A method for testing the permeability of a porous medium

Abstract

A method for testing the permeability of a porous medium, which relates to the field of testing the permeability of porous materials. The method for testing the permeability of a porous medium is to obtain the porosity and average pore size of a porous medium sample; determine the average porosity of the calculation domain of the porous medium sample and generate a pore-scale calculation grid and a macro-scale calculation grid; simulate the flow process of fluid flowing through the porous medium sample at the pore scale and the macro scale, calculate the fluid mechanical energy loss of the pore simulation when the flow process reaches the stable condition and the fluid mechanical energy loss of the macro simulation when the flow process reaches the stable condition, and calculate the permeability constant and permeability of the porous medium sample. The method for testing the permeability of a porous medium provided by the embodiments of the present application can simultaneously describe the dynamic behaviors of solids and fluids and effectively obtain the permeability of the porous medium through a numerical simulation method, without relying on a large number of complex irregular discrete grids of pure fluid domains, greatly reducing the calculation consumption and calculation difficulty.

Description

Technical Field

[0001] This application relates to the field of permeability testing of porous materials, and more particularly, to a method for testing the permeability of a porous medium. Background Art

[0002] The permeability of a porous medium is a measure of the ability of the porous medium to allow fluid to pass through. The property of a porous medium to allow fluid to pass through under a certain pressure difference is called permeability, and the ability to allow fluid to pass through is called permeability. The permeability of a porous medium is often expressed by Darcy's law.

[0003] The testing methods of the permeability of a porous medium are generally divided into two categories, namely physical tests and numerical tests. Physical test is to inject or pump water into the porous medium, record the change of water volume in the medium, and calculate the permeability in combination with Darcy's law; it can also be through a water pressure test, record the water pressure change and water flow velocity, and then calculate the permeability according to Darcy's law. Numerical tests generally predict the pressure loss of fluid passing through the porous medium under a given flow velocity condition or predict the flow velocity of fluid passing through the porous medium under a given pressure difference condition through computational fluid dynamics simulation, and calculate the permeability through Darcy's law.

[0004] The test period of physical tests for measuring the permeability of a porous medium is relatively long, relying on complex test equipment and test procedures, which brings significant inconvenience to engineering application tests; moreover, due to the microscopic differences of the tested samples and test errors, the permeability test results often have an order-of-magnitude deviation, affecting the engineering application effect. The numerical test method has the advantages of short test period, relatively simple test process, and good result consistency. However, the traditional computational fluid dynamics method can only consider the pure fluid domain, that is, it is necessary to draw the irregular fluid domain outside the porous medium skeleton and generate complex irregular grids, with high computational cost, poor accuracy, and poor computational stability. Summary of the Invention

[0005] The purpose of this application is to provide a method for testing the permeability of a porous medium, which can simultaneously describe the dynamic behaviors of solids and fluids and effectively obtain the permeability of the porous medium through numerical simulation methods, without relying on a large number of complex irregular discrete grids in the pure fluid domain, greatly reducing the computational consumption and computational difficulty.

[0006] The embodiments of this application are implemented as follows:

[0007] The embodiments of this application provide a method for testing the permeability of a porous medium, which includes the following steps:

[0008] Obtain the porosity φ and the average pore size d ;

[0009] Determine the computational domain Ω within the range of the porous medium sampleU Average porosity , generate a pore-scale computational grid with a grid cell size of x , and map the porosity of each grid point of the pore-scale computational grid based on the porosity φ 1; φ 1;

[0010] Perform pore-scale simulation on the flow process of fluid flowing through the porous medium sample, and calculate the fluid mechanical energy loss of the pore simulation when the flow process reaches the stable condition:

[0011] Generate a macro-scale computational grid with a grid cell size of U within the computational domain L , and map the porosity of each grid point of the macro-scale computational grid based on the porosity φ 2; φ 2;

[0012] Perform macro-scale simulation on the flow process of fluid flowing through the porous medium sample, and calculate the fluid mechanical energy loss of the macro simulation when the flow process reaches the stable condition;

[0013] Calculate the permeability constant and permeability of the porous medium sample according to the fluid mechanical energy loss of the pore simulation when the flow process reaches the stable condition and the fluid mechanical energy loss of the macro simulation when the flow process reaches the stable condition.

[0014] In some alternative embodiments, 10 d ≤ U ≤ Ω .

[0015] In some alternative embodiments, x ≤ 0.1 d .

[0016] In some alternative embodiments, based on the pore-scale computational grid, use the following control equations to perform pore-scale simulation on the flow process of fluid flowing through the porous medium sample:

[0017] ;

[0018] ;

[0019] In the formula, is the pore velocity at the next time step to be solved; is the time; is the porosity of each grid point of the pore-scale computational grid; is the dynamic pressure, is the viscosity of the fluid; is the latest pore velocity at the current time step that is known; is the time step.

[0020] In some alternative embodiments, the following formula is used to calculate the fluid mechanical energy loss of pore simulation when the flow process reaches the steady state condition p pore :

[0021] ;

[0022] wherein, p pore is the fluid mechanical energy loss of pore simulation when the flow process reaches the steady state condition; is the fluid mechanical energy after the fluid of pore simulation flows out of the porous medium sample, p 1 is the fluid pressure when the flow process of pore simulation reaches the steady state condition and flows out of the porous medium sample, u 1 is the fluid velocity when the flow process of pore simulation reaches the steady state condition and flows out of the porous medium sample; is the fluid mechanical energy before the fluid of pore simulation flows into the porous medium sample, p 0 is the fluid pressure when the flow process of pore simulation reaches the steady state condition and flows into the porous medium sample, u 0 is the fluid velocity when the flow process of pore simulation reaches the steady state condition and flows into the porous medium sample.

[0023] In some alternative embodiments, 16 d ≤ L .

[0024] In some alternative embodiments, the following control equations are used to perform macroscopic scale simulation of the flow process of fluid flowing through a porous medium sample based on a macroscopic scale computational grid:

[0025] ;

[0026] ;

[0027] wherein, is the pore velocity at the next time step to be solved; is time; is the porosity of each grid point of the macroscopic scale computational grid; is the dynamic pressure, is the viscosity of the fluid; is the latest pore velocity at the current time step that is known; is the time step.

[0028] In some alternative embodiments, the following formula is used to calculate the fluid mechanical energy loss obtained from macroscopic simulation when the flow reaches the steady state condition pmacro :

[0029] ;

[0030] Wherein, p macro is the fluid mechanical energy loss obtained from macroscopic simulation under the condition of stable flow, is the fluid mechanical energy calculated after the fluid flows out of the porous medium sample in macroscopic simulation, p 3 is the fluid pressure when the fluid flowing out of the porous medium sample reaches the stable condition in macroscopic simulation, u 3 is the fluid velocity when the fluid flowing out of the porous medium sample reaches the stable condition in macroscopic simulation; is the fluid mechanical energy before the fluid flows into the porous medium sample, p 2 is the fluid pressure when the fluid flowing into the porous medium sample reaches the stable condition in macroscopic simulation, u 2 is the fluid velocity when the fluid flowing into the porous medium sample reaches the stable condition in macroscopic simulation.

[0031] In some alternative embodiments, the permeability constant of the porous medium sample is calculated using the following formula K 0:

[0032] ;

[0033] Wherein, p macro is the fluid mechanical energy loss of macroscopic simulation when the flow process reaches the stable condition; p pore is the fluid mechanical energy loss of pore simulation when the flow process reaches the stable condition; is the average porosity of the computational domain U; is the viscosity of the fluid; is the time step.

[0034] In some alternative embodiments, the permeability of the porous medium sample is calculated according to the following formula:

[0035] ;

[0036] Wherein, p macro is the fluid mechanical energy loss of macroscopic simulation when the flow process reaches the stable condition; p pore is the fluid mechanical energy loss of pore simulation when the flow process reaches the stable condition; is the average porosity of the computational domain U; is the porosity of the porous medium sample; is the viscosity of the fluid; is the time step.

[0037] In some alternative embodiments, the porosity of the porous medium sample is obtained by X-ray or optical imaging.

[0038] The beneficial effects of the present application are as follows: The porous medium permeability test method provided by the embodiments of the present application includes the following steps: obtaining the porosity and average pore diameter of the porous medium sample; determining the computational domain within the range of the porous medium sample U of the average porosity , generating a pore-scale computational grid with a grid cell size of x , mapping the porosity of each grid point of the pore-scale computational grid based on the porosity φ ; performing a pore-scale simulation on the flow process of the fluid flowing through the porous medium sample, and calculating the fluid mechanical energy loss of the pore simulation when the flow process reaches the stable condition: generating a macro-scale computational grid with a grid cell size of U within the computational domain L , mapping the porosity of each grid point of the macro-scale computational grid based on the porosity φ ; performing a macro-scale simulation on the flow process of the fluid flowing through the porous medium sample, and calculating the fluid mechanical energy loss of the macro simulation when the flow process reaches the stable condition; calculating the permeability constant and permeability of the porous medium sample according to the fluid mechanical energy loss of the pore simulation and the fluid mechanical energy loss of the macro simulation when the flow process reaches the stable condition. The porous medium permeability test method provided by the embodiments of the present application can effectively measure the permeability of the porous medium through a numerical simulation method. This method can simultaneously describe the dynamic behaviors of solids and fluids, does not rely on a large number of complex irregular discrete grids of pure fluid domains, supports the use of simple and regular computational grids, thus greatly reducing the computational consumption and computational difficulty, solves the problems of long cycle and dependence on complex hardware equipment of traditional test methods, and at the same time overcomes the problems of difficult calculation and large analysis difficulty of traditional numerical simulation methods for complex porous medium problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present application, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0040] Figure 1 is a schematic flow chart of the porous medium permeability test method provided by the embodiments of the present application. DETAILED DESCRIPTION

[0041] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are some, but not all, of the embodiments of this application.

[0042] Therefore, the detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of this application that is claimed, but merely represents selected embodiments of this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of this application without creative efforts fall within the scope of protection of this application.

[0043] The features and performance of the porous medium permeability testing method of this application will be further described in detail below in conjunction with embodiments.

[0044] As Figure 1 shown, an embodiment of this application provides a porous medium permeability testing method, which includes the following steps:

[0045] Step 1: Obtain the porosity φ and the average pore size d of the porous medium sample; optionally, use X-ray or optical imaging to obtain the porosity φ of the porous medium sample;

[0046] Step 2: Determine the average porosity Ω of the computational domain U within the range of the porous medium sample, generate a pore-scale computational grid with a grid cell size of , and map to obtain the porosity x of each grid point of the pore-scale computational grid based on the porosity φ ; optionally, 10 φ ≤ d ≤ U ≤ Ω ; optionally, x ≤ 0.1 d .

[0047] Step 3: Perform pore-scale simulation on the flow process of the fluid flowing through the porous medium sample, and calculate the fluid mechanical energy loss of the pore simulation when the flow process reaches a stable condition:

[0048] Optionally, use the following control equations to perform pore-scale simulation on the flow process of the fluid flowing through the porous medium sample:

[0049] ;

[0050] ;

[0051] In the formula, is the pore velocity at the next time step to be solved, with the unit of m / s; is the time, with the unit of s; is the porosity of each grid point of the pore-scale computational grid, with the unit of 1; is the dynamic pressure, with the unit of m 2 / s 2 ; is the viscosity of the fluid, with the unit of m 2 / s; is the latest pore velocity at the current time step, with the unit of m / s; is the time step, with the unit of s.

[0052] Optionally, the following formula is used to calculate the fluid mechanical energy loss in pore simulation when the flow process reaches the stable condition p pore :

[0053] ;

[0054] In the formula, p pore is the fluid mechanical energy loss in pore simulation when the flow process reaches the stable condition; is the fluid mechanical energy of the fluid flowing out of the porous medium sample in pore simulation, p 1 is the fluid pressure of the fluid flowing out of the porous medium sample when the flow process in pore simulation reaches the stable condition, u 1 is the fluid velocity of the fluid flowing out of the porous medium sample when the flow process in pore simulation reaches the stable condition; is the fluid mechanical energy of the fluid flowing into the porous medium sample before pore simulation, p 0 is the fluid pressure of the fluid flowing into the porous medium sample when the flow process in pore simulation reaches the stable condition, u 0 is the fluid velocity of the fluid flowing into the porous medium sample when the flow process in pore simulation reaches the stable condition.

[0055] Step Four. Generate a macroscopic-scale computational grid with a grid cell size of U in the computational domain L , and map the porosity φ to obtain the porosity φ 2 of each grid point of the macroscopic-scale computational grid; optionally, 16 d ≤ L .

[0056] Step Five. Conduct a macroscopic-scale simulation of the fluid flow through the porous medium sample, and calculate the fluid mechanical energy loss in macroscopic simulation when the flow process reaches the stable condition.

[0057] Optionally, the following control equation is used to simulate the flow process of fluid flowing through a porous medium sample at a macroscopic scale:

[0058] ;

[0059] ;

[0060] In the formula, is the pore velocity at the next time step to be solved, with the unit of m / s; is the time, with the unit of s; is the porosity of each grid point of the macroscopic scale calculation grid, with the unit of 1; is the dynamic pressure, with the unit of m 2 / s 2 ; is the viscosity of the fluid, with the unit of m 2 / s; is the latest pore velocity at the current time step, with the unit of m / s; is the time step, with the unit of s.

[0061] Optionally, the following formula is used to calculate the fluid mechanical energy loss obtained from the macroscopic simulation under the condition of flow stability p macro :

[0062] ;

[0063] In the formula, p macro is the fluid mechanical energy loss obtained from the macroscopic simulation under the condition of flow stability, is the fluid mechanical energy calculated after the fluid flows out of the porous medium sample in the macroscopic simulation, p 3 is the fluid pressure when the flow process in the macroscopic simulation reaches the stable condition and flows out of the porous medium sample, u 3 is the fluid velocity when the flow process in the macroscopic simulation reaches the stable condition and flows out of the porous medium sample; is the fluid mechanical energy before the fluid flows into the porous medium sample, p 2 is the fluid pressure when the flow process in the macroscopic simulation reaches the stable condition and flows into the porous medium sample, u 2 is the fluid velocity when the flow process in the macroscopic simulation reaches the stable condition and flows into the porous medium sample.

[0064] Step Six: Calculate the permeability constant of the porous medium sample according to the fluid mechanical energy loss of the pore simulation and the fluid mechanical energy loss of the macroscopic simulation when the flow process reaches the stable condition;

[0065] Optionally, the permeability constant of the porous medium sample is calculated using the following formula K 0:

[0066] ;

[0067] wherein p macro is the fluid mechanical energy loss in the macroscopic simulation when the flow process reaches the stable condition; p pore is the fluid mechanical energy loss in the pore simulation when the flow process reaches the stable condition; is the average porosity of the computational domain U; is the viscosity of the fluid; is the time step.

[0068] Step 7. Calculate the permeability of the porous medium sample.

[0069] Optionally, the permeability of the porous medium sample is calculated according to the following formula K :

[0070] ;

[0071] wherein p macro is the fluid mechanical energy loss in the macroscopic simulation when the flow process reaches the stable condition; p pore is the fluid mechanical energy loss in the pore simulation when the flow process reaches the stable condition; is the average porosity of the computational domain U; is the porosity of the porous medium sample; is the viscosity of the fluid; is the time step.

[0072] The porous medium permeability testing method provided by the embodiments of the present application calculates the fluid mechanical energy losses of pore simulation and macroscopic simulation respectively when the fluid flow process through the porous medium sample reaches the stable condition by separately considering the hydrodynamic behaviors of the porous medium sample under pore simulation and macroscopic simulation conditions. Furthermore, the permeability constant and permeability of the porous medium sample are calculated based on the fluid mechanical energy loss of pore simulation and the fluid mechanical energy loss of macroscopic simulation when the flow process reaches the stable condition. It can effectively measure the permeability of the porous medium through numerical simulation methods. The numerical simulation method adopted by this method can describe the dynamic behaviors of solids and fluids simultaneously, without relying on a large number of complex irregular discrete grids of pure fluid domains, and supports the use of simple and regular computational grids, thus greatly reducing the computational consumption and result difficulty. It solves the problems of long cycle and dependence on complex hardware equipment of traditional test methods, and also overcomes the problems of incomputability and large analysis difficulty of traditional numerical simulation methods for complex porous medium problems, providing new ideas and methods for porous medium permeability testing.

[0073] It should be noted that the porosity of the porous medium sample obtained in the porous medium permeability testing method provided by the present application φ is the local porosity of the porous medium sample, and this local porosity is a quantity that varies with space. Similarly, the calculated permeability of the porous medium sample is also the corresponding local permeability, which is also a quantity that varies with space.

[0074] The embodiments described above are some, but not all, of the embodiments of the present application. The detailed description of the embodiments of the present application is not intended to limit the scope of the present application claimed, but merely represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts fall within the scope of protection of the present application.

Claims

1. A porous medium permeability testing method, characterized in that: It includes the following steps: Get the porosity of porous media samples and average pore diameter d; Determine the average porosity of the computational domain U within the range Ω of the porous medium sample Generate a pore-scale computational grid with a cell size of x, based on the porosity Mapping to obtain the porosity of each grid point of the pore scale calculation grid ; The flow process of the fluid flowing through the porous medium sample is simulated at the pore scale, and the mechanical energy loss of the fluid simulated in the pore when the flow process reaches a stable condition is calculated: Generate a macroscale computational grid with a grid cell size of L in the computational domain U based on the porosity Mapping to obtain the porosity of each grid point of the macro-scale computational grid ; Simulate the flow process of fluid through porous media samples at a macroscopic scale and calculate the mechanical energy loss of the fluid in the macroscopic simulation when the flow process reaches a stable condition; Calculating the permeability constant and the permeability of the porous medium sample according to the fluid mechanical energy loss of pore simulation when the flow process reaches a stable condition and the fluid mechanical energy loss of macroscopic simulation when the flow process reaches a stable condition; The permeability constant K0 and permeability K of porous media samples are calculated using the following formula: In the formula, Δp macro Δp is the fluid mechanical energy loss in macroscopic simulation when the flow process reaches stable conditions; pore The mechanical energy loss of the fluid simulated by the pores when the flow process reaches stable conditions; is the average porosity of the computational domain U; is the porosity of the porous medium sample; v is the viscosity of the fluid; Δt is the time step.

2. The porous medium permeability testing method according to claim 1, characterized in that: 10d≤U≤Ω.

3. The porous medium permeability testing method according to claim 1, characterized in that: x≤0.1d.

4. The porous medium permeability testing method according to claim 1, characterized in that: The flow process of the fluid through the porous media sample is simulated at the pore scale using the following governing equations based on the pore scale computational grid: Where u is the pore flow velocity at the next time step to be solved; t is time; The porosity of each grid point of the pore scale calculation grid; p is the dynamic pressure, ν is the viscosity of the fluid; u P is the latest known pore flow velocity in the current time step; Δt is the time step.

5. The porous medium permeability testing method according to claim 4, characterized in that: The following formula is used to calculate the fluid mechanical energy loss Δp of the pore simulation when the flow process reaches a stable condition: pore : Δp pore =[p1+0.5u1 2 ] out -[p0+0.5u0 2 ] in ; In the formula, Δp pore is the fluid mechanical energy loss of the pore simulation when the flow process reaches a stable condition; [p1+0.5u1 2 ] out is the fluid mechanical energy after the pore-simulated fluid flows out of the porous medium sample, p1 is the fluid pressure flowing out of the porous medium sample when the pore-simulated flow process reaches a stable condition, u1 is the fluid flow rate flowing out of the porous medium sample when the pore-simulated flow process reaches a stable condition; [p0+0.5u0 2 ] in is the fluid mechanical energy of the pore-simulated fluid before it flows into the porous medium sample, p0 is the fluid pressure flowing into the porous medium sample when the pore-simulated flow process reaches a stable condition, and u0 is the fluid flow rate flowing into the porous medium sample when the pore-simulated flow process reaches a stable condition.

6. The porous medium permeability testing method according to claim 1, characterized in that: 16d≤L.

7. The porous medium permeability testing method according to claim 1, characterized in that: The following control equations are used based on the macro-scale computational grid to simulate the flow process of the fluid through the porous medium sample at a macro-scale: Where u is the pore flow velocity at the next time step to be solved; t is time; is the porosity of each grid point of the macro-scale calculation grid; p is the dynamic pressure, ν is the viscosity of the fluid; u P is the latest known pore flow velocity in the current time step; Δt is the time step.

8. The porous medium permeability testing method according to claim 7, characterized in that: The following formula is used to calculate the fluid mechanical energy loss Δp obtained by macroscopic simulation under stable flow conditions: macro : Δp macro =[p3+0.5u3 2 ] out -[p2+0.5u2 2 ] in ; In the formula, Δp macro In order to achieve the fluid mechanical energy loss obtained by macroscopic simulation under stable flow conditions, [p3+0.5u3 2 ] out is the fluid mechanical energy calculated after the macroscopically simulated fluid flows out of the porous medium sample, p3 is the fluid pressure flowing out of the porous medium sample when the macroscopically simulated flow process reaches a stable condition, and u3 is the fluid flow rate flowing out of the porous medium sample when the macroscopically simulated flow process reaches a stable condition; [p2+0.5u2 2 ] in is the fluid mechanical energy before the fluid flows into the porous medium sample, p2 is the fluid pressure flowing into the porous medium sample when the macroscopic simulated flow process reaches a stable condition, and u2 is the fluid flow rate flowing into the porous medium sample when the macroscopic simulated flow process reaches a stable condition.

9. The porous medium permeability testing method according to claim 1, characterized in that: The porosity of the porous medium sample Acquired using X-ray or optical imaging.

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