U.S. patent application number 16/550336 was filed with the patent office on 2020-11-12 for method for acquiring opening timing of natural fracture under in-slit temporary plugging condition.
The applicant listed for this patent is Southwest Petroleum University. Invention is credited to Chi Chen, Jianchun Guo, Xianjun He, Meiping Li, Cong Lu, Yang Luo, Bin Qian, Yong Ren, Yongjun Xiao, Congbin Yin, Yunchuan Zheng, Ye Zhong.
Application Number | 20200355069 16/550336 |
Document ID | / |
Family ID | 1000004305571 |
Filed Date | 2020-11-12 |
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United States Patent
Application |
20200355069 |
Kind Code |
A1 |
Lu; Cong ; et al. |
November 12, 2020 |
METHOD FOR ACQUIRING OPENING TIMING OF NATURAL FRACTURE UNDER
IN-SLIT TEMPORARY PLUGGING CONDITION
Abstract
A method for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition and a device thereof
are provided. The method includes steps of: acquiring physical
parameters of stratum according to site geological data, and
measuring a slit length L of a hydraulic fracture; dividing the
hydraulic fracture into N unit bodies of equal length and numbering
them sequentially; and dividing a total calculation time t into in
time nodes with equal interval; calculating a width of each unit
body in the hydraulic fracture at the initial time; calculating a
fluid pressure in the hydraulic fracture at the k-th time node;
calculating a closed pressure at an entrance of the natural
fracture on an upper side and a lower side of the hydraulic
fracture at the k-th time node; and determining whether the natural
fracture is opened by a determining criteria based on the above
calculation results.
Inventors: |
Lu; Cong; (Chengdu City,
CN) ; Guo; Jianchun; (Chengdu City, CN) ; Luo;
Yang; (Chengdu City, CN) ; Qian; Bin; (Chengdu
City, CN) ; Li; Meiping; (Chengdu City, CN) ;
Yin; Congbin; (Chengdu City, CN) ; Zheng;
Yunchuan; (Chengdu City, CN) ; Ren; Yong;
(Chengdu City, CN) ; Zhong; Ye; (Chengdu City,
CN) ; Chen; Chi; (Chengdu City, CN) ; Xiao;
Yongjun; (Chengdu City, CN) ; He; Xianjun;
(Chengdu City, CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Southwest Petroleum University |
Chengdu City |
|
CN |
|
|
Family ID: |
1000004305571 |
Appl. No.: |
16/550336 |
Filed: |
August 26, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B 43/26 20130101;
E21B 49/00 20130101; E21B 33/138 20130101 |
International
Class: |
E21B 49/00 20060101
E21B049/00; E21B 43/26 20060101 E21B043/26; E21B 33/138 20060101
E21B033/138 |
Foreign Application Data
Date |
Code |
Application Number |
May 10, 2019 |
CN |
201910387470.0 |
Claims
1. A method for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition, applied to hydraulic
fracturing in oil and gas exploration and development, comprising:
step S10: an acquisition module acquiring physical parameters of
stratum according to site geological data, and measuring a slit
length L of a hydraulic fracture; step S20: dividing the hydraulic
fracture into N unit bodies of equal length and numbering them
sequentially, wherein the length of each unit body being L/N; and
using an in-slit temporary plugging time as an initial time t0, and
dividing a total calculation time t into m fractions of time with
equal interval, wherein an interval time of the adjacent time nodes
fractions of time being t/m; step S30: calculating a width of each
unit body in the hydraulic fracture at the initial time; step S40:
calculating a fluid pressure in the hydraulic fracture at the k-th
fraction of time; step S50: calculating a closed pressure at an
entrance of the natural fracture on an upper side and a lower side
of the hydraulic fracture at the k-th fraction of time; step S55:
providing a temporary plugging agent to artificially restricting a
hydraulic fracture tip to extend forward and forcing a sharp rise
in the fluid pressure for opening the natural fracture; and Step
S60: determining whether the natural fracture is opened by a
determining criteria based on the calculation results of the above
steps S40 and S50; if yes, the time t.sub.0+kt/m corresponding to
the fraction of time k is the opening time of the natural fracture;
if not, then letting k=k+1, repeating steps S40-S50 until the
natural fracture is opened or the temporary plugging section fails;
the determining criteria include: if a fluid pressure in the
hydraulic fracture at the k-th fraction of time is greater than the
closed pressure at the entrance of the natural fracture on the
upper side of the hydraulic fracture at the k-th fraction of time,
the upper side of the natural fracture is opened; if the fluid
pressure in the hydraulic fracture at the k-th fraction of time is
less than the closed pressure at the entrance of the natural
fracture on the lower side of the hydraulic fracture at the k-th
fraction of time, the lower side of the natural fracture is opened;
if the fluid pressure in the hydraulic fracture at the k-th
fraction of time is greater than a plugging strength of the
temporary plugging section and a fluid pressure of the stratum
being combined, the temporary plugging section fails; wherein a
calculation formula in the step S30 is: P 0 - .sigma. h = i = 1 N G
N .pi. L ( 1 - v ) { 1 - d i j .beta. [ d i j 2 + ( H / .alpha. ) 2
] .beta. / 2 } ( 1 2 j - 2 i + 1 - 1 2 j - 2 i + 1 ) W i 0 ( j = 1
, 2 , N ) ; ##EQU00034## wherein p.sup.0 is a fluid pressure in the
hydraulic fracture at the initial time t0, MPa; .sigma..sub.h is a
minimum horizontal principal stress of the stratum, MPa; G is a
shear modulus of a stratum rock, MPa; .nu. is the Poisson's ratio
of the stratum rock, no factor; L is a total length of hydraulic
fracture, meter; N is the divided number of unit bodies of the
hydraulic fracture; d.sub.ij is a distance between the midpoints of
the fracture unit body i and the fracture unit body j, meter; H is
a height of the hydraulic fracture, meter; .alpha., .beta. are
empirical coefficients, taken .alpha.=1, .beta.=2.3; i, j is the
number of the unit body of the hydraulic fracture; W.sub.i.sup.0 is
a width of the i-th unit body of the hydraulic fracture at the
initial time, meter, thereby the method for acquiring the opening
timing of natural fracture under the in-slit temporary plugging
condition applied to hydraulic fracturing facilitate increase in
fracturing range and increasing the reach range of production
wells.
2. (canceled)
3. The method for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition in claim 1, wherein
the step S40 includes the following sub-steps: sub-step S401:
calculating an estimated fluid pressure in the hydraulic fracture
at the k-th fraction of time according to the following formula: {
p ^ k = p 0 ( k = 1 ) p ^ k = 1 . 2 5 p k 1 ( k > 1 ) ;
##EQU00035## wherein p.sup.0 is the fluid pressure in the hydraulic
fracture at the initial time, MPa; p.sup.k-1 is an actual fluid
pressure in the hydraulic fracture at the (k-1)-th fraction of
time; {circumflex over (p)}.sup.k is an estimated fluid pressure in
the hydraulic fracture at the k-th fraction of time, MPa; sub-step
S402: calculating an estimated width of each unit body of the
hydraulic fracture at the k-th fraction of time according to the
estimated fluid pressure calculated above and the following
formula: P ^ k - .sigma. h = i = 1 N G N .pi. L ( 1 - v ) { 1 - d i
j .beta. [ d i j 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i
+ 1 - 1 2 j - 2 i + 1 ) W ^ i k ( j = 1 , 2 , N ) ; ##EQU00036##
wherein {circumflex over (p)}.sup.k is an estimated fluid pressure
in the hydraulic fracture at the k-th fraction of time, MPa;
.sigma..sub.h is a minimum horizontal principal stress of the
stratum, MPa; G is a shear modulus of a stratum rock, MPa; .nu. is
the Poisson's ratio of the stratum rock, no factor; L is a total
length of hydraulic fracture, meter; N is the divided number of
unit bodies of the hydraulic fracture; d.sub.ij is a distance
between the midpoints of the fracture unit body i and the fracture
unit body j, meter; H is a height of the hydraulic fracture, meter;
.alpha., .beta. are empirical coefficients, taken .alpha.=1,
.beta.=2.3; i, j is the number of the unit body of hydraulic
fracture; .sub.i.sup.k is an estimated width of each unit body of
the hydraulic fracture at the k-th fraction of time, meter;
sub-step S403: calculating an error .alpha. of the estimated width
by the following formula: .alpha. = H L ( = 1 N W ^ i k - i = 1 N W
i k - 1 ) N Q .DELTA. t ; ##EQU00037## wherein .sub.i.sup.k is an
estimated width of each unit of the hydraulic fracture at the k-th
fraction of time, meter; W.sub.i.sup.k-1 is an estimated width of
each unit of the hydraulic fracture at the (k-1)-th fraction of
time, meter; H is a height of the hydraulic fracture, meter; L is a
total length of the hydraulic fracture, meter; N is the divided
number of unit bodies of the hydraulic fracture; Q is a pumping
displacement of fracturing fluid after in-slit temporary plugging,
m3/s; .DELTA.t is an interval time of adjacent fractions of time,
s; i is the number of unit bodies of the hydraulic fracture;
.alpha. is the error; sub-step S404: setting solution accuracy
.epsilon., and comparing the error .alpha. obtained above with the
solution accuracy .epsilon.; if .alpha..ltoreq..epsilon.,
{circumflex over (P)}.sup.k and .sub.i.sup.k calculated in step
S402 and step S403 are respectively the fluid pressure in the
hydraulic fracture at the k-th fraction of time and the width of
each unit body; if .alpha.>.epsilon., then re-estimating the
fluid pressure using the following formula and repeating steps
S402-S404 until .alpha..ltoreq..epsilon. is satisfied; { P ^ k = P
^ k 1 + 1 0 .alpha. ( .alpha. > 0 ) P ^ k = ( 1 - 1 0 .alpha. )
P ^ k ( .alpha. < 0 ) ; ##EQU00038## wherein .epsilon. is a
solution accuracy; {circumflex over (p)}.sup.k is an estimated
fluid pressure in the hydraulic fracture at the k-th fraction of
time, MPa; .alpha. is an error.
4. The method for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition in claim 1, wherein a
calculation formula in the step S50 is: { .sigma. u k = ( .sigma. H
+ .sigma. h 2 - .sigma. H - .sigma. h 2 cos 2 .omega. ) + i = 1 N {
1 - d u i .beta. [ d u i 2 + ( H / .alpha. ) 2 ] .beta. / 2 } C u i
W i k .sigma. l k = ( .sigma. H + .sigma. h 2 - .sigma. H - .sigma.
h 2 cos 2 .omega. ) + i = 1 N { 1 - d l i .beta. [ d l i 2 + ( H /
.alpha. ) 2 ] .beta. / 2 } C l i W i k ; ##EQU00039## wherein
.sigma..sub.u.sup.k is a closed pressure at an entrance of the
natural fracture on an upper side of the hydraulic fracture at the
k-th fraction of time, MPa; .sigma..sub.l.sup.k is a closed
pressure at an entrance of the natural fracture on a lower side of
the hydraulic fracture at the k-th fraction of time, MPa;
.sigma..sub.H is a maximum horizontal principal stress of the
stratum, MPa; .sigma..sub.h is a minimum horizontal principal
stress of the stratum, MPa; .omega. is an angle between the
hydraulic fracture and the natural fracture; d.sub.ui is a distance
between the midpoint of the upper natural fracture entrance unit
and the midpoint of the hydraulic fracture unit i, meter; d.sub.li
is a distance between the midpoint of the lower natural fracture
entrance unit and the midpoint of the hydraulic fracture unit i,
meter; H is a height of the hydraulic fracture, meter; .alpha.,
.beta. is an empirical coefficient, taken .alpha.=1, .beta.=2.3;
W.sub.i.sup.k is a width of the unit body i of the hydraulic
fracture at the k-th fraction of time, meter; C.sup.ui, C.sup.li
are the shape coefficients of the upper and lower natural fracture
entrance unit bodies with respect to the unit body i of the
hydraulic fracture, respectively.
5. The method for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition in claim 4, wherein
the shape coefficients of the upper and lower natural fracture
entrance unit bodies with respect to the unit body i of the
hydraulic fracture are obtained by the following sub-steps:
sub-step S501: establishing a global coordinate system with a
center point of the first hydraulic fracture unit body as an
origin, a length direction of the hydraulic fracture as an X-axis,
a direction passing through the origin and perpendicular to the
wall surface of the hydraulic fracture as a Y-axis; sub-step S502:
expressing the coordinates of the midpoint of the upper and lower
natural fracture entrance unit bodies in the global coordinate
system as: { x u = x r + L N .cndot.cos .omega. y u = L N
.cndot.sin.omega. x l = x r - L N .cndot.cos.omega. y l = - L N
.cndot.sin .omega. ; ##EQU00040## wherein x.sub.u, y.sub.u is a
coordinate of the midpoint of the upper natural fracture entrance
unit bodies in the global coordinate system; x.sub.l, y.sub.l is a
coordinate of the midpoint of the lower natural fracture entrance
unit bodies in the global coordinate system; x.sub.r is an abscissa
of the point where the hydraulic fracture intersects the natural
fracture in the global coordinate system; L is a total length of
hydraulic fracture, meter; N is the divided number of unit bodies
of the hydraulic fracture; .omega. is an angle between the
hydraulic fracture and the natural fracture, degree; sub-step S503:
expressing the coordinates of the midpoint of the upper and lower
natural fracture entrance unit bodies in a local coordinate system
based on the midpoint of the hydraulic fracture unit body i as: { x
u i = ( x _ r + L N .cndot.cos .omega. - x i _ ) cos .omega. + ( L
N .cndot.sin .omega. - y _ i ) sin .omega. y u i = - ( x _ r + L N
.cndot.cos .omega. - x i _ ) sin .omega. + ( L N .cndot.sin .omega.
- y _ i ) cos .omega. x li = ( x _ r - L N .cndot.cos .omega. - x i
_ ) cos .omega. - ( L N .cndot.sin .omega. + y _ i ) sin .omega. y
li = - ( x _ r - L N .cndot.cos .omega. - x i _ ) sin .omega. - ( L
N .cndot.sin .omega. + y _ i ) cos.omega. ; ##EQU00041## wherein
x.sub.ui, y.sub.ui is a coordinate of the midpoint of the upper
natural fracture entrance unit bodies in the local coordinate
system; x.sub.li, y.sub.li is a coordinate of the midpoint of the
lower natural fracture entrance unit bodies in the local coordinate
system; x.sub.i, y.sub.i is a coordinate of the unit body i of the
hydraulic fracture in the global coordinate system; x.sub.r an
abscissa of the point where the hydraulic fracture intersects the
natural fracture in the global coordinate system; L is a total
length of hydraulic fracture, meter; N is the divided number of
unit bodies of hydraulic fracture; .omega. is an angle between the
hydraulic fracture and the natural fracture, degree; and sub-step
S504: placing the formula in sub-step (S503) into the following
formula for solution to obtain the shape coefficients of the upper
and lower natural fracture entrance unit bodies with respect to the
unit body i of the hydraulic fracture; C ij = 2 G [ - f 1 + y ij (
f 2 sin 2 .gamma. ij - f 3 cos 2 .gamma. ij ) ] ; ##EQU00042## { f
1 = 1 4 .pi. ( 1 - v ) [ x ij - a ( x ij - a ) 2 + y ij 2 - x ij +
a ( x ij + a ) 2 + y ij 2 ] f 2 = 1 4 .pi. ( 1 - v ) [ ( x ij - a )
2 - y ij 2 [ ( x ij - a ) 2 + y ij 2 ] 2 - ( x ij + a ) 2 - y ij 2
[ ( x ij + a ) 2 + y ij 2 ] 2 ] f 3 = 2 y ij 4 .pi. ( 1 - v ) [ x
ij - a [ ( x ij - a ) 2 + y ij 2 ] 2 - x ij + a [ ( x ij + a ) 2 +
y ij 2 ] 2 ] ; ##EQU00042.2## wherein .delta..sub.j.sup.k is a
normal stress of the fracture unit body j at the k-th fraction of
time, MPa; G is a shear modulus of the stratum rock, MPa; .nu. is
the Poisson's ratio of the stratum rock, no factor; d.sub.ij the
distance between the midpoints of the fracture unit i and the
fracture unit j, meter; H is a height of the hydraulic fracture,
meter; .alpha., .beta. are empirical coefficients, taken .alpha.=1,
.beta.=2.3; i, j is the number of the unit body of hydraulic
fracture; W.sub.i.sup.0 is a width of the i-th unit body of
hydraulic fracture at the initial time, meter; C.sup.ij is a shape
coefficient of the fracture unit j with respect to the unit body i
of the hydraulic fracture; .gamma..sup.ij is a deflection angle of
the fracture unit body i with respect to the fracture unit body j;
a is a half-length of the fracture unit body, that is, L/2N, meter;
x.sub.ij, y.sub.ij is a coordinate value of the midpoint of the
fracture unit body j in the local coordinate system based on the
midpoint of the fracture unit body i.
6.-10. (canceled)
Description
FIELD OF THE INVENTION
[0001] The present invention relates to a method for acquiring an
opening timing of natural fracture under an in-slit temporary
plugging condition and a device thereof, which belongs to the field
of oil and gas exploration and development.
BACKGROUND OF THE INVENTION
[0002] Hydraulic fracturing technology is an important means for
increased production of low permeability oil and gas reservoirs.
Hydraulic fracturing means that a set of ground high-pressure pumps
is used to pump the fracturing fluid into the stratum with a
displacement exceeding the absorption capacity of the stratum to
produce hydraulic fracture, and then a fracturing fluid with
proppant (sand particles) is continued to be injected to allow the
fracture to continue to extend and be further filled with the
proppant. When the fracturing fluid is discharged to return, the
proppant acts as a support in the fracture for preventing the
fracture from closing due to the pressure of the stratum, so that a
sand-filling fracture having a certain length and flowability is
formed in the stratum.
[0003] In-slit temporary plugging turnaround fracturing is a form
of hydraulic fracturing, specifically, refers to that during the
fracturing process, the temporary plugging agent is pumped to
temporarily block the hydraulic fracture tip, artificially
restricting the hydraulic fracture tip to extend forward, forcing
the fluid pressure inside the hydraulic fracture to rise sharply,
thereby opening natural fracture around the hydraulic fracture, so
as to increase the range of fracturing. Therefore, accurately
acquiring an opening timing for natural fracture under the in-slit
temporary plugging condition is of great significance for the
prediction of natural fracture extension process and the design in
temporary plugging turnaround fracturing process.
[0004] Temporary plugging failure refers to the phenomenon that the
fracturing fluid inside the hydraulic fracture breaks through
temporary plugging regions at the tip during the fracturing
process, causing the temporary plugging section to lose its
plugging effect, and then the hydraulic fracture continues to
extend forward along the original path. Generally, the temporary
plugging failure occurs when the difference between the pressures
on both sides of the temporary plugging section reaches a critical
value, which is also called temporary plugging strength, determined
by the property of the temporary plugging agent itself.
[0005] Natural fracture is named as opposed to artificial fracture
that are otherwise manmade, and natural fracture refers to a type
of fracture in the stratum that naturally occurs due to crustal
movement or other natural factors. During the hydraulic fracturing,
when the hydraulic fracture extends forward, it usually meets the
natural fracture, at which time there are two possible situations:
the hydraulic fracture passes directly through the natural fracture
to extend forward along the original path, or the hydraulic
fracture extends forward along the path where the natural fracture
is located. The temporary plugging turnaround fracturing in the
fracture is mainly applicable to the first situation, that is, when
the hydraulic fracture passes through the natural fracture, the
natural fracture remains closed, and then increasing the fluid
pressure inside the hydraulic fracture by pumping the temporary
plugging agent forces the natural fracture to open. In addition,
according to the relative position upon the hydraulic fracture
intersecting with the natural fracture, the intersection process
may be divided into two types: orthogonal (vertically intersecting)
and non-orthogonal.
[0006] Induced stress refers to a force induced by the other
positions of the material against the external force when a
position of the material is subjected to an external force. For
hydraulic fracturing, the length and width of hydraulic fracture
increase continuously during the fracturing process, resulting in a
continuously increased extrusion on the surrounding rocks, so that
the induced stress generated inside the rock increases
continuously, which may also indirectly affect the opening process
of the natural fracture.
[0007] In response to achieving a viable method for acquiring
opening timing of natural fracture during hydraulic fracturing,
scholars at home and abroad have done a lot of studies. However,
most of conventional studies only aim at determining the opening
time when the hydraulic fracture tip meets the natural fracture,
but without specifically analyzing the opening timing of the
natural fracture in the case of also applying in-slit temporary
plugging onto the tip after the hydraulic fracture passes through
the natural fracture. At the same time, for the case of
non-orthogonality between the hydraulic fracture and the natural
fracture, scholars only directly assume that natural fracture on
one side of hydraulic fracture will open, without comparing the
forces of natural fracture on both sides. Therefore, these
conventional methods may not reflect or predict well the actual
opening process of natural fracture under the in-slit temporary
plugging condition.
[0008] It should be noted that the above description of the
technical background is merely for the purpose of facilitating a
clear and complete description of technical solutions of the
present invention, and is convenient for understanding by those
skilled in the art. The above technical solutions should not be
considered to be well-known to those skilled in the art, simply
because these aspects are set forth in background section of the
present invention.
SUMMARY OF THE INVENTION
[0009] In order to solve the above problems in the prior art, it is
an object of the present invention to provide a method for
acquiring an opening timing of natural fracture under an in-slit
temporary plugging condition. The method is reliable in principle,
high in calculation accuracy, and may accurately calculate the
opening timing of natural fracture during the temporary plugging
turnaround fracturing, further providing effective guidance for
design in fracturing solution.
[0010] The method includes the following steps:
[0011] step S10: acquiring physical parameters of stratum according
to site geological data, and measuring a slit length L of a
hydraulic fracture;
[0012] step S20: dividing the hydraulic fracture into N unit bodies
of equal length and numbering them sequentially, wherein the length
of each unit body being L/N; and using an in-slit temporary
plugging time as an initial time t0, and dividing a total
calculation time t into m time nodes with equal interval, wherein
an interval time of the adjacent time nodes being t/m;
[0013] step S30: calculating a width of each unit body in the
hydraulic fracture at the initial time;
[0014] step S40: calculating a fluid pressure in the hydraulic
fracture at the k-th time node;
[0015] step S50: calculating a closed pressure at an entrance of
the natural fracture on an upper side and a lower side of the
hydraulic fracture at the k-th time node; and
[0016] Step S60: determining whether the natural fracture is opened
by a determining criteria based on the calculation results of the
above steps S40 and S50;
[0017] if yes, the time t.sub.0+kt/m corresponding to the time node
k is the opening time of the natural fracture;
[0018] if not, then letting k=k+1, repeating steps S40-S50 until
the natural fracture is opened or the temporary plugging section
fails;
[0019] the determining criteria include: [0020] if
P.sup.k>.sigma..sub.u.sup.k, the upper side of the natural
fracture is opened; [0021] if P.sup.k<.sigma..sub.l.sup.k, the
lower side of the natural fracture is opened; [0022] if
P.sup.k>P.sub.c+P.sub.r, the temporary plugging section
fails;
[0023] wherein P.sup.k is a fluid pressure in the hydraulic
fracture at the k-th time node; .sigma..sub.u.sup.k is the closed
pressure at the entrance of the natural fracture on the upper side
of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.l.sup.k is the closed pressure at the entrance of the
natural fracture on the lower side of the hydraulic fracture at the
k-th time node, MPa; P.sub.c is a plugging strength of the
temporary plugging section, MPa; P.sub.r is a fluid pressure of the
stratum, MPa.
[0024] In one embodiment, a calculation formula in the step S30
is:
P 0 - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W i 0 ( j = 1 , 2 , N ) ##EQU00001##
[0025] wherein P.sup.0 is a fluid pressure in the hydraulic
fracture at the initial time t0, MPa; .sigma..sub.h is a minimum
horizontal principal stress of the stratum, MPa; G is a shear
modulus of a stratum rock, MPa; .nu. is the Poisson's ratio of the
stratum rock, no factor; L is a total length of hydraulic fracture,
m; N is the divided number of unit bodies of the hydraulic
fracture; d.sub.ij is a distance between the midpoints of the
fracture unit body i and the fracture unit body j, m; H is a height
of the hydraulic fracture, m; .alpha., .beta. are empirical
coefficients, taken .alpha.=1, .beta.=2.3; i, j is the number of
the unit body of the hydraulic fracture; W.sub.i.sup.0 is a width
of the i-th unit body of the hydraulic fracture at the initial
time, m.
[0026] In one embodiment, the step S40 includes the following
sub-steps:
[0027] sub-step S401: calculating an estimated fluid pressure in
the hydraulic fracture at the k-th time node according to the
following formula:
{ p ^ k = p 0 ( k = 1 ) p ^ k = 1 . 2 5 p k - 1 ( k > 1 ) ;
##EQU00002##
[0028] wherein P.sup.0 is the fluid pressure in the hydraulic
fracture at the initial time, MPa; p.sup.k-1 is an actual fluid
pressure in the hydraulic fracture at the (k-1)-th time node;
{circumflex over (p)}.sup.k is an estimated fluid pressure in the
hydraulic fracture at the k-th time node, MPa;
[0029] sub-step S402: calculating an estimated width of each unit
body of the hydraulic fracture at the k-th time node according to
the estimated fluid pressure calculated above and the following
formula:
P ^ k - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W ^ i k ( j = 1 , 2 , N ) ; ##EQU00003##
[0030] wherein {circumflex over (p)}.sup.k is an estimated fluid
pressure in the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.h is a minimum horizontal principal stress of the
stratum, MPa; G is a shear modulus of a stratum rock, MPa; .nu. is
the Poisson's ratio of the stratum rock, no factor; L is a total
length of hydraulic fracture, in; N is the divided number of unit
bodies of the hydraulic fracture; d.sub.ij is a distance between
the midpoints of the fracture unit body i and the fracture unit
body j, m; H is a height of the hydraulic fracture, m; .alpha.,
.beta. are empirical coefficients, taken .alpha.=1, .beta.=2.3; i,
j is the number of the unit body of hydraulic fracture;
.sub.i.sup.k is an estimated width of each unit body of the
hydraulic fracture at the k-th time node, m;
[0031] sub-step S403: calculating an error a of the estimated width
by the following formula:
.alpha. = H L ( i = 1 N W ^ i k - i = 1 N W i k - 1 ) N Q .DELTA. t
; ##EQU00004##
[0032] wherein .sub.i.sup.k is an estimated width of each unit of
the hydraulic fracture at the k-th time node, m; W.sub.i.sup.k-1 is
an estimated width of each unit of the hydraulic fracture at the
(k-1)-th time node, m; H is a height of the hydraulic fracture, m;
L is a total length of the hydraulic fracture, m; N is the divided
number of unit bodies of the hydraulic fracture; Q is a pumping
displacement of fracturing fluid after in-slit temporary plugging,
m3/s; .DELTA.t is an interval time of adjacent time nodes, s; i is
the number of unit bodies of the hydraulic fracture; .alpha. is the
error; and
[0033] sub-step S404: setting solution accuracy .epsilon., and
comparing the error a obtained above with the solution accuracy
.epsilon.;
[0034] if .alpha..ltoreq..epsilon., {circumflex over (P)}.sup.k and
.sub.i.sup.k calculated in step S402 and step S403 are respectively
the fluid pressure in the hydraulic fracture at the k-th time node
and the width of each unit body; if .alpha.>.epsilon., then
re-estimating the fluid pressure using the following formula and
repeating steps S402-S404 until .alpha..ltoreq..epsilon. is
satisfied;
{ P ^ k = P ^ k 1 + 10 .alpha. ( .alpha. > 0 ) P ^ k = ( 1 - 10
.alpha. ) P ^ k ( .alpha. < 0 ) ; ##EQU00005##
[0035] wherein .epsilon. is a solution accuracy; {circumflex over
(P)}.sup.k is an estimated fluid pressure in the hydraulic fracture
at the k-th time node, MPa; .alpha. is an error.
[0036] In one embodiment, a calculation formula in the step S50
is:
{ .sigma. u k = ( .sigma. H + .sigma. h 2 - .sigma. H - .sigma. h 2
cos 2 .omega. ) + i = 1 N { 1 - d ui .beta. [ d ui 2 + ( H /
.alpha. ) 2 ] .beta. / 2 } C ui W i k .sigma. l k = ( .sigma. H +
.sigma. h 2 - .sigma. H - .sigma. h 2 cos 2 .omega. ) + i = 1 N { 1
- d li .beta. [ d li 2 + ( H / .alpha. ) 2 ] .beta. / 2 } C li W i
k ; ##EQU00006##
[0037] wherein .sigma..sub.u.sup.k is a closed pressure at an
entrance of the natural fracture on an upper side of the hydraulic
fracture at the k-th time node, MPa; .sigma..sub.l.sup.k is a
closed pressure at an entrance of the natural fracture on a lower
side of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.H is a maximum horizontal principal stress of the
stratum, MPa; .sigma..sub.h is a minimum horizontal principal
stress of the stratum, MPa; .omega. is an angle between the
hydraulic fracture and the natural fracture; d.sub.ij is a distance
between the midpoint of the upper natural fracture entrance unit
and the midpoint of the hydraulic fracture unit i, in; d.sub.h is a
distance between the midpoint of the lower natural fracture
entrance unit and the midpoint of the hydraulic fracture unit i,
in; H is a height of the hydraulic fracture, in; .alpha., .beta. is
an empirical coefficient, taken .alpha.=1, .beta.=2.3;
W.sub.i.sup.k is a width of the unit body i of the hydraulic
fracture at the k-th time node, m; C.sup.ui, C.sup.li are the shape
coefficients of the upper and lower natural fracture entrance unit
bodies with respect to the unit body i of the hydraulic fracture,
respectively.
[0038] In one embodiment, the shape coefficients of the upper and
lower natural fracture entrance unit bodies with respect to the
unit body i of the hydraulic fracture are obtained by the following
sub-steps:
[0039] sub-step S501: establishing a global coordinate system with
a center point of the first hydraulic fracture unit body as an
origin, a length direction of the hydraulic fracture as an X-axis,
a direction passing through the origin and perpendicular to the
wall surface of the hydraulic fracture as a Y-axis;
[0040] sub-step S502: expressing the coordinates of the midpoint of
the upper and lower natural fracture entrance unit bodies in the
global coordinate system as:
{ x _ u = x _ r + L N .cndot.cos .omega. y _ u = L N .cndot. sin
.omega. x _ = x _ r - L N .cndot.cos .omega. y _ l = - L N .cndot.
sin .omega. ; ##EQU00007##
[0041] wherein x.sub.u, y.sub.u is a coordinate of the midpoint of
the upper natural fracture entrance unit bodies in the global
coordinate system; x.sub.l, y.sub.l is a coordinate of the midpoint
of the lower natural fracture entrance unit bodies in the global
coordinate system; x.sub.r is an abscissa of the point where the
hydraulic fracture intersects the natural fracture in the global
coordinate system; L is a total length of hydraulic fracture, m; N
is the divided number of unit bodies of the hydraulic fracture;
.omega. is an angle between the hydraulic fracture and the natural
fracture, degree;
[0042] step S503: expressing the coordinates of the midpoint of the
upper and lower natural fracture entrance unit bodies in a local
coordinate system based on the midpoint of the hydraulic fracture
unit body i as:
{ x ui = ( x _ r + L N .cndot.cos .omega. - x _ i ) cos .omega. + (
L N .cndot.sin .omega. - y _ i ) sin .omega. y ui = - ( x _ r + L N
.cndot.cos .omega. - x _ i ) sin .omega. + ( L N .cndot. sin
.omega. - y _ i ) cos .omega. x li = ( x _ r - L N .cndot.cos
.omega. - x _ i ) cos .omega. - ( L N .cndot. sin .omega. + y _ i )
sin .omega. y li = - ( x _ r - L N .cndot.cos .omega. - x _ i ) sin
.omega. - ( L N .cndot. sin .omega. + y _ i ) cos .omega. ;
##EQU00008##
[0043] wherein x.sub.ui, y.sub.ui is a coordinate of the midpoint
of the upper natural fracture entrance unit bodies in the local
coordinate system; x.sub.li, y.sub.li is a coordinate of the
midpoint of the lower natural fracture entrance unit bodies in the
local coordinate system; x.sub.i, y.sub.i is a coordinate of the
unit body i of the hydraulic fracture in the global coordinate
system; x.sub.r an abscissa of the point where the hydraulic
fracture intersects the natural fracture in the global coordinate
system; L is a total length of hydraulic fracture, m; N is the
divided number of unit bodies of hydraulic fracture; .omega. is an
angle between the hydraulic fracture and the natural fracture,
degree; and
[0044] sub-step S504: placing the formula in sub-step (S503) into
the following formula for solution to obtain the shape coefficients
of the upper and lower natural fracture entrance unit bodies with
respect to the unit body i of the hydraulic fracture;
C ij = 2 G [ - f 1 + y ij ( f 2 sin 2 .gamma. ij - f 3 cos 2
.gamma. ij ) ] ; { f 1 = 1 4 .pi. ( 1 - v ) [ x ij - a ( x ij - a )
2 + y ij 2 - x ij + a ( x ij + a ) 2 + y ij 2 ] f 2 = 1 4 .pi. ( 1
- v ) [ ( x ij - a ) 2 - y ij 2 [ ( x ij - a ) 2 + y ij 2 ] 2 - ( x
ij + a ) 2 - y ij 2 [ ( x ij + a ) 2 + y ij 2 ] 2 ] f 3 = 2 y 4
.pi. ( 1 - v ) [ x ij - a [ ( x ij - a ) 2 + y ij 2 ] 2 - x ij + a
[ ( x ij + a ) 2 + y ij 2 ] 2 ] ; ##EQU00009##
[0045] wherein .delta..sub.j.sup.k is a normal stress of the
fracture unit body j at the k-th time node, MPa; G is a shear
modulus of the stratum rock, MPa; .nu. is the Poisson's ratio of
the stratum rock, no factor; d.sub.ij is the distance between the
midpoints of the fracture unit i and the fracture unit j, in; H is
a height of the hydraulic fracture, in; .alpha., .beta. are
empirical coefficients, taken .alpha.=1, .beta.=2.3; i, j is the
number of the unit body of hydraulic fracture; W.sub.i.sup.0 is a
width of the i-th unit body of hydraulic fracture at the initial
time, in; C.sup.ij is a shape coefficient of the fracture unit j
with respect to the unit body i of the hydraulic fracture;
.gamma..sup.ij is a deflection angle of the fracture unit body i
with respect to the fracture unit body j; a is a half-length of the
fracture unit body, that is, L/2N, in; x.sub.ij, y.sub.ij is a
coordinate value of the midpoint of the fracture unit body j in the
local coordinate system based on the midpoint of the fracture unit
body i.
[0046] According to another exemplary embodiment, a device for
acquiring an opening timing of natural fracture under an in-slit
temporary plugging condition is provided. The device includes an
acquisition module, a division module, a width calculation module,
a fluid pressure calculation module, a closed pressure calculation
module, and a determination module. The acquisition module is
configured to acquire physical parameters of stratum according to
site geological data, and measure a slit length L of a hydraulic
fracture. The division module is configured to divide the hydraulic
fracture into N unit bodies of equal length and number them
sequentially, wherein the length of each unit body being L/N; and
use an in-slit temporary plugging time as an initial time t0, and
divide a total calculation time t into m time nodes with equal
interval, wherein an interval time of the adjacent time nodes being
t/m. The width calculation module is configured to calculate a
width of each unit body in the hydraulic fracture at the initial
time. The fluid pressure calculation module is configured to
calculate a fluid pressure in the hydraulic fracture at the k-th
time node. The closed pressure calculation module is configured to
calculate a closed pressure at an entrance of the natural fracture
on an upper side and a lower side of the hydraulic fracture at the
k-th time node. The determination module is configured to determine
whether the natural fracture is opened by a determining criteria
based on calculation results of the fluid pressure calculation
module and the closed pressure calculation module. If yes, the time
t.sub.0+kt/m m corresponding to the time node k is the opening time
of the natural fracture; if not, then letting k=k+1, repeating
steps S40-S50 until the natural fracture is opened or the temporary
plugging section fails.
[0047] The determining criteria include: [0048] if
P.sup.k>.sigma..sub.u.sup.k, the upper side of the natural
fracture is opened; [0049] if P.sup.k<.sigma..sub.l.sup.k, the
lower side of the natural fracture is opened; [0050] if
P.sup.k>P.sub.c+P.sub.r, the temporary plugging section
fails;
[0051] wherein P.sup.k is a fluid pressure in the hydraulic
fracture at the k-th time node; .sigma..sub.u.sup.k is the closed
pressure at the entrance of the natural fracture on the upper side
of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.l.sup.k is the closed pressure at the entrance of the
natural fracture on the lower side of the hydraulic fracture at the
k-th time node, MPa; P.sub.c is a plugging strength of the
temporary plugging section, MPa; P.sub.r is a fluid pressure of the
stratum, MPa.
[0052] In one embodiment, the width calculation module is further
configured to calculate the width of each unit body in the
hydraulic fracture based on the following calculation formula:
P 0 - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W i 0 ( j = 1 , 2 , N ) ##EQU00010##
[0053] wherein p.sup.0 is a fluid pressure in the hydraulic
fracture at the initial time t0, MPa; .sigma..sub.h is a minimum
horizontal principal stress of the stratum, MPa; G is a shear
modulus of a stratum rock, MPa; .nu. is the Poisson's ratio of the
stratum rock, no factor; L is a total length of hydraulic fracture,
m; N is the divided number of unit bodies of the hydraulic
fracture; d.sub.ij is a distance between the midpoints of the
fracture unit body i and the fracture unit body j, m; H is a height
of the hydraulic fracture, m; .alpha., .beta. are empirical
coefficients, taken .alpha.=1, .beta.=2.3; i, j is the number of
the unit body of the hydraulic fracture; W.sub.i.sup.0 is a width
of the i-th unit body of the hydraulic fracture at the initial
time, m.
[0054] In one embodiment, the fluid pressure calculation module is
further configured to:
[0055] calculate an estimated fluid pressure in the hydraulic
fracture at the k-th time node according to the following
formula:
{ p ^ k = p 0 ( k = 1 ) p ^ k = 1 . 2 5 p k - 1 ( k > 1 ) ;
##EQU00011##
[0056] wherein p.sup.0 is the fluid pressure in the hydraulic
fracture at the initial time, MPa; p.sup.k-1 is an actual fluid
pressure in the hydraulic fracture at the (k-1)-th time node;
{circumflex over (p)}.sup.k is an estimated fluid pressure in the
hydraulic fracture at the k-th time node, MPa;
[0057] calculate an estimated width of each unit body of the
hydraulic fracture at the k-th time node according to the estimated
fluid pressure calculated above and the following formula:
P ^ k - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W ^ i k ( j = 1 , 2 , N ) ; ##EQU00012##
[0058] wherein {circumflex over (p)}.sup.k is an estimated fluid
pressure in the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.h is a minimum horizontal principal stress of the
stratum, MPa; G is a shear modulus of a stratum rock, MPa; .nu. is
the Poisson's ratio of the stratum rock, no factor; L is a total
length of hydraulic fracture, m; N is the divided number of unit
bodies of the hydraulic fracture; d.sub.ij is a distance between
the midpoints of the fracture unit body i and the fracture unit
body j, m; H is a height of the hydraulic fracture, m; .alpha.,
.beta. are empirical coefficients, taken .alpha.=1, .beta.=2.3; i,
j is the number of the unit body of hydraulic fracture;
.sub.i.sup.k is an estimated width of each unit body of the
hydraulic fracture at the k-th time node, m;
[0059] calculate an error .alpha. of the estimated width by the
following formula:
.alpha. = H L ( i = 1 N W ^ i k - i = 1 N W i k - 1 ) N Q .DELTA. t
; ##EQU00013##
[0060] wherein .sub.i.sup.k is an estimated width of each unit of
the hydraulic fracture at the k-th time node, m; W.sub.i.sup.k-1 is
an estimated width of each unit of the hydraulic fracture at the
(k-1)-th time node, m; H is a height of the hydraulic fracture, m;
L is a total length of the hydraulic fracture, m; N is the divided
number of unit bodies of the hydraulic fracture; Q is a pumping
displacement of fracturing fluid after in-slit temporary plugging,
m3/s; .DELTA.t is an interval time of adjacent time nodes, s; i is
the number of unit bodies of the hydraulic fracture; .alpha. is the
error; and
[0061] set solution accuracy .epsilon., and comparing the error
.alpha. obtained above with the solution accuracy .epsilon.;
[0062] if .alpha..ltoreq..epsilon., {circumflex over (P)}.sup.k and
.sub.i.sup.k calculated above are respectively the fluid pressure
in the hydraulic fracture at the k-th time node and the width of
each unit body; if .alpha.>.epsilon., then re-estimate the fluid
pressure using the following formula and repeating the above steps
until .alpha..ltoreq..epsilon. is satisfied;
{ P ^ k = P ^ k 1 + 10 .alpha. ( .alpha. > 0 ) P ^ k = ( 1 - 10
.alpha. ) P ^ k ( .alpha. < 0 ) ; ##EQU00014##
[0063] wherein .epsilon. is a solution accuracy; {circumflex over
(P)}.sup.k is an estimated fluid pressure in the hydraulic fracture
at the k-th time node, MPa; .alpha. is an error.
[0064] In one embodiment, the closed pressure calculation module is
configured to calculate the closed pressure at the entrance of the
natural fracture based on the following formula:
{ .sigma. u k = ( .sigma. H + .sigma. h 2 - .sigma. H - .sigma. h 2
cos 2 .omega. ) + i = 1 N { 1 - d ui .beta. [ d ui 2 + ( H /
.alpha. ) 2 ] .beta. / 2 } C ui W i k .sigma. l k = ( .sigma. H +
.sigma. h 2 - .sigma. H - .sigma. h 2 cos 2 .omega. ) + i = 1 N { 1
- d li .beta. [ d li 2 + ( H / .alpha. ) 2 ] .beta. / 2 } C li W i
k ; ##EQU00015##
[0065] wherein .sigma..sub.u.sup.k is a closed pressure at an
entrance of the natural fracture on an upper side of the hydraulic
fracture at the k-th time node, MPa; .sigma..sub.l.sup.k is a
closed pressure at an entrance of the natural fracture on a lower
side of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.H is a maximum horizontal principal stress of the
stratum, MPa; .sigma..sub.h is a minimum horizontal principal
stress of the stratum, MPa; .omega. is an angle between the
hydraulic fracture and the natural fracture; d.sub.ui is a distance
between the midpoint of the upper natural fracture entrance unit
and the midpoint of the hydraulic fracture unit m; d.sub.li is a
distance between the midpoint of the lower natural fracture
entrance unit and the midpoint of the hydraulic fracture unit i, m;
H is a height of the hydraulic fracture, m; .alpha., .beta. is an
empirical coefficient, taken .alpha.=1, .beta.=2.3; W.sub.i.sup.k
is a width of the unit body i of the hydraulic fracture at the k-th
time node, m; C.sup.ui, C.sup.li are the shape coefficients of the
upper and lower natural fracture entrance unit bodies with respect
to the unit body i of the hydraulic fracture, respectively.
[0066] In one embodiment, the closed pressure calculation module is
further configured to:
[0067] establish a global coordinate system with a center point of
the first hydraulic fracture unit body as an origin, a length
direction of the hydraulic fracture as an X-axis, a direction
passing through the origin and perpendicular to the wall surface of
the hydraulic fracture as a Y-axis;
[0068] express the coordinates of the midpoint of the upper and
lower natural fracture entrance unit bodies in the global
coordinate system as:
{ x _ u = x _ r + L N .cndot.cos .omega. y _ u = L N .cndot. sin
.omega. x _ l = x _ r - L N .cndot.cos .omega. y _ l = - L N
.cndot.sin .omega. ; ##EQU00016##
[0069] wherein x.sub.u, y.sub.u is a coordinate of the midpoint of
the upper natural fracture entrance unit bodies in the global
coordinate system; x.sub.l, y.sub.l is a coordinate of the midpoint
of the lower natural fracture entrance unit bodies in the global
coordinate system; x.sub.r is an abscissa of the point where the
hydraulic fracture intersects the natural fracture in the global
coordinate system; L is a total length of hydraulic fracture, in; N
is the divided number of unit bodies of the hydraulic fracture;
.omega. is an angle between the hydraulic fracture and the natural
fracture, degree;
[0070] express the coordinates of the midpoint of the upper and
lower natural fracture entrance unit bodies in a local coordinate
system based on the midpoint of the hydraulic fracture unit body i
as:
{ x ui = ( x _ r + L N .cndot.cos .omega. - x _ i ) cos .omega. + (
L N .cndot.sin .omega. - y _ i ) sin .omega. y ui = - ( x _ r + L N
.cndot.cos .omega. - x _ i ) sin .omega. + ( L N .cndot. sin
.omega. - y _ i ) cos .omega. x li = ( x _ r - L N .cndot.cos
.omega. - x _ i ) cos .omega. - ( L N .cndot. sin .omega. + y _ i )
sin .omega. y li = - ( x _ r - L N .cndot.cos .omega. - x _ i ) sin
.omega. - ( L N .cndot. sin .omega. + y _ i ) cos .omega. ;
##EQU00017##
[0071] wherein x.sub.ui, y.sub.ui is a coordinate of the midpoint
of the upper natural fracture entrance unit bodies in the local
coordinate system; x.sub.li, y.sub.li is a coordinate of the
midpoint of the lower natural fracture entrance unit bodies in the
local coordinate system; x.sub.i, y.sub.i is a coordinate of the
unit body i of the hydraulic fracture in the global coordinate
system; x.sub.r an abscissa of the point where the hydraulic
fracture intersects the natural fracture in the global coordinate
system; L is a total length of hydraulic fracture, in; N is the
divided number of unit bodies of hydraulic fracture; .omega. is an
angle between the hydraulic fracture and the natural fracture,
degree; and
[0072] place the above formula into the following formula for
solution to obtain the shape coefficients of the upper and lower
natural fracture entrance unit bodies with respect to the unit body
i of the hydraulic fracture;
C ij = 2 G [ - f 1 + y ij ( f 2 sin 2 .gamma. ij - f 3 cos 2
.gamma. ij ) ] ; ##EQU00018## { f 1 = 1 4 .pi. ( 1 - v ) [ x ij - a
( x ij - a ) 2 + y ij 2 - x ij + a ( x ij + a ) 2 + y ij 2 ] f 2 =
1 4 .pi. ( 1 - v ) [ ( x ij - a ) 2 - y ij 2 [ ( x ij - a ) 2 + y
ij 2 ] 2 - ( x ij + a ) 2 - y ij 2 [ ( x ij + a ) 2 + y ij 2 ] 2 ]
f 3 = 2 y 4 .pi. ( 1 - v ) [ x ij - a [ ( x ij - a ) 2 + y ij 2 ] 2
- x ij + a [ ( x ij + a ) 2 + y ij 2 ] 2 ] ; ##EQU00018.2##
[0073] wherein .delta..sub.j.sup.k is a normal stress of the
fracture unit body j at the k-th time node, MPa; G is a shear
modulus of the stratum rock, MPa; .nu. is the Poisson's ratio of
the stratum rock, no factor; d.sub.ij is the distance between the
midpoints of the fracture unit i and the fracture unit j, in; H is
a height of the hydraulic fracture, in; .alpha., .beta. are
empirical coefficients, taken .alpha.=1, .beta.=2.3; i, j is the
number of the unit body of hydraulic fracture; W.sub.i.sup.0 is a
width of the i-th unit body of hydraulic fracture at the initial
time, in; C.sup.ij is a shape coefficient of the fracture unit j
with respect to the unit body i of the hydraulic fracture;
.gamma..sup.ij is a deflection angle of the fracture unit body i
with respect to the fracture unit body j; a is a half-length of the
fracture unit body, that is, L/2N, in; x.sub.ij, y.sub.ij is a
coordinate value of the midpoint of the fracture unit body j in the
local coordinate system based on the midpoint of the fracture unit
body i.
[0074] The present invention has the following advantages: the
present invention is reliable in principle, high in calculation
accuracy, and may accurately calculate the opening timing of
natural fracture during the temporary plugging turnaround
fracturing, further providing effective guidance for fracturing
design.
BRIEF DESCRIPTION OF THE DRAWINGS
[0075] Aspects of the present invention are best understood from
the following detailed description when read with the accompanying
figures. It is noted that, in accordance with the standard practice
in the industry, various features are not drawn to scale. In fact,
the dimensions of the various features may be arbitrarily increased
or reduced for clarity of discussion.
[0076] FIG. 1 is a flowchart of a method for acquiring an opening
timing of natural fracture under an in-slit temporary plugging
condition according to an embodiment of the present invention.
[0077] FIG. 2 is a block diagram of a device for acquiring an
opening timing of natural fracture under an in-slit temporary
plugging condition according to an embodiment of the present
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0078] The following invention provides many different embodiments,
or examples, for implementing different features of the provided
subject matter. Specific examples of components and arrangements
are described below to simplify the present invention. These are,
of course, merely examples and are not intended to be limiting. For
example, the stratum of a first feature over or on a second feature
in the description that follows may include embodiments in which
the first and second features are formed in direct contact, and may
also include embodiments in which additional features may be formed
between the first and second features, such that the first and
second features may not be in direct contact. In addition, the
present invention may repeat reference numerals and/or letters in
the various examples. This repetition is for the purpose of
simplicity and clarity and does not in itself dictate a
relationship between the various embodiments and/or configurations
discussed.
[0079] Further, spatially relative terms, such as "beneath,"
"below," "lower," "above," "upper" and the like, may be used herein
for ease of description to describe one element or feature's
relationship to another element(s) or feature(s) as illustrated in
the figures. The spatially relative terms are intended to encompass
different orientations of the device in use or operation in
addition to the orientation depicted in the figures. The apparatus
may be otherwise oriented (rotated 90 degrees or at other
orientations) and the spatially relative descriptors used herein
may likewise be interpreted accordingly.
[0080] Please refer to FIG. 1. FIG. 1 is a flowchart of a method
for acquiring an opening timing of natural fracture under an
in-slit temporary plugging condition according to an embodiment of
the present invention. As shown in FIG. 1, the method for acquiring
the opening timing of natural fracture under the in-slit temporary
plugging condition includes the following steps.
[0081] Step S10: Acquiring physical parameters of stratum according
to ae site geological data, and measuring a slit length L of a
hydraulic fracture.
[0082] Step S20: Dividing the hydraulic fracture into N unit bodies
of equal length and numbering them (N unit bodies of the hydraulic
fracture) sequentially, i.e., the length of each unit body being
L/N; and using an in-slit temporary plugging time as an initial
time t0, and dividing a total calculation time t into m time nodes
with the same interval, an interval time of the adjacent time nodes
being t/m.
[0083] Step S30: Calculating a width of each unit body in the
hydraulic fracture at the initial time according to the following
formula (1);
P 0 - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W i 0 ( j = 1 , 2 , N ) ; ( 1 )
##EQU00019##
[0084] wherein p.sup.0 is a fluid pressure in the hydraulic
fracture at the initial time t0, MPa; .sigma..sub.h is a minimum
horizontal principal stress of the stratum, MPa; G is a shear
modulus of the stratum rock, MPa; .nu. is the Poisson's ratio of
the stratum rock, no factor; L is a total length of the hydraulic
fracture, m; N is the divided number of unit bodies of the
hydraulic fracture; d.sub.ij is a distance between midpoints of the
fracture unit body i and the fracture unit body j, m; H is a height
of the hydraulic fracture, m; .alpha., .beta. are empirical
coefficients, taken .alpha.=1, .delta.=2.3; i, j is the number of
the unit body of the hydraulic fracture; W.sub.i.sup.0 is a width
of the i-th unit body of the hydraulic fracture at the initial
time, m.
[0085] Step S40: Calculating a fluid pressure in the hydraulic
fracture at the k-th time node, which specifically includes the
following sub-steps:
[0086] Sub-step S401: Calculating an estimated fluid pressure in
the hydraulic fracture at the k-th time node according to the
following formula (2);
{ p ^ k = p 0 ( k = 1 ) p ^ k = 1 . 2 5 p k - 1 ( k > 1 ) ; ( 2
) ##EQU00020##
[0087] wherein p.sup.0 is the fluid pressure in the hydraulic
fracture at the initial time, MPa; p.sup.k-1 is an actual fluid
pressure in the hydraulic fracture at the (k-1)-th time node;
{circumflex over (p)}.sup.k is an estimated fluid pressure in the
hydraulic fracture at the k-th time node, MPa.
[0088] Sub-step S402: Calculating an estimated width of each unit
body of the hydraulic fracture at the k-th time node according to
the estimated fluid pressure calculated above and the following
formula (3);
P ^ k - .sigma. h = i = 1 N G N .pi. L ( 1 - .upsilon. ) { 1 - d ij
.beta. [ d ij 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i +
1 - 1 2 j - 2 i + 1 ) W ^ i k ( j = 1 , 2 , N ) ; ( 3 )
##EQU00021##
[0089] wherein {circumflex over (p)}.sup.k is an estimated fluid
pressure in the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.h is a minimum horizontal principal stress of the
stratum, MPa; G is a shear modulus of the stratum rock, MPa; .nu.
is the Poisson's ratio of the stratum rock, no factor; L is a total
length of hydraulic fracture, in; N is the divided number of unit
bodies of the hydraulic fracture; d.sub.ij is the distance between
the midpoints of the fracture unit body i and the fracture unit
body j, in; H is a height of the hydraulic fracture, in; .alpha.,
.beta. are empirical coefficients, taken .alpha.=1, .beta.=2.3; i,
j is the number of the unit body of hydraulic fracture;
.sub.i.sup.k is an estimated width of each unit body of the
hydraulic fracture at the k-th time node, m.
[0090] Sub-step S403: Calculating an error a of the estimated width
by the following formula (4);
.alpha. = H L ( i = 1 N W ^ i k - i = 1 N W i k - 1 ) N Q .DELTA. t
; ( 4 ) ##EQU00022##
[0091] wherein .sub.i.sup.k is an estimated width of each unit of
the hydraulic fracture at the k-th time node, m; W.sub.i.sup.k-1 is
an estimated width of each unit of the hydraulic fracture at the
(k-1)-th time node, m; H is the height of the hydraulic fracture,
m; L is the total length of the hydraulic fracture, m; N is the
divided number of unit bodies of the hydraulic fracture; Q is the
pumping displacement of fracturing fluid after in-slit temporary
plugging, m3/s; .DELTA.t is an interval time of adjacent time
nodes, s; i is the number of unit bodies of the hydraulic fracture;
.alpha. is the error.
[0092] Sub-step S404: Setting solution accuracy .epsilon., and
comparing the error a obtained above with the solution accuracy
.epsilon..
[0093] The solution accuracy is generally 5%, and the solution
accuracy depends mainly on the accuracy of the results in the
solution process; the closer the fracture width is to the true
value, the smaller the error a is; and if the solution accuracy
value is not satisfied by the error a obtained, iterating is
required to be continued.
[0094] If .alpha..ltoreq..epsilon., {circumflex over (P)}.sup.k and
.sub.i.sup.k calculated in step S402 and step S403 are respectively
the fluid pressure in the hydraulic fracture at the k-th time node
and the width of each unit body; if .alpha.>.epsilon., then
re-estimating the fluid pressure using the following formula (5)
and repeating steps S402-S404 until .alpha..ltoreq..epsilon. is
satisfied;
{ P ^ k = P ^ k 1 + 10 .alpha. ( .alpha. > 0 ) P ^ k = ( 1 - 10
.alpha. ) P ^ k ( .alpha. < 0 ) ; ( 5 ) ##EQU00023##
[0095] wherein .epsilon. is a solution accuracy; {circumflex over
(P)}.sup.k is an estimated fluid pressure in the hydraulic fracture
at the k-th time node, MPa; .alpha. is an error.
[0096] Step S50: Calculating a closed pressure at the entrance of
the natural fracture on the upper and lower sides of the hydraulic
fracture at the k-th time node by the following formula (6);
{ .sigma. u k = ( .sigma. H + .sigma. h 2 - .sigma. H - .sigma. h 2
cos 2 .omega. ) + i = 1 N { 1 - d u i .beta. [ d u i 2 + ( H /
.alpha. ) 2 ] .beta. / 2 } C ui W i k .sigma. l k = ( .sigma. H +
.sigma. h 2 - .sigma. H - .sigma. h 2 cos 2 .omega. ) + i = 1 N { 1
- d l i .beta. [ d l i 2 + ( H / .alpha. ) 2 ] .beta. / 2 } C l i W
i k ; ( 6 ) ##EQU00024##
[0097] wherein .sigma..sub.u.sup.k is the closed pressure at the
entrance of the natural fracture on the upper side of the hydraulic
fracture at the k-th time node, MPa; .sigma..sub.l.sup.k is the
closed pressure at the entrance of the natural fracture on the
lower side of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.H is a maximum horizontal principal stress of the
stratum, MPa; .sigma..sub.h is a minimum horizontal principal
stress of the stratum, MPa; .omega. is an angle between the
hydraulic fracture and the natural fracture; d.sub.ui is a distance
between the midpoint of the upper natural fracture entrance unit
and the midpoint of the hydraulic fracture unit i, d.sub.li is a
distance between the midpoint of the lower natural fracture
entrance unit and the midpoint of the hydraulic fracture unit i, H
is a height of the hydraulic fracture, in; .alpha., .beta. is an
empirical coefficient, taken .alpha.=1, .beta.=2.3; W.sub.i.sup.k
is a width of the unit body i of the hydraulic fracture at the k-th
time node, m; C.sup.ui, C.sup.li are the shape coefficients of the
upper and lower natural fracture entrance unit bodies with respect
to the unit body i of the hydraulic fracture, respectively.
[0098] The shape coefficients of the upper and lower natural
fracture entrance unit bodies with respect to the unit body i of
the hydraulic fracture are obtained by the following sub-steps.
[0099] Sub-step S501: Establishing a global coordinate system with
a center point of the first hydraulic fracture unit body as an
origin, a length direction of the hydraulic fracture as an X-axis,
a direction passing through the origin and perpendicular to the
wall surface of the hydraulic fracture as a Y-axis.
[0100] Sub-step S502: Expressing the coordinates of the midpoint of
the upper and lower natural fracture entrance unit bodies in the
global coordinate system as:
{ x _ u = x _ r + L N .cndot.cos .omega. y _ u = L N .cndot. sin
.omega. x _ l = x _ r - L N .cndot.cos .omega. y _ l = - L N
.cndot.sin .omega. ; ##EQU00025##
[0101] wherein x.sub.u, y.sub.u is a coordinate of the midpoint of
the upper natural fracture entrance unit bodies in the global
coordinate system; x.sub.l, y.sub.l is a coordinate of the midpoint
of the lower natural fracture entrance unit bodies in the global
coordinate system; x.sub.r an abscissa of the point where the
hydraulic fracture intersects the natural fracture in the global
coordinate system; L is a total length of hydraulic fracture, m; N
is the divided number of unit bodies of the hydraulic fracture;
.omega. is an angle between the hydraulic fracture and the natural
fracture, degree.
[0102] Sub-step S503: Expressing the coordinates of the midpoint of
the upper and lower natural fracture entrance unit bodies in a
local coordinate system based on the midpoint of the hydraulic
fracture unit body i as the following formula (7):
{ x ui = ( x _ r + L N .cndot.cos .omega. - x _ i ) cos .omega. + (
L N .cndot.sin .omega. - y _ i ) sin .omega. y ui = - ( x _ r + L N
.cndot.cos .omega. - x _ i ) sin .omega. + ( L N .cndot. sin
.omega. - y _ i ) cos .omega. x li = ( x _ r - L N .cndot.cos
.omega. - x _ i ) cos .omega. - ( L N .cndot. sin .omega. + y _ i )
sin .omega. y li = - ( x _ r - L N .cndot.cos .omega. - x _ i ) sin
.omega. - ( L N .cndot. sin .omega. + y _ i ) cos .omega. ; ( 7 )
##EQU00026##
[0103] wherein x.sub.ui, y.sub.ui is a coordinate of the midpoint
of the upper natural fracture entrance unit bodies in the local
coordinate system; x.sub.li, y.sub.li is a coordinate of the
midpoint of the lower natural fracture entrance unit bodies in the
local coordinate system; x.sub.i, y.sub.i is a coordinate of the
unit body i of the hydraulic fracture in the global coordinate
system; x.sub.r an abscissa of the point where the hydraulic
fracture intersects the natural fracture in the global coordinate
system; L is a total length of hydraulic fracture, in; N is the
divided number of unit bodies of hydraulic fracture; .omega. is an
angle between the hydraulic fracture and the natural fracture,
degree.
[0104] Sub-step S504: Placing the obtained coordinates of the
midpoint of the upper and lower natural fracture entrance unit
bodies in a local coordinate system in formula (7) in sub-step
(S503) into the following formula (8) for solution to obtain the
shape coefficients of the upper and lower natural fracture entrance
unit bodies with respect to the unit body i of the hydraulic
fracture;
C ij = 2 G [ - f 1 + y ij ( f 2 sin 2 .gamma. ij - f 3 cos 2
.gamma. ij ) ] ; { f 1 = 1 4 .pi. ( 1 - v ) [ x ij - a ( x ij - a )
2 + y ij 2 - x ij + a ( x ij + a ) 2 + y ij 2 ] f 2 = 1 4 .pi. ( 1
- v ) [ ( x ij - a ) 2 - y ij 2 [ ( x ij - a ) 2 + y ij 2 ] 2 - ( x
ij + a ) 2 - y ij 2 [ ( x ij + a ) 2 + y ij 2 ] 2 ] f 3 = 2 y 4
.pi. ( 1 - v ) [ x ij - a [ ( x ij - a ) 2 + y ij 2 ] 2 - x ij + a
[ ( x ij + a ) 2 + y ij 2 ] 2 ] ; ( 8 ) ##EQU00027##
[0105] wherein .delta..sub.j.sup.k is a normal stress of the
fracture unit body j at the k-th time node, MPa; G is a shear
modulus of the stratum rock, MPa; .nu. is the Poisson's ratio of
the stratum rock, no factor; d.sub.ij is the distance between the
midpoints of the fracture unit i and the fracture unit j, in; H is
a height of the hydraulic fracture, in; .alpha., .beta. are
empirical coefficients, taken .alpha.=1, .beta.=2.3; i, j is the
number of the unit body of hydraulic fracture; W.sub.i.sup.0 is a
width of the i-th unit body of hydraulic fracture at the initial
time, in; C.sup.ij is a shape coefficient of the fracture unit j
with respect to the unit body i of the hydraulic fracture;
.gamma..sup.ij is a deflection angle of the fracture unit body i
with respect to the fracture unit body j; a is a half-length of the
fracture unit body, that is, L/2N, m; x.sub.ij, y.sub.ij is a
coordinate value of the midpoint of the fracture unit body j in the
local coordinate system based on the midpoint of the fracture unit
body i.
[0106] Step S60: Determining whether the natural fracture is opened
by the following determining criteria based on the calculation
results of the above steps S40 and S50.
[0107] If yes, the time t.sub.0+kt/m corresponding to the time node
k is the opening time of the natural fracture;
[0108] if not, then letting k=k+1, repeating steps S40-S50 until
the natural fracture is opened or the temporary plugging section
fails.
[0109] The determining criteria include: [0110] if
P.sup.k>.sigma..sub.u.sup.k, the upper side of the natural
fracture is opened; [0111] if P.sup.k<.sigma..sub.l.sup.k, the
lower side of the natural fracture is opened; [0112] if
P.sup.k>P.sub.c+p.sub.r, the temporary plugging section
fails;
[0113] wherein P.sup.k is a fluid pressure in the hydraulic
fracture at the k-th time node; .sigma..sub.u.sup.k is the closed
pressure at the entrance of the natural fracture on the upper side
of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.l.sup.k is the closed pressure at the entrance of the
natural fracture on the lower side of the hydraulic fracture at the
k-th time node, MPa; P.sub.c is a plugging strength of the
temporary plugging section, MPa; P.sub.r is a fluid pressure of the
stratum, MPa.
[0114] The calculation formula for the width of each unit body in
the hydraulic fracture at the initial time in the present
embodiment is obtained according to the following steps:
[0115] 1) The relationship between the width of each unit body of
the hydraulic fracture and its internal fluid pressure at initial
time may be expressed as the following formulas (9), (10),
(11):
.delta. j k = i = 1 N { 1 - d ij .beta. [ d ij 2 + ( H / .alpha. )
2 ] .beta. / 2 } C ij W i 0 ( j = 1 , 2 , N ) ; ( 9 ) C ij = 2 G [
- f 1 + y ij ( f 2 sin 2 .gamma. ij - f 3 cos 2 .gamma. ij ) ] ; (
10 ) { f 1 = 1 4 .pi. ( 1 - v ) [ x ij - a ( x ij - a ) 2 + y ij 2
- x ij + a ( x ij + a ) 2 + y ij 2 ] f 2 = 1 4 .pi. ( 1 - v ) [ ( x
ij - a ) 2 - y ij 2 [ ( x ij - a ) 2 + y ij 2 ] 2 - ( x ij + a ) 2
- y ij 2 [ ( x ij + a ) 2 + y ij 2 ] 2 ] f 3 = 2 y 4 .pi. ( 1 - v )
[ x ij - a [ ( x ij - a ) 2 + y ij 2 ] 2 - x ij + a [ ( x ij + a )
2 + y ij 2 ] 2 ] ; ( 11 ) ##EQU00028##
[0116] wherein .delta..sub.j.sup.k is a normal stress of the
fracture unit body j at the k-th time node, MPa; G is a shear
modulus of the stratum rock, MPa; .nu. is the Poisson's ratio of
the stratum rock, no factor; d.sub.ij is the distance between the
midpoints of the fracture unit body i and the fracture unit body j,
in; H is a height of the hydraulic fracture, in; .alpha., .beta.
are empirical coefficients, taken .alpha.=1, .beta.=2.3; i, j is
the number of the unit body of hydraulic fracture; W.sub.i.sup.0 is
a width of the i-th unit body of hydraulic fracture at the initial
time, in; C.sup.ij is a shape coefficient of the fracture unit body
j with respect to the unit body i of the hydraulic fracture;
.gamma..sup.ij is a deflection angle of the fracture unit body i
with respect to the fracture unit body j; a is a half-length of the
fracture unit body (i.e., L/2N), m; x.sub.ij, y.sub.ij is a
coordinate value of the midpoint of the fracture unit body j in the
local coordinate system based on the midpoint of the fracture unit
body i; the local coordinate system taking a midpoint of the
fracture unit body i as the origin, a length direction of the
fracture as the X axis, and a direction perpendicular to the
fracture wall surface as the Y axis.
[0117] 2) Since the hydraulic fracture tends to extend
perpendicular to the direction of the minimum horizontal principal
stress, and the fracture unit body j may be externally subjected to
the minimum horizontal principal stress and may be subjected to
fluid pressure inside, the normal stress received may be expressed
as the following formula (12):
.delta..sub.n.sup.k=P.sup.0-.sigma..sub.h (12);
[0118] wherein p.sup.0 is a fluid pressure in the hydraulic
fracture at the initial time, determined by the actual pumping
process of the temporary plugging agent, MPa; .sigma..sub.h is a
minimum horizontal principal stress of the stratum, MPa.
[0119] 3) A global two-dimensional Cartesian coordinate system is
established with a center point of the first hydraulic fracture
unit as an origin, a length direction of the hydraulic fracture as
an X-axis, a direction passing through the origin and perpendicular
to the wall surface of the hydraulic fracture as a Y-axis; based on
this coordinate system, the coordinate of the midpoint of the i-th
hydraulic fracture unit body may be expressed as the following
formula (13):
{ x _ i = ( i - 1 ) L N y _ i = 0 ; ( 13 ) ##EQU00029##
[0120] wherein x.sub.i, y.sub.i is a coordinate value of the
fracture unit body i in the global coordinate system; i is a number
of the fracture unit body; L is a total length of hydraulic
fracture, m; N is the divided number of unit bodies of the
hydraulic fracture.
[0121] 4) According to the law between the local coordinates and
the global coordinates, the coordinate of the midpoint of the
fracture unit body j in the local coordinate system based on the
midpoint of the fracture unit body i may be expressed as the
following formula (14):
{ x ij = ( j - 1 ) L N - ( i - 1 ) L N = ( j - i ) L N y ij = 0 ; (
14 ) ##EQU00030##
[0122] wherein x.sub.ij, y.sub.ij is a coordinate value of the
midpoint of the fracture unit body j in the local coordinate system
based on the midpoint of the fracture unit body i; i, j is a number
of the fracture unit body; L is a total length of hydraulic
fracture, m; N is the divided number of unit bodies of the
hydraulic fracture.
[0123] 5) Substituting formula (12) into formula (9), and
substituting formula (14) into formula (10) and formula (11), which
may obtain a relationship formula (15) between the width
W.sub.i.sup.0 of each unit body of the hydraulic fracture and its
internal fluid pressure at initial time as follow:
P 0 - .sigma. h = i = 1 N G N .pi. L ( 1 - v ) { 1 - d i j .beta. [
d i j 2 + ( H / .alpha. ) 2 ] .beta. / 2 } ( 1 2 j - 2 i + 1 - 1 2
j - 2 i + 1 ) W i 0 ( j = 1 , 2 , N ) . ( 15 ) ##EQU00031##
[0124] In the present embodiment, the calculation formula for the
closed pressure at the entrance of the natural fracture on the
upper and lower sides of the hydraulic fracture at the k-th time
node is obtained by the following steps:
[0125] First, the upper and lower natural fracture of the hydraulic
fracture refer to the two wings of the same natural fracture, the
hydraulic fracture generally passes through the middle part of the
natural fracture to divide the original continuous natural fracture
into two, and the two wings of the natural fracture are located on
both sides of the hydraulic fracture (here distinguished by the
upper side and the lower side). When the hydraulic fracture is
orthogonal to the natural fracture, the natural fracture on both
sides may be simultaneously opened according to the symmetry; when
the hydraulic fracture is not orthogonal to the natural fracture,
the natural fracture on both sides have a sequence of opening, so
in determining the opening timing of natural fracture after
temporary plugging, it is also necessary to simultaneously
determine which side of the natural fracture is preferentially
opened, which is very important for determining the opening timing
of natural fracture.
[0126] Similarly, in order to ensure the uniformity of calculation
and the need to adapt to numerical solutions, the natural fracture
on both sides may also be considered to consist of multiple unit
bodies of length L/N, but the calculation process is only performed
for the first unit body at the entrance to the natural fracture on
both sides. In addition, there are a large number of natural
fracture around the hydraulic fracture. Here, the case of existing
only one natural fracture is used as an example to illustrate the
solution process. When there are multiple natural fracture, the
overall calculation method is similar.
[0127] Second, the closed pressure of natural fracture refers to
the force that forces the natural fracture to remain closed, and
may be divided into two parts, namely, a stratum normal stress and
a hydraulic fracture induced stress, wherein the stratum normal
stress may be expressed as the following formula (16):
.PHI. n k = .sigma. H + .sigma. h 2 - .sigma. H - .sigma. h 2 cos 2
.omega. ; ( 16 ) ##EQU00032##
[0128] wherein .phi..sub.n.sup.k a normal stress of the stratum
acting on the wall surface of the natural fracture, MPa; the force
of the stratum acting on natural fracture may be divided into a
normal stress and a shear stress, wherein only the normal stress
may force the natural fracture to close. [0129]
.sigma..sub.H--Maximum horizontal principal stress of stratum, MPa;
[0130] .sigma..sub.h--Minimum horizontal principal stress of
stratum, MPa; [0131] .omega.--Angle between the hydraulic fracture
and the natural fracture, degree.
[0132] The hydraulic fracture induced stress is still expressed by
the formula (15), and the formula (15) is superposed with the
formula (16) to obtain the following formula (17):
{ .sigma. u k = ( .sigma. H + .sigma. h 2 - .sigma. H - .sigma. h 2
cos 2 .omega. ) + i = 1 N { 1 - d u i .beta. [ d u i 2 + ( H /
.alpha. ) 2 ] .beta. / 2 } C m W i k .sigma. l k = ( .sigma. H +
.sigma. h 2 - .sigma. H - .sigma. h 2 cos 2 .omega. ) + i = 1 N { 1
- d l i .beta. [ d l i 2 + ( H / .alpha. ) 2 ] .beta. / 2 } C l i W
i k ; ( 17 ) ##EQU00033##
[0133] wherein .sigma..sub.u.sup.k is a closed pressure at the
natural fracture entrance on the upper side of the hydraulic
fracture at the k-th time node, MPa; .sigma..sub.l.sup.k is a
closed pressure at the natural fracture entrance on the lower side
of the hydraulic fracture at the k-th time node, MPa; .sigma..sub.H
is a maximum horizontal principal stress of the stratum, MPa;
.sigma..sub.h is a minimum horizontal principal stress of the
stratum, MPa; .omega. is an angle between the hydraulic fracture
and the natural fracture; d.sub.ui is a distance between the
midpoint of the upper natural fracture entrance unit and the
midpoint of the hydraulic fracture unit i, m; d.sub.li is a
distance between the midpoint of the lower natural fracture
entrance unit and the midpoint of the hydraulic fracture unit i, m;
H is a height of the hydraulic fracture, m; .alpha., .beta. is an
empirical coefficient, taken .alpha.=1, .beta.=2.3; W.sub.i.sup.k
is a width of the unit body i of the hydraulic fracture at the k-th
time node, m; C.sup.ui, C.sup.li are the shape coefficients of the
upper and lower natural fracture entrance unit bodies with respect
to the unit body i of the hydraulic fracture, respectively.
[0134] Please refer to FIG. 2. FIG. 2 is a block diagram of a
device 200 for acquiring an opening timing of natural fracture
under an in-slit temporary plugging condition according to an
embodiment of the present invention. As shown in FIG. 2, the device
200 includes an acquisition module 210, a division module 220, a
width calculation module 230, a fluid pressure calculation module
240, a closed pressure calculation module 250, and a determination
module 260. The acquisition module 210 is configured to acquire
physical parameters of stratum according to site geological data,
and measure a slit length L of a hydraulic fracture. The division
module 220 is configured to divide the hydraulic fracture into N
unit bodies of equal length and number them sequentially, wherein
the length of each unit body being L/N; and use an in-slit
temporary plugging time as an initial time t0, and divide a total
calculation time t into m time nodes with equal interval, wherein
an interval time of the adjacent time nodes being t/m. The width
calculation module 230 is configured to calculate a width of each
unit body in the hydraulic fracture at the initial time. The fluid
pressure calculation module 240 is configured to calculate a fluid
pressure in the hydraulic fracture at the k-th time node. The
closed pressure calculation module 250 is configured to calculate a
closed pressure at an entrance of the natural fracture on an upper
side and a lower side of the hydraulic fracture at the k-th time
node. The determination module 260 is configured to determine
whether the natural fracture is opened by a determining criteria
based on calculation results of the fluid pressure calculation
module and the closed pressure calculation module. If yes, the time
t.sub.0+kt/m corresponding to the time node k is the opening time
of the natural fracture; if not, then letting k=k+1, repeating
steps S40-S50 until the natural fracture is opened or the temporary
plugging section fails.
[0135] The determining criteria include: [0136] if
P.sup.k>.sigma..sub.u.sup.k, the upper side of the natural
fracture is opened; [0137] if P.sup.k<.sigma..sub.l.sup.k, the
lower side of the natural fracture is opened; [0138] if
P.sup.k>P.sub.c+P.sub.r, the temporary plugging section
fails;
[0139] wherein P.sup.k is a fluid pressure in the hydraulic
fracture at the k-th time node; .sigma..sub.u.sup.k is the closed
pressure at the entrance of the natural fracture on the upper side
of the hydraulic fracture at the k-th time node, MPa;
.sigma..sub.l.sup.k is the closed pressure at the entrance of the
natural fracture on the lower side of the hydraulic fracture at the
k-th time node, MPa; P.sub.c is a plugging strength of the
temporary plugging section, MPa; P.sub.r is a fluid pressure of the
stratum, MPa.
[0140] The beneficial effects of the present invention are as
follows: in the present invention, combined with the fractal
geometry theory, the fracture complexity coefficient of shale rocks
is redefined and calculated to accurately characterize the rock
fracture morphology, so that the characteristics of rock fracture
morphology may be correctly understood and the affecting factors of
fracture morphology may be analyzed.
[0141] By adopting the method for acquiring an opening timing of
natural fracture under an in-slit temporary plugging condition and
the device thereof of the present invention, the development of gas
(oil) reservoir layers of shale rocks can be improved, and the
reach range of production wells and the permeability of gas (oil)
reservoir layers can be increased. Therefore, gas (oil) production
of shale rocks can be improved, and production costs can be
reduced, so as to achieve commercial scale development.
[0142] The foregoing outlines features of several embodiments so
that those skilled in the art may better understand the aspects of
the present invention. Those skilled in the art should appreciate
that they may readily use the present invention as a basis for
designing or modifying other processes and structures for carrying
out the same purposes and/or achieving the same advantages of the
embodiments introduced herein. Those skilled in the art should also
realize that such equivalent constructions do not depart from the
spirit and scope of the present invention, and that they may make
various changes, substitutions, and alterations herein without
departing from the spirit and scope of the present invention.
* * * * *