CN-122021161-A - Fine particle migration numerical simulation method based on discrete element pore density flow method and dynamic self-adaptive grid

CN122021161ACN 122021161 ACN122021161 ACN 122021161ACN-122021161-A

Abstract

A fine particle migration numerical simulation method based on a discrete element pore density flow method comprises 1) constructing a discrete element stacking model and a pore network, namely, establishing a three-dimensional broken-graded stacking model based on discrete elements, dividing particles into coarse particles and fine particles, taking the coarse particles as a framework structure, 2) calculating pore seepage, namely, establishing a functional relation of fluid pressure, density and temperature in pores according to a fluid state equation, calculating seepage rate and flow rate between the pores, 3) calculating stress of the fine particles and pore parameters, namely, calculating the stress of the fine particles according to the average flow rate of the pores where the fine particles are located, 4) modeling fluid-solid coupling, namely, the coarse particles and the fine particles interact through contact force, the pore fluid exerts hydrostatic pressure on the coarse particles, exerts drag force on the fine particles, and the coarse particles and the fine particles displace under the action of the combined force, and 5) carrying out iterative solution and simulation operation, namely, realizing whole process dynamics of fine particle migration, blockage and seepage evolution under the three-dimensional discrete element fluid-solid coupling frame.

Inventors

XIA WENQIANG
LIU CHUN
LIU HUI
CAI JUNJIE

Assignees

南京大学

Dates

Publication Date: 20260512
Application Date: 20260129

Claims (7)

1. A fine particle migration numerical simulation method based on a discrete element pore density flow method is characterized by comprising the following steps of (1) constructing a discrete element stacking model and a pore network, namely, constructing a three-dimensional broken grading stacking model based on discrete elements, dividing particles into coarse particles and fine particles, taking the coarse particles as a framework structure, generating a three-dimensional tetrahedral pore network based on coarse particle coordinate nodes by adopting a Delaunay triangulation algorithm, constructing a topological mapping relation between the coarse particles and pores, and extracting geometric parameters of the pores and pore throats; (2) Pore seepage calculation, namely establishing a functional relation of fluid pressure, density and temperature in pores according to a fluid state equation, and assuming that the fluid property in a single pore is uniform; (3) Calculating the stress and the pore parameters of the fine particles, namely calculating the gravity, the buoyancy and the fluid drag force of the fine particles according to the average flow velocity of the pores where the fine particles are positioned; (4) Fluid-solid coupling action modeling, namely, coarse particles and fine particles interact through contact force, pore fluid applies hydrostatic pressure to the coarse particles and applies traction force to the fine particles, the coarse particles and the fine particles displace under the action of the combined force, and the pore volume and the shape are changed, so that bidirectional coupling of a particle system and a seepage field is realized; (5) And (3) performing iterative solution and simulation operation, namely circularly updating the particle motion state and pore fluid parameters by adopting an explicit time step iterative algorithm, and realizing the whole-process dynamic simulation of migration, blockage and seepage evolution of fine particles under a three-dimensional discrete element fluid-solid coupling frame.
2. The + discrete element pore density flow based fine particle migration numerical simulation method of claim 1, comprising the steps of: Step 10, generating a broken grading discrete element particle stack according to particle grading, and dividing particles into coarse particles and fine particles; Step 11, constructing a tetrahedron pore network by adopting Delaunay triangulation based on the coordinates of the spherical centers of the coarse particles, and step 12, calculating the pore volume, pore throat seepage area and length; step 13, calculating pore seepage based on a fluid state equation and Darcy's law; step 14, calculating the gravity, buoyancy and drag force of the fine particles; Step 15, updating the porosity and the permeability coefficient according to the distribution of the fine particles; step 16, calculating the hydrostatic pressure of the pore fluid on the coarse particles; step 17, updating the particle motion state, the fluid parameters and the pore geometry parameters, and triggering the dynamic grid updating if necessary; step 18, judging whether the solid particle system is balanced and whether the flow field is stable, if not, repeating the steps 13-17 until iteration is terminated; And 19, outputting a simulation result.
3. The + discrete element pore density flow based fine particle migration numerical simulation method of claim 1, wherein the detailed description of the associated method of calculating pore fluid seepage in step 13, step 20, according to the pore density flow method, the equation of state of the fluid is expressed as: Based on known fitting data for saturated vapor pressure, temperature, and density (e.g., at water temperature 20 ℃), the relationship of fluid pressure p to fluid density ρ is: Step 21 when there is a pressure difference between two adjacent pores, fluid will flow through the pore throats therebetween, and the seepage velocity is calculated in the form of Darcy's law: wherein k is the microscopic permeability coefficient of the pore throat, The pressure difference between two ends of the pore throat is represented by mu, the viscosity of fluid and l, the length of the pore throat; Step 22, under the condition that the pore volume is fixed, the seepage flow can cause the change of the mass of the fluid in the pore, and the calculation formula is as follows: Wherein the method comprises the steps of For the mass change of the pore fluid, For the fluid permeation rate at the ith pore throat position in the pore, The permeation area of the ith pore throat in the pore; step 23 derives a change in pore fluid density from the change in pore fluid mass; Step 24 further derives pore fluid pressure changes from the density changes in combination with the fluid state equation, resulting in real-time fluid pressure for each pore.
4. The method for simulating the migration of fine particles by using a discrete element pore density flow method according to claim 1, wherein the steps 30-34 are detailed calculation methods of the stress of the fine particles in the step 14; Step 30 obtaining the current velocity of the fine particles Radius r; step 31, calculating the buoyancy force of the fine particles, wherein the calculation formula is as follows: Wherein, the For the buoyancy force to which the fine particles are subjected, Is the density of the fluid; Step 32, based on the fluid velocity at four pore throats of the pore where the fine particles are located, performing pore throat area weighted average on the velocities in four pore throat directions to obtain an average fluid velocity representing the pore, and the calculation formula is as follows: Wherein, the Is the fluid velocity of the pore in which the fine particle is located, For the fluid velocity at the ith orifice throat, Is the unit normal vector of the ith pore throat section; Step 33 calculates the drag force to which the fine particles are subjected, as follows: Wherein, the The fluid drag force to which the fine particles are subjected, The drag coefficient beta is calculated according to the porosity epsilon in two cases: When the porosity is At this time, the drag coefficient β: Wherein, the Is the porosity of the material, which is the porous material, Is the dynamic viscosity of the fluid and, Is the diameter of the fine particles, in the case of high porosity The movement of the fine particles becomes weak by the influence of other particles, and the coefficient is derived from the nonlinear resistance applied to the fine particles: Wherein, the Is the fluid resistance coefficient, which depends on the reynolds number size of the particle: Wherein, the Is the reynolds number of the particle, which characterizes the dimensionless parameters of the particle motion characteristics: step 34 calculates the resultant force of the fine particles as follows: Wherein, the Is the resultant force to which the fine particles are subjected, Is subject to the force of gravity of the fine particles.
5. The method of claim 1, wherein step 15 calculates the current porosity and permeability coefficient according to the pore volume and the number and radius of the fine particles therein, and the calculation formula is as follows: Wherein, the Is the volume of a tetrahedron, And Coarse and fine particles occupy the volume of the tetrahedron, respectively, and k is the permeability coefficient of the pore.
6. The + discrete element pore density flow based fine particle migration numerical simulation method of claim 1 wherein step 16 calculates pore fluid hydrostatic pressure on coarse particles as follows: Wherein the method comprises the steps of Is the hydrostatic pressure to which the coarse particles are subjected, For the pressure of the ith adjacent fluid cell, Is the vector of the area of action of the corresponding fluid unit on the particle surface.
7. The method of claim 1, wherein steps 40-44 are detailed methods of dynamically updating the fluid grid in step 17, Step 40 calculates a quality factor for each fluid pore unit : Wherein, the The value range of (1) is 0,1 represents ideal regular tetrahedron, 0 represents completely degenerated tetrahedron (such as four-point coplanarity), 、 And Is a coefficient of the comprehensive shape factor, and 0.4, 0.4 and 0.2 are recommended respectively, Is the radius of a tangent circle in a tetrahedron, Is the radius of a tetrahedron circumscribing circle, Is the root mean square of six sides of the tetrahedron, Is the smallest dihedral angle of the tetrahedron, Dihedral angle of regular tetrahedron, value of The quality factor comprehensively considers the regularity, the side length uniformity and the angle distribution of the geometric shape, when any tetrahedron is used A value below a preset threshold (E.g., 0.3), the system determines that the quality of the regional grid is reduced, and an update is required to be triggered; Step 41 sets a quality threshold (Preferably 0.3) if all tetrahedrons Determining that the current grid quality meets the requirement without updating, and jumping to step 18 to continue the main simulation loop if at least one tetrahedron exists Judging that the grid needs to be updated, and executing the subsequent steps; step 42 will be all Is labeled "low quality tetrahedra"; for each low-quality tetrahedron, the system identifies its neighborhood tetrahedron according to a topological relation, specifically, all tetrahedrons sharing at least one vertex are listed as a first order neighborhood of the low-quality tetrahedron; Step 43, in order to ensure the continuity of the updated region and avoid immediate re-distortion after updating, the system brings both low-quality tetrahedrons and first-order neighborhood tetrahedrons thereof into the updated set; Step 44, in the extended updating area, identifying tetrahedrons located on the physical boundary of the model and marking the tetrahedrons as boundary constraint units, wherein the vertex connection relations on the boundary of the boundary constraint units are kept unchanged in the subsequent grid reconstruction process so as to ensure the continuity of the boundary conditions of the model; Step 45, deleting all tetrahedrons in the area to be updated but keeping the vertex connection relation of the boundary constraint units, and then executing a constraint Delaunay triangulation algorithm based on the spherical center coordinate point set of all coarse particles in the expanded updating area, wherein the algorithm takes the boundary triangle surface corresponding to the boundary constraint units as constraint conditions in the subdivision process, so as to ensure that the newly generated grid is consistent with the original model at the boundary; step 46, restricting the Delaunay triangulation algorithm to generate a group of new tetrahedral grids, and filling the extended updating area, wherein the newly generated tetrahedral grids are improved in geometric quality and are kept topologically compatible with grids of other areas of the model; step 47, establishing a space intersection relation between the old grid and the new grid, specifically, for each new tetrahedron, calculating the intersection volume of the new tetrahedron and each tetrahedron in the old grid by the system, and if the intersection volume is greater than zero, recording the new tetrahedron pair and the old tetrahedron pair and the intersection volume; Step 48, for each new tetrahedron, weighting and distributing the fluid mass and the temperature in the old tetrahedron to the new tetrahedron according to the intersecting volume ratio according to the intersecting volume calculated in step 47, wherein the specific distribution formula is as follows: Wherein, the For the mass of fluid to which the new tetrahedron is assigned, For the temperature of the new tetrahedra, For the intersection volume of the new tetrahedron with the ith old tetrahedron, For the volume of the ith old tetrahedron, And Fluid mass and temperature of the ith old tetrahedron, respectively.

Description

Fine particle migration numerical simulation method based on discrete element pore density flow method and dynamic self-adaptive grid Technical Field The invention relates to the field of geotechnical engineering seepage and fine particle migration simulation, in particular to a fine particle migration numerical simulation method based on a discrete element pore density flow method and an integrated dynamic self-adaptive grid updating technology, which is suitable for pore scale numerical analysis of piping seepage of earth and rockfill dams, petroleum sand discharge, hydraulic fracturing propping agent migration, particle loss and permeability evolution processes, and is particularly suitable for long-term evolution simulation of dynamic change of pore structures caused by particle movement. Background In the field of geotechnical engineering and energy development, migration of fine particles under the drive of fluid in a porous medium is a key microscopic mechanism for inducing engineering disasters and production risks. For example, piping erosion in the dike foundation, formation sand and sand plugging in hydrocarbon production, and uneven placement of proppants in hydraulic fracturing all directly result from this process. The dynamic rule of fine particle migration is accurately revealed, and the method has decisive significance for accurately predicting engineering structure instability, optimizing productivity and preventing and controlling major safety accidents. The development of a high-efficiency prediction method capable of truly reflecting such complex physical processes has become an urgent technical requirement for guaranteeing the safety and the operation efficiency of important engineering. Conventional macroscopic continuous media methods have difficulty revealing the microscopic mechanism of particle migration at the pore scale. The Discrete Element Method (DEM) is suitable for particle migration simulation due to the characteristic of discrete particles, but the existing fluid-solid coupling method such as DEM-CFD, DEM-SPH and the like has high calculation cost, and the particle migration process is difficult to accurately describe on the pore scale. Therefore, there is a need to develop a fine particle migration numerical method that can efficiently, accurately and dynamically adapt to structural changes on the pore scale, so as to make up for the shortfall of the current simulation approach in truly reflecting the microscopic seepage mechanism. Fluid-solid coupling (FSI) is a interdisciplinary numerical method and experimental technique that studies interactions between Fluid and solid domains, the core being capturing the deformation/movement of the solid caused by the forces of the Fluid, and the solid deformation/movement in turn changing the bi-directional coupling effect of the Fluid domain boundaries and flow field characteristics. The micro seepage mechanism has more application, such as CN2025115902459 applied by the inventor team, which is a pore solute migration numerical simulation method based on a discrete pore density flow method, 1) a porous medium framework is built based on a discrete element method and a pore network model, a topological mapping relation between pore space and adsorbent particles is built, a pore concentration and particle adsorption capacity are stored in a matrix mode based on a pore-pore throat channel thought of a solid particle stacking framework and a pore network model, 2) a solute convection item based on the pore network model is built through decoupling of a solute migration process, ① so as to describe solute convection dominated by fluid movement, ② is introduced into a solute diffusion item based on Fick second law, 3) based on an isothermal adsorption equation, a quasi-dynamic model is adopted to drive, the adsorption equilibrium state of each central pore and each associated particle system is evolved in a system, the solid-liquid distribution rule of the solute in a complex porous medium is represented, and particle pore-adsorption equilibrium is realized by adopting explicit time step iterative calculation. Disclosure of Invention The invention aims to: the invention aims to overcome the defects in the prior art, provides a fine particle numerical simulation method based on a discrete element pore density flow method and integrated with a dynamic self-adaptive grid updating mechanism, the method can efficiently and accurately simulate the migration, blockage and permeability evolution process of fine particles under the pore scale, can maintain the calculation accuracy and geometric rationality of the pore network in real time in the simulation process, and remarkably improves the simulation robustness and reliability under the long-time scale and complex working conditions. Also relates to a microscopic seepage mechanism and application thereof in rock and soil, oil and natural gas exploitation, environmental protection, capital co