mean that significant tortuosity will not be
encountered in soft formations or in vertical wells – it simply means that it is less likely.
Perforation Strategy. Often Service Companies are asked to treat wells which are already
perforated. In such wells, it is very difficult to control fracture initiation. However, sometimes
the well to be treated is new and we can perhaps influence the perforation strategy. This can
have a significant effect on the tortuosity, and is explained in detail in Section 14.
Horizontal Stress Contrast. As illustrated in Figure 10.1a, the contrast between the
maximum and minimum horizontal stresses can also influence the tortuosity. For the left hand
side of Figure 10.1a, there is a large contrast between σh,max and σh,min. This produces a
narrow fracture close to the wellbore and a very tight radius turn for the fracture. For the right
hand side of Figure 10.1a, there is little difference between the two horizontal stresses, so the
fracture starts with a wider width and gradually changes direction. Therefore, depending upon
the initial fracture orientation (which is turn is affected by the perforation strategy and wellbore
deviation), the contrast between horizontal stresses can have a significant effect on tortuosity.
σh,max ~= σh,min
σh,max >> σh,min
σh,max
σh,min
Figure 10.1a. Diagram illustrating the effects of horizontal stress contrast on tortuosity (after
GRI-AST 1996).
Curing Tortuosity. If tortuosity is detected before the main treatment (see Sections 15 and
16), it can sometimes be cured. This is done by pumping proppant slugs. The first company to
successfully accomplish this on a regular basis was Mærsk Olie og Gas, a Danish company
operating in the North Sea. Several SPE papers have been produced by Mærsk and their
contractors to document this. Mærsk had the advantage that they were operating off a large
frac boat, mixing gel with seawater on the fly. This meant that they had an effectively limitless
supply of both gel and proppant at their disposal – most of the time this is not the case.
To start with, Mærsk would pump a proppant slug in the minifrac, ideally at the maximum
anticipated proppant concentration for the main treatment. If this slug passed into the
formation without a significant rise in pressure, they could be reasonably sure that the
tortuosity would not significantly affect the treatment. Sometimes they would pump a series of
slugs, mixed at increasing proppant concentrations. If these slugs encountered a significant
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rise in pressure, or worse still screened the well out, they knew they had a problem. The cure
was to deliberately screen the tortuosity out.
This is done by pumping proppant slugs and then shutting down with the slug in the
perforations and near wellbore region. The effect of this is to block up the narrow channels
and force open the wide channels.
After a few years, Mærsk became so proficient at this – and so familiar with their formations –
that they developed a standard method used on every treatment. This involved pumping a
relatively long stage of 100 mesh sand at 1 or 2 ppa during the minifrac, followed by a
relatively short stage with 20/40 proppant at 4 or 5 ppa. The minifrac was shut down with the
20/40 proppant in the perforations. The 100 mesh sand blocked the narrow channels, whilst
the 20/40 proppant held open the wide channels, so that they would accept fluid when the
main treatment started. Using this method, Mærsk achieved a near perfect record for placing
treatments, in an area notorious for tortuosity problems.
10.2
Nolte Analysis
Nolte analysis is a branch of frac theory originally developed by Ken Nolte of Amoco in the
early 1980’s. It uses a plot of log Pnet against log time to determine the shape of the fracture,
as illustrated in Figure 10.2a:-
log Pnet
b
II
I
a
III
IV
log (job time)
Figure 10.2a – The Nolte plot
Basically, pressure is stored energy – or in the case of the fracturing fluid, stored energy per
unit volume. As work (a.k.a. horsepower) is the rate of using energy, on a graph of pressure
against time the gradient is the amount of work being performed. In this case, it is the amount
of work being performed by the fracturing fluid on the formation.
Nolte used a mathematical analysis to show that at certain gradients on the log Pnet against
log job time plot, certain fracture geometries will apply (with reference to Figure 10.2a):Mode I Mode II Mode IIIa Mode IIIb Mode IV -
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Good height containment, fracture propagates preferentially in the horizontal
direction.
Even fracture growth, fracture is propagating elliptically with vertical as well
as horizontal growth.
Screenout, fracture is filling with proppant and is having to balloon in order to
cope with the volume of fluid entering the fracture.
Screenout, near wellbore event. It is no longer possible to pump proppant into
the fracture.
Uncontrolled height growth. Also radial fracture geometry.
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Nolte’s work was carried out with respect to the three main 2-D models that were widely used
at the time. However, it is still a useful tool for the Frac Engineer to assess fracture geometry
without using a fracture simulator, or as a back up to a simulator.
Nolte analysis became popular at the same time that Service Companies began to use
computer monitoring and data storage systems on location. It became possible to have a
Nolte plot running real time – providing the industry with its first real-time fracture simulation
and diagnosis tool.
10.3
Dimensionless Fracture Conductivity
Dimensionless Fracture Conductivity (FCD or – as recently redefined by the API - CfD) or
Relative Fracture Conductivity is a measure of how conductive the fracture is compared to the
formation. In order to produce a production increase, the propped fracture has to be more
conductive than the formation (setting aside the effects of bypassing the skin damage). In
Section 2 we defined the fracture conductivity (FC) as being the product of the fracture width
and the permeability of the proppant. Dimensionless fracture conductivity is defined as
follows:CfD
Fc
=x k
f
=
kp w̄
xf k ......................................................... (10.1)
where xf is the fracture half length, kp is the permeability of the proppant, w̄ is the average
fracture width and k is the permeability of the formation. In order for the fracture to be more
conductive than the formation, the dimensionless fracture conductivity has to be greater than
one.
Equation 10.1 compares the ability of the formation to deliver fluids to the fracture, with the
ability of the fracture to delivery fluids to the wellbore. If the CfD is less than one, then post
treatment production increase is limited by the relatively low conductivity of the fracture, and
the fluids will flow more easily through the formation. If the CfD is significantly greater than 1,
then the limiting factor is the formation’s ability to deliver hydrocarbons to the fracture.
Of the four components on the right hand side of Equation 10.1, the permeability of the
formation is fixed, whilst the permeability of the proppant is defined by the proppant type, the
closure stress and the producing conditions. In order to maximise CfD, it is necessary to
control the fracture half-length, whilst at the same time getting the width and the proppant
permeability as large as possible. Under most circumstances – for any given fracture situation
– there is a fixed relationship between width and length. For so much length created, there
will be so much width created. However, created width is not the same as propped width,
unless the well has screened out from tip to wellbore. The more proppant that is placed per
unit area of the fracture, the wider the propped fracture will be. Therefore, two ways to
increase CfD are; one – pump more proppant; or two – pump better quality proppant.
In higher permeability formations, this is not enough. Even with the fracture completely full of
good quality proppant, the CfD can still be less than one. Therefore, a technique called the Tip
Screen Out must be used (see section 10.4, below).
10.4
The Tip Screen Out (TSO)
The Tip Screen Out is a technique used to artificially increase the width of the fracture,
without increasing the length. As previously discussed, for any given fracture, there is a fixed
relationship between width and length. If we can artificially overcome this, then we can
dramatically increase the CfD. Figure 10.4a illustrates this:-
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Proppant
Fracture Tip
∆P
Figure 10.4a – The Tip Screen Out
The TSO is a technique that is generally used in high permeability formations. The high
formation permeability means that it is very difficult to get a CfD greater than one. In order to
generate the TSO, proppant is pumped into the fracture earlier than would normally be the
case. As the formation has high permeability, the fracturing fluid is leaking off relatively
quickly. This acts to dehydrate the proppant-laden slurry. If the treatment is correctly
designed, this dehydration will cause the proppant to collect at the fracture tip. In order for the
fracture to continue to propagate, a positive Pnet must be maintained at the fracture tip. As the
proppant builds up in the fracture tip, fluid has to flow through it to reach the tip and maintain
the Pnet. Whilst flowing through the proppant build-up, the fluid loses pressure due to friction
as it passes between the proppant grains. When the proppant build-up gets large enough, the
∆P of the fluid equals and then exceeds Pnet and the fracture ceases to propagate.
At this point, fluid is still being pumped into the fracture and has to go somewhere. Some of
this fluid is leaking off, but not all of it – so the fracture volume still has to grow. This means
that the fracture starts to get wider. It also means a rise in net pressure as the formation gets
increasingly compacted – this is how the onset of a TSO is spotted during a treatment.
The TSO technique relies on two things; high permeability (and hence high fluid leakoff), and
low Young’s modulus. High leakoff is necessary so that the slurry will dehydrate sufficiently to
allow proppant build-up at the tip. Low Young’s modulus is necessary to allow the width to
increase. If the formation is too hard (i.e. Young’s modulus too high), the pressure will rise
very rapidly and quickly exceed the maximum treating pressure at surface.
10.5
Multiple Fractures and Limited Entry
As previously discussed, any perforation is potentially a source of fracture initiation. All it
takes is for the fluid pressure to exceed the fracture extension pressure at any given point and
a fracture is formed. How large that fracture is depends upon the volume of fluid the fracture
receives. Usually, most of the small fractures get “squeezed out” as larger fractures close by
develop. However, if the fractures are far enough apart (which is easy enough on deviated
wellbores), more than one fracture will develop into a significant size. This is often
detrimental, as multiple fractures that cover the same vertical plane are largely wasted, unless
they are widely spaced out. In addition, as the rate (and hence frac fluid volume) is split
between two or more fractures, the treatment ends up producing a range of smaller, narrower
(i.e. less conductive) fractures, rather than a single large fracture. Finally, although each
fracture receives only a fraction of the total rate, the proppant concentration remains
unchanged. As the fracture width is less, and the slurry velocity down each individual fracture
is decreased, there is a much greater chance of proppant bridging and a premature
screenout.
In short, multiple fractures can lead to less effective stimulation and an increased chance of
job failure.
The majority of wells worldwide are completed with more than one set of perforations. Unless
something is done to isolate these perforations and control the point of fracture initiation,
multiple fractures are likely. However, there is one situation where this is deliberately used to
produce stimulation of an entire interval at one go. This is called Limited Entry fracturing.
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Limited Entry Fracturing. Even whilst fracturing, fluids follow the path (or paths) of least
resistance. The resistance to the flow of the fluids comes from three sources:- perforation
friction; tortuosity; and the formation’s fracture extension pressure. All of these can vary with
fluid rate. However, the fracture extension pressure and tortuosity are not controllable,
whereas the perforation friction is. Therefore, if the fracture extension pressure of each
formation is known, as well as the tortuosity (usually assumed to be zero), the number and
size of the perforations can be varied to balance the fluid flow, so that each set of perforations
receives the same proportion of fluids. This technique is called Limited Entry, as we are trying
to limit and control the amount of fluids entering each zone.
This technique can be taken one step further. By further varying the number of perforations,
the proportion of each fluid going into each zone can be adjusted to produce the optimum
treatment for that zone – more fluid enters zones needing most stimulation, for example.
Obviously, the calculations for working out the size and number of perforations can get pretty
complex – once there are more than two zones you need a computer model to keep things
straight. In addition, the results are only as good as the data input – if you are guessing at the
frac gradient, then you are also guessing at the number of perforations needed. Finally, this
analysis also assumes perfect perforations – something that cannot be guaranteed.
Therefore, limited entry fracturing is unreliable unless exact data is available.
In addition to being unreliable, limited entry fracture treatments tend to be very big. The
treatment is trying to place effective fractures in several zones simultaneously. This means
lots of rate and large fluid volumes, as well as lots of proppant, as this treatment is trying to do
the work of several smaller treatments in one go.
10.6
Proppant Convection and Settling
Proppant Convection. Proppant Convection is caused by variation in slurry density, and can
lead to the majority of the proppant being placed in the bottom of the fracture. Put basically, a
10 ppa slurry is much denser than a – for instance – 5 ppa slurry. This means that if a 10 ppa
slurry follows a 5 ppa slurry into the formation, it will tend to slide beneath the lighter slurry,
leading to the placement of the higher proppant concentration at the bottom of the fracture,
where it may not necessarily connect with the perforations. This is illustrated in Figure 10.6a.
Obviously, proppant convection is not really an issue on TSO designs, as the plan is to
completely fill the fracture from tip to wellbore. However, when fracturing lower permeability
formations, proppant convection can cause significant problems. The way to prevent this is to
use long proppant stages mixed at the same concentration. Once in the formation, slurries will
dehydrate with time due to leakoff - increasing the ppa of the slurry - so it may be necessary
to gradually increase the proppant concentration at the blender as the treatment progresses.
Figure 10.6a – Proppant convection. As the heavier slurry enters the fracture it sinks and
displaces the lighter slurry upwards
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Proppant Settling. Proppant settling occurs when the frac fluid has insufficient viscosity to
suspend the proppant inside the fracture. Proppant moves downward, leading in the worst
cases to a fracture that only has proppant right at the bottom. This may be completely
unconnected to the wellbore. Once again, this phenomenon is not an issue when a TSO
treatment is being performed. However, on lower permeability formations, especially those
with very long closure times, settling can be a significant issue.
The key to preventing proppant settling is to design the frac fluid correctly. In order to prevent
settling, the frac fluid must exhibit good proppant transport qualities at BHST for at least the
anticipated job time, plus the anticipated closure time, plus a safety factor. This can be tested
by the use of the model 50 high temperature rheometer. A widely accepted criterion for
-1
proppant transport is to have at least 200 cp apparent viscosity at a shear rate of 40 sec .
Note that this criterion is not an API standard and is somewhat subjective – different
standards are used in different places.
Equation 10.2 gives an Equation for calculating the terminal velocity (i.e. the maximum
possible velocity) for a spherical particle falling through a power law fluid (note that this
assumes the fluid is almost at rest):vt
n'
+1
(SGp - SGf)
1 n' 0.04212 dp
= 36
............................ (10.2)
K'
where vt is the terminal velocity (ft/sec), dp is the proppant grain diameter (inches), SGp is the
proppant absolute specific gravity, SGf is the fluid specific gravity, n’ is the flow behaviour
n’ –2
index (dimensionless) and K’ is the consistency index (lbs.sec ft ).
10.7
Proppant Flowback
Proppant flowback is when the proppant that been placed in the fracture flows back into the
well during production. It has been the subject of intense industry debate and investigation
over the last 10 years. Some of the causes of proppant flowback are listed below:i)
Stress Cycling. Every time the well is drawn down, the closure stress on the
proppant increases, as the reservoir pressure in the fracture is effectively reduced.
When the well is shut in, the pressure builds up again and the closure pressure is
reduced. This is stress cycling, which was first identified in 1994 by Shell and StimLab as a major cause of proppant flowback. As the well is opened and closed, the
proppant pack expands and contracts slightly, weakening its integrity. If the stress is
cycled enough times – or too suddenly – the pack will literally break apart, allowing
proppant to flow back into the wellbore. Wells that have been fractured should be
handled with care – don’t shut them in unless there is no alternative, and if it has to
be done, then it should be done slowly.
ii)
Weak Formations. Obviously, if the formation holding the proppant in place falls
apart, then the proppant will flow back. Formations that are susceptible to this need to
be frac and packed, rather than just fractured.
iii)
Insufficient Fracture Conductivity. If the propped fracture has insufficient
conductivity, especially in the near wellbore area, then the higher velocity of the
produced fluids, coupled with the increased pressure gradient along the plane of the
fracture, will result in an increased net force acting to push individual proppant grains
out if the fracture.
iv)
Poor Quality Frac Fluid. If the frac fluid does not have sufficient viscosity to keep the
proppant suspended until the fracture closes, then the proppant will settle into the
bottom part of the fracture. In extreme cases, this can result in the bottom half of the
fracture having all the proppant, whilst the top half closes up on nothing. This creates
a void space at the top of the proppant pack, as illustrated in Figure 10.7a.
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No Proppant
Void Space
Proppant
Figure 10.7a – Illustration of the “Pipelining” effect.
As the well is produced, fluid flows rapidly across the top of the proppant pack,
through the void space, as this is the path of least resistance. As it does so, it picks
up proppant grains and can carry these out of the fracture and even up to the surface.
This effect is known as “pipelining” and can result in almost all of the proppant being
produced back out of the fracture.
Preventing Proppant Flowback
Once proppant flowback has started, it is usually very difficult to stop. Therefore, the best
option is to prevent proppant flowback from happening in the first place. Obviously, a well
designed treatment using a good quality frac fluid, together with good well management, can
go a long way to mitigating proppant flowback. However, it is also true that for some
formations, this is not sufficient. To combat this, there are several different methods which
can be employed:i)
Resin Coated Proppant. By far the most common method for controlling proppant
flowback, resin coated proppant (RCP) is simply proppant which has been coated
with a layer designed to make the proppant grains stick together. Usually, it requires
temperature and a closure stress for this to happen. RCP tends to come in two main
varieties, curable and pre-cured (or tempered). Curable RCP has a softer coating,
which is designed to chemically cure when exposed to temperature. Pre-cured RCP
has a harder resin coat, which relies more on the closure pressure to make the
proppant grains stick together. RCP has an additional effect, in that it makes the
proppant more tolerant to closure pressure, as the resin coat will capture
permeability-reducing fines produced as the fracture closes.
RCP is generally used as an alternative to ordinary proppant, either for the whole
treatment, or for the last few proppant stages. This latter method, whilst being
cheaper, is less reliable as there is no guarantee that the stage which is pumped last
will be the stage that is positioned by the wellbore (see earlier section on Proppant
Convection).
RCP can be highly effective, but has three main disadvantages. First, it is expensive,
often being more than twice as expensive as the non-coated proppant. Second, it can
have a significant effect on the fracturing fluid, especially at high pH’s, as some of the
resin is stripped off and dissolves in the fluid. Finally, the standard bulk pneumatic
systems generally used for handling large volumes of proppant cannot be used for
RCP, as it the resin coat can be chipped off.
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ii)
Micro-Fibers. Another method for preventing proppant flow back is to pump very
small fibers with the proppant. These fibers, if used in sufficient quantity, will form a
three dimensional mesh within the proppant pack, acting to prevent individual grains
slipping past one another. The use of these fibers can result in a slight decrease in
proppant pack permeability, but this can be allowed for in the frac design. The fibers
are usually made from a polymer.
The main problems with this system (other than its cost) are operational. Because the
fibers are very small, they have a very high surface area to mass ratio. This in turn
means that it can very difficult to actually mix the fibers into a fluid, especially on the
fly during a treatment. Because of the large difference in specific gravity between the
proppant and the fibers, it is also very difficult to mix the proppant and fibers together
before adding them to the gel.
The fibers also have a limited maximum temperature above which, they will
disintegrate. This significantly reduces the number of wells that are suitable for this
type of treatment. Finally, if used in the wrong proportions with the proppant (due
either to poor design or ineffective mixing), the fiber itself can be produced out of the
formation, sometimes resulting in a “hair ball” somewhere in the production facilities.
iii)
Micro-Sheets. In order to get around the patent held by one service company for the
micro-fibers, a competitor introduced a product that uses small sheets or platelets of
polymer, which act to wrap around the proppant grains. This has several effects. First,
and unfortunately foremost, is a significant reduction in permeability of the proppant
pack. Secondly, the sheets will form a three dimensional mesh, acting in a similar
fashion to the micro-fibers. The sheets also act a little like a resin coat, in that they
can cushion the proppant grains and tie up fines.
Unfortunately, the micro-sheets also suffer from many of the same operational and
temperature limitation problems experienced by the micro-fibers.
iv)
Deformable Particles, such as BJ’s FlexSand, is another approach. These particles,
mixed at 10 to 15% by weight with the proppant, will deform – to a limited extent –
around the proppant as the fracture closes. This acts to lock the proppant grains
together and reduce the tendency for them to slide past each other. The deformable
particles also have the effect of cushioning the proppant grains and increasing the
grain to grain area of contact. This acts to increase the proppant pack permeability,
by reducing the production of fines.
The main disadvantage of the deformable particles is the extra equipment needed to
handle it and mix it at the correct proportions. However, this is no worse than for the
micro-fibers and the micro-sheets.
10.8
Forced Closure
Forced closure is a technique used to produce a very tight proppant pack in the near wellbore
area. As soon as the treatment is finished, the well is opened up and flowed back at 0.5 to 1.0
bpm. This is before the fracture has closed and before the fluid has broken. Although the
exact mechanism by which this prevents proppant flowback is not clear, there is sufficient
empirical evidence to make this a valid technique, in a suitable formation. However, there are
no methods for deciding which formations are suitable, apart from actually trying the
technique.
Modern treatment monitoring software and fracture simulators are set up to allow for forced
closure. Many of them even allow input from a flowmeter placed on the flowback line whilst
monitoring the post-treatment pressure decline.
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10.9
Non-Darcy Flow
Darcy defined fluid flow through a porous media, in terms of the flow dimensions, the fluid
viscosity, the pressure differential and the permeability of the media, in an Equation that is
fundamental to the oil industry:q
=
kh∆P
µ (re/rw)
....................................................................... (10.3)
However, this doesn’t tell the whole story. Whilst this Equation can be very reliable for fluid
flow through relatively low permeability media (such as rocks), it does not take into account
inertial flow effects. On the microscopic scale, the fluid is constantly changing direction as it
moves through the pore throats and pore spaces. This represents a loss of kinetic energy,
and so also an increased loss in pressure per unit distance. This effect is quantified in the
Forcheimer Equation:-dP
L
µv
= k
p
(1)
(2)
2
+ β ρ v ............................................................. (10.4)
(3)
The term –dP/L is the pressure drop per unit length along the propped fracture, µ is the
viscosity, v is the overall “bulk” velocity of the fluid, kp is the permeability of the proppant pack,
β is a constant (the “beta” factor, non-Darcy flow factor or turbulence factor), and ρ is the
density of the fluid.
In Equation 10.4, parts (1) and (2) are essentially the Darcy Equation. Part (3) is the nonDarcy term, and is basically kinetic energy per unit volume. Obviously, the effect of the nonDarcy term varies with the square of the velocity, so at lower flow rates (such as for oil flowing
through a permeable rock) this effect is negligible. However, at high flow rates (such as for
gas flowing through a highly permeable fracture) this term becomes highly significant and can
produce a pressure gradient many times greater than that caused by Darcy flow.
Obviously, the magnitude of the non-Darcy effect is also highly dependent upon the beta
factor. The magnitude of beta is determined by a number of factors, but experimental
determination of beta factors, has revealed two relationships:-
β
∝ D................................................................................. (10.5)
where D is the average grain diameter, and:-
β
∝
1
........................................................................... (10.6)
kp
It is also true that artificial proppants tend to have lower beta factors than naturally occurring
sands, due to their greater sphericity and roundness. In practice, beta factors have been
determined for a wide range of proppants and closure stresses, and can be easily obtained
from the proppant manufacturers, such as in Table 10.1:Closure
Stress, psi
2000
4000
6000
8000
10000
12/18
0.0001
0.0002
0.0007
0.0018
β, atm sec2/gram
16/20
0.0001
0.0002
0.0003
0.0007
0.0023
20/40
0.0002
0.0003
0.0004
0.0007
0.0015
Table 10.1 – Beta factor data for CarboLite artificial ceramic proppant (Carbo Ceramics Inc)
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As the expected production rate from the treatment increases, so does the pressure loss due
to non-Darcy effects, and this should always be taken into account when selecting proppant
and predicting production increase.
References
Wright, C.A., Weijers, L., and Minner, W.A.: Advanced Stimulation Technology Deployment
Program, report GRI-09/0075, Gas Research Institute, March 1996
Cleary, M.P, et al.: ”Field Implementation of Proppant Slugs to Avoid Premature Screen-Out
of Hydraulic Fractures with Adequate Proppant Concentration”, paper SPE 25892, presented
at the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium, Denver CO,
April 1993.
Kogsball, H.H., Pits, M.J., and Owens, K.A.: “Effects of Tortuosity in Fracture Stimulation of
Horizontal Wells – A Case Study of the Dan Field”, paper SPE 26796, presented at the
Offshore Europe Conference, Aberdeen, UK, Sept 1993.
Nolte, K.G.: “The Application of Fracture Design Based on Fracturing Pressure Analysis”,
paper SPE 13393, SPEPE (Feb 1988) p31-42.
Nolte, K.G., and Smith, M.B.: “Interpretation of Fracturing Pressures”, paper SPE 8297, JPT
(Sept 1981) p1767-75.
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Vreeburg, R-J., Davies, D.R., and Penny, G.S.: “Proppant Backproduction During Hydraulic
Fracturing – A New Failure Mechanism for Resin Coated Proppants”, paper SPE 27382, JPT,
1994.
Ely, J.W.: “Experience proves forced closure works”, World Oil, Jan 1996, p 37 – 41.
Rickards, A., et al.: “Need Stress Relief? A New Approach to Reducing Stress Cycling
Induced Proppant Pack Failure”, paper SPE 49247, presented at the SPE Annual Technical
Conference and Exhibition, New Orleans, Sept 1998.
Forcheimer, P.: Wasserdewegung durch Boden. ZVDI (1901), Vol. 45, p. 1781. (in German)
Martins, J.P., Milton-Taylor, D, and Leung, H.K.: “Effect of non-Darcy Flow in Propped
Hydraulic Fractures”, paper SPE 20709
Vincent, M.C., Pearson, C.M., and Kullman, J.: “Non-Darcy and Multiphase Flow in Propped
Hydraulic Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity”, paper
SPE 54630, presented at the SPE Annual Technical Conference and Exhibition, Houston, Oct
1999.
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11. 3-D Fracture Simulators
11.
3-D Fracture Simulators
The three main fracture simulation models used in the industry today are FracPro, FracproPT
and MFrac. Between them, they are used on well over 90% of all treatments currently
performed. Other simulator’s, such as StimPlan, GOHFER and the proprietary simulators
produced by Schlumberger, Halliburton, Shell and others, are available, but their use is
limited mainly to Engineers who work for the actual company that produced the simulator.
Most of the 3-D and lumped-parameter 3-D simulators described below are produced by
companies whose main tasks are producing software or providing a fracturing service. As
such, there is a considerable amount of detail concerning these simulators that is proprietary
and not available in the public domain. Therefore, detailed descriptions of the actual
algorithms behind the model are not possible and in any case beyond the scope of this
manual. The reader is referred to the references for more information. The term pseudo or
lumped-parameter 3-D is applied to most of the simulators, as they relate everything back to a
single characteristic dimension (usually fracture half-length), which is found by a variety of
methods. Fully 3-D models have every dimension as independent variables.
As stated, most simulations are performed by one of three simulators (and it should be noted
that FracPro and FracproPT are essentially the same model). In the industry, there is a
perception that the FracPro-FracproPT model is more applicable to low permeability “hard”
formations, whilst the MFrac model is more applicable to high permeability “soft” formations.
The reliability of this perception is a matter of some debate, but it may be due to the
respective origins of the two models. In any case, it should be remembered that the producers
of these simulators are all competitors. Most of the discussions about the relative merits of
each model are subjective and partisan.
For a discussion on the limitations of the 3-D fracture simulators, refer to the discussion on
pressure matching in Section 19.1.
11.1
RES’ FracPro and Pinnacle Technologies’ FracproPT
FracPro and FracproPT originally started out as one
simulator, FracPro. The model was originally developed
using funding from the Gas Research Institute, a joint US
Government and gas industry funded organisation.
Eventually, a company called Resources Engineering
Systems (RES) produced a commercial simulator based on
the work carried out by the GRI. However, a couple of
years ago, a group of people dissatisfied with the
company’s approach, split away from RES and moved over
to Pinnacle Technologies. For a variety of reasons, they
were able to take the FracPro technology with them and FracproPT was the result. At this
point in time, there is very little difference between how the two models work. The major
differences between the two models concentrate on the way they interface with the user, and
with the on-screen graphics.
The FracPro approach has almost entirely done away with
the traditional concept of fracture toughness, which means
that users of simulators based on this model find that
changes to input fracture toughness values have little or no
effect on fracture geometry. Instead the theory states that
deep underground, the effect of the confining stress is
much more significant than the effect of the fracture
toughness. Thus Klc can be ignored if the following
condition is satisfied;
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11. 3-D Fracture Simulators
σ pR
>> KIc ................................................................................ (11.1)
where R is the radius of the fracture and is analogous to the characteristic fracture length
used in classical linear elastic fracture mechanics. The above Equation shows us that fracture
toughness is more significant for small fractures in shallow formations, such as during skin
bypass fracturing.
The fracturing fluid does not penetrate to the very end of the fracture. This means that there is
a very rapid change in net pressure at a distance ω from the tip of the fracture. If the condition
described in the above Equation is satisfied, then ω can be found as follows;
ω
R
≈ 2
2
Pnet
Pnet + Pc ....................................................... (11.2)
Because the fluid does not penetrate into the tip of the fracture, energy is lost as the tip of the
fracture deforms. It is postulated that this deformation occurs in a non-linear or dilatent
fashion (see Section 9.2). This crack tip dilatency reduces the energy left for the fracturing
fluid to propagate the fracture, and hence reduces the size of the fracture, for a given Pnet.
Once the energy absorbed by the fracture tip has been found, the model then goes on to
solve the fracture geometry using a series of Equations which relate mass conservation,
energy conservation, fluid dynamics and heat transfer. The model is 3-dimensional, allowing
separate rock mechanical and reservoir properties to be input for each different rock strata.
This model was the first to incorporate various aspects that are now taken as standard, such
as near wellbore friction, proppant convection and multiple fractures. This model also
incorporates a data conversion and editing facility, an acid fracture simulator and a simple
production simulator.
Although all of the three main simulators can model the fractures real time, only FracPro and
FracproPT have the ability to predict forward to the end of a job, whilst in the middle of a
treatment. This is a very powerful tool, which allows the fracture characteristics can be
predicted in the middle of a treatment. The model takes the treatment data received up to that
point, and then uses the remaining input treatment schedule to predict the fracture at the end
of the treatment. Thus the Frac Engineer can “see how things are going” based on actual
treatment data, and alter the treatment schedule as the job is being pumped. So far no other
commercially available simulator has mastered this.
11.2
Meyers & Associates’ MFrac
MFrac is produced and developed by Meyer and Associates. This methodology sticks much
more closely to the conventional Linear Elastic
Fracture Mechanics (LEFM) approach to fracture
propagation,
than
the
FracPro/FracproPT
approach. The model uses the basic LEFM
criterion, which states that in order for the fracture
to propagate, the stress intensity factor (K) must
be greater than KIc (the critical stress intensity factor, or fracture toughness). It uses a
characteristic length (referred to as Hξ) and a geometry factor, γ, in the classic LEFM
Equation:-
σc
=
KIc
........................................................................... (11.3)
γ Hξ
The actual value for g depends upon the fracture model being used (PKN, KZD, Ellipsoidal or
3-D), as does the dimension actually being used for the characteristic length. For the 3-D
model, the characteristic length is found from a set of partial differential Equations, which
relate mass conservation, mass continuity, momentum conservation, and vertical and lateral
propagation rates.
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11. 3-D Fracture Simulators
The authors of this fracture propagation model acknowledge that there is a “tip over-pressure”
effect that cannot be accounted for. This is handled by using an “over-pressure factor” - that
has to be obtained empirically - or by using huge values for fracture toughness.
11.3
Other Simulators
StimPlan
StimPlan is a pseudo 3-D numerical simulator produced by NSI Fracturing Technologies. The
simulator works by performing implicit finite difference solutions to basic Equations of mass
balance, elasticity, height growth, and fluid flow. The simulator is based on LEFM. It is
probably the most widely used of the non-FracPro/FracproPT/MFrac simulators.
Recently, NSI have started introducing E-StimPlan, a fully 3-D fracture simulator. This
simulator divides the formation into a series of grids of variable size, allowing fully 3-D fracture
growth and irregularly-shaped fractures (as opposed to the elliptical fractures almost always
predicted by the lumped–parameter 3-D models). This model also allows 2 dimensional
proppant transport. At the time of writing this manual, this simulator is still too slow for
practical use, but shows great promise
GOHFER
GOHFER (Grid Orientated Hydraulic Fracture Extension Replicator) has taken a completely
different approach to modelling fracture growth. Of the four main models described, only
GOHFER and E-StimPlan said to be fully 3-D and only GOHFER has a significant history of
use. The model takes a finite element approach to fracture propagation, modelling the
reservoir and the formations above and below it as a series of elements, rather than as a
continuum. The fracture propagates along a plane between elements, so in order to produce
fracture width, elements either side of the fracture have to be compressed. At the fracture tip,
there is a single element just ahead of the fracture, so that the tip is positioned at some point
on the side of the element. Fracture propagation occurs when the tensile stress in the
element exceeds the failure criterion for the material, and the element splits into two pieces,
along the plane of the fracture. The fracture has then propagated by a distance equal to the
width of the element.
The advantages of this approach are that it is very simple to give each element its own set of
rock mechanical and reservoir properties, making simulation of multiple formations very easy.
The main disadvantage is the use of a tensile failure criterion, which tends to make hard rocks
harder to fracture than soft rocks, which tends to be the opposite way around to conventional
theories. Additionally, because each element in the model can be assigned individual rock
mechanical and leakoff properties, it is very easy to "dial-a-frac", that is, produce a fracture
geometry that has more in common with uses wishes than with reality.
References
Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design and
th
Real-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56
California Regional Meeting of the SPE, Oakland CA, April 1986.
Cleary, M.P., Wright, C.A., and Wright, T.B.: “Experimental and Modeling Evidence for Major
Changes in Hydraulic Fracturing Design and Field Procedures”, paper SPE 21494, presented
at the SPE Gas Technology Symposium, Houston TX, Jan 1991.
Johnson, E., and Cleary, M.P.: “Implications of Recent Laboratory Experimental Results for
Hydraulic Fracturing”, paper SPE 21846, presented at the SPE Rocky Mountain Regional
Meeting and Low Permeability Reservoirs Symposium, Denver CO, April 1991.
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11. 3-D Fracture Simulators
Wright, T.B., Aud, W.W., Cipolla, C., Perry, K.F., and Cleary, M.P.: “Identification and
Comparison of True Net Fracturing Pressures Generated by Pumping Fluids with Different
Rheology into the Same Formations”, paper SPE 26153, presented at the SPE Gas
Technology Symposium, Calgary, Alberta, Canada, June 1993.
FracPro Version 8.0 onwards On-Line Help, RES/Gas Research Institute, March 1998
onwards.
FracproPT Version 9.0 onwards On-Line Help, Pinnacle Technologies/Gas Research
Institute, July 1999 onwards.
Meyer, B.R.: “Design Formulae for 2-D and 3-D Vertical Hydraulic Fractures: Model
Comparison and Parametric Studies”, paper SPE 15240, presented at the SPE
Unconventional Gas Technology Symposium, Louisville KY, May 1986.
Meyer, B.R.: “Three Dimensional Hydraulic Fracturing Simulation on Personal Computers:
Theory and Comparison Studies”, SPE 19329, presented at the SPE Eastern Regional
Meeting, Morgantown WV, Oct 1989.
Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic Fracturing
th
Simulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65 SPE
Annual Technical Conference and Exhibition, New Orleans LA, Sept 1990.
Hagel, M.W., and Meyer, B.R.: “Utilizing Mini-Frac Data to Improve Design and Production”,
Journal of Canadian Petroleum Technology, March 1994, pp. 26 – 35.
MFrac III Version 3.5 (onwards) On-Line Help, Meyer and Associates Inc, December 1999
onwards.
NSI Fracturing Technologies Web Site, www.nsitech.com
Barree, R.D.: “A Practical Numerical Simulator for Three-Dimensional Fracture Propagation in
Heterogeneous Media”, paper SPE 12273, presented at the SPE Reservoir Simulation
Symposium, San Francisco CA, Nov 1983.
StimLab division of CoreLab, Web Site, www.corelab.com/StimLab/Depts/GOHFER_
prodinfo.asp, 2002 onwards.
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12. Predicting Production Increase
12.
Predicting Production Increase
Being able to accurately predict a production increase from a formation is an important part of
the process of designing a frac treatment. All treatments have to be economically justifiable,
before approval by the operating company. In order to be able to produce an economic
justification, the Engineer must have a reasonable idea of what the post fracture production
increase will be. Moreover, this prediction must be reliable, as the Engineer will have a hard
time justifying subsequent treatments, if previous justifications have proved to be inaccurate.
In order to be able to produce an accurate prediction of the increase in production, the
Engineer needs accurate pre-treatment production data. Items like permeability, skin factor,
BHP and downhole producing rate are all critical. If accurate values for items such as these
cannot be obtained, then the subsequent predicted production increase will also be
inaccurate.
Nevertheless, because of the uncertainties associated with most of the data used in the
analyses below, any estimate of post fracture production remains just that – an estimate. The
Frac Engineer must make this clear to any customer. As a result, it is often more reliable to
base post-treatment production estimate on the results of offset wells, if any are available.
12.1
Steady State Production Increase
Steady state production is when all reservoir parameters remain unchanged during the
production process. Items such as radial extent and reservoir pressure are fixed. Most of the
time this does not exist, and the reservoir is at least in a pseudo-steady state (see below).
Consequently, production increases based on steady state are an approximation only.
However, they are often useful as a “first look”, “back-of-the-envelope” calculation, to quickly
see if a fracture is viable or not.
Darcy’s Equation (which is for steady state flow only) can be expressed as follows for a skin
damaged reservoir:q
=
0.00708 k h ∆P
............................................................ (12.1)
µ ln[re/(rw e-S)]
where q is the downhole producing rate in bpd, k is the effective reservoir permeability in md,
h is the net height of the formation in ft, ∆P is the pressure differential between the edge of
the reservoir and the wellbore (the drawdown) in psi, µ is the downhole viscosity of the
reservoir fluid in cp, re is the radial extent of the reservoir, rw is the wellbore radius and S is
the skin factor (dimensionless). Note that re and rw should always have the same units,
usually either feet or inches.
To provide a fair comparison between production at different times, which may be at varying
drawdown, the productivity index, J, is usually used instead of the production rate. The units
of productivity index (or PI) are usually bbls/day/psi, or bpd/psi.
J
=
0.00708 k h
µ ln[re/(rw e-S)]
................................................................ (12.2)
To avoid confusion, the symbol J will be used to signify the PI from a real, damaged reservoir.
Jo is used to represent the PI from an undamaged reservoir and Jf for the fractured reservoir.
In Darcy’s Equation, the term kh is often referred to as the permeability-thickness, or
conductivity. This equates to the fracture conductivity, Fc, of the propped fracture. By
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12. Predicting Production Increase
replacing the term kh with Fc we can obtain an expression for the PI of the fractured
reservoir:Jf
=
0.00708 Fc
.................................................................... (12.3)
µ ln(re/rw)
Equation 12.3 should be used with some caution. As explained earlier, this is a steady state
approximation to a situation that in reality is far from steady state. The Equation no longer
uses the skin factor term, as it is assumed that the fracture has completely bypassed the skin,
rendering it irrelevant. This Equation also assumes that all production into the wellbore comes
via the fracture. This is a valid assumption for fractures with a very high CfD, but becomes less
and less accurate as the contrast between the fracture and reservoir conductivity becomes
lower. Indeed, if the fracture conductivity is too low, this method may actually predict a
production decrease – something that is theoretically impossible, unless the fluid or proppant
somehow damages the formation. This Equation also assumes that the formation has no
difficulty delivering reservoir fluids to the fracture – the Equation is independent of fracture
length.
Nevertheless, Equation 12.3, still provides a “first guess” to see how viable a fracture
treatment is. However, it is less accurate for low permeability reservoirs and for fractures
which relatively low fracture conductivity.
The “folds of Increase” (Jf/J) can be calculated, by dividing Equation 12.3 by Equation 12.2,
which gives the following:-s
Jf
J
=
Fc ln[re/(rwe )]
......................................................... (12.4)
kh
ln(re/rw)
Another way of getting a “quick look” at potential post-treatment production is simply to use a
skin factor of -5 in Equation 12.1.
12.2
Pseudo-Steady State Production Increase
Pseudo-steady state flow is when the reservoir has been producing for a sufficient period of
time, so that the effects of reservoir boundary can be felt. In practical terms, this means that
the reservoir has an outer boundary.
Pr
Radius of Disturbed
Formation
Pressure
Increasing
Time
Pwb
0
rw
Distance from Well
re
Figure 12.2a – Transient production. The red lines illustrate the variation of pressure with
distance from the wellbore, as time increases. The radius of the disturbed formation is
continually increasing
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12. Predicting Production Increase
As the well is produced, the radius from the wellbore at which the reservoir has been
disturbed by production increases at a rate proportional to the square root of the producing
time. During this period, flow into the wellbore can be described as transient, as the effective
radial extent of the reservoir is continually increasing. However, at some point the area of
formation disturbed by the production from the well will hit an outer boundary. At this point,
the radial extent of the reservoir ceases to expand, and the reservoir pressure starts to fall. At
this point, the reservoir switches from transient to pseudo-steady state. The difference
between transient and pseudo-steady state is illustrated in Figures 12.2a and b.
Pr
Pressure
Increasing
Time
Pwb
0
rw
Distance from Well
re
Figure 12.2b – Pseudo-steady state production. The radius of the disturbed formation has
reached the reservoir boundary, re, and now the reservoir pressure is decreasing
Most reservoirs will spend the majority of their producing lives in pseudo-steady state
production.
McGuire and Sikora
The best known method for predicting production increase during pseudo-steady state
production was developed in 1960 by McGuire and Sikora. This work was based on earlier
work carried out on electrical circuits by Dyes, Kemp and Caudle. Basically, they used a
series of resistors and capacitors to represent the reservoir – resistors to represent
permeability (the lower the resistance the higher the permeability), capacitors to represent the
porosity or storage capacity of the reservoir, voltage to represent pressure and current to
represent flow rate.
These experimentally-derived curves, shown in Figure 12.2c, define for a given dimensionless
fracture length (L/re) and a given fracture relative conductivity (see below – note that this
definition is different from that used throughout the rest of this manual), the dimensionless
production increase that can be expected. McGuire and Sikora used L for fracture half length,
instead of the usual xf.
Note that the following use a different system of nomenclature than the rest of this manual:Relative conductivity =
Wkf
k
40
A ................................................... (12.5)
where W is the average propped fracture width in inches, kf is the permeability of the proppant
in md, k is the formation permeability in md, and A is the well spacing in acres.
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12. Predicting Production Increase
14
L/re = 1.0
.9
12
7.13
r
ln 0.472 r e
w
10
J/Jo
.8
k = AVERAGE FORMATION PERMEABILITY, md.
(BASED ON GROSS THICKNESS)
L = FRACTURE LENGTH FROM WELL BORE, Ft.
re= DRAINAGE RADIUS, FEET
A = WELL SPACING, ACRES
Wkf = CRACK CONDUCTIVITY, md-in.
W = PROPPED WIDTH OF FRACTURE, in.
kf = PERMEABILITY OF PROPPING
MATERIAL, md.
rw = WELL BORE RADIUS, FEET
J = PRODUCTIVITY INDEX AFTER
FRACTURING
Jo= PRODUCTIVITY INDEX
BEFORE FRACTURING
8
6
.7
.6
.5
.4
.3
.2
4
.1
2
0
1.E+02
1.E+03
1.E+04
RELATIVE CONDUCTIVITY,
1.E+05
Wkf
k
1.E+06
40
A
Figure 12.2c – The McGuire-Sikora Curves
L
Dimensionless fracture half length = r ........................................... (12.6)
e
Where L is the fracture half-length (xf normally) in feet and re is the reservoir drainage radius
or radial extent, also in feet.
Dimensionless production increase =
J
Jo
7.13
ln 0.472 (re/rw) .......... (12.7)
Where J is the pre-frac productivity index, Jo is the post-frac productivity index (Jf normally)
and rw is the wellbore radius.
McGuire and Sikora is an approximation based on the limits of the experimentation they
conducted. The main assumption is that the fracture is significantly more conductive than the
formation, so that the main rate limiting variable is the fracture half length. Vertical fluid flow is
assumed to be negligible, fluids are assumed to be incompressible and in single-phase flow
and skin factor is assumed to be zero. However, it is often relatively easy to find the
production increase if the skin was reduced to zero. The McGuire-Sikora production increase
can simply be added to this.
Skin Bypass Fracs
Rae et al presented a simple method for predicting the production increase from a skin
bypass frac. It combines elements of the McGuire-Sikora and Prats methods and allows for
the existence of a skin factor:Jf
J
Page 98
-S
=
ln[re/(rw . e )]
ln[4/(Fcd . xfD)] ................................................................ (12.8)
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12. Predicting Production Increase
This method is valid for fracture with a CfD greater than 1 – i.e. more conductive than the
formation.
12.3
Nodal Analysis
The most modern method for predicting production increase is the Nodal Analysis
programme. These simulators work by analysing the flow from the reservoir at a node, which
can be down hole at the “sand face”, at the wellhead or at some distance from the wellhead in
a separator. By defining the flowing conditions at this node, the software can then calculate
back to the flow rate from the reservoir.
Nodal analysis can be used to produce inflow performance relationship (IPR) curves, which
relate the ability of the reservoir to deliver fluids, with the ability of the completion to carry
fluids out of the reservoir. These curves are particularly useful for oil wells with a GOR (i.e.
real wells and not “black oil” approximations), gas wells and wells producing at significant
water cuts, where the ability of the completion to carry the fluids is not always easy or
straightforward to calculate. Figure 12.3a shows an example for a gas well with a fracture of
varying average propped fracture width.
3000
2500
FBHP, psi
2000
1500
Tubing
1000
500
Average Propped
Fracture Width, inches
0.1
0.2
5000
6000
0.3 0.4 0.5
0
0
1000
2000
3000
4000
7000
Gas Rate, mscfpd
Figure 12.3a – Nodal analysis IPR curves for a gas well with a fracture of varying propped
fracture width.
With reference to the example in Figure 12.3a, note the following points:•
•
•
The blue curves represent five different production scenarios. In this case, each curve
represents varying propped fracture width. However, they could just as easily be varying
skin factor, permeability or water cut. This ability to test the sensitivity of the system to
varying producing scenarios makes nodal analysis very powerful.
The blue curves are the inflow curves. For these, the node is fixed at bottom hole (or the
“sand face”). Each of these curves represents the inflow into the well from the formation
for hydrocarbons at various FBHP’s (flowing bottom hole pressures). The drawdown is
the difference between the reservoir pressure and the FBHP, so the smaller the FHBP,
the greater the drawdown.
The red curve is the outflow or tubing curve. This represents the ability of the completion
to carry the hydrocarbons out from the well. In this case, the node is fixed at the wellhead.
A set of wellhead conditions are specified, and then the software calculates (for a fixed
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12. Predicting Production Increase
•
FWHP – flowing wellhead pressure – and surface temperature) what the bottom hole
pressure must be for a variety of different flow rates.
The point at which the red curve and the blue curve cross represents the point at which
the two sets of conditions coincide. Therefore, this is the rate and FBHP at which the well
will produce. For instance, in Figure 12.3a, for a frac width of 0.2 inches, the well will flow
at 4250 mscfpd at a FBHP of +/- 1450 psi.
Most nodal analysis programmes allow the user to produce the well through a propped
hydraulic fracture of varying geometry. This is very useful to the Frac Engineer, who may well
end up spending more time with the nodal analysis than with the fracture simulator.
When using nodal analysis to predict production increase, the following steps should be
followed:1. Get production data from the well. If the well is new, get production data from an offset. If
no offsets are available, use the well test data.
2. History match the production data with the nodal analysis (and without a fracture being
present). Vary items such as skin factor, permeability and reservoir pressure to make the
nodal analysis production match the historical production data. The nodal analysis
production simulator is now tuned to the real data.
3. Introduce a fracture. Vary characteristics such as fracture length and fracture conductivity
(or average propped width) to produce the biggest possible increase in production.
4. Be aware of what is achievable and what is efficient. For instance, the nodal analysis may
indicate that doubling the fracture length gives an extra 50% production. What it does not
tell you is that doubling the fracture length means at least 4 times as much proppant, 8
times as much fluid and a corresponding increase in equipment. Such an increase in job
size may not be practical and could well be uneconomic.
5. Once the optimum fracture geometry has been obtained, go to the fracture simulator and
design a treatment to make a fracture of these dimensions. Often, it is at this point that
the Engineer finds out what is realistically achievable and so the final design may be the
product of several alternating runs on both the nodal analysis and the fracture simulator.
References
Prats, M.: “Effect of Vertical Fractures on Reservoir Behaviour – Incompressible Fluid Case”
Trans AIME (1961), 222 105-118
Dyes, A.B., Kemp, C.E. and Caudle, B.H.: “Effect of Fractures on Sweep-Out Pattern”, Trans
AIME (1958), 213, 245
McGuire, W.J. and Sikora, V.J.: “The Effect of Vertical Fractures on Well Productivity”, Trans
AIME (1960), 219, 401-403
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,
paper SPE 54673, presented at the 1999 SPE Annual Technical Conference and Exhibition,
Houston, Texas, Oct 3–6 1999.
Archer, J.S. and Wall, C.G.: Petroleum Engineering Principals and Practices, Graham &
Trotman, London, 1986.
TM
Perform (Well PERFORMance Analysis ) Nodal Analysis Software, version 3.00 and higher,
PSG/IHS Energy Group, Richardson, Texas, USA, 1999 onwards.
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13. Candidate Selection
13.
Candidate Selection
Virtually any zone in any well is a potential candidate for hydraulic fracturing. Given a free
hand, it is possible to produce an increase in productivity index in almost any formation using
hydraulic fracturing. However, often the Frac Engineer is limited by considerations such as
water-oil contacts, gas-oil contacts, poor cement bonding, completion restrictions and
placement of perforations. Moreover, the formation must also have the reserves and
production potential to economically justify the large expense often associated with fracturing.
This section of the manual is designed as a guide to the science and art of frac candidate
selection. Guidelines will be given, as to when an interval is a good candidate for fracturing
and when it is not. However, there are often considerable “grey areas” between good
candidates and poor candidates. In these cases, there is no substitute for experience.
It should never be forgotten that the best wells are also the best candidates for fracturing.
Fracturing cannot add reserves (although economically recoverable reserves and drainage
efficiency can be improved) nor can it increase reservoir pressure – if there is nothing there to
start with, there will be nothing there afterwards. A 50% increase in production from a good
well is often more valuable than a 500% increase from a poor well.
13.1
Economic Justification for Fracturing
Fracturing – as with any other operation performed on an oil or gas well – has to be
economically justified. That is to say, the increased revenue generated by the treatment must
satisfy economic criteria set by the operating company. This is vitally important – it is not
enough for the Frac Engineer to simply produce a production increase. Instead, the Frac
Engineer must usually either produce at least a minimum production increase or increase
economically recoverable reserves, in order to meet the economic criteria.
Part of the skill in designing a fracture treatment is deciding whether or not these economic
justifications can be met. An inability to meet these criteria is adequate grounds for rejecting a
well as a candidate for fracturing. However, given that a treatment such as a skin bypass
fracture can cost less than $20,000 to carry out, usually any reasonable criteria can be
satisfied, unless the well has very low productivity indeed.
Economic criteria can often be simple. For instance, many companies insist that the cost of
the treatment be paid back within a period of three months. In such a case, the Frac Engineer
has to estimate the increase in production and from that the total extra production over the
first three months. Once the extra production has been calculated, the total extra revenue can
easily be calculated by multiplying by the oil or gas price, as appropriate. If the total extra
revenue is greater than the cost of the treatment, then the treatment is economically justified.
All parties involved in the fracturing operation must be willing to accept a certain element of
risk. Fracturing is not an exact science. Although many of the theories associated with
fracturing are very rigorous and thoroughly proven, the fact remains that they are only as
good as the available data. Often this data is of poor quality or is absent entirely. Even when
considerable time, effort and expenditure have been taken to obtain data, it is usually only
valid for a few inches around the wellbore. In order to complete a frac design, the Engineer
has to assume this data is valid for sometimes hundreds of feet from the wellbore,
encompassing a huge volume of rock. In addition to this lack of adequate data, the Frac
Engineer also has to cope with the fact that no one really understands how the fracture
propagates through the formation. This is illustrated by the fact that there are several different
fracture simulators on the market, all using different methods to model the fracture.
This uncertainty regarding how the fracture will propagate is in addition to the standard risks
associated with any operation on an oil or gas well.
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13. Candidate Selection
Internal Rate of Return
Many operating companies use a criterion known as the Internal Rate of Return. This is a
percentage value, and any potential project requiring an AFE (Authorisation For Expenditure),
must make a return on investment greater than this value. The theory is that the company
would be better off spending the money elsewhere if a project cannot meet this criterion. For
instance, if a Company Man wishes to spend $1,000,000 on a project, and his company has
an internal rate of return criterion of 18% over one year, then the expenditure of $1,000,000
must generate additional production worth at least $1,180,000 in the first year after the
treatment.
The internal rate of return is also referred to as the discount factor, or DCF.
Net Present Value
Net Present Value (or NPV) is a useful tool that can be used in two ways. First, the operating
company can set an NPV criterion that has to be met. Secondly, it can be used to compare
different fracture designs, and decide which one is the most cost effective. For instance, a
Frac Engineer may be confronted with the following question – is it worth pumping twice the
quantity of proppant for only a 10% gain in production? This question can be answered by
using NPV analysis.
NPV is calculated using the following method:Net Revenue
= Production Increase x Price ...................................... (13.1)
where the Production Increase is the total extra production due to the fracture treatment.
n
Discounted Revenue
=
X=1
Net Revenue for year X
X
.................................. (13.2)
(1 + i)
where n is the payback period, usually measured in years, and i is the internal rate of return,
expressed as a fraction.
NPV =
Discounted Revenue – Total Treatment Costs ............. (13.3)
Remember that the Total Treatment Costs are the total cost that the customer has to pay,
which includes the cost of the frac job (i.e. BJ’s ticket), plus items such as rig time, workover
costs, wireline work, well testing, coil tubing etc.
Example – NPV Calculation
Calculate the NPV, given the following data:Oil price
Payback period
Internal rate of return
Total treatment costs
Production gain, yr 1
Production gain, yr 2
Production gain, yr 3
$20 per bbl
3 years
15%
$1,250,000
400,000 bbls
200,000 bbls
100,000 bbls
Therefore
Net Revenue, yr 1
=
=
400,000 bbls x $20 per bbl
$8,000,000
Net Revenue, yr 2
=
=
200,000 bbls x $20 per bbl
$4,000,000
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Net Revenue, yr 3
=
=
100,000 bbls x $20 per bbl
$2,000,000
And so
Discounted Revenue, yr 1
=
=
Discounted Revenue, yr 2
=
=
Discounted Revenue, yr 3
$8000000
1
(1 + 0.15)
$6,956,522
$4000000
2
(1 + 0.15)
$3,024,575
=
$2000000
3
(1 + 0.15)
$1,315,032
=
=
$6,956,522 + $3,024,575 + $1,315,032
$11,296,129
=
Therefore
Total Discounted Revenue
And finally
NPV
=
=
$11,296,129 - $1,250,000
$10,046,129
Now, let’s return to the Engineer’s original question - is it worth pumping twice the quantity of
proppant for only a 10% gain in production?
Let’s say that the cost of the actual fracturing was $500,000, and of that, the cost of the
proppant was $200,000 and the cost of the fluid was $50,000. If we double the amount of
proppant, we will probably need to at least double the amount of fluid. So the cost of the frac
job goes up by $250,000. The final cost of the frac is now $750,000 and the overall cost of the
treatment is now $1,500,000.
A 10% increase in production gives us the following:-
So that
and
which gives
Production gain, year 1 =
Production gain, year 2 =
Production gain, year 3 =
440,000 bbls
220,000 bbls
110,000 bbls
Discounted Revenue, yr 1 =
Discounted Revenue, yr 2 =
Discounted Revenue, yr 3 =
$7,652,174
$3,327,033
$1,446,535
Total Discounted Revenue =
$12,425,742
NPV
=
=
$12,425,742 - $1,500,000
$10,925,742
So the answer to the Engineer’s question is yes – in this case, using a payback period of 3
years and an internal rate of return of 15%, it is worth doubling the volume of proppant.
So the answer to the Engineer’s question is yes – in this case, using a payback period of 3
years and an internal rate of return of 15%, it is worth doubling the volume of proppant.
Of course, two other things that the Frac Engineer must consider are;
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1. Can the customer afford the increase in the initial treatment cost? Small operators cannot
always generate enough cash flow to do this.
2. Is it physically possible to place twice as much proppant in the fracture? Is this to be
accomplished by increasing the fracture length, width or by some combination of the two?
In more remote locations the Frac Engineer must also make sure that the equipment needed
to store and blend the extra fluids and proppant is available.
13.2
Completion Limitations
Tubing Cooldown
As relatively cold fracturing fluid is pumped down a completion, the tubing will start to cool
down. As it cools down, it will shrink and decrease in length. On some wells, this can result in
shrinkage of several feet
Usually, wells are completed using packers with polished seal bores, and tubing with seal
assemblies. When the completion is run, the packer is set at the required depth. Then the
tubing is run, complete with a seal assembly on the bottom.
The seal assembly is a length of pipe with a number of rubber seals on the outside. The idea
is that these seals slide into the polished bore of the production packer, providing the required
isolation. The seal assembly is usually several feet in length, so that it can slide up and down
inside the polished bore, allowing the tubing to expand or contract whilst still retaining
completion integrity.
However, if the tubing is cooled down too much, the seal assembly can sting right out of the
polished bore, and the completion will loose its integrity. This is highly undesirable.
Additionally, as the tubing re-heats after the treatment, it probably will not sting back into the
polished bore, and thus will produce additional stress on the packer, wellhead and other
completion components.
In order to prevent this from happening, special software programmes are used to simulate
the effects of tubing shrinkage, to predict if the tubing will shrink too much. BJ’s programme
for predicting this is DTools.
There are two obvious answers to a tubing cool down problem:1.
Reduce the size of the treatment, so that the tubing does not get cooled down as
much, or pump the treatment at a lower rate, so that the fluid heats up more as it
travels down the well.
2.
Heat up the treating fluid before it goes down the well. This can be done in two ways.
The first way is to pump the fluid through a heat exchanger, which contains a hot
fluid, such as steam or burning oil. Such heat exchangers are often called “hot oilers”.
The advantage of this system is that it can be used on the fly. The second way is to
circulate the fluid through a choke, using the high-pressure frac pumps. A frac tank of
fluid circulated through a choke can be quickly heated up – if the choke is set small
enough so that the pumps can develop significant horsepower. 4000 HHP produces
the approximately the same amount of energy as a 3MW power plant. The
disadvantages of this method is that heating multiple frac tanks can be very time
consuming, and individual tanks will cool down as other are heated up. Therefore, hot
oilers tend to be used for large treatments, whilst pumping through a choke is used
for smaller treatments.
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Tubing Expansion
Another effect of fracturing on tubing is to cause its expansion, due to an elevated internal –or
burst – pressure. This increase in diameter is usually not too much of a problem. However, as
the tubing expands radially and circumferentially, it also contracts axially, reducing the length
of the tubing string.
Obviously, the effect of tubing expansion and the effect of tubing cool down will combine to
produce an even worse effect. Once again, software must be used to model these effects.
There are two ways to help mitigate the effects of tubing expansion:1.
Put pressure on the outside of the tubing, as it is an increase in the differential
pressure across the tubing wall that causes the expansion. However, this is not
always possible – especially on a completion with multiple packers. If it is possible,
the maximum allowable pressure may be insufficient.
2.
Reduce the pumping rate. Obviously, the BHTP is pretty much fixed. However, by
reducing the rate, and hence the friction pressure, the internal pressure that most of
the tubing experiences can be reduced.
Maximum Wellhead Pressure
Often, a treatment will be constrained by a low maximum wellhead pressure. It is very rare
that a treatment is completely prevented by this, but a low wellhead rating can sometimes
severely limit what can be achieved by the treatment.
One solution to this problem is to use wellhead isolation tool or WIT (commonly referred to as
a “Tree Saver”). This tool, which is described in detail in Section 20, actually bypasses the
wellhead, by allowing the frac fluid to be pumped directly into the tubing, rather than through
the wellhead and into the tubing.
Another potential solution to this problem is to reduce the friction pressure. This can be done
by either reducing the pumping rate or by altering the friction properties of the fluid (which can
be done by either reducing the polymer loading or by delaying the crosslink). Both of these
parameters are usually flexible to a certain extent. However, some wells have a frac gradient
so high that even with zero friction pressure, the maximum wellhead pressure is exceeded.
A third method for reducing the wellhead pressure is to pump a high density frac fluid. This
has the effect of increasing the hydrostatic head, which in turn lowers the wellhead pressure.
These fluids are usually mixed using high density brine. Potassium chloride brines can be
used up to about 9.6 ppg, sodium chloride to about 10 ppg and calcium chloride to 11.0 ppg.
Above that, things start to get expensive and considerably less environmentally friendly.
Examples of materials used to weight brine above 11.0 ppg include caesium formate and zinc
bromide. It should also be remembered that heavy-weight brines are harder to recover from
the well after the treatment
Completion Jewelry
Completion jewelry is a general term, used describe all the various special tools that were
added to the completion as it was run. Examples include:•
•
•
•
Sub surface safety valves (SSSV)
Sliding side doors (SSD)
Gas lift mandrels
Blanks, used to close off gas lift mandrels
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•
•
Gauges and gauge carriers
Non-return valves
All of these items will have a pressure rating. Ideally, this should be in excess of the overall
pressure rating for the completion. However, this is not always the case, and such items
should be checked.
SSSV’s will form a restriction in the completion and may be abraded by the proppant. These
always need to be locked open during a treatment, as the potential damage caused by an
accidental closing is not worth the risk. Sometimes this can be performed from the surface,
using the hydraulic control lines. In other instances, this has to be performed by installing an
isolation sleeve by wireline.
SSD’s can be both beneficial and detrimental to a fracture treatment. They can be beneficial,
as they often allow the fracture treatment to be precisely injected into a specific zone. They
can be detrimental, as they can get stuck both open and closed, and even when fully
functional, usually require wireline intervention in order to manipulate them.
Non-return valves should be avoided. Obviously, treatments cannot be pumped through a
non-return valve. Treatments can be placed above a non-return valve, provided the nonreturn valve is isolated from the treatment by a bridge plug or similar tool.
Justifying a Workover
Often, the only feasible way to fracture a formation is to carry out a workover. This allows the
treatment to be pumped through a dedicated workstring, usually with some kind of packer.
Consequently, the Frac Engineer has maximum control over the process – the treatment is
placed in the right interval and the treatment can be pumped at relatively high rates and
pressures.
There are two ways to justify a workover; economically and technically. Generally, the first
kind carries all the influence – there are very few companies that will approve a workover
purely on technical grounds alone, unless there is some kind of research project going on.
Workover operations can vary from the very cheap (such as a shallow land well) to the very
expensive (offshore, deep water). Consequently, the grounds for justifying such a workover
can also vary. In general, the best way to justify the cost of the workover is to first obtain an
estimate for cost of the workover. Then, work out two different production increases. The first
production increase assumes that a workover is performed and the Frac Engineer can place
the optimum treatment. The second production increase uses the best stimulation method
available, assuming no workover (this may not even be a frac – it could be an acid treatment).
Then calculate rate of return and net present value for both of these methods. If the frac +
workover generates a better return on investment, then it is economically justified.
Another way to get a workover performed is to frac a well that is already in need of a
workover. Then the costs of the workover can be split between the frac and the existing
completion programme. Alternatively, a well can be selected for treatment that is in need of a
workover which cannot be economically justified. The combined effects of the frac and the
existing need may be enough to justify the additional expense.
13.3
Things to Look For
Listed below are a number of items that may make an interval a good, or bad, candidate for
hydraulic fracturing.
1.
Skin Factor. All wells have skin damage, to a greater or lesser extent, unless they
have been stimulated in some fashion. This means that all unstimulated wells are
producing significantly below their full potential. As a general principle, the higher the
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permeability, the higher the skin factor – so that the most productive wells are also
the ones which produce least efficiently. All this means that in practice, all wells are
potential candidates for fracturing.
Figure 13.3a shows the effect skin factor, S, has on the production of a well. The
horizontal axis shows the well’s original Skin Factor. The vertical axis shows the
effect this has on productivity, relative to the undamaged production (S = 0), so that
production from the undamaged well equals 100%. Note that this graph does not
include the stimulation effects of the frac – it merely illustrates how much production
is lost due to skin factors. A hydraulic fracture will punch a highly conductive path
through the skin damage, producing a production increase by two methods; through
bypassing the skin damage and through stimulation of the undamaged reservoir.
Therefore, an interval with a high skin factor is a good candidate for fracturing.
100
Production Relative to S = 0, %
80
60
re = 2000 ft
rw = 4.25 inches
40
20
0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Skin Factor, S
Figure 13.3a – The effect of skin factor upon production rate. Note that this Figure is based
purely on skin factor effects. No fracture stimulation is included.
2.
Low Permeability Wells. So-called “tight” formations are where fracturing first
became widely accepted by the industry. These formations cannot produce enough
hydrocarbons purely because the rock matrix itself is not conductive enough. Any
production loss due to the (usually) low skin factor is generally not significant.
Therefore, in order to unlock the potential of the reservoir, a fairly large hydraulic
fracture treatment is required.
3.
Weak or Unconsolidated Formations. Hydraulic fracturing is a very effective
method for completing a weak or unconsolidated formation. Fracturing can help
reduce or eliminate sand production by a number of methods:•
•
•
By reducing the drawdown on the formation
By re-stressing the formation
By acting as a filter, provided the proppant is sized correctly.
A hydraulic fracture can also be used as part of a gravel pack completion, providing a
so-called frac and pack treatment. This is probably the most effective way of
developing an unconsolidated formation.
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4.
Water and/or Gas Contacts. In general, these are to be avoided. The presence of a
water or gas contact close to the perforations can often prevent fracturing. If a
propped fracture were to propagate into a water or gas zone, then the well will quickly
stop producing oil, and start producing water or gas. Once a propped fracture has
connected with a water or gas zone, it is very difficult to halt the water or gas
production.
5.
Poor Cement Bond. If the bond between the casing and cement, or cement and
formation, is poor or non-existent, then fracturing should be avoided. In these
situations, it is possible to make the poor bond even worse and to connect with
separate formations above and below the zone of interest. However, in the case of a
“micro-annulus”, the pressures induced by the fracturing, coupled with the filter-cake
building properties of the fluid, will usually permit successful fracturing operations.
6.
Corroded Casing or Tubulars. Badly corroded casing or tubulars will probably not
stand up to the differential pressures produced by fracturing. Therefore these wells
should be avoided.
7.
Perforation Strategy. The position of the perforations can often prove to be the
difference between a successful and an unsuccessful frac. Section 14 discusses this
in more detail.
8.
Logistics. This is a measure of how easy it is to get materials and equipment to
location. For instance, there is a big difference between a land location a few miles
down the road from the base, and an offshore location on a satellite platform with a 5
tonne crane limitation. These two locations may have wells and formation that require
similar treatments. However, it is very unlikely that the offshore would be treated in
the same manner to the land well, unless a stimulation vessel was available. More
often than not, it is the logistics of the operations – rather than any formation
parameters – that has the biggest influence on the treatment.
References
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Archer, J.S. and Wall, C.G.: Petroleum Engineering – Principles and Practices, Graham and
Trotman, London (1986).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
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14. Perforating for Fracturing
14.
Perforating for Fracturing
Of all the things under our control, the position, number, size and phasing of the perforations
has the single biggest influence on the effectiveness of the hydraulic fracture treatment. Many
times this is outside of the control of the Frac Engineer, as a high proportion of treatments are
carried out on existing wells that have already been perforated. However, if a well or an
interval is new, the Frac Engineer can often greatly increase the effectiveness of a treatment
by perforating for fracturing, rather than in a more conventional manner.
When perforating for fracturing, it is often desirable to only perforate a very limited section of
wellbore, usually located towards the centre of the gross interval. This controls the point of
fracture initiation and helps to reduce tortuosity. However, there are quite legitimate reasons
for wanting to perforate all of the net pay (which can often result in several sets of
perforations). One of these reasons is well testing, which is used by reservoir engineers to
help determine the recoverable reserves in the formation - obviously a very important task.
Results from well test analysis can be misleading if the entire interval is not perforated,
especially if the formation contains several discrete intervals. Therefore, the need to reduce
the number of perforations and to reduce the length of the perforated interval, must be
balanced with the operating company'
s other interests. A compromise must be reached.
14.1
Controlling Fracture Initiation
Perforations can be used to control the point of fracture initiation, as illustrated in Figure
14.1a, below. On the left-hand side, there is an interval that has been perforated across its
entire section. When the treatment commences, fracture initiation takes place. At this point, it
should be remembered that fractures are initiated by pressure, not by rate. As Frac
Engineers, we often use rate to create pressure (as a consequence of Darcy’s law), but it’s
the pressure that makes the fracture. As the pressure increases, a fracture will initiate when
the pressure rises above the breakdown pressure of the weakest point along the perforated
interval. This can be in at the top of the zone (frac A, below), in the middle of the zone (B), at
the bottom of the zone (C) or somewhere else. There can also be more than one fracture –
wherever the fluid pressure exceeds the breakdown pressure, a fracture will be initiated.
Multiple fractures (see Section 10.5) can result in poor fracture conductivity and early
screenouts.
A
B
D
C
Figure 14.1a – The Effect of perforations on fracture initiation
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14. Perforating for Fracturing
If the interval is perforated as shown in the left-hand side of Figure 14.1a, the point at which
the fracture or fractures initiate is beyond the control of the Frac Engineer. Fracs A and C
have substantial sections propagated outside the interval. This results in poor coverage of the
interval and a considerable amount of wasted proppant. There is also a risk that Frac A could
penetrate into a gas cap or that Frac C could penetrate into a water zone.
Alternatively, the interval could be perforated as shown in the right-hand side of Figure 14.1a.
In this example, the zone has been perforated over a very short interval (5 to 10 ft). This
controls the point at which the fracture initiates, and dramatically reduces the chances of
multiple fractures forming. If this short perforated interval is in the center of the zone, then
there is a good chance that the fracture will propagate both up and down, covering the entire
section and using the proppant efficiently. Alternatively, if there is a water zone close by, the
interval can be perforated towards the top. This causes the fracture to initiate near the top,
reducing the chances of the fracture penetrating down into the water.
Of course, once the interval has been fractured, there is nothing - other than cost – to stop a
second perforation run being made to cover the rest of the interval. However, if the treatment
has been effective, the fracture will be many times more conductive than the formation.
Consequently, any perforation that is not directly connected to the fracture will be
unproductiv:We have recognized point-source perforating improves your ability to
successfully stimulate an interval........to improve our completions and ultimate
recoveries. We have learned from perforating for stimulation that it does not take
100 ft of perforations to produce a 100 ft zone. We have proven that 5ft placed in
the proper place will outperform all 100 ft.
Robert Lestz, Production Engineer, Chevron
Hart’s E&P, February 2000
Another example of perforating to control fracture initiation is the case when multiple zones
are treated simultaneously in a single treatment. The conventional method is to try a limited
entry treatment (see Section 10.10), but these are unreliable and difficult to control.
Figure 14.1b – Perforating for zonal coverage
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14. Perforating for Fracturing
Figure 14.1b illustrates this concept. Conventionally, each productive section of the formation
is perforated individually. When this well is fractured, a portion of the fluid (dependent upon a
number of variables) will enter each of the intervals, as in the left-hand side of Figure 14.1b.
Limited entry fracturing is all about controlling how much fluid goes into each interval and can
be very unreliable. However, if the well has not already been perforated, another method is to
perforate a small section in the center of the formation, and allow the fracture to connect up
all of the individual intervals (right-hand side of Figure 14.1b). Under any circumstances, a
treatment that produces a single fracture is much easier to predict and control than a
treatment that produces multiple fractures.
Once again, a small section (5 to 10 ft) of perforations is shot. These need to be placed
roughly in the center of the interval to be covered, or slightly towards the bottom, depending
upon the stress regime. Consequently, this may even mean deliberately perforating a nonproductive formation, such as a shale. It can often be quite hard to convince an oil or gas
company to deliberately do this.
Important Note:- Sometimes, if there is a significant contrast in Young’s modulus between
the various formations, sections were the fracture is significantly narrower than the average
can form. These narrow bands can act to prevent proppant transport, leaving formations
above and below un-propped. The reader should not use the above method unless reliable
information on Young’s modulus contrasts – such as from a sonic array log – is available.
Perforating to control fracture initiation also makes fracture simulation and post-treatment
pressure matching more reliable. By controlling the point of fracture initiation, the Frac
Engineer defines a significant simulation variable and reduces the complexity of any possible
solution by an order of magnitude.
14.2
Controlling Tortuosity
In order to minimise tortuosity, it must be as easy as possible for the fracture to propagate
from the perforations. Every single perforation is a potential source of fracture initiation, so
one of the steps taken is to reduce the number of perforations to an absolute minimum,
consistent with the anticipated production rate. This in turn means big holes.
Figure 14.2a – Perforation strategy for vertical wells
Another important factor is the phasing of the perforations. Ideally, this should be 180°, with
the guns oriented so that they shoot perpendicular to the maximum horizontal stress. This
way the holes are lined up with the direction of fracture propagation, minimising any changes
of direction between the hole in the casing and the main fracture. Most of the time it is not
possible to orientate the guns in this fashion – the best strategy will then depend upon factors
such as the contrast between the maximum and minimum horizontal stresses and the
formation’s Young’s modulus. The situation is complex, but in general it is best to minimise
the number of holes shot, to use big holes to minimise perforation friction, and to perforate to
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that the holes line up along the wellbore (see Figure 14.2a), rather than produce a spiral of
holes around the circumference. The best strategy for perforating for fracturing was presented
by Behrman in 1998. However, it is the author’s experience that 90º phasing usually produces
the least near wellbore friction in vertical or near-vertical wellbores, without getting involved in
very complex strategies.
Deviated Wellbores
Hydraulic fractures tend to propagate on a vertical or near vertical plane (see Section 7). On a
vertical well, this means that the fracture will propagate along or close to the wellbore. This
minimises the formation of multiple fractures, as the compression of the rock on either side of
the fracture will make it harder for parallel fractures to grow. However, on a deviated or
horizontal wellbore, the horizontal distance between potential points of fracture initiation is
much greater, making it much easier to produce tortuosity and/or multiple fractures.
Consequently, it is common practice for highly deviated or horizontal wells, to perforate a very
short section of the formation (+/- 2 ft or less), with as many big holes as possible. This is
shown in Figure 14.2b (for a horizontal well):-
Figure 14.2b – Perforation strategy for horizontal wells
14.3
Perforating for Skin Bypass Fracturing
3
2
1
Figure 14.3a – The Effect of fracture initiation point on skin bypass fracs
Skin Bypass Fracturing (SBF - see Section 3.4) is a special type of small-scale fracturing
operation designed to penetrate through skin damage, and to provide effective stimulation
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without the cost and logistics of larger-scale treatments. Whilst it is true that SBF’s may not
necessarily offer such a large production increase as conventional fracturing, the stimulation
is still effective, and is usually more than adequate to justify the cost of the treatment. As with
any type of fracturing, the position of the perforations can have a significant effect on the
results of the treatment.
A
B
C
Figure 14.3b – Multiple skin bypass fracs over a long interval
With reference to Figure 14.3a, it is easy to see how the point of fracture initiation can effect a
fracture not designed to cover the entire height of the formation, such as in skin bypass
fracturing. Obviously, fracture B will produce more stimulation than fractures A or C. If the
entire section of the formation is perforated, it is usually not possible to control the point of
fracture initiation (although a sand fill can be used to ensure that the fracture doesn’t initiate
towards the bottom). Therefore, when planning a perforation strategy, it would be better to
shoot holes over a small, central section, than over the entire interval.
Figure 14.3b shows a different approach to perforating for SBF’s. Over a large section, one of
the most cost effective methods of stimulation is to carry out several small consecutive
treatments, as listed below (with reference to Figure 14.3b):
Zone
Lower
Middle
Upper
All
Step
1
2
3
4
1
2
3
4
1
2
3
1
2
Action
Perforate bottom zone
Frac lower zone
Recover fluids
Isolate lower zone by placing bridge plug
Perforate middle zone
Frac Middle zone
Recover fluids
Isolate middle zone by placing bridge plug
Perforate upper zone
Frac upper zone
Recover fluids
Remove bridge plugs
Place on production
This method ensures maximum coverage of the interval for minimum of effort, although it
does involve three separate perforating runs and the use of coiled tubing to remove the bridge
plugs or sand fill.
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References
Behrmann, L.A.: “Perforating Requirements for Fracture Stimulations”, paper SPE 39453,
presented at the SPE International Symposium on Formation Damage Control, Lafayette LA,
Feb 1998.
Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,
paper SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, San
Antonio TX, Oct 1999.
Behrmann, L.A., and Nolte, K.G.: “Perforating Requirements for Fracture Stimulations”, paper
SPE 59480, SPE Drilling and Completions, December 1999, pp 228 – 234.
Venkitaraman, A., Behrmann, L.A., and Chow, C.V.: “Perforating Requirements for Sand
Control”, paper SPE 65187, presented at the SPE European Petroleum Conference, Paris,
Oct 2000.
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15. The Step Rate Test
15.
The Step Rate Test
Step rate tests are usually performed before a hydraulic fracture treatment, as part of the
fracture design process. Together with the minifrac (see next section), they are often referred
to as calibration tests, as they are used to adjust the fracture model to the actual pressure
response of the formation.
There are two types of step rate test, the step up test and the step down test. One is used for
determining fracture extension pressure, whilst the other is used for determining near
wellbore friction. Both tests can be extremely useful when designing the treatment. Whenever
possible, bottom hole pressure data should be used, as this is more accurate and reliable
than calculated BHTP.
15.1
The Step Up Test
The step up test is used to determine the fracture extension pressure, Pext. This is usually 100
to 300 psi higher than the fracture closure pressure, Pclosure, which is a very important factor in
fracture design. Usually the results of the step up test will be used to determine an upper
boundary for Pclosure and to give the expected BHTP.
To carry out the step rate test, it is common practice to use either KCl water or linear gel.
However, if this test is to be combined with the minifrac (see Section 16), then the actual frac
fluid should be used.
The test itself consists of pumping fluid into the formation at various rates. These rates start
off slowly and gradually increase. For example, these could be the pump rates for a typical
test; 0.25 bpm, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 5.0 and 10 bpm. The first step is usually the
lowest rate that the pumps can manage. It is important to get as many stages at low rate as
possible. At each stage, first achieve the rate, then wait for the pressure to stabilize and finally
record the exact pressure and rate. Then move on to the next stage.
Pressure
Pext
Rate
Figure 15.1a – The step up test
What is important with this test is to get stabilized pressure. It is not that important to get the
exact rates. Often, pump operators will fiddle with the rate for 30 seconds or so in order to get
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15. The Step Rate Test
exactly 0.75 bpm. This is not necessary. Get approximately the correct rate and then leave it
alone, so that the pressure can stabilise and be recorded. Once the test has been carried out,
a plot of pressure against rate can be made, as illustrated in Figure 15.1a.
The change in gradient of the slope shown in Figure 15.1a marks the change from Darcy
radial flow (lower rates) to Darcy linear flow at higher rates. This is the point at which our
fracture is created and hence this is our extension pressure.
When carrying out a step up test it is important that no artificially induced fracture exists prior
to the test. Thus, if any pumping above the frac gradient has already been carried out,
sufficient time should be taken for the fracture to heal up before commencing the step rate
test. On very tight rocks, this could be several days.
The step rate test can also provide an indication of fracture toughness, at least in the
formation close to the wellbore. In theory, the difference between the extension pressure and
the closure pressure (usually obtained from the minifrac) is directly related to the fracture
toughness. However, it is also heavily influenced by wellbore orientation, perforation strategy
and the orientation and magnitude of the horizontal stresses.
15.2
The Step Down Test
This test is used to determine the nature of any near wellbore friction that may exist, i.e. to
see if it is perforation or tortuosity dominated. As the name suggests, the step down test is the
opposite of the step up test. Instead of starting at low rates and increasing, the rates are
started high and decreased.
Pressure
Tortuosity Dominated
Perforation
Dominated
Rate
Figure 15.2a – The step down test
When performing the step down test, it is important that the fracture is open the whole time,
otherwise the test is invalid. Therefore, this test is often carried out after a step up test. It is
not uncommon to step up then step down right after. Another factor to remember when
conducting a step down test is keeping the stages short as the rate is stepped down. Unlike
the step up test, which starts with no fracture and ends with an open fracture, the step down
test must be performed with the fracture open all the way through. Consequently, if the steps
down take too long, the fracture will close before the end of the test, making the low rate data
points invalid. 4 or 5 steps down, taking 10 to 15 seconds each, is all that is required. Also,
make sure that before starting the step down, that the fracture has been open for at least 5
minutes - the longer the better, as smaller fractures will close more quickly than larger
fractures.
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15. The Step Rate Test
Figure 15.2a shows the relationships between pressure and rate for the step down test. The
different shapes of the curves indicate how the near wellbore friction is dominated by the
perforations, by the tortuosity or by a combination of the two.
For perforation friction:Pnwb ∝
2
Q .................................................................................. (15.1)
In theory, perforation friction follows the same theory as flow through orifices, involving
Bernoulli’s Equation and stagnation pressure. Allowances have to be made for the diameter
of the perforation (assumed to be constant) and for the discharge coefficient (a measure of
how “smooth” the flow is as it goes through the orifice). The discharge coefficient is also
assumed to be constant. As a result, the pressure loss is proportional to the rate per
perforation, as illustrated in Equation 2.3. Generally, at this stage no significant volumes of
proppant have been pumped and so the assumption that perforation diameter is constant is
valid.
For tortuosity:Pnwb ∝
Q .................................................................................. (15.2)
In theory, for tortuosity dominated near wellbore friction, as the pumping rate increases, so
does the width of the near wellbore flow channels, as the width of these is dependent upon
pressure – the higher the rate, the higher the pressure and hence the greater the width. This
is why, for tortuosity, Pnwb does not increase as fast as rate.
In reality, the relationship between rate and near wellbore friction may be a lot more complex
than that suggested by Equation 15.2. Recent work by the GRI suggests that Pnwb may be
0.25
proportional to Q
rather than the square root of rate. On top of this, it is likely that the
relationship between Pnwb and Q is also controlled by the nature of the tortuosity, so that
different relationships exist for tortuosity generated by perforations, for tortuosity generated by
horizontal stress contrasts, or for tortuosity generated by wellbore deviation (to name but
three potential causes). To further complicate the situation, it is entirely possible that a well
could experience tortuosity that is a combination of two or more causes. However, in spite of
this complex relationship between pressure loss and rate, the geometry of the tortuosity will
always be pressure-dependent and hence under most circumstances the pressure-rate
crossplot will have the characteristic convex shape for tortuosity-dominated near wellbore
friction.
Of course, usually the near wellbore friction is a combination of perforation friction and
tortuosity. Although Meyer’s MinFrac minifrac analysis programme is not recommended by
the author, as it is based on a rather simplistic 2-D analysis, the step rate test analysis section
within MinFrac is excellent, especially for the step down test. It incorporates a feature that
allows the theoretical perforation friction to be backed out, allowing the user to view the total
tortuosity-based friction, regardless of the exact relationship between pressure loss and rate.
In addition, both MFrac and Fracpro (both versions) allow data from a step down test to be
input directly into the simulator, so that the model can allow for the effects of tortuosity related
pressure losses when calculating net pressure. However, given that most step rate tests are
performed using a different fluid to the actual treatment (slick water rather than crosslinked
gel), it must be remembered that the actual pressure loss will probably be greater than data
generated by the step rate test indicates.
15.3
Step Rate Test Example – Step Up/Step Down Test
The following data was taken from a step rate test in which the rate was stepped up and then
immediately stepped down again, using slick water. The data generated by the step rate test
is given in table 15.3a.
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15. The Step Rate Test
Figure 15.3a shows the step up pressure-rate crossplot. Figure 15.3b shows the step down
crossplot, whilst Figure 15.3c shows the same step down crossplot using surface pressure.
This illustrates why bottom hole pressure must always be used for step rate test analysis,
even if it has to be calculated from surface data.
Rate
bpm
STP
psi
BHTP
psi
0.5
0.9
1.0
1.2
1.6
2.0
2.3
3.2
4.2
5.2
6.3
8.4
10.2
11.8
8.4
6.3
4.2
2.0
2030
2310
2445
2600
2730
2850
2910
3120
3450
3780
4224
5290
6280
7281
5180
4160
3271
2580
5958
6211
6337
6474
6559
6623
6636
6671
6753
6783
6838
6996
7041
7076
6886
6774
6574
6353
Table 15.3a – Example step rate test data.
7200
7000
BHTP, psi
6800
6600
Fracture Extension = +/- 6570 psi
6400
6200
6000
5800
0
2
4
6
8
10
Slurry Rate, bpm
Figure 15.3a – Step up pressure-rate crossplot using the example data. This plot shows the
fracture extension pressure to be at +/- 6570 psi.
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12
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15. The Step Rate Test
7200
BHTP, psi
7000
6800
Tortuosity Dominated
6600
6400
6200
0
2
4
6
8
10
12
Slurry Rate, bpm
Figure 15.3b – Step down pressure-rate crossplot for the example data. The convex shape of the
curve indicates near wellbore friction dominated by tortuosity.
8000
7000
STP, psi
6000
5000
Perforation Dominated?
4000
3000
2000
0
2
4
6
8
10
12
Slurry Rate, bpm
Figure 15.3c – Step down pressure-rate crossplot for the example data, using surface treating
pressure (STP). This graph illustrates the danger of using STP for step rate test analysis, as in
this case, the near wellbore friction would have been incorrectly diagnosed as being perforation
dominated.
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15. The Step Rate Test
References
Lacy, L.L. and Hudson, H.G.: ”Step Rate Test Analysis for Fracture Evaluation”, SPE 29591,
presented at the SPE Rocky Mountain Region/Low Permeability Reservoirs Symposium,
Denver, Colorado, March 1995.
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Cleary, M.P.:, Johnson, D.E., Kogsbøll, H-H., Owens, K.A.: Perry, K.F., de Pater, C.J.,
Stachel, A., Schmidt, H., and Tambini, M.:” Field Implementation of Proppant Slugs to Avoid
Premature Screen-Out of Hydraulic Fractures with Adequate Proppant Concentration”, paper
SPE 25892, presented at the SPE Ricky Mountain Regional/Low Permeability Reservoirs
Symposium, Denver CO., April 1993.
Cleary, M.P., Doyle, R.S., Meehan, D.N., Massaras, L.V. and Wright, T.B.: “Major New
Developments in Hydraulic Fracturing with Documented Reductions in Job Costs and
th
Increases in Normalized Production”, SPE 28565, presented at the SPE 69 Annual
Technical Conference and Exhibition, New Orleans, Louisiana, September 1994.
Wright, C.A., Weijers, L., and Minner, W.A.: Advanced Stimulation Technology Deployment
Program, report GRI-09/0075, Gas Research Institute, March 1996.
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16. The Minifrac
16.
The Minifrac
The purpose of the minifrac is to provide the best possible information on the formation, prior
to pumping the actual treatment. Any time that the quality of information available for a frac
candidate is poor, a minifrac should be planned. This includes most wells, as it is not usual to
have detailed rock mechanical and leakoff data for a formation (and for the non-productive
formations surrounding the zone of interest). The only time a minifrac should not be pumped
is when there is reliable data available from offset wells that have been fractured (as is often
the case in the US).
The minifrac is designed to be as close as possible to the actual treatment, without pumping
any significant volumes of proppant. The minifrac should be pumped using the anticipated
treatment fluid, at the anticipated rate. It should also be of sufficient volume to contact all the
formations that the estimated main treatment design is anticipated to contact. A well planned
and executed minifrac can provide data on fracture geometry, rock mechanical properties and
fluid leakoff – information that is vital to the success of the main treatment.
16.1
Planning and Execution
Bottom Hole Data
Do whatever it takes to get bottom hole pressure data for the minifrac (and also for the step
rate test), as this is far more accurate than data calculated from the surface pressure. Bottom
hole data can be obtained using three acquisition methods:1.
2.
3.
Real Time Gauges. These can be run on wireline or can be part of the well’s
completion. These gauges allow both pressure and temperature to be recorded real
time at the surface. Usually, it is possible to run a data cable so that the pressure data
can be incorporated real time with the standard frac data already being recorded.
This is the best possible situation for the Frac Engineer.
Memory Gauges. These are gauges that are run in on wireline or slick line, and hung
in either a specially designed gauge carrier, or some other suitable position (such as
an empty gas lift mandrel). Alternatively, they can just be held on slick line at a
specific depth. After the mini-frac and the step rate test are completed, the gauges
are retrieved and the data is downloaded at the surface. This data is then merged
with the surface data that has already been collected. This is the most common
method of using gauges, even though there is a delay caused by the retrieval of the
gauges.
Dead String/Live Annulus. Both of these methods work on the same principle. With
the live annulus, the well is completed with tubing but no packer (or the packer has
not been set, or the packer is fitted with a circulating valve that is left open during the
treatment). Basically, the annulus is exposed to the BHTP during the treatment, and
shows a corresponding surface pressure. As the fluid is not moving in the annulus,
BHTP can be easily calculated, provided the density of the fluid in the annulus is
known. Most fracture monitoring programmes have the capability to perform this real
time. A dead string relies on the same principle, but instead employs a small diameter
tubing string, inside the actual treatment tubing. A common example of this is coiled
tubing placed inside a large diameter frac string.
Remember that it is more important to get downhole pressure data during the minifrac and the
step rate test, than it is during the actual treatment. Companies that supply gauges are often
reluctant to have proppant pumped past them (this also applies to wireline cables).
Consequently, it is common to have the gauges in the well for the minifrac and the step rate
test, and then retrieve them prior to pumping any proppant.
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16. The Minifrac
Most bottom hole pressure gauges also record temperature. This data, whilst not as important
as pressure data, can also be useful:1.
2.
3.
The data can provide a good check of the bottom hole static temperature, to ensure
that the correct temperature has been used for designing the fluid system.
The data can provide a good value for the bottom hole treating temperature. This is
especially important when performing treatments with nitrogen and/or carbon dioxide
and also for treatments where tubing shrinkage due to cooldown is critical.
If the gauges have been run on wireline or slick line, then it is possible to run the
gauges past the perforations after the minifrac and the step rate test, to perform a
temperature log. This is a plot of temperature against depth. By looking at how far
each the perforations have cooled down – and how this cooling down varies across
the perforated interval – it is possible to get a qualitative indication of where the fluids
are going and hence were the fracture(s) is(are) initiating.
Because the rheology of the fracturing fluid is constantly changing as the minifrac is being
pumped, and because the well is continually cooling down, calculated friction pressures can
often be unreliable. This in turn means that a BHTP calculated from a STP can also be
unreliable. This is why it is important to obtain reliable downhole data, from which to base the
frac design.
Fluid Volumes and Rates
Deciding what volume to pump for the minifrac can be difficult. Ideally, we wish to pump the
minimum volume necessary to gather accurate formation and fracture data. However,
remember that we are not just interested in getting data on the producing formation – we are
also after data on any formation above and below that may be contacted by the fracture. This
means that as a minimum, we must pump at least the two-thirds of the anticipated pad
volume. On low permeability wells we may have to pump significantly more than the pad
volume.
The best method to decide the minifrac volume, is to run a few simulations for the minifrac,
based on the data used to design the main treatment. Adjust the minifrac volume such that it
will contact all the formations that main treatment will contact.
As we are trying to create a treatment that is a close as possible to the actual treatment
(minus the proppant), the minifrac should be pumped at the same rate as the anticipated
treatment.
The minifrac should be displaced with slick water. The displacement volume should be
enough to displace the minifrac to just short of the perforations, to ensure that the near
wellbore fracture(s) close on frac fluid, rather than slick water. To do this, it is common to
under-displace by +/- 5 bbls.
Fluid Type
As stated above, we are trying to create a test that is as close as possible to the actual
treatment, minus the proppant. This means that the minifrac should use the same fluid as the
anticipated treatment. In fact, every step should be taken to ensure that the fluids used in the
minifrac and the main treatment are as identical as possible, so that fluid related data
gathered in the minifrac is as valid as possible for the main treatment.
Often, an operating company will suggest using slick water for the minifrac, as a way of
saving time and money. This is a false economy, as the subsequent minifrac will have only a
passing resemblance to the fracture that will be created by the main treatment. In particular,
the fluid leakoff will be (usually) significantly greater with slick water. This results in faster than
normal fracture closure, and smaller than normal fracture geometry.
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Recently, some Engineers have argued that because of the wall building effects of the fluid
used in the minifrac, the leakoff for the main treatment can be lower than that for the minifrac.
To compensate for this, increased breaker loadings are used in the minifrac.
Wellbore Fluid
Usually, there is some kind of fluid in the wellbore prior to the minifrac. Often, this fluid will be
slick water from the step rate test, or produced fluids. Unless this fluid can be circulated out of
the well ahead of the minifrac fluid, it will be injected into the formation as part of the minifrac.
Obviously, having two different fluid types in the fracture makes the job of analysing the
minifrac data that much more difficult, so every effort should be taken to minimise the volume
of fluid ahead of the minifrac fluid. On some wells, this can be achieved by circulating the
minifrac fluid into position. However, on most wells this cannot be done, and the Frac
Engineer has to live with the situation.
Pressure Decline
The data collected during the pressure decline (i.e. after the minifrac has been displaced and
the pumps are shut down) is just as vital as the data collected whilst pumping. It is therefore
important to monitor the pressure decline, sometimes for up to 2 hours after the minifrac is
completed. During this period, it is important that nothing is done to compromise the quality of
this data. Any opening or closing of valves, hammering on equipment or circulating of fluids
should be avoided at all costs. In particular (and this may sound obvious, but it does happen)
the wellhead should not be closed during this period. There should also be no pumping into
the annulus, as this will affect the tubing pressure. Once the Frac Engineer is sure that the
fracture has closed, the well can be shut in and normal activities resumed.
Proppant Slugs
Many Engineers prefer to pump a proppant slug in the minifrac. This is a proppant stage in
the middle of the minifrac, often containing as little as 500 lbs of proppant. This slug will test
the near wellbore region for tortuosity. Ideally, the proppant slug should pass into the
formation with no detectable pressure rise. If the pressure rises when the proppant flows into
the formation (and worse still, if it rises and does not come down again), then there is
restricted flow in the near wellbore region – tortuosity. A series of proppant slugs of increasing
concentration can be use to effectively diagnose the severity of a tortuosity problem. See
Section 10.1 for more details on tortuosity.
Multiple Minifracs
Some companies, especially those operating in high permeability formations, prefer to use
more than one minifrac. The first minifrac is designed to be small, to penetrate only into the
zone of interest and provide good leakoff and closure data on this formation. The second
minifrac is larger, designed to penetrate further and give a better idea of the overall fracture
geometry. Obviously, the use of two minifracs provides more data than just a single
treatment. However, in most cases this is probably not necessary. A well-designed and
executed treatment should be able to provide the Frac Engineer with all the necessary data.
However, there are cases when it is very difficult to interpret the minifrac data, through no
fault of the treatment. Some formations are just too complex to easily analyse. In such cases,
when the data from the first minifrac defies scrutiny, often the only way to proceed is to pump
a second minifrac, in the hope that this data will be better.
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16. The Minifrac
16.2
Anatomy of a Minifrac
Figure 16.2a shows a typical job plot from a minifrac:-
Pressure, Rate
BHTP
STP
Rate
Time
Figure 16.2a – Typical minifrac job plot, showing BHTP, STP and rate
Three important parameters are used – to a greater or lesser extent – in obtaining the
required data from the minifrac. The BHTP (ideally actual pressure data, rather than
calculated) is the main variable, as this tells us the way the fracture is behaving and the
amount of work being performed on the formation by the fluid (or visa versa). The rate is
important for determining the fracture geometry, as the volume of fluid pumped into the
formation, less the volume of fluid which has leaked off, is equal to the volume of the fracture.
In addition to these two parameters, the proppant concentration can also be important, if
proppant slugs have been pumped.
BHP
Shut
Down
Pressure
Decline
Start
Pumping
Time
Figure 16.2b – Expanded plot showing BHTP
Figure 16.2b shows an expanded portion of Figure 16.2a, giving the BHTP more detail.
Generally, a large number of minifracs will have this same basic shape, although by no
means all. The area between the start of pumping and the shut down is often shaped like this,
with the pressure declining initially and then increasing towards the end. In terms of Nolte
analysis (see Section 10.2), this means that the fracture is initially growing in a shape which is
radial or preferentially vertical (rather than horizontal), but after a period of time the height
growth becomes more controlled, and the preferential growth direction is horizontal.
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16. The Minifrac
16.3
Decline Curve Analysis
As soon as the pumps shut down, the pressure will start to decline. Initially, the net pressure
will still be positive, and the fracture may still propagate. However, as soon as the fluid input
into the fracture stops, the fracture will start to decrease in volume, as fluid is still leaking into
the formation. As the fluid volume in the fracture (and hence the volume of the fracture itself)
decreases, the fracture width also decreases until the fluid volume in the fracture is zero – the
fracture has closed.
The time taken for the fracture to close defines the rate at which the leakoff is occurring,
whilst the pressure at which the fracture closes (and the difference between the treating
pressure and the closure pressure) tells us how hard it will be to produce the required
fracture. Both of these parameters have been more rigorously defined in previous sections of
this manual, but suffice to say that they are both extremely important parameters for defining
the size and shape of the fracture.
A typical pressure decline curve is shown in Figure 16.3a.
BHTP
BHP
ISIP
Closure Pressure
Linear
Flow
Radial Flow
Time
Figure 16.3a – Typical minifrac pressure decline curve
It is possible to see several distinct features on this curve, although it must be emphasized
that Figure 16.3a is idealised and that actual minifrac pressure decline curves are rarely this
clear. Features which the Frac Engineer needs to identify include:1.
2.
BHTP – the actual bottom hole treating pressure. This is the pressure inside the well,
at the middle of the perforated section that is being treated. Ideally, this should be
measured via a gauge or a dead string.
ISIP – the instantaneous shut-in pressure, also referred to as the instantaneous shut
down pressure, or ISDP. This is the bottom hole treating pressure just after the
pumps shut down, and before the pressure the pressure starts declining. Often, this
point is hidden by noise generated by “pipe ring” as the pressure suddenly drops. In
that case, the decline curve has to be extrapolated backwards in order to find the
ISIP.
The difference between the ISIP and the BHTP is due purely to friction pressure loses in the
near wellbore area. Therefore, this difference can often be used as a quantitative assessment
of tortuosity.
3.
Closure Pressure, Pclosure, is the pressure at which the fracture closes, and is often
denoted by a change in gradient on the pressure decline curve. The difference
between the ISIP and the closure pressure is referred to at the net pressure, or Pnet
(see Sections 2.2 and 10.2). As discussed previously, the net pressure is a measure
of how much energy is being used to create the fracture and so is a very important
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16. The Minifrac
4.
parameter. However, it should be remembered that the net pressure will usually vary
throughout the treatment, and that this method only captures the net pressure right at
the end of the treatment. The closure pressure is also a measure of the in-situ
stresses in the formation (see Section 6, Rock Mechanics).
Closure Time. The closure time is the time taken for the fracture to close, after the
pumps have shut down. If the geometry of the fracture is known (or, more likely, can
be estimated from a model), then the volume of fluid in the fracture is also known.
Therefore, if the length of time taken for the fracture to close is also known, the rate at
which the fluid is leaking off can be easily calculated.
The are various different methods for helping the Frac Engineer pick closure pressure, as
often it is very difficult to spot the change in gradient on the pressure decline curve.
Additionally, there may be more than one closure pressure, if multiple fractures are closing.
Finally, the effects of tortuosity may mask the closure pressure, as there is evidence to
suggest that the tortuosity can, in some cases, close before the main part of the fracture.
Various Methods for Displaying Time
In order to help find the closure pressure(s) on the pressure decline curve, various methods
have been developed for plotting the data. Some of these will be described in more detail
below. As part of these methods, and for general information, there are various methods of
plotting time along the horizontal axis, listed in Table 16.3a, below:Description
Time, general
Data Time
Pump Time
Shut in Time
Delta Time
Square Root Time
Horner Time
Symbol
t
tdata
tp
ts
∆t
Nolte Time or Dimensionless
Time
Delta Nolte Time
Nolte G Time or G Function
tD
∆tD
G
or G(∆tD)
Equal to
Usually time since start of pumping
Time since data collection started
Length of time spent pumping
Time since ISIP
t - tp
0.5
t
tp + ts
log10
ts
t
tp
t - tp
t
= t -1
tp
p
Dimensionless function of ∆tD (see
below)
Table 16.3a – Table illustrating the various ways of calculating and using time during pressure
decline analysis.
Square Root Time Plots
According to Equation 2.9, the volume of fluid leaked off into the formation (and hence the
fracture volume) is proportional to the square root of time that the fracture has been open.
However, once the fracture is closed, the fluid is no longer leaking off from the fracture faces,
and is now leaking off according to Darcy’s radial flow law:q
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=
k h ∆P
µ ln (re/rw)
...................................................................... (16.1)
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where q is the leakoff rate, k is the permeability of the formation, h is the net height of the
formation, µ is the fluid viscosity, re is the radial extent of the formation, rw is the wellbore
radius and ∆P is the pressure differential between the formation and the wellbore. Therefore,
if a plot is made, showing BHP as the y-axis and square root time as the x-axis, the period
before fracture closes should have the pressure decline as a straight line. The point at which
the fracture closes is defined as the point at which the straight line starts to curve, as
illustrated in Figure 16.3b:BHTP
BHP
ISIP
Closure Pressure
Linear
Flow
Radial Flow
Square Root Time
Figure 16.3b – Use of a square root time plot to determine closure pressure.
Square root time plots are both the easiest to use, and the easiest to understand, of all the
pressure decline curve plots. However, their usefulness is limited by the ease with which
multiple fractures and tortuosity can mask and obstruct the point at which the flow regime
changes. The method is also dependent upon the reliability of Equation 2.9, which itself is an
approximation, assuming that leakoff is independent of pressure. However, because of its
ease of use, the square root time plot is usually the first stop in an often rather involved
process.
Horner Plots
Horner plots are taken directly from well test theory, and can very useful in helping to
determine closure pressure. However, these plots must always be used in conjunction with
other methods, as the Horner plot will only determine the lowest possible pressure at which
closure could have existed. In other words, it will give a lower boundary, above which the
closure must be found. Remember that the step rate test (step up variety – see Section 15.1)
will give an upper boundary, so that using these two methods in conjunction will provide a
region within which the closure pressure lies.
Horner plots work by plotting BHP on the y-axis and the Horner time on the x-axis. Horner
time is defined as follows:tHorner =
log10
tp + ts
................................................................. (16.2)
ts
According to Horner’s theory, on a plot of pressure against Horner time, pseudo-radial flow
(which, for our purposes, means flow when the fracture is closed) produces a straight line on
the plot, and non-pseudo-radial flow (i.e. the fracture is open) produces a curve. A typical
minifrac pressure decline Horner plot is shown in Figure 16.3c:-
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BHP
Closure Pressure
Pres
0
Horner Time
Figure 16.3c – Typical minifrac pressure decline Horner plot
As the minifrac pressure decline progresses, the BHP will eventually reach the reservoir
pressure, Pres. So, for Equation 16.2, as ts tends to infinity, the right hand side of the Equation
tends to zero. This means that if the pressure decline is extrapolated back to the point where
tHorner equals zero, the average reservoir pressure can be determined (also referred to as P*).
Nolte G Time Analysis
Below is a summary of Nolte’s work on G Time and minifrac analysis. A full derivation of the
method is beyond the scope of this manual, and the reader is referred to the references.
Nolte derived the following relationships for the decline curve:3/2
g(∆tD)=
3/2
4/3(1 + ∆tD) - ∆tD
-1
-1/2
1/2 ................................. (16.3)
(1 +∆tD)sin (1 + ∆tD) + ∆tD
where the upper part of the RHS represents the upper boundary and the lower part of the
RHS is the lower boundary. In practice, to find the actual value of g(∆tD), both values are
calculated, and an extrapolation is made based on the power law exponent of the fracturing
fluid (n’) and the fracture geometry (radial, PKN or KZD). Remember that when calculating
from the lower boundary, the trigonometrical function works in radians, not degrees.
The extrapolation is performed between two values of the variable α. At the lower boundary α
= 0.5 and at the upper boundary α = 1. The actual value for α is given as follows:α
α
α
=
=
=
(2n’ + 2)/(2n’ + 3)
(n’ + 1)/(n’ + 2)
(4n’ + 4)/(3n’ + 6)
- PKN ......................................... (16.4)
- GDK ......................................... (16.5)
- radial ........................................ (16.6)
The actual value of α used for the extrapolation is dependent upon the fluid efficiency and n’.
Values tend to be almost always in the region of 0.5 to 0.7, and in practice 0.6 is often used.
Also, given the fact that n’ is often variable, a quicker method is just to take the average of the
upper and lower expressions for g(∆tD). As shown in Figure 16.3d, as ∆tD increases, the
difference between the upper and lower boundaries becomes smaller and eventually
becomes negligible compared to the accuracy of the rest of the system:-
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5
4
3
g (∆ t D)
-1
-1/2
Lower (α = 0.5, g (∆t D) = (1 + ∆t D)sin (1 + ∆t D)
2
1
1/2
+ ∆t D )
g (∆t D = 0) = π/2
Upper (α = 1, g (∆t D) = 4/3[(1 + ∆t D)
g (∆t D = 0) = 4/3
0
0.01
0.1
3/2
3/2
- ∆t D ])
1
10
Dimensionless Time, ∆t D
Figure 16.3d – Graph showing the variation of g(∆
∆tD) with ∆tD.
Nolte G time is then a function of tD such that:G(∆tD) =
g(∆tD) – g(∆tD = 0) .......................................................... (16.7)
Note that for α = 1 and α = 0.5, g(∆tD = 0) is equal to 4/3 and π/2 respectively.
A typical plot of a pressure decline against Nolte G time is shown below in Figure 16.4e.
Additional Fracture Extension
Closure Pressure
BHP
“Ideal” ISIP
0
G(∆
∆tD)
Figure 16.3e – Typical Nolte G time pressure decline plot. The match pressure is the gradient of
the straight line section in the middle of the decline, before closure.
Figure 16.3e illustrates three important points. First, the ISIP recorded using field data may be
artificially high, due to the effects of fracture storage and fluid friction. Second, that there is a
period of constant gradient before the fracture closes, which is often referred to as the match
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pressure (Pm) and has pressure units (as G time is dimensionless). This is an important
parameter in Nolte’s minifrac pressure decline analysis. Finally, closure occurs when the
decline pressure deviates from this constant gradient. At this point G(∆tD) = Gc.
It should be noted that if the closure time equals the pump time, then Gc = 1.
From the g(∆tD) time at closure [ = g(∆tcD)], the fluid efficiency can be determined as follows:-
η
=
g(∆tcD) - g(∆tD = 0)
g(∆tcD)
1 - vprop
................................ (16.8)
1 - vprop/η
where vprop is the fraction of the total fracture volume occupied by proppant. For a minifrac,
vprop will be equal to zero. Therefore:-
η
=
This can be simplified to:-
η
≈
g(∆tcD) - g(∆tD = 0)
..................................................... (16.9)
g(∆tcD)
Gc
2 + Gc .......................................................................... (16.10)
which is a quick and easy method for determining fluid efficiency. Most modern real time data
monitoring systems can plot G-Function real time, so if the closure pressure can be
determined, the fluid efficiency can be easily calculated from Equation (16.10).
The fluid loss coefficient can be calculated as follows:Ceff =
Pmβs
X ..................................................................... (16.11)
rp tp E'
where Pm is the match pressure (see Figure 16.3e), βs a geometry-dependent factor (see
below), rp is the ratio of fracture area in permeable formation over total fracture area (i.e. net
to gross area ratio for the fracture), E’ is the plane strain Young’s modulus (see below) and X
is a factor dependent upon which geometry model is being used, such that for KZD, X = 2xf,
2
for PKN, X = hf and for radial, X = (32R/ 3π ).
βs
≈
(2n’+2)/(2n’+3+a)
0.9
2
(3π /32)
PKN
KZD ........................................ (16.12)
Radial
where n’ is the power law exponent for the fluid and a is a variable describing how constant
the viscosity of the frac fluid is in the fracture, such that for a constant viscosity, a = 1 and for
a falling viscosity a < 1. Usually, a is assumed to be 1. Finally, the plane strain Young’s
modulus can be easily calculated:E’
=
E
2 ........................................................................... (16.13)
1-ν
Thus, not only is Nolte G time a useful tool for finding the “ideal” ISIP and the closure
pressure, it can also be used to find fluid efficiency and fluid leakoff (provided a 2-dimensional
fracture geometry is assumed).
Finally, Nolte G time can be used to find the fracture dimensions:Af
=
(1 - η)Vi
2 g(∆tD = 0)Ceffrp
tp
................................................... (16.14)
Where Af is the area of one fracture wing and Vi is the total volume of fluid injected.
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Given that for the 2-D models:Af
=
2xfhf
2xfhf
2
πR
PKN
KZD ............................................ (16.15)
Radial
then the fracture length or fracture radius can be easily found. Average fracture width can
also be obtained:w̄
=
2 g(∆tD = 0)Ceffrp
(1 - η)
tpη
.................................................. (16.16)
Derivative Plots
When carrying out pressure decline analysis, a lot of time is spent trying to find various
changes in gradient on the curve, or points were the pressure decline changes from a straight
line to a curve (or visa versa). Therefore, it is often easier to spot these changes in gradient
by actually plotting the gradient - or derivative – itself.
On a derivative plot, a horizontal line (i.e. constant gradient) indicates a straight line on the
parent plot (not necessarily horizontal, however). Changes in gradient on the parent plot,
produce rapid changes in value on the derivative plot. An example is shown below in Figure
16.3f.
All of the main types of plots - and their derivatives - can be plotted by most modern fracture
simulators with the minimum of effort. Often, these plots can be displayed real-time by the
data acquisition systems. Consequently, there is always a temptation to stop recording data
too early – the Frac Engineer notices a change in gradient and assumes the fracture is
closed. This is not necessarily the case, and so it is important to keep recording data for as
long as feasible. It takes relatively little effort to record the data for an extra 10 minutes and a
lot of embarrassment can be avoided.
BHP
Derivative
0
d(BHP)
dtHorner
Closure Pressure
tHorner
Figure 16.3f – Example derivative plot based on a Horner Plot
16.4
Pressure Matching
Another method for analysing minifrac data, is to carry out a process known as a pressure
match (also referred to as a history match). In this process, the fracture simulator is “tuned”
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until the simulator’s predicted net pressure matches the actual net pressure. This “tuning”
process is carried out by adjusting variables such as Young’s modulus, Poisson’s ratio,
fracture toughness, stress gradient, near wellbore friction, leakoff rate, and spurt loss.
Pressure matching, which is discussed in more detail in Section 19, is a very powerful tool,
providing the user is aware of the limitations. The user is actually adjusting the computer
model to produce the same pressure response as the formation. Once the model has been
adjusted (the pressures have been “matched”), any potential treatment schedule can be run
on the simulator, and its effects assessed. This means that once the match has been made,
the Frac Engineer can very quickly adjust the treatment schedule to produce a fracture of the
required geometry.
Limitations of Pressure Matching
1.
2.
3.
Complexity. Because so many variables are adjusted, in so many different rock
strata, a Frac Engineer may often have to keep track of 20 or more variables. Each of
these variables can affect the overall outcome of the simulation. Therefore, a Frac
Engineer must remain aware of what variable changes and values are realistic and
what are not.
Non-Unique Solution. Because there are so many variables to adjust, it is quite
possible for 2 Frac Engineers to produce good pressure matches, using different
values. Often, these solutions will only produce similar net pressure responses for the
particular data set being analysed, so that when a different treatment schedule is
simulated (such as the actual treatment schedule to be pumped), two significantly
different fractures are generated. Which one is closest to the truth?
Data Quality and Model Inaccuracies. As with any type of computer analysis, the
results are only as good as the raw data (garbage in = garbage out). In particular,
errors generated by the use of surface pressure data to calculate BHTP can
sometimes render pressure matching almost ineffective. For instance, it is quite
possible to interpret a gradual rise in STP as good fracture containment, whereas in
reality it may have been caused by variations in fluid properties. Even if the quality of
data is good, the final result is only as good as the model itself. Just because a model
predicts a fracture that is 150 ft long and 100 ft high, doesn’t mean that this is what
happens in the ground. In fact, two different fracture simulators will almost always
produce different fractures, when fed the same input data. Again, which one is closest
to the truth?
The study of the theory of how the fracture models work will only get a Frac Engineer so far in
trying to solve these conundrums, especially as the companies responsible for the most
widely used fracture models do not publish significant parts of their theory. Unfortunately, in
this case there is no substitute for experience.
16.5
Near Wellbore Effects and Multiple Fractures
Most of the time, minifrac analysis is not simple. Often, it is not possible to find closure
pressure, or obtain a pressure match. More often that not, this is due to the effects of
tortuosity and/or multiple fractures.
Both of these concepts were explained in Section 10. However, it is worth discussing the
particular effects that these phenomena can have on minifrac analysis.
Tortuosity
As previously discussed in Section 10, tortuosity consists of a number a small, restricted, flow
channels in the near wellbore area, connecting the perforations to the fracture(s). Generally,
this phenomenon is detected by the pressure drop it produces whilst the frac fluid is being
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pumped. Obviously, it is much easier to detect and quantify tortuosity from bottom hole
pressure data, as pipe friction effects can easily mask its effect if surface pressure data is
used.
Tortuosity can confuse the results of a minifrac analysis in two ways:1.
The pressure drop produced by tortuosity represents a loss of energy from the
fracturing fluid. This means that the frac fluid does not have as much energy as the
pressure data indicates. The pressure inside the fracture remains the same,
irrespective of whether or not tortuosity exists, as the fluid flow rate out of the near
wellbore area is the same as the flow rate into it. As the inlet rate and fluid properties
going into the fracture are unchanged, so the fracture dimensions remain unchanged
and hence the net pressure remains unchanged. Tortuosity does not produce a lower
than normal pressure in the fracture – it produces a higher than normal pressure in
the wellbore. However, the effect of this is to lead the Frac Engineer into believing
that the pressure in the fracture is higher than it actually is. Consequently, the Frac
Engineer is led to believe that the fracture is significantly bigger than it really is, and
can be tempted to plan a treatment with larger volumes of proppant than can actually
be pumped into the fracture.
2.
Tortuosity can also cloud the interpretation of the minifrac pressure decline. The
channels which form the tortuosity are always significantly narrower than the main
fracture (otherwise they wouldn’t produce a pressure drop), and so can often close
entirely before the main fracture(s) itself closes. This means that the main fracture is
no longer hydraulically connected to the wellbore and so the actual closure pressure
can be very difficult to spot. In addition, the pressure at which the tortuosity closes
can itself cause a change in gradient on the pressure decline plot, causing a false
value to be selected for closure pressure, at a higher pressure.
The only way to allow for these effects is to be fully aware of the existence of tortuosity, and
to have some idea of its magnitude. The main ways of obtaining this information is to use
bottom hole pressure data, and to pump a step down test (see Section 15).
Multiple Fractures
The existence and causes of multiple fractures have already been discussed in some detail in
Section 10. Sufficient to say that under the right circumstances multiple fractures are not only
possible, they are likely.
Of course, the classic way to identify multiple fractures is to see two or more closure
pressures on a minifrac pressure decline curve. However, in reality this very rarely happens.
In order for multiple closures to be apparent on a decline curve, there must be significant
differences in the actual closure pressures of each individual fracture, otherwise they will
merge into one closure on the plot. Usually, the multiple fractures all exist in the same
formation(s) and so will close at approximately the same pressure.
The main problems for minifrac analysis associated with multiple fractures are as follows:1.
Although the multiple fractures will close at approximately the same pressure, they
will almost never close at exactly the same pressure. Variations in depth and bisected
formations will cause a variation that could be as much as 20 psi or more. This means
that when the fractures close, instead of a nice, easy-to-spot, change in gradient on
the pressure decline curve, there is a significant region where the gradient gradually
changes between the open fracture environment and the Darcy flow wellbore leakoff
environment. This “smudging” of the closure pressure can make it very hard to
identify.
2.
As discussed above, multiple fractures will usually close at around the same
pressure, allowing for the effects of variations in depth. However, they probably will
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not have similar fracture geometries, and so some fractures will be much larger than
others. As stated previously, the leakoff rate is proportional to the fracture area, whilst
the time taken for the fracture to close depends upon the fracture volume. For most
fractures, the area of the fracture faces is proportional to the square of the length,
whilst the volume of the fracture is proportional to the cube of its length. So a fracture
which is twice the length of another fracture will leakoff at four times the rate, but will
have eight times as much volume to lose before closure, so that the fracture takes
twice as long to close.
Therefore the bigger fractures tend to take longer to close than smaller fractures.
However, all of our fractures are connected hydraulically via the wellbore. We know
that our fractures will tend to close at the same time, because they will all have similar
closure pressures. Therefore, in order to prevent the smaller fractures closing
significantly before the larger fractures, there must be fluid flow from the larger
fractures to the smaller fractures, at a rate equal to the difference in leakoff rates. This
means that the smaller fractures have an artificially long closure time and the large
fractures have an artificially short closure time. In a situation where there are several
fractures, the flow dynamics can get very complex indeed.
This flow of fluids from one fracture to another, as well as the pulling in of extra fluid
from the wellbore, can produce complex shapes on the pressure decline curve. This
can make analysis very difficult.
16.6
Minifrac Example 1 - 2D Minifrac Analysis
The following minifrac treatment was pumped into an oil-bearing formation, located in South
Kalimantan, in the Indonesian part of island of Borneo. Bottom hole memory gauge data was
available. This example will demonstrate the use of the Nolte G Function analysis technique
to obtain the leakoff coefficient, closure pressure, and fracture geometry.
Well and Formation Data
Reservoir Type:
Reservoir Temperature:
Reservoir Pressure:
Perforations:
Deviation at Perforations:
Liner:
Treating String:
Packer set at:
End of Tubing:
Top of Formation:
Bottom of Formation:
Permeability:
Porosity:
Young’s modulus:
Poisson’s ratio:
Oil
145 F
unknown
986 m (3235 ft) to 1032 m (3386 ft)
Vertical
7”, 23#
3.5”, 9.3# tbg
940 m (3084 ft)
950 m (3117 ft)
986 m (3235 ft)
1032 m (3386 ft)
6 mD
18%
500,000 psi (assumed)
0.25 (assumed)
Treatment Data
Wellbore Fluid:
Treatment Fluid:
Treatment Volume:
Displacement Fluid:
Displacement Volume:
Treatment Rate:
Page 134
Slick water
(from step rate test)
Crosslinked gel
(SpectraFrac G 4500, n’ at BH = 0.65)
3
50 m (314 bbls)
Slick water
3
5.3 m (33.3 bbls)
3
3 m /min (18.8 bpm)
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4,000
40
Gauge BHTP
30
STP
2,000
20
Slurry Rate
1,000
Slurry Rate, bpm
Pressure, psi
3,000
10
0
0
0
10
20
30
40
50
60
Elapsed Time, mins
Figure 16.6a – Minifrac example 1 job plot.
We can see from Figure 16.6a that the treatment was well executed, with the rate staying
constant. The pressure was monitored for a significant length of time, probably longer than
necessary. However, it is better to record too much data than too little. Figure 16.6a actually
shows merged bottom hole gauge and surface data. This plot would not have been available
whilst the treatment was being performed.
Figure 16.6b shows the gauge BHTP pressure decline in more detail, whilst Figure 16.6c
shows the pressure against the square root of elapsed time.
3,300
Gauge BHTP, psi
3,100
2,900
2,700
2,500
2,300
10
20
30
40
50
60
Elapsed Time
Figure 16.6b – BH gauge pressure decline against elapsed time. Possible closure pressure at +/2770 psi (where the two red lines cross, marking a change in gradient). Note the sudden drop of
about 50 psi as the pumps shut down at t = +/- 13 mins.
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3,300
Gauge BHTP, psi
3,100
2,900
2,700
2,500
2,300
3.0
4.0
5.0
6.0
7.0
8.0
Square Root Time, mins1/2
Figure 16.6c – BH gauge pressure decline against the square root of elapsed time. Possible
closure pressure at +/- 2790 psi (where the two red lines cross, marking a change from straight
line to curve).
These two plots are basically in agreement – closure pressure at about 2780 psi. On both
plots we see a sudden drop of about 50 psi, as soon as the pumps shut down. This is almost
certainly due to near wellbore friction. This drop in pressure makes the true ISIP (the treating
pressure inside the fracture) difficult to spot exactly. However, 50 psi is quite low and is
unlikely to cause any problems as far as pumping the treatment is concerned (see later
example number 3 for a case where near wellbore friction did effect the treatment).
Figure 16.6d shows the G Function plot, which should enable a “true” ISIP to be determined,
by extrapolating the straight line back to the y-axis:3,200
3,100
Gauge BHTP, psi
3,000
2,900
2,800
2,700
2,600
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
G Function
Figure 16.6d – G function plot. The “true” ISIP is at +/- 3150 psi, whilst the closure pressure
appears to be at +/- 2780 psi (where the two red lines cross). This gives a Gc of 1.30.
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3,500
Gauge BHTP
3,200
2,900
2,600
2,300
2,000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Horner Time
Figure 16.6e – Horner plot. The results from this plot are ambiguous and do not help in the
analysis.
Figure 16.6e shows the Horner plot for the minifrac pressure decline. As can be seen, there is
no clear change in gradient from linear flow to pseudo-radial – several different points could
be picked. Therefore this plot is not much help in the analysis. This is a common
phenomenon in minifrac analysis – one plot being ambiguous, whilst others show clearer
results. This is one reason why the Frac Engineer must be familiar with the various types of
plots that exist. Most fracture monitoring and analysis software packages allow the user to
easily display several different types of decline curve.
Results of Graphical Analysis
There is a high degree of agreement between the pressure decline plot, the square root time
plot, and the G function plot. In fact, any experienced Frac Engineer reading this example
may find this data suspicious – minifracs are rarely this easy to interpret. However, this is real
data – later on we shall see an example from a similar formation that is much less easy to
analyse.
To summarise the results of the graphical analysis:ISIP
Closure pressure
Closure time
Pump Time
G function at closure, Gc
3150 psi
2780 psi
31 mins (elapsed time)
17.5 mins (shut in time)
13.5 mins
1.30
Nolte G Function Analysis
Assumptions
Radial geometry, initial fracture radius estimate 50 ft, initial rp estimate 1.0 (i.e. the fracture is
completely contained in the production formation).
1.
From Equation 16.10, we can find the fracture efficiency at pump shut down:-
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η
2.
1/2
0.00686 ft/min
=
2
20,147.56 ft
From Equation 16.16 we can get the average width of the fracture:w̄
5.
=
From Equation 16.14, we can find the area of the fracture:Af
4.
39.9%
From Equation 16.11, we can find the leakoff coefficient:Ceff
3.
=
=
0.604 inches
From Equation 16.15 we can obtain a revised value for the fracture radius:R
=
80.1 ft
Obviously, this final result is significantly different from the initial fracture radius estimate of 50
ft. They both cannot be right, and are in fact both wrong. In order to find the final answer, an
iterative process must be performed, bringing the initial and final values of the fracture radius
closer and closer together until the difference is negligible.
To start the first iterative step (in this example) steps 1 to 5 are re-worked using the average
of the initial and final values for R, 65 ft. Remember that our formation height is 118 ft – and
our fracture height is now 130 ft (2R). In this case of radial geometry, once the fracture height
exceeds the formation height, the ratio of net to gross area (rp) must be less than 1. With a
fracture radius of 6 5ft, rp can be calculated (using relatively simple geometry) as 0.967.
6.
Using a new initial R of 65ft and a rp of 0.967, we get the following result:-
η
Ceff
Af
w̄
R
=
=
=
=
=
39.4 %
1/2
0.00922 ft/min
2
15,498.13 ft
0.785 inches
70.2 ft
(unchanged, as this depends upon Gc only)
The iterative process continues until the difference between the initial and final values for R
are negligible. This gives the final minifrac analysis result:
η
Ceff
Af
w̄
R
=
=
=
=
=
39.4 %
1/2
0.00988 ft/min
2
14,728 ft
0.826 inches
68.4 ft
These values can now be plugged into the 2-D fracture simulator as the basis for a simulated
treatment with proppant.
Note that in order to obtain this result, both Young’s modulus and Poisson’s ratio have to be
assumed. In addition, it was also assumed that the formations above and below the zone of
interest had the same rock mechanical properties as the main zone. Finally, it was assumed
that each fluid that entered the formation had the same leakoff properties. These are the
limitations of using a 2-D model.
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16. The Minifrac
16.7
Minifrac Example 2 – 3D Pressure Matching with FracProPT
The next example was pumped in an offshore well in Vietnamese waters. The well itself was
an exploration well that was extensively tested before and after the treatment – and then
abandoned. The operating company wished to determine if hydraulic fracturing was a viable
field development technique.
Well and Formation Data
Reservoir Type:
Reservoir Temperature:
Reservoir Pressure:
Perforations:
Deviation at Perforations:
Casing:
Treating String:
Packer set at:
Ported XOver Sub:
Top of Formation:
Bottom of Formation:
Permeability:
Porosity:
Gas Condensate
249 F
unknown
3122 m (10,243 ft) to 3137 m (10,293 ft)
Vertical
9-5/8”, 47#
3-1/2”, DST string
3094 m (10,151 ft)
3098 m (10,164 ft)
3116 m (10,222 ft)
3143 m (10,312 ft)
na
na
Treatment Data – Step Rate Test
Wellbore Fluid:
Treatment Fluid:
Treatment Volume:
Treatment Rate:
Seawater
Slick Water (20 ppt GW-27)
3
2.4 m (15 bbls)
3
0.08 to 2.4 m /min (0.5 to 15 bpm)
Treatment Data - Minifrac
Wellbore Fluid:
Treatment Fluid:
Treatment Volume:
Displacement Fluid:
Displacement Volume:
Treatment Rate:
Slick water
(from step rate test)
Crosslinked gel
(SpectraFrac G 4500)
3
18.9 m (119 bbls)
Slick water
3
5.3 m (33.3 bbls)
3
2.4 m /min (15 bpm)
Step Rate Test
Figure 16.7a shows the job plot for the step rate test. We can see from this Figure that this
was not a particularly well executed step rate test – the rate, and hence the pressure, never
really stabilises for each of the steps. Nevertheless, Figure 16.7b does show quite a marked
change in gradient, indicating that the fracture extension pressure is around 8700 psi, which
gives a frac gradient of 0.85 psi/ft – quite high, but not unheard of.
Unfortunately, there is no step down portion for this step rate test. This is recommended in
any situation where tortuosity is suspected. As this was a formation that had never been
fractured before, it would have been prudent to perform the step down test.
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16. The Minifrac
10,000
20
Gauge BHTP
6,000
16
12
Surface Pressure
4,000
Rate, bpm
Pressure, psi
8,000
8
2,000
4
Slurry Rate
0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0
16.0
14.0
Elapsed Time, mins
Figure 16.7a – Minifrac example 2 step rate test job plot.
However it appears that in this case there are no indications of tortuosity, as the step rate test
pressure decline shows no immediate drop in bottom hole pressure as the pumps are shut
down.
Also note that the bottom hole pressure is taken from memory gauges mounted in the DST
string. Therefore, the frac engineer on site did not have access to this data.
10,000
9,000
Gauge BHTP, psi
8,000
7,000
6,000
5,000
4,000
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
Slurry Rate, bpm
Figure 16.7b – Step rate test crossplot for minifrac example 2, step rate test, showing fracture
extension at +/- 8700 psi.
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16. The Minifrac
Minifrac
Figure 16.7c shows the job plot for the minifrac. Execution for this treatment was not perfect,
with significant variations in rate throughout the treatment.
10,000
20.0
Gauge BHTP
8,000
16.0
Surface Pressure
6,000
12.0
4,000
8.0
2,000
4.0
0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Rate, bpm
Pressure, psi
Slurry Rate
0.0
40.0
35.0
Elapsed Time, mins
Figure 16.7c – Minifrac example 2 job plot.
11,000
Calc BHTP
10,000
Pressure, psi
9,000
Gauge BHTP
8,000
7,000
6,000
5,000
0
5
10
15
20
25
30
35
40
Elapsed Time, mins
Figure 16.7d – Comparison between gauge and calculated BHTP for minifrac example 2. Note
that whilst the calculated BHTP follows the same general trend as the gauge BHTP, the actual
value is quite different. Short term variations in the trend of the calculated BHTP are caused by
the variations in rate. The general offset of the data is probably caused by incorrect input data in
the fracture monitoring package (in this case FracRT).
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9,000
0
8,900
-100
8,800
-200
8,700
-300
8,600
-400
8,500
14.0
15.0
16.0
17.0
18.0
19.0
20.0
Derivative dBHTP/dT
Gauge BHTP, psi
Figure 16.7d compares the gauge BHTP with the calculated BHTP. In this plot, we can see a
significant variation between the actual BHTP and the calculated value. This plot is included
to make an important point – be aware that any data you receive can contain errors. In this
case, it looks as though the fracture monitoring software had the wrong data entered. If the
calculated BHTP data had been used by itself, it would have indicated a large amount of
tortuosity (note the large drop in pressure at ISIP). Remember that there is no step down test
to corroborate this. In fact, as we can see from the gauge BHTP, there is very little near
wellbore friction.
-500
21.0
Elapsed Time, mins
9,000
0
8,900
-1000
8,800
-2000
8,700
-3000
8,600
-4000
8,500
-5000
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
Square Root Time, mins1/2
Figure 16.7f – Minifrac example 2 pressure decline square root time plot, with derivative.
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Derivative dP/dT0.5
Gauge BHTP, psi
Figure 16.7e – Minifrac example 2 pressure decline with derivative.
BJ Services’ Frac Manual
16. The Minifrac
Figure 16.7e shows the pressure decline for minifrac example two, together with it’s
derivative. There are two clear features to be noted on this plot. First, there appears to be an
immediate pressure loss at ISIP of +/- 60 psi, which is probably due to tortuosity. Second, the
derivative plot shows a clear change in gradient at about t = 16.1 minutes, giving a closure
pressure of +/- 8725 psi (which corresponds closely with the fracture extension pressure from
the SRT). Note that this closure pressure would have been very difficult to spot without the
derivative plot.
Figure 16.7f shows the same pressure decline, but this time against the square root of time.
Once again, the derivative is included. This plot seems to indicate similar results to the
previous plot (Figure 16.7e), with the fracture closure happening perhaps a little more quickly
and at a slightly higher pressure.
Pressure Match
The pressure match was performed using Pinnacle Technologies’ FracProPT fracture
simulation software package. The first step in the process was to merge the surface data
(collected in this case by FracRT) with the bottom hole data. This was performed using the
data merging, conversion and editing functions of the software.
Once this had been accomplished, the model was run with the “run from database data”
option selected.
Table 16.7a shows the initial formation data used to produce the initial fracture design and to
provide a basis for the design of the minifrac. As we can see, the reservoir is very layered,
with lots of thins beds of different strata. In reality it is often not necessary – or practical – to
use this much definition when designing a fracture. However, it is included in this example to
illustrate the detail that can be used if necessary.
Depth
ft
Lithology
Stress
psi
Leakoff
Coefficient
-05
ft/min
Young’s
Modulus
6
psi x 10
Poisson’s
Ratio
Fracture
Toughness
0.5
psi.in
0
10220
10278
10284
10312
10320
10342
10368
10386
10420
10430
10456
10477
Shaley Sand
Shaley Sand
Sandstone
Shale
Sandstone
Shale
Sandstone
Shale
Sandstone
Shaley Sand
Sandstone
Shale
Sandstone
7120
7154
6372
7712
6393
7740
6412
7776
6439
7294
6467
7842
6496
0.0024
0.0024
0.0024
0
0.0024
0
0.0024
0
0.0024
0.0024
0.0024
0
0.0024
3.75
3.75
3.5
6.0
3.5
6.0
3.5
6.0
3.5
3.75
3.5
6.0
3.5
0.225
0.225
0.2
0.25
0.2
0.25
0.2
0.25
0.2
0.225
0.2
0.25
0.2
1500
1500
1000
2000
1000
2000
1000
2000
1000
1500
1000
2000
1000
Table 16.7a – Initial simulator data before pressure match.
Figure 16.7g shows the initial pressure match, using the original input data. As we can see,
there is a large difference between the actual data and the simulated data, especially with
regard to the stress data.
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16. The Minifrac
Offshore Vietnam
Initial Pressure Match
Slurry Flow Rate (bpm)
Simulated Net Pressure (psi)
20.00
5000
Observed Net (psi)
5000
16.00
4000
4000
12.00
3000
3000
8.00
2000
2000
4.00
1000
1000
0.00
0
0.00
4.00
8.00
Time (mins)
12.00
16.00
20.00
0
Figure 16.7g – Initial pressure match for minifrac example 2.
The first step is to increase the stresses in the formation to produce an approximate match at
ISIP. Once this has been done, the match looks better, but is still not complete (see Figure
16.7h).
Offshore Vietnam
Interim Pressure Match
Slurry Flow Rate (bpm)
Simulated Net Pressure (psi)
20.00
1000
Observed Net (psi)
1000
16.00
800
800
12.00
600
600
8.00
400
400
4.00
200
200
0.00
0
0.00
4.00
8.00
Time (mins)
12.00
16.00
20.00
0
Figure 16.7h – Interim pressure match after the stresses have had a first approximate
adjustment. In this case, the stress gradient for the sandstone was increased from 0.62 to 0.68
psi/ft, and then 1300 psi was added to each stress. Note that the pressures are on a larger
vertical scale than in Figure 16.7g.
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16. The Minifrac
From this, there are some important points to be noted:•
•
•
•
•
•
From the decline curve analysis, we know that the fracture closes at t = +/- 16 minutes at
a bottom hole pressure of +/- 8725 psi. In Figure 16.7h, the simulated net pressure shows
fracture closure at +/-16.5 minutes. This is close to reality. However, we must remember
that this will change as we alter other variables.
The shape of the simulated curve is close to the actual data to start with, but then
deviates from the gauge data. Variables such as Young’s modulus, fracture toughness
and stress will be changed for all formations in order to match this.
Remember that changes in leakoff coefficient will affect the shape of the curve as well.
From the decline analysis, we observed +/- 60 psi tortuosity/near wellbore friction. This
should be remembered when matching the pressures. It should also be remembered that
this may not be constant throughout the treatment.
When pressure matching, it is essential to be able to differentiate between short term
variations, and long term trends. In this example, it will be hard to adjust the model so that
the pressure will rise after +/- 7 minutes, as the actual data does. This point corresponds
to the time when the wellbore fluid has been completely displaced with crosslinked fluid,
and this fluid now starts to enter the formation. This could be a function of tortuosity –
which is very sensitive to fluid viscosity – or it could be a sign that the fracture has now
started to extend at a relatively higher rate.
Given that we have a decrease in pressure after +/- t = 10 minutes, it is possible that the
rise and then fall in pressure is due to near wellbore effects. However, the Frac Engineer
should closely examine the fluid samples and question both the blender tender and the
lab technician, as this variation could be due to a change in crosslinked fluid properties
(i.e. loss or reduction of crosslinker and/or buffer).
Figure 16.7i shows the final pressure match, after all the adjustments have been made to the
simulator model.
Offshore Vietnam
Final Pressure Match
Slurry Flow Rate (bpm)
Simulated Net Pressure (psi)
20.00
1000
Observed Net (psi)
1000
16.00
800
800
12.00
600
600
8.00
400
400
4.00
200
200
0.00
0
0.00
4.00
8.00
Time (mins)
12.00
16.00
20.00
0
Minifrac Example 2
Figure 16.7i – Minifrac example 2 final pressure match
Note that in Figure 16.7i, it proved very difficult to model the observed net pressure after the
crosslinked fluid entered the formation. As discussed previously, this is almost certainly due to
near wellbore and/or tortuosity effects. Note also that the pressure decline after shut down
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16. The Minifrac
does not have the same curve as the observed net pressure. However, it does have the same
closure pressure and closure time, implying that the fluid must be leaking off at the same rate.
Depth
ft
Lithology
Stress
psi
Leakoff
Coefficient
-05
ft/min
Young’s
Modulus
6
psi x 10
Poisson’s
Ratio
Fracture
Toughness
0.5
psi.in
0
10220
10278
10284
10312
10320
10342
10368
10386
10420
10430
10456
10477
Shaley Sand
Shaley Sand
Sandstone
Shale
Sandstone
Shale
Sandstone
Shale
Sandstone
Shaley Sand
Sandstone
Shale
Sandstone
8530
8720
8550
8780
8480
8690
8480
8730
8510
8740
8540
8790
8590
0.0015
0.0015
0.0033
0
0.0033
0
0.0033
0
0.0033
0.0015
0.0033
0
0.0033
6.0
6.0
1.5
1.0
1.5
1.0
1.5
1.0
1.5
6.0
1.5
1.0
1.5
0.225
0.225
0.2
0.25
0.2
0.25
0.2
0.25
0.2
0.225
0.2
0.25
0.2
1500
1500
500
2000
500
2000
500
2000
500
1500
500
2000
500
Table 16.7b – Final simulator data after pressure match.
In the actual pressure matching process, it became apparent that fracture only penetrated the
top five formations, as described in Table 16.7b, above. Therefore, the only changes that
made any difference to the simulation where those made to formations 1 through 5. In fact, as
far as the simulation was concerned, the bottom 8 formations didn’t need to be in the
simulator at all. Figure 16.7j shows the estimated fracture profile, as produced by the nowcalibrated fracture simulator. As we can see, the fracture grows preferentially upwards.
Fracture Profile
Stress Profile
10200
10220
10240
Depth (ft)
10260
10280
10300
10320
10340
10360
Permeability
10380
Low
10400
8000
High
8500
9000
Closure Stress (psi)
9500
10000
100
75
50
Propped Length (ft)
25
0
25
50
75
Hydraulic Length (ft)
Figure 16.7j – FracProPT estimated fracture dimensions for minifrac example 2.
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16. The Minifrac
In order to get the pressure match, 60 psi of tortuosity was used. This was kept constant,
throughout the simulation. However, it is possible that some of the changes in observed net
pressure are due to changes in near wellbore friction (NWF), rather than the response of the
formations themselves. Using a modern fracture simulator like FracProPT means that the
NWF, and especially the tortuosity, can be adjusted on a continuous basis. As a result, the
simulated net pressure can be made to fit any pressure match, just be adjusting NWF. This is
one of the disadvantages of using these advanced models. Because they have so many
factors that can be adjusted, it is possible to make the simulator match any pressure profile
desired. However, it is up to the user to be able to understand which changes to the model
are realistic, and which are not. A certain level of expertise, in both frac theory and in the way
the model itself works, is required before the simulator can be use reliably. These are
definitely not “expert” systems.
After the treatment was redesigned, the job was pumped successfully and 100,000 lbs of
20/40 CarboProp was paced in the fracture. Post-treatment DST testing showed an increase
in PI of between 4 and 7 times – the uncertainty being due to a leak in the DST string.
16.8
Minifrac Example 3 - Problems with Tortuosity
This well, which is located in the same field as Minifrac Example 1 (although in a different,
slightly deeper formation), had a completely different response to the minifrac. Severe
problems were encountered with the formation’s response to the minifrac. Although efforts
were made to mitigate this, resources and expertise on location were limited, and the job
eventually screened out about two thirds of the way through the treatment.
Well and Formation Data
Reservoir Type:
Reservoir Temperature:
Reservoir Pressure:
Perforations:
Deviation at Perforations:
Liner:
Treating String:
Packer set at:
End of Tubing:
Top of Formation:
Bottom of Formation:
Permeability:
Porosity:
Oil
145 F
unknown
1121 m (3678 ft) to 1130 m (3707 ft)
Vertical
7”, 23#
3.5”, 9.3# tbg
1105 m (3625 ft)
1115 m (3658 ft)
1121 m (3678 ft)
1157 m (3796 ft)
30 mD
20%
Treatment Data
Wellbore Fluid:
Treatment Fluid:
Treatment Volume:
Displacement Fluid:
Displacement Volume:
Treatment Rate:
Produced Fluids
Crosslinked gel
(SpectraFrac G 4500)
3
45 m (314 bbls)
Slick water
3
5.3 m (33.3 bbls)
3
3 m /min (18.8 bpm)
Figure 16.8a shows the treatment plot for this minifrac. This is a well executed minifrac. There
is a slight spike in the rate, as it is being increased initially, but this is not significant. The
major point of interest, however, is the large pressure drop in the gauge BHTP just as the
pumps are shut down. This is shown in Figure 16.8b, which displays more detail of the BHTP
at shut down.
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16. The Minifrac
5,000
25
Slurry Rate
4,000
20
3,000
15
Surf. Press.
2,000
10
1,000
5
0
Rate, bpm
Pressure, psi
Gauge BHTP
0
0
10
20
30
40
50
60
Time, mins
Figure 16.8a – Minifrac example 3 treatment plot.
3,500
A
Gauge BHTP, psi
3,200
B
2,900
E
D
2,600
C
2,300
2,000
10
15
20
25
30
35
40
Time, mins
Figure 16.8b – Minifrac example 3, detail of post-treatment pressure decline.
Figure 16.8b shows 5 main points of interest, labeled A to E as follows
A
B
Initial pump shut down.
Note how the pressure drops immediately by 400 to 500 psi as soon as the pumps
shut down. This is due entirely to near wellbore friction. A step down test would be
required to tell for sure if this was due to perforation friction or tortuosity, but this was
not performed. However, as the zone had been re-perforated just prior to the minifrac,
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16. The Minifrac
it is likely that this pressure drop is due to tortuosity. This pressure drop is very large
and is an immediate cause for concern.
This point shows a clear change in gradient at +/- 2350 psi and is almost certainly
fracture closure.
This area of the plot is unusual. It is rare (but not unknown) to see a post treatment
pressure decline of this shape – especially as the decline actually increases for a
short period of time. This area of the plot is probably caused by poor communication
between the fracture and the wellbore, and is potentially another sign of tortuosity.
Point E, obtained by extrapolating the straight line pressure decline back until it gets
to the point at which the pumps were shut down, is probably a good approximation for
the true ISIP. A G function plot will be used to confirm this.
C
D
E
A post treatment pressure decline like Figure 16.8b should set alarm bells ringing in the head
of any experienced Frac Engineer. It is obvious that there is a severely restricted flow path in
the near wellbore area. This means that the net pressure, which initially appears to be +/- 900
psi, is in fact probably less than half of this. This in turn means that the fracture is
substantially smaller than it initially appears to be. In addition, the restricted flow paths
between the fracture(s) and the wellbore, will make it very difficult to place even moderate
concentrations of proppant.
Figure 16.8c shows the square root of time pressure decline plot. This plot shows a high
degree of similarity with the pressure decline plot in Figure 16.8b. On this plot, with a slightly
expanded vertical scale, the closure can be seen to be around 2320 psi.
3,200
3,000
Gauge BHTP, psi
2,800
2,600
2,400
2,200
2,000
4
4.5
5
5.5
6
6.5
7
Square Root Time, mins1/2
Figure 16.8c – Minifrac example 3, square root time pressure decline plot.
Figure 16.8d shows the Horner plot for the pressure decline. This plot is a little ambiguous,
with potentially two or three different gradients and y-axis intercepts. Consequently, this plot
will only be used if the other plots prove to be unreliable.
In order to help verify both the closure pressure and the true ISIP, a G function plot is used,
as shown in Figure 16.8e. Obviously, to do this we must assume a 2-D geometry. In this
case, radial geometry was assumed. However, the fact that the plot is based on 2-D geometry
does not detract from its ability to pick the true ISIP, and the closure pressure will also be
reasonably reliable.
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16. The Minifrac
2,800
Gauge BHTP, psi
2,600
2,400
2,200
2,000
1,800
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Horner Time
Figure 16.8d – Horner plot for minifrac example 3. Note that several lines may be fitted to the
final slope on the LHS of this plot. In fact, the reservoir pressure is substantially lower than that
indicated on the plot (as the well is produced by ESP’s), so all of these lines may be unreliable.
3,000
Gauge BHP, psi
2,800
2,600
2,400
2,200
2,000
0
0.5
1
1.5
2
2.5
G Function
Figure 16.8e – G Function plot for minifrac example 3. Note the true ISIP of +/- 2730 psi, and the
closure pressure of +/- 2320. These values are in agreement with the value obtained from other
plots, such as the pressure decline and the square root time plots.
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16. The Minifrac
Pressure Match with MFrac 3-D Fracture Simulator.
After the data was imported into the MFrac 3-D fracture simulator, via the data collection
programme MView, an initial run was performed to see how close the initial, pre-minifrac
fracture model was. The results are shown in Figure 16.8f, above.
Bottomhole Treating Pressure
20
BHTP
Measured BHTP
Measured Surface Rate
BHTP (psi)
4000
16
3500
12
3000
8
2500
4
2000
0
10
20
30
Time (min)
40
50
Rate (bpm)
4500
0
60
Figure 16.8f – MFrac output showing the initial pressure match before any adjustments were
made. There is very little agreement between the predicted and actual BHTP’s.
As can be seen in Figure 16.8f, to begin with there is very little agreement between the initial
fracture model and the actual response of the formation. Remember also that the BHTP is
from a gauge. We can see that the slope of the pressure decline is significantly different,
indicating (in this example), that the actual fluid loss rate was somewhat faster than predicted.
In addition, the pressures predicted whilst pumping are completely different both in magnitude
and in the trend that they follow. Clearly, this model needed significant adjustment. This is
why we perform minifracs.
The effects of tortuosity also manifest themselves on this plot. We can see that, because of
the huge pressure drop as the pumps shut down, the model predicts lower pressures whilst
pumping and higher pressures during the decline.
Obviously, some allowance needs to be made in the model for the tortuosity. It is at this point
that experience and intuition start to take over. The fact is, tortuosity is not necessarily
constant throughout the treatment. The fall in measured BHTP that we see whilst pumping
could be due entirely to a continuous decrease in near wellbore tortuosity. Or it could be due
to a reduction in perforation friction as more perforations are opened up. Worse still, it could
be due to a combination of tortuosity, perforation friction and fracture geometry effects.
However, three other factors help the Frac Engineer. Firstly, we need to remember that we
have pumped no proppant and we have kept the rate constant. Changes in tortuosity are
usually (but not always) associated with either a change in rate, or the action of the proppant.
Secondly, changes in tortuosity (other than those associated with rate) tend to produce rapid
changes in the BHTP (“spikes” and “dips”), rather than slow, smooth changes. Lastly, the
zone had just been re-perforated prior to the treatment, and probably had very low perforation
friction (although this cannot be guaranteed – perforating does go wrong occasionally).
Therefore, it is probably a reasonable assumption that – in this case - the pressure loss due
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16. The Minifrac
to tortuosity is relatively constant. However, the Frac Engineer must be aware that this is not
necessarily the case.
Bottomhole Treating Pressure
3500
20
BHTP (psi)
BHTP
Measured BHTP
Measured Surface Rate
15
3000
10
2500
5
2000
0
10
20
0
40
30
Time (min)
Rate (bpm)
4000
Figure 16.8g – Final MFrac output, after the model has been adjusted.
In Figure 16.8g, we can see the results of the pressure match. The match is not perfect, but is
pretty close. At the beginning of the treatment, the initial pressure spike has not been
matched. Later on, at the start of the pressure decline, matching the shape of the curve
proved to be very difficult. In this area, the general trend has been matched, whilst the curve
has not. The effects of the poor communication between the fracture(s) and the wellbore are
very difficult to model mathematically. The changes made to the model are listed in Table
16.8a.
Formation
Property
Upper Shale
Sandstone
Lower Shale
Before
After
Before
After
Before
After
0.75
0.62
0.70
0.62
0.75
0.62
Young’s modulus, psi x 10
0.6
0.3
0.4
0.3
0.6
0.3
Poisson’s ratio
0.25
0.25
0.25
0.25
0.25
0.25
1000
1000
1000
7500
1000
1000
0.0004
0.0004
0.007
0.015
0.0001
0.0001
na
na
0
550
na
na
Stress Gradient, psi/ft
6
1/2
Fracture Toughness, psi in
-1/2
Leakoff Coefficient, ft min
Tortuosity ∆P, psi
Table 16.8a – Changes made during the pressure matching process.
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Treatment Results
The fact that we now have a reasonable pressure match does not alter the fact that it will be
very difficult to place the treatment. The pressure drop due to tortuosity is very large. This
means that it will be very difficult to place proppant inside the fracture – it will almost certainly
bridge off in the near wellbore area. Therefore, the tortuosity needs to be removed. The
processes for doing this were described in Section 10.1, and were originally detailed by
Cleary et al in SPE 25892 and Køgsball et al in SPE 26796.
In fact, the normal process to cure tortuosity – such as pumping a series of proppant slugs –
were not an option in this instance. The well was drilled in a remote location and the expertise
necessary for such an operation was not available on location. In addition, the operating
company was not willing to go through the potentially lengthy processes needed – the
economics of the situation demanded low cost treatments, in order for them to be justifiable.
In the end, it was decided to place a +/- 6 ppa proppant slug in the middle of the pad, and
observe what happened as it went into the formation. If a significant pressure rise was
observed, the plan was to shut down and re-assess the situation.
In fact, the well screened out as soon as the proppant slug hit the perforations.
However, once the pressure had fallen and more fluids had been mixed, it was possible to
break down the formation again and re-start the treatment. This time, the well treated at a
significantly lower pressure – indicating that the proppant slug may have helped to remove
some of the tortuosity.
As it turns out, not all of the tortuosity was removed. The treatment screened out at 8 ppa,
with 35,000 lbs of the planned 50,000 lbs placed in the formation. The rapid pressure rise
associated with the screenout indicated a near wellbore event. However, the operator
considered this a success – given the circumstances – and the production increase more than
justified the expense of the treatment.
16.9
Minifrac Example 4 – Perforation Problems
This minifrac was carried out on a well in New Zealand, using an oil-based fracturing fluid. Oilbased fracturing fluids are harder to pressure match, as there is less data available on items
such as the wall-building coefficient and tubing friction. The properties of these fluids are
highly dependent upon the hydrocarbon used as the base for the fluid. Even fluids mixed with
diesel show a marked variation in properties, when using with different sources of diesel. Prejob testing is essential.
Luckily, on this treatment, bottom hole pressure gauges were used, allowing uncertainties due
to tubing friction to be eliminated.
New Zealand, as far as the fracturing industry is concerned, is a remote location and the
success or failure of these treatments depended as much upon the logistics and organisation
of the operations, as it did upon the formation or the skill of the crew.
Well and Formation Data
Reservoir Type:
Reservoir Temperature:
Reservoir Pressure:
Perforations:
Deviation at Perforations:
Casing:
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Gas
185 F
5200 psi
3397 m (11,145 ft) to 3407 m (11,178 ft)
Vertical
7”, 23#
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Treating String:
3.5”, 9.3# tbg to 3342.6 m (10,966 ft)
2 ”, 6.5# tbg to 3379 m (11,086 ft)
3343 m (10,968 ft)
3379 m (10,966 ft)
3397 m (11,145 ft)
3407 m (11,178 ft)
12 mD
n/a
Packer set at:
End of Tubing:
Top of Formation:
Bottom of Formation:
Permeability:
Porosity:
Treatment Data
Original Wellbore Fluid:
Treatment Fluid:
Formation water and gas
Crosslinked gelled diesel
(Super Rheogel 500)
3
237 m (1488 bbls)
Diesel + surfactant
3
15.3 m (96.1 bbls)
3
2.4 m /min (15 bpm)
Treatment Volume:
Displacement Fluid:
Displacement Volume:
Treatment Rate:
First Step Rate Test
The first step rate test was pumped using diesel with surfactant. Initially, a wellbore volume
was pumped ahead, to ensure that no gas remained in the well. Then the pumps were shut
down for 15 minutes, to ensure that the effects of this injection did not cloud the results of the
step rate test.
It should be remembered that on location, the first step rate test was followed immediately by
the minifrac, and neither where analysed until later on, after the BH gauge data had been
retrieved. Therefore, the results of the step rate test were not available before the minifrac
was pumped. The significance of this will become apparent as we progress.
Figure 16.9a shows the job plot for the first step rate test, Figure 16.9b shows the step up
crossplot and Figure 16.9c shows the step down crossplot.
12000
12
10000
10
Gauge BHTP
8
6000
6
Slurry Rate
4000
4
Surface Pressure
2000
2
0
0
0
10
20
30
40
50
60
70
80
Elapsed Time, mins
Figure 16.9a – Job plot for Minifrac Example 4, Step Rate Test 1
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90
Slurry Rate, bpm
Pressure, psi
8000
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16. The Minifrac
11000
Gauge BHTP, psi
10000
9000
Fracture Extension at +/- 9100 psi
8000
7000
6000
0
1
2
3
4
5
6
7
8
9
10
Slurry Rate, bpm
Figure 16.9b – Step up crossplot for Step Rate Test 1. Fracture extension seems to be at
approximately 9100 psi.
The step rate test was executed reasonably well, except for one mishap when bringing an
additional pump in line, when going for 10 bpm. The results from the analysis of the step up
crossplot, indicate a fracture extension of 9100 psi. This gives an extension gradient of 0.82
psi/ft – high, but not exceptionally so.
However, the real problems show themselves in Figure 16.9c – the step down crossplot. This
plot clearly shows the characteristic shape of perforation friction.
10500
Gauge BHTP, psi
10200
9900
9600
9300
9000
0
1
2
3
4
5
6
7
8
9
10
Slurry Rate, bpm
Figure 16.9c – Step down crossplot. Note the concave shape of the best fit curve, indicating that
the near wellbore friction is dominated by the perforations.
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Minifrac
12000
18
Gauge BHTP
15
Pressure, psi
8000
12
Surface Pressure
6000
9
Slurry Rate
4000
6
2000
Rate, bpm & Proppant Conc, ppa
10000
3
Proppant Conc
0
0
0
10
20
30
40
50
60
70
80
90
Elapsed Time, mins
Figure 16.9d – Minifrac Example 4 job plot.
The minifrac was pumped directly after the step rate test, before any analysis was carried out
on the step rate test data. Initially, the minifrac was programmed at 8 bpm and without a
proppant slug. However, previous experience had shown that these formations were subject
to tortuosity, and so it was decided to include the proppant slug, to assess how conductive the
near wellbore region was. Figure 16.9e shows what happened when the proppant slug arrived
at the formation. Note that this plot shows bottom hole proppant concentration.
10000
20
16
Slurry Rate
Pressure, psi
Gauge BHTP
9200
12
+/- 400 psi Pressure Rise
as Proppant Reaches Perfs
8800
8
8400
Rate, bpm & Proppant Conc, ppa
9600
4
Bottom Hole
Proppant Conc
8000
0
30
31
32
33
34
35
36
37
38
39
40
Elapsed Time, mins
Figure 16.9e – Detail of job plot showing bottom hole proppant concentration, gauge BHTP and
slurry rate, as the proppant slug enters the formation. Note the +/- 400 psi rise in pressure.
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16. The Minifrac
From Figure 16.9e, we can see a +/- 400 psi pressure rise as the proppant enters the
formation. This is not good, and indicates that we will not be able to get even moderate
proppant concentration slurries into the formation.
9500
Gauge BHTP, psi
9200
+/- 650 psi Near Wellbore Friction
8900
8600
Fracture Closure at +/- 8350 psi (0.75 psi/ft)
8300
8000
48
50
52
54
56
58
60
62
64
66
68
Elapsed Time, mins
Figure 16.9f – Minifrac pressure decline, showing +/- 650 psi near wellbore friction and a closure
pressure of +/- 8350 psi.
8800
Gauge BHTP, psi
8600
8400
Fracture Closure at +/- 8230 psi (0.74 psi/ft)
8200
8000
7800
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Square Root Time, mins0.5
Figure 16.9g – Square root of time plot for the minifrac pressure decline. This gives a slightly
lower closure pressure than Figure 16.9f, at +/- 8230 psi.
Figure 16.9f show the ISIP and pressure decline after the minifrac. As we can see, this also
does not look good. Immediately, we can see a +/- 650 psi pressure drop as the pumps are
shut down. This can only be due to near wellbore friction, as we are using gauge bottom hole
treating pressure. This result, together with the result from the step down test, indicates that
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16. The Minifrac
this well has severely restricted perforations. As a result of this analysis, the decision was
made to re-perforate and run another step rate test. We can also see a closure pressure of +/8350 psi, which is slightly different from the closure seen in Figure 16.9g, the square root of
time pressure decline plot. This gives a lower closure pressure of +/- 8230 psi. These closure
pressures translate to gradients of 0.748 and 0.739 psi/ft (16.9 to 16.7kPa/m) respectively.
Second Step Rate Test
10000
20
Gauge BHTP
16
Surface Pressure
6000
12
4000
Rate, bpm
Pressure, psi
8000
8
Slurry Rate
2000
4
0
0
0
5
10
15
20
25
30
35
40
45
50
Elapsed Time, mins
Figure 16.9h – Job plot for second step rate test.
9400
Gauge BHTP, psi
9200
9000
8800
8600
0
2
4
6
8
10
Slurry Rate, bpm
Figure 16.9i – Step down crossplot for the second step rate test.
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16. The Minifrac
The second step rate test was performed after the well was re-perforated. Originally, the
intent had been to re-perforate the entire 10 meter section of (original) perforations. However,
on entering the well, the wireline operators indicated that there was some kind of fill in the
well, sufficient to block access for the perforating guns to the lower 7 meters of perforated
interval. The decision was made on location to shot holes in the upper 3 meter section only.
After perforating the upper 3 meters of the zone, the BH pressure gauges were re-run into the
well, and the second step rate test was performed. Figure 16.9h shows the job plot for this,
whilst Figure 16.9i shows the step down crossplot.
By comparing Figures 16.9c and 16.9i, we can see that the near wellbore situation has
changed dramatically:1. The slope of the best fit curve as changed from concave (perforation dominated) to
convex (tortuosity dominated).
2. The overall bottom hole pressure has dropped significantly. At 8 bpm, the first step rate
test shows a BHTP of +/- 9950 psi, whereas at 8 bpm in the second step rate test, the
BHTP is +/- 9270 psi.
So, as a result of the re-perforation, the restricted perforations have been removed (actually,
by-passed) and the overall level of near wellbore friction appreciably reduced.
Minifrac Pressure Match
The minifrac was performed before the well was re-perforated, and so still includes the effects
of the restricted perforations. MFrac was used for this pressure match. Figure 16.9j shows the
predicted and actual bottom hole treating pressures before the pressure match was
performed, whilst the post pressure match pressures are shown in Figure 16.9k.
This treatment was difficult to pressure match, largely due to the dynamic nature of the
restricted flow path in the near wellbore. As we can see from Figure 16.9k, the early part of
the treatment, at the lower rate, was not matched. In fact, the only part of the treatment that
could be matched was after the proppant slug had entered the formation.
Consequently, because of the unreliable nature of the data and the analysis, the final design
had to be pretty cautious.
Figure 16.9j – Minifrac Example 4 BHTP plot before pressure matching.
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Figure 16.9k – Minifrac Example 4 pressure match using MFrac.
The minifrac was performed before the well was re-perforated, and so still includes the effects
of the restricted perforations. MFrac was used for this pressure match. Figure 16.9j shows the
predicted and actual bottom hole treating pressures before the pressure match was
performed, whilst the post pressure match pressures are shown in Figure 16.9k.
This treatment was difficult to pressure match, largely due to the dynamic nature of the
restricted flow path in the near wellbore. As we can see from Figure 16.9k, the early part of
the treatment, at the lower rate, was not matched. In fact, the only part of the treatment that
could be matched was after the proppant slug had entered the formation.
Consequently, because of the unreliable nature of the data and the analysis, the final design
had to be pretty cautious.
Stresses
Young’s Modulus
Leakoff
Perforations
Total NWB Friction
All the formations’ stresses had to be significantly increased.
All the formations’ moduli had to be significantly decreased.
The only way the leakoff could be matched to allow significant fluid
loss through the shale formations above and below the zone of
interest.
The initial model had 170 x 0.3” perforations. Obviously, with 7m of
the 10 m covered by fill, this number had to be reduced. However, in
order to get a pressure match, the perforations had to be modeled as
1 x 0.07”! This was the only way that the BHTP during the change in
rate at t = 46 minutes could be matched.
In addition to the restricted perforations, an extra 600 psi in near
wellbore friction had to be added, in order to match the pressure drop
as the pumps were shut down.
It is unlikely that the perforations had been reduced to the equivalent of one 0.07” diameter
perforation. For one thing, the average grain diameter of 20/40 Carbolite (the proppant used
in the proppant slug) is 730 microns or 0.029” (from manufacturer’s data). Thus, the
perforation opening is less than 2.5 times the median grain diameter. It is probable that a 4
ppg proppant slug would have blocked this off.
The simulator results also show that the overall near wellbore friction Figure is probably a
result of a combination of poor perforations and tortuosity.
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16. The Minifrac
This illustrates the two sides of using simulator. On one hand it is clear that we have very
restricted perforations and that something should to be done about this. (However, we
probably could have worked this out without the simulator, based on the step down test and
the pressure drop at the end of the minifrac.) On the other hand, the extent to which the
perforations are blocked is probably exaggerated by the simulator. Good engineering
judgement, based on experience and knowledge of the underlying theories, needs to be
applied in order to decide what is realistic and what is not.
As a consequence of the restricted near wellbore situation, and the fact that the well was reperforated, much of the data used to produce the pressure match is not relevant to the main
treatment design. Only the fluid leakoff data and – to a lesser extent – the stresses and
moduli – can be used. For modeling the final treatment, the perforation data was re-set to fifty
0.3” diameter holes, and the total near wellbore friction reduced to 200 psi (based on the
second step rate test). In an ideal world, where the Frac Engineer has a free hand with regard
to technical issues, the minifrac should have been repeated. In reality, it was not repeated, for
a variety of reasons.
Main Treatment
Although the re-perforating had dramatically improved the near wellbore situation, it was clear
that there were potentially still some problems with tortuosity. Without a minifrac, complete
with proppant slug, it was difficult to assess just how bad this problem was. Consequently, the
main treatment was designed with three proppant slugs in the pad.
1.
2.
3.
100 mesh sand at 1 ppa.
20/40 Carbolite at 4 ppa.
20/40 Carbolite at 6 ppa.
These stages were spaced out so that the effect of each one could be assessed before the
next one arrived at the perforations. Based on the response of the formation to these stages,
the treatment would be redesigned on the fly.
Figure 16.9l shows the main treatment job plot and Figure 16.9m shows a detail of the bottom
hole sand concentration as the 3 proppant slugs arrive at the formation hole sand
concentration as the 3 proppant slugs arrive at the formation.
10000
25
Calculated BHTP
20
Pressure, psi
Slurry Rate
6000
15
Surface Pressure
4000
10
2000
5
Proppant
Concentration
0
0
20
40
60
80
100
120
0
140
Elapsed Time, mins
Figure 16.9l – Job plot for the main treatment for Minifrac Example 4. Note the proppant
concentration is measured at the surface.
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Rate, bpm & Proppant Conc, ppa
8000
BJ Services’ Frac Manual
16. The Minifrac
8000
25
7600
20
7200
15
Slurry Rate
6800
10
Surface Pressure
6400
Rate, bpm & Proppant Conc, ppa
Pressure, psi
As we can see, there was very little response from the formation as these three stages went
through the perforations. On the basis of this, it was decided to continue with the treatment as
planned. As the job progressed, it became apparent that the proppant was entering the
formation very easily. Originally, the treatment had been planned for 107,000 lbs of proppant,
pumped at 1 to 6 ppa. After assessing the well’s response to the proppant slugs, and
watching the early proppant stages, it was decided to extend the treatment. 130,000 lbs of
proppant was placed, by extending the 4 and 5 ppa stages.
5
BH Proppant
Concentration
6000
0
25
30
35
40
45
50
Elapsed Time, mins
Figure 16.9m – Detail of the main treatment for Minifrac Example 4, showing the formation’s
response to the proppant slugs. Proppant concentration is bottom hole.
References
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Economides, M.J.: A Practical Companion to Reservoir Stimulation, Elsevier, 1992
Nolte, K.G.: “Determination of Fracture Parameters from Fracturing Pressure Decline”, paper
SPE 8341, 1979.
Dempsey, Brett.: “Competing with G Function Analysis”, BJ Services’ Engineering News, Vol.
12, No 1, Winter 2001
Nolte, K.G.: “A General Analysis of Fracture Pressure Decline With Application to Three
Models”, paper SPE 12941, SPEFE, p. 571-583, 1986
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16. The Minifrac
FracRT Version 4.6 User’s Manual, BJ Services, 1995
Cleary, M.P, et al.: ”Field Implementation of Proppant Slugs to Avoid Premature Screen-Out
of Hydraulic Fractures with Adequate Proppant Concentration”, paper SPE 25892, presented
at the SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium, Denver CO,
April 1993.
Køgsball, H.H., Pits, M.J., and Owens, K.A.: “Effects of Tortuosity in Fracture Stimulation of
Horizontal Wells – A Case Study of the Dan Field”, paper SPE 26796, presented at the
Offshore Europe Conference, Aberdeen, UK, Sept 1993.
FracproPT Version 9.0 onwards on-line Help, Pinnacle Technologies/Gas Research Institute,
July 1999 onwards.
MFrac III Version 3.5 onwards on-line Help, Meyer and Associates Inc, December 1999
onwards.
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17. Designing the Treatment
17.
Designing the Treatment
As previously discussed, different types of formation require different types of fracture. For
instance, a high permeability formation requires more fracture conductivity than a low
permeability formation. This section of the manual contains important tips on which fracture
characteristics the Engineer should be designing for, and how to go about achieving them.
As a quick rule-of-thumb, the following guidelines may be used:i)
ii)
iii)
iv)
17.1
Skin bypass fracturing is for when eliminating the effect of the skin or extremely low
cost are the primary goals.
High permeability fracturing is when maximising fracture conductivity is the primary
goal.
Low permeability fracturing is when maximising fracture inflow area is the primary
goal.
Frac and pack fracturing is when fracture conductivity and sand control are the dual
primary goals.
General
At its most basic level, every fracture is designed to do the same thing – increase the
productivity (or injectivity) of the fractured interval. At the limit, all a fracture has to be is more
conductive than the skin damage around the wellbore in order to do this. This is a relatively
easy thing to accomplish, which is why skin bypass fracture treatments are very low cost and
are also easy to perform.
However, often simply bypassing the skin is not enough – bigger production gains are needed
to economically justify the treatment or to efficiently develop the reservoir. In such cases, the
fracture has to be significantly more conductive than the formation. When this happens, it is
easier for the formation fluids to flow down the fracture, than it is to flow through the formation
and into the perforations, and the productive interval will have a negative skin. True
stimulation has occurred, rather than just simple damage removal or elimination. The best
way to assess if the fracture is more conductive is to calculate the relative or dimensionless
conductivity, CfD as previously discussed in Section 10.3:CfD =
kp w̄
xf k .............................................................................. (10.1)
where kp is the permeability of the proppant, w̄ is the average fracture width, xf is the fracture
half length and k is the permeability of the formation. Generally, if the CfD is greater than 1,
then the fracture is more conductive than the formation.
This seems easy enough to calculate, but there are two important points which can often
make estimates of CfD unreliable:1
The proppant permeability is often not easy to find, nor indeed is it a constant. The
permeability of the proppant will vary with closure pressure. As the reservoir pressure
drops (or the drawdown is increased), the closure pressure on the proppant will
change, possibly producing more fines and a permanent drop in permeability. If the
proppant or sand is at the upper limit of its closure stress range, a drop in reservoir
pressure can produce a significant drop in fracture conductivity. In addition, high rate
wells (especially gas wells) can experience non-Darcy flow through the proppant
pack, which can dramatically decrease the effective permeability. Lastly, multi-phase
and/or non-Darcy flow can also significantly reduce the proppant pack’s permeability.
Therefore, the value used for kp needs to be an effective permeability, under a given
set of production conditions. The Frac Engineer should also be aware of how these
production conditions can vary over the life of the well and design for this. Recent
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17. Designing the Treatment
information published by proppant vendors and the StimLab consortium, provides
detailed information for the effective permeability of different proppant types under
many different condition.
2.
The effective width has to be estimated from a fracture model or simulator. The width
generated by these models (which will vary from model to model, even when the
same formation and treatment parameters are used), is highly dependent upon the
Young’s modulus and closure pressure of the formation. These two parameters are
often unknown and may even (as in the case of Young’s modulus in certain
formations) be variable.
Therefore it is important to realise that a fracture must be designed with a safety margin built
into the fracture conductivity, to allow for all these uncertainties. It is therefore recommended
that the Frac Engineer design for a minimum CfD of 20 to 40% greater than theoretically
required (see Section 17.9)
Finally, the Frac Engineer should be aware of the upper limits for fracture conductivity. As the
conductivity increases, the contrast in conductivity between the formation and the fracture will
increase as well. Eventually, a point will be reached at which the formation is delivering
reservoir fluids to the fracture as fast as it can. Further increases in fracture conductivity (or
the conductivity contrast) will therefore produce no subsequent further increase in production.
This is the so-called infinite conductivity situation, where the fracture behaves as if it has an
infinite conductivity compared to the formation. Making a fracture this conductive is simply a
waste of proppant, as the same production increase can be achieved for a reduced propped
width. Generally, therefore, it is often not cost effective to design a treatment to produce a CfD
of greater than 10, unless the formation permeability is very low.
17.2
Designing for Skin Bypass
Skin bypass fractures are the easiest fractures to design. Operationally, they are simple to
execute and have a relatively low probability of screening out early. This is because they are
relatively insensitive to inaccuracies in formation data.
Often, the two biggest factors influencing the design of the skin bypass frac, are not
formation- or perforation-related. In fact, the biggest influences are the volume of fluid already
in the wellbore (which acts as additional pad fluid) and the volume of fluid and proppant that
can be pre-pared and pumped on often very limited or remote locations. (Remember that skin
bypass fracs are very low cost treatments, and that performing workovers or similar
operations - allowing the wellbore volume to be reduced or eliminated - are often unfeasible.)
The volume of fluid in the wellbore is often significantly greater than the desired pad volume.
This means that the size of the actual fracture created is usually out of the control of the Frac
Engineer, and the only factor that can be controlled is the volume of proppant pumped into
the fracture. This in turn is often limited by the available equipment or deck space. However, it
should be noted that highly effective skin bypass fracs can be placed with very small volumes
of proppant, provided the effective pad volume can be minimised (so that the proppant
doesn’t get too dispersed in the fracture).
This inability to control either minimum pad volume or maximum proppant volume, actually
makes designing skin bypass fracs very simple, as the number of variables available for the
Frac Engineer to alter are greatly reduced.
Skin bypass fracs should really be thought of as an alternative to acidising. Consequently,
they should be designed to be cost-effective, as compared to a matrix acid treatment.
Relative to other types of fracturing, this means that low cost and ease of operation are the
biggest single considerations. These treatments should be cheap, relatively low-tech and
easy to pump.
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The following Equation describes the production increase that can be expected from a skin
bypass treatment, as described in Section 12 (after SPE 56473):J
Jo
-s
=
ln[re/(rw.e )]
ln[4/(CfD.xfD)] ................................................................. (17.1)
This Equation provides a more realistic measure of the effectiveness of the fracture than
methods based solely on assessing the CfD, as it takes the skin factor into account.
Given that the dimensionless fracture half length, xfD, is defined as follows:xfD
=
xf
re ................................................................................. (17.2)
Then the lower part of the RHS of Equation 17.1 can be reduced as follows:CfD. xfD =
=
kp w̄
xf k
xf
re ........................................................................ (17.3)
kp w̄
re k ............................................................................... (17.4)
For skin bypass fracturing, it seems that the production increase is largely independent of
propped fracture length per se. However, it must not be forgotten that as average width is a
function of fracture length, (and vice versa). In this case, w̄ is the average propped fracture
width, not the average created fracture width. This is a significant difference that helps to
reinforce the concept that skin bypass fracture effectiveness is much more dependent upon
average propped fracture width than it is upon fracture length. This is why skin bypass fracs
can be so cost effective and easy to perform – almost any kind of pad will suffice, as long as
the proppant is kept near the wellbore at a sufficient concentration.
17.3
Designing for Tip Screenout
The tip screenout (or TSO), as previously described in Section 10.4, is a technique used to
artificially induce increased fracture width, whilst at the same time limiting fracture half-length
and height. In order to obtain the tip screenout, proppant has to be forced into the tip of the
fracture. Once sufficient proppant has been forced into the tip, the fracture fluid is no longer
able to maintain a positive net pressure at the tip, and the fracture stops propagating.
At this point, the fracturing fluid is still being pumped into the fracture at a rate substantially
greater than the leakoff rate. This means that the fracture volume has to increase somehow.
As the treatment has artificially stopped the fracture from increasing length or height, the
width has to increase. In order for the width to increase, extra net pressure (i.e. energy) is
required to further compress the formation either side of the fracture. This is why a TSO is
characterised by a steady increase in net (and hence surface) pressure from the point at
which the TSO initiates until the end of the treatment.
Obviously, the TSO must not happen too early. If this happens, the fracture may not achieve
the required vertical coverage of the formation. In addition, it must be remembered that the
longer the fracture is, the easier it is to produce width. Therefore, if the TSO occurs early, the
treatment may not be able to produce sufficient width before the maximum surface treating
pressure is exceeded – a screenout.
In order to generate a TSO at the correct point in the treatment, it is necessary to pump a
pad, sized such that it will have leaked off completely at the point at which the TSO must
occur. In order for the proppant following the pad stage to produce the TSO, all of the pad
fluid has to leak away, otherwise the proppant will not get into the fracture tip.
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Therefore, in order to achieve a TSO, a formation must have a relatively high fluid leakoff
rate. It is generally not possible to produce a TSO on very low permeability formations. This is
generally not a problem however, as TSO’s are usually only required on high permeability
formations.
In order to be able to predict (and hence control) the point at which the TSO occurs, it is
therefore essential to know the rate at which the pad fluid is leaking off. This can only usually
be achieved if a minifrac has been pumped prior to the treatment (unless there is a
considerable history of fracturing a particular formation, and the characteristics of this
formation have been shown to be reliable). In addition, it is essential to retain uniform frac
fluid characteristics throughout the minifrac and main treatment. If the fluid characteristics
change, the leakoff rate will almost certainly change.
The minifrac is also essential for determining the Young’s modulus of the formation. This has
a big influence on a TSO treatment, as it determines how much net pressure is required to
produce a given fracture width. It is the Young’s modulus that determines whether or not the
required width can be achieved without exceeding the maximum surface treating pressure.
Therefore, the two key points to designing a successful TSO treatment are the fluid leakoff
and the Young’s modulus. Every effort should be made to determine accurate values for
these variables.
17.4
Designing for Frac and Pack
Frac and Pack treatments contain all the elements described in Section 17.3 (above) for a
TSO design, plus some extra elements specific to the completion being installed.
Frac Pack
Slurry
Blank Pipe
‘Packed’ Gravel
or Proppant
Figure 17.4a – The diagram on the LHS illustrates the position of the slurry and the ‘pack’ at
screenout – with the top of the ‘packed’ proppant at the top of perforations, and the annular
space between the completion and the wellbore full of slurry, up until the crossover ports. The
RHS shows the position of the pack after all the proppant has been allowed to settle.
Figure 17.4a illustrates a schematic of the frac and pack completion, complete with the setting
tool (assumed to be in the squeeze position). Towards the end of the treatment – as with any
TSO design – the formation will screenout, preventing the pumping of any further slurry into
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17. Designing the Treatment
the formation. However, the frac and pack treatment is designed with an extra volume of
slurry on the end of the final stage. This stage is added so that the annular space between the
completion and the casing can be filled with proppant.
When the completion is made up, sections of “blank pipe” (usually regular P-110 tubing) are
added above the screens. This produces extra distance between the crossover ports (the
point at which the slurry enters the annulus) and the screens. This extra distance provides an
extra volume of slurry in the annulus after the screenout, so that once all the proppant has
settled down onto the pack, the height of the pack is significantly above the top of the
screens.
So - basically - the frac and pack treatment is a TSO treatment, designed with some extra
slurry on the final stage, so that the annular space is completely packed to above the height
of the screens. This is verified after the treatment by pumping a circulation test (also referred
to as re-stressing). By comparing the results of these with a similar pre-frac test, the height of
proppant in the annulus can be calculated, as follows:2
H
=
(Pfinal - Pinitial) kp A
2
0.45 .................................... (17.5)
(1279 µ q A) + (4.63 ρ q kp )
In Equation 17.5, Pinitial is the surface pressure for the pre-frac circulation test (psi), Pfinal is the
surface pressure for the post-frac circulation test (psi), kp is the proppant permeability
(darcies), A is the annular capacity between the casing and the blank pipe (ft3/ft), µ is the
viscosity of the fluid being circulated (cp), q is the flow rate (bpm) and ρ is the density of the
fluid (ppg). H is the height of proppant above the screens in feet. Use the same fluid, pumped
at the same rate, for both the pre- and the post-frac tests. The above relationship is based on
the Forcheimer Equation (Equation 10.4) and so allows for inertial flow effects.
17.5
Designing for Tight Formations
In general, tight formations have low permeability, hard rock and require some form of
stimulation in order to be economic. Normally, these formations require a completely different
approach to the treatments described in the previous sections. These previous treatments
have relied upon the bypassing of skin damage and on the conductivity of the fracture to
produce the production increase. This is not true of tight formations, in which the skin factor is
usually relatively low, and it is easy to obtain a fracture that is many times more conductive
than the formation.
In fact, for the purposes of fracture stimulation, it is possible to define a tight formation as one
in which the most important fracture characteristic is not propped width, but propped length.
When defining a tight formation, it is also useful to think in terms of mobility, rather than
simple permeability. Mobility, m, is defined as follows:m
=
k
µ
.................................................................................. (17.6)
where k is the permeability of the formation to the produced fluid and µ is the viscosity of that
fluid at reservoir conditions. This allows us to see that a tight oil formation has considerably
greater permeability than a tight gas formation.
In the case of a tight formation – especially a tight gas formation – it is relatively easy to
produce a fracture of essentially infinite conductivity (i.e. a fracture so conductive that any
further increase in fracture conductivity produces no subsequent increase in production). In
such a situation, the factor limiting the potential production increase is the ability of the
formation to deliver hydrocarbons to the fracture. This is controlled by the permeability of the
formation and by the inflow area of the fracture. Obviously, increasing the permeability of the
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entire formation is beyond the abilities of stimulation engineering. However, maximising inflow
area – by increasing the size of the fracture faces – is relatively easy.
Therefore, fractures in tight formations are designed to produce maximum size, with a
minimum necessary proppant concentration.
Of course, there are diminishing returns on increasing fracture size – doubling the fracture
length will increase the fracture area by approximately 4 times (as the height will increase at
the same relative rate as the length). This means that the proppant volume (which is spread
over the entire area of the fracture) is also increased by a factor of 4. As the fracture height
increases, an increasingly greater proportion of the fracture will be outside the zone of interest
(unless a “massive” formation is being fractured). Therefore, an increasing proportion of the
proppant will be placed out of zone (i.e. it is wasted). In addition, the fluid volume required will
increase by between 4 to 8 times. Thus, doubling the length – which at best can only double
the production – will can increase the cost of the treatment by 4 to 6 times.
Whilst fracture conductivity is not the most important consideration for tight formation
fracturing, it is important to remember that some fracture conductivity is required. Remember
that the proppant pack will lose permeability due to factors like residual polymers, non-Darcy
flow and multi-phase flow, and also that the pack may lose permeability as the reservoir
pressure depletes (i.e. as the closure pressure increases). Therefore, when designing a tight
formation fracture treatment, it is important to carefully define the minimum fracture
conductivity, and to ensure that the produced fracture always remains above this.
Tight formations – especially tight gas formations – tend to have the following characteristics:i)
ii)
iii)
Low permeability and hence low fluid leakoff
High Young’s modulus and hence;
Low fracture toughness
Because of the often extremely low fluid leakoff, it is possible to treat these formations with
very low pad volumes. Often, it is not necessary to crosslink the pad and a linear gel is used
(a "hybrid" frac). In some formations, it is even possible to frac without any pad whatsoever –
the formation can be fractured with the first slurry stage.
Because of the very low fluid leakoff, these fractures can take a long time to close after the
treatment is finished (work by Cleary et al suggests that some fractures may take 24 hours to
close). Therefore, it is important to design the fracturing fluid with very good proppant
transport characteristics, so that it is capable of supporting the proppant for as long as it takes
the fracture to close.
Another major issue for tight formations, especially tight gas formations, is fluid recovery. In
many cases, extra care and attention must be paid to the design of the fracturing fluid to
ensure that it does not form fluid blocks in the formation. This is usually done by adding
surfactants to reduce the surface tension of the fluid system. It is also important to break the
fluid to as low a viscosity as possible. Dry gas reservoirs may be sensitive to fluids or any
type – water or hydrocarbon. These can cause extensive damage due to changes in relative
permeability. In such formations, it is common practice to perform treatments using N2 or CO2
foams (or with binary foams), to reduce the liquid content to a minimum. Alternatively, it is
also common practice to treat dry gas wells with methanol-based fluids, as these are very
easily recovered after the treatment.
Tight gas fracturing is probably the single most common form of hydraulic fracturing. In many
areas of the world, tight gas reservoirs can only be produced economically because of
hydraulic fracturing. In these places, fracturing has become the accepted method of
completing wells and whole reservoirs are developed using this technique.
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17.6
Designing for Injection Wells
Injection wells are basically fractured in the same way as production wells, although there are
a number of minor points which must be observed:i)
ii)
iii)
iv)
v)
v)
vi)
17.7
Take careful note of the closure pressure after the treatment. When the well is placed
back on injection, on no account must this pressure be exceeded, as this will open up
the fracture and (potentially) allow the proppant to fall downwards.
Remember that the build-up of pressure in the near wellbore area (caused by the
injection) may act to reduce the local closure pressure.
Clean up the well after the fracture as much as possible before placing the well on
injection. Any polymer residue or proppant fines left in the proppant pack will act to
block the formation permeability and will not be produced back from the formation.
When fracturing existing injection wells, fluid leakoff will often be much higher than in
offset producing wells, due to the higher than normal water saturation of the
formation.
Do not use surfactants that leave the formation water-wet. These will act to reduce
the injectivity of the water.
When fracturing a new well, remember that water injection – and the control of where
the water goes – is an important part of reservoir management. Select the zone to be
fractured carefully and always in consultation with the Reservoir Engineer. Be aware
of the consequences of fracturing into high permeability and/or low pressure
formations.
Consider using polymer-free fracturing fluids (e.g. visco-elastic fluids or brine with
LiteProp). Such fluids have very low permeability once broken and no polymer
residues. Consequently, they do not have to be flowed back - simply place the well
back onto water injection once the fluid has broken
Designing CBM Treatments
The vast majority of the coal bed methane fracturing that takes place in the US in 9 or 10
major basins in the US, Australia and in China. In addition, CBM fracturing also takes place in
a number of locations, including the UK, the Middle East and Russia. In all of these places,
each particular coal field or basin tends to be dominated by a single operating company.
Each of these basins has its own particular characteristics, in terms of the age and maturity of
the coal, the reservoir pressure, the fines mobility, the water production and the mechanical
characteristics of the coal seams and their surrounding rock layers. As a result of this, each
operating company has developed its own particular method for producing the gas, and when
this involves fracturing, they have developed their own method for this as well.
CBM fracturing remains to this day very difficult to simulate on a computer. Conventional
models cannot be applied to the coal, due to the extensive cleat systems that exist in the
seams, the extremely plastic nature of the coal and the shear decoupling that exists between
the coal and the over- and under-lying rock strata. Without the aid of reliable fracture models,
Engineers have developed a number of “rules of thumb” for CBM fracturing, most of which are
specific to a particular basin.
In short, operating companies that are successfully producing coal bed methane, are those
which have been prepared to experiment, to try out a few different methods and to except a
few failures along the way.
Completions
i)
There are many different completions being used, from open hole to multiple
perforated monobores. There is very little agreement over which is ideal, although a
cemented and perforated completion is best when fracturing is being considered.
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ii)
iii)
iv)
v)
Formations tend to be several thin seams, rather than a single large seam. As such,
most completions contain several sets of perforations.
In such cases, it is essential that each set of perforations is broken down before the
fracturing operation. This usually involves using a straddle packer (or packer and
bridge plug) positioned over each set of perforations in turn. The breakdown is
achieved by pumping small quantities of acid (usually formic) into the zone. Some
companies prefer to do this with water.
The breakdown can also be achieved using ball sealers, but this is less reliable.
Without the breakdown of each individual zone, it is likely that most of the perforated
intervals will receive no stimulation during a treatment, whilst the other zones will
receive everything.
Fluid Systems
i)
ii)
iii)
iv)
All sorts of different fluid systems are still being used, including foams, fresh water,
slick water and crosslinked gels.
Slick water and fresh water have the advantages that they are very cheap and
potentially non-damaging to the coal seam. Their major disadvantage is that their low
viscosity makes it difficult to carry proppant deep into the cleat system. This can also
lead to pre-mature screenouts. However, neutral density proppants could potentially
revolutionise this type of treatment, although the cost of the proppant may be
uneconomic.
Foams have good proppant transport characteristics, and are very good for placing
the proppant in the wider cleats and not in the narrower channels. Foam is also very
good for unloading the well after the treatment. However, foam is very expensive to
use, requiring a lot of additional specialised equipment on location for the treatment.
The best fluid system to start out with seems to be a cheap, reasonably low polymer
loading crosslinked borate guar or guar derivative. This is a standard water-based
fracturing fluid, reduced to the minimum necessary to carry proppant into the cleat
system. Polymer loading would be 25 to 30 lbs/mgal. It is essential that an enzyme
breaker be used, as it has been shown that oxidizing breakers can seriously damage
the cleat faces.
Proppant Selection
i)
ii)
iii)
iv)
Generally, it is best to pump as large a proppant grain size as possible. This is for two
main reasons: First, the larger the proppant grain, the higher the proppant
permeability and the less susceptible the proppant is to embedment in the cleat
faces; Second, the larger proppant grains allow the coal fines to past through, rather
than collect and gradually plug up the conductivity.
The recommended proppant size is 12/20 Sand, although sometimes this can be
hard to obtain.
Some operators like to pump a fine grain sand (such as 100 mesh) in the early stages
of the treatment (in the pad). The purpose of this is to block up the narrow cleats, and
force the fracture and the larger main proppant grains into the wider cleats.
Proppant volume ranges from 3,000 to 10,000 lbs per vertical ft of net height. Some
operators claim to be able to place 15,000 lbs/ft, but this is not confirmed. A good
starting point is to aim to place 5,000 lbs per vertical ft of coal. If this is placed without
any problems, the proppant volume can be gradually increased on subsequent
treatments.
Fracture Geometry
i)
ii)
Although it is very difficult to predict the geometry of the fracture(s), it is still possible
to divide the fractures into two main regimes.
The first regime occurs when the fracture penetrates up and down into the over- and
under-lying rock strata. Fractures tend to have an overall radial or elliptical geometry,
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iii)
although the actual shape of the fracture(s) within the coal seam will be very complex.
This regime is characterised by a moderate to low frac gradient (0.5 to 0.7 psi/ft), as
the fracture is pushing against the minimum horizontal stress.
The second regime occurs when the coal seam shears relative to the over- and
under-lying rock strata, so that the fracture does not penetrate out of the coal seam.
This results in the famous T and I –shaped fractures, where the fracture grows
horizontally between the coal seam and the confining rock strata. This regime
produces better stimulation, as all of the proppant is placed in the coal seam.
However, pressures tend to be much higher, with the frac gradient being 1.0 psi/ft or
greater, as the fracture has to lift the overburden in order to propagate. Also, it is
important not to confuse the high pressures of this type of frac, with the high
pressures produced by near wellbore friction (see below).
Notes on Job Design
i)
ii)
iii)
iv)
v)
vi)
17.8
In addition to breaking down each set of perforations individually, it is also worthwhile
performing a full-scale minifrac. This involves pumping into the formation at the
anticipated treatment rate, using the actual treating fluid but no proppant. This allows
the frac engineer to assess the overall fracture geometry (from the frac gradient) and
the level of near wellbore friction (from the difference between the BHTP and the
ISIP).
Surface facilities should be designed to cope with fines production. All treatments,
regardless of the fluid used and the additives mixed into the fluid, will cause the
production of coal fines. These fines should be produced back to the surface and
handled there. If they are not produced back to surface, they will block up the
proppant pack and cause a loss in production that will increase with time.
Treatment pump rate should be 1.0 to 1.5 bpm per vertical ft of coal. Treatments
using fresh or slick water are usually pumped at higher rates. This is because the fluid
has no proppant transport characteristics, and so it is essential to keep the proppant
moving within the cleat system.
Pad volume should be 20 to 25% of the overall treatment volume, although this is an
area that varies considerably – some treatments use only 5% or even less.
Proppant concentration should be 6 to 8 ppg (lbs per gal) for the crosslinked fluid and
foam. Slick and fresh water systems are only capable of carrying proppant up to
about 2 ppg.
If significant near wellbore friction is present, then it is likely that 6 to 8 ppg will cause
a premature screenout. If this friction is detected, the maximum proppant
concentration should be reduced to 4 ppg. If this happens, more fluid will be required
to place the same volume of proppant.
Designing for Coiled Tubing Fracturing
Coiled tubing fracturing is really a method for placing the fracture treatment, rather than a
specific method of treating a type of formation. Any of the types of treatment previously
described can be placed with coiled tubing.
The advantages of using coiled tubing have already been explained in Section 3.6. To
summarize, they are as follows:i)
ii)
iii)
iv)
Isolation of completion.
Isolation of individual zones.
Rapid turn around between multiple treatments.
Use of the coil to gas lift the well back to production.
The main problem with fracturing through CT is the narrow diameter of the tubing itself. This
means that the most important factors in designing CT fracs are the friction pressure of the
fracturing fluid and the maximum allowable pressure that can be imposed on the CT.
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BJ’s Circa Coiled Tubing Simulator can be used to predict the maximum allowable injection
pressure, for any given CT string. However, it must be remembered that the CT string will be
static when the treatments are pumped. The maximum injection pressure usually generated
by CT simulators assumes that the CT is either moving in or moving out of the hole. This
means that the CT is being continuously plastically deformed, as the internal pressure is
applied. However, if the CT is static – and hence it is not being plastically deformed – the CT
will be able to withstand much greater internal pressures. For instance, normal maximum
injection pressures for CT are in the region of 5,000 to 6,000 psi. However, during static
fracturing operations, treatments have been pumped at pressures up to 13,000 psi.
However, in spite of this, the friction pressure of the frac fluid (and the subsequent surface
treating pressure it produces) will still dominate the design of the treatment. It is often
necessary to use very low friction pressure fluids (i.e. low polymer loading gels or viscoelastic surfactant-based fluids) in order to be able to maintain the desired rate. These fluids
are often significantly more expensive than their conventional alternatives.
Notwithstanding the increased allowable internal pressure and a possibly reduced friction
pressure, even with large diameter CT strings (2” or greater), the Frac Engineer will still be
rate limited to between 5 and 12 bpm. This can often significantly limit the size of treatment
that can be placed in the formation. Obviously, the shorter the string, and the larger the ID,
the greater the maximum rate. However, it should also be noted that generally with CT, the
larger the ID, the smaller the maximum allowable pressure (unless so-called heavy-walled CT
is used).
Therefore, the Frac Engineer has to balance the need for rate against the desire for a cheap
fluid and the maximum allowable injection pressure. Usually, the requirements of the
treatment take precedence over the cost of the fluid, allowing the Frac Engineer more
freedom to design a suitable pumping schedule.
CT fracturing has found niche applications in a number of areas, most notably southern
Alberta. However, it remains economically viable only in areas where there are relatively
shallow multi-zone formations, and where the cost of a workover is expensive.
17.9
Unified Fracture Design and Proppant Number
In 2002, Economides, Oligney and Valkó, published their principles of Unified Fracture
Design, and introduced the concept of a dimensionless proppant number, or Np. This was
defined as follows:Np
=
Np
=
2xf
re
π
CfD (radial flow system) ....................................... (17.7)
2xf
2
xe CfD (square reservoir, area = xe ) ............................ (17.8)
Rearranging and substituting in Equation 10.1 gives the following result, for a radial flow
system:Np
=
2kp w̄
........................................................................... (17.9)
re k π
According to the theory, for each value of Np there is a corresponding optimum value of CfD,
which produces the maximum production increase. Therefore, this theory allows the Frac
Engineer, for any given reservoir and proppant combination, the optimum balance between
average proppant width (w̄ ) and proppant fracture half length (xf), as illustrated in Figure
17.9a.
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17. Designing the Treatment
Figure 17.9a also shows us that for Np values less than 0.1 the optimum value of CfD is 1.6.
This gives the Frac Engineer a very powerful tool – for medium to high permeability fracturing
(i.e. Np < 0.1) the fracture should always be designed for CfD = 1.6. For low permeability
fracturing, the relationship is not so simplistic and specific values for Np have to be calculated
for each proppant-reservoir-fracture combination.
As can be seen from Equation 17.9, proppant number varies inversely with formation
permeability. It can therefore be thought of as a measure of the effectiveness of the proppant,
as a transport medium, relative to the formation. Whilst very low values of Np are easy to
obtain, in practice it is hard to get values higher than 10 (as re is limited).
Under most circumstances, the changeover from Np < 0.1 to Np > 0.1 occurs in the range of
0.5 to 5 mD formation permeability. Obviously, the exact value is highly dependent upon the
effective proppant permeability (allowing for the effects of multi-phase and non-Darcy flow).
Dimensionless Fracture Conductivity, CfD
100
10
C fD = 1.6 for N p < 0.1
1
Medium to High Permeability
0.1
0.0001
0.001
0.01
Low Permeability
0.1
1
10
100
Proppant Number, N p
Figure 17.9a – Optimum dimensionless fracture conductivity against dimensionless proppant
number (after Economides et al, 2002).
17.10 Net Present Value Analysis
Net Present Value (NPV) analysis is a method for comparing one treatment to another, on a
cost basis, to determine which treatment is the most cost effective. It allows one treatment to
be compared to another on economic grounds. NPV takes into account the cost of the
treatment, the revenue generated and the customer’s requirements. When comparing
treatments, the option that produces the greatest NPV should be selected. Within the
constraints of equipment, materials, completion and cost, the Frac Engineer should design for
maximum NPV.
A more detailed explanation of NPV analysis, together with an example, is contained in
Section 13.1.
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References
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Gidley, J.L., et al: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Bradley, H.B. (Ed): Petroleum Engineers Handbook, SPE, Richardson, Texas (1987)
Jiang, T., Shan W.W., Ding, Y.H., Wang, Y.H. and Wang, Y.L.: “Systematic Fracturing
Technology and its Application in Development of Low Permeability Reservoir”, SPE 50910,
presented at the SPE international Conference and Exhibition in China, Beijing, China,
November 1998.
Phillips, A.M. and Anderson, R.W.: “Use of Proppant Selection Models To Optimize Fracturing
Treatment Designs In Low-Permeability Reservoirs”, SPE/DOE 13855, presented at the
SPE/DOE 1985 Low Permeability Gas Reservoirs, Denver, Colorado, May 1985.
Voneiff, V.W., and Holditch, S.A.: “A Economic Assessment of Applying Recent Advances in
th
Fracturing Technology to Six Tight Gas Formations”, SPE 24888, presented at the 67
Annual Technical Conference and Exhibition, Washington, DC, October 1992.
Yong Fan, and Economides, M.J.: “Fracture Dimensions in Frac&pack Stimulation”, SPE
30469, presented at the SPE Annual technical Conference and Exhibition, Dallas, Texas,
October 1995.
Rae, P., Martin, A.N., and Sinanan, B.: “Skin Bypass Fracs: Proof that Size is Not Important”,
SPE 56473, presented at the SPE Annual Technical Conference and Exhibition, Houston,
October 1999.
O’Driscoll, K.: Middle-East Region Coal Bed Methane Fracturing Manual, BJ Services, 1995.
Gavin, W.G.: “Fracturing Through Coiled Tubing – Recent Developments and Case
Histories”, SPE 60690, presented at the 2000 SPE/ICoTA Coiled Tubing Roundtable,
Houston, April 2000.
Cramer, D.D.: “The Unique Aspects of Fracturing Western US Coal-beds”, SPE 21592,
presented at the Petroleum Society of CIM/Society of Petroleum Engineers International
Technical Meeting, June 10-13, 1992, Calgary, Alberta, Canada.
Nimerick, K.H., et al: “Design and Evaluation of Stimulation and Workover Treatments in Coal
Seam Reservoirs”, SPE 23455, presented at the Petroleum Society of CIM/Society of
Petroleum Engineers International Technical Meeting, June 10-13, 1990, Calgary, Alberta,
Canada.
Archer, J.S. and Wall, C.G.: Petroleum Engineering – Principles and Practices, Graham and
Trotman, London (1986).
Wong, G.K., Fors, R.R., Casassa, J.S., Hite, R.H., and Shlyapobersky, J.: “Design, Execution
and Evaluation of Frac and Pack (F and P) Treatments in Unconsolidated Sand Formations in
the Gulf of Mexico”, SPE 26563, presented at the SPE Annual Technical Conference and
Exhibition, Houston TX, Oct 1993.
Tiner, R.L., Ely, J.W. and Schraufnagel, R.: “Frac Packs – State of the Art”, SPE 36456,
presented at the SPE Annual Technical Conference and Exhibition, Denver CO, Oct 1996.
Economides, M.J., Oligney, R.E. & Valkó, P.P.: Unified Fracture Design, Orsa Press, Alvin,
TX, 2002.
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18
Real-Time Monitoring and On-Site Redesign
Thanks to the advent of electronic data gathering systems, personal computers and efficient,
reliable fracture simulators, it is now possible to actually model the fracture as the treatment
progresses. This process, known as Real-Time Monitoring, allows the Frac Engineer to
actually re-design the treatment on-the-fly.
The more traditional form of on-site redesign is when data from a step rate test and/or
minifrac is used to redesign the main treatment. This is usually carried out on-site, with the
whole of the frac spread and frac crew waiting for the Frac Engineer to produce the new frac
design.
18.1
Real-Time Data Gathering
Pressure
Transducers
Voltage
Bottom Hole
Pressure Data
Flowmeters
Frequency
3600 or
Isoplex
ASCII Data
JobMaster
Selected
ASCII Data
Frequency
Frac Model
Nuclear
Densometers
Redesigned
Treatment
Schedule
Frac
Engineer
Figure 18.1a – Process loop for real-time fracture modeling and redesign
With a modern frac spread, it is now possible to measure, record and monitor every single
treatment parameter, including items such as liquid additive rates, sand screw rpm’s and
annulus pressure. However, for the Frac Engineer, there are three main variables which are
required:- bottom hole pressure, proppant concentration and slurry rate. It is useful and often
necessary for a whole range of data to be recorded during the treatment, but it is only these
three variables which will be needed for the redesign. Often it is useful for the Frac Engineer
to use surface treating pressure, in order to calculate BHTP or pipe friction data. Also, is it
sometimes quite helpful for the Frac Engineer to record stage number, in order to keep track
of which stage is at the perforations (especially if there are tortuosity problems).
Data is recorded using three basic types of measuring devices; pressure transducers, nuclear
densometers and flow meters (as illustrated in Figure 18.1a).
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Flow Meters
Flow Meters come in three main types:- turbine, magnetic and inertial or mass flow meters.
Turbine flow meters are the most commonly used, as they are easy to employ, require no
external power supply and are cheap. They can also be used in high pressure flow lines. Fluid
flow is measured by a single turbine, which is positioned in the centre of the flow stream. This
turbine rotates when fluid passes through the flowmeter. The faster the fluid flow, the faster
the turbine spins. A magnetic pick up measures how fast the turbine is rotating, sending an
output in the form of a frequency to the control centre.
The turbine flowmeter has several disadvantages. It is easily obstructed or damaged by
debris in the frac fluid. This means that the flowmeter needs to be checked and potentially redressed after every treatment. The turbine flowmeter requires a separate calibration factor for
each different fluid type (i.e. linear gels, gelled acids, gelled oils etc). The turbine flowmeter
also has a relatively high flow rate threshold, below which the turbine will not rotate. This
means that for 2 or 3 different turbine flow meters are usually required for measuring over a
wide range of flow rates. Turbine flow meters can only be used for liquids.
Magnetic flow meters (often referred to as mag flowmeters) rely of the physics of generating
electrical current. This states that it you have motion and a magnetic field, then you will get
current flow, provided there is a conductive path. The magnetic flow meter provides the
magnetic field, the fluid provides the motion and a current is generated. The magnitude of the
current is proportional to the flow rate. These flow meters are easy to use (once they have
been set up) and very reliable, requiring little maintenance (they have no moving parts or
restrictions). The main disadvantages of these flow meters are that they require an external
power source, they are expensive and they can only be used for measuring conductive fluids
(so they cannot be used for measuring gelled hydrocarbons or gases).
Inertial or mass flow meters (such as the MicroMotion flowmeter) work by using two flow
loops. As the fluid enters the flow meters, it is split into two loops of equal diameter. One loop
measures the density of the fluid, whilst the other loop measures the mass flow rate.
Volumetric flow rate is obtained by dividing the mass flow rate by the density.
Density is measured by forcing the flow around a loop that is vibrating. This vibration is
produced by a calibrated agitation system, which always provides the same force, at the
same frequency. A measuring system compares the known “input” agitation with the vibration
of the flow loop. Generally, as the mass of the flow loop + fluid increases, the frequency with
which the loop vibrates will slow down. As the mass and volume of the flow loop is known, the
density of the fluid can be quickly calculated.
Mass flow rate is measured by the second flow loop. This loop is offset slightly from the main
direction of flow, so that the inertia of the fluid as it flows causes the loop to twist slightly. The
amount of twist is measured by a number of strain gauges placed along the flow loop. The
force causing the flow loop to twist (and hence the reading on the strain gauges) is directly
proportional to the mass flow rate.
This type of flow meter has several advantages. Most types of fluids can be measured by this
method, including gases, hydrocarbons and cryogenic fluids. The flow meter can also be used
to output density, eliminating the need for a separate densometer. If the pressure differential
across the flow meter is carefully measured, the apparent viscosity of the fluid can also be
obtained. Unfortunately, this flowmeter also has several disadvantages. Because the fluid
flow is forced around two flow loops, it cannot be used for abrasive fluids (the flow loops are
quickly abraded until they fail). These flow meters are quite large and heavy. They are
expensive. Finally, because of the sensitive measuring apparatus inside the flow meter, these
devices are also quite fragile.
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The above listed three methods are all direct methods of measurement. However, it should
also be noted that flow rate is often measured indirectly, by reading the rpm'
s of an input shaft
powering a pump (often referred to as a "stroke counter"). Basically, the computer reading the
rpm'
s has a calibration factor which converts rpm'
s to flow rate, a quickly and easily
calculation. Whilst these flowmeters are very easy to use and also very mechanically reliable,
they suffer from 2 main drawbacks. First, no pump is 100% efficient, and so the stroke
counter has to be calibrated to allow for this. Second, if the pump loses prime (or doesn'
t have
prime to start with), then the stroke counter will give a false reading. It is therefore advisable
to use a direct flow rate measurement as the primary source of flow rate measurement, using
stroke counters only as a back up.
Nuclear Densometers
Nuclear densometers (or densimeters, or densiometers) all work on the same basic principal.
A radioactive source is held on one side of the flow stream, whilst a detector on the opposite
side of the flow stream measures the radioactivity that passes through the flow stream, in
counts per second. Basically, the higher the density of the fluid, the lower the number of
counts per second.
Nuclear densometers vary in the type of output they provide. The basic densometer has no
data processing capabilities, and outputs a frequency signal (the same frequency as the
number of counts per second being received by the detector). A separate data processing
facility (such as a PC) is required to turn the basic data into a density or a proppant
concentration. It is this type of densometer that is most commonly used in the fracturing
industry. More sophisticated densometers come complete with data processing, and can
output density, SG, proppant concentration or acid %.
137
The radioactive source used in the densometer is usually Caesium 137 (or Ce). This metal
is a medium energy beta and gamma radiation emitter, with a half-life of 30 years. This
means that the radioactive source gradually gets weaker with time – after 30 years it is only
half as radioactive as it initially was. Consequently, all radioactive densometers have to be
regularly calibrated, to allow for the fact that the source is gradually producing less and less
radiation. Therefore, the data processing facility (usually a PC, an Isoplex or a 3600, but
sometimes also a box on the side of the densometer) has to have this calibration installed, in
order that density can be output.
Proppant concentration is easily calculated from the overall bulk density of the fluid, using the
following formula:PC =
(ρsl - ρgel)
(1 - [ρsl/ρp])
................................................................... (18.1)
where PC is the proppant concentration in ppa (see below), ρsl is the slurry density in lbs per
gallon (ppg), ρgel is the base fluid (usually gel) density in ppg and ρp is the proppant density,
also in ppg. Proppant density is often also quoted as an absolute volume in gals/lb. This is
simply the reciprocal of the density in ppg.
Proppant concentration is measured in ppa or Pounds of Proppant Added. This is the number
of pounds of proppant that have been added to 1 gallon of clean base fluid (which is how the
blender adds the proppant – it measures the clean flow rate in gallons per minute, and
calculates how many lbs per minute of proppant need to be added). Sometimes, proppant
concentrations are also quoted in ppg – meaning pounds of proppant per gallon of clean fluid.
The use of these units should be avoided for proppant concentrations, as they can get easily
confused with fluid or slurry densities.
Pressure Transducers
Pressure transducers are the simplest of the measuring devices used in fracturing. The
transducer is consists of a strain gauge, that is mounted so that as pressure is applied, the
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18. Real-Time Monitoring & On-Site Redesign
strain gauge is compressed. As the strain gauge is compressed, its electrical resistance will
increase slightly. The higher the applied pressure, the greater the increase in resistance.
The pressure transducer is connected, via a transducer cable, to a special measuring circuit
known as a Wheatstone’s Bridge. This is an electrical circuit consisting of three known
electrical resistances and an unknown electrical resistance (the transducer + cable). Because
of the nature of the circuit, if the potential difference (or voltage drop) across the bridge circuit
is known, the values of the three known resistances can be used to calculate the value of the
unknown resistance, to a high degree of precision. Therefore, if the resistance of the cable is
known, the resistance of the pressure transducer can be obtained. So in order to measure the
pressure applied to a transducer, the voltage drop must be measured.
Pressure transducers are regularly calibrated by applying a known pressure to them, usually
via a dead weight tester. This calibration produces a relationship between resistance and
pressure, so that if the resistance is known, the pressure can be quickly obtained.
Because a large increase in pressure produces only a relatively small change in electrical
resistance, it is important to have good quality cables that are well looked after (as the circuit
measures the resistance of the cable at the same time). This also means that the cables must
be of a fixed length, producing a limit to how far the control cabin can be away from the
pressure transducer. Transducer cables cannot be spliced, repaired or re-used if they are
damaged.
Processing the Data
Raw data from the transducers, flow meters and densometers is not usable by the monitoring
computers. It has to be converted to a digital form by an analogue to digital converter. Once
the data has passed through this, it can be processed to give the actual treatment
parameters.
For instance, the turbine flowmeter is actually measuring the number of times a turbine blade
passes the magnetic pick up, rather than a volumetric flow rate. Every time a blade passes
the pick up, electrical current is generated, reaching a peak as the blade is directly opposite
the pick up. As the blade moves away from pick-up, the current drops off. This means that
the output from a turbine flow meter is cyclic – the higher the frequency of these cycles, the
faster the turbine blades are rotating and the faster the fluid is flowing. The cyclic analogue
input is the converted to a digital output, by the analogue to digital converter. A digital output
simply means that the converter is sending the computer a number – in this case the number
of cycles per second, or frequency.
As stated, the output from the analogue to digital converter is passed on to a computer for
processing. This computer can be a PC, an Isoplex or a 3600. Whatever form it comes in, the
processing computer converts (in the case of the turbine flow meter) a number of cycles per
second, into a flow rate, by applying a calibration. This calibration is user input, and will vary
according to the type and size of flowmeter, and the fluid being used.
For pressure transducers, the analogue to digital converter measures the voltage across the
bridge circuit, and outputs this as a number. For the nuclear densometer, a similar process is
carried out as for the turbine flow meter, in which a frequency is converted into a number. The
processing computer will contain a calibration algorithm for each of these devices, converting
the numerical output from the analogue to digital converter, into psi or ppa as appropriate.
Displaying and Analysing the Data
Usually the Frac Operator or an electronics technician will run the JobMaster computer. This
computer will display all the parameters being monitored by the system, and is the primary
source of information for the person actually running the treatment. The Frac Operator usually
has the option to run several different displays, so that unprocessed data can be displayed
(such as real-time pressure, rate and proppant concentration), along with parameters that
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18. Real-Time Monitoring & On-Site Redesign
have been processed on the fly, such as calculated BHTP, cumulative volumes and of course
the Nolte plot.
The Frac Engineer usually operates the second computer. This machine receives selected
data from the first computer, almost always in ASCII format. The Frac Engineer will use a
specialised treatment monitoring programme or fracture simulator to display and analyse this
data.
The Frac Engineer’s computer is usually capable of receiving ASCII data from more than one
source. The primary source of data will almost always be the JobMaster computer. This data
usually comes in via the COM 1 serial port. However, if a second COM port is fitted to the
Engineer’s computer, it is possible to receive data from a second source (such as a bottom
hole pressure gauge) and merge it with the primary data, real time, so that it can be displayed
and analysed. Computers fitted with USB ports can use adapters to allow several COM ports
to be used simultaneously.
During the treatment, most of the people in the control centre will be watching the displays
controlled by the JobMaster computer.
Numerical
Display
JobMaster Displays
Figure 18.1b – Inside of a typical frac control van, showing the numerical display and some of
the displays being run by JobMaster.
Remote Data Transmission
Remote data transmission is a specialised service which allows the customer and the Frac
Engineer to remain in the office, whilst the treatment is carried out. Provided there is someone
on location to look after the fluids, run JobMaster and handle the data transmission process
(this will usually be a junior Engineer), then the only reason that the senior Engineers are
required on location is for data analysis.
If the data can be transmitted to a separate location, then the customer and service company
Engineers do not have to be on location. They can remain back at the office. This has
particular advantages when the treatment is being carried out in remote locations (such as
offshore). Instead of the Engineers being tied up for (sometimes) several days, remote data
transmission means that they are only directly involved in the treatment for a few hours – the
time taken for the step rate test and minifrac to be pumped, for the redesign to be carried out
in the office and for the main treatment to be performed.
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On Location
Data
Modem
Office
Satellite or
Cellular
Phone Line
Data
Modem
Data
Link
Satellite or
Cellular
Phone Line
Voice
Link
Figure 18.1c – Remote data transmission schematic
Data transmission is carried out real time, using software packages like JobMaster, which
have been specifically designed to carry out this process as part of its capabilities. Both the
transmitting and receiving computers run JobMaster, coordinated so that receiving computer
is expecting the same channels that the transmitting computer is sending. The voice link is an
essential part of the process, so that the data link can be properly coordinated and also so
that the on-site Engineer and keep the office-based Engineer’s fully informed of developments
and as they happen.
Thanks to modern communications, it is a relatively easy task to transmit the data real time.
Data transmission is usually pretty reliable, but interruptions can sometimes happen. In this
case, the software package should be set up so that transmission can be easily resumed, and
that data that is not transmitted during the break in communications is stored for transmission
as soon as communication is re-established.
The latest versions of the remote data transmission systems actually use internet-based
communications. Each control cabin or frac van has it'
s own web address, and broadcasts the
treatment onto the internet. Anyone with the job-specific password can log onto to monitor a
treatment, from any computer that has internet access.
It is also useful to have a separate file transfer programme or internet access for e-mail
installed on both computers, allowing quick and easy transmission of data files between
computers.
18.2
On Site Redesign
On site redesign is the science and art of redesigning a fracture treatment after the step rate
test and minifrac. Usually it is done on location (or - via remote data transition – back in the
office) whilst the frac crew and equipment are waiting. Consequently, there is usually a
reasonable amount of pressure on the Frac Engineer during this process, which may take
several hours. For example, in the offshore environment, were the rig may be costing over
$300,000 per day, every hour spent redesigning (which is usually down time for the rig), costs
the customer over $12,000.
However, this down time is usually money well spent. The Frac Engineer should take as
much time as is necessary and must not produce a hasty, poorly designed treatment. The
object of the fracturing exercise is to maximise production increase, after all. Minimising rig
time is obviously highly desirable, but it should not take precedence over the main objective.
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18. Real-Time Monitoring & On-Site Redesign
Minifrac
Analyser
Fracture
Simulator
Closure
ISIP
Pressure
Match
Fracture
Model
CONVENTIONAL ANALYSIS
PRESSURE MATCHING
Raw Data
Formation
Properties
Revised
Treatment
Schedule
Required
Fracture
Properties
Materials &
Equipment
on Location
Fracture
Simulator
Fracture
Meets
Requirements?
No
Yes
Customer
Approval?
No
Yes
Final
Treatment
Schedule
Figure 18.2a – On-site redesign process flowchart
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One way to minimise down time is to restrict the number of Engineer’s involved in the
redesign process. It is not exaggeration to state that the time taken for the redesign is
proportional to the square of the number of Engineer’s involved.
On site redesign is something that improves with practice and experience.
Figure 18.2a shows a process flow chart for the redesign process. The process starts with the
collection of the raw data. This includes not only the minifrac and step rate data (collected
either real-time or from separate files), but also other items such as wireline logs, completion
diagrams, tracer surveys, temperature logs, BHTP gauge data, data from previous fracs on
offset wells and so on. Once all this has been collected, the Frac Engineer can start to
analyse the data from the step rate test(s) (see Section 15) and the minifrac (see Section 16).
As discussed previously, this process can often take some time and can sometimes be
carried out under quite stressful conditions. Nevertheless, once this process has been
completed, the Frac Engineer should have been able to tune the fracture model, so that what
is in the computer is a reasonable representation of what is in the formation.
Once this has been achieved, the hardest part of the redesign process has been completed.
However, the Frac Engineer still has to produce the final treatment design. In order to do this,
the Engineer has to design a treatment schedule based on two important parameters:1.
The objectives of the treatment. Usually, the objective of the treatment is to place a
frac in the formation, with a certain geometry, and relative conductivity. These
objectives are usually set up before arriving on location. Usually, these objectives will
remain unchanged after the calibration tests (step rate test and minifrac). However,
the results of these tests may change the specifics of how this is achieved. For
instance, if the minifrac shows the permeability of the formation to be significantly
different from that anticipated, the optimum fracture geometry will have to be altered
in order to meet the CfD requirements.
2.
The available equipment and materials. Usually, the Frac Engineer has to work within
the limitations for the equipment available for the treatment, in terms of tank volumes,
maximum pumping rates etc., so that the Engineer is producing the optimum
treatment design the frac spread is capable of pumping. In remote locations (where
materials cannot be “hot-shotted” out to location), the Engineer can also be restricted
by the quantity of materials available on location (volume of gel that can be mixed
and the volume of proppant).
Working within these restrictions (and also remembering the maximum allowable pumping
pressure), the Frac Engineer must produce the optimum possible frac design. This is not just
a question of producing a production increase – for a lot formations, this is relatively easy to
do. The Frac Engineer must also maximise the production increase, to meet or exceed the
economic criteria for the treatment, as there is usually a significant cost associated with
fracturing, and a small production increase may not be sufficient.
18.3
Real-Time Fracture Modeling
Some fracture simulators, such as MFrac, FracPro and FracproPT, have a facility that
enables the fracture to be modeled real-time. This is a very powerful tool that - under the right
conditions - can enable the Frac Engineer to redesign the main treatment on-the-fly, as it is
being pumped.
The modeling computer is set up to receive data from either the data processing computer or
the Frac Engineer’s computer, usually in ASCII format. The user then runs the fracture model,
selecting the “real-time data input” option. The user enters the relevant formation data and
treatment schedule, which can be loaded from a previously created data file. The treatment
starts, and the computer starts to collect the data. As the treatment progresses, the simulator
models the created fracture. The model will take fluid, proppant, formation and wellbore
characteristics from the input model, and will take the pump rate, pressure and proppant
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18. Real-Time Monitoring & On-Site Redesign
concentration from the real time data. Using this data, the simulator will model the fracture
that has already been created, constantly updating as more data is collected. This enables
the user to perform two separate operations:1.
2.
The Frac Engineer can perform a pressure match with the data that has already been
collected by the simulator, until the net pressure predicted by the computer matches
up with the actual net pressure.
The Frac Engineer can instruct the simulator to run the job until completion, predicting
the characteristics of the fracture, based on the ongoing pressure match. For the
treatment schedule, the simulator will use the actual treatment data as far as
possible, and then project forward until the end of the job using the remaining input
treatment schedule. This allows the Engineer to predict the fracture characteristics,
based on the most accurate data possible. This process can be taken one step
further, as the Engineer can alter the remaining treatment schedule, and predict the
fracture characteristics based on this revised schedule. Thus the Engineer can
redesign the treatment schedule on-the-fly. This capability is limited to FracPro and
FracproPT.
Limitations of Real-Time Modeling
This ability to redesign on the fly – whilst usually not very popular with the frac crew – is a
very powerful tool, provided the Frac Engineer is aware of the following:1.
2.
3.
4.
Do not over-react to short term trends. All fracture simulators treat formations as
homogenous materials with uniform rock mechanical properties throughout. In reality
this is usually not the case. The fracture is constantly propagating through rock with
varying properties, producing unpredictable variations in the net pressure plot. In fact,
what the Frac Engineer should be doing is trying to find an “average” value for each
of these properties, such that the simulator’s predicted net pressure curve follows the
trend (and “average” value) of the job plot, but does not necessarily follow every
minute rise and fall in pressure.
However, the Frac Engineer must be able to react quickly when a short term trend
has become a long term trend. When this happens, it’s time to start adjusting some of
the formation properties.
Real-time modeling is only effective on long treatments, where the Engineer has time
to spot the long term trends, adjust the model, and still be able to make changes to
the treatment schedule in time for them to have some effect. If the job is too short, the
crew can be pumping the displacement before the Frac Engineer has finished the
pressure match.
The problem outlined in Point 3 (above) is exacerbated if the wellbore volume
represents a significant part of the treatment. If this is the case, the treatment can be
close to displacement before the proppant has even passed into the fracture. In such
cases, there is little point in modeling the fracture real-time.
References
Standard Practices Manual, BJ Services, January 2001 onwards
Equipment and Technology Catalogue, BJ Services, 1990 onwards
Gidley, J.L., et al: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Johnson, D.E., Wright, C.A., Stachel, A., Schmidt, H., and Cleary, M.P.: “On-Site Real-Time
Analysis Allows Optimal Propped Fracture Stimulation of a Complex Gas Reservoir”, paper
SPE 25414, presented at the SPE Production Operations Symposium, Oklahoma City, March
1993.
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18. Real-Time Monitoring & On-Site Redesign
Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design and
th
Real-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56
California Regional Meeting of the SPE, Oakland CA, April 1986.
Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic Fracturing
th
Simulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65 SPE
Annual Technical Conference and Exhibition, New Orleans LA, Sept 1990.
FracPro Version 8.0+ On-Line Help, RES/Gas Research Institute, March 1998 onwards.
FracproPT Version 9.0+ On-Line Help, Pinnacle Technologies/Gas Research Institute, July
1999 onwards.
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19. Post-Treatment Evaluation
19.
Post-Treatment Evaluation
The Frac Engineer’s job is not over once the treatment has been pumped. Aside from
monitoring fluid samples and preparing a post job report, the Engineer also needs to evaluate
exactly what has happened in the formation. This is essential if the operating company plans
to do more than one frac in a formation.
The simplest method for assessing the effectiveness of the treatment is to compare before
and after production. However, this does not really tell us much. In order to increase the
effectiveness of future treatments, we need some idea of the size and shape of the fracture
that was actually produced.
Some of the methods described below – such as pressure matching - are relatively easy for
the Frac Engineer to perform. However, other methods, such as tiltmeters and microseismic,
require considerable expenditure and planning by the operating company. This means that
plans for post-treatment evaluation must be made when planning for the treatment itself.
19.1
Pressure Matching
Pressure matching is part science and part art. In order to perform a quick and efficient
pressure match, it is essential to have a good knowledge of the fracturing process, an
understanding of the various rock mechanical properties, an understanding of fracture
mechanics and, ideally, a reasonable idea of how the fracture simulator works. In spite of this
need for an understanding of the physics behind the fracturing process and the fracture
simulation, there is still an art to pressure matching. Some Frac Engineers have a feeling for
this process, and some do not.
Pressure matching is a very powerful tool that allows the Frac Engineer to “tune” the fracture
simulator to the formation. The idea being that once the simulator has been tuned, further
fracture simulations can be performed with a high degree of accuracy.
The Process of Pressure Matching
Pressure matching is all about making the simulator predict the same pressure response as
the reaction actually produced by the formation. This is illustrated in Figure 19.1a, as shown
below:-
After
Net Pressure
Net Pressure
Before
Actual Net Pressure
Calculated Net Pressure
Job Time
Actual Net Pressure
Calculated Net Pressure
Job Time
Figure 19.1a – Pressure matching. The variables in the simulator are adjusted to make the
calculated net pressure match the actual net pressure.
With reference to Figure 19.1a, before the pressure match (LHS), the net pressure predicted
by the fracture simulator does not match the actual net pressure in any way. After the
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pressure match has been performed (RHS), the computer predicts a very similar pressure
response to that of the actual treatment data. Now - according to the theory - the simulator
has been “tuned” to the formation. This allows the Frac Engineer to input any desired
treatment schedule, and the simulator will be able to predict the fracture geometry with a
reasonable degree of precision.
There is no doubt that the advent of pressure matching has greatly improved the success rate
and effectiveness of hydraulic fracturing. Modern fracture simulators equipped with this facility
have gradually made the process increasingly user-friendly, helping to reduce the “black art”
associated with frac engineering, as more and more Engineers feel capable of designing a
fracture treatment.
However, there are some definite limitations to this process:1.
Garbage In = Garbage Out. The computer model of the formation generated by this
process is only as good as the data used to create it. Poor data on items such as
permeability, net height, fluid properties (both formation and fracturing fluids) and
perforations can make an otherwise perfect pressure match almost irrelevant.
Another major source of errors is the use of surface pressure data to calculate BHTP.
In order to calculate BHTP, the model first needs to calculate the fluid friction
pressure, something that is notoriously difficult to do for a crosslinking fluid. Variations
in fracturing fluid properties (such as those caused by problems with liquid additive
systems, or varying gel properties) can also be very difficult to account for. Therefore,
the Frac Engineer should do everything possible to get reliable bottom hole pressure
data, such as that from a gauge or dead string.
2.
No Unique Solution. The process of pressure matching involves adjusting four major
variables (Young’s modulus, stress, fracture toughness and leakoff) and many other
minor variables, for each rock strata affected by the fracture, until the pressure
response predicted by the model matches the actual pressure response of the
formation. This means that the Frac Engineer may have 30 or 40 variables available
for adjustment. It is therefore quite possible for two Frac Engineers to get good
pressure matches, but with significantly different sets of variables.
3.
The Fracture Model. At the end of the day, the results of the pressure match are only
as good as the fracture model itself. Without a doubt, modern fracture simulators are
tremendously advanced – the product of more than 20 years of innovation,
experimentation and inspiration. However, the fact remains that different fracture
simulators will predict different fracture geometries for the same input data. Which
one is right? Probably they are all wrong – so the correct question to ask is which one
is closest to the Truth? This is difficult to say, and the subject of considerable debate
in the fracturing industry. The popular conception is that one fracture simulator is
good for a certain type of formation, whilst another is good for a different type. The
debate continues.
It should also be remembered that in general (GOHFER excepted) the widely used frac
models all predict a single eliptically-shaped fracture, either side of the wellbore, symmetrical
around the wellbore. In reality, the fracture is probably much more complex than this. It is
highly unlikely that the fracture - or more likely fractures - behaves in such a regular and
predictable manner. What the fracture simulators do is predict a simplified fracture that
behaves, on average, in a similar fashion to a much more complex reality
The Four Main Variables
There are four main variables that the Frac Engineer should be adjusting in order to achieve
the pressure match – that is to say, four main variables in each formation affected by the
fracture. These variables are Young’s modulus, stress, fracture toughness and fluid leakoff.
So even for the most basic formation lithology, the Frac Engineer will have to be able to keep
track of a minimum of 12 variables (the zone of interest, plus the formations above and
below)..
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Of course, each fracture simulator comes complete with a whole plethora of variables that the
user can adjust. In fact there are so many, that it could be possible to vary several hundred
parameters for a complex reservoir with several rock strata. This is for fracture simulator and
rock mechanical experts only. Unless there is a really good reason, the Frac Engineer is
advised to stick to the four variables listed below.
Whilst pressure matching, the Frac Engineer should be aware of the fact that the process
works the opposite way around to designing a treatment. In pressure matching, the bottom
hole treating pressure is fixed, whereas it is a variable in fracture design. For example, an
increase in in-situ stress will have the effect of decreasing the net pressure in the pressure
matching process, whilst in the fracture design process, this net pressure will remain constant
and the bottom hole treating pressure will increase. In pressure matching, the Frac Engineer
adjusts unknown formation properties to match a known pressure. In treatment design, these
formation parameters are (hopefully) already known, and the process instead involves seeing
the effect they produce for a given treatment schedule.
Fracture Toughness, K1c
Strictly speaking, K1cis the critical stress intensity factor for failure mode 1 (see Section 9,
Fracture Mechanics). However, it is commonly referred to as the Fracture Toughness and is a
measure of how much energy it takes to propagate a fracture through a given material. In
hydraulic fracturing, where the energy needed to propagate the fracture comes in the form of
fluid pressure, fracture toughness tells us what proportion of the available energy is used to
physically split the rock apart at the fracture tip. As pressure is essentially energy per unit
volume, K1c tells the Frac Engineer how much net pressure is required to propagate the
fracture.
Generally speaking, soft plastic formations will have high fracture toughness, whilst hard
brittle formations will have low fracture toughness. There is also an approximate inverse
relationship between Young’s modulus and fracture toughness – hard formations tend to have
a high E and a low K1c, and soft formations tend to be the other way around. For the Frac
Engineer, increasing the value of fracture toughness will tend to make it harder for a fracture
to propagate through the rock. Therefore, an increase in fracture toughness will generally
make the fracture shorter and wider. However, an increase in fracture toughness for just one
formation will tend to divert the fracture into an adjacent formation. For example, if the K1c is
increased in the perforated interval, the fracture will grow into the adjacent formations, above
and below. This has the effect of limiting the fracture length and increasing the fracture height.
In soft formations, do not be afraid to use quite large values for this property, even several
times the default values included in the simulator
Fracture toughness is a material property and cannot be altered by anything under the control
of the Frac Engineer. It is also a property that is very difficult to measure. There are several
laboratory methods for determining K1c, but these are limited in their reliability, as fracture
toughness is highly dependent upon down hole conditions and the overall geometry of the
fracture. However, if core samples are available, fracture toughness can be estimated from
laboratory measurements of yield stress and Young’s modulus, provided this is determined
under tri-axial loading, at bottom hole temperature and pressure.
Remember that some fracture models (e.g. FracPro and FracproPT) have moved away from
the concept of Fracture Toughness and instead model non-linear elastic effects at the fracture
tip as being more significant. In such models, variations in Young’s modulus and in-situ
stresses are far more significant.
Young’s Modulus, E
In order for the fracture to propagate it must obtain width, to a greater or lesser extent. In
order to do this, the rock on either side of the fracture has to be compressed. As discussed in
Section 7 (Rock Mechanics), Young’s modulus defines how much energy is required to
perform this compression. Rocks with a high Young’s modulus will require a lot of energy
(a.k.a. net pressure) to compress. In these formations, fractures tend to be relatively thin, and
the rock is referred to as “hard”. Similarly, rocks with a low Young’s modulus require relatively
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little energy to produce width. In these formations, fractures tend to be relatively wide, and the
rock is referred to as “soft”.
Young’s modulus is a fundamental material property and, like the fracture toughness, cannot
be altered by anything under the Frac Engineer’s control. It can be measured from core
samples, provided these tests are carried out under tri-axial load conditions, at bottom hole
temperature and pressure. In some formations (especially weak or unconsolidated rocks),
Young’s modulus may not be constant.
Fracture mechanics, rock mechanics and fracture simulation require the use of the static
Young'
s modulus. This is the Young’s modulus measured under static - or relatively static –
conditions, such as those that occur whilst fracturing. Another form of Young’s modulus, the
dynamic Young’s modulus (the Young’s modulus measured under dynamic conditions), can
be measured by so-called “stress logs”. These logs, generated by a dipole sonic wireline tool
(also called a sonic array), measure dynamic Young’s modulus and Poisson’s ratio by
measuring the transit time of both shear and compression sonic waves. However, there can
often be a significant difference between dynamic and static values, which renders the actual
values reported on stress logs to be unreliable. This is covered in more detail in Section 7.10.
However, stress logs can accurately report contrasts in Young’s modulus, which are almost
as important as the absolute values themselves.
An increase in Young’s modulus makes it harder for the fracturing fluid to produce width.
Therefore, increasing this variable will make the fracture thinner, higher and longer, and vice
versa. Increasing E only in the perforated interval will have the effect of forcing the fracture
out of the zone of interest – i.e. increasing fracture height. A decrease in E has the opposite
effect.
In-Situ Stress, σ
In-situ stress (often referred to as confining stress or horizontal stress) is the stress induced in
the formation by the overburden and any tectonic activity. Put simply, it is pre-loading on the
formation, the stress that has to be overcome (or pressure that has to be applied) in order to
actually start pushing the formation apart. The actual bottom hole fracturing pressure is the
pressure required to overcome these in-situ stresses, plus the pressure required for
propagating the fracture (as a consequence of fracture toughness) and the pressure required
to produce width.
As previously discussed in Section 7, fractures will tend to propagate perpendicular to the
minimum horizontal stress (i.e. along the line of least resistance). So the in-situ stress of a
formation is the minimum horizontal stress of the formation, plus any tensile strength the rock
may posses, and less any effects due to reservoir pressure.
As the horizontal stress only exists because of the overburden (ignoring tectonic effects), it is
highly dependent upon the Poisson’s ratio of the formation, as illustrated in Equation 7.18. At
the limit, a Poisson’s ratio of zero means that the horizontal stresses are equal to zero, plus
the effects of pore pressure. This is a theoretical minimum – in practice no material will ever
have a Poisson’s ratio of zero. At the other limit, the maximum theoretical value for Poisson’s
Ratio is 0.5 – at this value, the horizontal stresses will be equal to the overburden, plus the
effects of pore pressure.
So-called “stress logs” actually measure the dynamic Young’s modulus and Poisson’s ratio of
the formation. Therefore, if the overburden is known (derived from a density logs and the TVD
of each formation), the approximate in-situ stress can be calculated. However, the stresses
generated from this procedure are derived from the dynamic (rather than static) Poisson’s
ratio. Therefore, any stresses generated by this method are unreliable. The absolute value of
these stresses cannot be trusted – however, stress contrasts between formations can be
used as an indication of potential fracture height containment.
In the pressure matching process, an increase in s means a reduction in net pressure (for a
fixed BHTP). This means that the fracturing fluid has less energy available to fracture the
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19. Post-Treatment Evaluation
formation, and so the width, the height and the length of the fracture are all decreased. This in
turn means that the volume of the fracture has decreased. However, the same volume of fluid
has been pumped into the formation, so an increase in s also has the effect of increasing
leakoff rate and decreasing fracture efficiency. The opposite effect applies for a decrease in
in-situ stresses.
Fluid Leakoff Rate, QL
The fluid leakoff rate can be controlled by altering a number of variables, depending upon the
fracture simulator being used, and the fluid leakoff model being employed:Pressure differential (fracturing fluid pressure minus pore pressure)
Formation permeability
Formation porosity
Formation compressibility
Formation fluid viscosity
Fracturing fluid filtrate viscosity
Fracturing fluid wall-building coefficient
Spurt loss.
A lot of these variables are difficult to measure or determine. However, the Frac Engineer
should remember the ultimate objective of determining fluid leakoff – to calculate the volume
of the fracture. To this end, the simulator has to be able to accurately calculate the volume of
fluid lost through each unit area of the fracture face. Whether or not this is achieved by
varying the permeability or the wall building coefficient is almost irrelevant. On top of this, fluid
leakoff can be dramatically complicated by fracture fluid flow into fissures or natural fractures,
the geometry of which can vary with the net pressure.
In most cases, the Frac Engineer will have reasonable data for some of these values – and
will have to guess at others. Therefore, a good strategy is to fix those values that have
reasonable data, and vary the others, until the desired leakoff is obtained.
Fluid leakoff is a loss of energy from the fracturing fluid, as the total energy available for
propagating the fracture is equal to the net pressure multiplied by the fracture volume. High
leakoff means low fracture volume, and vice versa. Therefore, and increase in fluid leakoff will
tend to decrease width, height and length. The opposite applies for a decrease in leakoff.
Summary of the Effects of the 4 Main Variables
The basic effect of each of these variables – when applied to a fracture in a single formation –
can be summarised in Table 19.1a, below:Effect of an Increase in Selected Variable
Variable
Height
Length
Width
Net
Pressure
Fracture Toughness, K1c
Decrease
Decrease
Increase
Increase
Young’s Modulus, E
Increase
Increase
Decrease
Increase
In-Situ Stress, σ
Decrease
Decrease
Decrease
Decrease
Fluid Leakoff Rate, QL
Decrease
Decrease
Decrease
Decrease
Table 19.1a – The effects of an increase in each of the four, main pressure matching variables.
Note that these are the overall effects when the change is taken in isolation (i.e. no other
changes take place). It also assumes that the fracture is unaffected by boundary layers above
and below.
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This table should be used with caution, as it applies only when the fracture is confined within
a single formation. If the fracture propagates into separate formations above and below the
productive interval, then an increase in (for instance) fracture toughness will make it harder
for the fracture to propagate through the main formation, forcing the fracture up and down.
So, in this instance, an isolated increase in a property in just one formation, can actually
increase the fracture height.
The Effect of Poisson’s Ratio
Poisson’s ratio is at the same time both important and largely irrelevant to pressure matching.
It is important, because it has a major effect of defining the horizontal stresses in a formation.
However, in most cases, the Frac Engineer will be determining these stresses form pressure
data, not from Poisson’s ratio data. In most fracture simulators, Poisson’s ratio is used in the
2
2
form (1 - ν ) to modify Young’s modulus (i.e. E/(1 - ν ) – the plane strain Young’s modulus).
This means that a large change in Poisson’s ratio, say from 0.25 to 0.35, only produces a
2
change in (1 - ν ) from 0.9375 to 0.8775 (so that a 40% increase in n produces only a 6.4%
2
decrease in(1 - ν ).
Therefore, the Frac Engineer should not spend too much time varying Poisson’s ratio during
the pressure match. Input what seem to be reasonable values, and then ignore it.
Tips for Pressure Matching
1.
“The Fundamental Interconnectedness of Everything” *
The Frac Engineer must be aware that the fracture is a continuous, dynamic entity. It is not
composed of a number of discrete pieces, functioning independently of each other. This
means that any change to any single variable will affect the whole of the fracture, to a greater
or lesser extent. This can sometimes be very discouraging for the Frac Engineer, as a change
to match one part of the pressure curve can alter a match already achieved in another part of
the curve. However, remember that in reality, a pressure match that only matches a limited
part of the plot is not really a pressure match at all.
This means that the Frac Engineer should try to change only one variable for each simulator
run. This can be time consuming, but is essential if the Engineer intends to keep track of how
individual changes affect the overall simulation.
* - Acknowledgement to Douglas Adams, Dirk Gently’s Holistic Detective Agency
2.
Ignore Short-Term Trends
Fracture simulators model a formation as a homogenous material, whose properties are
uniform throughout the material. In reality, this is not the case. Real rock formations will tend
to have variations – large and small – throughout their structure. These will produce any
number of short-term pressure spikes and drops during the treatment. Do not even attempt to
model them.
In practice during the pressure match, try to use average values for formation properties that
will produce a good “overall” value. Thus, the ideal pressure match will produce a relatively
smooth curve that closely follows the trend of the real data, but does not match every single
variation (see Figure 19.1a).
In particular, most treatments see a “break down” pressure, right at the beginning of the
treatment. This generally means a large pressure spike, followed by a lower, more stable
pressure. This pressure spike is caused by near wellbore effects and should not be matched.
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3.
Watch Out for Tortuosity
Tortuosity can seriously affect the bottom hole treating pressure. Remember that even if the
Frac Engineer has access to bottom hole gauge pressure data, this data will be from inside
the wellbore, not inside the fracture. Tortuosity can often vary significantly during a treatment.
In particular, an increase in proppant concentration can often produce a pressure rise if
tortuosity is present.
The various methods for identifying and quantifying tortuosity have been discussed in earlier
sections of this manual. If these methods are used it is possible – to a certain extent – to
allow for these effects.
Another thing to be careful of is an overuse of the tortuosity tables in the fracture simulator.
The latest versions of the main models allow different pressure drops to be entered for
different periods during the pumping. By putting enough detail and enough stages into these
tables, it is possible to get the simulator to predict virtually any net pressure profile
imaginable. The Frac Engineer must have a grasp of what is realistic and what is not. This
mainly comes with experience.
4.
Start with the Pressure Decline
The best place to start the pressure match is with the post-treatment pressure decline. This is
because the fluids are stationary and effects such as pipe friction, perforation friction and
tortuosity are eliminated. It is also often possible to identify the closure pressure on the
decline curve. This value is equal to the in-situ stress for the formation next to the
perforations. Once this value has been obtained, the end of treatment net pressure is defined
(the difference between the ISIP and the closure pressure). The four main variables should be
adjusted to produce this net pressure and to match the shape and length of the pressure
decline between ISIP and closure.
This gives the Frac Engineer a good starting point. Obviously, as the pressure match
continues and the Engineer alters variables to match the rest of the treatment, the pressure
match for the pressure decline will be altered. So further changes have to be made to bring
this back into match. Which in turn will affect the rest of the pressure match, and so on. This
is a part of pressure matching – the process of gradually making smaller and smaller changes
to the variables until all the seemingly contradictory requirements are met.
5.
Early Time vs Late Time
At the start of the treatment the fracture is relatively small, and will be confined to the
formations at, or near to, the perforations. Therefore, during this “Early Time” period, there is
little point in altering the properties of formations that are away from this area. However, as
the treatment progresses into “Late Time”, the fracture will become increasingly influenced by
the properties of formations vertically further away from the perforations.
Therefore, if the first stage in the pressure match process is to match the pressure decline,
the next stage is to match the Early Time fracture. At this point, there will be fewer variables
to alter. Once an Early Time match has been obtained, match the Late Time section. Then
keep repeating until the match has been achieved.
6.
Remember Nolte Analysis
In spite of the fact that Nolte analysis is based on PKN 2-D fracture modelling, the basic
principals can be very helpful when pressure matching. For instance, a gradual rise in the
next pressure plot indicates fracture containment, whilst a decline probably means a
preferential height growth and possibly a radial fracture (or GDK fracture geometry,
sometimes found when fracturing coal seams).
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19.2
Well Testing for Fracture Evaluation
Well testing is sometimes used both to assess the effect of the treatment and to help
determine the size and shape of the fracture. To do this, well tests have to be performed both
before and after the treatment. Data that is collected before the treatment is used to help
evaluate the fracture geometry afterwards.
Both pre- and post-treatment tests should be performed at constant rate (or as near as
possible), rather than at constant drawdown, and should be followed by a shut in (or pressure
build-up) period, lasting for at least as long as the flow time. In practice, it is possible to
monitor the pressure build-up real-time and see when the build-up can be terminated. The
post-treatment well test can take some time, as treatment fluids must be recovered first, and
the well must reach some kind of relatively steady flow.
Figure 19.2a illustrates the basic anatomy of a drawdown / build-up well test.
Pi
Pws(tp+∆
∆t)
BHP
∆Pdrawdown
∆Pbuild-up
Pwf(t)
Pwf(tp ) = Pws(∆
∆t = 0)
CONSTANT RATE DRAWDOWN
0
t
BUILD-UP
tp
∆t
Figure 19.2a – Anatomy of a drawdown / build-up well test (after Agarwal, 1980)
In Figure 19.2a, there are several variables that are often referred to in well test analysis,
which can be broken down into two groups – time and pressure. All pressures refer to BH
pressure. At the start of the well test t = 0, and the BHP = Pi, which ideally will be the reservoir
static pressure. Sometimes this is not the case, if the well has not been left static for a long
enough period. However, this can be allowed for in well test analysis. As the well is produced
at a constant rate, the length of time the well has produced for is called t and the flowing BHP
is referred to as Pwf. Because this variable is dependent upon t (the longer the well is
produced, the lower the BHP), it is said to be a function of t, and so the notation Pwf(t) is used
to denote this. The difference between the initial pressure (Pi) and the actual flowing pressure
(Pwf(t)) is referred to at the drawdown, or ∆Pdrawdown. The well is flowed at a constant rate
(which may require the varying of chokes) until it is shut in. At this point, t is said to equal the
producing time, tp (which is a constant, for any given test). After the well is shut in, the
nomenclature ∆t is used to describe the shut in time, such that at the point of shut in t = tp and
∆t = 0. Thereafter, time is described as tp + ∆t, with tp fixed and ∆t increasing as the build-up
progresses. At the point of shut in, the BHP pressure is referred to as Pwf(tp) – well flowing
wellbore pressure at tp – or as Pws(∆t = 0), the static wellbore pressure at ∆t = 0. These two
pressures are identical. After shut in, during the pressure build-up, the now static BHP is
referred to as Pws(tp+∆t) – this means that the wellbore static pressure (Pws) is a function of
shut in time (tp+∆t). Finally, the difference between the shut in pressure (Pwf(tp) or Pws(∆t=0))
and the wellbore static pressure (Pws(tp+∆t)) during the build-up is referred to as the build-up
pressure, or ∆Pbuild-up.
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Figure 19.2a illustrates the most basic type of well test, the constant rate drawdown and static
build-up test. This type of test can be applied to the well both before and after the treatment,
as discussed below. There are many other and more complex types of well test performed,
designed to get more accurate data under specific circumstances. A full discussion on the
current state of well testing and well test data analysis is beyond the scope of this manual and
the reader is invited to consult the references for further information.
Infinite or Finite Conductivity Fractures
From a pressure transient analysis perspective, propped hydraulic fractures fall into two
categories, infinite conductivity and finite conductivity. The pressure transient behaviour of
these two types of fracture is significantly different.
Infinite Conductivity fractures have no significant pressure drop as the fluid passes down
the fracture. Therefore, pressure transients happen outside of the fracture, either in the
wellbore or in the formation. With this type of fracture, the productivity of the well-fractureformation system is limited by the ability of the formation to deliver formation fluids to the
fracture, rather than by the ability of the fracture to transport the fluids. This type of fracture is
typical of low permeability and/or tight gas fracturing.
Finite Conductivity fractures have a significant pressure drop as the fluid passes down the
fracture. Therefore pressure transients occur inside the fracture, as well as in the wellbore
and the formation. With this type of fracture, the productivity of the well-fracture-formation
system is limited by the ability of the fracture to transport formation fluids to the wellbore, i.e.
by the fracture conductivity. This type of fracture is typical of high permeability fracturing.
Pressure Transient Analysis
When a well is flowing, it can be in one of three states – Steady, Pseudo or Transient. The
difference between these three states was discussed in Section 12 of this manual. During well
testing, the flow is usually in the transient state, which is the most complex of all to analyse,
and occasionally in pseudo-steady state. Put basically, steady state flow behaves as per
Darcy’s Equation, with a constant re and Pi, whilst transient flow behaves like there is no outer
boundary to the reservoir (so that the radius of investigation, rd, is continually increasing).
Pseudo-steady state is halfway between the two, with a constant re and reservoir pressure
that declines with production (i.e. a bounded reservoir). In reality, steady state Darcy radial
flow very rarely exists. The difference between transient and pseudo-steady state can be
seen from constant rate drawdown and pressure build-up tests, as shown in Figure 19.2b.
The basic Equation for pressure transient analysis is relatively easy to comprehend (although
its derivation is very complex).
Pi – Pr, t
=
q Bo µ
4π kh
φµcr2
1-e
4kt
............................................ (19.1)
where Pi is the static reservoir pressure, Pr, t is the pressure at radius r after time t, q is the
stabilised flow rate, Bo is the oil formation volume factor (a factor used to correct surface
volumes to bottom hole volumes) in rbbls/stb, µ is the viscosity of the produced fluid or fluids
(at bottom hole conditions), k is the permeability, h is the net height, φ is the porosity of the
formation and c is the overall compressibility of the formation and fluids (also called ct).
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Constant Rate Drawdown
Pressure Build Up
Transient
BHP
BHP
Pseudo-Steady State
Transient
Pseudo-Steady State
t
t
Figure 19.2b – Graphs illustrating the deviation from transient flow caused by a reservoir
boundary (i.e. pseudo-steady state flow)
Under constant rate drawdown Equation 19.1 can be simplified to:Pi - Pwf
=
q Bo µ
4π kh
loge
kt
φµcrw2
+ 0.809 ................................... (19.2)
In field units (pressure in psi, flow rate in bbls per day, viscosity in cp, distances in ft,
-1
compressibility in psi , permeability in mD, time in hours and porosity expressed as a
fraction):Pi - Pwf
=
162.6 q Boµ
kh
log10
kt
φµcrw2
- 3.23 ........................... (19.3)
So for transient flow, during a constant rate drawdown, a plot of Pwf against log t will produce
a straight line of gradient equal to (162.6qµ /kh). From this, if the flow rate, viscosity, volume
factor and net height are all known, the permeability can be evaluated by measuring the
gradient of the straight line portion of the curve, as shown in Figure 19.2c. This is a very
common method for evaluating permeability, but is dependent upon the well being produced
at a constant – or nearly constant - rate. The permeability value produced by the test is much
more useful for Frac Engineers than permeability derived from log or core analysis. First, this
value is an "average" Figure for the whole net height being produced. Second, well test
analysis is the only investigative method that penetrates deep into the reservoir and so the
results are not influenced by irrelevant near wellbore effects.
The radius of investigation of the test, rd, can be evaluated using Equation 19.4. This allows
the distance at which a boundary is observed (see Figure 19.2b) to be estimated, by setting
the value of t (in hours) to be when the drawdown semi-log plot starts to deviate from the
straight line.
rd
Page 195
=
2
0.00105 k t
........................................................... (19.4)
φµ c
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162.6 q Bo µ
kh
Pwf
slope =
log10 t
Figure 19.2c – Constant rate drawdown semi-log plot. The straight line section can be used to
evaluate the permeability. The deviation from the straight line at late time, is due to boundary
effects of the reservoir, as the transient flow changes to pseudo-steady state flow.
rd
=
2
0.00105 k t
........................................................... (19.4)
φµ c
After shut-in, the pressure in the well starts to build up, as illustrated in Figure 19.1a. The
Equation defining the behaviour of the pressure is as follows, in field units:-
P* (Transient)
slope = m =
Pws(tp+∆
∆t)
P* (PseudoSteady State)
162.6 q Bo µ
kh
INCREASING ∆t
0
log10
tp + ∆ t
∆t
Figure 19.2d – Example Horner plot, showing extrapolation of the straight line portion to obtain
P*, the average static reservoir pressure. Once again, deviation from the straight line is caused
by a change from transient flow to pseudo-steady state flow.
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Pi – Pws(tp+∆t)
=
162.6 q Boµ
tp+∆t
log10
....................................... (19.5)
kh
∆t
Therefore, a plot of Pws(tp+∆t) against log10[(tp+∆t)/∆t] will produce a straight line for transient
flow, which will have a slope equal to (162.6qµ /kh). This plot is often referred to as a Horner
plot and is a widely used tool in pressure transient analysis. An example is illustrated in
Figure 19.2d. Note that as ∆t tends to infinity, (tp+∆t)/∆t tends to 1 and hence log10[(tp+∆t)/∆t]
tends to 0. Therefore, by extrapolating the Horner plot back to where the x-axis equals zero,
an estimate for the static reservoir pressure can be made. This means that the pressure buildup portion of the well test can be more useful than the drawdown phase, and that the well
does not need to be shut in for a long time prior to the well test, in order to get an accurate
Figure for Pi.
So from the drawdown test, we can get reliable data for the average reservoir pressure and k
(or often, kh, as the net height may be unknown). We can also get the skin factor S (see
Section 2.5) from the build-up data by applying the API Skin Factor Equation, in field units:S
= 1.151
Pws(∆t = 1)-Pwf(tp)
k
- log10
+ 3.23 ..... (19.6)
m
φµcrw2
where Pws(∆t = 1) is the static wellbore pressure 1 hour after the well is shut in, and m is the
slope from the Horner plot, as shown in Figure 19.2d.
Once the skin is known, the pressure drop due to the skin, ∆Pskin can easily be calculated:∆Pskin
= 141.2
q Boµ
S
2πkh
(field units) ................................... (19.7)
Which can be worked back into Equation 19.3:Pi - Pwf
=
162.6 q Boµ
kh
log10
kt
φµcrw2
- 3.23 + S ................. (19.8)
Diagnostic Plots
Diagnostic plots are standard plots used to determine the characteristics of the reservoir.
Usually, the diagnostic plot will consist of a log-log plot of the change in wellbore pressure,
∆P, against shut in time, ∆t, for the pressure build-up. Sometimes, semi-log plots (∆P plotted
against log ∆t) are also used.
In addition, the derivative of the pressure build-up, ∆P’, is also plotted alongside the pressure
data. This is a slightly different derivative than that used in minifrac pressure decline analysis,
and is generally calculated as follows:∆P’
= ∆t
∆P
.................................................................... (19.9)
∆t
Usually, this will produce a very noisy derivative plot, and it is common practice to use some
kind of smoothing or averaging algorithm to produce a clear derivative trend. Modern
computer-based analysis makes this easy.
Example diagnostic plots for fractured and non-fractured wells are shown in Figures 19.2e to
19.2h, below (after Economides et al, 1994):-
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∆P
∆P
∆P'
∆P'
log10 t
log10 t
Figure 19.2e – Log-log diagnostic plot with
derivative for the pressure build-up of an
infinite-acting reservoir (i.e. no boundaries
and no pseudo-steady state flow).
Figure 19.2f – Log-log diagnostic plot with
derivative for the pressure build-up of
reservoir with a partial boundary (e.g. a
sealing fault).
∆P
∆P
∆P'
∆P'
log10 t
log10 t
Figure 19.2g – Log-log diagnostic plot
with derivative for the pressure buildup of an infinite conductivity fracture
Figure 19.2h – Log-log diagnostic plot
with derivative for the pressure buildup of a finite conductivity fracture
Gas Well Testing
Gas well testing is an order of magnitude more complex than oil/water well testing, due to the
fact that the above theory assumes that the produced fluid is incompressible. Obviously, this
is not the case for gas wells. To compensate for this, Equation 19.8 is modified as follows:2
Pi - Pwf
2
=
1639 Q µiziTBg
kh
log10
kt
φµicrw2
- 0.351 + 0.87S
(19.10)
This Equation is in field units, were Q is the gas flow rate in scf/d, µi is the gas viscosity at
static reservoir conditions, zi is the z-factor at static reservoir conditions (the z-factor is a
dimensionless factor used to correct the ideal gas Equation to allow for real gas behaviour,
and is calculated or measured for each reservoir), T is the reservoir absolute temperature in
rankine and Bg is the gas formation volume factor (this is a factor used to correct surface
volumes to reservoir volumes, with units of cuft/scf).
Usually, this Equation is rearranged so that it is more conveniently used:m(Pi) – m(Pwf)
Page 198
=
1639 QTBg
kh
(log10tD – 0.351 + 0.87S) .................. (19.11)
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where
2
m(Pi)
=
Pi
........................................................................... (19.12)
µi zi
m(Pwf)
=
Pwf
........................................................................... (19.13)
µi zi
tD
=
2.634 x 10 kt
........................................................... (19.14)
φµicrw2
2
and
-4
Note that in Equation 19.14, rw is in feet. m(P) is referred to as the gas pseudo-pressure.
By using Equation 19.11 for the drawdown, similar techniques can be used as for oil well
testing. However, this time m(Pwf ) is plotted on the y-axis, and the slope of the straight line
portion is equal to 1639 QTBg/kh.
For the pressure build-up, the transformation from incompressible to compressible is similar:m(Pi) – m(Pws)
1639 QTBg
kh
=
log10
tp+∆t
..................................... (19.15)
∆t
For the Horner plot, the x-axis remains unchanged, but the y-axis plots m(Pws). The straight
line portion can be extrapolated back to where the x-axis = 0, to give m(Pi).
Type Curve Matching
10 2
S = 20
S = 10
S =5
10
CD = 0
S =0
10 4
10 3
=
D
C
D
=
C
D
10 5
=
C
=
D
C
1
10 2
PwD
S = -5
10 -1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
tD
Figure 19.2i – Type curves for a single well in an infinite reservoir, with wellbore storage and skin
damage (after Agarwal, Al-Hussainy and Ramey, 1970).
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Type curve matching is a technique that involves matching field generated data curves to
experimentally or numerically derived type curves. The field data is moved over the type
curve, until the type curve that most closely matches the field data is found. This technique
has become very popular recently, as it is very easily performed by computers.
Usually, there will be several different type curves available, for wells with different
characteristics such as skin, wellbore storage (see below), number of wells and reservoir
boundaries. A typical set of type curves is shown in Figure 19.2i, which is for a single well in
an infinite system (i.e. no boundaries), with wellbore storage and skin damage.
Where PwD is dimensionless pressure:PwD
=
kh (Pi - Pwf)
141.2 q Boµ
(Oil Wells) ................................. (19.16)
PwD
=
kh [m(Pi)-m(Pwf)]
1424 Q BgT
(Gas Wells)............................... (19.17)
and tD is as defined in Equation 19.14.
Wellbore Storage
Wellbore storage is a measure of how much the volume of liquid and gas contained in the
wellbore effects the flow of the well. For instance, the pressure transient theory outlined
above, assumes that there is an instantaneous change from flowing to not flowing, when the
well is shut in and vice versa. This assumption is probably valid for a drill stem test (DST),
where the valve being opened and closed is located downhole. However, for most well tests,
the controlling valve will be at the surface. When the well is shut in, there will be some flow
from the reservoir into the wellbore, otherwise the pressure in the wellbore would not rise. The
only way this can happen is if the wellbore expands. Similarly, when the well is opened, and
the pressure drops, the wellbore contracts. This storage effect is greatest when the wellbore
volume is largest (i.e. flow through casing) or when the fluids are compressible (i.e. gas wells
or wells with significant associated gas production).
The wellbore storage coefficient, C, is defined as follows, with volume measured in bbls and
pressure in psi:C
=
∆V
............................................................................ (19.18)
∆P
So that C is a measure of how much change in volume is produced for a given change in
pressure. Dimensionless wellbore storage, CD, as used in the type curves, is defined as
follows:CD
=
5.6146C
2 ................................................................... (19.19)
2πφchrw
Type Curve Matching
Type curve matching is performed as follows.
1. Select a set of type curves which most closely suit the well and reservoir situation, based
on items such as reservoir boundaries, skin factor, wellbore storage, number of wells and
whether or not the well has a hydraulic fracture.
2. Produce a log-log plot of ∆t against ∆P (or ∆m(P) for gas wells) for the well test data. This
can be for a constant flow rate drawdown, a constant drawdown flow or for a build-up. An
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19. Post-Treatment Evaluation
example is illustrated in Figure 19.2j. When constructing this plot, make sure the axes are
of the same scale as the axes used in the type curves. This is a critical component of the
type curve matching process, and is made very easy by computer-based methods.
3. Move the log-log plot of the test data over the type curves, until the data matches up with
one of the type curves. This process can often be very difficult – especially if the data is
noisy - as several type curves may have very similar shapes. Once the curves have been
matched, the type curves will yield (as in the case of Figure 19.2i) the dimensionless
wellbore storage coefficient and the skin factor.
4. The final step is to obtain the match pressure and match time. With the test data curve
still positioned at its curve match, pick a point on the test data plot. This can be any point,
and does not necessarily have to be anywhere near the data. In fact, it is often easier to
pick a point where two major axes cross. Note the value of ∆t and ∆P at this point (these
values are referred to as ∆tM and ∆PM). Then note the corresponding values for this point
on the type curve, to give tDM and PwDM, the dimensionless match time and pressure. This
process is more easily visualised if we imagine we have two hard copies of the plots. The
type curve plot is on paper, whilst the test data log-log plot is on a transparency. The
transparency has been moved over the type curve to obtain the match. Then, we have
selected a point on the test data plot, and pushed a pin through both plots to make a
small hole in each. ∆tM and ∆PM are the coordinates of the pin hole in the test data plot,
and tDM and PwDM are the coordinates of the pin hole in the type curve plot.
5. The match pressures and times can now be used to obtain reservoir data. The match
pressures are substituted into Equations 19.16 and 19.17, in order to determine the
permeability-thickness (kh or conductivity) of the formation, as shown in Equations 19.20
and 19.21. If the net height is known, the permeability can easily be found.
kh
= 141.2qBoµ
PwDM
∆PM
kh
= 1424QBgT
PwDM
∆m(P)M
(for oil wells) ........................... (19.20)
(for gas wells) ........................ (19.21)
103
∆P (psi)
102
10
1
10-2
10-1
1
∆t (hours)
10
102
Figure 19.2j – Example of a log-log plot of ∆t against ∆P, used for type curve matching.
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19. Post-Treatment Evaluation
109
∆m(P) (psi2/cp)
108
1
4 Slope
107
106
10-2
10-1
1
∆t (hours)
10
102
103
Figure 19.2k – Post-treatment log-log plot of well test data for a finite conductivity fracture in a
gas well. An infinite conductivity fracture would have a half slope.
Similarly, Equation 19.14 can be re-arranged to yield the porosity-compressibility product,
which is another variable that will be useful in future analysis:-
φc
-3
=
2.637x10 k ∆tM
tDM .................................................. (19.22)
µ r w2
Post-Treatment Well Testing
Once the well has been fractured, and the fracturing fluid has been recovered, the well can be
tested again, to assess the performance of the fracture. Usually, this test will consist of a shut
in for one hour, a constant rate flow period of about 24 hours and finally a shut-in period of
about 48 hours. These numbers are typical for oil wells. Gas wells are a little more complex,
as the flow is much more affected by non-Darcy flow in the fracture and wellbore storage. For
gas wells, it is advisable to rely on previous experience, and where that is not available, be
prepared to change the well test plan on location.
Basically, for a fractured gas well, the log-log plot of the test data should look something like
Figure 19.2k. With reference to this Figure (which is also applicable to oil wells, with DP as
the vertical axis), flow from a fractured well should fall into 5 distinct regimes, in chronological
order:•
•
•
Wellbore storage dominated flow.
Fracture linear flow, in which the flow is dominated by liner flow down the fracture to the
wellbore. This is usually characterised by a half slope on the log-log test data plot. This
period of flow will also not last very long.
Bilinear flow, in which fluid flow along the fracture and through the formation
perpendicular to the fracture faces are both significant. This flow regime is characterised
by a quarter slope on the log-log plot and should be a prominent feature of the test, if the
treatment has been successful. This is the most useful portion of the test data.
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•
Formation linear flow, where the test data is dominated by linear flow through the
formation, perpendicular to the fracture faces.
Pseudo-radial flow. This flow regime comes last and is characterised by a combination of
linear flow perpendicular to the fracture faces, and by radial flow from the formation
beyond the fracture tip.
•
For a gas well, the test should continue until significant data has been obtained for the bilinear
flow data, whether for drawdown or build-up. The best way to assess this is to plot the log-log
plot real time and watch for the quarter slope.
A typical set of post-treatment type curves is shown in Figure 19.2l.
In Figure 19.2l, the x-axis variable is the fractured well dimensionless time, defined as
follows:-4
tDx
=
f
2.634x10 kt
........................................................... (19.23)
φµcxf2
Where xf is the fracture half-length. It should be noted that this style of type curve is only valid
if the fracture half-length is significantly less than the reservoir’s radial extent.
Matching the test data log-log plot to the type curve is easier than for the pre-fracture test.
When the match is performed, the quarter slope portion of the test data log-log plot is
matched within the shaded area of Figure 19.2l. As all the variables for the dimensionless
pressure are already known, the type curve match is used to obtain the dimensionless
fracture conductivity, CfD, and the match times. The match times are used to find the fracture
half length, as follows in Equation 19.24.
10
1
PwD
CfD =
0.1
0.5
1.0
10-1
5.0
Region of Bilinear Flow
10
50
100
500
10-2
10-5
10-4
10-3
10-2
10-1
1
tDxf
Figure 19.2l – Type curves for a well with a finite conductivity, vertical fracture (after Agarwal et
al, 1979 and Economides et al, 1987).
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xf
=
2
-4
∆tM
tDx M
f
2.634x10 k
µφc
................................... (19.24)
As k and φc where obtained in the pre-fracture well test, the fracture half-length can be quickly
determined. Once xf has been found, the value for dimensionless fracture conductivity can be
used to obtain the fracture conductivity from Equation 10.1.
Taking this one step further, if the permeability of the proppant, kp is known (remembering to
allow for proppant damage, non-Darcy flow and multi-phase flow), then the average width of
the fracture, w̄ , can also be obtained.
Quarter Slope versus Half Slope
According to the theory, as the well starts to flow the system passes through five distinct
phases of flow:- wellbore storage; fracture linear flow; bilinear flow; formation linear flow; and
finally pseudo-radial flow. In practice, wellbore storage occurs at very early time, and fracture
linear flow only occurs for a very short period of time. For the majority of the well test period,
the data will be dominated by bilinear flow or formation linear flow.
If the fracture has a finite conductivity, the flow will spend a considerable amount of time in
the bilinear flow regime, as characterised by a quarter slope on the plot of Log ∆P against Log
∆t (the log-log plot). However, if the fracture has infinite conductivity, then the flow quickly
moves from bi-linear to formation linear, which has a half slope on the log-log plot. In fact,
often the quarter slope section will not be detected.
Spotting the difference between the two is easy. Bi-linear flow (finite fracture conductivity)
0.25
produces a straight line on a plot of ∆P (or ∆m(P)) against ∆t , whilst formation linear flow
(infinite fracture conductivity) produces a straight line on a plot of ∆P (or ∆m(P)) against ∆t.
Useful information regarding the fracture dimensions can be obtained from these plots, as
follows:Finite conductivity fracture (field units):k pw =
44.1qBµ 2
h mbf
k pw =
444.8q zi T 2
h mbf
1
φµctk
1
(oil wells)................................. (19.25)
φµctk
(gas wells) .......................... (19.26)
Infinite conductivity fracture (field units):xf
=
4.064 q B
h mlf
xf
=
40.925 q zi T
h mlf
µ
kφct
(oil wells)....................................... (19.27)
µ
kφct
(gas wells) ............................... (19.28)
where mbf is the slope of the straight line portion of the bi-linear flow plot (i.e. ∆P against
0.25
∆t ), whilst mlf is the slope of the straight line portion of the linear flow plot (i.e. ∆P against
∆t). Therefore, by using these plots, the average propped fracture width (w̄ ) can be found
for finite conductivity fractures, and propped fracture half length (xf) can be found for finite
conductivity fractures, provided an accurate proppant permeability is known, under the
producing conditions.
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A Word of Caution
Type curve methods for obtaining the fracture geometry from well test data are notorious for
being non-unique. A glance at Figure 19.2h will show that all the curves in the bilinear flow
area have similar gradients. Additionally, the analysis is very sensitive to the quality and
reliability of the data obtained. Formation permeability, for instance, is not a constant. It will
change with fluid saturations, so if the well shows a change in GOR, GLR or WOR between
the pre-and post-treatment tests, the permeability will be suspect. Therefore, be aware of the
limitations and risks associated with relying entirely upon this type of analysis.
19.3
Other Diagnostic Techniques.
Tiltmeters
Tiltmeters are extremely sensitive devices for measuring changes in orientation from the
vertical. Surface and downhole tiltmeters are used to measure the azimuth and geometry of
the fracture versus time, as illustrated in Figure 19.3a.
Surface tiltmeters measure the deflection of the earth at the surface. Usually, they are placed
in 30 to 40 ft deep bore holes, and placed around the wellbore, from a distance of as little as
100ft, to as great as half a mile. These tiltmeters are used to measure the fracture azimuth, or
the direction of the fracture relative to north. Because the determination of fracture azimuth
can often be performed on a qualitative basis, the accuracy of the data required is less than
that for determining fracture geometry. Therefore, fracture azimuth can be quite reliably
determined from these devices, if used correctly. However, surface tiltmeters cannot provide
any useful data regarding the fracture geometry, as they are usually too far away from the
fracture and located on the wrong plane. Subsurface tiltmeters are placed in wells adjacent to
the well being treated, at the same vertical depth. Because they are often much closer to the
fracture than the surface tiltmeters, and they are located perpendicular to the most likely
plane of fracture propagation, it is possible to obtain fracture height, width and length from
them, against time.
Depth
Fracture-induced
surface trough
Surface tiltmeters
Fracture
Downhole
tiltmeters in
offset wells
Figure 19.3a – The principle of tiltmeter fracture diagnostics (after Cipolla and Wright, 2000).
The accuracy of fracture geometry determination is controlled by a number of factors. The
most important factor is the number of tiltmeters used, which in turn is controlled by the
number of available observation wells. Obviously, the fewer the number of tiltmeters, the less
accurate the analysis is. Unfortunately, many candidate wells do not observation wells
conveniently positioned, or else the operator is unwilling to shut these wells in for the duration
of the set up, treatment and rig down (sometimes several days). Another major factor
affecting the quantitative analysis required in order to obtain fracture geometry, is the quality
of the data on the rock mechanical properties of the affected formations. The tiltmeter is
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19. Post-Treatment Evaluation
basically measuring the angular deflection of the rock at a particular point. The magnitude of
this deflection will depend upon the distance between the fracture and the tiltmeters, and
upon the mechanical properties of the rock between them (chiefly Young’s modulus and
Poisson’s ratio). If these rock properties are unknown – or worse still if the formations are
heterogeneous – then the accuracy of the measurements will be significantly reduced.
Microseismic
Microseismic fracture diagnostics rely on the use of several highly accurate seismographs,
similar in principle to the seismographs used to detect and measure earthquakes. Essentially,
as the fracture propagates through the earth’s surface, it does not grow in a smooth,
homogenous fashion. Instead, the fracture will tend to propagate in short bursts, each one of
which produces a small seismic shock wave that can be detected and measured. As these
microseismic events occur mostly at the fracture tip, it is possible, by using 3 or more
microseismographs positioned in 3-D space around the well, to map the position of each of
the microseismic events and hence the position of the fracture tip against time. It should be
remembered that the fracture tip encompasses the entire perimeter of the fracture, and that
the fracture (or fractures) could well be propagating all the way along this perimeter.
Therefore, the technique can measure fracture height, length and the overall shape of the
fracture.
As with tiltmeters, this technique requires the use of measuring devices positioned in
observation wells. If there are no suitable observation wells, then the technique cannot be
applied.
It should be remembered that any seismic device measures time, not distance. In order to
convert time into distance, the velocity of the shock wave through the rock formation(s) must
be known. This can often be obtained from acoustic logs, but is highly dependent upon the
formation bulk density, which in turn is dependent upon the porosity and the relative
saturations of liquids and gases. These factors, coupled with heterogeneity in the formation,
tend to limit the resolution and accuracy of the results. However, provided enough suitably
located measuring devices are used, this technique can be used to give a good overall idea of
the fracture geometry and to detect multiple fractures.
Radioactive Tracers
Radioactive tracers are soluble radioactive isotopes that are added to the fracturing fluids
during the treatment, on the fly. After the treatment, the well is logged using a tool fitted with a
Geiger-Müller detector that can identify and quantify the presence of the isotope. The idea
behind this is to see where the fracturing fluid has gone.
The capabilities of this technique are further enhanced by the use of three different
46
124
192
radioactive isotopes, Scandium-46 ( Sc), Antimony-124 ( Sb) and Iridium-192 ( Ir). These
are run at different times during the treatment. By logging the well with a tool that can tell the
difference between the isotopes, it is possible to see if different sections of the treatment went
in different directions.
Using radioactive tracers has a couple of drawbacks:1. Storage and transportation of the radioactive materials, even these low activity isotopes,
is governed by strict regulations in most areas and can often be more trouble than this
information is worth. This is especially true if the isotopes have to cross a national frontier
or go offshore.
2. The rocks in the formation reduce the count measured by the detector. Therefore it is very
difficult to tell the difference between a low level of radioactivity close to the wellbore, and
a high level of radioactivity some distance away from the wellbore. This means that whilst
the technique can be used to see where the fracture is located at the perforations, and to
a certain extent which perforations took fluids at which time during the treatment, it cannot
be used to detect fracture height or width.
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Temperature Logs
Temperature logs are used to detect where the
treatment fluid has gone. By running a
temperature log right after a treatment, and
measuring the temperature of the well against
depth, it is possible to see where the cold treating
fluid cooled down the hot formation as it entered.
The center of this zone is the point of fracture
initiation, as illustrated in Figure 19.3b.
DEPTH
Figure 19.3b – Generic temperature log illustrating
that the treating fluid has entered only a small
portion of the perforated interval. The fracture will
have initiated in this small interval. However, this
does not necessarily mean that this is the center of
the fracture.
Perforated
Interval
Section of Perfs
that is actually
taking fluid
TEMPERATURE
References
Johnson, D.E., Wright, C.A., Stachel, A., Schmidt, H., and Cleary, M.P.: “On-Site Real-Time
Analysis Allows Optimal Propped Fracture Stimulation of a Complex Gas Reservoir”, paper
SPE 25414, presented at the SPE Production Operations Symposium, Oklahoma City, March
1993.
Crockett, A.R., Okusu, N.M., and Cleary, M.P.: “A Complete Integrated Model for Design and
th
Real-Time Analysis of Hydraulic Fracturing Options”, paper SPE 15069, presented at the 56
California Regional Meeting of the SPE, Oakland CA, April 1986.
Meyer, B.R., Cooper, G.D., and Nelson, S.G.: “Real-Time 3-D Hydraulic Fracturing
th
Simulation: Theory and Field Case Histories”, paper SPE 20658, presented at the 65 SPE
Annual Technical Conference and Exhibition, New Orleans LA, Sept 1990.
FracPro Version 8.0+ On-Line Help, RES/Gas Research Institute, March 1998.
FracproPT Version 9.0+ On-Line Help, Pinnacle Technologies/Gas Research Institute, July
1999.
Hagel, M.W., and Meyer, B.R.: “Utilizing Mini-Frac Data to Improve Design and Production”,
Journal of Canadian Petroleum Technology, March 1994, pp. 26 – 35.
MFrac III Version 3.5+ On-Line Help, Meyer and Associates Inc, December 1999.
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19. Post-Treatment Evaluation
Cipolla, C.L. and Wright, C.A.: “Diagnostic Techniques to Understand Hydraulic Fracturing:
What? Why? and How?”, paper SPE 59735, presented at the SPE/CERI Gas Technololgy
Symposium, Calgary, Alberta, Canada, April 2000.
Economides, M.J, Hill, A.D. and Ehlig-Economides, C.: Petroleum Production Systems,
Prentice Hall, Upper Saddle River, NJ, 1994
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Agarwal, R.G., Al-Hussainy, R. and Ramey, H.J., Jr.: “An Investigation of Wellbore Storage
and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment,” Soc. Pet. Eng. J. (Sept
1970); Trans., AIME, 249.
Agarwal, R.G., Carter, R.D. and Pollock, C.B.: “Evaluation and Performance Prediction of
Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing”, paper SPE 6838,
JPT, 362-372, March 1979.
Agarwal, R.G., Carter, R.D. and Pollock, C.B.: “Type Curves for Evaluation and Performance
Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing”, paper
SPE 8145, JPT, 651-656, May 1979. (Published as an accompaniment to SPE 6838, above).
Bostic, J.N., Agarwal, R.G. and Carter, R.D.: “Combined Analysis of Post Fracturing and
Pressure Buildup Data for Evaluating an MHF Gas Well”, paper SPE 8280, presented at the
th
SPE 54 Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979.
Agarwal, R.G.: “A New Method to Account for Producing Time Effects When Drawdown Type
Curves are Used to Analyze Pressure Buildup and Other Test Data”, paper SPE 9289,
th
presented at the SPE 55 Annual Technical Conference and Exhibition, Dallas, Texas,
September 1980
Crafton, J.W.: “Oil and Gas Well Evaluation Using the Reciprocal Productivity Index Method”,
paper SPE 37409, presented at the SPE Production Operations Symposium, Oklahoma City,
Oklahoma, March 1997.
Cramer, D.D.: “Evaluating Well Performance and Completion Effectiveness in Hydraulically
Fractured Low-Permeability Gas Wells”, paper SPE 84214, presented at the SPE Annual
Technical Conference and Exhibition, Denver, Colorado, October 2003
Archer, J.S. and Wall, C.G.: Petroleum Engineering Principals and Practices, Graham &
Trotman, London, 1986.
Dake, L.P.: Fundamentals of Reservoir Engineering, Elsevier, Amsterdam, 1978
Cipolla, C.L. and Mayerhofer, M.J.: “Understanding Fracture Performance by Integrating Well
Testing and Fracture Modelling”, paper 74632, SPEPF, November 2001.
Arihara, N., Abbaszadeh, M., Wright, C.A. and Hyodo, M.: “Integration of Fracturing Dynamics
and Pressure Transient Analysis for Hydraulic Fracture Evaluation”, paper SPE 36551,
presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado,
October 1996.
nd
Horne, R.N., Modern Well Test Analysis – A Computer-Aided Approach, 2 Edition, Petroway
Inc, Palo Alto CA, 2002.
Cipolla, C.L. and Wright, C.A.: “State-of-the-Art in Hydraulic Fracture Diagnostics”, paper SPE
64434, presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane,
Australia, October 2000.
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20. Equipment
20.
Equipment
20.1
Horsepower Requirements
Working out horsepower requirements is a relatively easy thing to do, provided you know the
expected treating pressure and slurry rate:HHP =
STP x Slurry Rate
......................................................... (20.1)
40.8
where STP is in psi and Slurry Rate is in bpm. The 40.8 is simply a conversion factor for the
units (in the SI system, pumping power – in kW – is directly equal to pressure (kPa) multiplied
by rate (m3/sec)). This formula will tell you how many pumps of what size you need on
location. Remember to have at least 20% excess horsepower on location and - as a minimum
- mobilise at least one spare pump. This excess capacity is required in case of pump failure or
higher than expected treating pressures.
It is also worthwhile looking at the set of curves supplied with each pump – called “pump
curves”. These curves show the maximum rate and pressure that the pump can run at in each
gear. Correctly speaking, these curves are showing maximum torque from the engine.
Remember that it is quite possible to be limited by torque, rather than by horsepower. In such
a situation, the pump may not be able to run at a given rate and pressure, even though it is
within the pump’s rated horsepower. Remember also that the reduction ratios between the
engine and transmission, and between the transmission and the pump, will affect the final
torque available. In reality, “pump curves” are in fact “pump-transmission-engine” curves.
Figure 20.1a shows an example.
If a treatment is going to be close to the maximum power for a given pumping unit, it is
recommended that the pump curves be consulted in order to confirm that the pump can
actually do the treatment.
Figure 20.1a – Typical pump curves. This set is for a 30-16-6 frac skid, with a 16V92TA engine, a
CLBT8962 transmission and a pacemaker pump with a 4.5 inch fluid end. Nominal rating of the
pump skid is 700 HHP
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20.2
Flow Lines
This section is intended as a guideline only. Full details on requirements for high and
low pressure flow lines can be found in the BJ Services Standard Practices Manual,
and it is recommend that this should be consulted before any rig-up is designed.
Suction Hoses
It is essential that sufficient suction hoses be used between the tanks and the blender. The
only force available to move the fluid to the blender is the suction of the inlet pump and
hydrostatic pressure from a difference in fluid levels. This is not much. In order to ensure that
the suction pump receives fluid at sufficient rate, a simple rule applies;
One 4” diameter 10’ suction hose will carry up to 10 bpm of gel
If 20 bpm is required, then two hoses will be needed, and so on. In addition, longer hoses will
carry less rate. For instance, 20’ of 4” diameter hose will only carry half as much rate, i.e. 5
bpm. So if 20 bpm were required from tanks which were 20’ away, 4 x 4” flow lines would be
required.
From this it is easy to see why the blender is usually placed as close as possible to the frac
tanks, and why the frac tanks are often manifolded together with 8” (or larger) diameter lines.
Also consider the comparative diameter of manifolds and suctions hoses. For instance:An 8” manifold has a flow are of 50.26 sq inches. This corresponds to the same flow area as
4 x 4 inch hoses (50.24 sq inches). Therefore, there is little point in building an 8” manifold
and then using only 3 x 4” suction hoses.
Finally, remember that there is a difference between suction and discharge hoses. Suction
hoses need to be rigid, otherwise the suction pump of the blender can suck them flat.
Discharge hoses, which generally do not have to carry suction, are often made from non-rigid
hoses, which collapse flat when there is no fluid in them. This makes for easier storage and
makes the hoses easier to carry. As a general rule-of-thumb, suction hoses can be used for
the discharge (provided they have the correct pressure rating) but discharge hoses cannot be
used on the suction.
Discharge Hoses
The discharge hoses run from the blender to the high pressure frac pumps. Generally, one
discharge hose is required from the blender to each pump. These hoses do not need to be
rigid (see above comments on suction hoses) but must have sufficient pressure rating. They
must also have crimped connections (similar to high pressure hydraulic hose connections)
and not the old-style clamps. Discharge hoses should also be fitted with "whip-checks" at
each connection.
For rates below 5 bpm per pump, a single 3" discharge hose is required for each pump. At
rates above 5 bpm, a single 4" hose should be used - although at very high rates (15 bpm +),
more than one hose may be required.
High Pressure Flow Lines
When pumping abrasive fluids – such as a frac gel with proppant – down a high pressure
treating line, there is a limit to how fast it is advisable to pump. Above this pump rate, seals on
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20. Equipment
chiksans, swivels and hammer unions start to wash out. It is generally accepted in the
-1
industry that the velocity of the frac fluid should not exceed 40 ft sec . Therefore:Qmax =
2
2.33 d ............................................................................ (20.2)
where Qmax is the maximum flow rate down any single high pressure line, in bpm, and d is the
inside diameter of the line, in inches.
Important Points
1.
The actual inside diameter of high pressure flow lines is often significantly less than
the nominal diameter. Equation 20.2 should be used with the actual diameter. This is
illustrated in Figure 20.2a.
2.
HP flexible lines, such as Coflexip hoses, have separate guidelines. For these, follow
the manufacturer’s instructions.
Velocity Chart
Figure 1502 HP Iron
120
100
Fluid Velocity, ft sec
-1
1.5"
2"
80
3"
4"
60
40
-1
40 ft sec Max Velocity for Abrasive Fluid
20
0
0
10
20
30
40
50
60
Fluid Rate, bpm
Figure 20.2a – Chart showing fluid velocity against fluid rate for various nominal diameters of
Figure 1502 high pressure iron.
20.3
High Pressure Pumps
Most high pressure pumps used in hydraulic fracturing are of the triplex variety, although
quintuplex pumps are becoming more popular. Triplex means that there are three pistons
acting to pump the fluid, quintuplex means that there are five. These pistons are driven by a
rotating crankshaft, as illustrated in Figure 20.3a.
Figures 20.3b and 20.3c show what happens whilst the pump is operating. Figure 20.3b
shows the suction or inlet stroke of the cycle. As the plunger moves back towards the power
end, fluid is pushed through the suction valve by the blender. The spring acting to close this
valve requires 20 to 40 psi just to lift it up, so the blender must provide a boost pressure
significantly greater than this in order to quickly fill the fluid end.
Figure 20.3c shows the power or discharge stroke. As the plunger moves away from the
power end, the increased pressure in the fluid end causes the suction valve to close, and
once this pressure is high enough, the discharge valve to open.
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20. Equipment
Power End
Fluid End
Figure 20.3a – Schematic diagram of a generic frac pump
Discharge Valve
Plunger
Suction Valve
Figure 20.3b – Generic frac pump, suction stroke
Figure 20.3c – Generic frac pump, discharge stroke
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20. Equipment
Frac pumps are usually powered by diesel engines, although some have been built with
electric motors and even gas turbines. For diesel powered units (which includes all of BJ’s
frac pumpers), there will be a transmission and a drive shaft in between the pump and the
engine. The transmission allows the pump operator to select which gear the pump is in. Low
gear is for high pressure/low rate, whilst high gear is for low pressure/high rate. The
transmission usually includes a torque converter, which amplifies the torque coming from the
engine, for a corresponding drop in rpm’s. The pump curves supplied with each pump will tell
the operator what the maximum rate and pressure is for each gear. These curves include the
engine/transmission gear ratio, which is the ratio for the torque converter. For instance a 2:1
engine transmission gear ration means that the torque converter reduces the input rpm’s by a
factor of 2, and increases the input toque by a factor of 2.
Also included on most pumpers is a lock-up device. This is a mechanism that allows slip
between the engine and the transmission. In the event of the pump stalling, this can prevent
serious damage to the transmission and engine. In order to make this device “lock up” (which
means that there is no “slip” in the lock up device), the engine needs to be turning at a
reasonable rate (usually 1700 to 1800 rpm). Below this speed, the torque converter is not
locked up. The pump is still working, but there is slippage between the engine and
transmission. It is possible to run a pumper out of lock up, but the transmission will quickly
overheat if this is maintained for too long.
Frac pumpers come in a variety of sizes, ranging from 350 HHP to 2700 HHP. Bigger pumps
are more cost effective for big treatments, but are very expensive and can be difficult to move
on roads and onto location. Smaller pumps may require more operators, more maintenance
(per horsepower – maintenance per pump unit is not significantly effected by size) and take
up more space on location. Figures 20.3d to 20.3g illustrate some of BJ’s fleet of frac
pumpers.
Figure 20.3d – Skid mounted 16V 92T pump
unit (700 HHP). Skid splits into two parts.
Figure 20.3e – Two views of a trailer-mounted
Gorilla pump unit (2700 HHP)
Figure 20.3f – Body-load Kodiak pump unit
(2200 HHP)
Figure 20.3g – Skid-mounted 1200 HHP
pump unit
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20. Equipment
20.4
Intensifiers
Intensifiers are devices that are used for pumping frac treatments for extended periods at high
pressure and rate. They reply on conventional frac pumps to power them, and work on the
principle that at constant power, high rate and low pressure is the same as low rate and high
pressure. BJ Services no longer supplies intensifiers.
At the power fluid end of the intensifier, the frac pumps supply power fluid at high rate and
(relatively) low pressure. This acts to displace a large diameter piston down the power end. At
the other end of this piston is a smaller diameter piston, which is mounted inside the
downhole fluid end. This acts to pump the frac fluid at high pressure and (relatively) low rate,
as illustrated in Figure 20.4a.
Suction Stroke – Hydraulic fluid is forced behind the power fluid piston to force the piston
back. This allows the downhole fluid end to fill with frac fluid from the blender.
Power Stroke – The pressure on the hydraulic fluid is released. At the same time, the inlet
valve from the frac pumps is opened, allowing the power end to fill with power fluid. This
forces the piston down the power fluid end. At the other side of the intensifier, the frac fluid is
forced out of the downhole fluid end at high pressure.
2
2
One important parameter for each intensifier is the intensification ratio. This is equal to D /d
(see Figure 20.4a). This defines by how much the intensifier converts high rate-low pressure
into low rate-high pressure. For instance, with an intensification ratio of 2.5, the fluid pressure
going downhole will be 2.5 times the power fluid pressure, whilst the fluid rate going down
hole will be 2.5 times less than the power fluid rate.
Figure 20.4b shows how the intensifier is rigged up with the other equipment, whilst Figures
20.4c and 20.4d show intensifiers on location.
TO POWER
FLUID UNIT
OPEN
D
d
SUCTION
STROKE
FROM
BLENDER
CLOSED
HYDRAULIC
FLUID IN
TO WELL
CLOSED
POWER
STROKE
OPEN
HYDRAULIC
FLUID OUT
FROM FRAC
PUMPS
Figure 20.4a – Schematic diagram of a generic intensifier
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20. Equipment
BLENDER
FRAC PUMP
INTENSIFIER
FRAC PUMP
FRAC PUMP
COOLER
BOOST
PUMP
RESERVOIR
TO
WELL
POWER FLUID UNIT
Figure 20.4b – Schematic diagram of the intensifier hook-up.
E
D
A
C
B
Figure 20.4c – Intensifier worksite. Each intensifier (A) is hooked up to three frac pumpers (B),
which are pumping the power fluid. Power fluid is handled by the power fluid unit (C). Intensifiers
are rigged into a manifold (D). Note that whilst there are three intensifiers and 9 power fluid
pumpers on location, there are also an additional two frac pumpers (E) rigged up to the
downhole line to provide extra horsepower.
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Figure 20.4d – Detail of an intensifier. In the foreground, on the RHS, is the downhole fluid end.
In the background, on the LHS, is the power end, complete with high pressure iron rigging it to
the frac pumpers.
20.5
Blending Equipment
The blender is the heart of the fracturing operation. Although modern blending equipment is
often highly automated, the blender operator (or Blender Tender) still retains one of the most
critical positions on any location. Figure 20.5a shows a generic schematic diagram of a frac
blender.
LIQUID ADDITIVE TANKS
DRY
ADD.
BIN
PROPPANT SILO
TO FRAC TANKS
SLURRY SIDE
FLOW METER
RADIOACTIVE
DENSIMETER
SUCTION
PUMP
CLEAN SIDE
FLOW METER
DISCHARGE
PUMP
DISCHARGE MANIFOLD
SUCTION MANIFOLD
FROM FRAC TANKS
BLENDER
TUB
TO HIGH PRESSURE PUMPS
LA METERING
PUMPS
RECIRCULATION LINE
Figure 20.5a – Generic flow diagram for a frac blender. Note that on a blender fitted with a
Condor tub (such as BJ’s Cyclone I & II blenders), the functions of the blender tub and the
discharge pump are combined into a single unit.
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20. Equipment
The blender performs the following functions:i)
ii)
iii)
iv)
v)
Pre-gelling tanks.
Blending liquid and dry additives on the fly.
Blending proppant on the fly.
Providing supercharge for the high pressure pumps.
Metering and recording a variety of job critical parameters.
Figures 20.5b to 20.5e show some of BJ’s fleet of frac blenders.
Figure 20.5b – 125D Frac blender, capable of 125
bpm and 35,000 lbs/min proppant rate
Figure 20.5d – Skid mounted Cyclone blender
Figure 20.5c – Body-load mounted Cyclone II
blender, capable of 25 bpm
Figure 20.5e – LFC hydration unit
When pumping a treatment the frac spread can be set up to either gel the frac tanks before
the treatment - so that all the fluids are prepared beforehand – or to mix the gel on the fly.
Treatments with Pre-Gelled Tanks
When carrying out a treatment with tanks that are pre-gelled, considerable time and effort has
been invested into gelling a number of frac tanks filled with water. During this process, the
blender will be used to circulate the tanks (via the suction manifold, suction pump, blender
tub, discharge pump and recirculation line – see Figure 20.5a), whilst adding the necessary
ingredients to produce the required gel.
Advantages of Pre-Gelling Tanks:-
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20. Equipment
i)
ii)
iii)
Intense quality control can be carried out on the gel, prior to each tank being
accepted. If necessary, a tank or poor quality gel can be rejected, disposed off and
then re-blended.
Fewer additives need to be mixed on the fly.
No need for an LFC Hydration Unit
Disadvantages of Pre-Gelling Tanks:i)
Considerable time can be taken up by blending the gel.
ii)
Gel properties cannot be varied on the fly.
iii)
Approximately 5% of the gel will be wasted as tank bottoms.
iv)
Bactericide must be blended with the fracturing fluid to prevent sulphate-reducing
bacteria from breaking down the gel.
Mixing Gel on the Fly
Mixing the frac gel on the fly requires less pre-job preparation, but involves the use of more
equipment and the extra cost of the LFC or XLFC (Liquid Frac Concentrate – see Section 5).
LFC is an oil-based slurry of the polymer, usually mixed so that there is 4 lbs of polymer per
gallon of slurry. The LFC is added to the water on the fly, allowing the gel to be prepared as it
is needed. This requires an LFC hydration unit (see Figure 20.5e). This piece of equipment
consists of an LFC storage tank, a metered LFC additive pump (usually progressing cavity
type), a hydration tank and a boost pump. Water is supplied to the LFC hydration unit, which
meters in the LFC at a controlled ratio, to provide the required gel strength. The hydrating
LFC/water mix passes into the hydration tank, which is large enough so that the gel spends 3
to 4 minutes in there, before it is transferred to the blender by the boost pump. This 3 to 4
minute hydration time allows the polymer to hydrate. Some LFC Hydration units are supplied
with a QC system – consisting of a viscometer and a pH probe – to provide real time gel QC
information.
Advantages of Mixing on the Fly:i)
No wasted gel. Only the amount of gel required is blended, so that there is no
wastage from tank bottoms or if the treatment ends prematurely.
ii)
Gel properties may be varied on the fly.
iii)
Less time and effort required for job preparation.
iv)
No need to use a bactericide.
Disadvantages of Pre-Gelling Tanks:i)
Extra cost of using LFC, rather than dry powder.
ii)
Extra cost of LFC Hydration Unit.
iii)
Loss of gel properties if the LFC Hydration Unit has an equipment problem.
20.6
Proppant Storage and Handling
Proppant has to be stored on location, ready for use. It has to be kept clean and dry, and
must be delivered to the blender smoothly and quickly. Figure 20.6a shows frac sand being
delivered to the hopper of a blender:-
Figure 20.6a – Frac sand being
delivered from a Sand King to the
hopper of a blender. Note that
there are two blenders in this
picture – one is on standby as a
backup in case of equipment
failure.
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There are two main methods for ensuring the smooth flow of proppant from the storage bin to
the blender. The first method is to use a gravity-feed system, which relies on the proppant
being stored in a bin which is higher than the blender hopper. A gate valve is used to control
the sand rate. This can be done with either large vertically mounted bins (Figure 20.6b) or
from a dump truck (Figure 20.6c):-
Figure 20.6b – Vertically
mounted, gravity feed
proppant bins
Figure 20.6c – Trailer mounted sand dumper
The second method is to use a conveyor system to move the proppant from the bin or
dumper, to the blender hopper. This method is typically used on larger frac jobs, as there is
usually insufficient space around the blender hopper for all the bins to be positioned. Usually,
BJ’s first option for storing large volumes of proppant is the Sand King, as shown in Figure
20.6d:-
Figure 20.6d – BJ Services Sand King
The Sand King is designed to be hauled to location empty, and then filled up with proppant.
BJ has two models, one with 250,000 lbs capacity and one with 400,000 lbs capacity. The
proppant is held in several separate bins along the length of the Sand King. During the
treatment, gates – positioned at the bottom of the hoppers – are opened to allow proppant to
fall onto a conveyor. This conveyor runs along the bottom of the entire length of the Sand
King, and will transport the proppant to the blender hopper. When a very large treatment is
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20. Equipment
planned, such that several Sand Kings have to be used, a separate Sand Belt Conveyor is
used, as shown in Figure 20.6e:-
Figure 20.6e – Sand belt conveyor
This device allows several Sand Kings to be placed on either side of the belt, each one
feeding onto the main belts of the Sand Belt Conveyor. This, in turn, feed the proppant to the
blender hopper.
During the treatment, it is important that the proppant system can produce a smooth,
uninterrupted flow of proppant to the blender, often at quite high rates. It must also be able to
keep the proppant dry, as wet proppant can cause the blender’s proppant screws to seize up.
20.7
Treatment Monitoring
On a modern frac spread, almost every parameter can be measured, displayed and recorded.
The place at which this data is displayed and recorded is the Treatment Monitoring Centre,
which is usually either a van or a container, as illustrated in Figures 20.7a and 20.7b, below:-
Figure 20.7a – External view of BJ’s Stimulation Van 1800
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20. Equipment
Figure 20.7b – External view of a treatment monitoring container
The fracturing treatment will be controlled from this facility. The Frac Supervisor, the Frac
Engineer, the Pump Operator and the Company Man can sit in relative comfort and quiet,
making treatment-critical decisions, based on the data that is being collected and displayed.
Figure 20.7c – Two internal views of treatment monitoring vans
Most modern treatment monitoring facilities also include the capability to transmit the
treatment data real time back to a specially set up remote data monitoring computer. This can
be located either in BJ’s office or in the customer’s. With this facility, Engineers no longer
have to waste productive time on location or travelling to and from the location. This is
especially significant offshore, where the costs of mobilising personnel can be significant.
With the remote data transmission, the Engineers get the same data displayed via similar
software (typically JobMaster), with only a second or two delay. Typically, there is also a voice
link so that the on-site Engineer can discuss various items or pass on instructions.
One other feature of most treatment monitoring containers or vans is a field lab. This will be a
compact QC/QA facility, designed to ensure the quality of the fluids and proppants. On larger
frac spreads this may even be a separate piece of equipment. Sometimes these are fitted
with a fluid rheology and pH flow loop, allowing real time viscosity and pH data to be
displayed and recorded.
20.8
The Wellhead Isolation Tool
The Wellhead Isolation Tool (WIT), often referred to as a ”Tree Saver”, is a device that allows
treatments to be pumped at a STP higher than the maximum pressure rating of the wellhead.
This allows treatments to be pumped at much higher rates than would normally be possible.
The WIT does this by completely isolating the wellhead from the treating fluid, as illustrated in
Figures 20.8a, b, c, and d.
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20. Equipment
The tool is used in the following manner:•
•
•
•
•
•
•
•
•
Prior to the treatment, the WIT operator obtains data for the type and size of wellhead top
flange connection, the distance from the top flange to the tubing hanger, the tubing size
and the tubing weight. This allows the WIT operator to assemble the stinger and seal
assembly to match the wellhead.
The wellhead master valve is closed, and any pressure between the master valve and the
top flange is bled off.
The WIT is assembled to the top flange, as illustrated in Figure 20.8a. Some WIT’s are
fitted with a master valve above the stinger (below the Tee section), whilst others require
additional valves to be fitted.
The WIT operator applies hydraulic pressure to the lower connection on the master
cylinder, to ensure that the tool is fully extended, or stung out of the wellhead.
The valves at the top of the WIT are closed and the tool is pressure tested.
The wellhead master valve is opened and the WIT is exposed to wellhead pressure.
The tool is stroked down by pumping hydraulic fluid into the top connection on the master
cylinder.
The stinger and the seal assembly are sized so that the seal assembly stings into the top
of the tubing, at the point when the stinger is fully stroked into the well.
The upper section of the WIT and the master cylinder are clamped together, so that
hydraulic pressure is no longer required to keep the tool stung into the tubing.
The WIT tool can be extremely useful,
as it can be operated on a live well. This
then eliminates the need killing the well
and replacing the wellhead.
Use of the WIT on a live well is a very
specialised process, requiring a trained
operator. The tool can be very
dangerous if not assembled or operated
correctly.
The WIT is generally available in two
main sizes, big and small. The small size
is used for stinging into most tubing
sizes, from 2-3/8” up to 4” or larger. The
large sized tool is used for stinging
directly into casing, with no tubing in the
well.
Hydraulic
Valve
Master Cylinder
Hydraulic Lines
Seal Assembly
Wellhead
Swab Valve
Sub Master Valve
Master Valve
Figure 20.8a – Generic wellhead isolation
tool rigged up to wellhead. The WIT is
connected to the wellhead via the
wellhead’s top flange. At this point the
wellhead master and sub master valves
are closed, maintaining control of the well
and allowing the frac lines and WIT to be
pressure tested.
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Isolation Tool
Tubing Hanger
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20. Equipment
In
Clamp
Hydraulic
Fluid
Out
Figures 20.8b (left) and 20.8c (right) – Once the WIT has been connected to the wellhead and
pressure tested (Fig 20.8a), the next stage is to close the valves of the frac lines (not shown –
note that some WIT’s have their own master valves) and open the master and sub master valves
on the wellhead. One the wellhead is open, the stinger is stroked down into the top of the tubing
by pumping hydraulic fluid into the master cylinder.
Figure 20.8d – Wellhead isolation tool
rigged up on location. Note the two 3”
frac lines connected to either side,
plus the remote actuated 4” plug
valve.
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20. Equipment
20.9
The Frac Spread – How it Fits Together
Treatment
Monitoring
Blender
Annulus Pump
Frac Pumps
Proppant
Fluid Tanks
LFC Hydration
Frac Pumps
Low Pressure Lines
High Pressure Lines
Control/Data Cables
Figure 20.9a – Schematic diagram of a frac spread
Figure 20.8a illustrates how all the various components of the frac spread fit together. All frac
spreads will basically look like this, although the size and number of components may vary.
Some treatments will not use an LFC hydration unit, as the gel will be batch mixed prior to the
treatment. Some treatments may use intensifiers, whilst some treatments (“batch” fracs, or
Liquid Proppant fracs) may not have separate proppant handling equipment.
However, the basic process is the same, no matter what kind of treatment is being performed.
Fluid (usually water) is moved from the storage tanks and is usually blended with gelling
agents to increase its viscosity. It is then blended with the proppant and pumped down the
well.
Figures 20.8b to 20.8f, below, show some typical frac spreads:-
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20. Equipment
Figure 20.9b – Large scale treatment, carried out on several low permeability zones
simultaneously. Note the number of Sand Kings and frac tanks on location, as well as the use of
two blenders (one for backup in case of equipment failure). This frac spread features a separate
mobile field lab (bottom left) and a third blender, just for gelling up the tanks and for pumping
fluid from the tanks that are located a significant distance from the blender (located just above
the bottom left hand row of frac tanks).
Figure 20.9c – The MV Blue Ray, a Gulf of Mexico frac boat, designed primarily for high
permeability, frac and pack treatments.
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20. Equipment
Figure 20.9d – Skin Bypass Frac spread, using the “batch” frac method. The two frac pumps are
positioned opposite each other, just below the wireline mast (the small read and yellow derrick).
A third pump (with “BJ” painted on its roof) is being used as an annulus pump. The two vertical
stainless steel tanks on the RHS are for fluid storage. The two batch mixers (each with two round
batch tanks - the blue batch mixer is 2 x 50 bbls, whilst the red one is 2 x 40 bbls), used to batch
mix the proppant into the gel, are located at the bottom of the picture.
Figure 20.9e – Coiled tubing frac spread. The wellhead is positioned directly below the CT
injector (center of picture), with the reel on the RHS. On the LHS are two nitrogen tankers. The
main part of the frac spread is positioned behind the injector, with the sand dump truck being
the most prominent feature.
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20. Equipment
Figure 20.9f – The MV Thanh Long. This was a boat put together for a single fracturing treatment,
for a customer operating offshore Vietnam. The aft deck holds the following equipment:- 4 x 1200
HHP frac pumps, Cyclone II blender, 2 x 640 cu ft proppant bins, treatment monitoring container
c/w field lab, 4 x 165 bbls tanks and a 100 bbl vertical tank.
References
Standard Practices Manual, BJ Services, January 2001 onwards
Corporate Safety Standards and Procedures Manual, BJ Services, January 2001 onwards
Equipment and Technology Catalogue, BJ Services, 1990 onwards
Bradley, H.B. (Ed): Petroleum Engineers Handbook, SPE, Richardson, Texas (1987)
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
Gidley, J.L., et al: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
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21. Designing Wells for Fracturing
21.
Designing Wells for Fracturing
The single biggest influence on the feasibility of the hydraulic fracturing process is the design
of the well, including its completion and perforations. The influence of perforations and how
they can be designed to maximise the effectiveness of hydraulic fracturing, has been
discussed in Section 14. In this section, we will discuss the philosophy and impact on well
planning and design of the hydraulic fracturing process. On a wider scale, we shall discuss
the influence hydraulic fracturing can have on field development, whilst on the smaller scale
we shall discuss how to plan individual wells for fracturing.
21.1
How Many Wells do I Need to Drill?
The answer is, not nearly as many as you think.
Very few operating companies outside of North America plan a field development with
stimulation in mind. Hydraulic fracturing is the most effective form of stimulation, but it is also
the type is most often restricted by the design of a well. Fracturing is often perceived by
Engineers who do not have first hand experience with the process, as a high risk operation.
Consequently, the Engineers who design the development of a field are either not aware of
the benefits of fracturing, or not aware of the chances of a successful treatment.
If a well is planned with hydraulic fracturing in mind, it is relatively realistic to expect at least
double the production from the treated well, compared to the untreated well. In many cases,
fracturing will produce a production increase significantly greater than this. In addition, often
production targets can be met at significantly lower drawdowns, which can have a
tremendous impact on reservoir management and can often prevent or significantly delay the
onset of water production from a WOC or gas production from a gas cap.
So if an operating company can produce at least twice as much oil from a given well, what
does this mean for reservoir development plans?
It means that the operating company needs to drill fewer wells, which can result in
tremendous cost savings - especially offshore, where the need for fewer wells may even
eliminate the need for entire platforms. Obviously, in highly faulted reservoirs, each “pool” will
need at least one well, but in reservoirs that would ordinarily require several wells, it is not
unreasonable to expect to eliminate up to half of these.
Injection wells can also be fractured very effectively. An additional benefit to fracturing is that
each zone in an injection well can be individually treated, allowing a specific fracture, of a
specific conductivity, to be placed in each zone. This allows the Reservoir Engineer to custom
design the injectivity profile of an injection well, to meet the requirements of long term
pressure maintenance.
Traditionally, the only sector of the industry that has a profound understanding of what can be
achieved by fracturing, is the tight gas sector. Most tight gas wells have to be fractured otherwise they would not be economic. In a lot of cases, these wells have to be fractured or
they would not produce at all. In these areas, the tight gas operating companies are totally
dependent upon the hydraulic fracturing process for the success or failure of their field
developments. Yet companies keep drilling wells, keep developing tight gas fields and keep
fracturing them – so the process must be successful.
If it works for tight gas wells, why not for oil wells or even high permeability gas wells? After
all, the basic process is the same, the equipment is the same, the proppants are the same
and the fluids are the same. The only thing that varies from well to well is the amount of each
of these items we use and the relative quantities in which they are used. Obviously, the
potential percentage production increase from fracturing a tight gas well is much greater than
for fracturing a high permeability oil well. However, which generates the most revenue –
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21. Designing Wells for Fracturing
increasing the production from a tight gas well from 50 mscfpd to 500 mscfpd, or increasing
the production of an oil well from 5,000 bopd to 10,000 bopd? Both of these production
increases are realistically achievable.
21.2
The Best Wells are also the Best Candidates for Fracturing
Too often, hydraulic fracturing is seen as a last-try-process, used because the company has a
bad well and needs to do something with it. Unfortunately, in most circumstances, hydraulic
fracturing cannot turn a bad well into a good well, unless the only reason for the low
production is a large skin factor. In all cases, the reservoir must have some potential in order
for the full benefits of the fracturing process to be realised.
In the late 1980’s, a company operating in the Danish sector of the North Sea, began
developing a new field. The oil was held in the highly same highly productive chalk
formations, which were responsible for the huge Ekofisk development, just across the border
in the Norwegian sector. The traditional way to develop these reservoirs was to drill deviated
or S-shaped wells through the chalks and then perform an acid frac. However, the operating
company – and its partners (which included some major US operating companies) - realised
that this may not be the best method.
Over a series of wells and a number of years, the operating company perfected a method for
developing their reservoirs that involved drilling long horizontal wells, each of which would
have between 8 and 15 fracs placed along its length, depending upon the length of the
productive section. Each of the horizontal liners was cemented in place – a bold new
approach in itself – and selectively perforated to control the point of fracture initiation (see
Section 13). These wells were also fitted with a special completion, which allowed individual
access to each of these perforated intervals.
Then, over a period of 4 to 8 weeks, each of these zones would be hydraulically fractured. As
time progressed and the technology improved, this time decreased, but still took weeks,
rather than days, to frac each well. In one well, the company successfully pumped over 13
million lbs of proppant, a record for a well that has only recently been passed.
How much did this cost? A lot. Each well drilled and completed in this fashion typically cost 3
times what a conventional well would cost, in a part of the world where drilling costs were
already huge. However, each well was also producing between 4 and 6 times what the typical
conventional well was producing. In addition, the conventional acid fractured wells had to
have the acid fracture repeated every 18 months to 2 years, as the highly plastic chalk
formations slowly deformed into the fractures. However, this was not the case with the
propped fractures, resulting in greatly reduced future expenditure.
The point of this story is that good wells are the best candidates for fracturing. The industry
should not be limited to remedial and low-productivity applications. When selecting
candidates for fracturing look for the good wells first.
21.3
Designing Wells for Fracturing
The best time to fracture a well is right after it has been drilled and cased – before the
completion has been run. This is another reason why it is important to consider the
implications of fracturing whilst planning the well. In general, completions act to restrict what
can be done with a treatment, and can often eliminate the fracturing option entirely.
Completions can limit fracturing operations for the following reasons:i)
Pressure limitations. Fractures are created by pressure, and as a result abnormally
high pressures can be generated by the treatment. Often, completions are not
designed to withstand this loading. Although it is often possible to reduce this effect
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21. Designing Wells for Fracturing
by placing pressure on the annulus, many are completed with two or more packers,
eliminating the effectiveness of annulus pressure.
ii)
Temperature limitations. The pumping of a cool frac fluid will cause the completion
to shrink. Sometimes, the completion can shrink so much that the tubing can sting out
of packers. The effect of the extra pressure acts to make this effect even worse.
iii)
Completion jewelry. Items such as sub-surface safety valves, gas lift mandrels and
sliding side doors can often take significantly less differential pressure than the actual
completion itself.
It should be noted that the above three limitations can be eliminated by the use of coiled
tubing in the fracturing process.
iv)
Multiple zones. Often, wells are completed with multiple sets of perforations. Whilst it
is possible to treat multiple zones at the same time, it is generally a much more
complex process, which requires more equipment and more materials (treating two
identical zones requires twice the pump rate, and twice the volume of proppants and
fluids. It may require significantly more than twice the hydraulic horsepower, as the
friction pressure will rise by significantly more than this factor).
In short, if the well can be fractured before it is completed, all the limitations imposed by the
completion can be eliminated. However, doing this requires a degree of forward planning,
faith in the fracturing process and increased up-front expenditure.
Fracturing before completion allows the perforate-stimulate-isolate method to be employed:1. Perforate
The individual zone is perforated, allowing each zone to be fractured with the
optimum treatment. By carefully positioning the perforations, the point of
fracture initiation can be controlled..
2. Stimulate
The fracture treatment is pumped either down the casing or through a frac
string.
3. Isolate
The zone is isolated by setting either a sand fill or a bridge plug.
Repeat steps 1 to 3 as often as necessary, moving from the bottom to the top of the well.
Obviously, this process can take a lot longer than the conventional drill and complete process.
However, the extra cost is more than offset by the substantially increased production from
these wells.
If the well cannot be fractured prior to completion, then the completion should be designed
with fracturing as a potential scenario. Packers and tubing jewelry should be designed to
withstand the pressures of fracturing. Seal assemblies should be long enough to cope with
the cooldown. Zones should be as isolated as possible.
Of course, all this requires substantial extra investment, which has to be justified purely on the
basis of faith in the fracturing process. However, in case after case, field development after
field development, this initial expenditure has proved its worth.
References
Nagel, W.B, et al.: “An Integrated Team Approach for Improving Company-Wide Stimulation
Design and Quality Control”, paper SPE 26142, presented at the SPE Gas Technology
Symposium, Calgary, June 1993.
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21. Designing Wells for Fracturing
Cipolla, C.L., Bernsten, B.A., Moos, H., Ginty, W.R., and Jensen, L.: “Case Study of Hydraulic
Fracture Completions in Horizontal Wells, South Arne Field Danish North Sea”, paper SPE
64383, presented at the SPE Asia-Pacific Oil and Gas Conference and Exhibition, Brisbane,
October 2000.
Owens, K.A., Pitts, M.J., Klampferer, H.J., and Kreuger, S.B.: “Practical Considerations for
Well Fracturing in the ‘Danish Chalk’”, paper SPE 25058, presented at the SPE European
Petroleum Conference, Cannes, France, November 1992.
Schubarth, S.K., Yeager, R.R., and Murphy, D.W.: “Advanced Fracturing and Reservoir
Description Techniques Improves Fracturing in......”, paper SPE 39777, presented at the SPE
Permian Oil Basin Oil and Gas Recovery Conference, Midland TX, 1998
Voneiff, G.W., and Holditch, S.A.: “An Economic Assessment of Applying of Applying Recent
Advances in Fracturing Technology to Six Tight Gas Formations”, paper SPE 24888,
presented at the SPE Annual Technical Conference and Exhibition, Washington DC, October
1992.
Stewart, B.R, et al.: “Economic Justification for Fracturing Moderate to High Permeability
Formations in Sand Control Environments”, paper SPE 30470, presented at the SPE Annual
Technical Conference and Exhibition, Dallas, October 1995.
Conway, M.W., et al.: “Expanding Recoverable Reserves Through Refracturing”, paper SPE
14376, presented at the SPE Annual Technical Conference and Exhibition, Las Vegas,
October 1985.
Church, D.C., and Peters, B.A.: “Improved Fracturing Technique Yields Increased Production
Potential”, paper SPE 17045, presented at the SPE Eastern Regional Meeting, Pittsburgh,
October 1997
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22. The Fracture Treatment
22.
The Fracture Treatment: From Start to Finish
22.1
Frac Job Flow Chart
Obtain Well data:
Logs, DST’s, Mud Logs,
Production History
(if any), PVT Data,
Completion Diagram,
Previous Treatments
Use Nodal
Analysis or
Similar
History Match
Production Data
IN OFFICE
Establish Base
Case Production
Input Speculative Fracture
Geometry into Production
Simulator
Run Production
Simulation with Fracture
Optimum
Fracture
Geometry?
No
Yes
Design Treatment for
Optimum Fracture Geometry
Using Fracture Simulator
Preliminary
Treatment
Schedule
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1
SRT Schedule
Minifrac Schedule
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22. The Fracture Treatment
1
Mobilise Equipment,
Materials and
Personnel
Rig Up, Mix Fluids,
Pressure Test
Pre-Job Safety
Meeting
ON LOCATION
Pump Step Rate
Test (Step Up and
Step Down)
Real Time
Data Modelling
Analyze SRT
Data
Fracture Extension
Pressure, Near
Wellbore Friction
Is NWF
Significant?
No
Pump
Minifrac
Yes
Pump Minifrac
with Proppant Slugs
Real Time
Data Modelling
No
Pressure
Rise due to Prop.
Slugs?
Yes
Pump Proppant
Slugs as per
SPE 25892
2
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22. The Fracture Treatment
2
Pressure Match Simulator
Output to Minifrac Data
Re-Design
Treatment
Final Treatment
Design
E, ν, Klc, Cl,ll, lll
Pnet, Pclosure, ηfrac
Load Proppant &
Additives. Mix Fluids
ON LOCATION
Pre-Job Safety
Meeting
Pump
Treatment
No
Monitor Pressure
until Fracture Closure
Real Time
Data Modelling
Premature
Screenout?
Yes
Shut in Well &
Bleed Off Pressure
ON LOCATION
OR IN OFFICE
Wait for Fluid
Samples to Break
Flow Back Well
Rig
Down
Analyze
Treatment Data
Post-Job
Report
Figure 22.1a – Frac job process flow diagram
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22. The Fracture Treatment
The design and execution of a frac job can be broken down into 5 major steps:-
1.
Data Collection
Collect as much data as possible on the well, and on treatments carried out on offset wells.
This data includes, but is not limited to:i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x)
xi)
xii)
xiii)
Wireline logs. Useful for spotting boundaries between formations, high and low
permeability and porosity, and also for spotting fluid contacts. Specialised logs can
also give dynamic Young’s modulus and Poisson’s ratio, stresses and the quality of
the cement bond. Get summary or evaluated logs whenever possible – there is no
point in doing a full log analysis when somebody else has already done this. Also – if
you are not confident with logs - a good first step is to mark where the perforations
are, as these will be the productive intervals.
Well test data. Useful for obtaining values such as reservoir pressure, permeability
and skin factor. Again, get the report with the analysis already done. No one will
expect you to be an expert well test analyst. These reports may also contain
calculated data for porosity, viscosity, fluid saturation and compressibility.
Completion diagram. Essential, as this will contain all the details you will need on
the perforations, depth and sizes of tubing and casing strings etc.
Wellhead diagram. Usually, all the Frac Engineer needs from this is a description of
the top connection, so that the crew can have the appropriate crossover when they
rig up to the wellhead. However, if a wellhead isolation tool is being used, a detailed
diagram will be required.
Deviation survey. If the well is not vertical, the Frac Engineer will need to know MVD
vs TVD for all formations, perforations and tubulars.
Core data. If the well has been cored, this report may contain useful data on porosity,
permeability and fluid saturation. In addition, the report may contain rock mechanical
data and mineralogy (useful if the formation is suspected to be “water-sensitive”).
Core samples. If core samples are available, get hold of them and have them tested
for Young’s modulus and Poisson’s ratio.
Reservoir fluid samples. It is important to carry out compatibility testing between the
frac fluid and the reservoir fluids. Problems are rare, but when they do occur they can
ruin a well.
Production data. Production data is useful for two reasons. First, this data is the
basis for post treatment production forecasts. Secondly, a qualitative analysis should
be performed to check for items such as water or gas coning and fines migration.
Produced sand samples. Essential if a frac and pack treatment is being designed,
as a sieve analysis will be required to find the correct proppant size. However, getting
a representative sample can be difficult. Surface samples tend to have a higher
proportion of fines, as these are more easily carried out of the well. Bottom hole
samples tend to be the other way around – high proportions of the fines have been
carried away out of the well.
Offset treatment data. Often, this is the most important and reliable source of data.
Perform a complete analysis of these treatments, including a pressure match, if the
data is available. If the data is reliable enough, this may even eliminate the need for a
minifrac and step rate test.
Location diagram. The Frac Engineer needs to know what size the location is, to
ensure that all the equipment can be placed. If not, a smaller treatment needs to be
designed. Especially important offshore, where additional factors such as crane
maximum lift and deck loading must also be considered.
Other information, such as production logs (i.e. spinner surveys), temperature logs,
caliper logs, mud logs, stress surveys, core flow testing, workover reports and drilling
records can all provide useful information.
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22. The Fracture Treatment
2.
Preliminary Design
This stage uses all the data gathered in step 1 to produce a preliminary frac design. The initial
step is to analyse the reservoir and production data and derive the optimum fracture geometry
required. This step is best accomplished using nodal analysis. Then the fracture simulator is
used to design a treatment to produce this fracture. Often, this design has to be tempered by
considerations such as cost, mobilisation and equipment availability, so that the Engineer
may go back and forth between the nodal analysis and the simulator several times.
Unless the Engineer has good data from offset treatments, a step rate test and a minifrac will
be required. The step rate test is pretty much standard for any well and an example is
included below. The minifrac needs to be designed on a well by well basis. It should be
pumped at the same rate as the preliminary frac design, using the same fluid and then
displaced at the same rate using slick water. The volume of the minifrac should be at least
equal to the anticipated pad volume. The minifrac fluid volume should be large enough to
contact every formation that the actual frac will contact. This means that for tip screen out
designs, the minifrac should be the same size as the pad, whereas for tight gas fracturing it
must be considerably larger. Remember – it is much better to pump too much fluid than too
little.
The minifrac is exactly what its name suggests – a small frac. In fact, it should be as close as
possible to the actual treatment, in order to produce data as relevant as possible.
Remember that if minifrac and step rate tests are being performed, there is no point in doing
too detailed a design at this stage. The real design work will be done on location after these
calibration tests. At this stage, what is required are reasonable estimates for the expected
production increase, the quantity of materials and equipment that must be mobilised and the
cost of the treatment.
Preliminary design work also includes designing the frac fluid. This often involves the use of
Fann 50 (or similar) HPHT rheometers in order to ensure that the frac fluid has the right
combination of stability and break.
3.
Calibration Tests and Redesign
Finally, the frac spread and crew gets mobilised and is rigged up on location. The next major
step in the design and execution process is to perform the calibration tests (minifrac and step
rate test). It is vitally important to get good data from these. Whenever possible, get bottom
hole pressure data, either from a gauge or from a dead string.
For the step rate test, remember the following points:i)
ii)
iii)
iv)
Get as many low rate steps as possible. Ideally, this means 4 steps below 2 bpm,
although this is not always easy with big frac pumps. However, the more steps that
can be taken before the frac starts to initiate, the better the results will be.
Don’t fiddle with the rate. When moving from one step to another, change the rate
and then leave it alone. Getting a stabilised pressure is difficult enough without
someone fiddling with the throttles. As long as the rate is approximately what it should
be, that is good enough.
Use the step rate test procedure as a guideline only, especially with regard to
volumes. Getting a stabilised rate and pressure for each step is what we are after.
Once this has been achieved, move on to the next step.
It is important that the step rate test (step up variety) is performed on an unfractured
formation. So either do the step rate test before the minifrac, or wait for a significant
period of time after the minifrac is finished.
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22. The Fracture Treatment
v)
vi)
The opposite is true for the step rate test. An open fracture is needed before the step
down begins, and the fracture must be open throughout the entire test. It is common
to combine the two tests – step up and then step down again.
Remember that the well must be full of fluid before the step rate test commences. If
the well has to be filled up, do it at low rate to ensure no fracture forms.
For a minifrac, the following points are important:i)
ii)
iii)
iv)
Keep the rate constant, even if this means pumping at a different rate than
programmed. This makes the analysis easier and more reliable.
Keep the fluid quality constant, again to make the analysis easier and more reliable. If
necessary, gel up a couple of frac tanks, rather than mixing on the fly.
Understand the wellbore fluid. Know its fluid properties and it’s volume. Remember
that this fluid will be injected into the fracture ahead of your carefully prepared
fracturing fluid. So if you don’t know the wellbore fluid, the careful preparation of the
frac fluid is wasted. If necessary, circulate the well to completion fluid, or something
similar before pumping the minifrac.
Monitor the pressure decline. During this period, don’t let the frac crew do anything,
except drink coffee. It is all too easy for a silly mistake to ruin data collection. The
Frac Engineer can also do his part by zero-ing out the rate on the fracturing
monitoring computer – so that any fluid pumping by the blender does not show up as
an erroneous downhole rate. Remember also to collect data for long enough – if data
collection stops before closure (or closures) has happened, then the minifrac will have
lost at least half of its value.
Finally, don’t forget the primary objective of the exercise – to produce a good frac design.
Other objectives – such as minimising rig time or trying to get the job in the ground before
nightfall – are desirable, but secondary. The customer should be aware of the fact that a
redesign can sometimes take several hours.
4.
Job Execution
After all the planning and preparation has taken place, the actual treatment can sometimes
take a surprisingly short period of time. During this period, the fate of the treatment no longer
rests in the hands of the Frac Engineer. It is now up to the Supervisor and the rest of the frac
crew to put the job in the ground as closely as possible to the revised treatment design.
Of course, on longer treatments, real-time redesign may be performed. In which case, the
Frac Engineer may still have some influence on the treatment. However, usually it is time for
the Engineer to sit back and let the crew get on with their job. Some Frac Engineers like to
run the monitoring computer or check the fluid samples – both these occupations are useful
and need to be performed. It is also important that the Frac Engineer stays in close contact
with the Supervisor, just in case something unexpected happens.
5.
Post Treatment Analysis
There is no such thing as the perfect frac job. Every job has room for improvement, however
slight. This applies to the Frac Engineer’s job as well and the post treatment analysis is the
way to find out what could have been done better.
Post treatment analysis comes in two parts:i)
Analysing the pressure and rate data from the job. The best way to do this is with a
pressure match, although don’t spend too much time on this if you have no downhole
pressure data. Results obtained from this will improve the success rate of future
treatments.
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22. The Fracture Treatment
ii)
Assessing the production increase. Sometimes it is easy to loose sight of the
objective of the entire process – to increase production. It is vitally important to keep
track of the production of fractured wells. Remember that production over the first few
days doesn’t really count – we should be looking at the stabilised production several
weeks after the treatment is performed. If production does not meet or exceed
expectations, then the following three questions must be satisfied; Was the well a
good candidate (i.e. reserves and pressure)? Was the optimum fracture placed in the
formation? And were the post treatment expectations realistic?
22.2
Example Treatment Schedules
Whilst BJ Services is not at liberty to publish confidential data, the example treatments were
actually pumped and all of them produced significant production increases for our customers.
These designs are included so that the reader can gain some idea of the size and scale of
fracturing treatments.
However, remember that each treatment must be designed individually for each well – these
schedules are for guidance only and are not meant as “ready-to-use” frac designs.
Typical Step Rate Test Schedule
Rate
Time
bpm
secs
0.7
120 +
1.0
30
1.5
30
2.0
30
3.0
30
5.0
30
7.0
30
9.0
30
11.0
30
15.0
30
12.0
15
9.0
15
6.0
15
3.0
15
Total Volume (gals)
Volume
gals
15
21
32
42
63
105
147
189
231
315
126
95
63
32
1476
The maximum rate can be raised if desired, but this will probably not be necessary for most
treatments. However, remember to hold the maximum rate for a few minutes to ensure that
the fracture is of sufficient volume. If the fracture is too small, it may close before the step
down portion can be completed.
Tight Gas Fracturing
Stage
1 (Pad)
2
3
4
5
6 (Flush)
Page 238
Fluid
Type
Linear
XLink
XLink
XLink
XLink
Sl/Water
Rate
bpm
40
40
40
40
40
40
Clean Vol
gals
20,000
20,000
40,000
40,000
100,000
8,300
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22. The Fracture Treatment
Notes
Linear
XLink
Sl/Water
= Linear gel (i.e. base gel with no crosslinker)
= Crosslinked gel
= Slick Water
Linear gel
2.5 gpt VSP
3
20,000 gals (75.7 m ) total
Crosslinked gel
Vistar 20
3
200,000 gals (757 m ) total
Slick Water
2 gpt VSP
3
8,300 gals (31.4 m ) total
Proppant
20/40 CarboLite
600,000 lbs (272 tonnes) total
Treating Pressure
5,100 psi
(352 bar, 35.2 MPa)
Pumping Capacity
+/- 5,000 HHP
(3,730 kW)
Frac and Pack
Stage
Fluid
Type
XLink
XLink
XLink
XLink
XLink
XLink
XLink
XLink
Sl/Water
1 (Pad)
2
3
4
5
6
7
8
9 (Flush)
Rate
bpm
15
15
15
15
15
15
15
15
15
Clean Vol
gals
1,200
1,250
600
800
1,000
1,250
1,850
2,000
7,830
Crosslinked gel
35 ppt Viking 1D
3
9,950 gals (37.6 m ) total
Slick Water
4 gpt XLFC-1 in CaCl2 brine
3
7,830 gals (29.6 m ) total
Proppant
20/40 EconoProp
70,000 lbs (31.8 tonnes) total
Treating Pressure
6,300 psi (maximum)
(434 bar, 43.4 MPa)
Pumping Capacity
+/- 2,300 HHP
(1,716 kW)
.
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22. The Fracture Treatment
Skin Bypass Fracturing
Stage
Fluid
Type
XLink
XLink
XLink
XLink
Sl/Water
1 (Pad)
2
3
4
5 (Flush)
Rate
bpm
8
8
8
8
8
Clean Vol
gals
4,000
1,300
1,100
1,050
2,540
Crosslinked gel
SpectraFrac G 3500 HT
3
7,500 gals (28.4 m ) total
Slick Water
4 gpt XLFC-1
3
2,540 gals (9.6 m ) total
Proppant
20/40 CarboLite
16,500 lbs (8.1 tonnes) total
Treating Pressure
900 psi
(62.0 bar, 6.2 MPa)
Pumping Capacity
+/- 200 HHP
(149 kW)
Prop. Conc.
ppa
0
2
5
8
0
References
Howard, G.C., and Fast, C.R.: Hydraulic Fracturing, Monograph Series Vol 2, SPE, Dallas,
Texas (1970).
Gidley , J.L., et al.: Recent Advances in Hydraulic Fracturing, Monograph Series Vol 12, SPE,
Richardson, Texas (1989).
Economides, M.J., and Nolte, K.G.: Reservoir Stimulation, Schlumberger Educational
Services, 1987.
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Nomenclature
Nomenclature
a
=
A
Af
=
=
AR
Bg
Bo
BHA
BHP
BHTP
c
C
CI
CII
CIII
cb
Cc
CD
Ceff
cf
CfD
cr
ct
Cv
Cw
d
dp
DCF
E
E’
Ed
f
F
Fc
Fcd
9
g(∆tD)
g(∆tcD)
G
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
G(∆tD) =
Gc
=
Glc
Gd
gf
GOR
GLR
h
hf
H
HD
HH
HHP
Page 241
=
=
=
=
=
=
=
=
=
=
=
fracture half length (Griffith crack)
or variable used in Nolte G time analysis.
Area, annular capacity
Total area of fracture (usually both wings, but for a single wing in
Nolte G-Function analysis).
aspect ratio
gas formation volume factor
oil formation volume factor
bottom hole assembly
bottom hole pressure
bottom hole treating pressure
total reservoir compressibility (also called ct)
wellbore storage coefficient
viscosity controlled leakoff coefficient
compressibility controlled leakoff coefficient
wall building controlled leakoff coefficient
bulk reservoir compressibility (i.e. with porosity)
compressibility controlled leakoff coefficient
dimensionless wellbore storage coefficient
effective or combined leakoff coefficient
fracture compliance, formation compressibility
dimensionless fracture conductivity (new API notation)
zero porosity reservoir compressibility (i.e. rock compressibility)
total reservoir compressibility (also called c)
viscosity controlled leakoff coefficient
wall building controlled leakoff coefficient
diameter, diameter of plastic zone at fracture tip
proppant grain diameter
discount factor
Young’s modulus
plane strain Young’s modulus
dynamic Young’s modulus
Fanning friction factor
force
fracture conductivity
dimensionless fracture conductivity (old – now CfD)
2
2
acceleration due to gravity (= 9.81 m/s or 32.18 ft/s )
dimensionless loss-volume function (Nolte minifrac analysis)
g(∆tD) at fracture closure
shear modulus,
or elastic energy release rate
Nolte G time
critical elastic energy release rate
or Nolte G time at fracture closure
critical elastic energy release rate – failure mode l
dynamic shear modulus
frac gradient
gas oil ratio
gas liquids ratio
height
fracture height at wellbore
depth, fracture height at wellbore
dimensionless fracture height
hydrostatic head
hydraulic horsepower
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Nomenclature
Hξ
ISDP
ISIP
IPR
J
J0
Jf
K
K’
K’’
Kl
K1c
=
=
=
=
=
=
=
=
=
=
=
=
k
Kd
kf
kp
kr
KZD
L
m
m(P)
N
n’
n’’
Np
NPV
NRe
p, P
P*
P’
Pb
Pclosure
Pext
Pfinal
Pfrict
Pi
Pinitial
Pm
Pnet
Pnwb
Pob
Pperf
Pr
Pr, t
Pres
Pv
Pwb
PwD
PwDM
Pwf
Pws
PC
PKN
q
Q
QL
Qmax
R
rd
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Page 242
characteristic length (MFrac)
instantaneous shut-down pressure (= ISIP)
instantaneous shut-in pressure
inflow performance relationship
original (pre-stimulation) productivity index with skin
undamaged productivity index
post-fracturing productivity index
bulk modulus
power law consistency index
Herschel-Buckley consistency index
stress intensity factor, failure mode 1
critical stress intensity factor – failure mode 1,
or fracture toughness
permeability
dynamic bulk modulus
formation permeability, permeability to frac fluid filtrate
proppant permeability
permeability to reservoir fluid
Kristianovich, Zheltov, Daneshy – 2 dimensional frac model
tubing of casing length, fracture half length (also xf)
mobility, gradient of curve
real gas pseudo-pressure
viscometer spring factor
power law exponent
Herschel-Buckley exponent
dimensionless proppant number (or simply proppant number)
net present value
Reynold’s number
pressure
average reservoir pressure from well test analysis
pressure derivative
breakdown pressure
closure pressure or Pc
fracture extension pressure
post-frac surface circulation pressure (frac and packs)
friction pressure (usually ∆Pfrict)
static reservoir pressure
pre-frac surface circulation pressure (frac and packs)
match pressure (Nolte minifrac analysis)
net pressure
near wellbore friction pressure (usually ∆Pnwb)
pressure due to overburden
perforation friction pressure (usually ∆Pperf)
pressure at a distance r from the wellbore
pressure at a distance r from the wellbore, after a time t.
reservoir pressure (also Pi)
plastic viscosity (Bingham plastic fluids)
wellbore pressure (usually bottom hole)
dimensionless wellbore pressure
dimensionless wellbore match pressure
flowing wellbore pressure
static wellbore pressure
proppant concentration
Perkins, Kern, Nordgren – 2 dimensional frac model
pump rate, average pump rate, liquid flow rate
pump rate, average pump rate, gas flow rate
fluid leakoff rate
maximum pump rate
frac radius (esp. radial model)
radius of investigation or disturbed radius
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Nomenclature
re
rp
=
=
rw
r w’
S
Sp
SG
SGf
SGp
STP
t
tD
tDM
tDx
=
=
=
=
=
=
=
=
=
=
=
=
reservoir radial extent
radius of plastic zone at fracture tip
or ratio of fracture area in permeable formation over total fracture
area (i.e. net to gross fracture area ratio) for 2-D fracture models.
wellbore radius
effective wellbore radius
skin factor
spurt loss coefficient
specific gravity
specific gravity, fluid
specific gravity, proppant
surface treating pressure
time
dimensionless time
dimensionless match time
fractured well dimensionless time
tDx M
=
fractured well dimensionless match time
tHorner
tma
tp
tsma
ts
T
TVD
U
Ufluid
U̇
v
vprop
V
Vi
Vs
W, w
W̄ ,w̄
Wmax
WOR
x, y, z
xe
xf
xfD
Yp
z
zi
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Horner time
rock matrix compression wave transit time
pump time, producing time, compression wave transit time
rock matrix shear wave transit time
shut in time (also ∆t), shear wave transit time
tensile strength, or temperature
true vertical depth
energy
energy in the fracturing fluid
energy per unit time, work, horsepower
velocity
fraction of fracture volume occupied by proppant
volume
total volume injected into fracture
spurt loss volume
fracture width
average fracture width
maximum fracture width
water oil ratio
mutually perpendicular directions, distances
2
length and width of a square reservoir (such that area = xe )
fracture half length
dimensionless fracture half length ( = xf/re)
yield point (Bingham plastic fluids)
gas z-factor
gas z-factor at static reservoir conditions
α
β
=
=
βs
γ
=
=
poroelastic constant (Biot), Nolte analysis boundary variables
flow capacity factor (Forcheimer Equation)
or shape factor (LEFM)
ratio of average to wellbore net pressures (Nolte minifrac analysis)
shear rate, proppant specific gravity,
or shape factor (MFrac)
real gas pseudo-pressure differential
real gas pseudo-pressure differential match
pressure differential, drawdown
drawdown (= Pi – Pwf)
build-up pressure ( = Pi – Pws)
pressure drop due to fluid tubing friction
test data log-log plot match pressure
f
f
∆m(P) =
∆m(P)M =
∆P
=
∆Pdrawdown =
∆Pbuild-up
=
∆Pfrict =
∆PM
=
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Nomenclature
∆Pnwb
∆Pperf
∆Pskin
∆t
∆tD
∆tcD
∆tM
ε
ε1
ε2,3
εx, y, z
η
θ
µ
µi
µapp
µf
µr
ν
νd
π
ρ
ρb
ρgel
ρp
ρsl
σ
σ1,2,3
σc
σH
σH, max
σH, min
σv
σxx, yy, zz
σy
τ
τ’o
φ
φp
ω
Page 244
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
pressure drop due to near wellbore friction
pressure drop due to perforations
pressure loss due to skin damage
change in time, time since shut-in or shut down.
change in dimensionless time a.k.a. delta Nolte time
delta Nolte time at closure
test data log-log plot match time
strain
strain in the vertical direction
strains due to the principle horizontal stresses, σ2 and σ3
strain in the x-, y- and z-directions
fluid efficiency, fracture efficiency
angle, viscometer dial reading
viscosity
viscosity at static reservoir conditions
apparent viscosity
viscosity of frac fluid filtrate
viscosity of reservoir fluid
Poisson’s ratio
dynamic Poisson’s ratio
Pi, the ratio of a circle’s circumference to it’s radius (= 3.1415926....)
density
proppant bulk density, formation bulk density
gel or base fluid density
proppant absolute density
slurry density
stress
principle (i.e. mutually perpendicular) stresses
critical stress
horizontal stress
maximum horizontal stress
minimum horizontal stress
vertical stress
principle stresses in the x-, y- and z- directions
yield stress
shear stress
initial or threshold shear stress (Herschel-Buckley fluids)
porosity
proppant bulk porosity
length of unwetted part of fracture (FracPro, FracproPT),
angular velocity, viscometer rotor speed
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Index
Index
A
Absolute volume ..................................................................................................................... 178
Additives .......................................................................................... see Fluid systems, additives
Always look.............................................................................................. on the bright side of life
Aluminates ..........................................................................................................see Crosslinkers
Aspect ratio................................................................................................................................. 7
B
Bacteria..................................................................................................................................... 41
Beta-factor ................................................................................................................................ 88
Bilinear flow ............................................................................................................................ 202
Binary foam fracturing .............................................................................................................. 39
Bingham plastic fluids .......................................................................................................... 20-21
Biocides, bactericides ............................................................................................................... 41
Biot’s constant ........................................................................................................ 58, 62, 64, 67
Blenders. blending equipment ......................................................................................... 216-218
Borates ...............................................................................................................see Crosslinkers
Breakers ................................................................................................................................... 41
Brines............................................................................................................................. 35-36, 51
Brittle fracture ........................................................................................................................... 75
Buffers ...................................................................................................................................... 41
Bulk modulus ............................................................................................................................ 57
Dynamic....................................................................................................................... 64
C
Calibration tests ............................................................................................................... 115-120
Candidate selection ................................................................................................. 101-108, 229
Cement bond .......................................................................................................................... 108
Circulation tests ...................................................................................................................... 168
Clay control.......................................................................................................................... 43-44
Cleats................................................................................................................................ 16, 170
Closure stress........................................................................................................................... 47
CO2 fracturing .................................................................................................................. 39, 169
Coflexip high pressure hoses ................................................................................................. 210
Completions..................................................................................................... 104-106, 229, 230
Jewelry........................................................................................................ 105-106, 230
Compressibility ....................................................................................................................... 202
Average reservoir .......................................................................................... 10, 64, 202
Formation......................................................................................................... 8, 64, 190
Compression wave ................................................................................................................... 63
Conductivity
Finite ........................................................................................................... 194, 203-205
Fracture .................................................................................. see Fracture, conductivity
Infinite ................................................................................................. 165, 194, 203-205
Corrosion, tubulars ................................................................................................................. 108
Crack driving force.................................................................................................................... 73
Crack tip dilatency ............................................................................................................... 75-76
Crack tip plasticity................................................................................................................ 76-77
Critical energy release rate....................................................................................................... 73
Critical fracture length............................................................................................................... 73
Critical micellar concentration................................................................................................... 35
Critical stress intensity factor.................................................................................................... 74
Constant external phase........................................................................................................... 37
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Index
Constant internal phase............................................................................................................ 37
Crosslinked fluid systems ...................................... see Fluid systems, water-based, crosslinked
Crosslinkers ................................................................................................................... 31-33, 41
Aluminates .............................................................................................................. 31-32
Borates ................................................................................................................... 31-32
Borates, exotic ........................................................................................................ 31-32
Titanates ................................................................................................................. 31-32
Zirconates ......................................................................................................... 31-32, 33
D
Darcy’s Equation..................................................................................................... 9, 88, 95, 194
Darcy’s law ................................................................................................... 2, 88, 109, 116, 126
data collection......................................................................................................................... 235
Data frac ....................................................................................................................see minifrac
Dead string ............................................................................................................................. 121
Decline curve analysis ..................................................................................................... 125-131
Density...................................................................................................................................... 19
Bulk, formation............................................................................................................. 63
Bulk, formation, log-derived......................................................................................... 63
Slurry, measurement of ..................................................................................... 177, 178
Densometers .......................................................................................................... 176, 178, 179
Mass flowmeter density measurement...................................................................... 177
Nuclear ...................................................................................................................... 178
Derivative plots, minifrac ........................................................................................................ 131
Derivative plots, well testing ............................................................................................ 197-198
Desorption ................................................................................................................................ 16
Discounted revenue................................................................................................................ 102
Dilatency ................................................................................................................................... 75
Dilatency contribution ............................................................................................................... 75
Dipole sonic logs.......................................................................................................... 63-67, 189
E
Economics ....................................................................................................................... 101-104
Elastic constants.................................................................................................................. 57-58
Elastic deformation .............................................................................................................. 54-57
Elastic energy release rate ....................................................................................................... 73
ElastraFrac ............................................................................................................................... 36
Emulsifier ............................................................................................................................ 35, 43
Emulsions ........................................................................................................................... 35, 42
Energy.......................................................................................................... 5, 73, 77, 77-79, 166
Kinetic .......................................................................................................................... 89
Rate of using................................................................................................................ 82
Energy balance.................................................................................................................... 77-79
Enzyme breakers...................................................................................................................... 41
Erosion...................................................................................................................................... 61
F
Failure mode............................................................................................................................. 73
FlexSand........................................................................................................................ 50-51, 88
Flow lines, high pressure................................................................................................. 209-210
Flow lines, low pressure ......................................................................................................... 209
Flowmeters ............................................................................................................. 176, 177, 179
Magnetic .................................................................................................................... 177
Mass or inertia ........................................................................................................... 177
Turbine....................................................................................................................... 177
Fluid efficiency .............................................................................................. 69, 70, 71, 128, 130
Fluid friction ......................................................................................................................... 27-28
Fluid leakoff .................................................................................. 8, 12, 122, 166, 169, 187, 190
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Index
Coefficient...................................................................................................................... 8
Compressibility-controlled coefficient ............................................................................ 8
Dynamic......................................................................................................................... 9
Harmonic ....................................................................................................................... 9
Spurt loss....................................................................................................................... 9
Viscosity-controlled coefficient ...................................................................................... 8
Wall-building coefficient...................................................................................... 8-9, 190
Fluid loss additives ................................................................................................................... 44
Fluid loss test........................................................................................................................... 8-9
Fluid mechanics................................................................................................................... 19-28
Fluid systems....................................................................................................................... 29-44
Additives ................................................................................................................. 39-44
Emulsion-based ........................................................................................................... 35
Energised................................................................................................................ 36-39
Oil-based ................................................................................................................ 33-35
Visco-elastic surfactant........................................................................................... 35-36
Water-based, crosslinked ....................................................................................... 30-33
Water-based, linear ................................................................................................ 29-30
Foam fracturing............................................................................................................ 36-39, 169
Proppant concentration ............................................................................................... 37
Stability ........................................................................................................................ 38
Quality.......................................................................................................................... 36
Viscosity....................................................................................................................... 38
Foaming agents ........................................................................................................................ 42
Forced closure .......................................................................................................................... 88
Forcheimer Equation ................................................................................................... 88-89, 168
Formation linear flow .............................................................................................................. 202
Frac and Pack...............................................................................................13-14, 167-168, 239
Frac job flowchart ............................................................................................................ 232-234
Frac spreads.................................................................................................................... 224-227
Fracture
Area ........................................................................................................................... 130
Closure time......................................................................................................... 12, 127
Conductivity ....................................................7, 12, 16, 45-48, 83, 86, 95, 96, 164, 203
Dimensionless conductivity ..................12, 82-83, 96, 98, 164, 166, 173, 174, 183, 203
Efficiency ...........................................................................................see Fluid efficiency
Gradient ............................................................................................................ 61-62, 67
Half length................................................ 7, 13, 69, 70, 71, 83, 164, 166, 202, 203, 205
Half length, dimensionless................................................................................... 97, 166
Height .......................................................................................................................... 68
Initiation, controlling............................................................................................ 109-111
Orientation ................................................................................................ 59-60, 80, 111
Relative conductivity.................................................................................................... 12
Fracture linear flow ................................................................................................................. 201
Fracture mechanics ............................................................................................................. 72-79
Fracture Models........................................................................................68-71, 91-94, 165, 186
2-D Models ..................................................................................................... 68-71, 128
3-D models ............................................................................................................. 91-94
FracPro ..................................................................................... 75, 91-92, 117, 183, 184
FracproPT..................................................................75, 91-92, 117, 135-147, 182, 184
Geertsma and de Klerk (GDK) ............................................................................... 69-70
GOHFER ..................................................................................................................... 93
Kristianovich and Zheltov – Daneshy (KZD) .................................. 69-70, 128, 130, 131
MFrac................................................................. 72, 92-93, 117, 151-152, 159-161, 182
MinFrac...................................................................................................................... 117
Penny-shaped......................................................................................................... 68-69
Perkins and Kern – Nordgren (PKN) .............................................. 70-71, 128, 130, 131
Radial.............................................................................................. 68-69, 128, 130, 131
Stimplan................................................................................................................. 72, 93
Fracture tip diameter ................................................................................................................ 76
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Index
Fracture toughness...................................................................... 72-75, 116, 169, 187, 188, 190
Fracturing........................................................................................................................... 1-3, 12
Batch fracs......................................................................................................... 224, 226
Coal bed methane ........................................................................................ 16, 170-172
Coiled tubing....................................................................................16-17, 172-173, 226
High permeability...................................................12, 166-167, 167-168, 225, 228, 239
Injection wells ............................................................................................. 169-170, 228
Low permeability, or tight gas................................12, 107, 168-169, 225, 228, 238-239
Multiple intervals ......................................................................................... 112-113, 230
Skin bypass ................................................. 15-16, 75, 98, 112-113, 165-166, 226, 240
Weak or unconsolidated formations .......................................................... 107, 225, 239
Friction factor (Fanning) ...................................................................................................... 27-28
G
G-function ............................................................................................................... 126, 129, 130
G-function analysis .......................................................................................................... 128-131
Example.............................................................................................................. 134-138
Gas contacts........................................................................................................................... 108
Gas lift....................................................................................................................................... 17
Gas oil ratio (GOR) ................................................................................................................... 99
Gauges, pressure ................................................................................................................... 121
Gel stabilisers ........................................................................................................................... 43
Gelling agents................................................................................................................ 30, 39-40
Carboxymethyl guar (CMG)............................................................................. 30, 33, 40
Carboxymethyl hydroxyethyl cellulose (CMHEC).................................................. 30, 40
Carboxymethyl hydroxypropyl guar (CMHPG) ................................................ 30, 33, 40
Cellulose ...................................................................................................................... 30
Guar................................................................................................................. 30, 33, 40
Hydroxyethyl cellulose (HEC)................................................................................ 30, 40
Hydroxypropyl guar (HPG) .................................................................................... 30, 40
Oil-based fluids ...................................................................................................... 34, 40
Starch .......................................................................................................................... 30
Polysaccharide ............................................................................................................ 40
Xanthan ................................................................................................................. 30, 40
Xanthan, derivatives of ................................................................................................ 30
Gravel pack............................................................................................................................... 14
Griffith crack......................................................................................................................... 72-73
Griffith failure criterion............................................................................................................... 73
H
Half length, fracture .................................................................................................................... 7
Hard rocks ................................................................................................................................ 80
Height ................................................................................................................................... 7, 16
Dimensionless ....................................................................................................... 15, 16
Helical screw rheometer ........................................................................................................... 24
Herschel-Buckley fluids ............................................................................................................ 22
High pressure flow lines .................................................................see Flow lines, high pressure
Hooke’s law ......................................................................................................................... 58-59
Horizontal wells....................................................................................................................... 112
Horner plot, minifrac ........................................................................................................ 127-128
Horner plot, well testing .................................................................................................. 195, 198
Hugoton field......................................................................................................................... 1, 33
Hydration unit................................................................................................................... 217-218
Hydraulic horsepower ..................................................................................................... 2, 4, 209
Hysteresis ........................................................................................................................... 55, 66
I
Independent Torpedo Company................................................................................................. 1
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Inflow performance relationship (IPR) ...................................................................................... 99
Injection wells .................................................................................................................. 169-170
Intensifiers ....................................................................................................................... 213-216
Internal rate of return .............................................................................................................. 102
ISDP ................................................................................................................................... 6, 125
ISIP ............................................................................................................. 6, 125, 127, 130, 192
J
Job design ...................................................................................................see treatment design
K
K-prime or K’.................................................................................................................. 21-22, 86
Klepper No 1 well.................................................................................................................. 1, 33
L
Laminar flow ....................................................................................................................... 26, 27
Leakoff ...............................................................................................................see Fluid Leakoff
Lightning ................................................................................................................................... 32
Limited entry fracturing ................................................................................................ 84-85, 110
Linear elastic fracture mechanics (LEFM) ........................................................................... 72-75
Liquid frac concentrate (LFC, XLC, GLFC, VSP) ..................................................................... 33
LiteProp ............................................................................................................................... 51-52
Live annulus............................................................................................................................ 121
Logistics.................................................................................................................................. 108
Low surface tension modifiers .................................................................................................. 42
M
McGuire and Sikora ............................................................................................................. 97-98
Medallion Frac .......................................................................................................................... 32
Medallion Frac HT .................................................................................................................... 33
Micelles ..................................................................................................................................... 35
Micro fibres .......................................................................................................................... 87-88
Micro sheets ............................................................................................................................. 88
Micriseismic .................................................................................................................... 186, 206
Minifracs ....................................................................... 8, 115, 121-163, 167, 181-183, 236-237
Anatomy of................................................................................................................. 124
Bottom hole data................................................................................................. 121-122
Examples ............................................................................................................ 134-162
Fluid type ................................................................................................................... 122
Planning and execution ...................................................................................... 121-123
Rate ........................................................................................................................... 122
Volume....................................................................................................................... 122
Mobility ................................................................................................................................... 168
Monobore.......................................................................................................................... 17, 170
Multi-phase flow................................................................................................ 47, 164, 169, 174
Multiple fractures ..................................................................................84-85, 109, 111, 133-134
Mutual solvents......................................................................................................................... 43
N
n-prime or n’................................................................................................... 21-22, 86, 128, 130
N2 fracturing ..................................................................................................................... 38, 169
Napalm ..................................................................................................................................... 33
Near wellbore damage ............................................................................................................... 9
Net height ....................................................................................................................... 200, 201
Net present value (NPV).......................................................................................... 102-104, 174
Net pressure ..................................................................................................... see pressure, net
Net revenue ............................................................................................................................ 102
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Newton’s law of fluids .......................................................................................................... 19-20
Newtonian fluids ................................................................................................................. 20, 22
Nodal analysis ................................................................................................................... 99-100
Nolte analysis ................................................................................................... 82, 124, 179, 192
Nolte G-function...................................................................................................................... 126
Nolte G-function analysis................................................................................................. 128-131
Example.............................................................................................................. 134-138
Non-Darcy flow .....................................................................12, 16, 47-48, 88-89, 164, 169, 174
Non-emulsifiers......................................................................................................................... 41
O
Oxidising breakers .................................................................................................................... 41
P
p-wave ...................................................................................................................................... 62
Perforations ....................................................................................................... 81, 108, 109-114
Deviated wells..................................................................................................... 111-112
Friction ................................................................................................................... 6, 116
Strategy ............................................................................................................... 81, 108
Vertical wells.............................................................................................................. 111
Permeability ........................................................................................................ 4, 169, 189, 194
Formation........................................................................................... 7, 10, 13, 100, 164
Proppant pack .................................................................... 7, 12, 13, 45-48, 83, 89, 164
Regained ................................................................................................................ 46-47
Pipelining ............................................................................................................................. 86-87
Plane strain............................................................................................................................... 74
Plastic deformation .................................................................................................. 54-55, 76, 77
Plastic zone ......................................................................................................................... 76-77
Plug flow ............................................................................................................................. 26, 27
Poisson’s ratio ...................................................................55-56, 58, 59, 60, 62, 68, 69, 70, 191
Dynamic......................................................................................................... 63, 66, 189
Polished bore receptacle .......................................................................................................... 17
Poly CO2 .................................................................................................................................. 39
Polyemulsion ............................................................................................................................ 35
Poroelastic constant ............................................................................................... 58, 62, 64, 67
Porosity........................................................................................................................... 190, 202
Formation............................................................................................................. 10, 190
Power........................................................................................................................................ 77
Power law fluids................................................................................................................... 21-22
Pressure ..................................................................................................................................... 5
Bottom hole flowing ............................................................................... 10, 99, 100, 193
Bottom hole static ...................................................................................................... 193
Bottom hole treating .............................................................................. 5, 122, 124, 125
Bottom hole treating, calculated ................................................ 122, 124, 176, 179, 187
Breakdown...................................................................................................... 61-62, 191
Build-up...................................................................................................................... 193
Closure .......................................................................... 6, 115, 116, 125, 127, 164, 192
Dimensionless ........................................................................................................... 199
Dimensionless, match ............................................................................................... 200
Drawdown.......................................................................................................... 193, 228
Extension ....................................................................................................... 6, 115, 116
Fluid friction .................................................................................................... 27-28, 186
Hydrostatic..................................................................................................................... 5
Instantaneous shut-in (ISIP) .......................................................... 6, 125, 127, 130, 192
Maximum wellhead .................................................................................................... 105
Near wellbore friction............................................................................................. 6, 117
Net .................................................6, 68, 69, 70, 71, 76, 79, 82, 84, 117, 125, 166, 192
Perforation friction.......................................................................................................... 6
Pore ................................................................................................................. 61, 62, 67
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Pseudo, gas....................................................................................................... 199, 201
Reservoir ........................................................................................................... 100, 128
Shut-in ....................................................................................................................... 193
Surface treating ..................................................................................................... 5, 122
Tubing.................................................................................................................... 5, 123
Tubing friction ............................................................................................. 5, 27-28, 176
Wellhead........................................................................................................................ 5
Wellhead, flowing......................................................................................................... 99
Pressure decline ..................................................................................................................... 123
Decline curve analysis ........................................................................................ 125-131
Pressure matching.............................................................................131-132, 183-184, 185-191
Examples ..............................................................................135-147, 151-152, 159-161
Limitations of...................................................................................................... 132, 184
Pressure transducers .............................................................................................. 176, 178-179
Pressure transient analysis ............................................................................................. 194-199
Production increase ........................................................................................................... 95-100
Dimensionless ............................................................................................................. 98
Pseudo-steady state............................................................................................... 96-98
Steady state............................................................................................................ 95-96
Productivity index (PI)........................................................................................... 95, 96, 98, 166
Proppant .......................................................................................................................... 4, 43-52
Average grain size ....................................................................................................... 46
Closure stress.............................................................................................................. 47
Concentration, areal ...................................................................................................... 7
Concentration, foams .................................................................................................. 37
Concentration, slurry ............................................................................................ 7, 178
Convection................................................................................................................... 85
Grain size distribution .................................................................................................. 41
Multi-phase flow........................................................................................................... 48
Non-Darcy flow ....................................................................................................... 47-48
Permeability ............................................................................ 7, 12, 45-48, 83, 164, 203
Pump more ............................................................................................... can’t go wrong
Regained permeability............................................................................................ 46-47
Resin-coated.......................................................................................................... 47, 87
Roundness................................................................................................................... 46
Selection ................................................................................................................. 47-49
Settling.................................................................................................................... 85-86
Slugs.................................................................................................................... 81, 123
Sphericity ..................................................................................................................... 46
Storage and handling ......................................................................................... 218-220
Substrate ..................................................................................................................... 45
Transport ............................................................................................................... 37, 85
Volume....................................................................................................................... 130
Proppant flowback ............................................................................................................... 86-88
Causes of................................................................................................................ 86-87
Forced closure ............................................................................................................. 88
Prevention of........................................................................................................... 87-88
Proppant number ............................................................................................................. 173-174
Pseudo radial flow .................................................................................................................. 202
Pseudo-steady state flow ................................................................................................. 97, 194
Pump curves........................................................................................................................... 209
Pumps, high pressure...................................................................................................... 211-213
Q
Quality, foams...................................................................................see Foam fracturing, quality
R
Radial extent (of reservoir) ....................................................................................................... 16
Radioactive tracers ................................................................................................................. 207
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Radius of investigation ................................................................................................... 194, 196
Rate ............................................................................................................................ is my friend
Re-design, treatment, on-site .......................................................................................... 181-183
Re-design, treatment, real-time ....................................................................................... 183-184
Relative conductivity................................................................................................................. 97
Relative fracture conductivity...................................82-83, 96, 98, 164, 166, 173, 174, 183, 203
Remote data transmission............................................................................................... 180-181
Resin-coated proppant ............................................................................................................. 47
Reynold’s number.......................................................................................................... 26-27, 28
Roundness................................................................................................................................ 46
S
s-wave ...................................................................................................................................... 63
Shear modulus..................................................................................................................... 56-57
Dynamic....................................................................................................................... 64
Shear rate ................................................................................................................................. 19
Shear strain .............................................................................................................................. 57
Shear stress (fluids).................................................................................................................. 19
Shear stress (solids) ................................................................................................................. 57
Shear-thickening fluids ............................................................................................................. 22
Shear-thinning fluids ................................................................................................................. 22
Shear wave............................................................................................................................... 63
Skin factor..................................................................... 9-11, 15, 16, 99, 100, 106-107, 196-197
Sliding side door (SSD) ................................................................................................... 105,106
SpectraFrac G .......................................................................................................................... 32
SpectraFrac G HT..................................................................................................................... 32
Sphericity .................................................................................................................................. 46
Spurt loss............................................................................................................................ 9, 200
Steady state flow .................................................................................................................... 194
Step down test ................................................................................................................. 116-117
Step rate test .................................................................... 115-120, 121, 181-183, 236-237, 238
Examples .............................................................. 117-119, 139-140, 154-155, 158-159
Step up test...................................................................................................................... 115-116
Strain ................................................................................................................................... 53-54
Stress........................................................................................................................................ 53
Closure ........................................................................................................................ 47
Cycling ......................................................................................................................... 86
Horizontal, maximum and minimum ......................................................58-59, 61-62, 81
Horizontal, contrasts ............................................................................................ 81, 117
In-situ ...........................................................................58-59, 60-61, 126, 187, 189, 190
Radial...................................................................................................................... 59-60
Tangential ............................................................................................................... 59-60
Vertical......................................................................................................................... 58
Wellbore-related ..................................................................................................... 59-61
Logs ................................................................................................................ 63-67, 189
Stress intensity factor .................................................................................................... 74-75, 76
Sub-surface safety valve (SSSV) .................................................................................... 105,106
Suction hoses ......................................................................................................................... 210
Surface tension......................................................................................................................... 42
Surfactants........................................................................................................................... 41-42
Amphoteric................................................................................................................... 41
Anionic ......................................................................................................................... 41
Cationic........................................................................................................................ 41
Emulsifying .................................................................................................................. 42
Foaming agents ........................................................................................................... 42
Low surface tension modifying .................................................................................... 42
Mutual solvents............................................................................................................ 42
Non-emulsifying ........................................................................................................... 41
Nonionic....................................................................................................................... 41
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Super RheoGel .................................................................................................................... 34-35
T
Temperature ...................................................................................................... 19, 121-122, 198
Temperature logs.................................................................................................................... 207
Tensile strength ............................................................................................................. 52, 61-62
Terminal velocity....................................................................................................................... 86
Tiltmeters ................................................................................................................. 186, 205-206
Time................................................................................................................................. 126-131
Closure .............................................................................................................. 126, 127
Data ........................................................................................................................... 126
Delta .......................................................................................................................... 126
Delta Nolte Time........................................................................................................ 126
Dimensionless, fractured well.................................................................................... 202
Dimensionless, match ............................................................................................... 200
Dimensionless, minifrac..................................................................................... 126, 128
Dimensionless, well testing ....................................................................................... 198
Horner......................................................................................................... 126, 127-128
Nolte time................................................................................................................... 126
Nolte G time....................................................................................... 126, 128, 129, 130
Producing................................................................................................................... 193
Pump ......................................................................................................................... 126
Shut in........................................................................................................................ 126
Square root time ......................................................................................... 126, 126-127
Tip screenout ..........................................................................................13, 83-84, 166-167, 167
Titanates .............................................................................................................see Crosslinkers
Tortuosity ......................................................................80-81, 111, 116, 117, 123, 132-133, 192
Controlling........................................................................................................... 111-112
Curing of ...................................................................................................................... 81
Example.............................................................................................................. 147-153
Tracer logs.............................................................................................................................. 207
Transient flow ........................................................................................................... 97, 193, 194
Transit time ............................................................................................................................... 63
Compression wave (p-wave) ....................................................................................... 63
Matrix ........................................................................................................................... 64
Shear wave (s-wave) ................................................................................................... 63
Treatment design..............................................................................................164-175, 232-238
Examples ............................................................................................................ 238-240
General ....................................................................................................... 164-165, 236
On-site redesign ................................................................................................. 181-183
Real-time redesign.............................................................................................. 183-184
Treatment monitoring....................................................................................................... 176-186
Analysis and display of data ...................................................................................... 179
Data processing......................................................................................................... 179
Equipment........................................................................................................... 220-221
FracRT....................................................................................................................... 143
Isoplex ....................................................................................................................... 179
JobMaster ................................................................................................... 179-180, 181
Remote data transmission.................................................................................. 180-181
Treesaver........................................................................................... see Wellhead isolation tool
Tubing cooldown..................................................................................................................... 104
Tubing expansion ................................................................................................................... 105
Turbulent flow ..................................................................................................................... 26, 28
U
Unified fracture theory ..................................................................................................... 173-172
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V
Viking ........................................................................................................................................ 32
Viking D .................................................................................................................................... 32
Visco-elastic surfactants (VES) ........................................................................................... 35-36
Viscometers ......................................................................................................................... 23-25
Brookfield..................................................................................................................... 25
Funnel.......................................................................................................................... 25
Model 35 ........................................................................................................... 23-24, 25
Model 50 ................................................................................................................ 24, 85
Viscosity.................................................................................................................. 10, 19, 20, 23
Apparent .............................................................................................................. 25, 177
Foams.......................................................................................................................... 38
Fracturing fluid filtrate ............................................................................................ 8, 190
Gas ............................................................................................................................ 198
Measurement of...................................................................................................... 23-25
Reservoir fluid.................................................................................................. 8, 10, 190
Vistar......................................................................................................................................... 33
von Mises’ yield criterion ..................................................................................................... 76-77
W
Water contact.................................................................................................................. 108, 228
Water cut .................................................................................................................................. 99
Weak formations....................................................................................................................... 86
Well testing ...................................................................................................................... 193-204
Build-up.............................................................................................................. 193, 194
Constant rate ..................................................................................................... 193, 194
Diagnostic plots .................................................................................................. 197-198
Drawdown.................................................................................................................. 193
Fractured wells .......................................................................................................... 201
Gas well testing .................................................................................................. 198-199
Post-treatment .................................................................................................... 202-204
Pressure transient analysis ................................................................................ 194-199
Type curve matching .......................................................................................... 199-202
Wellbore deviation .................................................................................................................... 80
Wellbore fluid, effects of ......................................................................................................... 123
Wellbore orientation.................................................................................................................. 61
Wellbore radius....................................................................................................... 10, 11, 16, 98
Wellbore radius, effective ......................................................................................................... 11
Wellbore storage............................................................................................................. 200, 202
Dimensionless ................................................................................................... 200, 202
Wellhead isolation tool..................................................................................................... 221-224
Wheatstone’s bridge ............................................................................................................... 178
Width........................................................................................................................................... 7
Average ....................................................................................... 7, 68, 69, 70, 203, 205
Average propped ........................................................................................... 13, 83, 164
Maximum ......................................................................................................... 68, 69, 70
Wireline logs ........................................................................................................................ 63-67
Y
Yield point ................................................................................................................................. 76
Young’s modulus .............. 13, 54-55, 68, 69, 70, 73, 80, 84, 130, 165, 167, 169, 187, 188-189,
........................................................................................................................................ 190, 191
Dynamic................................................................................................... 55, 63, 66, 189
Plane strain.................................................................................................. 55, 130, 191
Static...................................................................................................................... 55, 66
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Z
z-factor .................................................................................................................................... 198
Zirconates ...........................................................................................................see Crosslinkers
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