HF2D FRAC DESIGN SPREADSHEET
April 2001
(Updated May 30, 2006)
Dr Peter P. Valkó
Associate professor
Harold Vance Department Petroleum Engineering
Texas A&M University
HF2D
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TABLE OF CONTENTS
1
EXECUTIVE SUMMARY .......................................................................................... 4
2
DATA REQUIREMENT ............................................................................................ 5
3
CALCULATED RESULTS ....................................................................................... 8
4
THEORETICAL FRACTURE PERFORMANCE..................................................... 10
5
SUGGESTED DESIGN PROCEDURE BASED ON OPTIMAL PSEUDO-STEADY
STATE PERFORMANCE ....................................................................................... 20
6
SAMPLE RUNS...................................................................................................... 27
NOMENCLATURE ................................................................................................. 36
CASE STUDIES ..................................................................................................... 38
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1
EXECUTIVE SUMMARY
The HF2D Excel spreadsheet is a fast 2D design package for the 2D design of traditional (moderate
permeability and hard rock) and frac&pack (higher permeability and soft rock) fracture treatments.
Currently it contains the following worksheets:

Traditional design with PKN (Perkins-Kern-Nordgren) model

TSO (tip screen-out) design with PKN model

Design with CDM (Continuum Damage Mechanics) version of the PKN model
The unique feature of this design package is the logic it is based on. The design starts from the amount of
proppant available. Then the optimum dimensions of the fracture are determined. Finally, the treatment
schedule is found which will realize the optimum proppant placement. If the constraints do not allow
optimum placement, a sub-optimal placement is designed.
The results include fluid and proppant requirements, injection rates, added proppant concentrations (that
is the proppant schedule) and additional information on the evolution of the fracture dimensions.
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2
DATA REQUIREMENT
The following table contains the description of the input parameters.
Input Parameter
Remark
Proppant mass for (two wings), lab
This is the single most important decision variable of the design procedure
Sp grav of proppant material (water=1)
For instance, 2.65 for sand
Porosity of proppant pack
The porosity of the pack might vary with closure stress, a typical value is 0.3
Proppant pack permeability, md
Retained permeability including fluid residue and closure stress effects, might be
reduced by a factor as large as 10 in case of non-Darcy flow in the frac
Realistic
proppant pack permeability would be in the range from 10,000 to 100,000 md for in-situ
flow conditions. Values provided by manufacturers such, as 500,000 md for a “high
strength” proppant should be considered with caution.
Max prop diameter, Dpmax, inch
From mesh size, for 20/40 mesh sand it is 0.035 in.
Formation permeability, md
Effective permeability of the formation
Permeable (leakoff) thickness, ft
This parameter is used for Productivity Index calculation (as net thickness) and in
calculation of the apparent leakoff coefficient, because it is assumed there is no leakoff
(and spurt loss) outside the permeable thickness.
Well Radius, ft
Needed for pseudo skin factor calculation
Well drainage radius, ft
Needed for optimum design. (Do not underestimate the importance of this parameter!)
Pre-treatment skin factor
Can be set zero, it does not influence the design. It affects only the "folds of increase" in
productivity, because it is used as basis.
Fracture height, ft
Usually greater than the permeable height. One of the most critical design parameters.
Might come from lithology information, or can be adjusted iteratively by the user, to be
on the order of the frac length.
Plane strain modulus, E' (psi)
Defined as Young modulus divided by one minus squared Poisson ratio. E’=E/(1-2) It
is almost the same as Young modulus, and it is about twice as much as the shear
modulus, because the Poisson ratio has little effect on it. For hard rock it might be
106 psi, for soft rock 105 psi or less.
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Slurry injection rate (two wings, liq+ prop), bpm
The injection rate is considered constant. It includes both the fracturing fluid and
the proppant. The more proppant is added, the less the calculated liquid injection
rate will be. A typical value is 30 bpm.
Rheology, K' (lbf/ft^2)*s^n'
Power law consistency of the fracturing fluid (slurry, in fact)
Rheology, n'
Power law flow behavior index
Leakoff coefficient in pay layer, ft/min0.5
In general, the leakoff coefficient outside the pay layer may be less, than in the
pay. Hence a multiplier is used outside the pay, see below.
Spurt loss coefficient, Sp, gal/ft2
The spurt loss in the pay layer. Outside the permeable layer the spurt loss for
out of pay is considered zero. See the remark above.
Fluid loss multiplier for out of pay layer
If this multiplier is set zero, there is no leakoff and spurt loss outside the pay
layer. It is more realistic to use a multiplier between zero and one, say 0.5.
Max possible added proppant concentration, The most important equipment constraint. Some current mixers can provide
lbm/gallon fluid (ppga)
more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maximum technically possible concentration.
Multiply opt length by factor
This design parameter can be used for sub-optimal design. If the optimum length
is too small (and the fracture width is too large), a value greater than the one
used. If the optimum length is too large (and the fracture width is too small) , a
fractional value might be useful. This possibility of user intervention is advantageous to investigate the pros and contras of departing from the technical optimum. The default value should be 1. See more on this issue in the text.
Multiply pad by factor
In accordance with Nolte's suggestion, the exponent of the proppant concentration schedule and the pad fraction (relative to the total injected volume) are taken
to be equal. This happens if this design parameter is at its default value, which is
at 1. The user may experiment with other values. It will have the effect of shortening or elongating the pad period that is having less or more conservative
design. The program adjusts the proppant schedule accordingly, to ensure the
required amount of proppant is injected.
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Additional input parameters
TSO criterion Wdry/Wwet
This design parameter appears only for TSO design. It specifies the ratio of dry
width (assuming only the "dry" proppant is left in the fracture) to wet width
(dynamically achieved during pumping). According to our assumptions, the
screen-out happens when the ratio of dry to wet width reaches the user specified
value. We suggest a number between 0.5 and 0.75., but the best method is
gradually calibrate this parameter in the field by evaluating successful TSO
treatments.
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3
CALCULATED RESULTS
The results contain the optimum fracture dimensions, followed by the fracture dimensions achieved
taking into account the constraints (max possible added proppant concentration.) The constraints may or
may not allow to achieve the technical optimum fracture dimensions. A red message will tell whether the
optimum dimensions could be achieved.
The main fracture dimensions, such as half-length, average width, areal proppant concentration determine
the performance of the fractured well, which is given in terms of dimensionless productivity index and
also as pseudo-skin factor.
The fluid and proppant requirements are given in cumulative terms and the injection rate of the fluid and
the added proppant concentration are presented as functions of time.
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The results include:
t, min
time elapsed from start of pumping
qi_liq, bpm
liquid injection rate (for two wings)
cum liq, gal
cumulative liquid injected up to time t
cadd, lbm/gal
added proppant to one gallon of liquid, in other words ppga
cum prop, lbm cumulative proppant injected up to time t
xf, ft
half-length of the fracture at time t
wave, in.
average width of the fracture at time t
wave / Dpmx
the ratio of average width of the fracture to the maximum proppant diameter, should be at least 3
wdry / wwet
the ratio of dry to wet width.
During pumping the actual wet width is 2 to 10 times larger than the dry width, that would be necessary to
contain the same amount of proppant without any fluid and packed densely. Usually it should be less than a
prescribed number, such as 0.2 for avoiding screen-out during the job.
The TSO criterion in the TSO version of the design spreadsheet is formulated in terms of this output variable.
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4
THEORETICAL FRACTURE PERFORMANCE
The fracture design should be based on sound principles of fluid flow in porous media. We start the
description of the fractured well performance with the pseudo-steady state Productivity Index. It is well
understood that in tight gas the transient regime might last for a considerable time therefore well production is affected by the transient process. Nevertheless, it is impossible to understand the well behavior
without first considering the pseudo-state flow regime.
We consider a fully penetrating vertical fracture in a pay layer of thickness h, see Fig. 1 for notation.
2xf
2xf
h
w
w
xe
2re
Fig. 1. Notation for fracture performance
Note that in reality the drainage area is neither circular nor rectangular. Using re or xe is only a matter of
convenience. The relation between re and xf is given by
A  re2  xe2 ................................................................... (1)
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where A is the drainage area.
Productivity Index
The pseudo-steady state productivity index relates production rate to pressure drawdown:
J
q
2kh

J D ........................................................... (2)
p  pwf 1 B
where JD is called the dimensionless productivity index, k is the formation permeability, h is the pay
thickness, B is the formation volume factor,  is the fluid viscosity and 1 is a conversion constant (one
for a coherent system).
For a well located in the center of a circular drainage area the dimensionless productivity index reduces
to
JD 
1
r
3
ln e   s
rw 4
.............................................................. (3)
In the case of a propped fracture there are several ways to incorporate the stimulation effect into the
productivity index. One can use the pseudo-skin concept:
JD 
1
............................................................. (4)
re 3
ln   s f
rw 4
or the equivalent wellbore radius concept:
JD 
1
r
3
ln e 
r'w 4
................................................................ (5)
or one can just provide the dimensionless productivity index as a function of the fracture parameters:
JD = function(drainage-volume geometry, fracture parameters )
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All three options give exactly the same results (if done coherently). The last option is the most general
and convenient, especially if we wish to consider fractured wells in a rectangular drainage area.
Many authors have provided charts and correlations in one or another form for special geometries, reservoir types, etc. Unfortunately, most of the results are less obvious to apply in high permeability environment. Also there are quite large discrepancies as shown for instance on Fig. 12-13 of Reservoir Stimulation 3rd edition, 2000. Therefore we provide a fresh look at the partly known results.
Proppant Number
For a vertical well intersecting a rectangular vertical fracture which penetrates fully from the bottom to
the top of the rectangular drainage volume the performance is known to depend on the x-directional
penetration ratio:
Ix 
2x f
xe
...................................................................... (6)
and on the dimensionless fracture conductivity:
C fD 
kf w
kx f
.................................................................... (7)
where xf is the fracture half length, xe is the side length of the square drainage area, k is the formation
permeability, kf is the proppant pack permeability, and w is the average fracture width.
The key to formulating a meaningful technical optimization problem is to realize that penetration and
dimensionless fracture conductivity (through width) are competing for the same resource: the propped
volume. Once the reservoir and proppant properties and the amount of proppant are fixed, one has to
make the optimal compromise between width and length. The available propped volume puts a constraint
on the two dimensionless numbers. To handle the constraint easily we introduce the dimensionless proppant number:
N prop  I x2 C fD 
HF2D
4k f x f w
kxe2
 const ................................................. (8)
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Note that only that part of the proppant counts into the propped volume, that reaches the pay. If for instance the fracture height is three times the net pay thickness, then the V prop can be calculated as the bulk
volume of one third of the injected proppant, if it is closely packed.
The Dimensionless Proppant Number, Nprop, is nothing else but the ratio of two volumes: the propped
volume in the pay divided by the reservoir volume in the pay, both volumes weighted by their permeability, respectively. (In addition, a factor of two is used in front of the propped volume.) As we will see, the
proppant number is the most important parameter in fracture design.
A convenient algorithm to calculate JD is available1. Fig. 2 shows JD represented in a traditional manner,
as a function of dimensionless fracture conductivity, CfD, with Ix as a parameter. Similar “productivity
increase” graphs are numerous in the published literature2,3.
1
Valkó, P. P. and Economides,M.J.: “Heavy Crude Production from Shallow Formations: Long Horizontal Wells
Versus Horizontal Fractures,” paper SPE 50421, 1998.
2
McGuire, W.J. and Sikora, V.J.: “The Effect of Vertical Fractures on Well Productivity,” Trans. AIME (1960)
219, 401-405.
3
Soliman, M.Y.: “Modifications to Production Increase Calculations for a Hydraulically Fractured Well,” JPT (Jan.
1983) 170-178.
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Dimensionless Productivity index, JD
2
Ix = 1
0.9
0.8
ye = xe
1.5
2xf
0.7
0.6
xe
0.5
1
0.4
0.3
0.2
0.5
0.1
0.01
0
0.01
0.1
1
10
100
1000
Dimensionless Fracture Conductivity, CfD
10000
Fig. 2. Calculated dimensionless productivity index as a function of dimensionless fracture conductivity and penetration
Fig. 2 is not very helpful to solve the optimization problem involving any fixed amount of proppant. For
this purpose in Figs 3 and 4 we present the same results, but the individual curves correspond to JD at a
fixed value of the proppant number, Nprop.
Fig 3 a and Fig. 3 b emphasize the importance of the proppant number.
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0.5
Dimensionless Productivity Index, JD
Xe=Ye
Ye
Ix=1
2Xf
0.4
Np=0.1
Xe
Np=0.06
Np=0.03
0.3
Np=0.01
Np=0.006
Np=0.003
Np=0.001
0.2
Np=0.0006
Np=0.0003
Np=0.0001
-4
-3
10
-2
10
-1
0
1
10
10
10
Dimensionless Fracture Conductivity, CfD
10
2
10
Fig. 3a. Dimensionless productivity index as a function of dimensionless fracture conductivity and
proppant number (for Nprop < 0.1)
2.0
Dimensionless Productivity Index, JD
Xe=Ye
Ye
Ix=1
2Xf
Np=100
1.5
Np=60
Xe
Np=30
Np=10
Np=6
1.0
Np=3
Np=1
Np=0.6
Np=0.3
0.5
Np=0.1
0.1
1
10
100
1000
Dimensionless Fracture Conductivity, CfD
Fig. 3b. Dimensionless productivity index as a function of dimensionless fracture conductivity
and proppant number (for Nprop > 0.1)
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0.45
Dimensionless Productivity Index, JD
Xe=Ye
Ye
0.40
Np=0.1
2Xf
Np=0.06
0.35
Xe
Np=0.03
0.30
Np=0.01
Np=0.006
0.25
Np=0.003
0.20
Np=0.001
Np=0.0006
Np=0.0003
0.15
Np=0.0001
-1
-2
-3
10
10
Penetration Rate, IX
10
0
10
Fig. 4.a Dimensionless productivity index as a function of penetration ratio and proppant number
(for Nprop < 0.1)
Np=100
Dimensionless Productivity Index, DJ
1.8
1.6
Np=30
Xe=Ye
Ye
Np=10
2Xf
Np=6
1.4
1.2
Xe
Np=3
1.0
0.8
Np=1
Np=0.6
0.6
Np=0.3
0.4
Np=0.1
0.01
0.1
1
Penetration Rate, I X
Fig. 4.b Dimensionless productivity index as a function of penetration ratio and proppant number
(for Nprop > 0.1)
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As seen from Figs. 3 a and b, for a given value of Nprop , that is for a fixed amount of available proppant,
there exists an optimal dimensionless fracture conductivity, representing the optimal compromise between
the ability of the fracture to conduct the flow into the wellbore and its ability to get inflow from the
formation.
Figs. 4 a and 4 b show the performance as a function of penetration ratio. The large JD values (above
JD = 0.8) correspond to streamlines parallel to the y axis in pseudo-steady state, a highly desirable, but
extremely difficult (if not impossible) to achieve situation.
It is important to understand that Figs 3 a and 4 a are equivalent, and their correct use should lead to the
same results. Similarly, Figures 3 b and 4 b carry equivalent information.
One of the main result seen from the figures is, that at "low" proppant numbers (low proppant volume
and/or high formation permeability), the optimal compromise occurs at CfD = 1.6. The behavior at large
Nprop is as anticipated because we know that the absolute maximum for JD is 6/ = 1.909 (this value is the
productivity index for a perfect linear flow in a square reservoir.
When the propped volume increases, the optimal compromise happens at larger dimensionless fracture
conductivities because the penetration cannot exceed unity. Figure 2.b shows this effect clearly.
In “medium and high” permeability formations, that is above 50 md, it is practically impossible to achieve
a proppant number larger than 0.1. For Frac-and Pack typical proppant numbers range between 0.0001
and 0.01 . Therefore, for medium/high permeability formations the optimum dimensionless fracture
conductivity is always CfDopt = 1.6.
In “tight gas” it is possible to achieve large dimensionless proppant numbers, at least in principle. If one
calculates the proppant number with a limited drainage area and does not question whether the proppant
really reached the pay layer, dimensionless proppant number 1 or even 5 can be calculated. However, the
personal belief of this author is that proppant numbers larger than one are impossible to realize. The
reason is that for large treatments there is a great uncertainty of where the proppant goes both in horizontal and in vertical direction. One has to be very optimistic to believe that the proppant injected remains in
the pay layer vertically and also remains contained in the lateral direction with respect to the targeted
drainage area.
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For large treatments the drainage area is oftentimes dynamic in the sense that the extreme fracture length
causes increase of the drainage area with respect to the originally targeted or even with respect to the
existing well spacing.
This author’s opinion is that a dimensionless proppant number larger than 0.5 is rarely realized, because the proppant can not be contained in the pay and within the drainage area.
Unfortunately, in case of regular well-spacing the proppant extending laterally outside the drainage area
can be totally discounted. It does not contribute to the proppant number and to the performance.
The situation is more complex in case of an individual well in a larger area. Then the large fracture length
tends to increase the drainage area and hence the proppant number decreases. Ultimately, the large fracture is beneficial, but the approximate upper limit (0.5) on the realizable proppant number still remains
valid.
The maximum possible dimensionless Productivity Index for Nprop = 0.5 is JD = 0.75 . The dimensionless Productivity Index of an undamaged vertical well is between 0.12 and 0.14 depending on the well
spacing and assumed well radius. Therefore, there is a realistic maximum for the “ folds of increase” of
the pseudo-steady state productivity (with respect to the zero skin case) and it is given by 0.75 / 0.13 ~
6 . Any hope to achieve larger folds of increase (raised mostly by the simplicistic view: “equivalent
wellbore radius equals xf/2”) ultimately has to face reality. Of course, much larger folds of increase can
be achieved with respect to an originally damaged well (where the pre treatment skin factor is positive.)
Another common misunderstanding is connected with the existence of the transient regime. In transient
regime the Productivity Index (and hence the production rate) is larger than in pseudo-steady state. With
this qualitative picture in mind it is easy to discard the pseudo-steady state optimization procedure and to
“shoot” for very high dimensionless fracture conductivity and/or to anticipate much more folds of increase in the transient period. In reality, the existence of the transient period does not change the previous
conclusions on optimal dimensions and should not induce too high anticipations. Our calculations show,
that there is no reason to depart from the optimum compromise described above, even if the well will
produce in transient regime for a considerable time (several months or even years.)
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5
SUGGESTED DESIGN PROCEDURE BASED
ON OPTIMAL PSEUDO-STEADY STATE
PERFORMANCE
To exploit the potentials of a given proppant number one has to place the proppant optimally (or near
optimally). Therefore, the optimal design of a fracture treatment consists of two steps. The first one is to
make a decision on size (in fact on proppant number). The second one is to design the treatment in such a
way that we make maximum use of the potential of the realized proppant number. These issues are discussed in the following section.
Sizing
Specify the goal of the treatment in form of amount of proppant reaching the target layer. (Denote it by
Vprop = 2Vf ). Calculate the proppant number, from that the maximum possible pseudo-steady state
Productivity Index can already be computed.
The target proppant number has to be at least 0.0001, otherwise there is no stimulation effect. It seems
reasonable to select Nprop= 0.0005 - 0.001 as a target for many high permeability formations, because that
would provide a JD about 0.2. Since wells in high permeability formations are often damaged (the pretreatment skin is a large positive number) most of the economic benefit comes from bypassing the original damage. To increase the JD significantly beyond 0.2, one would need order of magnitude larger proppant numbers, that is economically (and sometimes even technically) not feasible.
It is the experience of this author that for tight gas it seems reasonable to select a target proppant number
in the range between Nprop = 0.1 to 0.5 or sometimes around 1.
The majority of formations are, however, not tight and neither of extreme high permeability. For those
“medium” reservoirs the Nprop = 0.1 seems to be a reasonable target.
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Of course, the above suggestions should be taken only as starting point. The actual sizing process should
consider a whole range of proppant numbers including and evaluate the options by Net Present Value
analysis.
The most important thing to remember about the proppant number is that it has to be calculated with the
proppant placed into the pay layer and with the representative in-situ conductivity of the proppant pack.
The first problem requires the understanding of the layered structure of the reservoir and of the stress
situation controlling fracture height containment (if any). In this respect, fracture propagation (3D or P3D
modeling) plays an important role, but one has to be aware how the fracture dimensions will affect the
final performance, and oftentimes in reality, this effect is less than that the literature and common belief
suggest. The reason is that once the amount of proppant reaching the pay is already fixed, the actual
fracture shape (especially the length) has limited effect on the final performance. To put it in simple
words: the real question is not “what the length would be” but rather how much proppant would be placed
into the target layer”. One of the most important concepts of the design procedure is the percentage of
proppant reaching the target layer(s). If, for instance, several shale layers are imbedded between the pay
layers, the actual proppant reaching the target might be less than 50 %, even with perfect height containment!
The other important issue is the actual proppant pack permeability. The proppant number (and dimensionless fracture conductivity) have to be calculated with the in-situ representative permeability of the
proppant pack. For instance, a proppant manufacturer may report 500 Darcy or even 1000 Darcy nominal
permeability of the proppant at the estimated closure stress. In reality, however, because of the residue
from the fluid, the actual retained permeability can be, for instance, 10 times less. If two phase flow is
involved (gas with significant water, for instance) an other effect will dramatically decrease the effective
(or apparent) permeability of the propped fracture. That effect is often referred to as non-Darcy flow. In
the two-phase flow situation the origin of the additional energy loss in the fracture is due to the periodic
acceleration and deceleration of the liquid droplets. This effect may be detrimental and may call for an
additional factor of 5 or 10 to obtain a representative apparent permeability of the proppant pack. The
understanding of the in-situ proppant permeability (conductivity) is therefore another important issue in
fracture design. There is a large amount of information available on the actual in-situ conductivity of the
proppant packs and it should be of primary concern of every design. Any other factor (such as vertical
stress profile and variation of the Poisson ratio, dilatancy and/or apparent fracture toughness, wall building and/or radial leakoff, shear thickening and/or viscoelasticity, just to mention a few) should be consid-
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ered after the sizing has been done correctly, taking into account the main issues such as: net pay thickness, formation permeability, percentage of proppant reaching the pay, apparent proppant permeability.
In the sizing phase of the fracture design we make a decision on the dimensionless proppant number to
realize. This determines the maximum possible Productivity Index and the optimum fracture dimensions
are those realizing this “best” performance.
Optimum fracture dimensions
The optimum design represents the best compromise between width and length. Once we know the
volume of the propped one-wing in the pay layer, Vf (note that this is half of the propped volume in the
pay layer : Vf = Vprop /2 and, naturally, much less than half of the proppant volume injected) then we
can use the definition of dimensionless fracture conductivity to obtain the optimum width and length:
 Vf k f 

xf  
C

hk
fDopt


1/ 2
 C fDoptV f k 

w
 hk

f


............................................................... (9)
1/ 2
............................................................ (10)
Once we know the proppant number, the optimum dimensionless fracture conductivity can be read from
Fig. 3 a or b or calculated from suitable correlations built into the HF2D spreadsheet. Most often the
optimum CfD will be 1.6, but the program can do the optimization for very large proppant numbers as
well, where the optimum dimensionless fracture conductivity will be largergher.
The fracture dimensions obtained from Eqs. 9 and 10 will realize the previously determined maximum
possible Productivity Index.
Of course, the above half-length and width are meant as “equivalent length” and “equivalent average
propped width”, because the performance model represents the vertical fracture by a crude approximation as a rectangular fracture with constant width.
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The actual shape of the fracture might be different but that can bring only minor deviations from the
results presented here. (The most difficult thing in petroleum engineering is the separation of the really
important effects from the lots parameters of secondary importance. )
Pumping Schedule
Once the target length and width is known, one can proceed with the actual design of the treatment. The
design includes the determination of the injection time, the necessary maximum added proppant concentration and the detailed proppant schedule realizing the optimum dimensions. The basic algorithm is
described in the Appendix.
If technical constraints do not allow the realization of the “optimum placement”, one has to make a departure from it, but only to the extent it is really necessary. For instance, in very low permeability formations
the optimum width might be less than two or three proppant diameters. Then we have to put a constraint
on the minimum width and modify the target width and length accordingly (still providing the target
proppant number.) It can be shown with the presented curves that such a departure – if done only to the
necessary extent - causes a loss of productivity that is within reasonable limits and most often not important at all.
It is important to note that:
o
There is no theoretical difference between low and high permeability fracturing. In both cases
there exists a technically optimal fracture, and in both cases it should have a dimensionless fracture conductivity depending solely on the proppant number. While in a low permeability formation this requirement results in a long and narrow fracture, in high permeability formations, a
short and wide fracture will provide the same dimensionless conductivity.
o
Increasing the volume of proppant or the permeability of the proppant pack by a given factor (for
example, 2 ) has exactly the same effect on the productivity if otherwise the proppant is placed
optimally.
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o
To achieve the same post-treatment skin factor in a low and a high permeability formation the
volume of proppant placed to the pay layer should be increased by the ratio of the formation permeabilities, provided all the other formation and proppant parameters are the same.
o
Since not all proppant will be placed into the permeable layer, the optimum length and width
should be calculated with the effective volume, subtracting the proppant placed in the nonproductive layers.
o
In high permeability formations, the indicated fracture length might not be enough to bypass the
damaged zone, therefore a minimum length should be applied.
o
Considerable fracture width can be lost because of proppant embedment into soft formations. For
gas wells, non-Darcy effects may create a dependence of the apparent permeability of the proppant pack on the production rate itself. These issues are best handled by using proper effective
width and effective peremeabilities in the conductivity expression (both in the proppant number
and in the dimensionless proppant conductivity).
Of course it is possible that the technical constraints (first of all maximum possible proppant concentration in the slurry) does not allow optimal placement. In case of conflict the design engineer has several
options: e.g. choosing another type of fluid and/or equipment, but for higher permeability formations
most likely a tip screenout (TSO) design has to be considered.
The TSO design differs from the above procedure in one basic feature: it uses a TSO criterion to separate
the lateral fracture propagation period from the width inflation period. In our design model this criterion
is based on “dry to wet” average width ratio. The “TSO criterion” specifies the ratio of dry width (assuming only the "dry" proppant is left in the fracture) to wet width (dynamically achieved during pumping).
According to our assumptions, the screen-out happens and fracture propagation stops when the ratio of
dry to wet width reaches the user specified critical value. After the TSO is triggered, only the width is
inflated, as far as additional slurry is injected. It is possible to schedule the proppant to such that the
critical dry to wet width ratio is reached at that moment when the fracture length arrived at the desired
distance. With TSO design, practically any width can be achieved, at least in principle. We suggest a
number between 0.5 and 0.75. for the “TSO criterion: dry/wet width” parameter, but there is no good
theoretical model behind this suggestion.
(Unfortunately, if the formation does not allow it, it might be impossible to arrest fracture propagation
(the rock is not soft enough, the elasticity modulus is too high, the leakoff is too high, etc.) There is no
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clear procedure to predict if a TSO-type width inflation will be possible in the given formation or not.
Engineering intuition and previous experience are of crucial importance in making that judgment.)
Note that we use the word “optimum” for placing a given amount of proppant the best possible way into
the formation. The determination of the optimum amount of proppant is called sizing. For optimum sizing
one needs to know the costs and revenues. The costs increase with proppant number in a well defined
manner. The revenues also increase with proppant number, and that can be calculated knowing the targeted Productivity Index. There is no need to do a detailed fracture design in order to size a treatment. (In
fact sizing and detailed design should be separated. Optimum sizing should be done exclusively by the
operator and not by the service company.)
In case of conflict the design engineer may consider using another type of fluid and/or consider using
equipment providing a higher maximum proppant concentration, and/or tip screenout design.
There are several other checks the design engineer has to conduct. For instance, at the end of the pad
injection the current hydraulic width should be large enough to accommodate proppant that is wet width
per dry width should be at least 3.
The TSO design differs from the above procedure in one basic feature: it uses the TSO criterion (critical
ratio of wet width per dry width) to separate the lateral fracture propagation period from the width inflation period.
It is possible that the design does not require a tip screenout. This is indicated by a message and then the
user is suggested to run a traditional design without TSO.
If the constraints do not allow the best placement of the proppant, the traditional PKN algorithms still
provides a design, but the created fracture will be suboptimal. Warning messages indicate suboptimality
and possible modification of injected proppant. In modifying the requirements the program takes the easy
road, that is it reduces the amount of proppant placed. Sometimes this is acceptable, but more often you
should explore other options.
The first thing to look at is to use various fluids (that is changing rheology and leakoff), changing the
injection rate or assuring larger maximum possible added proppant concentration by selecting a better
equipment.
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Often the optimum proppant placement can be realized by a tip-screenout design, and in such case the
user should use the PKN-TSO method. The TSO design is not a well established procedure, because the
prediction of the tip screen-out point is not based on sound physical principles. In our model a TSO
criterion is used to trigger TSO and this criterion has to be selected carefully. That design parameter is
only for TSO design. It specifies the ratio of dry width (assuming only the "dry" proppant is left in the
fracture) to wet width (dynamically achieved during pumping). According to our assumptions, the screenout happens when the ratio of dry to wet width reaches the user specified value. We suggest a number
between 0.5 and 0.75., but there is no good theoretical model behind this suggestion.
Unfortunately, TSO treatment can be impossible, if the formation does not allow it (the rock is not soft
enough, the leakoff is too high, etc.) There is no clear procedure to predict if a frac&pack type width
inflation will be possible in the given formation or not. Engineering intuition and previous experience are
of crucial importance in such case.
If the given amount of proppant can not be placed optimally by a traditional design and you can not apply
a TSO design (because the high leakoff, and/or high elastic modulus, and/or consolidated rock make it
impossible) the traditional PKN design procedure should be used with an additional design factor that
becomes especially important. In the spreadsheet it is called “multiply opt length by a factor”.
Once you see the error message “Optimum placement of proppant is not possible” and you have tried all
other options you have to make a decision on which design goal to relax. If you still want to place the
originally specified amount of proppant, you have to depart from the optimum length. In such case you
specify a factor of 2, 3, or even 10 to multiply the theoretically optimum length. With large enough factor
used, you will be able to place all the proppant into the formation. The resulting suboptimal design will
yield a reduced PI (compared to the optimum one.) At this point you have to decide whether it was a
good idea to stick with the original amount of proppant. (It is possible that the answer is NO. As you will
find, often a fraction of the original amount of proppant, BUT PLACED OPTIMALLY, gives almost the
same PI as the large SUBOPTIMAL treatment while the cost of a small treatment is, of course, considerably less.)
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6
HF2D
SAMPLE RUNS
Page 25
1) Traditional PKN design
Input
Proppant mass for (two wings), lbm
150,000
Sp grav of proppant material (water=1)
2.65
Porosity of proppant material
0.38
Proppant pack permeability, md
60,000
Max prop diameter, Dpmax, inch
0.031
Formation permeability, md
0.5
Permeable (leakoff) thickness, ft
45
Well Radius, ft
0.30
Well drainage radius, ft
2100
Pre-treatment skin factor
0.0
Fracture height, ft
120
Plane strain modulus, E' (psi)
2.00E+6
Slurry injection rate (two wings, liq+ prop), bpm
20
Rheology, K' (lbf/ft^2)*s^n'
0.0180
Rheology, n'
0.65
Leakoff coefficient in permeable layer, ft/min^0.5
0.00400
Spurt loss coefficient, Sp, gal/ft^2
0.01000
Fluid loss multiplier outside the pay
0
Max possible added proppant concentration, lbm/gal
neat fluid
12
Multiply opt length by factor
1
Multiply Nolte pad by factor
1
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Page 26
Part of Output
Optimum placement without constraints
Proppant number, Nprop
0.211
Dimensionless PI, JDopt
0.56
Optimal dimensionless fracture cond, CfDopt
1.7
Optimal half length, xfopt, ft
661.1
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-6.33
Folds of increase of PI
4.57
Constraints allow optimum placement
Actual placement
Proppant mass placed (2 wing)
150,000
Proppant number, Nprop
0.2111
Dimensionless PI, JDact
0.56
Dimensionless fracture cond, CfD
1.7
Half length, xf, ft
661.1
Propped width, w, inch
0.11
Post treatment pseudo skin factor, sf
-6.33
Folds of increase of PI
4.57
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Treatment details
Efficiency, eta, %
33.1
Pumping time, te, min
84.5
Pad pumping time, te, min
42.5
Exponent of added proppant concentration, eps
0.5029
Uniform proppant concentration in frac at end, lbm/ft^3
47.8
Areal proppant concentration after closure, lbm/ft^2
0.9
Max added proppant concentration, lb per gal clean fluid
9.0
Net pressure at end of pumping, psi
262.5
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2) PKN-TSO design
Input
Proppant mass for (two wings), lbm
50,000
Sp grav of proppant material (water=1)
2.65
Porosity of proppant material
0.38
Proppant pack permeability, md
60,000
Max propp diameter, Dpmax, inch
0.031
Formation permeability, md
15
Permeable (leakoff) thickness, ft
45
Well Radius, ft
0.30
Well drainage radius, ft
2,100
Pre-treatment skin factor
0.0
Fracture height, ft
75.0
Plane strain modulus, E' (psi)
2.00E+05
Slurry injection rate (two wings, liq+ prop), bpm
15.0
Rheology, K' (lbf/ft^2)*s^n'
0.0180
Rheology, n'
0.45
Leakoff coefficient in permeable layer, ft/min^0.5
0.00600
Spurt loss coefficient, Sp, gal/ft^2
0.02000
Fluid loss multiplier outside the pay
0
Max possible added proppant concentration, lbm/gallon
fluid
16
Multiply opt length by factor
1
TSO criterion Wwet/Wdry
0.7
Multiply pad by factor
1
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Page 29
Part of Output
Optimum placement without constraints
Proppant number, Nprop
0.0038
Dimensionless PI, JDopt
0.26
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
89.1
Optimal propped width, wopt, inch
0.4
Post treatment pseudo skin factor, sf
-4.32
Folds of increase of PI
2.14
Optimum placement
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Page 30
TSO criterion was achieved
Actual placement
Proppant mass placed (2 wing)
50,000
Proppant number, Nprop
0.0038
Dimensionless PI, JDact
0.2644
Dimensionless fracture cond, CfD
1.64
Half length, xf, ft
89.1
Propped width, w, inch
0.4375
Post treatment pseudo skin factor, sf
-4.32
Folds of increase of PI
2.14
Treatment details
Pad pumping time, min
0.37
TSO time, min
7.1
Total pumping time, min
16.2
Mass of proppant in frac at TSO, lbm
13,628
Added proppant concentration at TSO, ca, lbm/gal liq
4.0
Half length at TSO, xf, ft
89.1
Average width at TSO, inch
0.6
Net pressure at TSO, psi
30.1
Max added proppant concentration at end, lbm/gal-liq
16.0
Areal proppant concentration after closure, lbm/ft^2
1.7
Net pressure at end of pumping, psi
79
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Page 31
HF2D
Page 32
NOMENCLATURE
Bo = oil formation volume factor, RB/STB
CfD = dimensionless fracture conductivity
CL = leakoff coefficient, ft/min1/2
h = pay thickness, ft
hp = net pay thickness, permeable thickness, ft
hf = fracture height, ft

Ix = penetration ratio, calculated for a square drainage area
J = productivity index, BOPD/psi
JD = dimensionless productivity index

E' = plain strain modulus, psi

k = effective formation permeability, mD

kf = effective proppant pack permeability, mD

K' = Power law consistency index , lbf/(ft2-sec)

n' = Power law flow behavior index

Nprop = proppant number
p = average reservoir pressure, psi
pwf = flowing bottomhole pressure, psi
q = oil flow rate, STB/D
qi = fluid injection rate, bpm

rp = permeable to total area ratio

rw = wellbore radius, ft

r'w = equivalent wellbore radius due to fracture, ft
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Page 33

Rf = created fracture radius, ft
sf = pseudo skin factor due to fracture
te = pumping time, min

Vi = injected volume, ft3

Vp = propped volume of the two wing contained in the pay layer, ft3

Vr = drainage volume: net height by drainage area, ft3
xf = fracture half length, ft
xe = size of study area in x-direction
ye = size of study area in y-direction

w = propped fracture width, ft

1 = conversion factor (for field units 887.22)

 = pad fraction

 = Nolte exponent

p = proppant pack porosity, fraction

 = opening time distribution factor, dimensionless

 = formation fluid viscosity, cp

 = fluid (slurry) efficiency, fraction
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Page 34
A
CASE STUDIES
Table 1 Overview
Medium Permeability Formation MPF
Standard MPF01
Pushing the limit MPF02
Proppant Embedment MPF03
Non-Darcy
Fracture face skin
High Permeability Formation HPF
Standard MPF01
Extreme High MPF02
Low Permeability Formation LPF
HF2D
Low Permeability (tight gas) LPF01
Page 35
A.1 A Typical Preliminary Design: Medium Permeability Formation, MPF01
In the remaining part of this chapter we will illustrate the design logic incorporated in the Unified Fracture Design. We will intentionally consider cases, where only limited data are available.
Table 2 shows available data for a “medium” permeability formation (with permeability 1.7 md. and net
pay of 76 ft). The input data contains the well radius and the drainage radius (calculated from 40 acre
spacing). These important reservoir parameters should not be missed.
A preliminary sizing decision is that 90,000 lbm proppant should be injected.
At the closure stress anticipated (5000 psi) the selected resin coated 20/40 mesh sand will have an in-situ
permeability of 60,000 md. In this number we already incorporated the effect of some proppant crushing
and the decrease of proppant pack permeability due to imperfect breaking of the gel. Obviously, this is
one of the key parameters of the design, and the design engineer has to do everything in her/his power to
make this estimate as relevant as possible. (Buying an expensive 3D program with vendor provided
proppant data and clicking the name of the proppant is obviously not enough.)
The plane-strain modulus (that is basically the Young modulus) is 2106 psi. Minifrac tests in the same
formation with the same fluid usually result in a leakoff coefficient 0.005 ft/min1/2 and some spurt loss is
also anticipated. (Note that these values are with respect to the pay layer. It is assumed, that outside the
pay there is no leakoff.) The fluid rheology parameters are provided by the service company and (because
of pressure limitations in this case) the injection rate is 20 bpm.
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Page 36
Table 2. Input Data For MPF01
Proppant mass for (two wings), lbm
90,000
Sp grav of proppant material (water=1)
2.65
Porosity of proppant pack
0.38
Proppant pack permeability, md
60,000
Max propp diameter, Dpmax, inch
0.031
Formation permeability, md
1.7
Permeable (leakoff) thickness, ft
76
Well Radius, ft
0.25
Well drainage radius, ft
745
Pre-treatment skin factor
0.0
Fracture height, ft
Plane strain modulus, E' (psi)
2.0E+06
Slurry injection rate (two wings, liq+ prop), bpm
20.0
Rheology, K' (lbf/ft2)sn'
0.07
Rheology, n'
0.45
Leakoff coefficient in permeable layer, ft/min1/2
0.005
Spurt loss coefficient, Sp, gal/ft^2
0.010
The input data are summarized in Table 2. The line of fracture height is still left empty. We know that the
gross pay is 100 ft, that is the distance between the top and bottom perforations is 100 ft. Within this
interval, only 76 ft is pay, though. A preliminary estimate of fracture height should be minimum 100 ft,
but the actual height will be related to several other factors.
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Page 37
A reasonable assumption – in the absence of any reliable data on stress contrast – is, that the aspect ratio
of the created fracture is 2:1 . In other words, we will find the fracture height, hf, by adjusting it to the
target length, according to hf = xf .
At this point we put a starting estimate of hf =100 ft into our design spreadsheet and we specify the
following operational constraint/parameters, as shown in Table 3:
Table 3. Additional Input For MPF01
Max possible added proppant concentration, lb m/gal neat fluid
12
Multiply opt length by factor
1
Multiply Nolte pad by factor
1
The maximum available proppant concentration in ppga (lbm proppant added to 1 gallon of neat fracturing fluid) is 12 according to the service company. The other two parameters are fixed at their default
value.
The output of the first run of our design spreadsheet contains three parts. In the first part a “wish-list” is
shown.
Table 4. Theoretical Optimum for MPF01-1
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Page 38
Output
Optimum placement without constraints
Proppant number, Nprop
0.3552
Dimensionless PI, JDopt
0.65
Optimal dimensionless fracture cond, CfDopt
1.8
Optimal half length, xfopt, ft
294.2
Optimal propped width, wopt, inch
0.2
Post treatment pseudo skin factor, sf
-5.72
Folds of increase of PI
4.74
It states that the proppant number is 0.35 and with the proppant placed optimally we could achieve a
dimensionless productivity index of 0.65 that is a skin factor as negative as –5.72. The Folds of increase
in productivity (with respect to the zero skin situation we fixed in line 10 of the input as the basis of
comparison ) is 4.74 .
A red warning message is, however, indicating, that our wish-list could not be realized:
Suboptimal placement with constraints satisfied
Mass of proppant reduced
The actual placement, the design program was able to produce is somewhat disappointing, as shown in
Table 5:
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Page 39
Table 5. Actual placement for MPF01-1
Actual placement
Proppant mass placed (2 wing)
58,501
Proppant number, Nprop
0.2309
Dimensionless PI, JDact
0.57
Dimensionless fracture cond, CfD
1.2
Half length, xf, ft
294.2
Propped width, w, inch
0.12
Post treatment pseudo skin factor, sf
-5.50
Folds of increase of PI
4.15
In other words, the design program can assure only the placement of 58,500 lbm proppant. The reason
for this will be discussed later. At this point we should not pay too much attention to it, because our
specified fracture height (100 ft) was not realistic.
To approach our required aspect ratio: hf =xf we increase the fracture height to 200 ft. The calculated
theoretical optimum target length is now hf = 216 ft. A third adjustment to hf =211 ft will finally establish
the required aspect ratio.
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Table 6. Theoretical Optimum for MPF01-3 ( hf = 211 ft )
Optimum placement without constraints
Proppant number, Nprop
0.1684
Dimensionless PI, Jdopt
0.53
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
211.1
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-5.37
Folds of increase of PI
3.85
We see that the proppant number is significantly less: 0.168, than previously. Why did this happen?
Because the increase in fracture height decreases the volumetric proppant efficiency, that is the part of
proppant “working for us”. The optimum length corresponding to this proppant number is 211 ft, and that
means that our fracture – if it can be realized – will have the desired 2:1 aspect ratio. But can it be realized?
The red message:
Constraints allow optimum placement
shows that yes, the optimum placement can be realized.
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Table 6. Actual Placement MPF01-3 ( hf = 211 ft )
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.1684
Dimensionless PI, JDact
0.53
Dimensionless fracture cond, CfD
1.6
Half length, xf, ft
211.1
Propped width, w, inch
0.12
Post treatment pseudo skin factor, sf
-5.37
Folds of increase of PI
3.85
We found that the 90,000 lbm proppant can be safely placed into the well. Not all of the proppant will be
placed into the pay layer, though.
The part of the proppant reaching the pay will represent a proppant number Nprop = 0.168, and the optimum half length corresponding to it is 211 ft. The treatment will establish a dimensionless productivity
index, JDact = 0.53 in other words a negative equivalent skin, sf = -5.37 will be created.
Note that the whole design logic is based on the proppant number concept. We do not specify an arbitrary
length, rather we obtain the optimum length and the design process makes sure that the desired length is
realized and the desired amount of proppant is placed uniformly.
Some details of the treatment are shown in Table 7.
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Page 42
Table 7. Some Details of the Actual Placement MPF01-3 ( hf = 211 ft )
Treatment details
Efficiency, eta, %
34.5
Pumping time, te, min
40.4
Pad pumping time, te, min
19.7
Exponent of added proppant concentration, eps
0.4871
Uniform proppant concentration in frac at end, lbm/ft^3
57.5
Areal proppant concentration after closure, lb m/ft2
1.0
Max added proppant concentration, lb per gal clean fluid
11.8
Net pressure at end of pumping, psi
132.5
More details can be found by running the spreadsheet.
A.2 Pushing the limit: Medium Permeability Formation, MPF02
For illustrative purposes we will consider MPF01 as our base case. In this section we ask the question:
can we place 150,000 lb proppant in a similar manner? If yes, what good will it do for the well productivity?
The reader is now able to do the design so we will not show the detailed “iteration”, only the main results.
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Table 8. Some Details of the Input MPF02-3 ( hf = 248 ft )
Proppant mass for (two wings), lbm
150,000
…
Fracture height, ft
248
…
Table 9. Theoretical optimum for MPF02-3 ( hf = 248 ft )
Output
Optimum placement without constraints
Proppant number, Nprop
0.2387
Dimensionless PI, JDopt
0.58
Optimal dimensionless fracture cond, CfDopt
1.7
Optimal half length, xfopt, ft
248.0
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-5.54
Folds of increase of PI
4.23
The first thing we should note that the increase of proppant and corresponding increase of proppant
number will result – even if everything goes well – only a marginal improvement in productivity. This
should make us think whether it is worth “pushing the limit”. Even more food for thought is provided by
the message:
Suboptimal placement with constraints satisfied
Mass of proppant reduced
and by the next output:
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Page 44
Table 10. Actual placement for MPF02-3 ( hf = 248 ft )
Actual placement
Proppant mass placed (2 wing)
136,965
Proppant number, Nprop
0.2180
Dimensionless PI, JDact
0.57
Dimensionless fracture cond, CfD
1.5
Half length, xf, ft
248.0
Propped width, w, inch
0.13
Post treatment pseudo skin factor, sf
-5.49
Folds of increase of PI
4.12
Treatment details
Efficiency, eta, %
36.1
Pumping time, te, min
58.0
Pad pumping time, te, min
27.2
Exponent of added proppant concentration, eps
0.4694
Uniform proppant concentration in frac at end, lbm/ft^3
58.2
Areal proppant concentration after closure, lbm/ft^2
1.1
Max added proppant concentration, lb per gal clean fluid
12.0
Net pressure at end of pumping, psi
122.9
As we see the design program had to reduce the amount of proppant placed into the formation. With this
reduction the actual folds of increase is hardly more than what we can achieve with 90,000 lb proppant
and it is obvious that “pushing the limit” in this case is not worth the effort and money.
But is it really obvious? Several service companies would rather suggest a better equipment capable to do
as high proppant concentration as 16 ppga.
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Table 11. Actual placement for MPF02-4 ( hf = 248 ft, max possible conc: 16 ppga )
Max possible added proppant concentration, lbm/gal neat fluid
16
The message is now encouraging:
Constraints allow optimum placement
Table 12. Actual placement for MPF02-3 ( hf = 248 ft, max possible conc: 16 ppga )
Actual placement
Proppant mass placed (2 wing)
150,000
Proppant number, Nprop
0.2387
Dimensionless PI, JDact
0.58
Dimensionless fracture cond, CfD
1.7
Half length, xf, ft
248.0
Propped width, w, inch
0.14
Post treatment pseudo skin factor, sf
-5.54
Folds of increase of PI
4.23
Treatment details
Efficiency, eta, %
64.0
Pumping time, te, min
32.7
Pad pumping time, te, min
7.2
Exponent of added proppant concentration, eps
0.2191
Uniform proppant concentration in frac at end, lbm/ft^3
63.7
Areal proppant concentration after closure, lbm/ft^2
1.2
Max added proppant concentration, lb per gal clean fluid
13.9
Net pressure at end of pumping, psi
122.9
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Page 46
The increase in the maximum possible proppant concentration did the trick. It is now possible to place the
required quantity of proppant (because larger concentration allows to put more proppant into the same
width). In fact we did not even use all the capabilities of the equipment, a 14 ppga maximum proppant
concentration would be enough.
Also it is clear that our actual design now realizes the “wish-list” originally stated in Table 9. The question, whether it is worth doing the larger treatment or not, is however, still open. Only careful economic
calculations can tell if it is worth doing the larger treatment, that will be about 50 % more expensive, but
will realize a post treatment skin of –5.54 instead of the –5.50 calculated for our base case, MPF01-3.
Since the difference is clearly in the “error margin” it is difficult to believe that a manager would decide
on the more expensive (and more risky) larger treatment.
A.3 Proppant Embedment: MPF03
It is well-known, that in softer formations a considerable part of the injected proppant might be “lost”
because it is embedded into the formation wall. Some estimates talk about 30 % loss of width because of
embedment (Lacy, 1994)
Let us assume that the rock mechanics lab measured a 33.3 % embedment for the given formation and
closure stress. How can we incorporate this into the design?
The easiest way is to say that the proppant pack permeability (now 60,000 md) will apparently be reduced
to 40,000 md.
Changing one input line of case MPF01-3, that is putting
Proppant pack permeability, md
HF2D
40,000
Page 47
Table 13. Theoretical Optimum for MPF03-3 ( hf = 185 ft )
Optimum placement without constraints
Proppant number, Nprop
0.1280
Dimensionless PI, JDopt
0.50
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
185.2
Optimal propped width, wopt, inch
0.2
Post treatment pseudo skin factor, sf
-5.23
Folds of increase of PI
3.60
As we see, now the maximum possible dimensionless productivity index is less, only 0.50, but even this
can not be realized as the error message indicates:
Suboptimal placement with constraints satisfied
Mass of proppant reduced
Table 13. Theoretical Optimum for MPF03-3 ( hf = 185 ft )
Actual placement
Proppant mass placed (2 wing)
65,285
Proppant number, Nprop
0.0929
Dimensionless PI, JDact
0.46
Dimensionless fracture cond, CfD
1.2
Half length, xf, ft
185.2
Propped width, w, inch
0.11
Post treatment pseudo skin factor, sf
-5.06
Folds of increase of PI
3.31
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In fact only 65,300 lb proppant can be placed because the width at 185 ft is less than it was at 211 ft and
because we need more width to compensate for the loss of conductivity (due to embedment.)
To make the design possible we will depart from the optimum by multiplying the theoretical optimum
length by a factor. In this case we select the factor to target 250 ft for length, so we change the height to
250 ft (remember, we still use the 2:1 aspect ratio as most probable) and then we have to find a factor
resulting in the half length 250 ft. This value is 1.58:
Table 14. Height and Constraint for MPF03-4
Fracture height, ft
250
Max possible added proppant concentration, lbm/gal
neat fluid
12
Multiply opt length by factor
1.58
Multiply Nolte pad by factor
1
Table 15. First Part of Output for MPF03-4
Output
Optimum placement without constraints
Proppant number, Nprop
0.0947
Dimensionless PI, JDopt
0.46
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
158.9
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-5.08
Folds of increase of PI
3.34
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The message shows that the sub-optimal placement with the required modification can be realized:
Suboptimal placement with constraints satisfied
Length modified
Table 16. Additional Output for MPF03-4
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.0947
Dimensionless PI, Jdact
0.44
Dimensionless fracture cond, CfD
0.7
Half length, xf, ft
251.0
Propped width, w, inch
0.08
Post treatment pseudo skin factor, sf
-4.98
Folds of increase of PI
3.19
Now we can place all the 90,000 lb proppant but we have to depart from the theoretical optimum placement. The “success” is, however, questionable, because with all the 90,000 lb proppant placed we still
create only a - 4.98 equivalent skin, while the 65,300 lb – placed according to MPF03-3 – actually creates a better skin: -5.06.
By now the reader might feel why we call our approach “Unified Fracture Design”. The systematic use of
the proppant number and the optimality criterion makes the decisions more transparent.
A.4 Non-Darcy Flow in the fracture
For high-rate gas wells, where a certain percentage liquid content of the gas is inevitable, the concept of
proppant pack permeability deserves special attention. When the gas-liquid mixture flows in the propped
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fracture with high velocity, the liquid droplets collide with the proppant grains and the result is a significant dissipation of energy (loss of pressure). As a result, the nominal permeability contrast (in the fracture
vs in the formation) is not representative for the relative magnitude of pressure losses. The fracture behaves, as if its apparent permeability were much less, than the nominal value measured at single phase
flow conditions. There is an extensive literature available describing this non-Darcy flow effect in the
fracture (Jin and Penny, 2000, Cikes, M. 2000, Milton-Tayler, 1993, Gidley, 1990, Guppy et al., 1982).
From our point of view it is enough to understand, that at actual flow conditions the proppant pack can be
described by an apparent permeability – or if we wish – a correction factor multiplying the nominal
permeability. Depending on the actual velocity of the gas, the liquid content and the droplet size distribution, in addition to the proppant quality, the correction factor can be as low as 0.1.
The treatment of this phenomenon within the Unified Fracture Design is relatively simple. Using an
estimate of the correction factor, the apparent proppant permeability should be reduced, for instance from
60,000 md to 10,000 md. From the calculated maximum productivity index – corresponding to the corrected proppant number – a better estimate of the anticipated gas velocity can be obtained. (For this
calculation a drawdown has to be assumed and the properties of the gas – liquid mixture have to be
known.) With the improved estimate of gas velocity, an improved estimate of the non-Darcy flow correction factor can be obtained and the design can be continued using the corrected proppant number.
For instance, in our previous example the proppant number calculated with a nominal permeability:
60,000 md was obtained as Nprop = 0.095 . In the presence of significant non-Darcy effect, this number
should be reduced to Nprop = 0.05 or – in extreme cases – to Nprop = 0.01. If we want to compensate for the
loss of productivity, we have to increase the amount of proppant placed into the pay by the same factor.
A.5 Compensating for fracture face skin
In a certain reservoir it is suspected that the fracturing fluid filtrate will interact with the formation and an
estimated fracture face skin sff = 1 will be created. What is the effect of this phenomenon on the productivity of the well and how can we compensate for it? Assume the proppant number of the suggested
treatment is about Nprop = 0.1.
We recall, that the maximum of the dimensionless productivity index that can be achieved with
Nprop = 0.1 is (see Chapter 3):
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J D max 
1
 0.47
0.99  0.5 ln N prop
(8)
If there is a fracture face skin sff = 1, (and we assume the simple case of uniform influx) then the actual
productivity will be
J D actual 
1
 0.32
0.99  0.5 ln N prop  1
(9)
The fracture face skin causes a considerable decrease in productivity. From the equation it is seen that
approximately e2 = 7.4 times more proppant would compensate for the loss of productivity caused by a
fracture face skin of one.
A.6 Fracture Design for High Permeability Formation: HPF01
In high permeability formations the optimality criterion will result in a short and wide fracture. To have a
basis for comparison, we will use the previous data set except for the following variables: permeability,
plane strain modulus, spurt loss and leakoff coefficient.
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Table 17. Input Data For MPF01
Proppant mass for (two wings), lbm
90,000
Sp grav of proppant material (water=1)
2.65
Porosity of proppant pack
0.38
Proppant pack permeability, md
60,000
Max propp diameter, Dpmax, inch
0.031
Formation permeability, md
50
Permeable (leakoff) thickness, ft
76
Well Radius, ft
0.25
Well drainage radius, ft
745
Pre-treatment skin factor
0.0
Fracture height, ft
Plane strain modulus, E' (psi)
7.5E+05
Slurry injection rate (two wings, liq+ prop), bpm
20.0
Rheology, K' (lbf/ft2)sn'
0.07
Rheology, n'
0.45
Leakoff coefficient in permeable layer, ft/min1/2
0.01
Spurt loss coefficient, Sp, gal/ft^2
0.02
The line of fracture height is still left empty. We know that the gross pay is 100 ft, that is the distance
between the top and bottom perforations is 100 ft. A reasonable assumption for high permeability fracturing – in the absence of any reliable data on stress contrast – is, that extensive height growth will not
occur as far as the target length is less than half of the height. At this point we put a starting estimate of
hf =100 ft into our design spreadsheet and we specify the following operational constraint/parameters, as
shown in Table 18:
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Table 18. Additional Input For HPF01
Max possible added proppant concentration, lbm/gallon fluid
16
Multiply opt length by factor
1
Multiply pad by factor
1
Table 19. Theoretical optimum for HPF01-1
Optimum placement without constraints
Proppant number, Nprop
0.0121
Dimensionless PI, Jdopt
0.31
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
56.7
Optimal propped width, wopt, inch
0.9
Post treatment pseudo skin factor, sf
-4.05
Folds of increase of PI
2.27
From the first design attempt we see that the proppant number is Nprop = 0.012 . This is a typical situation
for high permeability formations: not even a considerable amount of proppant and well contained fracture
height will produce large proppant numbers. The message says that
Suboptimal placement with constraints satisfied
Mass of proppant reduced
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Table 20. Actual placement without TSO design: HPF01-1
Actual placement
Proppant mass placed (2 wing)
10,702
Proppant number, Nprop
0.0014
Dimensionless PI, JDact
0.21
Dimensionless fracture cond, CfD
0.2
Half length, xf, ft
56.7
Propped width, w, inch
0.11
Post treatment pseudo skin factor, sf
-2.50
Folds of increase of PI
1.53
In fact only 10,700 lbm proppant can be placed into the formation, if the target length is 56.7 ft. Such a
treatment would realize a very low proppant number and an equivalent skin of –2.5, that is usually not
satisfactory, especially because other factors can decrease further the stimulation effect.
The problem is, that the width of the fracture (even though this is a relatively “soft” formation) created
during normal fracture propagation is not enough to accept more proppant. (Note that we have already
increased the maximum possible proppant concentration to 16 ppga, but that is still not enough.)
The solution to the problem is to design a TSO treatment. Knowing that the formation is “soft” and relatively unconsolidated, we intentionally arrest fracture propagation at the target length (56.7 ft) and inflate
the fracture from there on.
For the TSO design we use exactly the same input as previously, the only additional parameter is:
TSO criterion Wdry/Wwet
0.7
The meaning of this parameter is, that we anticipate the fracture to stop propagating if – because of fluid
loss, in other words dehydration – the “dry width” is already near to the “wet width”. The dry width is
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defined as the width of the fracture after all fluid have leaked off, while the wet width is the width during
the treatment when still part of the proppant carrying fluid has not leaked off. We use the critical value
of 0.7, but depending on the actual fracture shape and proppant type the value might vary.
Table 21. Actual placement with TSO design: HPF01-TSO
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.0121
Dimensionless PI, JDact
0.3127
Dimensionless fracture cond, CfD
1.64
Half length, xf, ft
56.7
Propped width, w, inch
0.9282
Post treatment pseudo skin factor, sf
-4.05
Folds of increase of PI
2.27
From the output we see, that with TSO we could place all the proppant into the 57-ft long fracture. This is
achieved by (internally) adjusting the proppant schedule to reach the critical proppant concentration in the
fracture when the lateral extension reaches the target length.
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Table 22. Actual placement with TSO design: HPF01-TSO
Treatment details
Pad pumping time, min
0.41
TSO time, min
7.9
Total pumping time, min
24.8
Mass of proppant in frac at TSO, lbm
11,065
Added proppant concentration at TSO, ca, lbm/gal liq
2.0
Half length at TSO, xf, ft
56.7
Average width at TSO, inch
1.2
Net pressure at TSO, psi
81.1
Max added proppant concentration at end, lbm/gal-liq
16.0
Areal proppant concentration after closure, lbm/ft^2
1.3
Net pressure at end of pumping, psi
482
In fact 11,000 lb proppant is placed into the fracture in a usual manner in less than 8 minutes. After that
18
16
14
12
10
8
6
4
2
0
20
15
10
5
0
0
5
10
15
20
25
30
600
Net pressure, psi
25
ca, lbm prop added to
gallon liquid
Liquid injection rate, bpm
the fracture length remains constant and only the width inflated.
500
400
300
200
100
0
0
5
Pumping time, min
10
15
20
25
30
Pumping time, min
Fig. 3 Fluid, proppant schedule and net pressure forecast for the TSO treatment.
The net pressure is considerable, almost 500 psi at the end of the treatment. This is anticipated, because
the optimum placement calls for an almost 1-inch propped fracture width.
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A.7 Extreme High Permeability: HPF02
In naturally fractured formations several hundred md permeabilities are not uncommon. To investigate
this territory we repeat the design with the same input, except for
Formation permeability, md
500
Table 23. Theoretical optimum for: HPF02
Optimum placement without constraints
Proppant number, Nprop
0.0012
Dimensionless PI, JDopt
0.23
Optimal dimensionless fracture cond, CfDopt
1.6
Optimal half length, xfopt, ft
17.9
Optimal propped width, wopt, inch
2.9
Post treatment pseudo skin factor, sf
-2.90
Folds of increase of PI
1.67
As we see, the target length is now 18 ft. In fact the design program can produce a TSO design for this
case also:
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Table 24. First attempt for HPF02
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.0012
Dimensionless PI, JDact
0.2299
Dimensionless fracture cond, CfD
1.64
Half length, xf, ft
17.9
Propped width, w, inch
2.9351
Post treatment pseudo skin factor, sf
-2.90
Folds of increase of PI
1.67
but the design cannot be accepted, because it would result in an extremely high net pressure, as seen from
Table 25.
Table 25. First attempt for HPF02
Treatment details
Pad pumping time, min
0.06
TSO time, min
1.2
Total pumping time, min
18.6
Mass of proppant in frac at TSO, lbm
2,353
Added proppant concentration at TSO, ca, lbm/gal liq
3.0
Half length at TSO, xf, ft
17.9
Average width at TSO, inch
5.4
Net pressure at TSO, psi
54.5
Max added proppant concentration at end, lbm/gal-liq
16.0
Areal proppant concentration after closure, lbm/ft^2
0.9
Net pressure at end of pumping, psi
2142
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Several parameters have unrealistic values in the results of the first attempt. The extremely short fracture
– even if it could be realized – would not be necessarily useful, because the near wellbore damage might
be still dominating at such distances. A reasonable design would call for longer fracture. From an operational point of view, net pressure limitation is the most important constraint in high permeability fracturing. A maximum allowable net pressure should be specified from safety considerations. A typical value
would be for instance 1000 psi. Therefore we will modify our design in order to satisfy this limitation.
We have several options.
One possibility is to depart from the optimum length, that is multiplying it by a factor. A realistic design
would try to keep the 1:1 aspect ratio, therefore we select
Multiply opt length by factor
3
That would give us a placement
Table 26. HPF02 with modified length
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.0012
Dimensionless PI, JDact
0.2058
Dimensionless fracture cond, CfD
0.18
Half length, xf, ft
53.8
Propped width, w, inch
0.9784
Post treatment pseudo skin factor, sf
-2.39
Folds of increase of PI
1.49
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Treatment details
Pad pumping time, min
0.38
TSO time, min
7.2
Total pumping time, min
24.2
Mass of proppant in frac at TSO, lbm
10,308
Added proppant concentration at TSO, ca, lbm/gal liq
2.1
Half length at TSO, xf, ft
53.8
Average width at TSO, inch
1.3
Net pressure at TSO, psi
79.7
Max added proppant concentration at end, lbm/gal-liq
16.0
Areal proppant concentration after closure, lbm/ft^2
1.3
Net pressure at end of pumping, psi
521
Such a treatment already satisfies the net pressure constraint. The calculated design calls for starting the
addition of proppant almost from the beginning of the treatment. Unfortunately, the design depends
heavily on the selected TSO criterion and on the accuracy of the leakoff description. In reality, it is difficult to predict the TSO with such an accuracy. The art of arresting fracture propagation but still avoiding
a near-wellbore screenout (that would cause us to stop the treatment) often requires the intuition and
experience of the fracturing engineer. The operator company may increase the chance for success by
reducing the risks associated with the treatment. That leads us to another possibility: to reduce the amount
of proppant and multiply the optimum length by a factor, at the same time:
Proppant mass for (two wings), lbm
45,000
Multiply opt length by factor
4
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Table 27. HPF02 with less proppant and modified length
Proppant number, Nprop
0.0006
Actual placement
Proppant mass placed (2 wing)
45,000
Proppant number, Nprop
0.0006
Dimensionless PI, JDact
0.1847
Dimensionless fracture cond, CfD
0.10
Half length, xf, ft
50.7
Propped width, w, inch
0.5189
Post treatment pseudo skin factor, sf
-1.84
Folds of increase of PI
1.34
Treatment details
Pad pumping time, min
0.34
TSO time, min
6.5
Total pumping time, min
14.0
Mass of proppant in frac at TSO, lbm
9,523
Added proppant concentration at TSO, ca, lbm/gal liq
2.1
Half length at TSO, xf, ft
50.7
Average width at TSO, inch
0.6
Net pressure at TSO, psi
78.1
Max added proppant concentration at end, lbm/gal-liq
16.0
Areal proppant concentration after closure, lbm/ft^2
1.2
Net pressure at end of pumping, psi
239
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The important thing to note is, that there is little to lose when we reduce the proppant number from
0.0012 to 0.0006. In this proppant number region the dimensionless productivity index is less sensitive to
the amount of proppant or to the departure from the optimum length, as a matter of fact. Only a moderately negative equivalent skin factor can be realized at such low proppant numbers. This explains the
widely accepted view that in extremely high permeability formations the most important issue is “to get
behind the damage” and create a pack (“halo”) around the screen. The actual fracture length has less
significance. Many high permeability fracturing treatments use only 50,000 lbm or less proppant.
A.8 Low Permeability Fracturing: LPF01
To maintain consistency with our previous examples we consider a low permeability formation with most
of the input parameters similar to our base case:
Table 28. Input for LPF01
Proppant mass for (two wings), lbm
90,000
Sp grav of proppant material (water=1)
2.65
Porosity of proppant pack
0.38
Proppant pack permeability, md
60,000
Max
0.031
rop diameter, Dpmax, inch
Formation permeability, md
0.5
Permeable (leakoff) thickness, ft
76
Well Radius, ft
0.25
Well drainage radius, ft
745
Pre-treatment skin factor
0.0
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Fracture height, ft
Plane strain modulus, E' (psi)
2.00E+06
Slurry injection rate (two wings, liq+ prop), bpm
20.0
Rheology, K' (lbf/ft^2)*s^n'
0.070
Rheology, n'
0.45
Leakoff coefficient in permeable layer, ft/min^0.5
0.0020
Spurt loss coefficient, Sp, gal/ft^2
0.0010
Max possible added proppant concentration, lbm/gal neat fluid
12
Multiply opt length by factor
1
Multiply Nolte pad by factor
1
Again we will start the design by specifying hf = 100 ft.
Table 29. Theoretical optimum assuming 100 ft fracture height: LPF01
Optimum placement without constraints
Proppant number, Nprop
1.2077
Dimensionless PI, JDopt
1.06
Optimal dimensionless fracture cond, CfDopt
2.9
Optimal half length, xfopt, ft
423.0
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-6.30
Folds of increase of PI
7.66
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The proppant number is large, because of the large contrast in permeabilities. At such large proppant
number the indicated fracture half length is already near to the “side length” of the drainage area (this is
why the optimum dimensionless fracture conductivity is significantly more than 1.6).
If such a fracture could be realized, an extremely large dimensionless productivity index would be established. Unfortunately, there is little chance that a fracture with aspect ratio 8:1 could be created without
height increase. It is more likely that an aspect ratio of about 2:1 will be obtained.
Therefore we base our design on the assumption of aspect ratio 2:1. Changing the fracture height to
300 ft, the theoretical optimum values become more realistic, because the decrease of volumetric proppant efficiency reduces the proppant number .
Table 29. Theoretical optimum assuming 300 ft fracture height: LPF01-1
Optimum placement without constraints
Proppant number, Nprop
0.4026
Dimensionless PI, JDopt
0.68
Optimal dimensionless fracture cond, CfDopt
1.8
Optimal half length, xfopt, ft
309.4
Optimal propped width, wopt, inch
0.1
Post treatment pseudo skin factor, sf
-5.78
Folds of increase of PI
4.92
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Table 29. Actual placement assuming 300 ft fracture height but unchanged leakoff coefficient:
LPF01-2
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.4026
Dimensionless PI, JDact
0.68
Dimensionless fracture cond, CfD
1.8
Half length, xf, ft
309.4
Propped width, w, inch
0.06
Post treatment pseudo skin factor, sf
-5.78
Folds of increase of PI
4.92
Treatment details
Efficiency, eta, %
67.1
Pumping time, te, min
52.7
Pad pumping time, te, min
10.4
Exponent of added proppant concentration, eps
0.1966
Uniform proppant concentration in frac at end, lbm/ft^3
22.6
Areal proppant concentration after closure, lbm/ft^2
0.5
Max added proppant concentration, lb per gal clean fluid
3.5
Net pressure at end of pumping, psi
113.7
While the design is now more realistic, one variable deserves special attention. The fluid efficiency
increased to 67 %. Why did this happen? The reason is that, according to our definition, leakoff happens
only in the pay layer (with net thickness 76 ft). Now, that the actual fracture height is taken as 300 ft, only
one quarter of the total surface contributes to leakoff and the efficiency is very high. In reality it is not
likely, that perfectly non-permeable shale is surrounding the pay. Therefore it is wise to reconsider the
leakoff (and spurt loss) parameters once a significant change in fracture height has been introduced.
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Repeating the design with correspondingly adjusted leakoff and spurt loss coefficients:
Leakoff coefficient in permeable layer, ft/min^0.5
0.0050
Spurt loss coefficient, Sp, gal/ft^2
0.00250
we obtain the results in Table 30.
Table 30. Actual placement assuming 300 ft fracture height and adjusted leakoff and spurt loss
coefficients: LPF01-3
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.4026
Dimensionless PI, JDact
0.68
Dimensionless fracture cond, CfD
1.8
Half length, xf, ft
309.4
Propped width, w, inch
0.06
Post treatment pseudo skin factor, sf
-5.78
Folds of increase of PI
4.92
Treatment details
Efficiency, eta, %
38.2
Pumping time, te, min
92.8
Pad pumping time, te, min
41.5
Exponent of added proppant concentration, eps
0.4475
Uniform proppant concentration in frac at end, lbm/ft^3
22.6
Areal proppant concentration after closure, lbm/ft^2
0.5
Max added proppant concentration, lb per gal clean fluid
3.5
Net pressure at end of pumping, psi
113.7
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The fluid efficiency is more realistic now, but the final fracture length and propped width is exactly the
same as previously. How is it possible that such a large change in the leakoff parameters does not affect
the final results? The answer to this question reveals the main difference between simulation and design.
In our design procedure the target length and target propped width are derived from the reservoir and
proppant properties. The leakoff parameters (and other variables) determine how we achieve our final
goal, but the goal is the same, whether there is intensive leakoff or not. The change in the leakoff parameters shows up in the actual proppant schedule. Now we have to pump for a considerably longer time.
Experienced fracturing engineers would probably not accept the design yet. The point is that the indicated
propped fracture width is only 0.06 inch, that is less than 3 grains of the 20/40 mesh proppant. A good
design ensures a certain minimum width (or a certain minimum areal proppant concentration.)
At this point we either increase the amount of proppant or depart from the indicated optimum length, now
multiplying it by a factor less than one. The advantage of creating a shorter fracture shows up also in the
volumetric proppant efficiency: in other words keeping the aspect ratio 2:1 we will have less proppant
“avoiding” the pay. The relevant lines of the input are shown in Table 31.
Table 31. Final design: LPF01-4
Proppant mass for (two wings), lbm
90,000
…
Fracture height, ft
200.0
…
Leakoff coefficient in permeable layer, ft/min^0.5
0.0050
Spurt loss coefficient, Sp, gal/ft^2
0.0025
Max possible added proppant concentration, lbm/gal neat fluid
12
Multiply opt length by factor
0.55
Multiply Nolte pad by factor
1
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Table 32. Actual placement: LPF01-4
Actual placement
Proppant mass placed (2 wing)
90,000
Proppant number, Nprop
0.6039
Dimensionless PI, JDact
0.67
Dimensionless fracture cond, CfD
6.7
Half length, xf, ft
198.3
Propped width, w, inch
0.13
Post treatment pseudo skin factor, sf
-5.76
Folds of increase of PI
4.85
Table 33. Some Details of the Actual placement: LPF01-4
Treatment details
Efficiency, eta, %
38.3
Pumping time, te, min
38.5
Pad pumping time, te, min
17.2
Exponent of added proppant concentration, eps
0.4457
Uniform proppant concentration in frac at end, lbm/ft^3
54.3
Areal proppant concentration after closure, lbm/ft^2
1.1
Max added proppant concentration, lb per gal clean fluid
10.8
Net pressure at end of pumping, psi
166.4
Note that targeting the smaller fracture allowed us to reduce the assumed height as well. Therefore, the
design can utilize more efficiently the 90,000 lbm proppant. The post-treatment dimensionless productivity index and equivalent skin factor are basically the same as in the case of LPF01-3. The final design,
LPF01-4, is more practical and certainly easier to carry out.
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A.9 Summary
In this Appendix we showed some examples of practical fracture design. The concept of proppant number and dimensionless productivity index helped us to make important decisions without going into
unnecessary details. The design spreadsheet was used extensively to consider what-if scenarios and
investigate options. In hydraulic fracture design, where the reliability of the available input data is always
limited and the process itself is inherently stochastic, it is extremely important to proceed in an evolutionary manner, continuously improving the design process. The simple spreadsheet does not substitute the
sophisticated “3D” fracture simulators. Rather, it provides a flexible tool to make the basic decisions
before the final design.
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