Method for measuring rock gas relative permeability based on lattice boltzmann method

Abstract

The application discloses a kind of rock gas relative permeability measurement method based on lattice Boltzmann method, comprising the following steps: (1) determining the porosity corresponding to each water saturation grade of rock, using four-parameter growth method to generate the rock porous medium model consistent with the porosity of each water saturation grade rock;(2) using lattice Boltzmann method to carry out gas seepage simulation, the bias pressure of gas boundary is applied to the rock porous medium model, the gas permeability and relative permeability of rock porous medium model under different porosity are calculated;(3) draw the curve of rock gas relative permeability and different water saturation, determine the relative permeability of rock under different water saturation.The application carries out gas seepage simulation by rock porous medium model and lattice Boltzmann method, obtains the permeability of rock porous medium model under different water saturation, and then calculates the relative permeability, constructs the functional relationship between rock sample water saturation and relative permeability, to determine the rock gas relative permeability simply and effectively.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical analysis of geotechnical engineering, in particular to a method for determining gas relative permeability of rock based on lattice Boltzmann method. BACKGROUND

[0002] Compact rock often appears in oil and gas exploitation, underground water storage, nuclear waste storage and other engineering, because of its low porosity (<15%) and permeability (<10 -15 m 2 ) and is widely concerned. The compact structure of rock makes it difficult for water, oil and other fluids to pass through, increasing the difficulty of determining its permeability, and in actual situations, gas-water, gas-oil and even oil-gas-water three-phase flow exist widely. Research on gas relative permeability of rock under different water saturation is of great significance to deep resource exploitation and underground storage engineering.

[0003] Experimental research on the evolution law of gas seepage of rock with different water saturation requires homogeneous rock samples and precise instruments and equipment, especially the preparation of rock samples with different water saturation and uniform water content is more difficult. Numerical simulation methods are divided into macro, meso and micro methods according to simulation scale. Macro method is a widely used simulation method by establishing micro flow control equation conforming to flow pattern, adding boundary conditions and initial conditions, and solving control equation to obtain macro physical quantity. But the macro method is not suitable for the study of compact rock pore seepage, and the calculation result is not intuitive. Molecular dynamics method is a numerical simulation method that truly simulates the motion of micro gas molecules, but it requires high computing performance, and can only simulate nanoscale and nanosecond time changes. In the meso method, the moving particles have macro scale size, and the different flow states of gas in different porosity and pore shape porous medium models can be obtained for seepage simulation of porous medium.

[0004] When determining the gas relative permeability of rock with different water saturation, how to accurately calculate the gas relative permeability of rock porous medium model with different water saturation and predict the gas relative permeability of rock with different water saturation is a technical problem to be discussed. SUMMARY

[0005] The present application provides a method for determining gas relative permeability of rock based on lattice Boltzmann method, which aims to solve the problems of difficulty in preparing rock samples with different water saturation and insufficient accuracy in gas permeability measurement in the prior art. The method determines the gas relative permeability of rock with different saturation by numerical simulation method, and further determines the relative permeability of laboratory test rock sample under different water saturation conditions.

[0006] Technical solution: The rock gas relative permeability calculation method based on the lattice Boltzmann method comprises the following steps:

[0007] (1) The porosity of the rock sample under different water saturation conditions is determined by using indoor test, backscattered electron imaging (BSE) is performed on the rock sample to obtain the micro-pore structure, the four-parameter growth method and Matlab programming are used, the parameters are set according to the porosity and pore shape of the rock under different water saturations, the region size is set, the region is required to represent the pore structure of the rock, the porosity of the rock porous medium model is determined according to the porosity under each saturation condition, the initial growth core and the growth direction probability parameters are set, and the rock porous medium model consistent with the porosity of the rock sample under different water saturations and similar to the pore shape is generated.

[0008] (2) The bias pressure is applied to the gas inlet and outlet boundary of the rock porous medium model, the lattice Boltzmann method is used for gas seepage simulation, the bias pressure is applied to the gas inlet and outlet boundary of the rock porous medium model, and the gas permeability of the rock porous medium model under different porosities (corresponding to the water saturation level) and the gas relative permeability of the rock under different water saturations are calculated.

[0009] (3) The test results of the gas relative permeability under different water saturations are fitted, the relationship curve between the rock gas relative permeability and different water saturations is drawn, the functional relationship between the relative permeability and different water saturations is obtained, and the gas relative permeability of the rock under different water saturations is calculated.

[0010] In step (1), the four-parameter growth method is used, the porosity, the initial growth core and the growth direction probability are controlled, the porous medium model consistent with the porosity of the rock sample under different water saturations and similar to the microstructure is generated, the porous medium model is converted into the rock porous medium model for lattice Boltzmann gas seepage simulation by setting the solid matrix, pore space and solid boundary parameters, and the rock porous medium model consistent with the porosity of the rock sample under different water saturations and similar to the pore shape is generated.

[0011] In step (1), the method for generating the rock porous medium model is as follows: (1.1) first, the size of the unit body (REV) representing the pore structure of the rock is determined, the N*N region is set in the four-parameter growth method, the porosity parameter is input according to the porosity of the rock under each water saturation, the initial growth core parameter and the growth direction probability parameter are set according to the pore size and pore distribution of the rock sample BSE imaging, and the.txt file of the porous medium model represented by pores and solids consistent with the porosity of the rock sample and consistent with the pore structure is generated.

[0012] (1.2) Through Matlab programming, the porous medium model is changed into the.dat file of the different water saturation rock porous medium model for lattice Boltzmann gas seepage simulation composed of pore space, pore boundary part and solid skeleton part.

[0013] In step (2), the influence of different water saturations on gas seepage is represented by the porosity of the rock porous medium model, the gas seepage simulation of the rock porous medium model similar to the sample is performed using the lattice Boltzmann method, and the gas permeability and gas relative permeability of the rock at each water saturation are calculated through unit conversion. The gas relative permeability of the rock at different water saturations is calculated using the lattice Boltzmann method, the gas relative permeability curve is obtained, the functional relationship between the gas relative permeability and the different water saturations is obtained, and thus the gas relative permeability of the rock at different water saturations is obtained.

[0014] Specifically, in step (2), the method for calculating the gas relative permeability of the rock at different water saturations using the lattice Boltzmann method is as follows: (2.1) First, in step (2), the porosity of the rock porous medium model is used to represent its different water saturations S w , the gas seepage simulation is performed using the lattice Boltzmann method, step (2) sets different boundary conditions for different parts of the rock porous medium model, and the boundary conditions are as follows: gas can flow (pore space), bounce-back boundary (pore boundary), and no change (solid skeleton). (2.2) The gas seepage simulation is performed by inputting the gas bias pressure of the inlet and outlet boundaries of the rock porous medium model, the gas permeability of the rock porous medium model at different water saturations is obtained, and the gas relative permeability is calculated. The lattice Boltzmann method is used to calculate the gas permeability of the rock porous medium model based on Darcy's law, and through unit conversion, the gas permeability and gas relative permeability of the rock at each water saturation are calculated from the gas permeability simulation results.

[0015] In step (3), the gas relative permeability calculation results are fitted with an empirical model to obtain the gas relative permeability curve of the rock at different water saturations and the functional relationship between them, and thus the gas relative permeability of the rock at different water saturations is predicted through numerical simulation method.

[0016] Working principle: the present application adopts lattice Boltzmann method to simulate mesoscale gas seepage numerical method, including rock porous medium model generation, gas seepage simulation based on lattice Boltzmann method and rock gas relative permeability calculation and prediction process.The present application constructs the rock porous medium model similar to the porosity of the rock sample of different water saturation levels, uses lattice Boltzmann method to simulate gas seepage, obtains the permeability of the rock porous medium model under different water saturation, and further calculates the relative permeability, constructs the function relationship between the water saturation of the rock sample and the relative permeability, so that the rock gas relative permeability is determined simply and effectively.

[0017] The present application first determines the porosity of rock corresponding to each water saturation level, generates the rock porous medium model similar to the porosity of the rock of each water saturation level using four-parameter growth method; then uses lattice Boltzmann method to simulate gas seepage, applies bias pressure to the gas inlet and outlet boundary of the rock porous medium model, calculates the gas permeability and relative permeability of the rock porous medium model with different porosity (corresponding to the water saturation level); and then draws the rock gas relative permeability and different water saturation relationship curve, obtains the function relationship, and determines the relative permeability of rock under different water saturation.

[0018] Advantages: compared with the prior art, the present application has the following advantages:

[0019] (1) the present application simulates mesoscale gas seepage by lattice Boltzmann method, the calculation process is convenient, the calculation result is accurate, and the method is suitable for simulating gas seepage of rock porous medium model with different porosity and pore shape.

[0020] (2) the present application generates the rock porous medium model similar to the porosity, pore structure and distribution of rock by four-parameter growth method and Matlab programming, simulates gas seepage based on lattice Boltzmann method, obtains the gas relative permeability change curve of rock under different saturation, determines the gas relative permeability of rock under different saturation by numerical simulation method, and further determines the relative permeability of the laboratory test rock sample under different water saturation conditions, so that the technical defects of the prior art, such as difficulty in preparing rock samples with different water saturation and insufficient gas permeability measurement accuracy, are overcome. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 The present application is based on the process diagram of rock gas relative permeability calculation based on lattice Boltzmann method;

[0022] Figure 2 (a) is a rock porous medium model contrast drawing generated by BSE imaging method of rock sample in the embodiment;

[0023] Figure 2(b) is a contrast chart of rock BSE imaging and rock porous medium model generated by four-parameter growth method in the embodiment;

[0024] Figure 3 (a) is a fitting curve chart of rock gas relative permeability empirical formula at different saturations calculated by lattice Boltzmann gas seepage simulation when the osmotic pressure is 0.05 MPa in the embodiment;

[0025] Figure 3 (b) is a fitting curve chart of rock gas relative permeability empirical formula at different saturations calculated by lattice Boltzmann gas seepage simulation when the osmotic pressure is 0.05 MPa in the embodiment. DETAILED DESCRIPTION

[0026] The rock gas relative permeability calculation method based on the lattice Boltzmann method of the present application comprises the following steps:

[0027] Step (1), according to the porosity of the rock sample under different water saturation conditions and the pore microstructure obtained by backscattered electron imaging (BSE), a rock porous medium model is generated:

[0028] (1.1) according to the measured porosity and the pore microstructure displayed by BSE imaging, using four-parameter growth method, the model area N×N is set, the porosity initial growth core parameters P cd and growth direction probability parameters P di , a similar rock sample with different water saturations is generated, and the porous medium model (.txt file) represented by 0 (pore) and 1 (solid) is generated;

[0029] max_i=300;max_j=300;

[0030] d1=0.01;d2=0.01;d3=0.01;d4=0.01;

[0031] d5=0.04 / 4;d6=0.04 / 4;d7=0.04 / 4;d8=0.04 / 4;

[0032] cdd=0.1;i=0;

[0033] dlmwrite('n.txt',Seed);

[0034] (n is porosity, cdd is initial growth core parameter, d1-d8 is growth direction probability parameter)

[0035] (1.2) Using Matlab programming, change the porous medium model to a different water saturation rock porous medium model (.dat file) for lattice Boltzmann gas seepage simulation consisting of 0 (pore space) part, 1 (pore boundary) part and 2 (solid skeleton) part.

[0036]

[0037]

[0038] (Read the porous medium model (.txt) file, add the solid matrix part)

[0039] Step (2), gas seepage simulation and gas relative permeability calculation of different water saturation rock porous media based on the lattice Boltzmann method, relative permeability curve drawing, specifically including the following steps:

[0040] (2.1) In step 1, the porosity of the rock porous medium model is used to represent its different water saturations S w , based on the lattice Boltzmann method, using Palabos software for gas seepage simulation, first set the velocity set D2Q9, then set different boundary conditions for different parts of the rock porous medium model, mainly: 0 (pore space) part, gas through, 1 (pore boundary) part, bounce-back boundary, representing the collision process of gas molecules with the boundary; 2 (solid skeleton) part, no change.

[0041] typedef double T;

[0042] #define DESCRIPTOR descriptors::D2Q9Descriptor

[0043] (Setting D2Q9 velocity set)

[0044] pcout << "Definition of the geometry." << std::endl;

[0045] (Define boundary conditions)

[0046] defineDynamics(lattice, geometry, new BounceBack<T, DESCRIPTOR>(), 1);

[0047] (1 is the bounce-back boundary)

[0048] defineDynamics(lattice, geometry, new NoDynamics<T, DESCRIPTOR>(), 2);

[0049] (2 is the no change region)

[0050] (2.2) By inputting the gas pressure on the upper and lower boundaries of the rock porous medium model, a bias pressure ΔP is generated, usually 0.05 MPa, and gas seepage simulation is carried out using Palabos software.

[0051] pcout << "Definition of inlet / outlet." << std::endl;

[0052] Box2D inlet(1, nx-2, ny-1, ny-1);

[0053] boundaryCondition->addPressureBoundary1P(inlet, lattice);

[0054] setBoundaryDensity(lattice, inlet, (T)1.);

[0055] (Inlet boundary pressure is set to 1)

[0056] Box2D outlet(1, nx-2, 0, 0);

[0057] boundaryCondition->addPressureBoundary1N(outlet, lattice);

[0058] setBoundaryDensity(lattice, outlet, (T)1.-deltaP*DESCRIPTOR <t>::invCs2);

[0059] (Outlet boundary pressure set to 1-ΔP)

[0060] (permeability n.dat n / NNΔP

[0061] (simulation start command, permeability is simulation program (.cpp), N is the size of rock porous medium model region; n is different water saturation; n.dat is the porosity of rock porous medium model file; n is data output file; ΔP is bias pressure)

[0062] (3) The lattice Boltzmann method is used to calculate the gas permeability of the rock porous medium model. Based on Darcy's law, the gas permeability k and the gas relative permeability kr of the rock at each water saturation are calculated from the gas permeability simulation results through unit conversion. rg .

[0063]

[0064] wherein k is the gas permeability, m 2 ; μ is the dynamic viscosity, Pa·s; u is the average velocity, m / s; ΔL is the length of the flow-through region, m; and ΔP is the pressure difference between the inlet and outlet, MPa.

[0065] After unit conversion, the actual permeability calculation formula is:

[0066]

[0067] wherein v represents the physical space fluid motion viscosity, m 2 / s; v L represents the lattice space fluid motion viscosity, m 2 / s; and ΔL represents the distance between adjacent lattice points in the lattice space, dimensionless.

[0068] Step 3: The gas permeability corresponding to different water saturations obtained from the permeability simulation of different rock porous medium models is used to calculate the gas relative permeability. According to the simulation results of the lattice Boltzmann rock porous medium model gas relative permeability, a classical model fitting is used to obtain the function relationship between the gas relative permeability and the water saturation.

[0069]

[0070] wherein k(S w ) is the effective permeability of the rock sample at the water saturation S w , and k0(S w =0) is the gas permeability of the dry rock sample.

[0071] The classical models are Brooks-Corey model and Van Genuchten-Mualem model.

[0072] The Brooks-Corey model is expressed as follows,

[0073]

[0074] where k is the relative permeability of gas; S is the water saturation; S is the residual water saturation; S is the residual gas saturation; n is the fitting parameter. rg w wc gc where k is the relative permeability of gas; S is the water saturation; S is the residual water saturation; S is the residual gas saturation; n is the fitting parameter.

[0075] The Van Genuchten-Mualem model is expressed as follows

[0076]

[0077] where η is the tortuosity parameter; m is the fitting parameter, m = 1-1 / n, n > 1.

[0078] The relative permeability of gas of the rock at different water saturations is obtained by the two classical models, and the relative permeability of gas of the rock at different water saturations is predicted according to the curve.

[0079] Embodiment

[0080] Taking a sandstone rock sample as an example, the relative permeability of the rock sample is determined by the following steps using a numerical method:

[0081] Step 1: The sandstone rock sample is a standard cylindrical sample with a diameter of Φ50 mm and a height of 50 mm, which is prepared into rock samples with different water saturations, and the water saturations and porosities of the rock samples are shown in Table 1.

[0082] Table 1 Rock parameters at different saturations

[0083]

[0084] According to the porosities of the rocks at different saturations in Table 1 and the BSE image as shown in Figure 2 (a), a similar rock porous medium model is generated as shown in Figure 2 (b);

[0085] Step 2: Based on the lattice Boltzmann method, the Palabos software is used to simulate the gas seepage of the porous medium rock at different water saturations (argon), and the simulation parameter settings are shown in Table 2.

[0086] Table 2 Physical parameters and lattice parameter calculation results

[0087] ​​​

[0088] The results are shown in Table 3 below.

[0089] Table 3 Lattice Boltzmann simulation of gas permeability and relative permeability

[0090]

[0091] Step 3: The relative permeability results obtained by simulation are fitted using Brooks_Corey and Van Genuchten-Mualem models respectively, and the fitting curves of the empirical formula of the relative permeability of the rock at different saturations are obtained, as shown in Figs. 4(a) and 4(b), and the fitting parameters are shown in Table 4. Figure 3

[0092]

[0093] It can be seen that for the dense sandstone selected in this example, the function relationship between the relative permeability and the different water saturation is,

[0094]

[0095] or,

[0096]

[0097] The water saturation S w is calculated, and the relative permeability of the rock to the gas is calculated.​< / t>

Claims

1. A method for calculating the relative permeability of gas in rocks based on the lattice Boltzmann method, characterized in that: Includes the following steps: (1) The porosity of rock samples under different water saturation conditions was determined by indoor experiments. Backscattered electron imaging was performed on the rock samples to obtain the micro pore structure. The four-parameter growth method was used to set parameters according to the porosity and pore morphology of the rock under different water saturation conditions to generate a rock porous medium model with the same porosity and pore morphology as the rock samples under different water saturation conditions. (2) Apply bias pressure to the gas inlet and outlet boundaries of the porous rock medium model, and use the lattice Boltzmann method to simulate gas seepage. Apply bias pressure to the gas inlet and outlet boundaries of the porous rock medium model, and calculate the gas permeability of the porous rock medium model with different porosity and the relative gas permeability of rocks with different water saturation. (3) Fit the test results of relative gas permeability under different water saturation, plot the relationship curve between relative gas permeability of rock and different water saturation, obtain the functional relationship between relative permeability and different water saturation, and thus deduce the relative gas permeability under different water saturation.

2. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: In step (1), a four-parameter growth method is used to generate a porous medium model with the same porosity and similar microstructure as rock samples with different water saturation by controlling porosity, initial growth nuclei and growth direction probability. By setting solid matrix, pore space and solid boundary parameters, the porous medium model is transformed into a rock porous medium model for lattice Boltzmann gas flow simulation, generating a rock porous medium model with the same porosity and similar pore morphology as rock samples with different water saturation.

3. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: In step (1), the process of generating the porous rock medium model is as follows: (1.1) Determine the size of the unit cell characterizing the pore structure of the rock, set it as an N×N region in the four-parameter growth method, input the porosity parameters according to the porosity of the rock at various water saturation levels, set the initial growth nucleus parameters and growth direction probability parameters according to the pore size and pore distribution of the rock sample BSE imaging, and generate a .txt file of a porous medium model represented by pores and solids that is consistent with the porosity and pore structure of the rock sample. (1.2) Using Matlab programming, the porous media model was changed into a .dat file of a rock porous media model with different water saturation, consisting of pore space, pore boundary part and solid skeleton part, for lattice Boltzmann gas flow simulation.

4. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: In step (2), the relative gas permeability of rocks with different water saturation is calculated using the lattice Boltzmann method, and the relative gas permeability curve is obtained. The functional relationship between relative gas permeability and different water saturation is obtained, and thus the relative gas permeability of rocks with different water saturation is derived.

5. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: The different porosities calculated in step (2) correspond to the water saturation.

6. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: In step (2), the method for calculating the relative gas permeability of rocks with different water saturation using the lattice Boltzmann method is as follows: (2.1) In step (2), the porosity of the rock porous media model is used to characterize different water saturation S. w Gas seepage simulation was performed using the lattice Boltzmann method, setting boundary conditions for different parts of the rock porous media model, including pore space, pore boundary, and solid skeleton. (2.2) By inputting the gas deflection pressure at the gas inlet and outlet boundaries of the porous rock medium model, gas seepage simulation is performed to obtain the gas permeability of the porous rock medium model with different water saturation, and the relative gas permeability is calculated.

7. The method for calculating the relative permeability of rock gas based on the lattice Boltzmann method according to claim 1, characterized in that: In step (3), after obtaining the functional relationship between relative permeability and different water saturation, a water saturation is selected, and the relative gas permeability of the rock at the water saturation is calculated.

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