U.S. patent application number 13/531031 was filed with the patent office on 2012-12-27 for method for determining spacing of hydraulic fractures in a rock formation.
Invention is credited to Nicolas P. Roussel, Mukul M. Sharma.
Application Number | 20120325462 13/531031 |
Document ID | / |
Family ID | 47360733 |
Filed Date | 2012-12-27 |
View All Diagrams
United States Patent
Application |
20120325462 |
Kind Code |
A1 |
Roussel; Nicolas P. ; et
al. |
December 27, 2012 |
Method for Determining Spacing of Hydraulic Fractures in a Rock
Formation
Abstract
Methods of the present disclosure include determining an
expected trajectory of induced fractures in a rock formation,
analyzing net pressure associated with the induced fractures, and
determining at least one of spacing of induced fractures and a
property of the induced fractures based on the net pressure.
Computer-readable medium containing the method are also disclosed.
Other related methods are also disclosed.
Inventors: |
Roussel; Nicolas P.;
(Houston, TX) ; Sharma; Mukul M.; (Austin,
TX) |
Family ID: |
47360733 |
Appl. No.: |
13/531031 |
Filed: |
June 22, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61501003 |
Jun 24, 2011 |
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Current U.S.
Class: |
166/250.1 |
Current CPC
Class: |
G01V 2210/624 20130101;
E21B 43/26 20130101; G01V 1/306 20130101 |
Class at
Publication: |
166/250.1 |
International
Class: |
E21B 49/00 20060101
E21B049/00 |
Goverment Interests
GOVERNMENT LICENSE RIGHTS
[0002] This invention was made with government support under
DE-AC26-07NT42677 awarded by The Department of Energy. The United
States Government has certain rights in the invention.
Claims
1. A method comprising: determining an expected trajectory of
induced fractures; analyzing net pressure associated with the
induced fractures; and determining at least one of spacing of
induced fractures and a property of the induced fractures based on
the net pressure.
2. The method of claim 1, wherein determining an expected
trajectory of induced factures comprises: analyzing stresses prior
to inducing fracturing; modeling a trajectory of a first fracture;
determining effects on the stresses based on the modeled trajectory
of the first fracture; and modeling a trajectory of a subsequent
fracture based on the effects on the stresses caused by the first
fracture.
3. The method of claim 2, further comprising decreasing the spacing
of induced fractures based at least on the modeling of the first
and subsequent fractures.
4. The method of claim 1, further comprising determining a maximum
horizontal stress.
5. The method of claim 1, wherein the property of the induced
fractures includes an expected trajectory of a subsequently induced
fracture.
6. The method of claim 1, wherein the net pressure is determined by
at least one of surface pressures or down-hole pressures during
fracturing.
7. A method of optimizing fracture spacing comprising: propagating
an initial fracture; measuring pressure associated with propagating
the initial fracture; determining a minimum spacing required to
prevent a second fracture from intersecting the initial fracture;
and propagating the second fracture at least the minimum spacing
distance away from the initial fracture.
8. The method of optimizing fracture spacing of claim 7, further
comprising: measuring pressure associated with propagating the
second fracture; determining a second minimum spacing required to
prevent a third fracture from intersecting the second fracture; and
propagating the third fracture at least the second minimum spacing
distance away from the second fracture.
9. The method of optimizing fracture spacing of claim 8, wherein
determining the second minimum spacing is based at least on the
pressure associated with propagating the second fracture.
10. The method of optimizing fracture spacing of claim 7, wherein
the second fracture is propagated at a distance sufficient to allow
a third fracture to be propagated between the first and the second
fractures.
11. The method of optimizing fracture spacing of claim 10, further
comprising: determining spacing required to prevent the third
fracture from intersecting the first and second fractures based at
least on the pressure associated with propagating the first and the
second fractures; and determining a decreased distance between a
fourth and the second fracture based at least on the spacing
required to prevent the third fracture intersecting the first and
second fractures and the pressure associated with propagating the
second fracture.
12. The method of optimizing fracture spacing of claim 7, wherein
determining the minimum spacing comprises: modeling stresses caused
by the first fracture based at least on the pressure associated
with propagating the first fracture; and modeling a trajectory of
the second fracture based on the modeled stresses.
13. The method of optimizing fracture spacing of claim 7, wherein
determining the minimum spacing comprises modeling at least one of
an attraction zone and a repulsion zone associated with the first
fracture based at least on net pressure, in-situ stress contrast,
or average angle of deviation from a trajectory of the first
fracture.
14. The method of optimizing fracture spacing of claim 13, wherein
the minimum spacing is outside of the attraction zone associated
with the first fracture.
15. The method of optimizing fracture spacing of claim 13, wherein
determining the minimum spacing further comprises modeling a stress
reversal region.
16. A method of optimizing fracture spacing comprising: analyzing
stresses associated with a first set of at least one fractures
associated with a first well; analyzing stresses associated with a
second set of at least one fractures associated with a second well;
and determining spacing of a fracture associated with a third well
such that the fracture associated with the third well does not
intersect with the first set and the second set of fractures, the
third well running between the first and second wells.
17. The method of optimizing fracture spacing of claim 16, wherein
determining spacing of the fracture associated with the third well
comprises: modeling the stresses associated with the first and the
second set of fractures; modeling a trajectory of the fracture
associated with the third well.
18. The method of optimizing fracture spacing of claim 16, wherein
analyzing stresses associated with the first set of at least one
fractures is based at least on net pressure of propagating the
first set of at least one fractures.
19. The method of optimizing fracture spacing of claim 16, wherein
the first set and the second set of fractures comprise at least two
fractures and are spaced such that the fracture associated with the
third well is substantially between a first and a second fracture
of the first set of fractures and between a first and a second
fracture of the second set of fractures.
20. The method of optimizing fracture spacing of claim 19, further
comprising determining a decreased distance between a third and the
second fracture of the first set of fractures and a third and the
second fracture of the second set of fractures based at least on
the spacing required to prevent the fracture associated with the
third well from intersecting the first and the second set of
fractures, the distance determined such that a second fracture
associated with the third well may be propagated between the second
and the third fractures of the first set of fractures and the
second and the third fractures of the second set of fractures
without intersecting the first or the second set of fractures.
21. A method of determining maximum horizontal pressure comprising:
measuring an actual pressure during each stage of fracturing of a
rock formation; determining a theoretical expected pressure during
each stage of fracturing of the rock formation; determining a
maximum horizontal pressure of the rock formation based at least on
a comparison of the theoretical expected pressure and the measured
actual pressure.
Description
RELATED APPLICATION
[0001] This application claims benefit under 35 U.S.C. .sctn.119(e)
of U.S. Provisional Application Ser. No. 61/501,003, entitled
"METHOD FOR DETERMINING SPACING OF HYDRAULIC FRACTURES IN A ROCK
FORMATION," filed Jun. 24, 2011, the entire content of which is
incorporated herein by reference.
TECHNICAL FIELD
[0003] The present disclosure relates in general to well drilling
and, more particularly, to a method for determining spacing of
hydraulic fractures in a rock formation.
BACKGROUND
[0004] Hydrocarbon (e.g., oil, natural gas, etc.) reservoirs may be
found in geologic formations that have little to no porosity (e.g.,
shale, sandstone etc.). The hydrocarbons may be trapped within
fractures and pore spaces of the formation. Additionally, the
hydrocarbons may be adsorbed onto organic material of the shale
formation. The rapid development of extracting hydrocarbons from
these unconventional reservoirs can be tied to the combination of
horizontal drilling and hydraulic fracturing ("fracing") of the
formations. Horizontal drilling has allowed for drilling along and
within hydrocarbon reservoirs of a formation to better capture the
hydrocarbons trapped within the reservoirs. Additionally, more
hydrocarbons may be captured by increasing the number of fractures
in the formation and/or increasing the size of already present
fractures through fracing. The spacing between fractures as well as
the ability to stimulate the fractures naturally present in the
rock may be major factors in the success of horizontal completions
in unconventional hydrocarbon reservoirs.
SUMMARY
[0005] In one embodiment, a method is disclosed comprising
determining an expected trajectory of induced fractures, analyzing
net pressure associated with the induced fractures, and determining
at least one of spacing of induced fractures and a property of the
induced fractures based on the net pressure. Computer-readable
medium containing the same are also disclosed.
[0006] In an alternative embodiment, a method of optimizing
fracture spacing is disclosed. The method includes propagating an
initial fracture, measuring pressure associated with propagating
the initial fracture, determining a minimum spacing required to
prevent a second fracture from intersecting the initial fracture,
and propagating the second fracture at least the minimum spacing
distance away from the initial fracture.
[0007] In other embodiments, also disclosed is a method of
optimizing fracture spacing. The method includes analyzing stresses
associated with a first set of at least one fractures associated
with a first well, analyzing stresses associated with a second set
of at least one fractures associated with a second well, and
determining spacing of a fracture associated with a third well such
that the fracture associated with the third well does not intersect
with the first set and the second set of fractures, the third well
running between the first and second wells.
[0008] In still other embodiments, also disclosed is a method of
determining maximum horizontal pressure. The method includes
measuring an actual pressure during each stage of fracturing of a
rock formation, determining a theoretical expected pressure during
each stage of fracturing of the rock formation, and determining a
maximum horizontal pressure of the rock formation based at least on
a comparison of the theoretical expected pressure and the measured
actual pressure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 illustrates an example schematic of a gas well
configured to extract natural gas from a gas rich shale formation,
according to some embodiments of the present disclosure;
[0010] FIGS. 2a and 2b illustrate examples of the reorientation of
stresses in a rock formation due to the placement of a fracture
orthogonal to a horizontal well according to some embodiments of
the present disclosure;
[0011] FIG. 3 illustrates the geometry of a single transverse
fracture of a shale formation that includes a pay zone that may
include hydrocarbons (e.g., natural gas) and bounding layers that
may bound the pay zone, according to some embodiments of the
present disclosure;
[0012] FIG. 4 illustrates a three dimensional model of multiple
transverse fractures in a layered rock formation according to some
embodiments of the present disclosure;
[0013] FIG. 5 illustrates the calculated propagation of a
subsequent fracture (n+1) based on the mechanical stress
interference of a previous fracture (n), according to some
embodiments of the present disclosure;
[0014] FIG. 6 illustrates the results of calculating fracture
propagation with each fracture spaced approximately 400 feet apart,
according to some embodiments of the present disclosure;
[0015] FIG. 7 illustrates the results of calculating fracture
propagation with each fracture spaced approximately 300 feet apart,
according to some embodiments of the present disclosure;
[0016] FIG. 8 illustrates the stress distribution of a rock
formation with the stress distribution being influenced by the
propagation of a fracture produced during a fourth stage of a
fracture treatment, according to some embodiments of the present
disclosure;
[0017] FIG. 9 illustrates fracture propagation with the fracture
spacing reduced to 250 ft., according to some embodiments of the
present disclosure;
[0018] FIG. 10 illustrates the stress distribution of a rock
formation caused by fractures of FIG. 9, according to some
embodiments of the present disclosure;
[0019] FIG. 11 illustrates fracture propagation with the fracture
spacing reduced to 200 ft., according to some embodiments of the
present disclosure;
[0020] FIG. 12 illustrates fracture propagation with the fracture
spacing reduced to 150 ft., according to some embodiments of the
present disclosure;
[0021] FIGS. 13a and 13b illustrate the impact of fracture spacing
on the angle of deviation of the fractures from the orthogonal
path, according to some embodiments of the present disclosure;
[0022] FIG. 14 illustrates the impact of fracture spacing on the
evolution of the net closure stress, according to some embodiments
of the present disclosure;
[0023] FIGS. 15a and 15b illustrate the horizontal stress of a rock
formation with a stress reversal region associated with a fracture,
according to some embodiments of the present disclosure;
[0024] FIGS. 16a and 16b illustrate the differences between
performing consecutive fracturing and alternate fracturing,
according to some embodiments of the present disclosure;
[0025] FIGS. 17a and 17b illustrate the stress orientation of a
rock formation with stress reversal regions associated with a first
fracture and a second fracture, according to some embodiments of
the present disclosure;
[0026] FIG. 18 shows a spacing of fractures for which the stress
contrast may be lowest, according to some embodiments of the
present disclosure;
[0027] FIG. 19 illustrates that the deviatoric stress may approach
zero in a near wellbore region in the case of optimum spacing in an
alternate fracturing sequence, according to some embodiments of the
present disclosure;
[0028] FIG. 20 illustrates an example of fracture spacing that may
be done with multiple horizontal lateral wells, according to some
embodiments of the present disclosure;
[0029] FIGS. 21a and 21b illustrate the stress distribution between
two pairs of fractures propagated from outside lateral wells,
according to some embodiments of the present disclosure;
[0030] FIG. 22 illustrates the relationship between the length of a
"middle fracture" propagating from a center lateral well for
different values of the fracture length with respect to the
inter-well spacing, according to some embodiments of the present
disclosure; and
[0031] FIG. 23 illustrates the local stress contrast that may be
recorded along the assumed propagation direction of a middle
fracture, according to some embodiments of the present
disclosure.
DETAILED DESCRIPTION
[0032] FIG. 1 illustrates an example schematic of a gas well 100
configured to extract natural gas from a gas rich shale formation
102. Well 100 may be drilled using horizontal drilling methods to
create a wellbore 104 that runs within and along shale formation
102. In the present example, wellbore 104 may be drilled such that
wellbore 104 runs perpendicular to the maximum horizontal in-situ
stresses of shale formation 102 to obtain better production of well
100.
[0033] Shale formation 102 may produce natural gas that is trapped
in fractures and pore spaces of shale formation 102. The natural
gas may also be adsorbed in organic material included in the shale
of shale formation 102. As well bore 104 runs through shale
formation 102, well bore 104 may also run through fractures (not
expressly shown) of shale formation 102. The gas in the fractures
may enter well bore 104 and may accordingly be retrieved at a
drilling rig 106 of well 100. As gas leaves the fractures of shale
formation 102, the gas adsorbed on the organic material may be
released into the fractures such that the adsorbed gas may also be
retrieved. As the number of fractures of shale formation 102 that
well bore 104 passes through increases, the amount of gas that may
be produced by well 100 may also increase. Therefore, increasing
the number of fractures in shale formation 102 along well bore 104
may increase the gas production of well 100.
[0034] The number and/or size of fractures in shale formation 102
may be increased using hydraulic fracturing ("fracing"). Fracing
may refer to any process used to initiate and propagate a fracture
in a rock formation. Additionally fracing may be used to increase
existing fractures in a rock formation. Fracing may include forcing
a hydraulic fluid in a fracture of a rock formation to increase the
size of the fracture and introducing proppant (e.g., sand) in the
newly induced fracture to keep the fracture open. The fracture may
be an existing fracture in the formation, or may be initiated using
a variety of techniques known in the art. The amount of pressure
needed to extend and propagate the fracture may be referred to as
the "fracturing pressure."
[0035] As shown in further detail with respect to FIGS. 2a and 2b,
producing fractures during fracing may change the stress properties
of a rock formation. Accordingly, subsequent transverse fractures
initiated from a horizontal well may deviate toward or away from
the previous fracture depending on the stress reorientation caused
by the fracing. The stress reorientation may be a function of
mechanical properties of the reservoir rock, fracture spacing, and
the orientation of the previous fracture. As described in further
detail below, in some instances spacing frac treatments too close
together may result in a subsequent fracture intersecting with a
previous fracture. Therefore, in such instances, the contribution
of the subsequent fracture in hydrocarbon production may be reduced
or minimized.
[0036] As disclosed in further detail below, the spacing of
performing fracturing operations for a hydrocarbon well, such as
gas well 100, may be determined using net pressure measurements to
determine a minimum frac spacing that also reduces the likelihood
of subsequent fractures intersecting and interfering with previous
fractures. In some instances, net pressure may be determined by
surface pressures or down-hole pressures during fracturing.
Therefore, the selection of fracture spacing may be such that the
number of fractures initiated from a horizontal wellbore may be
increased while also reducing the likelihood that the fractures may
interfere and/or intersect with each other to allow for better
production rates and depletion of hydrocarbons with each induced
fracture. Therefore, the economic efficiency of fracturing may be
improved and the cost of retrieving hydrocarbons from tight rock
formations (e.g., shale formation 102) may be reduced.
[0037] Modifications, additions or omissions may be made to FIG. 1
without departing from the present disclosure. For example,
although FIG. 1 is described as performing fracing with respect to
a shale gas formation, the present disclosure may be used to
improve frac spacing for any suitable formation (e.g., a tight sand
formation, coalbed methane, sandstone, limestone, oil shale).
Additionally, although well 100 is described as being used to
extract natural gas, it is understood that the principles described
herein may be used to extract any other suitable hydrocarbon.
[0038] FIGS. 2a and 2b illustrate examples of the reorientation of
stresses in a rock formation due to the placement of a fracture
orthogonal (or transverse) to a horizontal well according to some
embodiments of the present disclosure. The opening of a propped
transverse fracture in horizontal wells through hydraulic
fracturing may cause a reorientation of stresses in the rock
formation surrounding the fracture.
[0039] FIG. 2a may represent the stress of the rock formation in a
horizontal plane (e.g., a plane substantially parallel to the
ground. Accordingly, the vertical axis of FIG. 2a may represent the
distance in the x direction from the center of a substantially
horizontal wellbore 204. The horizontal axis of FIG. 2a may
represent the distance in the y direction from the center of a
fracture 202 opened using a fracturing technique. Fracture 202 in
FIG. 2a may follow the vertical axis in FIG. 2a, such that fracture
202 may be substantially transverse to horizontal wellbore 204. In
the present example, fracture 202 may extend approximately 500 feet
from the center of wellbore 204. FIG. 2a illustrates that the
direction of stress on the rock formation in the area surrounding
the fracture is substantially orthogonal to the fracture and also
orthogonal to the in-situ direction of maximum horizontal stress of
the rock formation. The reversal of stress orientation in the area
surrounding the fracture may be due to the pressures exerted on the
formation from fracturing. This area where the stress orientation
is reversed may be referred to as a stress reversal region as shown
by stress reversal region 206 of FIG. 2.
[0040] The degree of reorientation of the stress with respect to
the in-situ direction of the maximum horizontal stress may be
expressed as an angle from the in-situ direction of stress. FIG. 2b
illustrates the stress reorientation with respect to the maximum
horizontal stress as caused by creating fracture 202 of FIG. 2a.
For example, in stress reversal region 206 of FIG. 2a, the
orientation of the stress may be substantially orthogonal to the
orientation of the in-situ stress such that stress reversal region
206 may be referred to as having a 90.degree. stress reorientation.
The point where the stress reversal region ends may be referred to
as an isotropic point, which may be seen at approximately 140 feet
from the center of the fracture along the horizontal axis as shown
in FIGS. 2a and 2b. The distance between fracture 202 and the
isotropic point is depicted as s.sub.90.degree. in FIG. 2b.
[0041] Outside of the stress reversal region, the stresses may
still be at an orientation that is not parallel with the maximum
horizontal stress of the rock formation. For example, the direction
of maximum horizontal stress in FIG. 2a just outside of stress
reversal region 206 progressively moves from being parallel with
the horizontal axis to being parallel with the vertical axis.
Additionally, it can be seen in FIG. 2b that the orientation angle
of the stress adjacent to fracture 204 progressively moves from
90.degree. to 0.degree.. For example, as shown in FIG. 2b, in the
present example, at approximately 320 feet from fracture 202 in the
positive y-direction and at approximately 300 feet from wellbore
204 in the positive x-direction the rock formation may have a
stress reorientation of 10.degree. as shown by s.sub.10.degree..
Similarly, in the present example, the stress reorientation of rock
formation 200 may be 5.degree. at approximately 450 feet from
fracture 202 in the positive x-direction and at approximately 400
feet from wellbore 204 in the positive y-direction as shown by
s.sub.5.degree..
[0042] The reorientation of stresses may in turn affect the
direction of propagation of subsequent fractures. For example,
performing fracturing within the stress reversal region of fracture
202 of FIGS. 2a and 2b may result in the subsequent fracture
propagating parallel to wellbore 204 (longitudinal fracture). In
such instances, this phenomenon, often referred to as stress
shadowing, may negatively impact the efficiency of the frac stage.
As an additional example, performing fracturing around
s.sub.10.degree.. may cause the subsequent fracture to deviate from
a path substantially orthogonal to wellbore 204 by approximately
10.degree.. Therefore, as described in further detail below, by
mapping the angle of stress reorientation and the horizontal stress
in multiple fractured horizontal wells, the trajectory of each
fracture may be estimated. By mapping the trajectory of each
induced fracture, the induced fracture spacing may be determined
such that it may be minimized without compromising the efficiency
of each frac stage.
[0043] FIG. 3 illustrates the geometry of a single transverse
fracture 302 of a shale formation 300 that includes a pay zone 304
that may include hydrocarbons (e.g., natural gas) and bounding
layers 306a and 306b that may bound pay zone 304, according to some
embodiments of the present disclosure. Fracture 300 may be modeled
based on a variety of properties that may be expressed
mathematically. The modeling may be performed by various computer
programs, models or combination thereof, configured to simulate and
design fracturing operations. The programs and models may include
instructions stored on a computer readable medium that are operable
to perform, when executed, one or more of the steps described
below. The computer readable media may include any system,
apparatus or device configured to store and retrieve programs or
instructions such as a hard disk drive, a compact disc, flash
memory or any other suitable device. The programs and models may be
configured to direct a processor or other suitable unit to retrieve
and execute the instructions from the computer readable media. The
following nomenclature may be used for modeling fracture 302 to
describe various properties of fracture 302: [0044] E.sub.p=Young's
modulus of the pay zone, Pa (psi) E.sub.b=Young's modulus of the
bounding layers, Pa (psi) v.sub.p=Poisson's ratio in the pay zone
v.sub.b=Poisson's ratio in the bounding layers K=dry bulk modulus,
Pa (psi) G=shear modulus, Pa (psi) L.sub.f=fracture half-length, m
(ft) h.sub.f=fracture half-height, m (ft) h.sub.p=pay zone
half-thickness, m (ft) w.sub.0=maximum fracture width, m (ft)
.sigma..sub.v=vertical in-situ stress, Pa (psi)
.sigma..sub.hmax=maximum horizontal in-situ stress, Pa (psi)
.sigma..sub.hmin=minimum horizontal in-situ stress, Pa (psi)
[0045] The bounding layers 306a and 306b may have mechanical
properties (E.sub.b, v.sub.b) differing from the mechanical
properties of pay zone 304 (E.sub.p, v.sub.p). In the present
example, fracture 302 may be modeled using a numerical model and
may have a length in the direction of the x-axis that is equal to
2L.sub.f, may have a height in the z-direction that is equal to
2h.sub.f and may also have width in the y-direction that is not
shown.
[0046] The mechanical behavior of the continuous three-dimensional
medium of shale formation 300 may be described mathematically by
the equations of equilibrium Eq. (1), the definition of strain Eq.
(2) and the constitutive equations Eq. (3). The algebraic system of
15 equations for 15 unknowns (6 components of stress .sigma. and
strain .epsilon., plus the 3 components of the velocity vector v)
may be solved at each node using an explicit, finite difference
numerical scheme. The Einstein summation convention may apply to
indices i, j and k, which take the values 1, 2, 3:
.sigma. ij , j = .rho. v i t ( 1 ) ij t = v i , j + v j , i 2 ( 2 )
##EQU00001##
[0047] Pay zone 304 may be homogeneous, isotropic, and purely
elastic. Hooke's law relates the components of the strain and
stress tensors (constitutive equation):
.sigma. ij 2 G ij + ( K - 2 3 G ) kk .delta. ij ( 3 )
##EQU00002##
[0048] Where,
K = 3 2 ( 1 - 2 v ) ##EQU00003##
and
G = E 2 ( 1 + v ) ##EQU00004##
[0049] The impacts of poroelastic effects on the stress
reorientation around a producing transverse fracture may be ignored
in the present example because of the very low permeability of
shale and the small amount of fluid leak-off during fracturing.
However, in other models of other rock formations, the poroelastic
effects may be determined and included.
[0050] Shale formation 300 and fracture 302 may also be modeled
using a variety of boundary conditions. Displacement along the
faces of fracture 302 may be allowed where a constant stress, equal
to the net pressure, p.sub.net, plus the minimum in-situ horizontal
stress .sigma..sub.hmin, is imposed on the faces of fracture 302 to
create fracture 302, or in the present example, to simulate and
model the creation of fracture 302. Therefore, the size (e.g.,
width, length, height) of fracture 302 may partially be a function
of p.sub.net.
[0051] At the end of the fracturing process, fracture 302 may close
down on proppant (e.g., sand), which keeps fracture 302 open. The
width of the propped-open fracture may depend on the fractured
length and the amount of proppant pumped during the fracturing
process. The uniform stress boundary condition applied on the
fracture face is approximately equal to the pressure required for
the proppant to maintain an opening of maximum width w.sub.0. This
pressure value may be smaller than the pressure required to
propagate a hydraulic fracture in the same rock. To simulate a
large enough reservoir volume and avoid boundary effects, the
far-field boundaries may be placed at a distance from the fracture
equal to at least three times the fracture half-length L.sub.f. A
constant stress boundary condition normal to the "block" faces is
applied at outside boundaries. In-situ stresses are initialized
prior to the opening of the fracture:
{ .sigma. xx = - .sigma. h max .sigma. yy = - .sigma. h min .sigma.
zz = - .sigma. V ( 4 ) ##EQU00005##
[0052] Following modeling of the first fracture, subsequent
fractures may also be modeled. After the first fracture is created,
its geometry may be represented as being fixed (e.g., no further
displacement is allowed). In the present example, it may be assumed
that the compression of the proppant placed inside the previous
fractures is negligible as subsequent fractures are opened.
Subsequent transverse fractures may be modeled using boundary
conditions similar to the first fracture as described above. FIG. 4
illustrates a three dimensional model of multiple transverse
fractures in a layered rock formation (e.g., shale formation 300
with pay zone 304 and boundary zones 306 of FIG. 3).
[0053] The net pressure required to achieve a specified fracture
width may increase with each additional fracture. An iterative
process may be programmed in order to determine for each fracture,
the net pressure corresponding to a given maximum fracture width
w.sub.0. The evolution of the net closure stress in the sequential
fracturing of a horizontal well is described further below.
[0054] Traditional fracture modeling methods may model fractures
perfectly orthogonal to the horizontal wells. However, in order to
better quantify the evolution of the direction of propagation of
consecutive transverse fractures, it may be advantageous to model
subsequent fractures as deviating from the orthogonal path due to
the stress reorientation that may be caused by previous
fractures.
[0055] Model simplifications may be made in order to tackle this
problem. As opposed to perfectly orthogonal fractures, multiple
inclined fractures are challenging to model on a single numerical
mesh. In a finite difference model, the geometry of all fractures
may be set from the beginning, which may be very difficult, as the
angle of propagation of the subsequent transverse fracture may
depend on the mechanical stress perturbation generated by the
previous fractures. This may require a complex and time consuming
re-meshing after every single fracture stage.
[0056] Accordingly, for a more a simplified approach, in the
present example, the net closure stress and the propagation
direction may be calculated based on the mechanical stress
interference of only the previous fracture. FIG. 5 illustrates the
calculated propagation of a subsequent fracture (n+1) based on the
mechanical stress interference of a previous fracture (n). For each
subsequent fracture (e.g., fracture (n+1)), the stress created by
the previous propped fracture (e.g., fracture (n)) in the direction
perpendicular to it is computed at some distance from the fracture.
The net closure stress in the subsequent fracture is equal to the
net closure stress of a single transverse fracture (without stress
shadow) plus the stresses generated by the previous fracture as
shown by Eq. (5) below:
p.sub.net.sup.n+1+p.sub.net.sup.1+.DELTA..sigma..sub.yy.sup.n(s.sub.f)
(5)
[0057] Based on the stress distribution around a transverse
fracture, the trajectory of the subsequent fracture may be
approximated by assuming that it will follow the direction of
maximum horizontal stress. This may be done by determining the
direction of the maximum horizontal stress at one point and having
the fracture propagate in that direction. Then, the direction of
the maximum horizontal stress may be calculated at another point
along the trajectory of the propagation from the previous point and
so on to approximate a trajectory for the subsequent fracture as
shown for fracture (n+1) of FIG. 5.
[0058] A determined average angle of deviation may be seen in
fracture (n) of FIG. 5. The average angle of deviation may be
calculated for fracture (n+1) (e.g., .theta..sub.f(s.sub.f)) from
the coordinates of the final position of fracture (n+1). It may be
used to model fracture (n+1) in order to calculate the net pressure
and trajectory of the subsequent fracture (n+2).
[0059] As mentioned above, the propagation direction of subsequent
fractures may be a function of the location of the subsequent
fracture with respect to areas of the rock formation that have
experienced stress reorientation caused by propagating previous
fractures. Accordingly, the spacing between a previous fracture and
a subsequent fracture may influence the propagation direction of
the subsequent fracture. FIGS. 6, 7, 9, 11 and 12 described further
below illustrate examples of the trajectory of multiple fractures
according to various spacing distances between the fractures. The
fractures in FIGS. 6, 7, 9, 11 and 12 may be determined using the
process described above with respect to FIGS. 3 through 5 and may
be done by any suitable computer program. In FIGS. 6, 7, 9, 11 and
12, the fractures depicted may be induced in separate consecutive
stages. For example, fracture 1 of FIGS. 6, 7, 9, 11 and 12 may be
induced first, fracture 2 may be induced second, etc. As described
further below, the results of the different simulations with
respect to different spacing distances between fractures may be
used to determine optimum fracture spacing for a particular well
and/or formation. TABLE 1 below illustrates the parameters of the
rock formation used in the examples of FIGS. 6-23 as taken from a
shale gas well in the Barnett shale in Texas.
TABLE-US-00001 TABLE 1 Reservoir parameters for Barnett shale gas
well Barnett shale gas Pay zone Young's Modulus E.sub.p (psi) 7.3
.times. 10.sup.6 Bounding layer Young's Modulus E.sub.b (psi) 3.0
.times. 10.sup.6 Poisson's Ratio .nu..sub.p = .nu..sub.b 0.2
.sigma..sub.hmax (psi) 6400 .sigma..sub.hmin (psi) 6300 Depth (ft)
7000 Pay zone half-thickness h.sub.p (ft) 150 Fracture half-height
h.sub.f (ft) 150 Fracture half-length L.sub.f (ft) 500 Fracture
maximum width w.sub.0 (mm) 4
[0060] FIG. 6 illustrates the results of calculating fracture
propagation with each fracture spaced approximately 400 feet apart.
For a 400-ft. spacing, transverse fractures may propagate away from
the previous fracture with a small angle of deviation from the
orthogonal path (less than 2.degree.), as expected from the angle
of stress reorientation profile shown in FIG. 1 (simulated using
the same parameters). When the spacing is reduced to 300 ft. (as
shown in FIG. 7), the average angle of deviation from the
orthogonal path increases to a little over 5.degree. (e.g., after
stage 4, the average angle of deviation converges toward a value
.theta..sub.f=5.7.degree.). A closer look at the fracture
trajectory shows that after fracture 5, the fracture may initially
propagate toward the previous fracture and then at some distance
from the wellbore, the fracture may start propagating away from the
previous fracture. Plotting the stress distribution around an
oblique fracture reveals the explanation behind this non-trivial
trend as shown in FIG. 8.
[0061] FIG. 8 illustrates the stress distribution of a rock
formation 800 with the stress distribution being influenced by the
propagation of fracture 4 of FIG. 7. From the stress redistribution
caused by fracture 4 it may be possible to draw a stress reversal
zone 804, a zone where the subsequent fracture (e.g., a fracture 5
of FIG. 7) may be attracted by the previous fracture (e.g., an
attraction zone 806), and another zone where the subsequent
fracture may propagate away from the previous fracture (e.g., a
repulsion zone 808). In some cases, subsequent transverse fractures
may propagate in both zones as shown by fracture 5. The size of
attraction zone 806 may be function of the net pressure, the
in-situ stress contrast and the average angle of deviation from the
orthogonal path of fracture 4. In the present example, for fracture
spacings lower than 400 ft., the initiation point of fracture 5 may
be located within attraction zone 806 caused by the propagation of
fracture 4, thus fracture 5 may initially propagate back toward
fracture 4 until it leaves attraction zone 806.
[0062] FIG. 9 illustrates fracture propagation with the fracture
spacing reduced to 250 ft. in accordance with the present example.
Because of the closer spacing, the amount of fracture deviation is
larger. For instance, fractures 2, 5 and 8 may propagate away from
the previous fracture at an angle .theta..sub.f>5.degree.. But
what mostly stands out is the fact that under a critical value of
the fracture spacing, the attraction zone associated with fractures
2, 5 and 8 may cause fractures 3, 6, and 9, respectively, to
intersect fractures 2, 5 and 8 respectively. The practical
consequence of such intersections may be much less efficient
drainage of the reservoir, even if the fractures are initiated
closer to each other.
[0063] Additionally, it may be noted that to calculate the
trajectory of fractures 4, 7 and 10, a two-fracture system may be
simulated to calculate the stress distribution of the rock
formation. For example, because the fracture 3 may intersect with
fracture 2, the stress distribution that may affect the fracture 4
may be modeled based on both the fractures 2 and 3. The stress
distribution around the fracture system with respect to the
fractures 2 and 3 is shown in FIG. 10.
[0064] FIGS. 11 and 12 also illustrate fracture propagation as
calculated for a 200-ft. and a 150-ft. spacing respectively of the
present example simulation. In those examples, the "unsuccessful"
fractures (e.g., fractures 3, 5, 7 and 10 of FIG. 11 and fractures
2, 4, 6, 8 and 10 of FIG. 12) may not only intersect the previous
fracture but may propagate longitudinally to the horizontal well
such that increased hydrocarbon production may not be realized
through the inducement of these fractures. For such small values of
the fracture spacing, the unsuccessful fractures may be caused by
initiating the fractures within the stress reversal region of the
previous fracture, which is located inside the attraction zone
associated with the previous fracture (e.g., attraction zone 806 of
FIG. 8). In the present example (150-ft. spacing), only every other
fracturing stage effectively stimulates the shale, thus possibly
leaving significant portions of the reservoir inadequately
drained.
[0065] FIGS. 13a and 13b illustrate the impact of fracture spacing
on the angle of deviation of the fractures from the orthogonal
path. Below a critical value of the fracture spacing, the
efficiency of fracturing stages may be negatively affected as shown
by the large variations in deviation angles with respect to
spacings 250, 200 and 150 feet apart. Accordingly, the gain in
reservoir drainage at these spacings may be marginal compared to
the additional cost represented by an increased number of fracture
stages. This result suggests that because of mechanical stress
interference, spacing transverse fractures ever closer to each
other may not be a desirable completion strategy.
[0066] FIG. 14 illustrates the impact of fracture spacing on the
evolution of the net closure stress. As shown in FIG. 14, for
fracture spacings of 400 ft. and 300 ft., the net closure stress
only increases with each new stage until reaching a plateau.
However for the 250, 200 and 150 ft. fracture spacings, the net
pressure may have an up and down trend.
[0067] Counting the number of times the net fracturing pressure
decreases from one stage to another, may indicate the number of
unsuccessful fracture stages identified in FIGS. 10, 12, 13a and
13b. The decrease in the fracture closure stress (from one stage to
another) may be a consequence of the smaller mechanical stress
interference (stress shadow) generated by the previous fracture
when propagating into stimulated regions of the reservoir instead
of orthogonal to the well.
[0068] Therefore, as an example, in the case of the smallest
spacing, while the designed value is 150 ft., the effective spacing
may only equal to 300 ft., as every other fracture may be
longitudinal with respect to the wellbore. Accordingly, doubling
the number of stages for 150 ft. spacing compared to the 300 ft.
spacing may grant very little improvement in well production.
[0069] Thus, as shown above, modeling deviation from the orthogonal
path for fractures may reveal a new up-and-down trend in the
evolution of the net closure stress. This up and down trend may
indicate that the spacing between fractures may be too close to
generate any improvement in well production. Therefore, the net
closure stress at various spacings may be analyzed to determine the
closest spacing that may not yield an up and down net pressure such
that optimal spacing of fractures may be determined. Additionally,
to determine the proper net closure stress, the propagation
direction of each fracture may be estimated instead of assuming
that the propagation direction is orthogonal to the well as is
traditionally done.
[0070] Fracture spacing may also be determined by analyzing the
stress reversal region associated with a previous fracture and by
initiating the subsequent fracture outside of the stress reversal
region. For example, FIGS. 15a and 15b illustrate the horizontal
stress of a rock formation 1500 with a stress reversal region 1502
associated with a fracture (n+1). Fracture (n+1) may run along the
vertical axis of FIGS. 15a and 15b and a wellbore 1504 may run
along the horizontal axis. As shown in FIGS. 15a and 15b, stress
reversal region 1502 may extend approximately 230 ft. from fracture
1502 along wellbore 1504 as shown by isotropic point
s.sub.90.degree.. Accordingly a subsequent fracture (e.g., a
fracture (n+2)) may not be initiated closer than 230 ft. from
fracture (n+1) because, as mentioned above, the subsequent fracture
may propagate parallel with wellbore 1504 and may not increase
hydrocarbon production from wellbore 1504.
[0071] Further, FIG. 15b illustrates that in the present example at
point s.sub.10.degree., (e.g., approximately 430 ft. from fracture
(n+1)) the stress reorientation of rock formation 1500 may be
10.degree. and at point s.sub.5.degree. (e.g., 600 ft. from
fracture (n+1)) the stress reorientation of rock formation 1500 may
be 5.degree.. The stress reorientations of 10.degree. and 5.degree.
may be such that a subsequent fracture (e.g., a fracture (n+2))
initiated between points s.sub.10.degree. and s.sub.5.degree. may
not intersect fracture (n+1) although the subsequent fracture may
deviate somewhat from an orthogonal path due to the stress
reorientation.
[0072] The above example illustrates how analyzing the size of the
stress reversal region may be used to determine the spacing of
fractures when the fractures are initiated consecutively, however,
the spacing of fractures initiated alternately may also be
determined by analyzing the stress reversal region associated with
fractures. FIGS. 16a and 16b illustrate the differences between
performing consecutive fracturing and alternate fracturing. In FIG.
16a it can be seen that each fracture starting with fracture "1"
may be initiated one after another in a consecutive order. However,
in FIG. 16b it can be seen that two fractures may be initiated
consecutively (e.g., fractures "1" and "2" of FIG. 16b), however
the two previous fractures may be sufficiently far apart that a
third fracture (e.g., fracture "3" of FIG. 16b) may be initiated
between the two previous fractures, such that the fractures
alternate.
[0073] FIGS. 17a and 17b illustrate the stress orientation of a
rock formation 1700 with stress reversal regions 1701 and 1702
associated with a fracture "1" and fracture "2" respectively. In
the present example, fractures "1" and "2" may be placed
approximately 650 ft. from each other. FIG. 17b illustrates that
the distance between stress reversal regions 1701 and 1702 may be
approximately 20 ft. in the present example. Therefore, by
initiating fracture "3" in the middle of fractures "1" and "2,"
both stress reversal regions 1701 and 1702 may be avoided by a
narrow margin of 20 ft. In some instances, such a small margin may
be deemed too small and accordingly the spacing between fractures
"1" and "2" may be increased. FIGS. 17a and 17b illustrate that the
spacing of fractures "1" and "2" may be determined such that stress
reversal regions 1701 and 1702 may not intersect, but also such
that they are sufficiently far apart to allow for the initiation of
a third fracture between them. Accordingly, by analyzing the size
of the stress reversal regions of the two "end" fractures (e.g.,
fractures "1" and "2") in alternate fracturing, the spacing between
the two may be more efficiently determined for placement of the
"middle" fracture (e.g., fracture "3").
[0074] Additionally, by analyzing the stress profile of rock
formation 1700 due to fractures "1" and "2," it can be seen that
the stress reorientation caused by fractures "1" and "2" may
substantially cancel each other out such that fracture "3" may
propagate in a substantially orthogonal path equidistant from
fractures "1" and "2". Accordingly, the advantages of alternate
fracturing may be further illustrated and supported by analyzing
the stress reversal regions.
[0075] The impact of fracture sequencing may also affect fracture
complexity. Hydraulic fracture interaction with pre-existing
natural fractures may be a function of a term called the relative
net pressure R.sub.n. This parameter may be inversely proportional
to the local deviatoric stress in which the fracture propagates as
shown below in Equation (6).
R n = p f - .sigma. h min .sigma. h max - .sigma. h min ( 6 )
##EQU00006##
[0076] High values of the relative net pressure R.sub.n may favor
fracture path complexity. Thus, a hydraulic fracture propagating in
a region of low stress contrast may create larger networks of
interconnected fractures. By calculating the local stress contrast
experienced by a propagating fracture, the propensity of the
alternate fracturing sequence to generate fracture complexity may
be quantified and compared to the more conventional fracturing
approach. The average value of the stress contrast seen by a
propagating middle fracture in the alternate fracturing sequence
may be measured for different values of the spacing between the
outside fractures (2s.sub.f). In the present example, FIG. 18 shows
that the spacing for which the stress contrast is lowest may be
equal to the minimum fracture spacing previously calculated (325
ft). Thus, the minimum fracture spacing in the alternate fracturing
sequence may also be the optimum case for creating fracture
complexity.
[0077] A comparison of the local stress contrast seen by a fracture
along its direction of propagation, in the consecutive and
alternate fracture sequence, demonstrates improvement in generating
fracture complexity using alternate fracturing versus consecutive
fracturing. FIG. 19 illustrates that the deviatoric stress may
approach zero in the near wellbore region in the case of the
optimum spacing in the alternate fracturing sequence (325 ft). In
the present example, along the first half of propagation, the
stress contrast may remain lower than 10 psi, which may be equal to
10% of the in-situ stress contrast. It is only in the second half
of the fracture propagation that the local stress contrast
increases significantly. Thus, choosing the alternate fracturing
sequence, may result in high fracture complexity in the
near-wellbore region as a result of the propagation of the "middle
fracture".
[0078] Analysis of the stress experienced by rock formations may
also be used to determine fracture spacing with respect to multiple
horizontal lateral wells. FIG. 20 illustrates an example of
fracture spacing that may be done with multiple horizontal lateral
wells. FIG. 20 illustrates three horizontal wells (HW.sub.1,
HW.sub.2 and HW.sub.3) that may run substantially parallel to each
other through a hydrocarbon reservoir in a horizontal plane that
may be substantially parallel with the ground.
[0079] The wells of FIG. 20 may be described by variables
representing fracture dimensions (L.sub.f, h.sub.f), fracture
spacing (s.sub.f) and the inter-well spacing (s.sub.w). In the
present example, the middle well (HW.sub.2) may be used to
propagate a fracture (e.g., fracture "3") in between two pairs of
fractures previously initiated from the outside wells (e.g.,
fractures "1" and "2" of well HW.sub.1 and fractures "1'" and "2'"
of well HW.sub.3). The same strategy may be adopted in any
horizontal completions having an uneven number of laterals (and of
course more than just one lateral). Such strategy may allow for
benefiting from the propagation of a "middle fracture", like in
alternate fracturing completions, without the need for special
downhole tools. Indeed, in each lateral well (e.g., HW.sub.1,
HW.sub.2 and HW.sub.3) the fractures may be initiated in a
conventional consecutive sequence.
[0080] The spacing between fractures in such multi-lateral
sequences may be determined by analyzing the stress distribution
(e.g., stress reversal regions) associated with the fractures. For
example, the stress distribution between two pairs of fractures
(e.g., fractures "1" and "2" of well HW.sub.1 and fractures "1'"
and "2'" of well HW.sub.3 of FIG. 20) propagated from the outside
laterals HW.sub.1 and HW.sub.3 is shown in FIGS. 21a and 21b. In
the present example, for the reservoir properties and fracture
geometry of Table 1, it may be determined based on the stress
orientation and distribution caused by fractures "1" and "2" of
well HW.sub.1 and fractures "1'" and "2,'" that a fracture spacing
s.sub.f associated with the fractures of each well (e.g., spacing
between fractures "1", "2", "4", "6", "8", etc., of well HW.sub.1,
fractures "3", "5", "7", "9", etc., of well HW and fractures "1'",
"2'", "4'", "6'", "8'", etc., of well HW.sub.3) may be equal to 600
ft. and a well spacing (s.sub.w) between wells HW.sub.1, HW.sub.2
and HW.sub.3 may be approximately equal to 500 ft. The above
spacing may be determined by analyzing the direction of maximum
horizontal stress associated with the fractures. For example, the
direction of maximum horizontal stress may be reversed everywhere
along the outside laterals as shown in FIGS. 21a and 21b. Thus, the
outside fractures "1" and "2" are too closely spaced to allow
propagation of a transverse fracture from the outside laterals
HW.sub.1 and HW.sub.3, similarly to the alternate fracturing
sequence.
[0081] When considering refracturing the center lateral, the
direction of maximum horizontal stress may still allow propagation
of a transverse fracture. For example, the distance of transverse
propagation, L.sub.transverse, of fracture "3" of HW.sub.2 may be
at a maximum at mid-distance from the previous fractures and may be
function of not only the spacing between the outside fractures but
also the inter-well spacing (s.sub.w). The zone of transverse
fracture propagation can also be identified when plotting the angle
of stress reorientation as shown in FIG. 21b.
[0082] FIG. 22 illustrates the relationship between the length of a
"middle fracture" propagating from a center lateral well (e.g.,
fracture "3" of HW.sub.2 with a length L.sub.transverse) for
different values of the fracture length with respect to the
inter-well spacing. It can be seen that if the wells are spaced too
close to each other, the opportunity to propagate a transverse
middle fracture from the center lateral well may not exist at all
(e.g., s.sub.w/L.sub.f=0.1) because the fracture may very quickly
intersect with the other lateral wells bordering the center lateral
well. For example, if HW.sub.1 and HW.sub.3 are sufficiently close
to HW.sub.2 with respect to the length of fracture "3" in FIG. 20,
fracture "3" may quickly intersect with at least one other fracture
and/or well. Therefore, the length of transverse fracture
propagation may increase with inter-well spacing and may reach its
maximum value when the inter-well spacing is at least equal to the
fracture length (e.g., s.sub.w/L.sub.f=2).
[0083] L.sub.transverse may also increase with the spacing between
the outside fractures (s.sub.f). Transverse fracture propagation
may not be affected if the fracture spacing is at least equal to
twice the minimum fracture spacing in the alternate fracturing
sequence (2s.sub.f=650 ft). In this case, the stress reorientation
angle may be equal to zero everywhere along a line equidistant from
the outside fractures.
[0084] FIG. 23 illustrates the local stress contrast that may be
recorded along the assumed propagation direction of a middle
fracture (e.g., fracture "3" of FIG. 20). This quantity may be
minimum for the minimum possible inter-well spacing
(s.sub.w/L.sub.f=1) and may also be more sensitive to the
inter-well spacing than to the fracture spacing. Thus, it may be
advantageous to position the horizontal laterals close to each
other, but not closer than a distance equal to the fracture
half-height. Otherwise, the benefit of propagating long transverse
fractures may be lost. Indeed, that may result in fracturing zones
of the reservoir that are already stimulated.
[0085] Looking back at FIG. 21a, the distance of transverse
fracture propagation may be sensitive to the fracture spacing when
the inter-well spacing is small. Transverse propagation length may
be decreased by over 50% as the fracture spacing decreases from 650
ft. to 600 ft., which is only a 50 ft. spacing differential.
Therefore, in the present example and similarly to the case of the
alternate fracturing sequence in a single well, the spacing between
the outside fractures may be at least be equal to 650 ft.
[0086] Finally, the optimum multi-lateral completion strategy in
the present example of a typical Barnett shale gas well may be
summarized below:
{ s w = L f = 500 ft s f = 650 ft ##EQU00007##
[0087] The predicted values of the transverse fracture propagation
and average stress contrast for the middle fracture are:
{ L transverse = L f = 500 ft .DELTA. .sigma. hmiddlefrac = 0.24
.DELTA. .sigma. hi = 24 psi ##EQU00008##
[0088] We can finally note that while a 650-ft. spacing may not be
practical in some alternate fracturing sequence (e.g., when the
refracturing interval may only be 20-ft. wide), this spacing may
suffice in a multi-lateral completion. In the latter case, the
middle fracture may be initiated from the middle well (and not from
the outside well), where the refracturing interval is wide enough
to allow fracture initiation from multiple perforation
clusters.
[0089] Therefore, by analyzing the stress reorientation regions of
rock formations due to fracturing operations, the spacing of the
fractures may be determined to improve production from wells, while
also improving the efficiency of each fracturing operation. Such
stress reorientation analysis may be used for consecutive
fracturing, for alternate fracturing and/or for multiple horizontal
fracturing operations.
[0090] Further, the in-situ stress contrast, which is the
difference between the maximum horizontal stress and the minimum
horizontal stress, may influence the stress interference created by
multiple consecutive fractures, including fracture intersection. As
a result, the evolution of the fracturing pressures during
multi-stage fracturing of horizontal wells may be impacted by the
in-situ stress contrast, just like it is impacted by the fracture
spacing (e.g., as shown in FIG. 14).
[0091] Although the minimum horizontal stress may be easily
obtained from a mini-frac test, the maximum horizontal stress may
be more difficult to evaluate in the field. Knowing the value of
the maximum horizontal stress may prove useful in modeling multiple
engineering problems in the oil and gas industry, including
hydraulic fracturing and wellbore stability and sand production
issues.
[0092] The proposed method may be used to calculate the evolution
of the net closure stress in a given well for different values of
the maximum horizontal stress. By comparing the calculated pressure
profiles to the field-measured fracturing pressures, the value of
the maximum horizontal stress may be determined for the well in
question.
[0093] Modifications, additions and omissions may be made to the
above FIGURES without departing from the scope of the present
disclosure. For example, the above models and FIGURES have been
described with respect to specific rock properties and fracture
sizes for illustrative purposes only. The principles described
above may be used for any other suitable rock formation.
[0094] Additionally, it is also understood that the stress
redistribution of a rock formation caused by propagating a fracture
may also be a function of the induced fracture length, fracture
width, fluid rheology and the injection rates associated with
propagating the fracture. As mentioned above, the propagation of
subsequent fractures may be a function of the stress redistribution
caused by previous fractures. Therefore, the analysis described
above may also be used to determine one or more of the above
mentioned properties to better improve fracturing efficiency. For
example, in some instances for a particular fracture size, the
determined optimal spacing may be too far apart. Accordingly, the
spacing may be set at a fixed value and another factor that may
affect stress reorientation (e.g., fracture width) may be modified.
The stress reorientation, and the propagation and net closure
stress of consecutive fractures may be calculated for different
values of the fracture width such that an optimum width of the
fractures may be determined.
* * * * *