Method for optimizing fracturing cluster spacing near deep shale gas fault

Abstract

Data is acquired. Next a characterization model of an inhomogeneous in-situ stress field is established, calculate a stress field near a pre-fractured fault and produce stress distribution maps (fig.2

Description

[0002] Deep shale gas is the main battlefield of building and scale production, and is an important direction of shale gas exploration and development at present. However, the shale experienced multi-stage tectonic movement, the uplift and denudation effect was obvious, the stratum strength anisotropy was strong, and the faults in the shale stratum were generally developed, which results in the inhomogeneous distribution of the in-situ stress field around the shale, the non-planar, asymmetric and irregular extension behavior of the hydraulic fracture, and then affects the SRV (stimulated reservoir volume). Therefore, under the inhomogeneous in-situ stress field, the appropriate cluster spacing design has important significance to enhance the distribution area of the deep shale pressure fracture network and improve the effect of the deep shale gas after reservoir pressure.

[0003] Some scholars at home and abroad have carried out a series of researches on the characterization of in-situ stress near faults and the design of horizontal well cluster spacing of the shale gas. In terms of in-situ stress characterization, Lin et al. found that the changes of in-situ stress and pore pressure would be affected by fault slip, and provided a pore elasticity calculation method, which could quantitatively predict the 3D in-situ stress and pore pressure of shale reservoirs with fault structure. NI, Wei et al. divided the faults into parallel faults and cross faults, and used the finite element method to simulate the in-situ stress under the two faults. In the cluster spacing design of shale gas horizontal well, Guo et al. found that when the cluster fracture extends, the middle fracture was squeezed and the opening was limited and the extension was insufficient, resulting in failure of sand adding to avoid such situation, the cluster spacing was qualitatively optimized. Liu et al. considered the change of the in-situ stress caused by multiple fractures, and formed the in-situ stress diverting area, which was regarded as the potential reservoir reconstruction area and then quantitatively optimized the cluster spacing.

[0004] In conclusion, the in-situ stress characterization, and the cluster spacing design of horizontal wells with shale gas near faults are more sufficient, but none of the above studies has further analyzed the influence of inhomogeneous in-situ stress field generated by faults on the propagation of pressure fracture network. None of the above cluster spacing designs has targeted reservoir SRV, a key parameter affecting shale fractured yield.

[0005] Therefore, it is urgently necessary to establish a method for optimizing fracturing cluster spacing near a deep shale gas fault, which will help to better deploy the horizontal well position, optimize the interval of perforation clusters, and improve the fracturing effect of shale reservoir near faults. SUMMARY

[0006] In order to overcome the problems of the prior art, the present invention provides a method for optimizing fracturing cluster spacing near a deep shale gas fault.

[0007] The technical solution provided by the present invention for solving the above-mentioned technical problem is: a method for optimizing fracturing cluster spacing near a deep shale gas fault, which includes the steps of:

[0008] Step 1: acquiring fault parameters, reservoir geological parameters, fracturing construction parameters, natural fracture parameters and model grid parameters;

[0009] Step 2: establishing a characterization model of an inhomogeneous in-situ stress field near a deep shale gas fault, calculating an induced in-situ stress field generated by a hydraulic fracture by a displacement discontinuity method (DDM) based on an elastic mechanics theory model, calculating the induced in-situ stress by linear superposition of the original in-situ stress field and the fault induced in-situ stress field, then calculating the inhomogeneous in-situ stress field near the pre-fractured fault by a superposition principle, and drawing the in-situ stress deflection angle distribution map and the horizontal in-situ stress difference distribution map near the fault respectively;

[0010] Step 3: establishing a hydraulic fracture network expansion model of horizontal well subsection multi-cluster fracturing near a deep shale gas fault, and calculating hydraulic fracture extension parameters, in-fracture pressure, filtration, and fracture location parameters of each cluster combining initial and boundary conditions;

[0011] Step 4: taking the current reservoir pressure field distribution as an initial condition, taking the in-fracture pressure calculated in the hydraulic fracture extension part and the fracture position parameters as internal boundary conditions, and solving the reservoir pressure field near the fault using a finite difference method;

[0012] Step 5: according to a Warpinski two-dimensional criterion, establishing a failure criterion for determining a natural fracture of any occurrence using a tensor calculation method, and respectively determining grid elements of natural fracture positions of tensile failure and shear failure;

[0013] Step 6: calculating the sum of the reservoir shear failure reconstruction volume and the tensile failure reconstruction volume through spatial numerical integration according to the grid element of the natural fracture position of the tensile failure and the shear failure to obtain an SRV (stimulated reservoir volume);

[0014] Step 7: repeating steps 4 to 6 until a set time step is reached, and obtaining a hydraulic fracture extension map and an SRV of each cluster at a perforation by numerical simulation; and

[0015] Step 8: determining the optimal perforation cluster spacing by simulating the dynamic expansion of the SRV near the inhomogeneous in-situ stress field with an objective of maximizing the SRV, and drawing a graph of the variation of the SRV with the cluster spacing.

[0016] In a further technical solution, the fault parameters include a fault type, a fault length, a fault height, a fault tilt angle, a fault strike, and a fault displacement;

[0017] the reservoir geological parameters include a stratum maximum horizontal principal in-situ stress, a stratum minimum horizontal principal in-situ stress, a stratum horizontal in-situ stress difference, a stratum rock fracturing toughness, a stratum rock Young’s modulus, and a stratum rock Poisson’s ratio;

[0018] the fracturing construction parameters include a fracture displacement, a fracturing fluid amount, a fracturing time, a fracturing fluid viscosity, a fracturing leak off factor, a fracturing fluid density, an average concentration in fracturing injection propping agent, the number of perforation clusters, a single cluster perforation number, a perforation hole diameter and a cluster spacing;

[0019] the natural fracture parameters include a natural fracture average tilt angle, a natural fracture average approximation angle, a natural fracture average length, and a natural fracture average height;

[0020] the model grid parameters include model x-direction boundaries, y-direction boundaries, and z-direction boundaries.

[0021] In a further technical solution, the characterization model of the inhomogeneous in-situ stress field near a deep shale gas fault includes an equation for calculating the induced

[0022]

[0023]

[0024]

[0025]

[0026] in-situ stress component and an equation for calculating the inhomogeneous in-situ stress field near the pre-fractured fault; wherein the equation for calculating the induced in-situ stress component is: = , + + + 2^(1 - v) +        [2e2F3 - 2egFi + ^F, - gF6)] 2^(1 - v) ^yy = 2^-v) + ^2 ” g2~ + GD - -......................-..................1.......................7 [2g2F3 + 2egF4 + £(eF - gF6)] 2^(1- v) Ao- = GD" £(gF6 - eF.) +  GD' [R + £(gF. + eF6)] ” 2^(l-v) 2^(l-v) Act,, = v(Aa + Act,,) wherein Aaxx, Ao\y, Acrzz and Aaxy respectively represent the fault-induced in-situ stress component, MPa; G represents the shear modulus of the reservoir rock. Pa; v represents Poisson’s ratio of reservoir rocks, dimensionless; Dn and / A represent a normal fault distance and tangential fault displacement of fault respectively, m; ^represents a value of y in a global coordinate system converted into a local coordinate system; e and g are the cosine values of an included angle between a 7 axis of the local coordinate system and an x-axis and y-axis of the global coordinate system, respectively; and Fk represents a partial derivative equation of Papkovitch function, {3-6};

[0028] the equation for calculating the in-situ stress field near the pre-fractured fault is: ^xx ^xz + Act ............ XX As’+Acr^ 0029] ^yy — yx (j^ + Act yy yy yZ &ZX &zz ct^ + Act zx xz (°) ct^ + Act zz zz

[0030] wherein aFF (yFF cGF (?xFF VyFF and represent the original in-situ stress value component, Pa; Oxx, oyy, azz, oxy, oyz, and n- represent the current in-situ stress value component, Pa.

[0031] In a further technical solution, the fracture network extension model of the horizontal well subsection multi-cluster fracturing hydraulic fracture near the deep shale gas fault includes a material balance equation, an in-fracture flow equation, a fracture opening equation, a fracture height equation, a fracture diverting equation, a fracture flow distribution equation, a fracture extension boundary condition, and an initial condition equation;

[0032] wherein the material balance equation is: dqi (s, t) 2C^ (5)      (5, t)

[0033] --------= . +-------h^s) os     yj t - t(s)      Ot

[0034] qy = t=l

[0035] wherein #f represents an in-fracture flow, m3 / s; I represents time, s; Af represents a height of the fracture, m; C9f represents an opening of the fracture, m; Cl represents a leak off factor of an injected fracturing fluid, m / s05; 1(5) represents the time at which the fracturing fluid begins to drain at a position along a length direction of the fracture, s; N represents the number of hydraulic fracture; qj represents a total flow rate of fracturing fluid injection, m3 / s; and qi represents the flow rate obtained from the distribution of the ith fracture, m3 / s;

[0036] wherein the in-fracture flow equation is:

[0038] wherein pt represents a fluid pressure within the fracture, Pa; p represents a viscosity of fluid in the fracture, Pa s; and q\ represents a leak off rate, m / s;

[0039] wherein the fracture opening equation is:

[0040] (cr,), = X (M„ )9 (U, ) + X (Mm )ff (Un) j=i                      J=l

[0041]      ). = £(M,„ )„ fA ), + £ (),, ('A.), J=l ' ' j=l

[0042] ® / C)=(C),|Se,

[0043] wherein A represents a total number of discrete elements of the fracture; i and j represent fracture units, with a value of 1-A; (4^)., represents a tangential in-situ stress component on an i-unit caused by the j-unit tangential displacement discontinuity, (Mit) / ) represents a tangential in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity, (Mn)y represents a normal in-situ stress component on the i-unit caused by the j-unit tangential displacement discontinuity, and (Mn)j represents a normal in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity; (ot); and (an)? respectively represent the shear in-situ stress and normal in-situ stress of the unit i in a local coordinate system, Pa; (Ut)j and (Un)j respectively represent tangential strain and normal strain in the local coordinate system, m; (Un), i represents a normal offset of the unit i, m; and 5 represents a fracture length direction coordinate, m;

[0044] wherein the fracture height equation is: 2

[0045] ^=- (-------) 7t — cy i ri close

[0046] wherein (7ciOSe represents closing in-situ stress acting on a fracture wall, Pa; Kic represents fracturing toughness of a reservoir rock, Pa / m05; wherein the fracture diverting equation is: sin +   (3 cos -1) = 0

[0047]

[0048]

[0049]

[0050]

[0051] wherein a represents a half-length of a discrete fracture unit, m; 0hf represents a hydraulic fracture extension diverting angle, °;

[0052] wherein the fracture flow distribution equation is:

[0053] Ph   Ph,I ”1” Ps.l

[0054] wherein / represents each cluster number; k represents a horizontal section number; ph represents a heel end pressure of a horizontal well, Pa; p^,i represents the fracturing pressure at the l-th cluster fracture hole, Pa; psj represents the net pressure at a fracture of the first cluster of fractures, Pa; Apr,k represents a flow pressure drop of the kth horizontal section, Pa; Ap[V,i represents a frictional pressure drop at the 1th cluster fracture hole;

[0055] wherein the equation for the fracture extension boundary conditions and the initial conditions is:

[0056] <s=F ^"close s=L{

[0057] wherein Lf represents a hydraulic fracture length, m.

[0058] In a further technical solution, the solving equation in step four includes a continuity equation and an equation for the equivalent permeability after natural fracture failure;

[0059] wherein the continuity equation is: 6 dp A d ( dp\ dp

[0060] — kx(x,y,t)^~ +— ky(x,y,t)-f = p0Ct — dx y dx y dy y dy y dt

[0061] wherein (p represents porosity, dimensionless; p represents fluid pressure, MPa; Ct represents reservoir comprehensive compressibility, MPa’1; kx and ky represent permeability in the x and y directions, respectively, D;

[0062] wherein the equation for the equivalent permeability after natural fracture failure is:

[0063]

[0064] kx (x, y, / ) = sin2 0 • kDF + kc

[0065] ky (x, y, t) = cos 0 • kDF + kc

[0066] wherein Ztf represents a spacing of natural fractures, m; con represents opening of the natural fracture, m; and kc represents initial permeability, D

[0067] In a further technical solution, the failure criteria for determining any occurrence of a natural fracture includes a unit normal vector of the natural fracture, a normal in-situ stress on a surface of the natural fracture, a shear in-situ stress on a surface of the natural fracture, a determination equation for a tensile failure of the natural fracture and a determination equation for a shear failure of the natural fracture;

[0068] wherein the unit normal vector of the natural fracture is:

[0069] n = yijejj = \nx ny nz)

[0070] wherein the normal in-situ stress at a natural fracture face is: [0071 ] am = F-n = npiknk

[0072] wherein the shear in-situ stress at the natural fracture face is:

[0073] CT = jFF — (7   (7 = J(7 ,71,(7 ,n, — (7   (7 L J tt y nn nn y jk k jk k nn nn

[0074] wherein the determination equation of the natural fracture tensile failure is:

[0075] pf>(ynn+T^

[0076] wherein Ts represents the natural fracture tensile strength, Pa; and pf represents a fluid pressure within the fracture, MPa;

[0077] wherein the determination equation of the natural fracture shear failure is:

[0078] 7tt >Fnj + fmc • (7nn ~ pf )

[0079] wherein fmc represents a friction factor of natural fractures, dimensionless; Fnj represents cohesion of a natural fracture, MPa.

[0080] In a further technical solution, the equation for calculating the SRV in Step 6 is: [oo8i] ^ = 7 + ^,= X MO'AKO'MO

[0082] wherein Ktotai represents a total reservoir reconstruction volume, m3; K represents a reservoir shear failure reconstruction volume, m3; Kt represents a reservoir tensile failure reconstruction volume, m3; es represents a grid element of the shear failure, £t represents the grid element of the tensile failure; Ax(e), Aj(e) an Az(e) represent a side length of the grid element in the x, y, and z directions, m.

[0083] In a further aspect, the hydraulic fracture extension parameters include a fracture extension length, a fracture extension height, a fracture opening, in-fracture pressure and an in-fracture flow.

[0084] In a further technical solution, the hydraulic fracture extension parameter obtained in step 7 converges with the hydraulic fracture extension parameter obtained in the previous step; wherein the fracture opening is a fracture width, and if the calculated fracture width does not converge, then the pressure in the fracture is changed to perform iterative calculation until the fracture width converges; if the calculated in-fracture flow rate does not converge, then the fracture length is changed to carry out iterative calculation until the in-fracture flow rate converges; if the calculated leak off does not converge, the in-fracture pressure is changed for iterative calculation until the leak off converges.

[0085] The present invention has the following advantageous effects:

[0086] 1. the method is targeted at the mechanical characteristics of shale reservoir near faults, a characterization model of inhomogeneous in-situ stress field near a deep shale gas fault, a hydraulic fracture network expansion model of multi-cluster fracturing in horizontal wells near a deep shale gas fault, and a numerical calculation model of SRV near a deep shale gas fault are established, and thus a method for optimizing fracturing cluster spacing near a deep shale gas fault is provided;

[0087] 2. due to the inhomogeneous distribution of in-situ stress near deep shale reservoir faults, the hydraulic fractures may have non-planar, asymmetric and irregular extension behavior, and the influence behavior of cluster spacing on the SRV of shale gas reservoir pressure in horizontal well sub-cluster fracturing is comprehensively considered. An ultimate goal of cluster spacing design is to maximize fractured yield. Therefore, according to the inhomogeneous distribution of in-situ stress near deep shale reservoir faults, the hydraulic fracture network expansion model can be established, the SRV can be calculated numerically, the SRV is taken as the optimization objective, the cluster spacing can be optimized to solve the problem of optimizing the horizontal well fracturing cluster spacing near the lack of a deep shale gas fault. BRIEF DESCRIPTION OF DRAWINGS

[0088] FIG. 1A and FIG. IB is a computational flow diagram according to the present invention;

[0089] FIG. 2 is a graph of the in-situ stress deflection angle distribution near a deep shale gas faults;

[0090] FIG. 3 is a graph of horizontal in-situ stress difference distribution near a deep shale gas fault;

[0091] FIG. 4 is a graph of the inhomogeneous in-situ stress field distribution near a deep shale gas fault;

[0092] FIG. 5 is a graph of the fracture network spread at a perforation cluster spacing of 5 m;

[0093] FIG. 6 is a graph of the fracture network spread at a perforation cluster spacing of 7m;

[0094] FIG. 7 is a graph of the fracture network spread at a perforation cluster spacing of 8m;

[0095] FIG. 8 is a graph of SRV (stimulated reservoir volume) as a function of cluster spacing. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0096] The technical solutions of the present invention will be described clearly and completely with reference to the drawings, and it should be apparent that the described embodiments are some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by a person of ordinary skill in the art without inventive effort fall within the scope of the present invention.

[0097] A method for optimizing fracturing cluster spacing near a deep shale gas fault according to the present invention includes the steps of:

[0098] Step 1: acquiring fault parameters, reservoir geological parameters, fracturing construction parameters, natural fracture parameters and model grid parameters;

[0099] wherein the fault parameters include a fault type, a fault length, a fault height, a fault tilt angle, a fault strike, and a fault displacement;

[00100] the reservoir geological parameters include a stratum maximum horizontal principal in-situ stress, a stratum minimum horizontal principal in-situ stress, a stratum horizontal in-situ stress difference, a stratum rock fracturing toughness, a stratum rock Young’s modulus and a stratum rock Poisson’s ratio;

[00101] the fracturing construction parameters include a fracture displacement, a fracturing fluid amount, a fracturing time, a fracturing fluid viscosity, a fracturing leak off factor, a fracturing fluid density, an average concentration in fracturing injection propping agent, the number of perforation clusters, a single cluster perforation number, a perforation hole diameter and a cluster spacing;

[00102] the natural fracture parameters include a natural fracture average tilt angle, a natural fracture average approximation angle, a natural fracture average length, and a natural fracture average height, etc.;

[00103] the model grid parameters include model x-direction boundaries, y-direction boundaries, and z-direction boundaries;

[00104] Step 2: establishing a characterization model of an inhomogeneous in-situ stress field near a deep shale gas fault, calculating an induced in-situ stress field generated by a hydraulic fracture by a displacement discontinuity method (DDM) based on an elastic mechanics theory model, calculating the induced in-situ stress by linear superposition of the original in-situ stress field and the fault induced in-situ stress field, then calculating the inhomogeneous in-situ stress field near the pre-fractured fault by a superposition principle, and drawing the in-situ stress deflection angle distribution map and the horizontal in-situ stress difference distribution map near the fault respectively;

[00105] the characterization model of the inhomogeneous in-situ stress field near a deep shale gas fault includes an equation for calculating the induced in-situ stress component and an equation for calculating the inhomogeneous in-situ stress field near the pre-fractured fault;

[00106] wherein the equation for calculating the induced in-situ stress component is: = GF VegF, + (^2 - g>4 + C(g^ + 6¾ )1 2^-(1- v)

[00107] (1) + o \ [2^2F3 - 2egF4 + - gF.)] 2^(1-v) = —^-[2egF3 + (e2 - g2)F4 - ^(gF5 + eF6)] 2^-(1 - v)

[00108] (2) - . Z1 \ [2g2F3 + 2egF4 + ^(eF5 - gF6)] 2^-(1 - v) GD            GD

[00109] Ac =-......................-...............a....................;<(g^ -eF5) + -......................-.................*.......................-[F4 + C(gF5 + eF6)] (3) 2^-(1-v) 2^-(1 -v)

[00110] ^zz = + Aa^) (4)

[00111] wherein Ao^, Aoyy, Acrzz and respectively represent the fault-induced in-situ stress component, MPa; G represents the shear modulus of the reservoir rock, Pa; r represents Poisson’s ratio of reservoir rocks, dimensionless; and A represent a normal fault distance and tangential fault displacement of fault respectively, m; frepresents a value of y in a global coordinate system converted into a local coordinate system; e and g are the cosine values of an included angle between a £ axis of the local coordinate system and an x-axis and y-axis of the global coordinate system, respectively; and Ft represents a partial derivative equation of Papkovitch function, {3-6};

[00112] wherein the equation for calculating the pre-fractured inhomogeneous in-situ stress field is: (7^ ^xy ^xz cr^ + Acr^ (7^ + Act xz xz 00113] ^yx — y* ¢7^ +Acr yy yy yz (5) &zx zx (777 zz cr^ + (0) (7 a'"' + Aa77 zz zz

[00114] wherein ffyy^, Ox^°\ qJ'C and ffxz^ represent the original in-situ stress value component. Pa; <7XV, cr^, a--, o>, and oXz represent the current in-situ stress value component, Pa;

[00115] Step 3: establishing a hydraulic fracture network expansion model of horizontal well subsection multi-cluster fracturing near a deep shale gas fault, and calculating hydraulic fracture extension parameters, in-fracture pressure, filtration and fracture location parameters of each cluster combining initial and boundary conditions;

[00116] the fracture network extension model of the horizontal well subsection multi-cluster fracturing hydraulic fracture near the deep shale gas fault includes a material balance equation, an in-fracture flow equation, a fracture opening equation, a fracture height equation, a fracture diverting equation, a fracture flow distribution equation, a fracture extension boundary condition and an initial condition equation;

[00117] wherein the material balance equation is: 3¾ (s, t) 2CLht (s)      (s, t)

[00118] —---= I +------h^s) (6) & y / t - t(s) Ot N

[00119] q-, / =1

[00120] wherein qt represents an in-fracture flow, m3 / s; t represents time, s; hy represents a height of the fracture, m; cof represents an opening of the fracture, m; Cl represents a leak off factor of an injected fracturing fluid, m / s05; 1(5) represents the time at which the fracturing fluid begins to drain at a position along a length direction of the fracture, s; N represents the number of hydraulic fracture; qy represents a total flow rate of fracturing fluid injection, m3 / s; and qx represents the flow rate obtained from the distribution of the i* fracture, m3 / s;

[00121] wherein the in-fracture flow equation is:

[00122] (8)

[00123] wherein pt represents a fluid pressure within the fracture, Pa; u represents a viscosity of fluid in the fracture, Pa s; and qL represents a leak off rate, m / s;

[00124] wherein the fracture opening equation is: 7=1 7=1

[00125]

[00126]

[00127] (ff»). =2(^).,(^), +Z(K.)„^ (10) 7=1 ' ' 7=1

[00128] wherein A represents a total number of discrete elements of the fracture; i and / represent fracture units, with a value of I-A; (Mt)y represents a tangential in-situ stress component on an i-unit caused by the j-unit tangential displacement discontinuity, (Mit)y represents a tangential in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity, (Mn)y represents a normal in-situ stress component on the i-unit caused by the j-unit tangential displacement discontinuity, and (Mnjj represents a normal in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity; (gi)> and (On): respectively represent the shear in-situ stress and normal in-situ stress of the unit i in a local coordinate system, Pa; (Ut)j and (Un), respectively represent tangential strain and normal strain in the local coordinate system, m; (Un), i represents a normal offset of the unit i, m; and 5 represents a fracture length direction coordinate, m;

[00129] wherein the fracture height equation is: , 2 K,. 2

[00130] hf=—(---------) (12) 71 p{ — CTclose

[00131] wherein Ociose represents closing in-situ stress acting on a fracture wall, Pa; Xie represents fracturing toughness of a reservoir rock, Pa / m05;

[00132] wherein the fracture diverting equation is:

[00133] ^810^+^(3008^-1) = 0 (13) VTkG

[00134] K,=—---(14) 4(1

[00135] ^n= —---(15) 4(hr^

[00136] wherein a represents a half-length of a discrete fracture unit, m; Ohf represents a hydraulic fracture extension diverting angle, °;

[00137] wherein the fracture flow distribution equation is:

[00138] A <16> 7=1

[00139] wherein / represents each cluster number; k represents a horizontal section number; Ph represents a heel end pressure of a horizontal well, Pa; pt>,i represents the fracturing pressure at the I-111 cluster fracture hole, Pa; ps,i represents the net pressure at a fracture of the first cluster of fractures, Pa; Apyk represents a flow pressure drop of the kth horizontal section, Pa; Aptpj represents a frictional pressure drop at the 1th cluster fracture hole;

[00140] wherein the equation for the fracture extension boundary conditions and the initial conditions is:

[00141] s=L( “ 0 ^1 / =0=^

[00142] wherein Zf represents a hydraulic fracture length, m;

[00143] Step 4: taking the current reservoir pressure field distribution as an initial condition, taking the in-fracture pressure calculated in the hydraulic fracture extension part and the fracture position parameters as internal boundary conditions, and solving the reservoir pressure field near the fault using a finite difference method;

[00144] the solving equation in step four includes a continuity equation and an equivalent permeability equation after natural fracture failure;

[00145] wherein the continuity equation is:

[00146] (18)

[00147] wherein (p represents porosity, dimensionless; p represents fluid pressure, MPa; Ct represents reservoir comprehensive compressibility, MPa'1; kx and ky represent permeability in the x and y directions, respectively, D;

[00148] wherein the equation for the equivalent permeability after natural fracture failure is:

[00149]

[00150]

[00151] F - ^DF °F (19) k(x,y,t) sin O-k +kr (20) kv (x, y,t) = cos2 9 • kDF +kc (21)

[00152] wherein Ltf represents a spacing of natural fractures, m; (otf represents opening of the natural fracture, m; and kC represents initial permeability, D.

[00153] Step 5: according to a Warpinski two-dimensional criterion, establishing a failure criterion for determining a natural fracture of any occurrence using a tensor calculation method, and respectively determining grid elements of natural fracture positions of tensile failure and shear failure;

[00154] wherein the failure criteria for determining any occurrence of a natural fracture includes a unit normal vector of the natural fracture, a normal in-situ stress on a surface of the natural fracture, a shear in-situ stress on a surface of the natural fracture, a determination equation for a tensile failure of the natural fracture and a determination equation for a shear failure of the natural fracture;

[00155] wherein the unit normal vector of the natural fracture is:

[00156] = = ny nz^ (22)

[00157] wherein the normal in-situ stress at a natural fracture face is:

[00158] ann = F • n =           (23)

[00159] wherein the shear in-situ stress at the natural fracture face is:

[00160] a = JF-F-a -c = .a.n.Cin,-a -a (24) L J tt y nn nn y jk k jk k nn nn v 7

[00161] wherein the determination equation of the natural fracture tensile failure is:

[00162] Pf>&„„+Ts (25)

[00163] wherein Ts represents the natural fracture tensile strength, Pa; and pf represents a fluid pressure within the fracture, MPa;

[00164] wherein the determination equation of the natural fracture shear failure is:

[00165] <7„ >FnJ + • (CT^ - pf ) (26)

[00166] wherein fmc represents a friction factor of natural fractures, dimensionless; Fnj represents cohesion of a natural fracture, MPa.

[00167] Step 6: calculating the sum of the reservoir shear failure reconstruction volume and the tensile failure reconstruction volume through spatial numerical integration according to the grid element of the natural fracture position of the tensile failure and the shear failure to obtain an SRV (stimulated reservoir volume);

[00168] the equation for calculating the SRV in Step 6 is:

[00169] Ko.al = ^+^,= X (27) sess<jsest

[00170] wherein Etotai represents a total reservoir reconstruction volume, m3; Fs represents a reservoir shear failure reconstruction volume, m3; Kt represents a reservoir tensile failure reconstruction volume, m3; es represents a grid element of the shear failure, £t represents the grid element of the tensile failure; Ax(e), Aj(e) an Az(e) represent a side length of the grid element in the x, y, and z directions, m.

[00171] Step 7: repeating steps 4 to 6 until a set time step is reached, and obtaining a hydraulic fracture extension map and an SRV of each cluster at a perforation by numerical simulation; and

[00172] the hydraulic fracture extension parameter obtained in step 7 converges with the hydraulic fracture extension parameter obtained in the previous step; wherein the fracture opening is a fracture width, and if the calculated fracture width does not converge, then the pressure in the fracture is changed to perform iterative calculation until the fracture width converges; if the calculated in-fracture flow rate does not converge, then the fracture length is changed to carry out iterative calculation until the in-fracture flow rate converges; if the calculated leak off does not converge, the in-fracture pressure is changed for iterative calculation until the leak off converges;

[00173] wherein the difference between the hydraulic fracture extension parameter calculated in this cycle and the hydraulic fracture extension parameter calculated in the previous cycle is not more than 1%, i.e., convergence;

[00174] Step 8: determining the optimal perforation cluster spacing by simulating the dynamic expansion of the SRV near the inhomogeneous in-situ stress field with an objective of maximizing the SRV, and drawing a graph of the variation of the SRV with the cluster spacing.

[00175] Examples

[00176] It is known that the actual parameters of a deep shale gas well near a typical fault are as shown in table 1, and an example calculation is carried out according to the flow chart in FIG. 1A and FIG. IB:

[00177] Table 1 List of actual parameters of deep shale gas well near a fault Parameter type Parameter Numerical value Unit Fault parameter Tangential fault displacement 0.2 m Length 2121.3 m Reservoir geological parameters Minimum horizontal principal in-situ stress 94.35 MPa Stratum maximum horizontal principal in-situ stress 117.16 MPa Stratum rock Young’s modulus 47.2 GPa Stratum rock Poisson’s ratio 0.24 Dimensionless Fracturing construction parameters Fracture displacement 16.0 m3 / min Fracturing fluid amount 1800 m3 Fracturing time 110 min Fracturing fluid viscosity 3 mPas Fracturing leak off factor 0.000084 m / (s0'5) Fracturing fluid density 1000 kg / m3 Average concentration in fracturing injection propping agent 82.5 kg / m3 Number of perforation clusters 6 Cluster Single cluster perforation number 8 Perforation hole diameter 9.5 mm Natural fracture parameter Natural fracture tilt angle 60 o Natural fracture approximation angle 15 o Natural fracture length 0.9 m Natural fracture height 0.5 m

[00178] Firstly, the inhomogeneous in-situ stress field characterization model near a deep shale gas fault is established, and the displacement discontinuity method is used to solve and calculate the stratum induced in-situ stress component caused by fault structure in any point of Example 1 by combining the following equation:

[00179] the specific steps are: with simultaneous equations (1)-(5), the induced in-situ stress component caused by fault structure at any point in the reservoir is calculated by a displacement discontinuity method;

[00180] Secondly, the in-situ stress deflection angle distribution map near the deep shale gas fault (as shown in FIG. 2) and the horizontal in-situ stress difference distribution map near the deep shale gas fault (as shown in FIG. 3) are plotted;

[00181] then, a model for the hydraulic fracture network expansion of horizontal well multi-cluster fracturing near the deep shale gas fault is established using a fluid-solid coupling theory, and the hydraulic fracture extension in Example 1 is calculated with the following equation:

[00182] the specific steps are: with simultaneous equations (6)-(11), the extension length, height, opening of each hydraulic fracture and the pressure inside the fracture in the fracturing process near deep shale gas horizontal well fault are calculated by using a finite difference method.

[00183] Then, the deep shale gas reservoir pressure field with the fault structure is solved, and the pressure at any point in the reservoir in Example 1 is calculated in combination with the following equation:

[00184] the specific steps are: with simultaneous equations (12)-(21), the pressure field equation of deep shale gas reservoir under fault structure is solved by a finite difference method, and the pressure at any point in the reservoir is calculated.

[00185] Then, according to a Warpinski’s two-dimensional criterion, using the tensor calculation method, in combination with the following equation, the failure criterion for determining the natural fracture of any occurrence in Example 1 is derived:

[00186] the specific steps are: based on the simultaneous equations (22)-(26), the failure criteria of any occurrence natural fractures in deep shale reservoirs affected by faults are derived by using a tensor calculation method.

[00187] Then, combined with the following equation, the change of the SRV with the cluster spacing in the horizontal well of shale gas in Example 1 was calculated;

[00188] The specific steps are: in conjunction with equation (27), the SRV of a horizontal shale gas well at different cluster spacings in Example 1 is calculated using numerical integration;

[00189] then, an example calculation is carried out by using the numerical calculation flow chart of the method for the present invention as shown in FIG. 1A and FIG. IB, and according to the calculation result, the distribution map of the inhomogeneous in-situ stress field near a deep shale gas fault (as shown in FIG. 4) and the fracture network distribution under different perforation cluster spacings are respectively drawn (as shown in FIGS. 5-7: 5 m, 7 m, and 9 m); a plot of SRV as a function of cluster spacing (as shown in FIG. 8). When the cluster spacing of a shale gas horizontal well is 7. Im, the maximum SRV is 53.1 * 104m3.

[00190] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed by the above embodiments, it is not intended to limit the present invention. A person skilled in the art will recognize that changes and modifications may be made to the disclosed embodiments without departing from the spirit and scope of the invention. However, any simple modification, equivalent change and modification to the above embodiments according to the technical spirit of the present invention are still within the scope of the technical solution of the present invention. 09 12 24

Claims

1. A method for optimizing fracturing cluster spacing near a deep shale gas fault, comprising the steps of:Step 1: acquiring fault parameters, reservoir geological parameters, fracturing construction parameters, natural fracture parameters and model grid parameters;Step 2: establishing a characterization model of an inhomogeneous in-situ stress field near a deep shale gas fault, comprising: calculating a fault induced in-situ stress field by a displacement discontinuity method based on an elastic mechanics theory model, calculating an inhomogeneous in-situ stress field near the deep shale gas fault by linear superposition of an original in-situ stress field and the fault induced in-situ stress field, and drawing an in-situ stress deflection angle distribution map and a horizontal in-situ stress difference distribution map near the deep shale gas fault respectively;Step 3: taking the inhomogeneous in-situ stress field near the deep shale gas fault as an initial stress condition, establishing a hydraulic fracture network expansion model of horizontal well subsection multi-cluster fracturing near the deep shale gas fault, and calculating hydraulic fracture extension parameters, in-fracture pressure, filtration and fracture location parameters of each cluster;Step 4: taking a current reservoir pressure field distribution as an initial condition, taking the in-fracture pressure and the fracture location parameters calculated in the step 3 as internal boundary conditions, and solving a reservoir pressure field near the fault using a finite difference method to calculate a pressure at any point in the reservoir;Step 5: establishing a failure criterion for determining a natural fracture of any occurrence using the calculated pressure according to a tensor calculation method, and respectively determining grid elements of natural fracture positions of tensile failure and shear failure based on the failure criterion;Step 6: calculating a sum of a reservoir shear failure reconstruction volume and a tensile failure reconstruction volume through spatial numerical integration according to the grid elements of the natural fracture position of the tensile failure and the shear failure to obtain a stimulated reservoir volume;Step 7: repeating steps 4 to 6 until a set time step is reached, and obtaining a hydraulic fracture extension map and the stimulated reservoir volume of each cluster at a perforation by numerical simulation; andStep 8: determining an optimal perforation cluster spacing by simulating dynamicexpansion of the stimulated reservoir volume near the inhomogeneous in-situ stress field with an objective of maximizing the stimulated reservoir volume, and drawing a graph of the variation of the stimulated reservoir volume with the cluster spacing.09 12 242. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the fault parameters comprise a fault type, a fault length, a fault height, a fault tilt angle, a fault strike, and a fault displacement;the reservoir geological parameters comprise a stratum maximum horizontal principal in-situ stress, a stratum minimum horizontal principal in-situ stress, a stratum horizontal in-situ stress difference, a stratum rock fracturing toughness, a stratum rock Young’s modulus, and a stratum rock Poisson’s ratio;the fracturing construction parameters comprise a fracture displacement, a fracturing fluid amount, a fracturing time, a fracturing fluid viscosity, a fracturing leak off factor, a fracturing fluid density, an average concentration in fracturing injection propping agent, the number of perforation clusters, a single cluster perforation number, a perforation hole diameter and a cluster spacing;the natural fracture parameters comprise a natural fracture average tilt angle, a natural fracture average approximation angle, a natural fracture average length, and a natural fracture average height;the model grid parameters comprise model x-direction boundaries, y-direction boundaries, and z-direction boundaries.

3. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the characterization model of the inhomogeneous in-situ stress field near a deep shale gas fault comprises an equation for calculating the fault induced in-situ stress field and an equation for calculating the inhomogeneous in-situ stress field near the pre-fractured fault; wherein the equation for calculating the fault induced in-situ stress field is:= + “ g2^ + + eF^GD+    ..........—[2e2F3 - 2egF4 + F(eF5 - gF6)]=     " \2egF3 + (e2 - g2)F, - £(gF5 + eF6)]2^-(1 -v)~ J2g2F3 + 2egF4 + (eF, - gFe)] 2^(1- v)= ~eF) + F + + <F)]2^(1-v)             2^(1 -v)Act =v(A<r +A<r )09 12 24wherein Aa», &(ryy, F> and Aaxy respectively represent the fault-induced in-situ stress component, MPa; G represents the shear modulus of the reservoir rock, Pa; v represents Poisson’s ratio of reservoir rocks, dimensionless; Dn and Dt represent a normal fault distance and tangential fault displacement of fault respectively, m; represents a value of y in a global coordinate system converted into a local coordinate system; e and g are the cosine values of an included angle between a £ axis of the local coordinate system and an x-axis and y-axis of the global coordinate system, respectively; and Ft represents a partial derivative equation of Papkovitch function, {3-6};wherein the equation for calculating inhomogeneous in-situ stress field near the deep shale gas fault is:O’XX @’xy C^ c^ + Ac -l.t (°) c xy c^ + Ac XZ xz yx yy C yz (0) ^yx c^ + Ac yy yy to) c yz ^zx °zz_ C^ + Ac zx xz 7 + Aczzwherein oF0), Oy^, Ozz^, Oxy^, Oyz^, and Oxz^ represent the original in-situ stress value component, Pa; oXx, ayy, Ozz, oxy, oyz, and Oxz represent the current in-situ stress value component, Pa.

4. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the fracture network extension model of the horizontal well subsection multi-cluster fracturing hydraulic fracture near the deep shale gas fault comprises a material balance equation, an in-fracture flow equation, a fracture opening equation, a fracture height equation, a fracture diverting equation, a fracture flow distribution equation, a fracture extension boundary condition and an initial condition equation;wherein the material balance equation is:ds2CA£) s / t-r(s)dt fwherein q? represents an in-fracture flow, m3 / s; t represents time, s; hi represents a height of the fracture, m; on represents an opening of the fracture, m; Cl represents a leak off factor of an injected fracturing fluid, m / s05; t(s) represents the time at which the fracturing fluid begins to drain at a position along a length direction of the fracture, s; N represents the number of hydraulic fracture; qy represents a total flow rate of fracturing fluid injection, m3 / s; and q, represents the flow rate obtained from the distribution of the i* fracture, m3 / s;wherein the in-fracture flow equation is:09 12 24dpf—) = dswherein pi represents a fluid pressure within the fracture, Pa; u represents a viscosity of fluid in the fracture, Pa s; and q^ represents a leak off rate, m / s;wherein the fracture opening equation is:A A(^t \ — (Mtt (U, + )y (^n ) j / =1 7=1(^),=2(^(^.),+2^7=1 / =1= (c), Uwherein A represents a total number of discrete elements of the fracture; i and j represent fracture units, with a value of 1-A; (A / nrepresents a tangential in-situ stress component on an i-unit caused by the j-unit tangential displacement discontinuity, (A / nt) / ? represents a tangential in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity, (Mn)v represents a normal in-situ stress component on the i-unit caused by the j-unit tangential displacement discontinuity, and (Mm)y represents a normal in-situ stress component on the i-unit caused by the j-unit normal displacement discontinuity; (ot); and (on) / respectively represent the shear in-situ stress and normal in-situ stress of the unit i in alocal coordinate system, Pa; (Ut)j and (Un)j respectively represent tangential strain and normal strain in the local coordinate system, m; (Un)i i represents a normal offset of the unit i, m; and 5 represents a fracture length direction coordinate, m;wherein the fracture height equation is:_ 2 ^IC )271 Pf — <7closewherein <7ciOse represents closing in-situ stress acting on a fracture wall, Pa; Kic represents fracturing toughness of a reservoir rock, Pa / m°5;wherein the fracture diverting equation is:sin +   (3 cos ^-1) = 009 12 24wherein a represents a half-length of a discrete fracture unit, m; #hf represents a hydraulic fracture extension diverting angle, °;wherein the fracture flow distribution equation is:iPi = Pij+p>j+E +aaw7=1wherein I represents each cluster number; k represents a horizontal section number; p^ represents a heel end pressure of a horizontal well, Pa; p\p represents the fracturing pressure at the l-th cluster fracture hole, Pa; ps,i represents the net pressure at a fracture of the first cluster of fractures, Pa; Apt,k represents a flow pressure drop of the k"' horizontal section, Pa; ApfPri represents a frictional pressure drop at the 1th cluster fracture hole;wherein the equation for the fracture extension boundary conditions and the initial conditions is:5 —JL / £rrclose?f ^L, = 0wherein Lf represents a hydraulic fracture length, m.09 12 245. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the equation for solving the reservoir pressure field in step 4 comprises a continuity equation and an equation for the equivalent permeability after natural fracture failure;wherein the continuity equation is:kx^,y,t)5 f dpy+ — k dy)wherein (p represents porosity, dimensionless; p represents fluid pressure, MPa; Ct represents reservoir comprehensive compressibility, MPa'1; kx and ky represent permeability in the x and y directions, respectively, D;wherein the equation for the equivalent permeability after natural fracture failure is:7 _ tf°F " 12¼k (x, y, 0 = sin2 0 ■ k^ + kr X                                      LJi'        Czky (x, y, t) = cos2 0-kDF + kcwherein Ln represents a spacing of natural fractures, m; cotr represents opening of the natural fracture, m; kc represents permeability of natural fractures, D; and kc represents initial permeability, D.

6. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the failure criteria for determining any occurrence of a natural09 12 24fracture comprises a unit normal vector of the natural fracture, a normal in-situ stress on a surface of the natural fracture, a shear in-situ stress on a surface of the natural fracture, a determination equation for a tensile failure of the natural fracture and a determination equation for a shear failure of the natural fracture;wherein the unit normal vector of the natural fracture is:n = {n e\ = (nx n n\\ J J ) \ x y £ jwherein the normal in-situ stress at a natural fracture face is:a = F * n = n cr , n ,nn 1 jk^kwherein the shear in-situ stress at the natural fracture face is:cr = JF-F-cr -a = Ja.rijCr-a -(7tt y nn nn y jk k jk k nn nnwherein, when a fluid pressure in the natural fracture is greater than a sum of the normal in-situ stress at a natural fracture face and a natural fracture tensile strength, a natural fracture tensile failure occurs, and a determination equation of the natural fracture tensile failure is:p .> C +Twherein Ts represents the natural fracture tensile strength, Pa; and p / represents a fluid pressure within the fracture, MPa;wherein, when the natural fracture tensile failure does not occurs and the shear in-situ stress at the natural fracture face is greater than a natural fracture shear strength, a natural fracture shear failure occurs, and a determination equation of the natural fracture shear failure is:g > F + f -(g - nA tt nj   J me \ nn t j / wherein / mc represents a friction factor of natural fractures, dimensionless; Fn) represents cohesion of a natural fracture, MPa.

7. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 6, wherein the equation for calculating the stimulated reservoir volume in Step 6 is:= K+K = E09 12 24wherein Ktotai represents a total reservoir reconstruction volume, m3; Ks represents a reservoir shear failure reconstruction volume, m3; Kt represents a reservoir tensile failure reconstruction volume, m3; £s represents a grid element of the shear failure, Et represents the grid element of the tensile failure; Ax(s), Aj(e) an Az(s) represent a side length of the grid element in the x. y, and z directions, m.

8. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 1, wherein the hydraulic fracture extension parameters comprise a fracture extension length, a fracture extension height, a fracture opening, an in-fracture pressure, and an in-fracture flow.

9. The method for optimizing fracturing cluster spacing near a deep shale gas fault according to claim 8, wherein the hydraulic fracture extension parameter obtained in step 7 converges with the hydraulic fracture extension parameter obtained in the previous step; wherein the fracture opening is a fracture width, and if the calculated fracture width does not converge, then the pressure in the fracture is changed to perform iterative calculation until the fracture width converges; if the calculated in-fracture flow rate does not converge, then the fracture length is changed to carry out iterative calculation until the in-fracture flow rate converges; if the calculated leak off does not converge, the in-fracture pressure is changed for iterative calculation until the leak off converges.

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