A method for simulating particle migration in loose sandstone based on discrete element method

Abstract

The present invention discloses a loose sandstone particle migration simulation method based on discrete elements, and belongs to the field of oil and gas engineering technology. The present invention mainly solves the migration and blockage of particles in pore throats and the evaluation of permeability improvement or damage during the production process of loose sandstone reservoirs. The present invention establishes a loose sandstone particle migration simulation method based on discrete elements, which can intuitively and accurately characterize the particle migration process during the production process from a microscopic scale, accurately capture the pore structure differences before and after particle migration, thereby enhancing the field engineers' understanding of the particle migration law in loose sandstone reservoirs, and then improve production measures.

Description

Technical Field

[0001] The invention relates to a loose sandstone particle migration simulation method based on discrete elements, belonging to the technical field of oil and gas engineering. Background Art

[0002] The phenomenon of particle migration in loose sandstone reservoirs is common in the process of oil and gas development and is considered to be an important reason for reservoir permeability damage and reduced oil and gas production capacity. Reservoir particles refer to some tiny mineral components cemented on skeleton particles or loosely adsorbed between pores. Under the combined action of physical-chemical, chemical, hydrodynamic and mechanical effects, they loosen, release, migrate and precipitate, eventually blocking the pore throat and causing reservoir damage. However, to date, the evaluation of loose sandstone particle migration still mainly relies on experimental methods to study particle migration damage, such as micro-models, sand filling models and core displacement flow experiments. It is impossible to quantitatively and visually characterize the particle migration process from a microscopic perspective, reveal the damage mechanism of particle migration to the reservoir, and it is difficult to accurately understand the coupling problem between particles, fluids and pore structures in the production process. Summary of the invention

[0003] The purpose of the present invention is to provide a loose sandstone particle migration simulation method based on discrete elements, which can truly simulate the particle migration process in the production process of loose sandstone reservoirs, quantitatively and visually reveal the degree and mechanism of damage to the reservoir caused by particle migration from a microscopic perspective, and provide technical support for optimizing production measures to prevent and control particle migration damage.

[0004] The present invention provides a loose sandstone particle migration simulation method based on discrete elements, which comprises the following steps:

[0005] S1. Set the calculation area and determine the porosity φ of loose sandstone, the particle size distribution curve PDF of skeleton particles, and the particle size d of clay particles. fine , generate particles through initial equilibrium calculation and construct a physical model of pore structure;

[0006] S2. According to the mineral types of skeleton particles and clay particles, different rock mechanical parameters (Young's modulus E, Poisson's ratio υ, clay particle friction coefficient μ) are assigned to clay particles and skeleton particles in discrete elements. p-p ), cementation parameters (cohesive energy density k), giving different cohesion to clay particles-skeleton particles, skeleton particles-skeleton particles, clay particles-clay particles for cementation, and generating discrete element numerical models;

[0007] S3. Divide the study area into grids, add the seepage field according to the production parameters and assign the corresponding flow parameters, and use the CFD-DEM coupling method to simulate the particle migration process in the pore throat of loose sandstone;

[0008] S4. During the simulation, the movement, blockage and distribution of clay particles in the pore throats are monitored in real time. When the fluid drag force exceeds the cohesion between clay particles and skeleton particles, the particles fall off and, along with the migration of the fluid, block or penetrate the physical model, and then analyze the changes in the pore structure. When there is no obvious shedding or migration of clay particles in the entire model, the simulation ends, and the simulation results are exported and saved.

[0009] Preferably, in step S1, the calculation area size should be representative of the heterogeneity of the loose sandstone;

[0010] Further preferably, the size of the generated particles should sufficiently match the simulated loose sandstone particle size distribution curve to ensure simulation accuracy;

[0011] Further preferably, the porosity of the reservoir physical model should match the porosity of the unconsolidated sandstone;

[0012] Further preferably, the particle size of the clay microparticles should be at least one order of magnitude smaller than the particle size of the skeleton particles;

[0013] Further preferably, when generating the reservoir physical model according to the particle rejection method, the ratio of the average unbalanced force between particles to the average contact force should be less than 10 -6 ;

[0014] According to the present invention, preferably, in step S2, different cohesive energy densities k are given to clay particles-skeleton particles, skeleton particles-skeleton particles, and clay particles-clay particles in discrete elements according to the mineral types of skeleton particles and clay particles;

[0015] Preferably, the inter-particle cohesion calculation model adopts a simplified JKR model:

[0016] F sjkr = kA

[0017] Where k is the cohesive energy density and A is the particle contact area.

[0018] Further preferably, the particles are bonded according to a parallel bonding model based on cohesion.

[0019] Further preferably, the cohesive energy density between clay particles-clay particles, skeleton particles-skeleton particles, and clay particles-skeleton particles should have obvious differences and be representative, and the cohesive energy density between clay particles-skeleton particles should be much smaller than the cohesive energy density between skeleton particles-skeleton particles;

[0020] Further preferably, the rock mechanical parameters of loose sandstone are measured in the laboratory, including Young's modulus E, Poisson's ratio υ, and clay particle friction coefficient μ p-p , and calibrate the discrete element parameters used in the simulation based on it; further preferably, the elastic modulus of the clay microparticles should be smaller than that of the skeleton particles;

[0021] According to the present invention, preferably, in step S3, a structured grid is used to mesh the study area, the grid quality is not less than 90%, and the grid accuracy is adjusted according to the grid quality, and the diameter of a single grid should be less than 3 particle diameters;

[0022] Further preferably, the external forces on the clay particles during their migration include their own gravity, drag force, buoyancy, contact force, etc., and the motion control equation is:

[0023]

[0024] In the formula, F p,n and F p,t are the normal contact force and the tangential contact force, F p,g is gravity, F p,e The forces exerted on the particle by the fluid around the particle, such as drag force, pressure gradient force and buoyancy force, r p,c and T p,r are the particle vector radius and the particle's additional torque, u p and ω p are the translational speed and rotational speed, m p and I p The particle mass and moment of inertia are respectively.

[0025] Further preferably, the contact force between particles (clay particles, skeleton particles) can be expressed as shear force, spring force, tangential and normal damping force:

[0026] F=(k n δn ij -γ n v ij )+(k t δt ij -γ t vt ij )

[0027] Where the first term is the normal contact force and the second term is the tangential contact force. n and k t are the normal elastic coefficient and the tangential elastic coefficient, γ n and γ t are the normal and tangential drag coefficients, vn ij and γ t vt ij are the normal and tangential components of the relative velocity, δn ij and δt ij are the normal overlap and tangential displacement vector between contacting particles, respectively.

[0028] Further preferably, the voids around the contact particles in the generated pore structure physical model are set as flow domains, and the fluid is injected from the porous medium under a certain production pressure gradient ΔP. The fluid changes the force of the particles around the fluid during the injection process. When the shear stress between the clay particles and the skeleton particles exceeds the shear strength limit, that is, when the following formula is satisfied, relative slip occurs between the clay particles and the skeleton particles and they fall off:

[0029]

[0030] Where τ is the shear stress at the particle bonding point, is the internal friction angle between particles.

[0031] Further preferably, when the bonding state between particles is destroyed, the parallel bonding model between particles degenerates into a Hertzian model;

[0032] Further preferably, the coupling between particles (clay particles, skeleton particles) and fluid is solved by an analytical CFD-DEM method, using a virtual domain to represent the particles, and the virtual domain has the same velocity as the particles themselves, such as Figure 5 As shown, where Ω F and Ω s are the fluid domain and particle virtual domain, Γ and Γ s The fluid domain is governed by the incompressible Navier-Stokes equations:

[0033]

[0034] Continuity equation:

[0035]

[0036] The velocity at the fluid domain boundary is expressed as:

[0037] u f =u Γ on Γ

[0038] The velocity at the fluid-particle interface has the following relationship:

[0039]

[0040] Where σ is the fluid stress tensor, is the traction vector, u P is the particle velocity, u f is the fluid velocity. The initial boundary condition is expressed as:

[0041] u f (x,t=0)=u0(x)inΩ F

[0042] Further preferably, the boundary conditions of the fluid setting include the fluid density ρ f 、Fluid viscosity μ f , production pressure gradient ΔP, flow type and flow pattern;

[0043] Further preferably, the fluid flow pattern is determined according to the Reynolds number Re;

[0044] Further preferably, before the simulation starts, the permeability of the loose sandstone before the particle migration is calculated according to Darcy's law:

[0045]

[0046] Where Q is the flow rate under the pressure difference ΔP, and A is the cross-sectional area of ​​the boundary wall cylinder.

[0047] Preferably, the results should be pre-verified before the simulation begins, and the theoretical calculation results of the Ergun equation should be selected for matching to verify its reliability;

[0048] According to the present invention, preferably, in step S4, when there is no obvious shedding or migration of clay particles in the entire model, the simulation ends, and the simulation results are exported and saved.

[0049] Further preferably, after the simulation is completed, the changes in the pore structure of the loose sandstone, the movement, blockage and distribution of clay particles are analyzed;

[0050] Further preferably, after the simulation is completed, the permeability of the loose sandstone after particle migration is calculated according to Darcy's law;

[0051] The present invention has the following beneficial technical effects:

[0052] 1. The loose sandstone particle migration simulation method based on discrete elements provided by the present invention can quantitatively and visually characterize the particle migration process from a microscopic scale, explain the damage mechanism of particle migration to the reservoir, and accurately capture the particle shedding, migration, blockage and redistribution.

[0053] 2. The discrete element-based loose sandstone particle migration simulation method provided by the present invention takes into account the pore structure, component structure, rock mechanical properties, and production process of the loose sandstone reservoir, and directly integrates and solves the clay particle-skeleton particle-fluid interaction during the particle migration process, so that the obtained simulation results are more consistent with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Flow chart of the simulation method of the present invention.

[0055] Figure 2 This is the process of generating the physical model of the pore structure of loose sandstone in the embodiment of the present invention.

[0056] Figure 3 Schematic diagram of the particle contact model in the simulation method of the present invention.

[0057] Figure 4 Schematic diagram of the particle cohesion model in the simulation method of the present invention.

[0058] Figure 5 It is a fluid meshing scheme in the fluid-particle coupling solution process in the simulation method of the present invention.

[0059] Figure 6 The numerical simulation results of the simulation method of the present invention are compared with the theoretical calculation results of the Ergun equation.

[0060] Figure 7 It shows the pore structure and clay particle distribution after the simulation by the simulation method of the present invention is completed. DETAILED DESCRIPTION

[0061] Unless otherwise specified, the experimental methods used in the following examples are conventional methods.

[0062] Unless otherwise specified, the materials and reagents used in the following examples can be obtained from commercial sources.

[0063] According to the method of the present invention, the migration of particles in the loose sandstone reservoir of Bozhong 28-2 South Oilfield is simulated and analyzed. The process is as follows Figure 1 As shown:

[0064] S1. According to the loose sandstone reservoir parameters of Bozhong 28-2 South Oilfield, a pore structure physical model is constructed by initial equilibrium calculation in discrete element (such as Figure 2 shown);

[0065] S2, according to the mineral types of skeleton particles and clay particles, different rock mechanical parameters and cementation parameters are assigned to clay particles and skeleton particles in the discrete element (Table 1; Figure 3 ), giving different cohesion to clay particles-skeleton particles, skeleton particles-skeleton particles, clay particles-clay particles for cementation ( Figure 4 ), generate discrete element numerical model;

[0066] Table 1 Rock mechanics parameters set according to the characteristics of the loose sandstone reservoir in Bozhong 28-2 South Oilfield

[0067]

[0068] S3. Divide the study area into grids ( Figure 5), according to the production parameters of Bozhong 28-2 South Oilfield, the seepage field was added and the corresponding flow parameters were assigned (Table 2), and the computational fluid dynamics (CFD)-discrete element (DEM) coupling method was used to simulate the particle migration process in the pore throat of loose sandstone;

[0069] Table 2 Fluid domain parameters set according to the production characteristics of the loose sandstone reservoir in Bozhong 28-2 South Oilfield

[0070]

[0071] S4. During the simulation, the movement, blockage and distribution of clay particles in the pore throats are monitored in real time. When the fluid drag exceeds the cohesion between clay particles and skeleton particles, the particles fall off and, along with the migration of fluid, block or penetrate the physical model, and then analyze the changes in the pore structure. When there is no obvious shedding or migration of clay particles in the entire model, the simulation ends, and the simulation results are exported and saved.

[0072] The difference in apparent velocity obtained by numerical simulation and Ergun equation is compared to verify the accuracy of the model, such as Figure 6 As shown, it can be found that the error is less than 3%, which shows that the simulation method of the present invention has high accuracy.

[0073] During the fluid production process, a large shear force is generated on the clay particles, which causes them to fall off and migrate. The particle distribution after the simulation is as follows: Figure 7 In this state, along the flow direction of the fluid, a large number of clay particles fall off at the injection end, resulting in an increase in the particle concentration in the fluid, and then a large number of blockages at the outflow end.

[0074] The technical contents not elaborated in detail in the present invention belong to the common knowledge of those skilled in the art.

[0075] Although the preferred embodiments of the present invention have been illustrated and described, it should be clear to those skilled in the art that the present invention is not limited to the scope of the preferred embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

Claims

1. A method for simulating the migration of loose sandstone particles based on discrete elements, comprising the following steps: S1. Determine the simulation area, determine the porosity φ of loose sandstone, the particle size distribution curve PDF of skeleton particles and the particle size d of clay particles fine Based on this, a physical model of the pore structure composed of clay particles and skeleton particles is constructed in the discrete element through initial equilibrium calculation; The process of step S1 is as follows: S 11 , generating a boundary wall in the simulation area, wherein the boundary wall is a cylinder with a bottom diameter D and a height H; S 12 , determine the loose sandstone porosity φ, the skeleton particle size gradation curve PDF and the clay particle size d fine ; S 13 According to the loose sandstone porosity φ, the skeleton particle size gradation curve PDF and the clay particle size d fine , in the simulation area, the pore structure physical model consisting of the clay particles and the skeleton particles is generated according to the particle exclusion method, when the ratio of the average unbalanced force to the average contact force is less than 10 -6 When , the initial equilibrium calculation ends; S2. According to the mineral types of skeleton particles and clay particles, rock mechanical parameters and cementation parameters are assigned to clay particles and skeleton particles in discrete elements, and different cohesion forces are assigned to clay particles-skeleton particles, skeleton particles-skeleton particles, and clay particles-clay particles for cementation to generate a discrete element numerical model; S3. Divide the study area into grids, add the seepage field according to the production parameters and assign the corresponding flow parameters, and use the computational fluid dynamics-discrete element coupling method to simulate the particle migration process in the pore throat of loose sandstone; S4. During the simulation of the particle migration process, the movement, blockage and distribution state of the clay particles in the pore throat are monitored in real time. When the fluid drag force exceeds the cohesion of the clay particles-skeleton particles, the clay particles fall off and are accompanied by fluid migration, resulting in blockage or penetration of the physical model, thereby analyzing the changes in the pore structure. When there is no obvious falling off and migration of clay particles in the entire model, the simulation ends, and the simulation results are exported and saved.

2. The loose sandstone particle migration simulation method according to claim 1, characterized in that: Step S2, the bonding parameter is the cohesive energy density k, bonding is performed according to the parallel bonding model, and the inter-particle cohesion calculation model adopts the simplified JKR model: F sjkr =kA Where k is the cohesive energy density and A is the particle contact area.

3. The loose sandstone particle migration simulation method according to claim 1 or 2, characterized in that: In step S2, the rock mechanics parameters include Young's modulus E, Poisson's ratio υ and clay particle friction coefficient; The rock mechanical parameters are measured in a laboratory, and the clay particles and the skeleton particles used in discrete element simulation are calibrated based on the results.

4. The loose sandstone particle migration simulation method according to claim 1 or 2, characterized in that: In step S3, the grid division adopts structured grid, and the grid accuracy is adjusted according to the grid quality to ensure that the simulation conditions including the particle migration process under different production conditions and pore structures are met; The flow parameters include pressure gradient ΔP, fluid density ρ f and fluid viscosity μ f .

5. The loose sandstone particle migration simulation method according to claim 4, characterized in that: The steps of step S3 are as follows: S 31 1. Mesh the cylindrical boundary wall with a mesh quality of no less than 90% and adjust the mesh accuracy according to the mesh quality. The diameter of a single mesh should be less than 3 particle diameters. S 32 , set the gap around the contact particles in the pore structure physical model as the flow domain, and set the fluid density ρ f 、Fluid viscosity μ f ; The fluid is injected from the porous medium under a specific pressure gradient ΔP. During the injection process, the fluid changes the force acting on the particles around the fluid, causing the particle cementation force chain to break and inducing particle displacement; S 33 The external forces on the clay particles during their migration include their own gravity, drag force, buoyancy, and contact force, and the motion control equation is: In the formula, F p,n and F p,t are the normal contact force and the tangential contact force, F p,g is gravity, F p,e The forces exerted on the particles by the fluid around the particles include drag force, pressure gradient force and buoyancy force, r p,c and T p,r are the particle vector radius and the particle's additional torque, u p and ω p are the translational speed and rotational speed, m p and I p The particle mass and moment of inertia, respectively; S 34 , in each cycle calculation step of the simulation process, the bonding state between the clay particles and the skeleton particles and between the clay particles and the clay particles is monitored in real time. When the shear force of the fluid on the clay particles exceeds the shear strength limit, that is, when the following formula is satisfied, relative slip occurs between the particles and they fall off: Where τ is the shear stress at the particle bonding point, is the internal friction angle between particles; S 35 , the coupling effect between particles and fluid is analyzed by fluid mechanics-discrete element coupling method, and a virtual domain is used to represent the particles. The virtual domain has the same speed as the particles themselves. The particles shown represent the clay particles and the skeleton particles; wherein, Ω F is the fluid domain, Γ and Γ s They are the computational boundary and the particle boundary respectively. The fluid domain is governed by the incompressible Navier-Stokes equations: Continuity equation: ▽·in f =0inΩ F The velocity at the fluid domain boundary is expressed as: the f =the Γ onΓ The velocity at the fluid-particle interface has the following relationship: Where σ is the fluid stress tensor, is the traction vector, u P is the particle velocity, u f is the fluid velocity; the initial boundary condition is expressed as: u f (x,t=0)=u0(x)inΩ F 6. The loose sandstone particle migration simulation method according to claim 1 or 2, characterized in that: Before and after simulation, the method includes calculating the permeability of the unconsolidated sandstone before and after the migration of the clay particles according to Darcy's law.

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