A method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs

Abstract

The invention discloses a method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs, comprising the following steps: establish a physical model of the natural fracture; establish a hydraulic fracture propagation calculation equation; establish a natural fracture failure model, calculate the natural fracture aperture, and then calculate the natural fracture permeability, and finally convert the natural fracture permeability into the permeability of the porous medium; couple the hydraulic fracture propagation calculation equation with the permeability of the porous medium through the fracture propagation criterion and the fluid loss to obtain a pore elastic model of the coupled natural fracture considering the influence of the natural fracture; work out the stress and displacement distribution of the hydraulic fracture wall with the pore elastic model of the coupled natural fracture, and analyze the offset and discontinuity of the hydraulic fracture wall according to the displacement.

Claims

1. A method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs, comprising the following steps: acquire geological parameters of the fractured reservoir, and establish a physical model of the natural fracture based on the fracture continuum model according to the length, width, height and other physical conditions of the natural fracture; establish a hydraulic fracture propagation calculation equation on the basis of the in-fracture flow equation, fluid loss equation, width equation and material balance equation; establish a natural fracture failure model according to the Mohr-Coulomb rule, work out the natural fracture aperture according to the natural fracture failure model, calculate the natural fracture permeability based on the natural fracture aperture, and convert the fracture permeability into the permeability of the porous medium with the fracture continuum model; couple the hydraulic fracture propagation calculation equation with the permeability of the porous medium through the fracture propagation criterion and the fluid loss to obtain a pore elastic model of the coupled natural fracture considering the influence of the natural fracture; and work out the stress and displacement distribution of the hydraulic fracture wall with the pore elastic model of the coupled natural fracture, and analyze the offset and discontinuity of the hydraulic fracture wall according to the displacement.

2. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 1, wherein the geological parameters are obtained by logging or fracturing, specifically including initial aperture of natural fracture, matrix initial permeability, initial porosity, elastic modulus and Poisson's ratio.

3. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 1, wherein the fracture continuum model is as follows: $\begin{array}{cc}{k}_{\mathrm{ij}}=k_{\mathrm{nf}}\left[\begin{array}{ccc}{\left(n_2\right)}^2+{\left(n_3\right)}^2& -n_1.Math.n_2& -n_3.Math.n_1\\ -n_1.Math.n_2& {\left(n_2\right)}^2+{\left(n_3\right)}^2& -n_2.Math.n_3\\ -n_3.Math.n_1& -n_2.Math.n_3& {\left(n_2\right)}^2+{\left(n_3\right)}^2\end{array}\right]& \left(1\right)\end{array}$ Where, k.sub.ij is the matrix permeability tensor, in m.sup.2; k.sub.nf is the natural fracture permeability, in m.sup.2; n.sub.1, n.sub.2 and n.sub.3 are calculated as follows: $\begin{array}{cc}{n}_1=\cos \left(.Math.\frac{}{180}\right).Math.\sin \left(.Math.\frac{}{180}\right).Math..Math.n_2=\cos \left(.Math.\frac{}{180}\right).Math.\cos \left(.Math.\frac{}{180}\right).Math..Math.n_3=-\sin \left(.Math.\frac{}{180}\right)& \left(2\right)\end{array}$ Where, is the dip angle, in ; is the approaching angle, in ; The natural fracture permeability k.sub.nf is calculated as follows: $\begin{array}{cc}{k}_{\mathrm{nf}}=\frac{w_{\mathrm{NF}}^3}{12.Math.d}& \left(3\right)\end{array}$ Where, w.sub.NF is the natural fracture aperture, in m; d is the natural fracture spacing, in m.

4. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 3, wherein the hydraulic fracture propagation calculation equation is worked out by substituting the in-fracture flow equation, fluid loss equation and width equation into the material balance equation; the substitution of in-fracture flow equation, fluid loss equation, width equation and the material balance equation are as follows: $\begin{array}{cc}\frac{p_{\mathrm{HF}}}{s}=-\frac{64.Math.}{.Math..Math.h_f.Math.w_{\mathrm{HF}}^3}.Math.q& \left(4\right)\\ q_L=\frac{S}{}.Math.f\left(p_{\mathrm{HF}}-p_p\right)& \left(5\right)\\ w_{\mathrm{HF}}=\left(u^{+}-u^{-}\right).Math.n& \left(6\right)\\ \frac{q\left(s,t\right)}{s}=q_L\left(s,t\right).Math.h_f+\frac{w_{\mathrm{HF}}\left(s,t\right)}{t}.Math.h_f& \left(7\right)\end{array}$ Where, is the partial differential symbol; p.sub.HF is the pressure in the fracture, in Pa; s is the coordinate of fracture length direction, in m; is the fluid viscosity, in mPa.Math.s; h.sub.f is the hydraulic fracture height, in m; w.sub.HF is the hydraulic fracture aperture, in m; q is the flow in the hydraulic fracture, in m.sup.3/s; q.sub.L is the fracturing fluid loss rate, in m/s; S is the fracturing fluid loss area, in m.sup.2; f is the fluid loss coefficient, in 1/m; p.sub.p is the reservoir pore pressure, in MPa; u.sup.+ and u.sup. are displacements on the left and right sides of the hydraulic fracture, in m; n is the unit normal vector on the hydraulic fracture surface, dimensionless; t is the fracturing time, in min.

5. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 4, wherein the natural fracture failure model is as follows:
.sub.>.sub.0+tan(.sub.basic)(.sub.np.sub.NF)(8)
p.sub.NF.sub.n+K.sub.t(9)
w.sub.NF=a.sub.0+a.sub.NFT+a.sub.NFS(10) Where, .sub. is the shear stress on the natural fracture wall, in MPa; .sub.0 is the natural fracture cohesion, in MPa; .sub.basic is the basic friction angle, in ; .sub.n is the normal stress on the natural fracture surface, in MPa; p.sub.NF is the fluid pressure in the natural fracture, in MPa; K.sub.t is the tensile strength of the natural fracture, in MPa; a.sub.0 is the initial aperture of the natural fracture, in m; a.sub.NFT is the extensional aperture of the natural fracture, in m; a.sub.NFS is the shear aperture of the natural fracture, in m.

6. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 5, wherein the basic friction angle is within a range from 30 to 40.

7. The method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs according to claim 5, wherein the pore elastic model of the coupled natural fracture is as follows: $\begin{array}{cc}.Math.\left[.Math.u+.Math.u^T+.Math..Math.\mathrm{Itr}\left(u\right)\right]+.Math.{}_i-b.Math.p_p+b.Math.p_i=0& \left(11\right)\\ \left(\frac{1}{M}+\frac{b^2}{K_{\mathrm{dr}}}\right).Math.\frac{p_p^n}{t}-\frac{b^2}{K_{\mathrm{dr}}}.Math.\frac{p_p^{n-1}}{t}+b.Math.\frac{\left(.Math.u\right)}{t}-\frac{k_{\mathrm{ij}}}{}.Math.\left({}^2.Math.p_p^n\right)=q& \left(12\right)\end{array}$ Where, is the Laplacian operator; u is the displacement tensor, in m; T is the matrix transpose; is the lame constant, in MPa; Itr is the integral symbol; .sub.i is the stress tensor, in MPa; b is the Biot effective coefficient, dimensionless; p.sub.i is the initial pore pressure, in MPa; M is the Biot modulus, in MPa; K.sub.dr is the bulk modulus in the drainage process, in MPa.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following will make a brief introduction to the drawings needed in the description of the embodiments or the prior art. Obviously, the drawings in the following description are merely some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without any creative effort.

[0027] FIG. 1 is a schematic diagram of physical model of natural fracture in the present invention.

[0028] FIG. 2 is a cloud chart of stress distribution after fracturing in Embodiment 1.

[0029] FIG. 3 is a cloud chart of displacement distribution after fracturing in Embodiment 1.

[0030] FIG. 4 is a schematic diagram of discontinuous distribution of the hydraulic fracture wall in Embodiment 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] The present invention is further described with reference to the drawings and embodiments. It should be noted that the embodiments in this application and the technical features in the embodiments can be combined with each other without conflict.

[0032] A method for simulating the discontinuity of the hydraulic fracture wall in fractured reservoirs, comprising the following steps:

[0033] Firstly, acquire geological parameters of the fractured reservoir, and establish a physical model of the natural fracture based on the fracture continuum model according to the length, width, height and other physical conditions of the natural fracture; the geological parameters are obtained by logging or fracturing, specifically including initial aperture of natural fracture, matrix initial permeability, initial porosity, elastic modulus and Poisson's ratio. The fracture continuum model is as follows:

[00006]$\begin{array}{cc}{k}_{\mathrm{ij}}=k_{\mathrm{nf}}\left[\begin{array}{ccc}{\left(n_2\right)}^2+{\left(n_3\right)}^2& -n_1.Math.n_2& -n_3.Math.n_1\\ -n_1.Math.n_2& {\left(n_2\right)}^2+{\left(n_3\right)}^2& -n_2.Math.n_3\\ -n_3.Math.n_1& -n_2.Math.n_3& {\left(n_2\right)}^2+{\left(n_3\right)}^2\end{array}\right]& \left(1\right)\end{array}$

Where,

[0034] k.sub.ij is the matrix permeability tensor, in m.sup.2;
k.sub.nf is the natural fracture permeability, in m.sup.2;
n.sub.1, n.sub.2 and n.sub.3 are calculated as follows:

[00007]$\begin{array}{cc}{n}_1=\cos \left(.Math.\frac{}{180}\right).Math.\sin \left(.Math.\frac{}{180}\right).Math..Math.n_2=\cos \left(.Math.\frac{}{180}\right).Math.\cos \left(.Math.\frac{}{180}\right).Math..Math.n_3=-\sin \left(.Math.\frac{}{180}\right)& \left(2\right)\end{array}$

Where,

[0035] is the dip angle, in ;
is the approaching angle, in ;

[0036] The natural fracture permeability k.sub.nf is calculated as follows:

[00008]$\begin{array}{cc}{k}_{\mathrm{nf}}=\frac{w_{\mathrm{NF}}^3}{12.Math.d}& \left(3\right)\end{array}$

Where,

[0037] w.sub.NF is the natural fracture aperture, in m;
d is the natural fracture spacing, in m.

[0038] Secondly, establish the hydraulic fracture propagation calculation equation on the basis of the in-fracture flow equation, fluid loss equation, width equation and material balance equation, and work out it by substituting the flow equation, fluid loss equation and width equation into the material balance equation. The substitution of in-fracture flow equation, fluid loss equation, width equation and the material balance equation are as follows:

[00009]$\begin{array}{cc}\frac{p_{\mathrm{HF}}}{s}=-\frac{64.Math.}{.Math..Math.h_f.Math.w_{\mathrm{HF}}^3}.Math.q& \left(4\right)\\ q_L=\frac{S}{}.Math.f\left(p_{\mathrm{HF}}-p_p\right)& \left(5\right)\\ w_{\mathrm{HF}}=\left(u^{+}-u^{-}\right).Math.n& \left(6\right)\\ \frac{q\left(s,t\right)}{s}=q_L\left(s,t\right).Math.h_f+\frac{w_{\mathrm{HF}}\left(s,t\right)}{t}.Math.h_f& \left(7\right)\end{array}$

Where,

[0039] is the partial differential symbol;
p.sub.HF is the pressure in the fracture, in Pa;
s is the coordinate of fracture length direction, in m;
is the fluid viscosity, in mPa.Math.s;
h.sub.f is the hydraulic fracture height, in m;
w.sub.HF is the hydraulic fracture aperture, in m;
q is the flow in the hydraulic fracture, in m.sup.3/s;
q.sub.L is the fracturing fluid loss rate, in m/s;
S is the fracturing fluid loss area, in m.sup.2;
f is the fluid loss coefficient, in 1/m;
p.sub.p is the reservoir pore pressure, in MPa;
u.sup.+ and u.sup. are displacements on the left and right sides of the hydraulic fracture, in m;
n is the unit normal vector on the hydraulic fracture surface, dimensionless;
t is the fracturing time, in min.

[0040] Thirdly, establish the natural fracture failure model according to the Mohr-Coulomb rule, obtain the natural fracture aperture according to the natural fracture failure model, work out the natural fracture permeability based on the natural fracture aperture, and convert the fracture permeability into the permeability of the porous medium by the fracture continuum model. The natural fracture failure model is as follows:

.sub.>.sub.0+tan(.sub.basic)(.sub.np.sub.NF)(8)

p.sub.NF.sub.n+K.sub.t(9)

w.sub.NF=a.sub.0+a.sub.NFT+a.sub.NFS(10)

[0041] Where,

.sub. is the shear stress on the natural fracture wall, in MPa;
.sub.0 is the natural fracture cohesion, in MPa;
.sub.basic is the basic friction angle, in ;
.sub.n is the normal stress on the natural fracture surface, in MPa;
p.sub.NF is the fluid pressure in the natural fracture, in MPa;
K.sub.t is the tensile strength of the natural fracture, in MPa;
a.sub.0 is the initial aperture of the natural fracture, in m;
a.sub.NFT is the extensional aperture of the natural fracture, in m;
a.sub.NFS is the shear aperture of the natural fracture, in m.

[0042] Optionally, the basic friction angle is within a range from 30 to 40.

[0043] Fourthly, couple the hydraulic fracture propagation calculation equation with the permeability of the porous medium through the fracture propagation criterion and the fluid loss to obtain a pore elastic model of the coupled natural fracture considering the influence of the natural fracture. The pore elastic model of the coupled natural fracture is as follows:

[00010]$\begin{array}{cc}.Math.\left[.Math.u+.Math.u^T+.Math..Math.\mathrm{Itr}\left(u\right)\right]+.Math.{}_i-b.Math.p_p+b.Math.p_i=0& \left(11\right)\\ \left(\frac{1}{M}+\frac{b^2}{K_{\mathrm{dr}}}\right).Math.\frac{p_p^n}{t}-\frac{b^2}{K_{\mathrm{dr}}}.Math.\frac{p_p^{n-1}}{t}+b.Math.\frac{\left(.Math.u\right)}{t}-\frac{k_{\mathrm{ij}}}{}.Math.\left({}^2.Math.p_p^n\right)=q& \left(12\right)\end{array}$

Where,

[0044] is the Laplacian operator;
u is the displacement tensor, in m;
T is the matrix transpose;
is the lame constant, in MPa;
Itr is the integral symbol;
.sub.i is the stress tensor, in MPa;
b is the Biot effective coefficient, dimensionless;
p.sub.i is the initial pore pressure, in MPa;
M is the Biot modulus, in MPa;
K.sub.dr is the bulk modulus in the drainage process, in MPa.

[0045] Finally, work out the stress and displacement distribution of the hydraulic fracture wall with the pore elastic model of the coupled natural fracture, and analyze the offset and discontinuity of the hydraulic fracture wall according to the displacement.

Embodiment 1

[0046] A typical unconventional reservoir in a block of Fuling is taken as the fractured reservoir to be simulated. The geological and construction parameters of the block are obtained through field logging and well testing, as shown in Table 1.

TABLE-US-00001 TABLE 1 Geological Parameters and Construction Parameters of Fractured Reservoir to be Simulated Parameters Value Parameters Value Displacement (m.sup.3/h) 11 Natural fracture 0.4 spacing (m) Fluid viscosity 10 Rock compressibil- 4 10.sup.3 (MPa .Math. S) ity (MPa.sup.1) Total volume injected 1500 Fluid compressibil- 8 10.sup.4 (m.sup.3) ity (MPa.sup.1) Cluster spacing (m) 10 Natural fracture 35 approaching angle () Number of clusters 1 Natural fracture dip 90 angle () Model size (H W 40*60*400 Vertical principal 55 L) (m) stress (MPa) Initial pore pressure 35 Horizontal minimum 54 (MPa) principal stress (MPa) Matrix initial 0.01~0.1 Horizontal maximum 60 permeability (mD) principal stress (MPa) Initial porosity of 0.041 Initial aperture of .sup.10.sup.4 the reservoir the natural fracture (m) Elastic modulus 3 10.sup.4 Poisson's ratio 0.2 (MPa)

[0047] Establish a physical model of the natural fracture according to the geological parameters and the length, width, height and other physical conditions of natural fracture, as shown in FIG. 1.

[0048] Work out the natural fracture aperture according to the natural fracture failure model of Equations (8) to (10), and then calculate the natural fracture permeability with Equation (3), and finally convert the natural fracture permeability into the permeability of the porous medium with Equations (1) and (2).

[0049] Substitute Equations (4) to (6) into Equation (7) to obtain the hydraulic fracture propagation calculation equation, and couple the hydraulic fracture propagation calculation equation with the permeability of the porous medium through the fracture propagation criterion and the fluid loss to obtain pore elastic model of the coupled natural fracture considering the influence of the natural fracture.

[0050] Work out the the stress and displacement distribution (as shown in FIG. 3) of hydraulic fracture wall with the pore elastic model of the coupled natural fracture, and analyze the offset and discontinuity of the hydraulic fracture wall according to the displacement. The offset and discontinuity distribution of the hydraulic fracture wall, at 25 minutes, 50 minutes, and 75 minutes of the hydraulic fracturing, are shown in FIG. 4.

[0051] The above are only the preferred embodiments of the present invention, not intended to limit the present invention in any form. Although the present invention has been disclosed as above with the preferred embodiments, it is not intended to limit the present invention. Those skilled in the art, within the scope of the technical solution of the present invention, can use the disclosed technical content to make a few changes or modify the equivalent embodiment with equivalent changes. Within the scope of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still regarded as a part of the technical solution of the present invention.