Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
Hydraulic Fracture Design
Background: Hydraulic fracturing is a widely applied well stimulation technique used
in the oil and gas industry. It is particularly important for tight reservoirs, which are
reservoirs that have a low permeability (typically less than 1 md). These tight reservoirs
occur in well-cemented sandstones, shales and coalbeds, and are classified as
unconventional oil and gas resources. As much as 95% of these unconventional
resource wells are hydraulically fractured. These wells would be uneconomic without
hydraulic fracturing, and thus the resource could not be exploited otherwise.
Hydraulic fracturing is the process of injecting fluid at high rates into the well until the
pressure exceeds the strength of the rock, such that the rock cracks open. The fracture is
typically a vertical plane that propagates away from the wellbore. Dimensions of interest
are the length, height and width (opening). Lengths can range from 100’s to 1000’s of
feet, height is typically 100’s of feet and the opening is on the order of fractions of an
inch.
(from US DOE, NETL web site)
In the United States, ten’s of thousands of wells are hydraulically fractured each year. As
already mentioned, these are largely tight wells, but there is another special application
which is called the FRACPACK. Frac-pack candidate wells are high permeability wells
in poorly cemented sandstones that have a tendency to produce the formation sand along
with oil and/or gas (this is commonly a problem for high-rate Gulf of Mexico wells).
This produced sand represents a safety hazard because it can act as a sand-blasting agent,
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
cutting through valves and pipes and causing leaks. To prevent formation sand from
entering the wellbore, production engineers will install gravel packs (this process is
called sand control), which are essentially downhole filters that exclude solids from
entering the wellbore. The problem with a gravel pack is that it takes a portion of the
energy available for flow to just get through the filter, so a gravel pack hurts the
production rate of a well. Since hydraulic fractures enhance flow rate, they are often
combined with gravel packs to counter-act the negative effects, and this combination is
what is called a Frac-Pack.
It is incredibly fortunate for us that the stresses in the earth tend toward lower stress in
the reservoir (sandstone) and higher in the boundary layers (shale), such that the
hydraulic fracture preferentially grows in the reservoir. This is important because that is
where we want to enhance the flow rate in order to recover more oil and gas.
Exercise 1 – Hydraulic Fractures and Stress
a) Shmax direction - For reservoirs that have wells that are hydraulically fractured, the
wells are typically spaced farther apart along the hydraulic fracture direction than
perpendicular to it, as shown below. Unfractured wells would be more equally spaced in
both directions. The reason the well arrangement is rectangular for hydraulically
fractured wells is because the drainage pattern is skewed by the presence of the fracture –
there is greater reach and drainage in the direction of the hydraulic fracture than
fracture
well
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
perpendicular to it.
The preferential hydraulic fracture propagation direction is determined by the orientation
of the in situ stress – vertical fractures align with Shmax. A good source for this kind of
data is the World Stress Map Project:
http://www-wsm.physik.uni-karlsruhe.de/pub/stress_data/stress_data_frame.html
i) What is the fracture direction in East Texas?
ii) How about the San Joaquin Basin in Southern California?
b) Pressure required for fracturing In order for a hydrualic fracture to open, the fluid
pressure inside the fracture has to be pushing out harder than the earth’s stress is pushing
to close the fracture. For a vertical fracture, the opening is working against the horizontal
earth stress. We call this the minimum horizontal stress (Shmin, in psi) or the frac gradient
(Shmin/z, in psi/ft). A rule of thumb is that the fracturing pressure is somewhere
between the pore pressure and the vertical stress (lithostatic stress). The exception is in
areas of active thrust faulting, where the vertical stress is the minimum stress, and
hydraulic fractures propagate as horizontal planes instead of vertical planes.
Pfrac
Shmin
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
All stresses in the earth scale with depth. Let’s look at how this works for the vertical
stress. Imagine a column of rock that has an area of 1 m2 and a height of 1 km. What is
the weight of that column? It will depend on density, and 2.3 g/cc is a reasonable
density of saturated rock. Using this value, the weight of our column of rock is:
Weight = Force=F=
Weight is a force, and this entire force is acting downward, due to gravity, on the 1
square meter at the bottom of the column, just like your weight acts on the floor through
the area of the bottom of your shoes. This force divided by area is stress.
Stress= Force/Area=
The taller our column of rock, the more stress we have acting at the base, so a 2 km tall
column would have twice the weight and twice the stress acting at the base. The same is
true for the subsurface – the deeper you go, the greater the column of rock above you,
and the greater the stress. If the density if fairly constant in the earth, we can calculate a
representative stress gradient, or stress per incremental depth. Using the example above,
how much stress should be expect to accumulate per km of depth? Use the units of MPa /
km.
Stress gradient =
MPa/km
You can convert this result from metric to English units by using the conversion factors
of 1 MPa = 145 psi and 1 ft = .3048 m.
Stress gradient =
psi/ft
Under what are called “normal” conditions, the pressure (same conceptually as stress,
pressure = force/area) in the fluid is proportional only to the density of the fluid in the
connected pore space in the rock. So instead of a kilometer tall column of rock, imagine
a kilometer tall column of water. What would be the pressure (stress) at the base of this
column?
Stress =
What would be the normal pore pressure gradient (also know as hydrostatic gradient) in
metric units?
Pore pressure gradient =
Hydraulic Fracturing
MPa/km
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
What would it be in English units?
Pore pressure gradient =
psi/ft
Typical values for the frac gradient range from 0.6 to 0.8 psi/ft. We can directly measure
the frac gradient by increasing the fluid pressure in the well until the formation “breaks
down” or fractures. We are going to analyze a test called a step-rate test to get a
measure of the fracturing stress, and then we will compute the frac gradient. A step-rate
test steps up in injection rate, in equal magnitude steps, held for a constant time interval,
recording pressure throughout the test.
c) Stress Measurement
Look at the Texas Railroad Commission handout to see the recommended procedures for
running a step-rate test for a water injection well. For oil and gas operations, we usually
do a quicker test. The pressure and rate record on the next page is from a test run in the
Hugoton Gas field in Kansas. To analyze this, we need to:
1. Pick the rates for each step.
2. Pick the final (~stabilized) pressure for each step.
3. Plot the pressure vs rate.
4. Find the change in slope of the pressure vs. rate plot, and this pressure is
approximately equal to the fracturing pressure.
Write downt the fracturing pressure you determined from the chart, Psurf, which is a
surface pressure.
Psurf =
psi (surface pressure)
The fracturing is actually not happening at the surface, it is happening at the bottom of
the wellbore. We need to add the extra pressure from the hydrostatic column of fluid in
the wellbore to get the bottomhole pressure to get the proper answer for the fracturing
pressure. The depth of the reservoir is approximately 2800 ft.
Hydrostatic pressure from 2800 ft of brine in wellbore
Phyd = (g) z =
Bottomhole fracturing pressure
Shmin ~ Psurf + Phyd =
Calculate the fracture gradient.
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
Frac gradient = Shmin / depth =
This number should calculate to be less than the vertical stress gradient and more than the
pore pressure gradient for the area in question.
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
Exercise 2 - Proppant Design
Proppant is the material that is left to fill the hydraulic fracture after it is pumped. It is
trapped by the closing fracture, between the 2 sides of the fracture, and is held under
stress proportional to the earth stress (Shmin). It turns out the permeability of the proppant
varies with the stress, partly because higher stress compacts the proppant into closer
packing and partly because higher stress can crush the proppant. Crushing generates
fines, and these plug up the pore throats in the hydraulic fracture.
The engineering aspect of proppant design is determining the closure stress on the
proppant and deciding whether it is worth spending the extra money to pump stronger
proppant. For instance, Brady sand, quarried at the surface near Brady, Texas, costs
approximately $0.10/lb. Bauxite costs about $1.00/lb. So if you can get away with it,
you would prefer to use sand.
To design your proppant, you need to know the closure stress acting on the proppant, and
you need to know how important the proppant permeability is to the performance of your
hydraulic fracture.
a) Stress and Proppant Permeability
Imagine three different reservoirs at different depths. If we know the earth stress, we can
calculate the stress on the proppant, and find the permeability. Fill out the table below
assuming you are using 20/40 proppant size.
Depth, ft
Shmin (assume
0.7 psi/ft
gradient)
Subsurface
Temperature,
F
Brady Sand
Perm, D
Bauxite Perm, D
1000
5000
10000
Mesh sizes for proppant correspond to the diameter of the proppant grains. The higher
the mesh size, the smaller the proppant diameter. A 20/40 mesh size proppant means all
the grains that passed through the 20 mesh and were trapped by the 40 mesh. The mesh
size openings in millimeters are listed below.
Mesh
6
8
12
16
20
30
40
70
Opening 3.35
2.38
1.68
1.20
0.841 0.595 0.422 0.211
(mm)
What do the proppant permeability charts suggest is the relationship between grain size
and permeability?
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Hydraulic Fracturing
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
8
Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Hydraulic Fracturing
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
9
Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
Exercise 3 - Productivity Analysis
Darcy’s Law can be written as the equation below (for single phase oil flow),
q
kh
P
141.2 B PD  s  .
where q is the oil rate in bbl/day, k is formation permeability in md, h is the thickness of
the reservoir in ft, P is the difference between pore pressure and wellbore pressure (flow
is toward the lowest pressure), B is formation value factor for oil (about 1 RB/STB),  is
viscosity in cp, PD is a dimensionless number related to the flow geometry, and s is the
skin factor. Hydraulic fracturing comes into this equation by altering the skin factor,
which is considered part of the well geometry. This improves the production rate
because a hydraulic fracture makes s negative.
To compare well performance before and after a frac job, we can use something else
called the productivity index ratio, J/Jo. For instance, if J/Jo=10, that means the fractured
well would produce at 10 times the rate of the unfractured well. This factor is a function
of the conductivity of the fracture and the length of the fracture. Usually, the longer the
fracture, the better the production, and the fatter the fracture, the better the production.
However, the formation permeability determines whether fat or long is more important.
As an engineer, we want to get the best result for the least cost, which means we want to
get away with the shortest and thinnest fracture we can that will still give us the
production response we want. Plus we want to use the cheapest proppant possible.
a) Fracture Design using the McGuire-Sikora chart
We are going to consider two extreme examples, a South Texas tight gas sandstone and a
Gulf of Mexico high permeability frac-pack candidate. If you look at the McGuireSikora chart, you have basically one calculation to make, which is the relative
conductivity, which compares the flow capacity of the hydraulic fracture (w*kf) to the
flow capacity of the formation (k). The J/Jo on the chart (the y-axis) is calibrated for a
reservoir drainage area (Ad) of 40 acres. We will assume our case is a 40 acre case for
simplicity.
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
i) South Texas tight sandstone (Frio Formation) – Assume the following parameters:
k=0.01 md
w=0.1 inches
depth, z=10,000 ft
Based on your J/Jo results, decide on the most cost-effective fracture design strategy
choosing from the following options:
Proppant – Bauxite or Brady Sand
Fracture length – choose from 0.1 to 1.0 times the reservoir radius
ii) Gulf of Mexico frac-pack
k=100 md
w=1 inches
depth, z=10,000 ft
Based on your J/Jo results, decide on the most cost-effective fracture design strategy
choosing from the following options:
Proppant – Bauxite or Brady Sand
Fracture length – choose from 0.1 to 1.0 times the reservoir radius
Hydraulic Fracturing
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Energy, Climate & Water in the 21st Century
TXESS Revolution Summer Institute
Hydraulic Fracturing
Dr. Jon Olson
Dept. of Petroleum & Geosystems Engineering
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