Fracturing fluid spontaneous imbibition numerical simulation method considering chemical osmotic pressure

Abstract

The invention discloses a fracturing fluid spontaneous imbibition numerical simulation method considering chemical osmotic pressure, and belongs to the technical field of unconventional oil-gas exploration and development, and the fracturing fluid spontaneous imbibition numerical simulation method comprises the following steps: step 1, describing mathematical problems in a fracturing fluid spontaneous imbibition phenomenon, and carrying out mathematical model assumption; 2, determining the real speed of the water phase based on the seepage speed of the water phase; 3, determining a salt ion migration control equation under an oil-water two-phase flow condition; 4, based on the oil-water two-phase flow control equation considering the chemical osmotic pressure and the salt ion migration control equation under the oil-water two-phase flow condition, establishing a fracturing fluid spontaneous imbibition mathematical model considering the chemical osmotic pressure; 5, spatial discretization is conducted on the fracturing fluid spontaneous imbibition mathematical model; and step 6, determining spontaneous imbibition numerical simulation parameters, and performing numerical method solution on the fracturing fluid spontaneous imbibition mathematical model. According to the method, the accuracy of spontaneous imbibition numerical simulation of the fracturing fluid can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of unconventional oil and gas exploration and development, and in particular relates to a numerical simulation method for spontaneous imbibition of fracturing fluid taking chemical osmotic pressure into consideration. Background Art

[0002] Shale oil and gas, tight oil and gas, and coalbed methane are unconventional oil and gas resources that are difficult to explore and develop. They usually have no natural industrial stable production capacity. Large-scale volume fracturing is required to improve the seepage capacity of the reservoir near the wellbore, thereby increasing the production capacity of a single well. After hydraulic fracturing, well shut-in measures are generally required. It is generally believed that the spontaneous imbibition of fracturing fluid during the well shut-in process is very beneficial to increasing reservoir production. It is generally believed that capillary force is the main driving force for spontaneous imbibition, but in the field of unconventional oil and gas, in addition to capillary force, chemical osmotic pressure also plays an important role in the process of fracturing fluid infiltration into the reservoir.

[0003] For shale oil and tight oil, the commonly used methods for evaluating the spontaneous imbibition effect of fracturing fluids currently include indoor experimental methods and mathematical model methods. Common indoor experimental methods are mainly volumetric methods or weighing methods. Both methods can optimize the parameters of spontaneous imbibition experiments, but it is difficult to quantitatively study the influence of chemical osmotic pressure, and they have high requirements for samples and experimental conditions and a long experimental cycle. Common mathematical model methods are mainly analytical formula methods and numerical simulation methods. The analytical formula method is difficult to display the seepage field in an interfacial manner, and the research results are not intuitive enough compared to the numerical simulation method. At present, there are numerical simulation methods for spontaneous imbibition of fracturing fluids that take capillary forces into account, but they ignore the role of chemical osmotic pressure in spontaneous imbibition.

[0004] In summary, the traditional numerical simulation method of spontaneous imbibition of fracturing fluid without considering chemical osmotic pressure is no longer applicable to the development of shale oil and tight oil.

[0005] Based on this, the present application aims to make up for the defect that the existing numerical simulation method of spontaneous imbibition of fracturing fluid does not take chemical osmotic pressure into consideration. Based on the oil-water two-phase flow control equation taking chemical osmotic pressure into consideration and the salt ion migration control equation under oil-water two-phase flow conditions, a mathematical model of spontaneous imbibition of fracturing fluid taking chemical osmotic pressure into consideration is established. This can effectively improve the accuracy of numerical simulation of spontaneous imbibition of fracturing fluid. In the field of unconventional oil and gas development, it can effectively evaluate the imbibition recovery degree of fracturing fluid, and then explore the influence of different parameters on the imbibition recovery degree of fracturing fluid, and provide simulation data for the study of the change law of fracturing fluid imbibition. Summary of the invention

[0006] The purpose of the present invention is to overcome the above-mentioned deficiencies of the prior art and to provide a numerical simulation method for spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure.

[0007] To achieve the above object, the present invention adopts the following technical solution:

[0008] The numerical simulation method of spontaneous imbibition of fracturing fluid considering chemical osmotic pressure includes the following steps:

[0009] Step 1, describe the mathematical problems in the spontaneous imbibition phenomenon of fracturing fluid and make mathematical model assumptions;

[0010] Step 2, determining the real velocity of the water phase based on the water phase seepage velocity;

[0011] Step 3, determining the salt ion migration control equation under oil-water two-phase flow conditions;

[0012] Step 4, based on the oil-water two-phase flow control equation considering the chemical osmotic pressure and the salt ion migration control equation under the oil-water two-phase flow condition, a mathematical model of spontaneous imbibition of fracturing fluid considering the chemical osmotic pressure is established;

[0013] Step 5, spatially discretizing the mathematical model of spontaneous imbibition of fracturing fluid;

[0014] Step 6, determine the numerical simulation parameters of spontaneous imbibition, and solve the mathematical model of spontaneous imbibition of fracturing fluid by numerical method.

[0015] Preferably, in step 2, the method for determining the true velocity of the water phase is as follows:

[0016] In the case of oil-water two-phase flow, the water phase flow velocity is expressed as:

[0017]

[0018] In the formula, v w is the water phase seepage velocity; Q w is the water phase seepage; A is the seepage cross-sectional area;

[0019] In the case of oil-water two-phase flow, the true velocity of the water phase is expressed as:

[0020]

[0021] In the formula, u w is the real velocity of water phase; A pw is the water phase pore area of ​​the seepage cross section;

[0022] Take a uniform porous medium microelement with a porosity of φ, then the pore area of ​​the seepage cross section is:

[0023] A p =Aφ (1-3)

[0024] In the formula, A p is the pore area of ​​the seepage cross section;

[0025] In the case of oil-water two-phase seepage, since the pores on the seepage cross section are occupied by both oil and water, the pore area of ​​the water phase is:

[0026] A pw =S w A p (1-4)

[0027] In the formula, S w is the water saturation.

[0028] From equations (1-1), (1-2), (1-3) and (1-4), it can be deduced that the relationship between the true velocity of the water phase and the water phase seepage velocity is:

[0029]

[0030] Preferably, in step 3, the method for determining the salt ion migration control equation under oil-water two-phase flow conditions is as follows:

[0031] Step 31, classifying the pores at the rock cross section;

[0032] Based on the semipermeable membrane effect of rock, the membrane efficiency E is used to describe the effectiveness of the semipermeable membrane in removing solutes, where:

[0033]

[0034] Where, E is the membrane efficiency; P π is the actual osmotic pressure; p π is the ideal osmotic pressure;

[0035] Redefine membrane efficiency: The seepage channel at the rock cross section is composed of water phase pores and oil phase pores. Among the water phase pores, the proportion of water phase pores with ideal osmotic pressure is E, and the proportion of water phase pores with actual osmotic pressure of 0 is (1-E). Salt ions cannot pass through water phase pores with ideal osmotic pressure, but can freely pass through water phase pores with actual osmotic pressure of 0.

[0036] According to the redefined membrane efficiency, the total pore area of ​​the water phase with the ideal osmotic pressure is recorded as A π , which accounts for a proportion of the water phase pore area E. This type of pore cannot transport salt ions. The total area of ​​the water phase pores with an actual osmotic pressure of 0 is recorded as A wD , accounting for the proportion of the water phase pore area (1-E). The flow of water in this type of pores follows Darcy's law, and salt ions can pass freely;

[0037] According to formula (1-3) and (1-4), A wD It can be expressed as:

[0038] A wD =(1-E)Apw =(1-E)φS w A (2-2)

[0039] In the formula, A wD is the total area of ​​water phase pores with actual osmotic pressure of 0; A is the seepage cross-sectional area, that is, the rock cross-sectional area;

[0040] Step 32, describing the movement of salt ions under advection;

[0041] The flow of water in the water pores with an actual osmotic pressure of 0 conforms to Darcy's law. Salt ions and water flow forward at the same speed under the action of advection. Considering the one-dimensional oil-water two-phase flow condition of the mathematical model, according to formula (2-2), the number of ions in the x direction per unit time passes through A due to advection. wD The amount of salt in the pore area is:

[0042] Cu wD A wD =Cu wD (1-E)φS w A (2-3)

[0043] Where C is the salt concentration of the solution inside the rock; u wD is the true velocity of the water phase in the water phase pores with an actual osmotic pressure of 0; the x direction refers to the movement direction of the fracturing fluid along the axial direction of the transverse cylindrical rock;

[0044] According to formula (1-5), the true velocity of the water phase in the water phase pore with an actual osmotic pressure of 0 can be expressed as:

[0045]

[0046] In the formula, v wD is the Darcy seepage velocity of water phase;

[0047] Step 33, describing the movement of salt ions under the action of hydrodynamic dispersion;

[0048] Fick's law is used to describe the diffusion rate of solutes in salt solutions:

[0049]

[0050] In the formula, J diff is the fluid dynamic diffusion flux; D is the fluid dynamic diffusion coefficient; is the gradient operator;

[0051] According to equations (2-2) and (2-5), the amount of fluid dynamics in the x direction per unit time is proportional to the amount of fluid dynamics in the x direction. wD The amount of salt in the pore area is:

[0052]

[0053] Step 34, describing the movement of salt ions in the porous medium;

[0054] In the flow area, take any tiny unit body, the unit body length is Δx, the unit body cross-sectional area is A, and the horizontal right direction is the positive direction of the x-axis;

[0055] There are two migration phenomena of salt ions: advection described by Darcy's law and fluid dynamic dispersion described by Fick's law. If F represents the amount of salt transported per unit time along the x direction through a unit rock cross-sectional area, we can get from equations (2-3) and (2-6):

[0056]

[0057] The total amount of salt that enters the unit cell during the time Δt is F| x AΔt;

[0058] The total amount of salt flowing out of the unit cell in Δt time is F| x+Δx AΔt;

[0059] The salt increment of the unit cell in the same time is (CφS w )| t+Δt AΔx-(CφS w )| t AΔx;

[0060] According to the principle of conservation of matter, we can get:

[0061] F| x AΔt-F| x+Δx AΔt=(CφS w )| t+Δt AΔx-(CφS w )| t AΔx (2-8)

[0062] Divide both ends of formula (2-8) by ΔxΔtA, and take the limit when Δx and Δt approach 0, and we get:

[0063]

[0064] Substituting formula (2-7) into formula (2-9), we can get:

[0065]

[0066] Substituting formula (2-4) into formula (2-10), the salt ion migration control equation under oil-water two-phase flow conditions is obtained:

[0067]

[0068] Preferably, step 4 includes the following sub-steps:

[0069] Step 41, determining the motion equation of oil-water two-phase flow;

[0070] Under Darcy's law, the motion equation of oil-water two-phase flow is expressed as:

[0071]

[0072] In the formula, v oD is the Darcy flow velocity of the oil phase; k is the rock permeability; k rw is the relative permeability of water phase; k ro is the relative permeability of the oil phase; μ w is the viscosity of the water phase; μ o is the viscosity of the oil phase; x is the coordinate of the flow direction; p w is the water phase pressure; p o is the oil phase pressure;

[0073] The Darcy flow considering chemical osmotic pressure is used to describe the flow of water in rocks. The motion equation of oil-water two-phase flow considering chemical osmotic pressure is:

[0074]

[0075] In the formula, v o is the oil phase seepage velocity;

[0076] The ideal osmotic pressure of a solution is described as:

[0077] p π =αRTC (3-3)

[0078] In the formula, α is the dissociation coefficient; R is the ideal gas constant; T is the absolute temperature;

[0079] Step 42, determining the oil-water two-phase flow control equation;

[0080] The continuity equation for oil-water two-phase flow is:

[0081]

[0082] In the formula, S o is oil saturation; t is time;

[0083] Substituting formula (3-2) into formula (3-4), the control equation of oil-water two-phase flow considering chemical osmotic pressure is obtained as follows:

[0084]

[0085] Step 43, coupling the salt ion transport control equation;

[0086] Substituting formula (3-1) into (2-11) we can obtain:

[0087]

[0088] Step 44, determine initial conditions and boundary conditions

[0089] The initial conditions are:

[0090]

[0091] In the formula, S wc is the bound water saturation; C 0 is the initial salt concentration of the solution inside the rock; p 0 is the initial oil phase pressure inside the rock, and L is the length of the rock.

[0092] The left boundary is a constant pressure boundary, and the right boundary is a closed boundary, where the salt concentration of the solution outside the rock is constant;

[0093] The boundary conditions are:

[0094]

[0095] In the formula, p cb is the capillary back pressure; C w is the salt concentration of the solution outside the rock;

[0096] Step 45, determining the auxiliary equation;

[0097] Capillary force constraints:

[0098] p c =p o -p w (3-9)

[0099] In the formula, p c is the capillary force between oil and water phases;

[0100] Saturation constraints:

[0101] S w +S o =1 (3-10)

[0102] Phase permeability curve:

[0103]

[0104] Where n w is the fitting index of water phase relative permeability curve; n o is the fitting index of oil phase relative permeability curve; S or is the residual oil saturation; k rw (S or) is the relative permeability of water phase under residual oil saturation; k ro (S wc ) is the relative permeability of the oil phase at irreducible water saturation.

[0105] Capillary force curve:

[0106]

[0107] In the formula, p mc is the maximum capillary force; n c is the capillary force curve fitting index;

[0108] Spontaneous imbibition extraction degree:

[0109]

[0110] Where e is the imbibition recovery degree.

[0111] Preferably, in step 5, a block center grid is used, and the grid sizes are equal, the grid step length is consistent with the unit body length, both are Δx, and the total number of grids is n; let the i=1 grid be the water source grid, the i=n grid be the boundary grid, and the grids from i=2 to i=n represent rocks;

[0112] In the water source grid, the water phase pressure is always zero, the oil phase pressure is always the capillary back pressure, and the water saturation is always 1.

[0113] Preferably, step 6 comprises the following sub-steps:

[0114] Step 61, obtain the water phase pressure of grid i at time m+1

[0115] Combine the oil phase equation and the water phase equation in equation (3-5) and substitute them into equation (3-10) to eliminate the variable S in the equation system. o and S w , and obtain the pressure equation (3-14);

[0116]

[0117] Among them, λ o ,λ w They represent the flow coefficients of the oil and water phases respectively, and λ represents the sum of the flow coefficients of the oil and water phases;

[0118]

[0119] λ=λ o +λ w (3-17)

[0120] Perform differential discretization on equation (3-14), where the subscript represents the grid and the superscript represents time:

[0121]

[0122] The unknown quantity in formula (3-18) is the water phase pressure of grid i at time m+1 Solve to obtain the water phase pressure of grid i at time m+1

[0123] Step 62, obtain the water saturation of the grid i at time m+1 Oil saturation Capillary force Oil phase pressure

[0124] The differential discretization format of the water phase equation in formula (3-5) is:

[0125]

[0126] The unknown quantity in formula (3-19) is the water saturation of grid i at time m+1 Solve to obtain the water saturation of grid i at time m+1 Then, the oil saturation of grid i at time m+1 is calculated using the saturation constraint formula (3-10): The capillary force of the i-grid at time m+1 can be calculated from the capillary force curve formula (3-12): The oil phase pressure of grid i at time m+1 is obtained from the capillary force constraint condition (3-9):

[0127] Step 63, obtain the salt concentration of the rock solution in the grid i at time m+1 Ideal osmotic pressure Actual osmotic pressure

[0128] Formula (3-6) is discretized by finite difference, and the coefficients C and λ take the values ​​at time m. The discrete format is:

[0129]

[0130] The unknown quantity in formula (3-20) is the salt concentration of grid i at time m+1 Solve to obtain the salt concentration of the rock solution in grid i at time m+1 Then the ideal osmotic pressure is calculated from the chemical osmotic pressure formula (3-3) Then use formula (2-1) to calculate the actual osmotic pressure

[0131] Step 64, obtain the imbibition extraction degree of the i grid at time m+1

[0132]

[0133] Step 65, determining the spontaneous imbibition numerical simulation parameters based on the grid parameters, initial conditions, boundary conditions, grid step size Δx, total number of grids n, time step Δt, total simulation time t max According to steps 61 to 64, the numerical simulation model of spontaneous imbibition of fracturing fluid is iteratively solved in sequence.

[0134] Preferably, in step 6, the spontaneous imbibition numerical simulation parameters include: rock length L; rock cross-sectional area A; porosity φ; rock permeability k; oil phase viscosity μ o ; Viscosity of water phase μ w ; Dissociation coefficient α; Absolute temperature T; Membrane efficiency E; Bound water saturation S wc ; Initial oil phase pressure inside rock p 0 ; Capillary back pressure p cb ; ideal gas constant R; fluid dynamic diffusion coefficient D; rock external solution salt concentration C w ; Initial salt concentration of rock internal solution C 0 ; Relative permeability of oil phase at irreducible water saturation k ro (S wc ); Relative permeability of water phase at residual oil saturation k rw (S or );n o is the fitting index of oil phase relative permeability curve; n w is the fitting index of water phase relative permeability curve; the maximum capillary force p mc ; Capillary force curve fitting index n c ; Grid step size Δx, total number of grids n, time step size Δt, total simulation time t max .

[0135] Preferably, in step 6, the numerical simulation model of spontaneous imbibition of the fracturing fluid is iteratively solved in sequence to obtain the water phase pressure p inside the rock. w Data, water saturation S inside the rock w data, rock internal salt concentration C data, rock internal actual osmotic pressure P π Distribution data and imbibition extraction degree data at different times.

[0136] Preferably, in step 6, the imbibition extraction degree e at time m+1 is m+1 is the average value of the imbibition recovery degree from grids i=2 to i=n, ​​specifically:

[0137]

[0138] The beneficial effects of the present invention are:

[0139] The present invention is based on making up for the defect that the existing numerical simulation method of spontaneous imbibition of fracturing fluid does not take chemical osmotic pressure into consideration. Based on the oil-water two-phase flow control equation taking chemical osmotic pressure into consideration and the salt ion migration control equation under oil-water two-phase flow conditions, a mathematical model of spontaneous imbibition of fracturing fluid taking chemical osmotic pressure into consideration is established. The accuracy of numerical simulation of spontaneous imbibition of fracturing fluid can be effectively improved. In the field of unconventional oil and gas development, the degree of imbibition recovery of fracturing fluid can be effectively evaluated, and the influence of different parameters on the degree of imbibition recovery of fracturing fluid can be explored, and simulation data can be provided for the study of the change law of imbibition of fracturing fluid. BRIEF DESCRIPTION OF THE DRAWINGS

[0140] The drawings in the specification, which constitute a part of the present application, are used to provide further understanding of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute improper limitations on the present application.

[0141] Figure 1 is a flow chart of a numerical simulation method for spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure of the present invention;

[0142] Figure 2 Schematic diagram of the spontaneous imbibition phenomenon of the fracturing fluid in the present invention;

[0143] Figure 3 is a pore classification diagram at a rock cross section in the present invention;

[0144] Figure 4 It is a schematic diagram of a one-dimensional flow unit in the present invention;

[0145] Figure 5 is a schematic diagram of fracture-rock grid division in the present invention;

[0146] Figure 6 It is the distribution diagram of water phase pressure inside the rock;

[0147] Figure 7 It is the distribution diagram of water saturation inside the rock;

[0148] Figure 8 is the distribution map of salt concentration inside the rock;

[0149] Fig. 9 It is the actual osmotic pressure distribution field diagram inside the rock;

[0150] Fig.10 It is the curve diagram of spontaneous imbibition and production degree of fracturing fluid;

[0151] Fig.11 It is a curve diagram of the imbibition extraction degree of different rock external solution salt concentrations;

[0152] Fig.12 It is a graph of the degree of imbibition recovery at different rock lengths;

[0153] Fig.13 It is a curve diagram of the imbibition recovery degree with different oil phase viscosities. DETAILED DESCRIPTION

[0154] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0155] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0156] like Figure 1 As shown, the numerical simulation method of spontaneous imbibition of fracturing fluid considering chemical osmotic pressure includes the following steps:

[0157] Step 1: Describe the mathematical problems in the spontaneous imbibition phenomenon of fracturing fluid and make mathematical model assumptions.

[0158] The rock adopts a transverse cylindrical model, in which the side and right side of the rock are completely closed, and the left end face is completely in contact with the liquid phase. The imbibition mode is a one-dimensional linear reverse imbibition, and the imbibition direction is along the horizontal direction.

[0159] In this application, the spontaneous imbibition phenomenon of fracturing fluid is approximated as a one-dimensional oil-water two-phase flow problem for study. During the imbibition process, the rock side and right end face are completely closed, leaving only the left end face completely in contact with the liquid phase. The imbibition mode is a one-dimensional linear reverse imbibition, and the imbibition direction is along the horizontal direction. Figure 2 As shown, the spontaneous imbibition mathematical model constructed by the present invention corresponds to the fracture-matrix system in the formation, and can simulate the spontaneous imbibition of the fracturing fluid occurring at the fracture-matrix interface. In this application, the following assumptions are made for the spontaneous imbibition mathematical model: (1) the porous medium is assumed to be homogeneous and isotropic; (2) the flow is steady-state flow and obeys Darcy's law; (3) the imbibition process is an isothermal process; (4) the rock and fluid compression effects are not considered; (5) the influence of solute migration on fluid density is not considered.

[0160] Step 2: Determine the true velocity of the water phase based on the water phase seepage velocity.

[0161] Specifically, in step 2, the method for determining the true velocity of the water phase is as follows:

[0162] There are two velocities for fluid flow in porous media, namely the seepage velocity and the true velocity, which are not equal. The seepage velocity is defined as the ratio of the seepage volume of the porous medium to the seepage cross-sectional area. In the case of oil-water two-phase seepage, the water phase seepage velocity is expressed as:

[0163]

[0164] In the formula, v w is the water phase seepage velocity, cm·s -1 ;Q w is the water phase seepage rate, cm 3 ·s -1 ; A is the seepage cross-sectional area, cm 2 ;

[0165] The ratio of the seepage volume to the pore area of ​​the seepage cross section is called the true velocity of the liquid. In the case of oil-water two-phase seepage, the true velocity of the water phase is expressed as:

[0166]

[0167] In the formula, u w is the real velocity of the water phase, cm·s -1 ; A pw is the water phase pore area of ​​the seepage cross section, cm 2 ;

[0168] Take a uniform porous medium microelement with a porosity of φ, then the pore area of ​​the seepage cross section is:

[0169] A p =Aφ (1-3)

[0170] In the formula, A p is the pore area of ​​the seepage cross section, cm 2 ;

[0171] In the case of oil-water two-phase seepage, since the pores on the seepage cross section are occupied by both oil and water, the pore area of ​​the water phase is:

[0172] A pw =S w A p (1-4)

[0173] In the formula, S w is the water saturation.

[0174] From equations (1-1), (1-2), (1-3) and (1-4), it can be deduced that the relationship between the true velocity of the water phase and the water phase seepage velocity is:

[0175]

[0176] Step 3: Determine the salt ion migration control equation under oil-water two-phase flow conditions.

[0177] Specifically, in step 3, the method for determining the salt ion migration control equation under the oil-water two-phase flow condition is as follows:

[0178] Step 31, classifying the pores at the rock cross section;

[0179] The presence of clay minerals and the low porosity and low permeability of oil and gas reservoirs make rocks have a semipermeable membrane effect on a macro scale. Based on the semipermeable membrane effect of rocks, the membrane efficiency E is used to describe the effectiveness of the semipermeable membrane in removing solutes, where E represents the actual osmotic pressure P during water phase seepage. π and ideal osmotic pressure p π Ratio:

[0180]

[0181] Where, E is the membrane efficiency; P π is the actual osmotic pressure, MPa; p π is the ideal osmotic pressure, MPa;

[0182] Redefine membrane efficiency: The seepage channel at the rock cross section is composed of water phase pores and oil phase pores. Among the water phase pores, the proportion of water phase pores with ideal osmotic pressure is E, and the proportion of water phase pores with actual osmotic pressure of 0 is (1-E). Salt ions cannot pass through the water phase pores with ideal osmotic pressure, but can freely pass through the water phase pores with actual osmotic pressure of 0. Specifically, Figure 2 Make a cross section of the rock shown in Figure 3 As shown, there is no osmotic pressure in the oil phase pores, but there is osmotic pressure in the water phase pores, and according to the newly defined membrane efficiency, it can be divided into water phase pores with ideal osmotic pressure and water phase pores with actual osmotic pressure of 0;

[0183] According to the above definition, verification calculation is performed, as shown in formula (2-1-1), the newly defined membrane efficiency is still consistent with its original physical definition formula (2-1);

[0184] E×p π +(1-E)×0=P π (2-1-1)

[0185] According to the redefined membrane efficiency, the total pore area of ​​the water phase with the ideal osmotic pressure is recorded as A π , which accounts for a proportion of the water phase pore area E. This type of pore cannot transport salt ions. The total area of ​​the water phase pores with an actual osmotic pressure of 0 is recorded as A wD , accounting for the proportion of the water phase pore area (1-E). The flow of water in this type of pores follows Darcy's law, and salt ions can pass freely;

[0186] According to formula (1-3) and (1-4), A wD It can be expressed as:

[0187] A wD =(1-E)A pw =(1-E)φS w A (2-2)

[0188] In the formula, A wD is the total area of ​​water phase pores with actual osmotic pressure of 0, cm 2 ; A is the seepage cross-sectional area, that is, the rock cross-sectional area, cm 2 ;

[0189] Step 32, describing the movement of salt ions under advection;

[0190] The flow of water in the water pores with an actual osmotic pressure of 0 conforms to Darcy's law. Salt ions and water flow forward at the same speed under the action of advection. Considering the one-dimensional oil-water two-phase flow condition of the mathematical model, according to formula (2-2), the number of ions in the x direction per unit time passes through A due to advection. wD The amount of salt in the pore area is:

[0191] Cu wD A wD =Cu wD (1-E)φS w A (2-3)

[0192] Where C is the salt concentration of the solution inside the rock, mol cm -3 ;u wD is the true velocity of the water phase in the water phase pores with an actual osmotic pressure of 0, cm·s -1 ; The x direction refers to the movement direction of the fracturing fluid along the axial direction of the transverse cylindrical rock;

[0193] According to formula (1-5), the true velocity of the water phase in the water phase pore with an actual osmotic pressure of 0 can be expressed as:

[0194]

[0195] In the formula, v wD is the water phase Darcy flow velocity, cm·s -1 ;

[0196] Step 33, describing the movement of salt ions under the action of hydrodynamic dispersion;

[0197] Hydrodynamic dispersion is the diffusion phenomenon when the solute is diluted. Hydrodynamic dispersion is related to the concentration gradient. Fick's law is used to describe the diffusion rate of solutes in salt solutions:

[0198]

[0199] In the formula, J diff is the hydrodynamic diffusion flux, mol·cm -2 ·s -1 ; D is the fluid dynamic diffusion coefficient, cm 2 ·s -1 ; is the gradient operator;

[0200] According to equations (2-2) and (2-5), the amount of fluid dynamics in the x direction per unit time is proportional to the amount of fluid dynamics in the x direction. wD The amount of salt in the pore area is:

[0201]

[0202] Step 34, describing the movement of salt ions in the porous medium;

[0203] like Figure 4 As shown, take any tiny unit in the flow area, the unit length is Δx, the unit cross-sectional area is A, and the horizontal right direction is the positive direction of the x-axis;

[0204] There are two migration phenomena of salt ions: advection described by Darcy's law and fluid dynamic dispersion described by Fick's law. If F represents the amount of salt transported per unit time along the x direction through a unit rock cross-sectional area, we can get from equations (2-3) and (2-6):

[0205]

[0206] The total amount of salt that enters the unit cell during the time Δt is F| x AΔt;

[0207] The total amount of salt flowing out of the unit cell in Δt time is F| x+Δx AΔt;

[0208] The salt increment of the unit cell in the same time is (CφS w )| t+Δt AΔx-(CφS w )| t AΔx;

[0209] According to the principle of conservation of matter, we can get:

[0210] F| x AΔt-F| x+Δx AΔt=(CφS w )| t+Δt AΔx-(CφS w )| t AΔx (2-8)

[0211] Divide both ends of formula (2-8) by ΔxΔtA, and take the limit when Δx and Δt approach 0, and we get:

[0212]

[0213] Substituting formula (2-7) into formula (2-9), we can get:

[0214]

[0215] Substituting formula (2-4) into formula (2-10), we can get the salt ion migration control equation under oil-water two-phase flow conditions:

[0216]

[0217] Step 4: Based on the oil-water two-phase flow control equation considering chemical osmotic pressure and the salt ion migration control equation under oil-water two-phase flow conditions, a mathematical model of spontaneous imbibition of fracturing fluid considering chemical osmotic pressure is established.

[0218] Specifically, step 4 includes the following sub-steps:

[0219] Step 41, determining the motion equation of oil-water two-phase flow;

[0220] Under Darcy's law, the motion equation of oil-water two-phase flow is expressed as:

[0221]

[0222] In the formula, v oD is the Darcy flow velocity of the oil phase, cm·s -1 ; k is rock permeability, μm 2 ;k rw is the relative permeability of water phase; k ro is the relative permeability of the oil phase; μ w is the viscosity of the water phase, mPa·s; μ o is the oil phase viscosity, mPa·s; x is the coordinate of the flow direction; p w is the water phase pressure, 10 5 Pa; p o is the oil phase pressure, 10 5 Pa;

[0223] The Darcy flow considering chemical osmotic pressure is used to describe the flow of water in rocks. The motion equation of oil-water two-phase flow considering chemical osmotic pressure is:

[0224]

[0225] In the formula, v o is the oil phase seepage velocity, cm·s -1 ;

[0226] The ideal osmotic pressure of a solution is described as:

[0227] p π =αRTC (3-3)

[0228] Where α is the dissociation coefficient; R is the ideal gas constant, J·K -1·mol -1 ; T is absolute temperature, K;

[0229] Step 42, determining the oil-water two-phase flow control equation;

[0230] The continuity equation for oil-water two-phase flow is:

[0231]

[0232] In the formula, S o is oil saturation; t is time, s;

[0233] Substituting formula (3-2) into formula (3-4), the control equation of oil-water two-phase flow considering chemical osmotic pressure is obtained as follows:

[0234]

[0235] Step 43, coupling the salt ion transport control equation;

[0236] Osmotic pressure is a function of salt concentration. After adding the osmotic pressure as a driving force to the numerical simulation model of spontaneous imbibition of fracturing fluid, it is also necessary to consider the change of salt concentration, that is, to couple the salt ion migration control equation. Substituting formula (3-1) into (2-11) yields:

[0237]

[0238] Step 44, determine initial conditions and boundary conditions

[0239] The initial conditions are:

[0240]

[0241] In the formula, S wc is the bound water saturation; C 0 is the initial salt concentration of the solution inside the rock, mol·cm -3 ;p 0 is the initial oil phase pressure inside the rock, 10 5 Pa, L is the rock length, cm.

[0242] The left boundary is a constant pressure boundary, and the right boundary is a closed boundary, where the salt concentration of the solution outside the rock is constant;

[0243] The boundary conditions are:

[0244]

[0245] In the formula, p cb is the capillary back pressure, 10 5 Pa; C w is the salt concentration of the solution outside the rock, mol·cm-3 ;

[0246] Step 45, determining the auxiliary equation;

[0247] Capillary force constraints:

[0248] p c =p o -p w (3-9)

[0249] In the formula, p c is the capillary force between oil and water phases, 10 5 Pa;

[0250] Saturation constraints:

[0251] S w +S o =1 (3-10)

[0252] Phase permeability curve:

[0253]

[0254] Where n w is the fitting index of water phase relative permeability curve; n o is the fitting index of oil phase relative permeability curve; S or is the residual oil saturation; k rw (S or ) is the relative permeability of water phase under residual oil saturation; k ro (S wc ) is the relative permeability of the oil phase at irreducible water saturation.

[0255] Capillary force curve:

[0256]

[0257] In the formula, p mc is the maximum capillary force, 10 5 Pa;n c is the capillary force curve fitting index;

[0258] Spontaneous imbibition extraction degree:

[0259]

[0260] Where e is the imbibition recovery degree.

[0261] Step 5, spatially discretizing the mathematical model of spontaneous imbibition of fracturing fluid;

[0262] Fracture-rock meshing Figure 5As shown, a block center grid is used, and the grid size is equal. The grid step is consistent with the unit body length, both are Δx, and the total number of grids is n; let the i=1 grid be the water source grid, the i=n grid be the boundary grid, and the grids from i=2 to i=n represent rocks;

[0263] In the water source grid, the water phase pressure is always zero, the oil phase pressure is always the capillary back pressure, and the water saturation is always 1.

[0264] Step 6, determine the numerical simulation parameters of spontaneous imbibition, and solve the mathematical model of spontaneous imbibition of fracturing fluid by numerical method.

[0265] Under the requirements of ensuring calculation accuracy and controlling calculation cost, the implicit pressure explicit saturation method (IMPES method) is used to combine initial conditions, boundary conditions and auxiliary equations to implicitly solve the water phase pressure first, and then explicitly solve the water saturation and salt concentration. The solution process from time m to time m+1 is shown below. This method can be used to start from the initial time and solve step by step until the required time is obtained.

[0266] Specifically, step 6 includes the following sub-steps:

[0267] Step 61, obtain the water phase pressure of grid i at time m+1

[0268] Combine the oil phase equation and the water phase equation in equation (3-5) and substitute them into equation (3-10) to eliminate the variable S in the equation system. o and S w , and obtain the pressure equation (3-14);

[0269]

[0270] Among them, λ o ,λ w They represent the flow coefficients of the oil and water phases respectively, and λ represents the sum of the flow coefficients of the oil and water phases;

[0271]

[0272] λ=λ o +λ w (3-17)

[0273] Perform differential discretization on equation (3-14), where the subscript represents the grid and the superscript represents time:

[0274]

[0275] The unknown quantity in formula (3-18) is the water phase pressure of grid i at time m+1 The solution is:

[0276] (1) For the 2nd to n-1th grids, the coefficient λ uses the value at time m and takes the upstream weight, then equation (3-18) can be transformed into:

[0277]

[0278] (2) For the first grid, in formula (3-18) The coefficient λ uses the value at time m and takes the upstream weight, then equation (3-18) can be transformed into:

[0279]

[0280] (3) For the nth grid, in formula (3-18) The coefficient λ uses the value at time m and takes the upstream weight, then equation (3-18) can be transformed into:

[0281]

[0282] Formula (3-18-1), Formula (3-18-2) and Formula (3-18-3) constitute a linear algebraic equation system from i=1 to i=n grids. The coefficient matrix of the equation system is a tridiagonal matrix. The Thomas method is used to solve it and the water phase pressure of the i grid at time m+1 is obtained.

[0283] Step 62, obtain the water saturation of the grid i at time m+1 Oil saturation Capillary force Oil phase pressure

[0284] The differential discretization format of the water phase equation in formula (3-5) is:

[0285]

[0286] The unknown quantity in formula (3-19) is the water saturation of grid i at time m+1 The solution is:

[0287] (1) For the 2nd to n-1th grids, the coefficient λ uses the value at time m and takes the upstream weight, and equation (3-19) can be transformed into:

[0288]

[0289] (2) For the first grid, The coefficient λ uses the value at time m and takes the upstream weight, then equation (3-19) can be transformed into:

[0290]

[0291] (3) For the nth grid, The coefficient λ uses the value at time m and takes the upstream weight, then equation (3-19) can be transformed into:

[0292]

[0293] Using equations (3-19-1), (3-19-2) and (3-19-3), calculate the water saturation of grid i at time m+1 Then, the oil saturation of grid i at time m+1 is calculated by the saturation constraint formula (3-10): The capillary force of the i-grid at time m+1 can be calculated from the capillary force curve formula (3-12): The oil phase pressure of grid i at time m+1 is obtained from the capillary force constraint condition (3-9):

[0294] Step 63, obtain the salt concentration of the rock solution in the grid i at time m+1 Ideal osmotic pressure Actual osmotic pressure

[0295] Formula (3-6) is discretized by finite difference, and the coefficients C and λ take the values ​​at time m. The discrete format is:

[0296]

[0297] The unknown quantity in formula (3-20) is the salt concentration of grid i at time m+1 There are three situations:

[0298] (1) For the 2nd to n-1th grids, the coefficients C and λ take the upstream weights, and equation (3-20) can be transformed into:

[0299]

[0300] (2) For the first grid, in formula (3-20) The coefficients C and λ are taken as upstream weights, then equation (3-20) can be transformed into:

[0301]

[0302] (3) For the nth grid, in formula (3-20) The coefficients C and λ are taken as upstream weights, then equation (3-20) can be transformed into:

[0303]

[0304] Using equations (3-20-1), (3-20-2) and (3-20-3), we can calculate the salt concentration of the rock solution in grid i at time m+1. Then the ideal osmotic pressure is calculated from the chemical osmotic pressure formula (3-3): Then use formula (2-1) to calculate the actual osmotic pressure

[0305] Step 64, obtain the imbibition extraction degree of the grid i at time m+1

[0306]

[0307] Step 65, determining the spontaneous imbibition numerical simulation parameters based on the grid parameters, initial conditions, boundary conditions, grid step size Δx, total number of grids n, time step Δt, total simulation time t max According to steps 61 to 64, the numerical simulation model of spontaneous imbibition of fracturing fluid is iteratively solved in sequence.

[0308] Specifically, in step 6, the spontaneous imbibition numerical simulation parameters include: rock length L; rock cross-sectional area A; porosity φ; rock permeability k; oil phase viscosity μ o ; Viscosity of water phase μ w ; Dissociation coefficient α; Absolute temperature T; Membrane efficiency E; Bound water saturation S wc ; Initial oil phase pressure inside rock p 0 ; Capillary back pressure p cb ; ideal gas constant R; fluid dynamic diffusion coefficient D; rock external solution salt concentration C w ; Initial salt concentration of rock internal solution C 0 ; Oil phase relative permeability k at irreducible water saturation ro (S wc ); Relative permeability of water phase at residual oil saturation k rw (S or );n o is the fitting index of oil phase relative permeability curve; n w is the fitting index of water phase relative permeability curve; the maximum capillary force p mc ; Capillary force curve fitting index n c ; Grid step size Δx, total number of grids n, time step size Δt, total simulation time t max .

[0309] Specifically, in step 6, the numerical simulation model of spontaneous imbibition of fracturing fluid is solved iteratively in sequence to obtain the water phase pressure p inside the rock. w Data, water saturation S inside the rock w data, rock internal salt concentration C data, rock internal actual osmotic pressure P π Distribution data and imbibition extraction degree data at different times.

[0310] Specifically, in step 6, the imbibition extraction degree e at time m+1 is m+1 is the average value of the imbibition recovery degree from grids i=2 to i=n, ​​specifically:

[0311]

[0312] Among them, in this application, according to the solution steps shown in step 6, a numerical solution program is compiled in a computer using open source programming languages ​​such as Python to perform numerical simulation calculations.

[0313] Example:

[0314] Determine the spontaneous imbibition numerical simulation parameters, and perform simulation calculations according to the spontaneous imbibition numerical simulation method of the fracturing fluid considering the chemical osmotic pressure of the present application, wherein the spontaneous imbibition numerical simulation parameters are shown in Table 1 below.

[0315] Table 1 Parameters of spontaneous imbibition numerical simulation

[0316]

[0317]

[0318] After simulation calculation, the water phase pressure p inside the rock based on the spontaneous imbibition numerical simulation parameters in Table 1 is obtained. w Data, water saturation S inside the rock w data, rock internal salt concentration C data, rock internal actual osmotic pressure P π Distribution data and the imbibition extraction degree e data at different times. After drawing, we get Figure 6 The water phase pressure distribution diagram inside the rock is shown. Figure 7 The water saturation distribution diagram inside the rock is shown. Figure 8 The distribution of salt concentration inside the rock is shown in the figure. Fig. 9 The actual osmotic pressure distribution field diagram inside the rock shown in Fig.10 The spontaneous imbibition recovery curve of the fracturing fluid is shown.

[0319] When only the rock external solution salt concentration C in Table 1 is changed w When Fig.11 The imbibition recovery curve for different rock external solution salt concentrations is shown.

[0320] When only the rock length L in Table 1 is changed, we get Fig.12 The imbibition recovery curve for different rock lengths is shown.

[0321] When only the oil phase viscosity μ in Table 1 is changed o When Fig.13 The imbibition recovery curve for different oil phase viscosities is shown.

[0322] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not a limitation of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the protection scope of the present invention.

Claims

1. A numerical simulation method for spontaneous imbibition of fracturing fluid considering chemical osmotic pressure, characterized in that: The following steps are involved: Step 1, describe the mathematical problems in the spontaneous imbibition phenomenon of fracturing fluid and make mathematical model assumptions; Step 2, determining the real velocity of the water phase based on the water phase seepage velocity; Step 3, determining the salt ion migration control equation under oil-water two-phase flow conditions; Step 4, based on the oil-water two-phase flow control equation considering the chemical osmotic pressure and the salt ion migration control equation under the oil-water two-phase flow condition, a mathematical model of spontaneous imbibition of fracturing fluid considering the chemical osmotic pressure is established; Step 5, spatially discretizing the mathematical model of spontaneous imbibition of fracturing fluid; Step 6, determine the numerical simulation parameters of spontaneous imbibition, and solve the mathematical model of spontaneous imbibition of fracturing fluid by numerical method.

2. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 1, characterized in that: In step 2, the method for determining the true velocity of the water phase is as follows: In the case of oil-water two-phase flow, the water phase flow velocity is expressed as: In the formula, v w is the water phase seepage velocity; Q w is the water phase seepage; A is the seepage cross-sectional area; In the case of oil-water two-phase flow, the true velocity of the water phase is expressed as: In the formula, u w is the real velocity of water phase; A pw is the water phase pore area of ​​the seepage cross section; Take a uniform porous medium microelement with a porosity of φ, then the pore area of ​​the seepage cross section is: And p =Aφ (1-3) In the formula, A p is the pore area of ​​the seepage cross section; In the case of oil-water two-phase seepage, since the pores on the seepage cross section are occupied by both oil and water, the pore area of ​​the water phase is: A pw =S w A p (1-4) In the formula, S w is the water saturation. From equations (1-1), (1-2), (1-3) and (1-4), it can be deduced that the relationship between the true velocity of the water phase and the water phase seepage velocity is:

3. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 2, characterized in that: In step 3, the method for determining the salt ion migration control equation under the oil-water two-phase flow condition is as follows: Step 31, classifying the pores at the rock cross section; Based on the semipermeable membrane effect of rock, the membrane efficiency E is used to describe the effectiveness of the semipermeable membrane in removing solutes, where: Where, E is the membrane efficiency; P π is the actual osmotic pressure; p π is the ideal osmotic pressure; Redefine membrane efficiency: The seepage channel at the rock cross section is composed of water phase pores and oil phase pores. Among the water phase pores, the proportion of water phase pores with ideal osmotic pressure is E, and the proportion of water phase pores with actual osmotic pressure of 0 is (1-E). Salt ions cannot pass through water phase pores with ideal osmotic pressure, but can freely pass through water phase pores with actual osmotic pressure of 0. According to the redefined membrane efficiency, the total pore area of ​​the water phase with the ideal osmotic pressure is recorded as A π , which accounts for a proportion of the water phase pore area E. This type of pore cannot transport salt ions. The total area of ​​the water phase pores with an actual osmotic pressure of 0 is recorded as A wD , accounting for the proportion of the water phase pore area (1-E). The flow of water in this type of pores follows Darcy's law, and salt ions can pass freely; According to formula (1-3) and (1-4), A wD It can be expressed as: TO wD =(1-E)A pw =(1-E)φS w A (2-2) In the formula, A wD is the total area of ​​water phase pores with actual osmotic pressure of 0; A is the seepage cross-sectional area, that is, the rock cross-sectional area; Step 32, describing the movement of salt ions under advection; The flow of water in the water pores with an actual osmotic pressure of 0 conforms to Darcy's law. Salt ions and water flow forward at the same speed under the action of advection. Considering the one-dimensional oil-water two-phase flow condition of the mathematical model, according to formula (2-2), the number of ions in the x direction per unit time passes through A due to advection. wD The amount of salt in the pore area is: With wD A wD =With wD (1-E)φS w A (2-3) Where C is the salt concentration of the solution inside the rock; u wD is the real velocity of the water phase in the water phase pores with an actual osmotic pressure of 0; the x direction refers to the movement direction of the fracturing fluid along the axial direction of the transverse cylindrical rock; According to formula (1-5), the true velocity of the water phase in the water phase pore with an actual osmotic pressure of 0 can be expressed as: In the formula, v wD is the Darcy seepage velocity of water phase; Step 33, describing the movement of salt ions under the action of hydrodynamic dispersion; Fick's law is used to describe the diffusion rate of solutes in salt solutions: J diff =-D▽C (2-5) In the formula, J diff is the fluid dynamic diffusion flux; D is the fluid dynamic diffusion coefficient; ▽ is the gradient operator; According to equations (2-2) and (2-5), the amount of fluid dynamics in the x direction per unit time is proportional to the amount of fluid dynamics in the x direction. wD The amount of salt in the pore area is: Step 34, describing the movement of salt ions in the porous medium; In the flow area, take any tiny unit body, the unit body length is Δx, the unit body cross-sectional area is A, and the horizontal right direction is the positive direction of the x-axis; There are two migration phenomena of salt ions: advection described by Darcy's law and fluid dynamic dispersion described by Fick's law. If F represents the amount of salt transported per unit time along the x direction through a unit rock cross-sectional area, we can get from equations (2-3) and (2-6): The total amount of salt that enters the unit cell during the time Δt is F| x AΔt; The total amount of salt flowing out of the unit cell in Δt time is F| x+Δx AΔt; The salt increment of the unit cell in the same time is (CφS w )| t+Δt AΔx-(CφS w )| t AΔx; According to the principle of conservation of matter, we can get: F| x AΔt-F| x+Δx AΔt=(CφS w )| t+Δt AΔx-(CφS w )| t AΔx (2-8) Divide both ends of formula (2-8) by ΔxΔtA, and take the limit when Δx and Δt approach 0, and we get: Substituting formula (2-7) into formula (2-9), we can get: Substituting formula (2-4) into formula (2-10), we can get the salt ion migration control equation under oil-water two-phase flow conditions:

4. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 3, characterized in that: The step 4 includes the following sub-steps: Step 41, determining the motion equation of oil-water two-phase flow; Under Darcy's law, the motion equation of oil-water two-phase flow is expressed as: In the formula, v oD is the Darcy flow velocity of the oil phase; k is the rock permeability; k rw is the relative permeability of water phase; k ro is the relative permeability of the oil phase; μ w is the viscosity of the water phase; μ o is the viscosity of the oil phase; x is the coordinate of the flow direction; p w is the water phase pressure; p o is the oil phase pressure; The Darcy flow considering chemical osmotic pressure is used to describe the flow of water in rocks. The motion equation of oil-water two-phase flow considering chemical osmotic pressure is: In the formula, v o is the oil phase seepage velocity; The ideal osmotic pressure of a solution is described as: p π =αRTC (3-3) In the formula, α is the dissociation coefficient; R is the ideal gas constant; T is the absolute temperature; Step 42, determining the oil-water two-phase flow control equation; The continuity equation for oil-water two-phase flow is: In the formula, S o is oil saturation; t is time; Substituting formula (3-2) into formula (3-4), the control equation of oil-water two-phase flow considering chemical osmotic pressure is obtained as follows: Step 43, coupling the salt ion transport control equation; Substituting formula (3-1) into (2-11) we can obtain: Step 44, determine initial conditions and boundary conditions The initial conditions are: In the formula, S wc is the bound water saturation; C 0 is the initial salt concentration of the solution inside the rock; p 0 is the initial oil phase pressure inside the rock, and L is the length of the rock. The left boundary is a constant pressure boundary, and the right boundary is a closed boundary, where the salt concentration of the solution outside the rock is constant; The boundary conditions are: In the formula, p cb is the capillary back pressure; C w is the salt concentration of the solution outside the rock; Step 45, determining the auxiliary equation; Capillary force constraints: p c =p o -p w (3-9) In the formula, p c is the capillary force between oil and water phases; Saturation constraints: S w +S o =1 (3-10) Phase permeability curve: Where n w is the fitting index of water phase relative permeability curve; n o is the fitting index of oil phase relative permeability curve; S or is the residual oil saturation; k rw (S or ) is the relative permeability of water phase under residual oil saturation; k ro (S wc ) is the relative permeability of the oil phase at irreducible water saturation. Capillary force curve: In the formula, p mc is the maximum capillary force; n c is the capillary force curve fitting index; Spontaneous imbibition extraction degree: Where e is the imbibition recovery degree.

5. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 4, characterized in that: In step 5, a block center grid is used, and the grid size is equal, the grid step length is consistent with the unit body length, both are Δx, and the total number of grids is n; let the i=1 grid be the water source grid, the i=n grid be the boundary grid, and the grids from i=2 to i=n represent rocks; In the water source grid, the water phase pressure is always zero, the oil phase pressure is always the capillary back pressure, and the water saturation is always 1.

6. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 5, characterized in that: The step 6 comprises the following sub-steps: Step 61, obtain the water phase pressure of grid i at time m+1 Combine the oil phase equation and the water phase equation in equation (3-5) and substitute them into equation (3-10) to eliminate the variable S in the equation system. o and S w , and obtain the pressure equation (3-14); Among them, λ o ,λ w They represent the flow coefficients of the oil and water phases respectively, and λ represents the sum of the flow coefficients of the oil and water phases; λ=λ o +λ w (3-17) Perform differential discretization on equation (3-14), where the subscript represents the grid and the superscript represents time: The unknown quantity in formula (3-18) is the water phase pressure of grid i at time m+1 Solve to obtain the water phase pressure of grid i at time m+1 Step 62, obtain the water saturation of the grid i at time m+1 Oil saturation Capillary force Oil phase pressure The differential discretization format of the water phase equation in formula (3-5) is: The unknown quantity in formula (3-19) is the water saturation of grid i at time m+1 Solve to obtain the water saturation of grid i at time m+1 Then, the oil saturation of grid i at time m+1 is calculated by the saturation constraint formula (3-10): The capillary force of the i-grid at time m+1 can be calculated from the capillary force curve formula (3-12): The oil phase pressure of grid i at time m+1 is obtained from the capillary force constraint condition (3-9): Step 63, obtain the salt concentration of the rock solution in the grid i at time m+1 Ideal osmotic pressure Actual osmotic pressure Formula (3-6) is discretized by finite difference, and the coefficients C and λ take the values ​​at time m. The discrete format is: The unknown quantity in formula (3-20) is the salt concentration of grid i at time m+1 Solve to obtain the salt concentration of the rock solution in grid i at time m+1 Then the ideal osmotic pressure is calculated from the chemical osmotic pressure formula (3-3): Then use formula (2-1) to calculate the actual osmotic pressure Step 64, obtain the imbibition extraction degree of the grid i at time m+1 Step 65, determining the spontaneous imbibition numerical simulation parameters based on the grid parameters, initial conditions, boundary conditions, grid step size Δx, total number of grids n, time step Δt, total simulation time t max According to steps 61 to 64, the numerical simulation model of spontaneous imbibition of fracturing fluid is iteratively solved in sequence.

7. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 6, characterized in that: In step 6, the spontaneous imbibition numerical simulation parameters include: rock length L; rock cross-sectional area A; porosity φ; rock permeability k; oil phase viscosity μ o ; Viscosity of water phase μ w ; Dissociation coefficient α; Absolute temperature T; Membrane efficiency E; Bound water saturation S wc ; Initial oil phase pressure inside rock p 0 ; Capillary back pressure p cb ; ideal gas constant R; fluid dynamic diffusion coefficient D; rock external solution salt concentration C w ; Initial salt concentration of rock internal solution C 0 ; Relative permeability of oil phase at irreducible water saturation k ro (S wc ); Relative permeability of water phase at residual oil saturation k rw (S or );n o is the fitting index of oil phase relative permeability curve; n w is the fitting index of water phase relative permeability curve; the maximum capillary force p mc ; Capillary force curve fitting index n c Grid step size Δx, total number of grids n, time step size Δt, total simulation time t max .

8. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 7, characterized in that: In step 6, the numerical simulation model of spontaneous imbibition of fracturing fluid is solved iteratively in sequence to obtain the water phase pressure p inside the rock. w Data, water saturation S inside the rock w data, rock internal salt concentration C data, rock internal actual osmotic pressure P π Distribution data and imbibition extraction degree data at different times.

9. The method for numerically simulating spontaneous imbibition of fracturing fluid taking into account chemical osmotic pressure according to claim 8, characterized in that: In step 6, the imbibition extraction degree e at time m+1 m+1 is the average value of the imbibition recovery degree from grids i=2 to i=n, ​​specifically:

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