Gas-water two-phase unsteady-state seepage simulation method based on lattice Boltzmann

Abstract

The invention discloses a lattice Boltzmann-based gas-water two-phase unsteady-state seepage simulation method, and belongs to the technical field of oil-gas field development. The method comprises the following steps: firstly, constructing a carbonate rock three-dimensional digital core by carrying out a micro-CT scanning experiment, and accurately representing a real storage space form of the carbonate rock; secondly, simulating a gas-water two-phase unsteady-state seepage process in the three-dimensional digital rock core of the carbonate rock by writing a programming language and using a lattice Boltzmann method based on a Stan-Chen acting force model, and intuitively displaying water invasion front edges and water invasion dynamic states in the carbonate rock at different moments; and finally, obtaining the fluid pressure and flow velocity distribution in the carbonate rock at different moments, and obtaining the water invasion dynamic characteristics of the carbonate rock. The method can provide guidance and theoretical basis for efficient development of water-driven gas reservoirs (especially carbonate rock water-containing gas reservoirs), and the practical application effect is remarkable.

Description

Technical Field

[0001] The present invention specifically relates to a method for simulating unsteady gas-water two-phase seepage based on the lattice Boltzmann method, and specifically relates to the simulation of the unsteady flow process of gas-water two-phase in the real reservoir space of rocks, belonging to the technical field of oil and gas field development. Background Technique

[0002] Most of the gas reservoirs in the development stage in China are edge water drive gas reservoirs, bottom water drive gas reservoirs or edge-bottom water drive gas reservoirs, and these gas reservoirs are collectively referred to as water drive gas reservoirs. As the formation pressure decreases, formation water invades the gas reservoir, seals the gas, and occupies part of the seepage channels of the gas, reducing the productivity of gas wells and the recovery rate of gas reservoirs.

[0003] At present, the simulation of steady-state or unsteady-state gas-water two-phase seepage is generally carried out based on the pore network model constructed by regular channels (circular or triangular) to understand the microscopic-scale water invasion process and water invasion dynamics in water drive gas reservoirs. However, these methods cannot accurately reflect the gas-water two-phase seepage characteristics under the real reservoir space morphology of rocks. At the same time, in carbonate gas reservoirs, pores, caves and fractures coexist, and the reservoir space morphology is more complex, making it extremely difficult to accurately understand its gas-water two-phase seepage characteristics. Summary of the Invention

[0004] Aiming at the deficiencies of the existing methods for simulating unsteady gas-water two-phase seepage, the present invention proposes a method for simulating unsteady gas-water two-phase seepage based on the lattice Boltzmann method, which can accurately simulate the unsteady gas-water two-phase seepage process in the real reservoir space including pores, caves and fractures. The simulation process is logically rigorous and highly accurate, and can provide guidance and theoretical basis for the efficient development of water drive gas reservoirs (especially carbonate rock gas reservoirs with water), and the actual application effect is remarkable.

[0005] In order to achieve the above technical objectives, the following technical solutions are proposed:

[0006] A method for simulating unsteady gas-water two-phase seepage based on the lattice Boltzmann method, comprising the following steps:

[0007] S1: Conduct a micro-CT scanning experiment to construct a three-dimensional digital core of carbonate rock;

[0008] Take a carbonate rock sample and conduct a micro-CT scanning experiment to obtain a two-dimensional CT image of the carbonate rock sample;

[0009] Perform median filtering and binarization processing on the two-dimensional CT image to establish a three-dimensional digital core containing pores, caves and fractures, and accurately characterize the pore space properties of the carbonate rock sample;

[0010] S2: Use the lattice Boltzmann method to simulate the unsteady gas-water two-phase flow in the three-dimensional digital core of carbonate rock;

[0011] Set the property parameters of the gas-phase fluid and the water-phase fluid. The lattice Boltzmann equations for the two-phase fluid are as follows:

[0012] f i k (x + e i δt, t + δt) - f i k (x, t) = -Ω[f k i (x, t) - f i k,eq (x, t)] (1);

[0013] In Equation (1), f i is the particle distribution function, kg / m 3 ; i = 0, 1, …, 18, representing 19 lattice velocity directions; e i is the lattice velocity, m / s; t is the time, s; Ω is the collision matrix, Ω = M -1 SM, where M is the transformation matrix of the particle distribution function f i ; k = 1 represents the water phase, k = 2 represents the gas phase; f i eq is the equilibrium particle distribution function, as follows:

[0014]

[0015] In Equation (2), ρ is the fluid density, kg / m 3 ; w i is the weight coefficient; u is the fluid velocity, m / s; c s is the speed of sound, m / s;

[0016] Initialize the velocity fields u 1 (x, 0), u 2 (x, 0), the density fields ρ 1 (x, 0), ρ 2 (x, 0) and the distribution functions:

[0017]

[0018] Subsequently, set the boundary conditions and start evolving according to Equation (1) with the pressure gradient ▽P. Perform the collision at each grid point x:

[0019]

[0020] Perform the migration:

[0021]

[0022] Or perform the bounce:

[0023]

[0024] In Equation (4), τ 1 is the dimensionless relaxation time of the aqueous phase, and τ 2 is the dimensionless relaxation time of the gas phase;

[0025] That is, by simulating the unsteady flow process of gas-water two-phase in a three-dimensional digital core of carbonate rock, the water invasion front and water invasion dynamics can be visually displayed;

[0026] S3: Every several iterations, calculate the velocity field and density field in the rock. Among them, the fluid velocity u:

[0027]

[0028] The fluid density ρ:

[0029]

[0030] The fluid pressure p:

[0031] p k = ρ k R g T (9);

[0032] In Equation (9), R g is the gas constant; T is the kinetic temperature of the gas;

[0033] That is, the fluid pressure, aqueous phase flow velocity, and gas phase flow velocity at different positions in the carbonate rock at different times are obtained, and the water invasion dynamic characteristics of the carbonate rock are obtained.

[0034] In addition, this technical solution also provides: A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the gas-water two-phase unsteady seepage simulation method based on lattice Boltzmann.

[0035] And, this technical solution also provides: An information data processing terminal for the gas-water two-phase unsteady seepage simulation method based on lattice Boltzmann.

[0036] Adopting this technical solution, the beneficial technical effects brought are:

[0037] 1. The present invention combines a three-dimensional digital core of carbonate rock and the lattice Boltzmann method based on the Shan-Chen force model, and for the first time realizes the accurate simulation of the gas-water two-phase seepage process in the real reservoir space containing pores, karst caves and fractures, which helps to improve the understanding of the water invasion dynamics and characteristics of carbonate reservoirs; this method is easy to use, the simulation process is logically rigorous and highly accurate, and can provide guidance and theoretical basis for the efficient development of water drive gas reservoirs (especially carbonate gas reservoirs with water);

[0038] 2. The present invention can simulate the unsteady seepage process of gas-water two-phase flow in pores, karst caves and fractures. Compared with the prior art (such as: CN112098293A), the research object involved is more complex; moreover, the present invention uses the lattice Boltzmann method to simulate gas-water two-phase seepage. Compared with the prior art (the maximum sphere algorithm, the sphere-rod model), the lattice Boltzmann method has the characteristics of a mesoscopic model between the microscopic molecular dynamics model and the macroscopic continuous model. Therefore, the present invention has the advantages of simple description of fluid interaction, easy setting of complex boundaries, easy parallel calculation, and easy implementation of the program. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the constructed three-dimensional digital core of carbonate rock (600×600×600);

[0040] Figure 2 is D 3 Q 19 is the schematic diagram of the model;

[0041] Figure 3 is the simulation results of water drive gas at different times of the carbonate digital core (20,000 time steps);

[0042] Figure 4 is the simulation results of water drive gas at different times of the carbonate digital core (40,000 time steps);

[0043] Figure 5 is the simulation results of water drive gas at different times of the carbonate digital core (80,000 time steps);

[0044] Figure 6 is the comparison chart of water saturation at different displacement nodes between the numerical simulation calculation of the model and the laboratory water drive collaborative micro-CT scanning experiment;

[0045] Figure 7 is the relative permeability simulation curve of the water drive gas invasion process and the gas drive water production process of the carbonate core;

[0046] Figure 8 is the simulation results of water drive gas at different times under the conventional injection and production conditions of the carbonate core (20,000 time steps);

[0047] Figure 9 Simulated results of water displacing gas at different times under the condition of increased gas viscosity in carbonate rock cores (step size: 20,000);

[0048] Figure 10 Simulated results of water displacing gas at different times under the condition of increased displacement pressure in carbonate rock cores (step size: 20,000);

[0049] Figure 11 Gas - water relative permeability curves in carbonate rock cores under different injection - production conditions. Specific implementation manners

[0050] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] Embodiment 1

[0052] In this embodiment, by conducting micro - CT scanning experiments, a three - dimensional digital core of carbonate rock is constructed to accurately characterize the true reservoir space morphology. Subsequently, by programming, the lattice Boltzmann method based on the Shan - Chen force model is used to simulate the unsteady gas - water two - phase seepage process in the three - dimensional digital core of carbonate rock, visually demonstrating the water invasion front at different times. Finally, the fluid pressure and velocity distributions in the carbonate rock at different times are obtained, that is, the simulation of unsteady gas - water two - phase seepage based on the lattice Boltzmann method is realized. The specific steps are as follows:

[0053] (1) Cut the carbonate rock sample into a cylinder with a diameter and length of 2.5 cm, conduct micro - CT scanning experiments with a resolution of 13 microns to obtain its two - dimensional CT images. Subsequently, perform median filtering and binarization processing on the two - dimensional CT images to establish a three - dimensional digital core containing pores, caves, and fractures, accurately characterizing the pore space properties of the rock sample, such as Figure 1 ;

[0054] (2) Set the viscosity ratio of the water phase to the gas phase as 5:1, set the force coefficient G in the Shan - Chen model as 0.1, and set the wall - surface interaction coefficient in the Shan - Chen model as G 1 = 0.08 and G 2 = - 0.08; Use the lattice Boltzmann method to simulate the unsteady two - phase flow of gas and water in the three - dimensional digital core of carbonate rock. The two - phase flow lattice Boltzmann equation (D 3 Q 19 model, such as Figure 2 ) is:

[0055] fi k (x + e i δt, t + δt) - f i k (x, t) = -Ω[f k i (x, t) - f i k,eq (x, t)] (1);

[0056] Initialize the velocity fields u 1 (x, 0), u 2 (x, 0), the density field ρ 1 (x, 0), ρ 2 (x, 0) and the distribution function; Subsequently, set the inlet and outlet ends of the digital core as fixed-pressure boundaries, and the upper and lower ends as bounce boundaries; Set the aqueous-phase pressure at the inlet end of the digital core to 20 MPa, and the aqueous-phase pressure at the outlet to 19.9 MPa. The two-phase fluid seepage starts to evolve according to Equation (1) under the pressure gradient ▽P. At each grid point x, collision and migration are performed, and bounce occurs at the wall surface, that is, the simulation of the unsteady flow process of gas-water two-phase in the three-dimensional digital core of carbonate rock is realized, and the water invasion front and water invasion dynamics can be intuitively displayed, such as Figures 3 - 5 , and the water invasion front morphology and water invasion dynamics at different times can be clearly displayed;

[0057] (3) Every several iterations, calculate the velocity field and density field in the rock. Among them, the fluid velocity u:

[0058]

[0059] The fluid density ρ:

[0060]

[0061] The fluid pressure p:

[0062] p k =ρ k R g T (9);

[0063] That is, the fluid pressure and aqueous-phase flow velocity at different positions in the carbonate rock at different times are obtained, and the water invasion dynamic characteristics of the carbonate rock are obtained. From Figure 6 It can be seen that the simulation results are in good agreement with the experimental results, and it can be considered that the corresponding parameter settings are reasonable, and a digital core model of two-phase flow is successfully established.

[0064] Example 2

[0065] Based on Embodiment 1, this embodiment provides: a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the gas-water two-phase unsteady seepage simulation method based on the lattice Boltzmann are implemented.

[0066] Embodiment 3

[0067] Based on Embodiment 1, this embodiment provides: an information data processing terminal for the gas-water two-phase unsteady seepage simulation method based on the lattice Boltzmann.

[0068] Embodiment 4

[0069] Based on Embodiment 1, the established gas-water two-phase unsteady seepage model in this embodiment can accurately simulate the phase permeability changes during the water displacing gas intrusion process and the gas displacing water production process. Among them, the simulation conditions are set as follows:

[0070] The gas-water viscosity ratio is 1:10, the displacement pressure is 0.916 MPa / m, and the gas-water interfacial tension is 70 mN / m;

[0071] The simulation results of the gas-water two-phase flow seepage curve are shown in Figure 7 , and the gas-phase permeability curve parameters of water displacing gas under different injection-production conditions are shown in Table 1.

[0072] Table 1

[0073] Parameter Water drive gas Gas drive water Irreducible gas saturation 42.97％ 42.97％ Residual water saturation 0％ 19.46％ <![CDATA[k rg @S wi > 1 0.9998 <![CDATA[k rw @S gr > 0.9652 1 <![CDATA[Corey equation n g > 3.15 3.45 <![CDATA[Corey equation n w > 3.10 2.58 Relative permeability at the isosmotic point 0.1127 0.1268 Isosmotic point saturation 71.48％ 64.13％ Mutual permeability zone 57.03％ 37.57％

[0074] It can be seen from the simulation results that:

[0075] ① During the water phase intrusion process, due to the initial absence of the water phase, the water phase needs to reach a certain volume to have a significant increase in permeability. Therefore, the Corey equation water phase index nw is slightly higher than that in the gas displacing water process, and the gas phase index ng in the gas production process of gas displacing water is higher;

[0076] ② During the gas production process of gas displacing water, due to the presence of the strongly wettable water phase, the equal permeability point shifts towards the water-wet direction (low gas saturation).

[0077] Embodiment 5

[0078] Based on Embodiment 1, the established gas-water two-phase unsteady seepage model in this embodiment is used for numerical simulation calculation of the hydrocarbon accumulation process. By changing the gas viscosity and displacement pressure, the influence of different displacement conditions on the phase permeability curve is clarified, specifically including simulating the water displacing gas process under conventional injection-production, increased gas viscosity, and increased displacement pressure conditions. The gas-phase permeability curve parameters of water displacing gas under different injection-production conditions are shown in Table 2. The results are as Figures 8 - 11 shown.

[0079] Table 2

[0080] Parameter Conventional injection - production conditions Gas viscosity increase Displacement pressure increase Irreducible water saturation 35.91％ 21.27％ 11.95％ Residual gas saturation 19.62％ 26.90％ 28.34％ <![CDATA[k rg @s wi > 0.9272 0.9154 0.9956 <![CDATA[Corey equation n g > 3.53 3.56 3.21 <![CDATA[Corey equation n w > 3.02 3.03 3.33 Relative permeability at the isosmotic point 0.1005 0.09828 0.1034 Isosmotic point saturation 57.20％ 51.66％ 58.66％ Mutual permeability zone 44.48％ 51.84％ 59.71％

[0081] It can be seen from the simulation results that:

[0082] ①Both increasing the displacement pressure and the gas viscosity can increase the co-permeation zone range and improve the displacement efficiency;

[0083] ②Increasing the displacement pressure can give the aqueous phase higher energy, and the gas phase is more likely to converge. Therefore, the gas-phase exponent of the Corey equation decreases and the aqueous-phase exponent increases, while the increase in gas viscosity has little effect on the relative permeability exponent.

[0084] Furthermore, the present invention helps to improve the understanding of the water invasion dynamics and water invasion laws of carbonate reservoirs, and can provide guidance for the efficient development of gas reservoirs.

[0085] The above are the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A gas-water two-phase unsteady-state seepage simulation method based on lattice Boltzmann, characterized in that: include: Through micro-CT scanning experiments, two-dimensional CT images were obtained; Process the two-dimensional CT images to construct a three-dimensional digital core of carbonate rocks containing pores, caves and fractures; Based on the lattice Boltzmann method, the non-steady-state seepage process of gas-water two-phase in the three-dimensional digital core of carbonate rock is simulated; According to the non-steady-state seepage process of gas-water two-phase in the three-dimensional digital core of carbonate rock, the fluid pressure and velocity distribution at different positions in the carbonate rock at different times are obtained, and the dynamic characteristics of water invasion of carbonate rock are obtained.

2. The gas-water two-phase unsteady-state seepage simulation method based on lattice Boltzmann according to claim 1 is characterized in that: The processing of the two-dimensional CT image includes: performing median filtering and binarization processing on the two-dimensional CT image.

3. The gas-water two-phase unsteady-state seepage simulation method based on lattice Boltzmann according to claim 1, characterized in that: The simulating of the gas-water two-phase unsteady-state seepage process in the three-dimensional digital core of carbonate rock according to the lattice Boltzmann method specifically includes: Set the property parameters of the gas-water two-phase fluid, and the equation in the lattice Boltzmann method is as follows: f i k (x+e i δt,t+δt)-f i k (x,t)=-Ω[f k i (x,t)-f i k,eq (x,t)](1); In formula (1), f i is the particle distribution function, kg / m 3 ; i = 0, 1, ..., 18, representing 19 grid velocity directions; e i is the lattice velocity, m / s; t is the time, s; Ω is the collision matrix, Ω=M -1 SM, M is the particle distribution function f i The transformation matrix; k = 1 represents the water phase, k = 2 represents the gas phase; f i eq is the equilibrium particle distribution function, as follows: In formula (2), ρ is the fluid density, kg / m 3 ;w i is the weight coefficient; u is the fluid velocity, m / s; c s is the speed of sound, m / s; Initialize the velocity field u1(x, 0), u2(x, 0), density field ρ1(x, 0), ρ2(x, 0) and distribution function of the gas-water two-phase fluid: Then, the boundary conditions are set, and the evolution starts with the pressure gradient ▽P according to equation (1), and a collision is performed at each grid point x: Execute the migration: Or perform a rebound: In formula (4), τ1 is the dimensionless relaxation time of the water phase, and τ2 is the dimensionless relaxation time of the gas phase.

4. The gas-water two-phase unsteady-state seepage simulation method based on lattice Boltzmann according to claim 3 is characterized in that: According to the non-steady-state seepage process of gas-water two-phase in the three-dimensional digital core of carbonate rock, the fluid pressure and flow velocity distribution at different positions in the carbonate rock at different times are obtained, and the dynamic characteristics of water invasion of carbonate rock are obtained, which specifically include: After every several iterations, the velocity field and density field in the rock are calculated, where the fluid velocity u is: Fluid density ρ: Fluid pressure p: p k =ρ k R g T(9); In formula (9), R g is the gas constant; T is the kinetic temperature of the gas.

5. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the gas-water two-phase non-steady-state seepage simulation method based on lattice Boltzmann as described in any one of claims 1 to 4 are implemented.

6. An information data processing terminal according to the lattice Boltzmann-based gas-water two-phase unsteady-state seepage simulation method according to any one of claims 1 to 4.

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