METHOD FOR COUPLING HYDRAULIC FRACTURE NETWORK EXTENSION AND PRODUCTION PERFORMANCE OF HORIZONTAL WELL IN UNCONVENTIONAL OIL AND GAS RESERVOIR

Abstract

A method for coupling hydraulic fracture network extension and production performance of a horizontal well in an unconventional oil and gas reservoir includes: establishing a complex hydraulic fracture network model of a fractured horizontal well in an unconventional oil and gas reservoir based on a fracture extension theory; constructing three-dimensional three-phase mathematical models of seepage for the fractured horizontal well based on an embedded discrete fracture model; and constructing a fully implicit numerical calculation model by a finite difference method through three-dimensional orthogonal grids, and solving iteratively, thereby accurately predicting a production performance characteristic of the fractured horizontal well in the unconventional oil and gas reservoir. The method combines a fracture extension model with a production performance prediction model to realize the coupled simulation and prediction of the hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir.

Claims

1. A method for coupling hydraulic fracture network extension and production performance of a horizontal well in an unconventional oil and gas reservoir, comprising the following steps: S1: constructing, based on a displacement discontinuity method, a displacement discontinuity and stress relationship model of a fracture element and a fracture failure type criterion; S2: constructing a numerical model for hydraulic fracture network extension of the horizontal well by comprehensively considering a reservoir's natural fracture distribution characteristic and hydraulic fracture flow, extension and deformation, and acquiring, through iterative simultaneous solution, an extension shape and a spatial distribution characteristic of a hydraulic fracture network; S3: generating a geological body of a fractured horizontal well based on the extension shape and the spatial distribution characteristic of the hydraulic fracture network, and performing spatial grid discretization by three-dimensional orthogonal grids; S4: constructing, based on an embedded discrete fracture model, three-dimensional three-phase mathematical models of seepage for the fractured horizontal well and a fully implicit numerical model based on a finite difference algorithm; and S5: iteratively solving the fully implicit numerical model, and predicting a post-fracture production performance characteristic of the horizontal well.

2. The method for coupling hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir according to claim 1, wherein step S1 comprises: S11: assuming a vertical height of a pseudo-three-dimensional fracture with a series of line segment elements horizontally to be a reservoir thickness, wherein when the fracture is subjected to an external load, relative sliding occurs between upper and lower surfaces of the fracture element; and defining variables to be calculated in each fracture element, namely a normal displacement D.sub.n and a tangential displacement D.sub.s, as displacement discontinuities:
D.sub.s=u.sub.x(x,0.sup.−)−u.sub.x(x,0.sup.+)  (1)=
D.sub.n=u.sub.y(x,0.sup.−)−u.sub.y(x,0.sup.+)  (2) wherein, u.sub.x(x,y), u.sub.y(x,y) denote surface displacements of the fracture element at a point (x,y) along an x-axis and a y-axis, respectively, m; and 0.sup.+ and 0.sup.− denote upper and lower wall surfaces of the fracture element along the y-axis, respectively; expressing a stress, a strain and a displacement of the fracture element at any point in space by the displacement discontinuities:
u.sub.x=[2(1−v)f′.sub.y−yf′.sub.xx]+[−(1−2v)g′.sub.x−yg′.sub.xy]  (3)
u.sub.y=[(1−2v)f′.sub.x−yf′.sub.xy]+[2(1−v)g′.sub.y−yg′.sub.yy]  (4)
σ.sub.xx=2G[2f′.sub.xy+yf′.sub.xyy]+2G[g′.sub.yy+yg′.sub.yyy]  (5)
σ.sub.yy=2G[−yf′.sub.xyy]+2G[g′.sub.yy−yg′.sub.yyy]  (6)
τ.sub.xy=2G[2f′.sub.yy+yf′.sub.yyy]+2G[−yg′.sub.xyy]  (7) wherein, σ(.Math.) denotes a stress tensor of the fracture element, with a subscript xx denoting a stress perpendicular to a yz plane, and a subscript yy denoting a stress perpendicular to an xz plane; T denotes a shear stress tensor of the fracture element; G denotes a shear modulus of an elastic medium; v denotes a Poisson's ratio; y denotes a y-axis coordinate at any point; f′(.Math.) and g′(.Math.) denote derivations of integral functions f and g, respectively, with a subscript denoting an independent variable, for example: $f_{\mathrm{xyy}}^{\prime }=\frac{{\partial }^{3}f}{\partial x{\partial }^{2}y};$ f and g respectively denote Green's function integrals along the fracture element, which are given by: $\begin{array}{cc}f\left(x,y\right)=\frac{-1}{4\pi \left(1-v\right)}\underset{-a}{\overset{a}{\int }}{D}_s\left(\xi \right)\ln \left[\sqrt{{\left(x-\xi \right)}^2+y^2}\right]d\xi & \left(8\right)\end{array}$ $\begin{array}{cc}g\left(x,y\right)=\frac{-1}{4\pi \left(1-v\right)}\underset{-a}{\overset{a}{\int }}{D}_n\left(\xi \right)\ln \left[\sqrt{{\left(x-\xi \right)}^2+y^2}\right]d\xi & \left(9\right)\end{array}$ wherein, x and y denote point coordinates of the fracture element; and a denotes a displacement; the stress and strain of any fracture element under the external load are calculated according to equations (3) to (9); regarding fracture extension, a fracture boundary condition is provided by a fluid in the fracture, and a normal stress is equal to a fluid pressure; since the fluid does not have shear resistance, a shear stress at a fracture boundary is 0; and therefore, the fracture boundary condition is:
σ.sub.n=−p  (10)
τ=0  (11) wherein, p denotes the fluid pressure in the fracture, MPa; σ.sub.n denotes the normal stress at the fracture boundary; and r denotes the shear stress at the fracture boundary; regarding the line segment elements of the fracture, all the stress of any line segment element is a sum of an induced stress acting on the fracture element, so matrix equations of the line segment elements of the fracture are: $\begin{array}{cc}\left[\begin{array}{cccc}{a}_{s11}& a_{s12}& .Math.& a_{s1N}\\ .Math.& .Math.& a_{\mathrm{sij}}& .Math.\\ a_{\mathrm{sN}1}& a_{\mathrm{sN}2}& .Math.& a_{\mathrm{sNN}}\\ a_{n11}& a_{n12}& .Math.& a_{n1N}\\ .Math.& .Math.& a_{\mathrm{nij}}& .Math.\\ a_{\mathrm{nN}1}& a_{\mathrm{nN}2}& .Math.& a_{\mathrm{nNN}}\end{array}\right]\left[\begin{array}{c}{D}_{1s}\\ .Math.\\ D_{Ns}\\ D_{1n}\\ .Math.\\ D_{\mathrm{Nn}}\end{array}\right]=\left[\begin{array}{c}{\tau }_1\\ .Math.\\ {\tau }_N\\ p_1\\ .Math.\\ p_N\end{array}\right]& \left(12\right)\end{array}$ wherein, D.sub.Ns denotes a tangential displacement of an N-th fracture element; D.sub.Nn denotes a normal displacement of the N-th fracture element; N denotes a number of line segment elements of the fracture; a.sub.sij denotes a tangential displacement component caused by a tangential displacement of a j-th element along the y-axis on an i-th element along the x-axis; a.sub.nij denotes a normal displacement component caused by a normal displacement of the j-th element along the y-axis on the i-th element along the x-axis; τ.sub.N denotes a shear stress at the N-th fracture element; and p.sub.N denotes a fluid pressure at the N-th fracture element; a.sub.sij and a.sub.nij are expressed as follows: $\begin{array}{cc}{a}_{\mathrm{sij}}=\frac{G}{2\pi \left(1-v\right)}\left[2n_j{l}_j\left(n_j^2+l_j^2\right)F_1+\left(n_j^2-l_j^2\right)F_2+2n_j{l}_l{\zeta }_{\mathrm{ij}}\left(n_j{F}_3-l_j{F}_4\right)+{\zeta }_{\mathrm{ij}}\left(n_j^2-l_j^2\right)\left(l_j{F}_3+n_j{F}_4\right)\right]& \left(13\right)\end{array}$ $\begin{array}{cc}{a}_{\mathrm{nij}}=\frac{G}{2\pi \left(1-v\right)}\left[\left(2n_j{l}_j^3+2n_j^3{l}_j\right)F_1+\left(n_j^2-l_j^2\right)\left(l_j^2+n_j^2\right)F_2+{\zeta }_{\mathrm{ij}}\left(l_j^2-n_j^2\right)\left(l_j{F}_3+n_j{F}_4\right)+2n_j{l}_j{\zeta }_{\mathrm{ij}}\left(l_j{F}_4-n_j{F}_3\right)\right]& \left(14\right)\end{array}$ wherein $\begin{array}{cc}{F}_1=\frac{\left(n_j^2-l_j^2\right){\zeta }_{\mathrm{ij}}-2n_j{l}_j\left({\xi }_{\mathrm{ij}}+M_j\right)}{{\left({\xi }_{\mathrm{ij}}+a_j\right)}^2+{\zeta }_{\mathrm{ij}}^2}-\frac{{\left(n_j^2-l_j^2\right)}_{\mathrm{ij}}-2n_j{l}_j\left({\xi }_{\mathrm{ij}}-M_j\right)}{{\left({\xi }_{\mathrm{ij}}-M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2}& \left(15\right)\end{array}$ $\begin{array}{cc}{F}_2=-\frac{2n_j{l}_j{\zeta }_{\mathrm{ij}}+\left(n_j^2-l_j^2\right)\left({\xi }_{\mathrm{ij}}+M_j\right)}{{\left({\xi }_{\mathrm{ij}}+M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2}+\frac{2n_j{l}_j{\zeta }_{\mathrm{ij}}+\left(n_j^2-l_j^2\right)\left({\xi }_{\mathrm{ij}}-M_j\right)}{{\left({\xi }_{\mathrm{ij}}-M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2}& \left(16\right)\end{array}$ $\begin{array}{cc}{F}_3=\frac{n_j\left(n_j^2-3l_j^2\right)\left[{\left({\xi }_{\mathrm{ij}}+M_j\right)}^2-{\zeta }_{\mathrm{ij}}^2\right]+2l_j\left(3n_j^2-l_j^2\right)\left({\xi }_{\mathrm{ij}}+M_j\right){\zeta }_{\mathrm{ij}}}{{\left[{\left(\xi +M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2\right]}^2}-\frac{n_j\left[(n_j^2-3{l_j^2\left({\xi }_{\mathrm{ij}}-M_j\right)}^2-{\zeta }_{\mathrm{ij}}^2\right]+2l_j\left(3n_j^2-l_j^2\right)\left({\xi }_{\mathrm{ij}}-M_j\right){\zeta }_{\mathrm{ij}}}{{\left[{\left(\xi -M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2\right]}^2}& \left(17\right)\end{array}$ $\begin{array}{cc}{F}_4=\frac{2n_j\left(n_j^2-3l_j^2\right)\left({\xi }_{\mathrm{ij}}+M_j\right){\zeta }_{\mathrm{ij}}-l_j\left(3n_j^2-l_j^2\right)\left[{\left({\xi }_{\mathrm{ij}}+M_j\right)}^2-{\zeta }_{\mathrm{ij}}^2\right]}{{\left[{\left(\xi +M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2\right]}^2}-\frac{2n_j\left(n_j^2-3l_j^2\right)\left({\xi }_{\mathrm{ij}}-M_j\right){\zeta }_{\mathrm{ij}}-l_j\left(3n_j^2-l_j^2\right)\left[{\left({\xi }_{\mathrm{ij}}-M_j\right)}^2-{\zeta }_{\mathrm{ij}}^2\right]}{{\left[{\left(\xi -M_j\right)}^2+{\zeta }_{\mathrm{ij}}^2\right]}^2}& \left(18\right)\end{array}$ a conversion formula between global coordinates and local coordinates is:
ξ=n(x−c)−l(y−d)  (19)
ζ=l(x−c)+n(y−d)  (20) wherein, ξ.sub.ij and ζ.sub.ij denote local coordinate values; l and n denote cosine values of angles between a ζ-axis and the x-axis and the y-axis, with a subscript j denoting a cosine value of an angle of the j-th fracture element; c and d denote distances from an origin of a ξ-ζ local coordinate system to the x-axis and the y-axis of a global coordinate system, respectively; and M.sub.j denotes a half-length of the j-th fracture element; solving equation (12) to obtain a deformation of each fracture element, and bringing the deformation into equations (3) to (7) to obtain a stress distribution on a solution domain; and S12: determining whether the fracture extends at a tip position by a stress intensity factor K; the stress intensity factor K is calculated by the displacement discontinuity method: $\begin{array}{cc}{K}_I=\frac{0.806E\sqrt{\pi }}{4\left(1-v^2\right)\sqrt{2\alpha }}{D}_s& \left(21\right)\end{array}$ $K_{\mathrm{II}}=\frac{0.806E\sqrt{\pi }}{4\left(1-v^2\right)\sqrt{2\alpha }}{D}_n$ wherein, K.sub.I and K.sub.II denote stress intensity factors of type I and type II, respectively; E denotes a Young's modulus; and α denotes a half-length of a tip element; defining a criterion F to determine a direction of fracture initiation and extension: $\begin{array}{cc}F={\left(\frac{K_I\left(\theta \right)}{K_{\mathrm{IC}}}\right)}^2+{\left(\frac{K_{\mathrm{II}}\left(\theta \right)}{K_{\mathrm{IIC}}}\right)}^2& \left(22\right)\end{array}$ $\begin{array}{cc}{K}_I\left(\theta \right)=\frac{1}{2}\cos \left(\frac{\theta }{2}\right)\left[K_I\left(1+\cos \theta \right)-3K_{\mathrm{II}}\sin \theta \right]& \left(23\right)\end{array}$ $\begin{array}{cc}{K}_{\mathrm{II}}\left(\theta \right)=\frac{1}{2}\cos \left(\frac{\theta }{2}\right)\left[K_I\sin \theta +K_{\mathrm{II}}\left(3\cos \theta -1\right)\right]& \left(24\right)\end{array}$ wherein, θ denotes a tip deflection angle of the fracture; K.sub.I and K.sub.II denote the stress intensity factors of type I and type II, respectively; and K.sub.IC and K.sub.IIC denote cracking toughness of type I and type II, respectively; and determining, by a maximum value of F, a direction of fracture extension; and determining that the fracture starts to extend when F>1.

3. The method for coupling hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir according to claim 1, wherein step S2 comprises: S21: generating a random point, a random azimuth and a random length by a random number generation method to model the natural fracture distribution characteristic, wherein a random point N (N.sub.x,N.sub.y) conforms to a uniform distribution on an interval [0,1]:
N.sub.x=r.sub.l×rand.sub.k  (25)
N.sub.y=r.sub.w×rand.sub.k+1  (26) wherein, r.sub.l denotes a reservoir length; r.sub.w denotes a reservoir width; and rand denotes a random number, with a subscript denoting a random number of times to generate the random number; a fracture azimuth and a fracture length are expressed as follows:
θ.sub.p=π×rand.sub.k+2  (27)
l.sub.p=L.sub.max×rand.sub.k+3  (28) wherein, θ.sub.p denotes the fracture azimuth; and l.sub.p denotes the random fracture length; S22: constructing a hydraulic fracture network extension model of the horizontal well by considering hydraulic fracture flow, extension and deformation, and constructing a mass conservation equation of a pure fracturing fluid component f by considering leakage: $\begin{array}{cc}-\nabla .Math.\left[{\rho }_f{v}_{\mathrm{fl}}{x}_f\left(1-\underset{p}{.Math.}{c}_p\right)w_F\right]+q_{f,\mathrm{wf}}-q_{\mathrm{leak}}\left(1-\underset{p}{.Math.}{c}_p\right)\underset{f}{.Math.}{x}_f{\rho }_f{w}_F=\frac{\partial }{\partial t}\left[{\rho }_f{x}_f\left(1-\underset{p}{.Math.}{c}_p\right)w_F\right]& \left(29\right)\end{array}$ wherein, ρ.sub.f denotes a density of the fracturing fluid component f in the fracture; v.sub.fl denotes a seepage velocity of the fracturing fluid component f in an element l; x.sub.f denotes a half-length of the fracture; c.sub.p denotes a compressibility of a proppant component P; w.sub.F denotes a fracture aperture; and q.sub.f,wf denotes a seepage flow rate from a natural fracture to a hydraulic fracture; q.sub.leak denotes a one-dimensional leakage rate, and is expressed as: $\begin{array}{cc}{q}_{\mathrm{leak}}=\frac{C_{\mathrm{leak}}}{\sqrt{t-\tau }}& \left(30\right)\end{array}$ wherein, C.sub.leak denotes a leakage coefficient; t denotes a production time; and τ denotes a shear stress at the fracture boundary; deriving a mass conservation equation of the proppant component P: $\begin{array}{cc}-\nabla .Math.\left[{\rho }_p{v}_p{c}_p{w}_F\right]+q_{p,\mathrm{wf}}=\frac{\partial }{\partial t}\left[{\rho }_p{c}_p{w}_F\right]& \left(31\right)\end{array}$ wherein, ρ.sub.p denotes a density of the proppant component P in the fracture; v.sub.p denotes a migration velocity of the proppant component P; and q.sub.p,wf denotes a flowback amount of the proppant component P under a bottomhole pressure; based on a principle of mass conservation, a sand-carrying liquid in the fracture satisfies: $\begin{array}{cc}-\nabla .Math.\left[{\rho }_{\mathrm{sl}}{v}_{\mathrm{sl}}{w}_F\right]+q_{\mathrm{sl},\mathrm{wf}}-q_{\mathrm{leak}}\left(1-\underset{p}{.Math.}{c}_p\right)\underset{f}{.Math.}{x}_f{\rho }_f{w}_F=\frac{\partial }{\partial t}\left[{\rho }_{{\mathrm{sl}}^{W_F}}\right]& \left(32\right)\end{array}$ wherein, ρ.sub.sl denotes a density of the sand-carrying liquid; and q.sub.sl,wf denotes a flowback amount of the sand-carrying liquid under the bottomhole pressure; a flow velocity of the sand-carrying liquid is expressed as: $\begin{array}{cc}{v}_{\mathrm{sl}}=-\frac{w_F^2}{12{\mu }_{\mathrm{sl}}}\nabla \left(P\right)& \left(33\right)\end{array}$ wherein, μ.sub.sl denotes a viscosity of the sand-carrying liquid; a total flow rate Q.sub.T of an injected fluid satisfies a flow conservation relation: $\begin{array}{cc}{Q}_T=\underset{i}{\overset{2}{.Math.}}\underset{j=1}{\overset{N_F}{.Math.}}{Q}_{\mathrm{ji}}& \left(34\right)\end{array}$ wherein, N.sub.F denotes a total number of hydraulic fractures; and Q.sub.ji denotes a flow rate of an i-th section of a j-th fracture, i=1 denoting an upper wing of the hydraulic fracture, and i=2 denoting a lower wing of the hydraulic fracture; setting any fracture to have an internal pressure of P.sub.f,ji and a bottom pressure of P.sub.w,ji:
P.sub.w,ji=P.sub.f,ji+P.sub.vf,ji  (35) wherein, P.sub.vf,ji denotes a perforation friction pressure drop of the fracture, and is calculated as follows: $\begin{array}{cc}{P}_{\mathrm{vf},\mathrm{ji}}=\frac{Q_{\mathrm{ji}}^2\rho }{n_p^2{d}^4{K}_d^2}& \left(36\right)\end{array}$ wherein, K.sub.d denotes an empirical constant; d and n.sub.p denote a diameter of a perforation cluster and a number of perforation points, respectively; and ρ denotes a density of the fracturing fluid; assuming that an injection pressure at a heel end of the horizontal well is P.sub.0, then:
P.sub.0=(P.sub.w,ji+P.sub.cf,ji  (37) wherein, P.sub.cf,ji denotes a fluid flow friction pressure drop on the upper wing or the lower wing of the j-th fracture; equations (34) to (37) constitute equations for solving fluid flow in a wellbore, and 2N.sub.F+1 equations are constructed for 2N.sub.F+1 unknowns (2N.sub.F fracture flow rates Q.sub.ji and bottomhole injection pressures P.sub.0); wellbore flow and hydraulic fracture flow are linked by an injection flow rate and a fracture pressure, and a fluid-solid coupled relationship between the fracture flow and the fracture extension deformation is constructed by the normal discontinuous displacement D.sub.n of the fracture and the fracture aperture w.sub.F:
D.sub.n=−w.sub.F  (38) constructing a fluid-solid coupled hydraulic fracture extension model: $\begin{array}{cc}{N}_f\{\begin{array}{c}\underset{j}{\overset{N_f}{.Math.}}{B}^{1j}{D}_{N_f}^j-{\sigma }_{n,1}=0\\ .Math.\\ \underset{j}{\overset{N_f}{.Math.}}{B}^{\mathrm{nj}}{D}_{N_f}^j-{\sigma }_{n,N_f}=0\end{array}& \left(39\right)\end{array}$ $N_f\{\begin{array}{c}-\nabla .Math.{\left[{\rho }_{\mathrm{sl}}{v}_{\mathrm{sl}}w\right]}_1+{\left(q_{\mathrm{sl},\mathrm{wf}}\right)}_1-{\left[q_{\mathrm{leak}}\left(1-\underset{p}{.Math.}{c}_p\right)\underset{f}{.Math.}{x}_f{\rho }_{f}w\right]}_1=\frac{\partial }{\partial t}{\left[{\rho }_{\mathrm{sl}}w\right]}_1\\ .Math.\\ -\nabla .Math.{\left[{\rho }_{\mathrm{sl}}{v}_{\mathrm{sl}}w\right]}_{N_f}+{\left(q_{\mathrm{sl},\mathrm{wf}}\right)}_{N_f}-{\left[q_{\mathrm{leak}}\left(1-\underset{p}{.Math.}{c}_p\right)\underset{f}{.Math.}{x}_f{\rho }_{f}w\right]}_{N_f}=\\ \frac{\partial }{\partial t}{\left[{\rho }_{\mathrm{sl}}w\right]}_{N_f}\end{array}$ $1:Q_0=\underset{i=1}{\overset{2}{.Math.}}\underset{j}{\overset{N_{\mathrm{pref}}}{.Math.}}{Q}_{\mathrm{ji}}$ $N_{\mathrm{pref}}*2\{\begin{array}{c}{P}_0=P_{w,1}+P_{cf,1}\\ .Math.\\ P_0=P_{w,N_{\mathrm{pref}}*2}+P_{\mathrm{cf},N_{\mathrm{pref}}*2}\end{array}$ wherein, B.sup.nj denotes a partial derivative of a shape function of the j-th fracture element; D.sub.N.sub.f.sup.j denotes an elastic coefficient of a material of the j-th fracture element; σ.sub.n,N.sub.f denotes a stress acting on an N.sub.f-th fracture element; w denotes a width of a fracture grid element; N.sub.pref denotes a number of perforation holes; and N.sub.f denotes a total number of fractures; and solving main variables x.sup.T=[D.sub.n,1, D.sub.n,2, . . . , D.sub.n,N.sub.f, P.sub.1, P.sub.2, . . . P.sub.N.sub.f, P.sub.0, Q.sub.1, Q.sub.2, . . . , Q.sub.N.sub.pref.sub.*2] through an iterative algorithm, and updating the proppant component and the fracturing fluid component in a time step by equations (29) and (32).

4. The method for coupling hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir according to claim 1, wherein step S3 comprises: S31: generating a geological body based on an actual geological condition of a research area, a trajectory of the horizontal well, and distribution characteristics of the hydraulic fracture and the natural fracture; and S32: editing and importing data of the geological body, and generating a discrete model by three-dimensional orthogonal grids.

5. The method for coupling hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir according to claim 1, wherein step S4 comprises: S41: constructing, based on the embedded discrete fracture model, the three-dimensional three-phase mathematical models of seepage for the fractured horizontal well, wherein for a matrix system: $\begin{array}{cc}.Math.q_{\mathrm{omm}}+.Math.q_{\mathrm{onf}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left[\frac{\left(1-s_{gm}-s_{wm}\right){\varphi }_m}{B_{om}}\right]& \left(40\right)\end{array}$ $\begin{array}{cc}.Math.q_{wmm}+.Math.q_{\mathrm{wmf}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left(\frac{S_{wm}{\varphi }_m}{B_{wm}}\right)& \left(41\right)\end{array}$ $\begin{array}{cc}.Math.q_{\mathrm{gmm}}+.Math.q_{\mathrm{gmf}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left[\frac{S_{\mathrm{gm}}{\varphi }_m}{B_{\mathrm{gm}}}+\frac{\left(1-s_{\mathrm{gm}}-s_{\mathrm{wm}}\right)R_s{\varphi }_m}{B_{om}}\right]& \left(42\right)\end{array}$ and for a fracture system: $\begin{array}{cc}.Math.q_{\mathrm{of}}+q_{\mathrm{ofm}}+.Math.q_{\mathrm{off}}+q_{\mathrm{ofw}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left[\frac{\left(1-s_g-s_{\mathrm{wf}}\right){\varphi }_f}{B_{\mathrm{of}}}\right]& \left(43\right)\end{array}$ $\begin{array}{cc}.Math.q_{\mathrm{wf}}+q_{\mathrm{wfm}}+.Math.q_{\mathrm{wff}}+q_{\mathrm{wfw}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left(\frac{S_{\mathrm{wf}}{\varphi }_f}{B_{\mathrm{wf}}}\right)& \left(44\right)\end{array}$ $\begin{array}{cc}.Math.q_{\mathrm{gf}}+q_{\mathrm{gfm}}+.Math.q_{\mathrm{gff}}+q_{\mathrm{gfw}}=\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left[\frac{s_{\mathrm{gf}}{\varphi }_f}{B_{\mathrm{gf}}}+\frac{\left(1-s_{\mathrm{gf}}-s_{\mathrm{wf}}\right)R_s{\varphi }_f}{B_{\mathrm{of}}}\right]& \left(45\right)\end{array}$ wherein, subscripts o, g and w denote oil, gas and water phases, respectively; s(.Math.) denotes a saturation, that is, a ratio of a fluid volume to a total pore volume, dimensionless, and involving the oil, gas and water phases, with subscripts m and f denoting the matrix system and the fracture system, respectively; B(.Math.) denotes a fluid volume factor wherein the fluid volume factor is a ratio of a volume of the fluid of a same mass in the reservoir to a volume under a surface standard condition, dimensionless, and involving oil, gas and water phases in the matrix system and oil, gas and water phases in the fracture system, with subscripts m and f denoting the matrix system and the fracture system, respectively; V.sub.b denotes a volume of a matrix grid block, m.sup.3; α.sub.c denotes a volume conversion factor, and takes 1 in case of a metric unit; Δt denotes a time difference between two time points, d; ϕ.sub.m and ϕ.sub.f denote ratios of pore volumes in a matrix grid and a fracture grid to the volume of the matrix grid block (a matrix grid with a fracture embedded), respectively, dimensionless; Σq.sub.(.Math.)mm denotes a total flow rate from all matrix grids adjacent to the matrix grid into the matrix grid during a period of time Δt, m.sup.3/d, involving oil, gas and water phases; Σq.sub.(.Math.)mf denotes a total flow rate from all fracture grids embedded in the matrix grid into the matrix grid during the period of time Δt, m.sup.3/d, involving oil, gas and water phases; Σq.sub.(.Math.)f denotes a total flow rate from all adjacent fracture grids with a common edge in the fracture where the fracture grid is located into the fracture grid during the period of time Δt, m.sup.3/d, involving oil, gas and water phases; q.sub.(.Math.)fm denotes a flow rate from the matrix grid where the fracture grid is embedded into the fracture grid during the period of time Δt, m.sup.3/d, involving oil, gas and water phases; Σq.sub.(.Math.)ff denotes a total flow rate from all fracture grids, intersected by the fracture grid and located in the matrix grid where the fracture grid is embedded, into the fracture grid during the period of time Δt, involving oil, gas and water phases, m.sup.3/d; q.sub.(.Math.)fw denotes a flow rate from a well grid passing through the fracture grid into the fracture grid during the period of time Δt, involving oil, gas and water phases, and being a negative value when the horizontal well is a production well, m.sup.3/d; and R.sub.s denotes a solution gas-oil ratio of crude oil, and reflects an amount of dissolved gas in formation oil under a reservoir temperature and pressure; equations (40) to (45) define the three-dimensional three-phase mathematical models for the seepage of the fractured horizontal well; various fluid exchange terms in the equations can be written in a unified format of a product of a conductivity and a potential difference so as to expand the potential difference, and can also be expressed as a sum of fluid exchange induced by a pressure difference and a gravitational potential difference; and therefore, a fluid exchange expression of oil, gas and water is derived as follows: $\begin{array}{cc}q=T\left({\Phi }_2-{\Phi }_1\right)=\{\begin{array}{c}{T}_p\left(p_{o2}-p_{o1}\right)+T_Z\left(Z_{o2}-Z_{o1}\right)\\ T_p\left(p_{o2}-p_{o1}+p_{\mathrm{cow}1}-p_{\mathrm{cow}2}\right)+T_Z\left(Z_{w2}-Z_{w1}\right)\\ T_p\left(p_{o2}-p_{o1}+p_{\mathrm{cog}2}-p_{\mathrm{cog}1}\right)+T_Z\left(Z_{g2}-Z_{g1}\right)\end{array}& \left(46\right)\end{array}$ wherein, the conductivity T, T.sub.p and Tz are expanded as follows:
T=G.Math.f.sub.p(p.sub.o).Math.f.sub.s(s.sub.w,s.sub.g)=G.Math.f.sub.p.Math.f.sub.s  (47) wherein, G denotes a geometric parameter; f.sub.p denotes a pressure-related function; and f.sub.s denotes a saturation-related function; the geometric parameter G is different in each connection pair, f.sub.p and f.sub.s differ slightly in different positions of the flow equation, and G, f.sub.p and f.sub.s are specifically defined as follows, wherein, L=w, o: $\begin{array}{cc}G\equiv {\beta }_c\frac{kA}{\Delta l}& \left(48\right)\end{array}$ $\begin{array}{cc}{f}_p\equiv \frac{1}{{\mu }_L{B}_L}\mathrm{or}\frac{{\gamma }_L}{{\mu }_L{B}_L}\mathrm{or}\frac{R_s}{{\mu }_o{B}_o}\mathrm{or}\frac{R_s{\gamma }_0}{{\mu }_o{B}_o}& \left(49\right)\end{array}$ $\begin{array}{cc}{f}_s\equiv k_{\mathrm{rL}}& \left(50\right)\end{array}$ S42: constructing the fully implicit numerical model based on the finite difference method: $\begin{array}{cc}\begin{array}{c}{q}^{n+1}\approx q^{\left(v+1\right)}=q^{\left(v\right)}+\stackrel{\_}{\delta }q\\ =q^{\left(v\right)}+\frac{\partial q}{\partial p_{\mathrm{oi}}}{\overline{\delta }}_{P_{\mathrm{oi}}}+\frac{\partial q}{\partial p_{\mathrm{oj}}}\overline{\delta }{p}_{\mathrm{oj}}+\frac{\partial q}{\partial s_{\mathrm{wi}}}\overline{\delta }{s}_{\mathrm{wi}}+\\ \frac{\partial q}{\partial s_{\mathrm{wj}}}\overline{\delta }{s}_{\mathrm{wj}}+\frac{\partial q}{\partial s_{\mathrm{gi}}}\overline{\delta }{s}_{\mathrm{gi}}+\frac{\partial q}{\partial s_{\mathrm{gj}}}\overline{\delta }{s}_{\mathrm{gj}}\end{array}& \left(51\right)\end{array}$ $\begin{array}{cc}\begin{array}{c}\frac{V_b}{{\alpha }_c\Delta t}{\Delta }_t\left(\frac{s\varphi }{B}\right)=\frac{V_b}{{\alpha }_c\Delta t}\left[{\left(\frac{s\varphi }{B}\right)}^{n+1}-{\left(\frac{s\varphi }{B}\right)}^n\right]\approx \frac{V_b}{{\alpha }_c\Delta t}\left[{\left(\frac{s\varphi }{B}\right)}^{\left(v+1\right)}-{\left(\frac{s\varphi }{B}\right)}^n\right]\\ =\frac{V_b}{{\alpha }_c\Delta t}\left[{\left(\frac{s\varphi }{B}\right)}^{\left(v\right)}+\overline{\delta }\left(\frac{s\varphi }{B}\right)-{\left(\frac{s\varphi }{B}\right)}^n\right]\\ =\frac{V_b}{{\alpha }_c\Delta t}[{\left(\frac{s\varphi }{B}\right)}^{\left(v\right)}-{\left(\frac{s\varphi }{B}\right)}^n+\frac{\partial \left(\frac{s\varphi }{B}\right)}{\partial p_{\mathrm{oi}}}{\overline{\delta }}_{P_{\mathrm{oi}}}+\\ \frac{\partial \left(\frac{s\varphi }{B}\right)}{\partial s_{\mathrm{wi}}}\overline{\delta }{s}_{\mathrm{wi}}+\frac{\partial \left(\frac{s\varphi }{B}\right)}{\partial s_{\mathrm{gi}}}\overline{\delta }{s}_{\mathrm{gi}}]\end{array}& \left(52\right)\end{array}$ wherein, superscripts n and n+1 denote n-th and (n+1)-th time steps, and superscripts (v) and (v+1) denote v-th and (v+1)-th iteration steps; when a value of the (v+1)-th iteration step approaches a value of the (n+1)-th time step, a satisfied iteration accuracy is achieved; δ denotes a parameter change value between two iteration steps; and a subscript i denotes a grid expressed by the seepage equation, and a subscript j denotes a grid in fluid exchange with the i-th grid.

6. The method for coupling hydraulic fracture network extension and production performance of the horizontal well in the unconventional oil and gas reservoir according to claim 5, wherein in step S5, the step of iteratively solving the constructed fully implicit numerical model, and predicting the post-fracture production performance characteristic of the horizontal well comprises: assuming there are N fracture grids in M matrix grids, each grid being expressed by three equations of oil, gas and water and having three unknowns δp.sub.oi, δs.sub.wi and δs.sub.gi, then constructing a fully implicit calculation matrix considering reservoir seepage and hydraulic fracture flow:
E.sub.3(M+N)×3(M+N)×δX.sub.3(M+N)×1F.sub.3(M+N)×1  (53) wherein, E.sub.3(M+N)×3(M+N) denotes a coefficient matrix; δX.sub.3(M+N)×1 denotes an unknown vector; and F.sub.3(M+N)×1 denotes a constant vector; iteratively calculating for each time step until a satisfied accuracy of the unknown vector δX.sub.3(M+N)×1 thereby obtaining a pressure value and a saturation value at the (n+1)-th time step; and starting a cycle at a next time step; and finally, outputting pressure and saturation distributions of the reservoir at each time step, and calculating a production performance of the fractured horizontal well according to a production formula, wherein since each fractured horizontal well comprises multiple hydraulic fractures, an output of the fractured horizontal well is a sum of flow rates of all fractures flowing into a wellbore; and a flow rate of each fracture flowing into the wellbore is: wherein, $$\begin{gathered} \begin{array}{cc}{q}_L={\mathrm{WI}}_f{f}_s{f}_p\left(P_{\mathrm{wf}}-p_f\right) \\ {\mathrm{WI}}_f=\frac{\mathrm{\Delta \theta }.Math.k_f{\omega }_f}{\ln \left(\frac{0.14\sqrt{L_f^2+h_f^2}}{r_w}\right)}& \left(54\right)\end{array} \end{gathered}$$ wherein, p.sub.wf denotes a flowing bottomhole pressure; p.sub.f denotes a pressure of the fracture grid; k.sub.f denotes a fracture permeability, D; ω.sub.f denotes a fracture aperture, m; L.sup.f and h.sub.f respectively denote a length and a height of a fracture section, m; and Δθ denotes a central angle of a radial well in the fracture, rad.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a flowchart of a method for coupling hydraulic fracture network extension and production performance of a horizontal well in an unconventional oil and gas reservoir;

[0014] FIG. 2 is a schematic view of a hydraulic fracture extension shape of the horizontal well considering a natural fracture distribution;

[0015] FIG. 3 is a schematic view of three-dimensional grid partition of the horizontal well and a fracture network;

[0016] FIG. 4 shows a production pressure distribution of the fractured horizontal well;

[0017] FIG. 5 shows a forecast curve of daily oil production and cumulative oil production;

[0018] FIG. 6 shows a forecast curve of daily water production and cumulative water production; and

[0019] FIG. 7 shows a forecast curve of daily gas production and cumulative gas production.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] To describe the technical features, objectives and beneficial effects of the present disclosure more clearly, the technical solutions of the present disclosure are described in detail below, but it should not be construed that the protection scope of the present disclosure is limited thereto. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts should fall within the protection scope of the present disclosure.

[0021] The present disclosure is described in further detail below with reference to the drawings and embodiments.

[0022] (1) First, geomechanical parameters, natural fracture parameters and engineering parameters of the reservoir are input, and simulation is performed based on a fracture failure type criterion, to obtain the shape and spatial distribution characteristics of the hydraulic fracture network, as shown in FIG. 2.

[0023] The specific parameters used in this embodiment are shown in Table 1.

TABLE-US-00001 TABLE 1 Case calculation parameters Parameter Value Unit Minimum horizontal principal stress 40 MPa Maximum horizontal principal stress 40.5 MPa Young's modulus 30 GPa Poisson's ratio 0.25 — Fluid viscosity 9 cp Proppant diameter 0.00015 m Proppant density 2800 kg/m.sup.3 Fracture spacing 30 m Type I cracking toughness of matrix rock 2 MPa .Math. m.sup.1/2 Type II cracking toughness of matrix rock 4 MPa .Math. m.sup.1/2 Initial aperture of natural fracture 0.2 1e.sup.−5 m Closure aperture of natural fracture 1 1e.sup.−5 m Compressibility of natural fracture 0.05 MPa.sup.−1 Friction angle of natural fracture 20 °

[0024] (2) Spatial grid partition is performed on the extension shape of the generated hydraulic fracture network by using three-dimensional orthogonal grids. The total calculation area has a volume is 400×200×20 m.sup.3, and the length of the horizontal well section in the calculation area is 200 m. A five-section multi-stage hydraulic fracture is created through hydraulic fracturing, as shown in FIG. 3.

[0025] (3) Based on the reservoir grid partition results are combined with the three-dimensional three-phase fully implicit numerical model of fractured horizontal well. The basic parameters of the model (Table 2), the pressure-volume-temperature (PVT) parameters (Table 3) of crude oil and natural gas, matrix permeability data (Table 4 and Table 5), and matrix capillary force data (Table 6) are brought to obtain the production performance data of the simulated well, and the post-fracture production performance characteristics of the horizontal well are predicted, as shown in FIGS. 4 to 7.

TABLE-US-00002 TABLE 2 Basic parameters of model Parameter Value Parameter Value Matrix permeability,    0.001 Formation water 4 × 10.sup.−4 D compressibility, MPa.sup.−1 Rock compressibility,   10.sup.−4 Formation water 0.0009 MPa.sup.−1 viscosity, Pa .Math. s Initial porosity,   0.1 Initial water saturation, 0.3 dimensionless dimensionless Hydraulic fracture 25 Initial oil saturation, 0.7 permeability, D dimensionless Initial oil-phase 20 Flowing bottom-hole 8 pressure, MPa pressure, MPa Initial volume factor of    1.01 Aperture of hydraulic 0.005 formation water, fracture, m dimensionless Initial density of 1010  Aperture of natural 0.003 formation water, fracture, m kg/m.sup.3

TABLE-US-00003 TABLE 3 PVT parameters of crude oil and natural gas Crude oil Solution gas-oil Natural gas Pressure Density Viscosity Volume factor ratio Density Viscosity Volume factor (kPa) (kg/m.sup.3) (cP) Dimensionless Dimensionless (kg/m.sup.3) (cP) Dimensionless 3000 660.13 1.17 1.1806 45.93 25.9351 0.012654 0.035502 4500 652.26 0.97 1.2104 57.63 38.6406 0.01315 0.023019 6000 644.92 0.85 1.2397 69.43 51.8383 0.013675 0.016821 7500 637.83 0.76 1.2698 81.65 65.6071 0.014254 0.013138 9000 630.87 0.69 1.3010 94.44 79.956 0.014907 0.010714 10500 623.96 0.64 1.3338 107.92 94.848 0.015649 0.009012 12000 617.07 0.58 1.3734 122.18 110.212 0.016493 0.007762 13500 617.83 0.58 1.3697 122.18 — — — 15000 619.82 0.60 1.3653 122.18 — — — 16500 621.74 0.61 1.3611 122.18 — — — 18000 623.58 0.63 1.3571 122.18 — — — 19500 625.34 0.64 1.3533 122.18 — — — 21000 627.04 0.66 1.3496 122.18 — — —

TABLE-US-00004 TABLE 4 Matrix oil-water permeability s.sub.w k.sub.rw k.sub.ro 0.21 0.0000 1.0000 0.24 0.0074 0.8565 0.27 0.0209 0.7291 0.30 0.0385 0.6164 0.33 0.0592 0.5174 0.36 0.0827 0.4307 0.39 0.1088 0.3555 0.42 0.1371 0.2905 0.45 0.1674 0.2349 0.48 0.1998 0.1877 0.51 0.2340 0.1480 0.54 0.2700 0.1150 0.57 0.3076 0.0878 0.60 0.3469 0.0657 0.63 0.3876 0.0481 0.66 0.4299 0.0343 0.69 0.4736 0.0237 0.72 0.5187 0.0158 0.75 0.5651 0.0100 0.78 0.6129 0.0060 0.81 0.6619 0.0033 0.84 0.7121 0.0017 0.87 0.7636 0.0007 0.90 0.8163 0.0003

TABLE-US-00005 TABLE 5 Matrix oil-gas permeability s.sub.g k.sub.rg k.sub.ro 0.04 0 1 0.08 0.01103 0.70778 0.12 0.02912 0.55844 0.16 0.05138 0.4454 0.20 0.07687 0.35562 0.24 0.10506 0.28302 0.28 0.13561 0.22392 0.32 0.16827 0.17574 0.36 0.20286 0.13656 0.40 0.23923 0.10485 0.44 0.27725 0.07938 0.48 0.31683 0.05912 0.52 0.35788 0.04319 0.56 0.40031 0.03084 0.60 0.44408 0.02143 0.64 0.48911 0.01442 0.68 0.53536 0.00933 0.72 0.58279 0.00574 0.76 0.63134 0.00332 0.79 0.67989 0.0009

TABLE-US-00006 TABLE 6 Matrix oil-water and gas-oil capillary force s.sub.w, p.sub.cow, 1-s.sub.g, p.sub.cgo, dimensionless kPa dimensionless kPa 0.2 8000 0.21 4760 0.25 4300 0.26 2940 0.3 3000 0.31 2220 0.4 1780 0.41 1490 0.5 1210 0.51 1040 0.6 790 0.66 510 0.7 430 0.76 270 0.8 100 0.96 0 0.9 0

[0026] The present disclosure is described above with reference to the preferred embodiments, but those skilled in the art should understand that these embodiments are only intended to describe the present disclosure, rather than to limit the scope of the present disclosure. Further improvements of the present disclosure made without departing from the principle of the present disclosure should also be deemed as falling within the protection scope of the present disclosure.