A method for simulating depletion development of carbonate gas reservoir based on lattice-Boltzmann and application thereof

Abstract

The application discloses a method for simulating depletion development of a carbonate rock gas reservoir based on a lattice-Boltzmann method and application, and relates to the technical field of carbonate rock gas reservoir development, and comprises the following steps: S1, testing basic physical properties of a full-diameter carbonate rock sample, and determining resolution of a micro-CT scanning carbonate rock core; S2, constructing a three-dimensional digital rock core of the carbonate rock; S3, simulating gas depletion flow in the three-dimensional digital rock core of the full-diameter carbonate rock by using the lattice-Boltzmann method; and S4, analyzing changes of gas pressure and gas flow rate at different positions in the carbonate rock reservoir rock under different production systems, obtaining mining dynamic characteristics of different types of carbonate rock gas reservoirs, and solving the problems that in the prior art, it is difficult to accurately record overall changes of the gas pressure in the strong heterogeneous carbonate rock, it is impossible to truly reflect mining dynamic characteristics and reserve producing degree, and it is also impossible to intuitively display the internal relation between the rock pore structure and the reserve producing degree.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of carbonate gas reservoir development, and particularly relates to a method for simulating depletion development of a carbonate gas reservoir based on a lattice-Boltzmann method and application. BACKGROUND

[0002] Depletion production is an important way of gas reservoir development, and the pore structure of rock will significantly affect the reserve producing degree of a gas reservoir. In the past, a physical simulation experiment of core depletion production recorded the pressure change of a small number of positions on the surface of rock in a depletion process by using a pressure sensor, so as to analyze the influence of the pore structure of rock on the production dynamic characteristics and the reserve producing degree of a gas reservoir. This method has achieved good application effect on relatively homogeneous gas reservoirs such as sandstone, and is also an important means to understand the production capacity of a gas reservoir. However, for carbonate gas reservoirs in which pores, fractures and caves coexist in the reservoir rock, the reservoir space is complex, the heterogeneity is strong, and the production dynamic characteristics are more complex. The physical simulation experiment of core depletion production is difficult to accurately record the overall change of the gas pressure in the strong heterogeneous carbonate rock, and cannot truly reflect the production dynamic characteristics and the reserve producing degree of the carbonate rock, nor can it directly show the internal relationship between the pore structure of rock and the reserve producing degree. Meanwhile, the high-temperature and high-pressure full-diameter core depletion experiment has high cost and poor repeatability. SUMMARY

[0003] The present application aims to provide a method for simulating depletion development of a carbonate gas reservoir based on a lattice-Boltzmann method, which can accurately record the overall change of the gas pressure in the strong heterogeneous carbonate rock, truly reflect the production dynamic characteristics and the reserve producing degree of the carbonate rock, and directly show the internal relationship between the pore structure of rock and the reserve producing degree. Compared with the high-temperature and high-pressure full-diameter core depletion experiment, the method has lower cost and good repeatability.

[0004] The present application is realized by the following technical scheme:

[0005] A method for simulating depletion development of a carbonate gas reservoir based on a lattice-Boltzmann method, comprising the following steps:

[0006] S1, testing the basic physical properties of a full-diameter carbonate rock sample, and determining the resolution of the micro-CT scanning of the carbonate rock core;

[0007] S2, constructing a three-dimensional digital core of the carbonate rock based on the two-dimensional micro-CT scanning image obtained under the preferred resolution in step S1;

[0008] S3, simulating the gas depletion flow in the three-dimensional digital core of the full-diameter carbonate rock by using a lattice-Boltzmann method;

[0009] S4. Based on the results of lattice-Boltzmann simulation, the changes in gas pressure and gas velocity at different locations in carbonate reservoirs under different production regimes are analyzed to obtain the dynamic characteristics of the exploitation of different types of carbonate gas reservoirs.

[0010] Furthermore, in step S1, the basic physical properties include porosity ε and permeability k.

[0011] Furthermore, the basic physical properties were obtained through conventional core analysis experiments.

[0012] Furthermore, in step S1, the method for determining the resolution of the carbonate rock core for micro-CT scanning is as follows:

[0013] By scanning core samples at different resolutions, three-dimensional digital cores with different properties are reconstructed, and their three-dimensional pore networks are extracted using intelligent threshold segmentation technology. Then, by comparing the rock pore throat distribution characteristics of the core samples, the optimal scanning resolution for the digital core is selected.

[0014] Furthermore, the rock pore throat distribution characteristics of the core sample were obtained through mercury intrusion porosimetry simulation experiments.

[0015] Furthermore, in step S2, the method for constructing the three-dimensional digital core of the carbonate rock is as follows:

[0016] S2.1 Perform median filtering and binarization on the obtained two-dimensional micro-CT scan image with better resolution;

[0017] S2.2 Establish a three-dimensional digital core of the rock sample to accurately characterize the spatial properties of the rock sample pores.

[0018] Furthermore, in step S3, the simulated gas depletion flow in the three-dimensional digital core of a full-diameter carbonate rock is as follows:

[0019] S3.1. Using the lattice-Boltzmann method, the evolution equation of the particle distribution function in the D3Q19 model is as follows:

[0020] f i (x+e i δt,t+δt)-f i (x,t)=-Ω[f i (x,t)-f i eq (x,t)] (1)

[0021] In equation (1), f i Let be the particle distribution function, kg / m 3 ;e i Ω is the lattice velocity, m / s; t is time, s; Ω is the collision matrix, Ω = M -1 SM, where M is the particle distribution function fi The transformation matrix; x is the position of the particle, m; δt is the time step, s;

[0022] f i eq The equilibrium particle distribution function is:

[0023]

[0024] In equation (2), ρ is the fluid density, kg / m³ 3 ;w i The weighting coefficient is denoted by ; u is the fluid velocity, m / s; c is the fluid velocity. s The speed of sound is in m / s;

[0025] S3.2. Apply a certain pressure gradient ▽P to the porous medium and start to evolve according to Equation (1) to realize the simulation of gas exhaustion flow in the three-dimensional digital core of carbonate rock.

[0026] Furthermore, in step S4, the method for analyzing the changes in gas pressure and gas velocity at different locations in a full-diameter carbonate reservoir under different production regimes is as follows:

[0027] S4.1 Based on the results of lattice-Boltzmann simulation, the changes in gas pressure and gas velocity at different locations in carbonate reservoirs under different production regimes are analyzed. The gas velocity u at different locations in the porous medium satisfies the following equation (3):

[0028]

[0029] Gas density ρ at different locations in a porous medium:

[0030]

[0031] Further, the gas pressure p at different locations in the porous medium was obtained:

[0032] p = ρR g T (5)

[0033] In equation (5), Rg is the gas constant; T is the gas kinetic temperature.

[0034] S4.2 Based on S4.1, obtain the dynamic characteristics of carbonate gas reservoir exploitation and establish the intrinsic relationship between the degree of reserve utilization and pore structure.

[0035] Furthermore, the intrinsic relationship between the degree of reserve utilization and pore structure refers to the calculation of gas flow rate in carbonate reservoirs under different production regimes using the Darcy flow model, based on the simulation of changes in gas pressure and gas flow rate at different locations in the rocks under different production regimes. Then, the degree of reserve utilization in the porous medium is calculated, and the intrinsic relationship between the degree of reserve utilization and the pore structure parameters of the porous medium obtained based on CT scan reconstruction is established.

[0036] An application of the aforementioned method for lattice-Boltzmann simulation of carbonate gas reservoir depletion development in fluid flow simulation of carbonate gas reservoirs with coexisting pores, fractures, and caverns.

[0037] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0038] I. Compared with existing physical simulation methods for core-based depletion mining, this invention provides a method for carbonate gas reservoir depletion development based on lattice-Boltzmann simulation. Through lattice-Boltzmann simulation, it determines the pressure and velocity variations at different locations within full-diameter carbonate reservoirs under different regimes. For the first time, it achieves accurate simulation of the gas depletion mining process and reserve utilization in full-diameter carbonate rocks with complex pore morphology. This method is convenient to use, highly accurate, and beneficial for improving the understanding of the dynamic characteristics of carbonate gas reservoir development and the degree of reserve utilization, providing important guidance for better development of complex gas reservoirs. Attached Figure Description

[0039] Figure 1 This is a CT scan image (13 μm) of carbonate rock in the XY direction.

[0040] Figure 2 This is a CT scan image (13 μm) of carbonate rock in the XZ direction.

[0041] Figure 3 This is a CT scan image (13 μm) of carbonate rock along the YZ direction.

[0042] Figure 4 This is a map showing the gas velocity distribution in carbonate rocks over 10,000 time steps under different pressure gradients.

[0043] Figure 5 This is a map showing the gas velocity distribution in carbonate rocks over 50,000 time steps under different pressure gradients.

[0044] Figure 6 This is a map showing the gas velocity distribution in carbonate rocks over 90,000 time steps under different pressure gradients.

[0045] Figure 7It is a pressure distribution map of different locations in carbonate rocks at 1000 time steps at different times.

[0046] Figure 8 It is a pressure distribution map of different locations in carbonate rocks at 10,000 time steps at different times.

[0047] Figure 9 It is a pressure distribution map of different locations in carbonate rocks at 20,000 time steps at different times.

[0048] Figure 10 This is a graph showing the variation of gas velocity at different locations in carbonate rocks under different pressure gradients.

[0049] Figure 11 It is a graph showing the pressure changes at different locations in a carbonate rock at different times. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to embodiments, but the implementation of the present invention is not limited thereto.

[0051] Example 1

[0052] This embodiment proposes a method for simulating the depletion and development of carbonate gas reservoirs based on lattice-Boltzmann simulation, belonging to the field of carbonate gas reservoir development technology. By testing the basic physical properties of full-diameter carbonate rock samples, the optimal resolution suitable for micro-CT scanning of the carbonate rock core is selected, and a three-dimensional digital core of the carbonate rock is constructed. Using the lattice-Boltzmann method, the gas depletion flow in the three-dimensional digital core of the carbonate rock is simulated, and the changes in gas pressure and gas velocity at different locations in the full-diameter carbonate reservoir under different production regimes are analyzed. For the first time, an accurate simulation of the actual carbonate rock depletion exploitation process and reserve utilization is achieved. The specific steps are as follows:

[0053] Step 1: Test the basic physical properties of the full-diameter carbonate rock sample and obtain the rock pore throat distribution characteristics of the carbonate rock sample.

[0054] S1.1 Before conducting full-diameter micro-CT scanning of carbonate rocks, the basic physical properties of the core samples used were tested through conventional core analysis experiments, including porosity ε and permeability k.

[0055] S1.2. Apply different resolutions to scan core samples, reconstruct three-dimensional digital cores with different properties, and apply intelligent threshold segmentation technology to extract their three-dimensional pore network.

[0056] S1.3. By comparing the rock pore throat distribution characteristics obtained from mercury intrusion porosimetry simulation experiments, the optimal scanning resolution of digital cores is selected.

[0057] In this embodiment, the porosity ε of the full-diameter carbonate rock sample was measured to be 6.55%, and the permeability k was 9.083 mD. When scanning the rock sample using micro-CT scanning, the optimal scanning resolution for digital core scanning was selected by comparing the rock pore throat distribution characteristics obtained from mercury intrusion porosimetry simulation experiments. This allowed for the reconstruction of three-dimensional digital cores with different properties, and the three-dimensional pore network was extracted using intelligent threshold segmentation technology. In this embodiment, the optimal resolution for micro-CT scanning of the carbonate rock core was determined to be 13 μm.

[0058] Figures 1-3 The images are CT scans of carbonate rocks in the XY, XZ, and YZ directions, obtained using a 13μm resolution scan.

[0059] Step 2: Based on the obtained two-dimensional micro-CT scan images with the best resolution, construct a three-dimensional digital core of carbonate rocks.

[0060] S2.1 Perform median filtering and binarization on the obtained optimal resolution two-dimensional micro-CT scan image;

[0061] S2.2 Establish a three-dimensional digital core of the rock sample to accurately characterize the spatial properties of the rock sample pores.

[0062] Step 3: Using the lattice-Boltzmann method, simulate the gas exhaustion flow in a three-dimensional digital core of a full-diameter carbonate rock.

[0063] The specific method is as follows:

[0064] S3.1. Using the lattice-Boltzmann method, the evolution equation of the particle distribution function in the D3Q19 model is as follows:

[0065] f i (x+e i δt,t+δt)-f i (x,t)=-Ω[f i (x,t)-f i eq (x,t)] (1)

[0066] In equation (1), f i Let be the particle distribution function, kg / m 3 ;e i Ω is the lattice velocity, m / s; t is time, s; Ω is the collision matrix, Ω = M -1 SM, where M is the particle distribution function f i The transformation matrix; f i eq The equilibrium particle distribution function is:

[0067]

[0068] In equation (2), ρ is the fluid density, kg / m³ 3 ;w i The weighting coefficient is denoted by ; u is the fluid velocity, m / s; c is the fluid velocity. s The speed of sound is in m / s;

[0069] S3.2. Apply a certain pressure gradient ▽P to the porous medium and start to evolve according to Equation (1) to realize the simulation of gas exhaustion flow in the three-dimensional digital core of carbonate rock.

[0070] Specifically, a certain pressure gradient ▽P is applied to the three-dimensional digital core to cause equation (1) to begin to evolve, and the gas exhaustion flow process in the three-dimensional digital core of carbonate rocks under different conditions is simulated using the lattice-Boltzmann method.

[0071] Step 4: Based on the results of lattice-Boltzmann simulation, analyze the changes in gas pressure and gas velocity at different locations in full-diameter carbonate reservoirs under different production regimes, and obtain the dynamic characteristics of the exploitation of different types of carbonate gas reservoirs.

[0072] Specifically, the steps include the following:

[0073] S4.1 Based on the results of lattice-Boltzmann simulation, the changes in gas pressure and gas velocity at different locations in carbonate reservoirs under different production regimes are analyzed. The gas velocity u at different locations in the porous medium satisfies the following equation (3):

[0074]

[0075] Gas density ρ at different locations in a porous medium:

[0076]

[0077] Further, the gas pressure p at different locations in the porous medium was obtained:

[0078] p = ρR g T (5),

[0079] In equation (5), Rg is the gas constant; T is the gas kinetic temperature.

[0080] S4.2 Subsequently, the gas flow rate of the rock under different production regimes was calculated using the Darcy flow equation, thereby obtaining the degree of reserve utilization in carbonate gas reservoirs under different production regimes. The intrinsic relationship between the degree of reserve utilization and pore structure refers to the calculation of the gas flow rate of the rock under different production regimes using the Darcy flow model, based on the simulation of gas pressure and gas velocity changes at different locations in the carbonate reservoir rock under different production regimes, and then the calculation of the degree of reserve utilization in the porous medium. Finally, the intrinsic relationship between the degree of reserve utilization and the pore structure parameters characterizing the porous medium obtained based on CT scan reconstruction was established.

[0081] refer to Figures 4-11 , Figures 4-6 The distribution of gas velocity in carbonate rocks under different pressure gradients. Figures 7-9 This represents the pressure distribution at different locations within carbonate rocks at different times. Figure 10 The curves show the gas velocity variations at different locations in carbonate rocks under different pressure gradients. Figure 11 The curves show the pressure changes at different locations in the carbonate rock at different times.

[0082] By combining the calculated reserve utilization levels of carbonate gas reservoirs under different production regimes with the connectivity, size, and other pore structure parameters of porous media obtained from CT scan reconstruction, the intrinsic relationship between the reserve utilization level and pore structure can be further established. This method is highly accurate and has great practical value.

[0083] This invention proposes a method for simulating the depletion and development of carbonate gas reservoirs based on lattice-Boltzmann simulation. Combining micro-CT scanning experiments and the lattice-Boltzmann method, it simulates the gas depletion and flow process in a three-dimensional digital core of a full-diameter carbonate rock, achieving an accurate simulation of the actual depletion and exploitation process and reserve utilization in carbonate rocks. This method is easy to use, and after multiple experimental verifications, it has been determined to have good repeatability, high accuracy, and good practicality.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for developing depleted carbonate gas reservoirs based on lattice-Boltzmann simulation, characterized in that, Includes the following steps: S1. Test the basic physical properties of full-diameter carbonate rock samples and determine the resolution for micro-CT scanning of carbonate rock cores; S2. Based on the two-dimensional micro-CT scan image obtained at the best resolution in step S1, construct a three-dimensional digital core of carbonate rock. S3. Using the lattice-Boltzmann method, simulate the gas exhaustion flow in a three-dimensional digital core of a full-diameter carbonate rock. S4. Based on the results of lattice-Boltzmann simulation, the changes in gas pressure and gas velocity at different locations in carbonate reservoirs under different production regimes are analyzed to obtain the dynamic characteristics of the exploitation of different types of carbonate gas reservoirs. In step S4, the method for analyzing the changes in gas pressure and gas velocity at different locations in full-diameter carbonate reservoirs under different production regimes is as follows: S4.1 Based on lattice-Boltzmann simulation results, analyze the changes in gas pressure and gas velocity at different locations in carbonate reservoirs under different production regimes, including the gas velocity at different locations in porous media. u Satisfy the following equation (3): （3） Gas density at different locations in a porous medium ρ : （4） Further, the gas pressure at different locations in the porous medium was obtained. p : （5） In equation (5), R g It is the gas constant; T It is the kinetic temperature of the gas; f i Let be the particle distribution function, kg / m 3 ; e i The lattice velocity is in m / s; S4.2 Based on S4.1, obtain the dynamic characteristics of carbonate gas reservoir development and establish the intrinsic relationship between the degree of reserve utilization and pore structure. The intrinsic relationship between the degree of reserve utilization and pore structure refers to the calculation of gas flow rate in carbonate reservoirs under different production regimes using the Darcy flow model, based on the simulation of changes in gas pressure and gas flow rate at different locations in the rocks under different production regimes. Then, the degree of reserve utilization in the porous medium is calculated, and the intrinsic relationship between the degree of reserve utilization and the pore structure parameters of the porous medium obtained based on CT scan reconstruction is established.

2. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 1, characterized in that, In step S1, the basic physical properties include porosity ε and permeability k.

3. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 2, characterized in that, The basic physical properties were obtained through conventional core analysis experiments.

4. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 1, characterized in that, In step S1, the method for determining the resolution of the carbonate rock core for micro-CT scanning is as follows: By scanning core samples at different resolutions, three-dimensional digital cores with different properties are reconstructed, and their three-dimensional pore networks are extracted using intelligent threshold segmentation technology. Then, by comparing the rock pore throat distribution characteristics of the core samples, the optimal scanning resolution for the digital core is selected.

5. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 4, characterized in that, The rock pore throat distribution characteristics of the core samples were obtained through mercury intrusion porosimetry simulation experiments.

6. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 1, characterized in that, In step S2, the method for constructing a three-dimensional digital core of carbonate rock is as follows: S2.1 Perform median filtering and binarization on the obtained two-dimensional micro-CT scan image with better resolution; S2.2 Establish a three-dimensional digital core of the rock sample to accurately characterize the spatial properties of the rock sample pores.

7. The method for developing carbonate gas reservoir depletion based on lattice-Boltzmann simulation according to claim 1, characterized in that, In step S3, the simulated gas depletion flow in the three-dimensional digital core of a full-diameter carbonate rock is as follows: S3.

1. Using the lattice-Boltzmann method, the evolution equation of the particle distribution function in the D3Q19 model is as follows: （1） In equation (1), f i Let be the particle distribution function, kg / m 3 ; e i t is the lattice velocity, m / s; t is time, s; Ω is the collision matrix, Ω= M -1 SM , M Particle distribution function f i The transformation matrix; x Let m be the position of the particle; δt Let be the time step, in seconds; f i eq The equilibrium particle distribution function is: （2）， In equation (2), ρ Fluid density, kg / m³ 3 ; w i The weighting coefficient is denoted by ; u is the fluid velocity, in m / s; c s The speed of sound is in m / s; S3.2 Apply a certain pressure gradient to the porous medium. P The evolution begins according to equation (1), thus simulating the gas depletion flow in the three-dimensional digital core of carbonate rocks.

8. The application of the method for developing depletion of carbonate gas reservoirs based on lattice-Boltzmann simulation as described in claim 1 in the simulation method of fluid flow in carbonate gas reservoirs with coexisting pores, fractures and caverns.

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