Method for predicting the optimal shut-in duration by coupling fluid flow and geological stress

Abstract

The invention discloses a method for predicting the optimal shut-in duration by coupling fluid flow and geological stress, comprising the following steps: determine basic parameters; obtain the fracture length, fracture width and reservoir stress distribution based on the basic parameters; calculate the oil saturation, pore pressure, and permeability and porosity after coupling change in different shut-in durations on the basis of the principle of fluid-solid coupling; take the oil saturation, pore pressure, and permeability and porosity obtained in Step 3 as initial parameters and calculate the production corresponding to different shut-in time on the basis of the productivity model; finally select the optimal shut-in time based on the principle of fastest cost recovery. The present invention can accurately predict the optimal shut-in duration after fracturing to improve the oil and gas recovery ratio in tight oil and gas reservoirs with difficulty in development and low recovery.

Claims

1. A method for predicting the optimal shut-in duration by coupling fluid flow and geological stress, comprising the following steps: Step 1: Establish a simulated physical model range to determine the basic parameters based on geological parameters, construction parameters, boundary conditions and initial conditions; Step 2: Establish a fracture propagation and stress interference model to obtain the fracture length, fracture width and reservoir stress distribution based on the basic parameters, in combination with the Reynolds equation, the fracture width equation and the reservoir elastic deformation equation; Step 3: Take the fracture length, fracture width and reservoir stress distribution obtained in Step 2 as the initial parameters, and calculate the oil saturation, pore pressure, and permeability and porosity after coupling change in different shut-in durations on the basis of the principle of fluid-solid coupling; and Step 4: Take the oil saturation, pore pressure, and permeability and porosity obtained in Step 3 as initial parameters and calculate the production corresponding to different shut-in time on the basis of the productivity model, and finally select the optimal shut-in time based on the principle of fastest cost recovery.

2. The method for predicting the optimal shut-in duration by coupling fluid flow and geological stress according to claim 1, wherein the geological parameters include initial permeability, initial porosity, elastic modulus and Poisson's ratio, and the construction parameters include injection displacement and fracturing fluid viscosity.

3. The method for predicting the optimal shut-in duration by coupling fluid flow and geological stress according to claim 1, wherein the following equation applies to the establishment of the fracture propagation and stress interference model is established based on the Reynolds equation, the fracture width equation and the reservoir elastic deformation equation in Step 2: $W\left(x\right)=\frac{2.Math.\left(1-{}^2\right).Math.H\left(P_f\left(x\right)-{}_n\right)}{E}$ $\frac{}{6.Math.4.Math.{}_f}.Math.\frac{}{x}.Math.\left(W^3.Math.\frac{\left(P_f-{}_n\right)}{x}\right)=\frac{K.Math..Math..Math..Math.\mathrm{xH}.Math.P_f}{{}_f.Math.y}+\frac{}{4}.Math.\frac{W}{t}$ $Q_0=4.Math.\mathrm{HFdx}+\frac{.Math.H}{4}.Math.\frac{.Math.W}{.Math.t}.Math.\mathrm{dx}$ $L_f=L_0+\underset{j=0}{\overset{k}{.Math.}}.Math..Math..Math.x_j$ $G.Math.{}^2.Math.u_i+\left(G+\right).Math.\frac{}{x_i}.Math.\left(.Math.u\right)={}_p.Math.\frac{p}{x_i}$ ${}_{\mathrm{ij}}.Math.=2.Math.G.Math..Math.{\mathrm{.Math.}}_{\mathrm{ij}}+.Math.{\mathrm{.Math.}}_v.Math.{}_{\mathrm{ij}}-{}_p.Math.p.Math..Math.{}_{\mathrm{ij}}$ Where, W is the fracture width, in m; H is the fracture height, in m; E is the elastic modulus of the reservoir, in MPa; t is the construction time, in d; x is the abscissa of the model, in m; y is the ordinate of the model, in m; x is the unit length of the fracture, in m; P.sub.f is the fracture fluid pressure, in MPa; .sub.f is the viscosity of the injected fluid, in mPa.Math.s; v is the Poisson's ratio of the reservoir rock, dimensionless; .sub.n is the minimum horizontal principal stress, in MPa; K is the fracture wall permeability, in m.sup.2; Q.sub.0 is the injection rate, in m.sup.3/d; F is the fluid loss rate, in m/d; L.sub.f is the fracture length, in m; L.sub.0 is the initial length of the fracture, in m; k is the total number of fracture division units, dimensionless; j is the j.sup.th fracture unit, dimensionless; G is the shear modulus of the rock, in MPa; is the Lame constant, in MPa; .sub.ij is the Kronecker symbol; p is the pore pressure, in MPa; .sub.ij is the strain component, dimensionless; .sub.v is the volumetric strain, dimensionless; .sub.p is the Biot constant, dimensionless; u.sub.i is the displacement of the reservoir in the i direction, in m; u is the displacement tensor, in m.

4. The method for predicting the optimal shut-in duration by coupling fluid flow and geological stress according to claim 1, wherein the calculation equation in Step 3 is: $.Math.\left({}_1.Math.\frac{K.Math.K_r}{{}_1}.Math.p\right)+q_v=\frac{\left(.Math..Math.S\right)}{t}-.Math.S.Math.{}_p.Math.\frac{{\mathrm{.Math.}}_v}{t}$ $={}_i.Math.\frac{e^{-c_{}.Math..Math.}}{1-{}_i\left(1-e^{-c_{}.Math..Math.}\right)}$ $K=K_i.Math.\frac{e^{-c_{}.Math..Math.}}{1-{}_i\left(1-e^{-c_{}.Math..Math.}\right)}$ Where, .sub.1 is the fluid density, in kg/m.sup.3; K is the absolute permeability of the reservoir, in mD; K.sub.r is the relative permeability of the reservoir, dimensionless; .sub.1 is the viscosity of the reservoir fluid, in mPa.Math.s; q.sub.v is the source sink term in the reservoir, in m.sup.3/min; t is the construction time, in d; is the porosity, dimensionless; S is the fluid saturation, dimensionless; .sub.i is the initial porosity, dimensionless; K.sub.i is the initial permeability, dimensionless; is the stress difference, in MPa; c.sub. is the compressibility of reservoir rock, in MPa.sup.1.

5. The method for predicting the optimal shut-in duration by coupling fluid flow and geological stress according to claim 1, wherein the productivity model in Step 4 is: $q_{\mathrm{iwell}}={}_1.Math.\frac{K.Math.K_r}{{}_1}.Math.\frac{2.Math..Math.H}{\ln \left(r_e/r_w\right)+a}.Math.\left(p-p_w\right)$ Where, q.sub.lwell is the exchange term between fracture and production well, in m.sup.3; H is the fracture height, in m; K is the absolute permeability of the reservoir, in mD; K.sub.r is the relative permeability of the reservoir, dimensionless; .sub.1 is the viscosity of the reservoir fluid, in mPa.Math.s; r.sub.e is the effective radius of the production well, in m; r.sub.w is the well radius, in m; a is the correction factor, dimensionless; p is the pore pressure, in MPa; p.sub.w is the downhole pressure, in MPa.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a model diagram.

[0021] FIG. 2 is a diagram of stress distribution after fracturing.

[0022] FIG. 3 is a curve of permeability changing with time in shut-in process.

[0023] FIG. 4 is a curve of porosity changing with time in shut-in process.

[0024] FIG. 5 is a diagram of relationship between the optimal shut-in duration, displacement and total injection volume.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] The present invention will be further described with the following embodiments and figures.

[0026] The method for predicting the optimal shut-in duration by coupling fluid flow and geological stress disclosed in the present invention includes the following steps:

[0027] Step 1: Obtain the geological parameters by field logging and well testing, and establish the simulated physical model range to determine the basic parameters based on geological parameters, construction parameters, boundary conditions and initial conditions;

[0028] The geological parameters include initial permeability, initial porosity, elastic modulus and Poisson's ratio, and the construction parameters include injection displacement and fracturing fluid viscosity;

[0029] Step 2: Establish a fracture propagation and stress interference model to obtain the fracture length, fracture width and reservoir stress distribution based on the basic parameters, in combination with the Reynolds equation, the fracture width equation and the reservoir elastic deformation equation;

[0030] The calculation equations of the above steps are Equations (1), (2), (3), (4), (5) and (6);

[00004]$\begin{array}{cc}W\left(x\right)=\frac{2.Math.\left(1-{}^2\right).Math.H\left(P_f\left(x\right)-{}_n\right)}{E}& \left(1\right)\\ \frac{}{6.Math.4.Math.{}_f}.Math.\frac{}{x}.Math.\left(W^3.Math.\frac{\left(P_f-{}_n\right)}{x}\right)=\frac{K.Math..Math..Math..Math.\mathrm{xH}.Math.P_f}{{}_f.Math.y}+\frac{}{4}.Math.\frac{W}{t}& \left(2\right)\\ Q_0=4.Math.\mathrm{HFdx}+\frac{.Math.H}{4}.Math.\frac{.Math.W}{.Math.t}.Math.\mathrm{dx}& \left(3\right)\\ L_f=L_0+\underset{j=0}{\overset{k}{.Math.}}.Math..Math..Math.x_j& \left(4\right)\\ G.Math.{}^2.Math.u_i+\left(G+\right).Math.\frac{}{x_i}.Math.\left(.Math.u\right)={}_p.Math.\frac{p}{x_i}& \left(5\right)\\ {}_{\mathrm{ij}}.Math.=2.Math.G.Math..Math.{\mathrm{.Math.}}_{\mathrm{ij}}+.Math.{\mathrm{.Math.}}_v.Math.{}_{\mathrm{ij}}-{}_p.Math.p.Math..Math.{}_{\mathrm{ij}}& \left(6\right)\end{array}$

[0031] Where, W is the fracture width, in m; H is the fracture height, in m; E is the elastic modulus of the reservoir, in MPa; t is the construction time, in d; x is the abscissa of the model, in m; y is the ordinate of the model, in m; x is the unit length of the fracture, in m; P.sub.f is the fracture fluid pressure, in MPa; .sub.f is the viscosity of the injected fluid, in mPa.Math.s; v is the Poisson's ratio of the reservoir rock, dimensionless; .sub.n is the minimum horizontal principal stress, in MPa; K is the fracture wall permeability, in m.sup.2; Q.sub.0 is the injection rate, in m.sup.3/d; F is the fluid loss rate, in m/d; L.sub.f is the fracture length, in m; L.sub.0 is the initial length of the fracture, in m; k is the total number of fracture division units, dimensionless; j is the j.sup.th fracture unit, dimensionless; G is the shear modulus of the rock, in MPa; is the Lame constant, in MPa; .sub.ij is the Kronecker symbol; p is the pore pressure, in MPa; .sub.ij is the strain component, dimensionless; .sub.v is the volumetric strain, dimensionless; .sub.p is the Biot constant, dimensionless; u.sub.i is the displacement of the reservoir in the i direction, in m; u is the displacement tensor, in m.

[0032] Step 3: Substitute the fracture length, fracture width and reservoir stress distribution obtained in Step 2 into Step 3 as the initial conditions; then, based on the principle of fluid-solid coupling, calculate the oil saturation and pore pressure in different shut-in durations by Equation (7), and work out the permeability and porosity after coupling change by Equations (8) and (9);

[00005]$\begin{array}{cc}.Math.\left({}_1.Math.\frac{K.Math.K_r}{{}_1}.Math.p\right)+q_v=\frac{\left(.Math..Math.S\right)}{t}-.Math.S.Math.{}_p.Math.\frac{{\mathrm{.Math.}}_v}{t}& \left(7\right)\\ ={}_i.Math.\frac{e^{-c_{}.Math..Math.}}{1-{}_i\left(1-e^{-c_{}.Math..Math.}\right)}& \left(8\right)\\ K=K_i.Math.\frac{e^{-c_{}.Math..Math.}}{1-{}_i\left(1-e^{-c_{}.Math..Math.}\right)}& \left(9\right)\end{array}$

[0033] Where, .sub.1 is the fluid density, in kg/m.sup.3; K is the absolute permeability of the reservoir, in mD; K.sub.r is the relative permeability of the reservoir, dimensionless; .sub.1 is the viscosity of the reservoir fluid, in mPa.Math.s; q.sub.v is the source sink term in the reservoir, in m.sup.3/min; t is the construction time, in d; is the porosity, dimensionless; S is the fluid saturation, dimensionless; .sub.i is the initial porosity, dimensionless; K.sub.i is the initial permeability, dimensionless; is the stress difference, in MPa; c.sub. is the compressibility of reservoir rock, in MPa.sup.1.

[0034] Step 4: Take the oil saturation, pore pressure, and permeability and porosity obtained in Step 3 as initial parameters and calculate the production corresponding to different shut-in time on the basis of the productivity model, and finally select the optimal shut-in time based on the principle of fastest cost recovery.

[00006]$\begin{array}{cc}{q}_{\mathrm{iwell}}={}_1.Math.\frac{K.Math.K_r}{{}_1}.Math.\frac{2.Math..Math.H}{\ln \left(r_e/r_w\right)+a}.Math.\left(p-p_w\right)& \left(10\right)\end{array}$

[0035] Where, q.sub.lwell is the exchange term between fracture and production well, in m.sup.3; H is the fracture height, in m; K is the absolute permeability of the reservoir, in mD; K.sub.r is the relative permeability of the reservoir, dimensionless; .sub.1 is the viscosity of the reservoir fluid, in mPa.Math.s; r.sub.e is the effective radius of the production well, in m; r.sub.w is the well radius, in m; a is the correction factor, dimensionless; p is the pore pressure, in MPa; p.sub.w is the downhole pressure, in MPa.

Embodiment 1

[0036] A block in Qinghai Oilfield has the typical characteristics of tight oil reservoir. The geological data of the block is obtained with field logging and well testing, and the parameters acquired are representative, that is, the reservoir has the characteristics of low porosity and low permeability.

[0037] The schematic diagram of the simulated physical model is shown in FIG. 1. The specific steps are described as follows:

[0038] 1. Obtain the geological parameters by field logging and well testing: the injection displacement is 7 m.sup.3/min, the fracturing fluid viscosity is 1.1 mPs.Math.s, the fracture spacing is 20 m, the number of fracture clusters is 3, the Poisson's ratio of the rock is 0.25, the rock elastic modulus is 28,799 MPa, the initial oil saturation is 0.65, the initial absolute permeability of the reservoir is 0.1 mD, the initial porosity is 0.15, the density of crude oil is 964 kg/m.sup.3, the density of reservoir water is 980 kg/m.sup.3, and the oil viscosity is 1.25 mPs.Math.s, the water viscosity is 1.1 mPs.Math.s, the initial pore pressure is 15 MPa, the maximum principal stress is 30 MPa, the minimum principal stress is 27 MPa, and the Biot effective constant is 1.

[0039] 2. Use simultaneous Equations (1), (2), and (3) to obtain two equations with two unknowns by the finite difference method, then use the Picard iteration method to obtain the fracture width in the length direction of the fracture, the fluid pressure distribution in the fracture and the fracture length distribution, and use the stress-strain equations and stress-displacement equations of Equations (5) and (6) to obtain the induced stress distribution generated by hydraulic fracturing (as shown in FIG. 2).

[0040] 3. In Step 3, link and solve Equations (5) and (7) and use the five-point difference method to obtain the discrete form of Equations (5) and (7); work out the pore pressure and saturation distribution at first and then work out the induced stress caused by the pore pressure based on the principle of fluid-solid coupling; calculate the permeability and porosity distribution (as shown in FIGS. 3 and 4) after considering the fluid-solid coupling changes by Equations (8) and (9). According to the selection of different well times, the calculation process can be cycled multiple times to obtain the distribution of parameters such as permeability and porosity in different shut-in durations.

[0041] 4. Finally, take the obtained pore pressure, permeability, porosity and saturation as the initial conditions of the productivity model, and then obtain the productivity in different shut-in durations by Equation (10), and select the optimal shut-in duration according to production optimization. The diagram shown in FIG. 5 can be obtained according to the construction parameters concerned on site and the optimal shut-in duration obtained by simulation.

[0042] According to the simulation steps of the present invention, the optimal shut-in duration can be worked out for the blocks with different geological parameters, and the working system can be optimized reasonably by adjusting the shut-in time after fracturing to achieve the goals of increasing the production and the recovery ratio.

[0043] The above are not intended to limit the present invention in any form. Although the present invention has been disclosed as above with 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.