Method for determining stacking strength of foam surface particles and method for optimizing particle size distribution of foam stabilizing particles

Abstract

The invention provides a foam surface particle stacking strength determination method and a foam stabilizing particle size distribution optimization method. The foam surface particle stacking strength determination method comprises the following steps: performing particle construction according to particle size distribution of target surface particles, uniformly distributing the constructed particles in a gridding target area at an initial moment, and endowing each constructed particle with an initial speed; repulsive force, attractive force, friction force, radial force Brown force and stress generated by the flow field action borne by each particle and the liquid phase volume fraction of each grid are determined; further determining the flow field velocity of each grid; further determining the resultant force, the dragging force and the lifting force of the gravity and the buoyancy borne by each particle; further determining the speed and the position of the particles in the next time step length; the steps are repeated until the simulation time requirement is met, and then the mechanical strength borne by the particle system is determined based on the repulsive force, the attraction force, the friction force, the radial force Brown force, the resultant force of the gravity and the buoyancy force, the dragging force and the lifting force borne by the particles.

Description

Technical Field

[0001] The invention relates to the technical field of shale gas development, and in particular to a method for determining the stacking strength of foam surface particles and a method for optimizing the particle size distribution of foam-stabilizing particles. Background Art

[0002] Foam drainage and gas production technology is developed by utilizing the foaming property of surfactants. By introducing some surfactants or high molecular polymers with special functions into the mineralized water at the bottom of the well, the gas-liquid two-phase vertical mixed flow process produces a variety of physical and chemical effects such as foam, dispersion, drag reduction, and washing, reducing the "slippage loss" of the liquid during the vertical lifting of the airflow in the wellbore, and achieving the purpose of drainage and gas production.

[0003] Due to the effect of gravity, the liquid discharged from the foam liquid film is concentrated at the bottom of the foam phase through the liquid channels between the bubbles, which is the phenomenon of gravity drainage. According to literature data, when the liquid volume fraction ratio in the foam is reduced to below 35%, the bubbles are no longer regular spheres, but change into irregular polyhedrons. The flat area formed by the compression between the bubbles is the liquid film, and the liquid flows through the bubble gap composed of the film, Plateau boundary and nodes. In addition to the effect of gravity, when there is a liquid fraction gradient, capillary flow under microgravity will also occur, and the drainage process will continue slowly. Since the foam stabilized by a single surfactant has the disadvantages of thin liquid film and fast drainage rate, it is usually necessary to take some further measures to improve the stability of the foam. At present, the stability of the foam is mainly improved by mixed surfactants, surfactant-polymer compounding, surfactant-nanoparticle compounding and other ways.

[0004] The above-mentioned methods can improve the stability of foam and promote the technological progress and development in related fields, but the application under harsh conditions still faces many challenges. High temperature is an important factor that limits the application performance of foam. For high-temperature reservoirs, the foam decays rapidly after entering the deep wellbore, resulting in the inability of the foam system to effectively carry liquid. Polymer-surfactant composite foam can enhance the stability of foam to a certain extent, but it is difficult to play a role because polymers are prone to thermal decomposition under high temperature conditions. Although the effect of high temperature on foam performance can be reduced to a certain extent by increasing the molecular weight of the polymer or chemically grafting heat-resistant groups, the process complexity and application cost are increased. Inorganic nanoparticles such as SiO2 can improve the temperature resistance of foam, but their application is limited by defects such as high cost and non-degradability. Therefore, accurately predicting the stacking strength characteristics of particles on the foam surface to improve the efficiency of nanoparticles in stabilizing foam is the key to restricting the application of foam drainage. Summary of the invention

[0005] The purpose of the present invention is to provide a technical solution that can determine the stacking strength of foam surface particles, and a technical solution for optimizing the particle size distribution of foam-stabilizing particles based on the stacking strength of foam surface particles. In order to achieve the above purpose, the present invention provides the following ten technical solutions.

[0006] In a first aspect, the present invention provides a method for determining the stacking strength of foam surface particles, the method comprising:

[0007] 1) Step 101, obtaining the particle size distribution of the target surface particles, and constructing the particles according to the particle size distribution of the target surface particles; at the initial moment, the constructed particles are evenly distributed in the gridded target area and an initial velocity is assigned to each constructed particle;

[0008] 2) Based on the position and velocity of each particle in the gridded target area, determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid;

[0009] 3) Determine the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force and stress generated by the flow field in each grid on each particle in each grid;

[0010] 4) Based on the flow field velocity in each grid, determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0011] 5) Determine the velocity and position of the particles in the next time step based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0012] 6) Repeat steps 2) to 5) until the simulation time requirement is met, and then determine the mechanical strength of the particle system based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

[0013] In a second aspect, the present invention provides a method for optimizing the particle size distribution of foam-stabilizing particles, the method comprising:

[0014] A. respectively determining the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models; using the method for determining the packing strength of the foam surface particles provided in the first aspect, respectively determining the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determining the optimal continuous particle size model; wherein the particle size upper limit, particle size lower limit, and average particle size of each continuous particle size distribution model are the same;

[0015] B. Determine the corresponding particle size distribution of the foam stabilizing particles when the characteristic parameter values ​​are different under the optimal continuous particle size model; adopt the method for determining the packing strength of the foam surface particles provided in the first aspect to determine the packing strength of the foam surface particles under the corresponding particle size distribution of the foam stabilizing particles when the characteristic parameter values ​​are different under the optimal continuous particle size model, and then determine the optimal characteristic parameter values ​​under the optimal continuous particle size model.

[0016] In a third aspect, the present invention provides a device for determining the stacking strength of foam surface particles, the device comprising:

[0017] The first module is used to obtain the particle size distribution of the target surface particles and construct the particles according to the particle size distribution of the target surface particles; at the initial moment, the constructed particles are evenly distributed in the gridded target area and an initial velocity is assigned to each constructed particle;

[0018] The second module is used to determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid based on the position and velocity of each particle in the gridded target area, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid;

[0019] The third module is used to determine the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force and stress generated by the flow field in each grid on each particle in each grid;

[0020] The fourth module is used to determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid based on the flow field velocity in each grid;

[0021] The fifth module is used to determine the velocity and position of the particles in the next time step based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0022] The sixth module is used to repeatedly use the second module, the third module, the fourth module and the fifth module to determine the speed and position of the particles in each time step until the simulation time requirement is met, and then the mechanical strength of the particle system is determined based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

[0023] In a fourth aspect, the present invention provides a device for optimizing the particle size distribution of foam-stabilizing particles, the device comprising:

[0024] The first unit 401 is used to respectively determine the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models; using the packing strength determination device of the foam surface particles provided by the third aspect, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determine the optimal continuous particle size model; wherein the particle size upper limit, particle size lower limit, and average particle size of each continuous particle size distribution model are the same;

[0025] The second unit 402 is used to respectively determine the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model; using the device for determining the packing strength of the foam surface particles provided by the third aspect, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model, and then determine the optimal characteristic parameter value under the optimal continuous particle size model.

[0026] In a fifth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for determining the stacking strength of foam surface particles provided in the first aspect is implemented.

[0027] In a sixth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the particle size distribution optimization method for the foam stabilizing particles provided in the second aspect when executing the computer program.

[0028] In a seventh aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method for determining the stacking strength of foam surface particles provided in the first aspect.

[0029] In an eighth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the particle size distribution optimization method for the bubble-stabilizing particles provided in the second aspect.

[0030] In a ninth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method for determining the stacking strength of foam surface particles provided in the first aspect.

[0031] In a tenth aspect, the present invention provides a computer program product, which includes a computer program, and when the computer program is executed by a processor, it implements the particle size distribution optimization method of the bubble stabilizing particles provided in the second aspect.

[0032] The technical solution provided by the present invention determines the packing strength of particles on the foam surface based on the force and the aggregation of particles on the surface of the bubbles, and optimizes the particle size distribution of the stabilizing particles based on the packing strength of the particles on the foam surface. DETAILED DESCRIPTION

[0033] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the embodiments of the present invention are further described in detail below. Here, the exemplary embodiments of the present invention and their description are used to explain the present invention, but are not intended to limit the present invention.

[0034] In the description of this specification, the terms "include", "including", "have", "contain", etc. are all open terms, which mean including but not limited to. The descriptions with reference to the terms "one embodiment", "a specific embodiment", "some embodiments", "for example", etc. mean that the specific features, structures or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. The order of steps involved in each embodiment is used to schematically illustrate the implementation of the present application, and the order of steps is not limited and can be appropriately adjusted as needed.

[0035] An embodiment of the present invention provides a method for determining the stacking strength of particles on a foam surface, the method comprising the following steps:

[0036] Step 101, obtaining the particle size distribution of the target surface particles, and constructing the particles according to the particle size distribution of the target surface particles; at the initial moment, evenly distributing the constructed particles in the gridded target area and assigning an initial velocity to each constructed particle;

[0037] Step 102, based on the position of each particle in the gridded target area and the velocity of each particle, determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid;

[0038] Step 103, determining the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid and the stress generated by the flow field in each grid;

[0039] Step 104, based on the flow field velocity in each grid, determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0040] Step 105, based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid, determine the velocity and position of the particle in the next time step;

[0041] Step 106, repeating steps 102 to 105 until the simulation time requirement is met, and determining the mechanical strength of the particle system based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

[0042] In one embodiment, in step 101, when assigning an initial velocity to each constructed particle, the initial velocity is randomly selected between [-1, 1], and the positive and negative values ​​represent the direction of movement.

[0043] In one embodiment, in step 102, the repulsive force exerted on a particle by another particle is determined by the following formula:

[0044] When ij <D ij When (the distance between the two particles is less than the equilibrium distance), in,

[0045] When ij ≥D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F rij =0;

[0046] In the formula, r ij is the center distance between particles i and j, m, r ij =r j -r i , r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; F rij is the repulsive force between particles i and j, N.

[0047] In one embodiment, in step 102, the attraction force exerted on a particle by another particle is determined by the following formula:

[0048] When ij >D ij When (the distance between the two particles is greater than the equilibrium distance), in, b=a ia j sinθ / D ij ,

[0049] When ij ≤D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F aij =0;

[0050] In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, r j is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; F aij is the attraction between particles i and j, N; δ ij is the range of the attractive interaction between particles i and j relative to the average diameter, m; ε ij is the range of the interaction force between particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ; b is the radius of the interface between particles i and j, m.

[0051] In one embodiment, in step 102, the friction force exerted on a particle by another particle is determined by the following formula:

[0052]

[0053] Among them, R ij =2a i a j / (a i +a j )

[0054] In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 is 1; R ij is the harmonic mean radius of particles i and j; a i is the radius of particle i, m; a j is the radius of particle j, m; is the friction force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; v ij is the relative velocity between particles i and j, m / s; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ij is the unit vector pointing from particle i to particle j, dimensionless.

[0055] In one embodiment, in step 102, the radial Brownian force exerted on a particle by another particle is determined by the following formula:

[0056]

[0057] Among them, R ij =2a i a j / (a i +a j )

[0058] In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 =1; ij (t) is a random number with unit variance, ranging from 0 to 1; R ij is the harmonic mean radius of particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; is the radial Brownian force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ij is the unit vector pointing from particle i to particle j, dimensionless; δt is the time step adopted, s; ​​k is the Boltzmann constant, J / K; T is the temperature, K.

[0059] In one embodiment, in step 102, the stress generated by the flow field is determined by the following formula:

[0060] τ i =a i r ij F i s / D ij

[0061] τj =a j r ij F i s / D ij

[0062] in, b=a i a j sinθ / D ij

[0063] In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; is the shear force at the center of particle i, N; is the shear force at the center of particle j, N; b is the radius of the interface between particles i and j, m; u ij is the vertical displacement of particles i and j relative to the contact point, m; τ i is the component of shear stress in the i direction, Pa; τ j is the component of shear stress in the j direction, Pa.

[0064] In one embodiment, in step 102, determining the liquid volume fraction of each grid may specifically include:

[0065] Based on the positions of each particle in the gridded target area, determining the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure;

[0066] Based on the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure, the porosity of each grid is determined to be the liquid phase volume fraction of each grid;

[0067] Furthermore, the polydispersity index of particles within a grid is determined by the following formula:

[0068]

[0069] Where PDI is the polydispersity index of the particles in the grid; M w is the weight average molecular weight of the particles in the grid; M nis the number average molecular weight of the particles in the grid; M i is the relative molecular mass of the i-th particle in the grid; N is the total number of particles in the grid;

[0070] Furthermore, the influence of particles in each grid on the structure is determined by the following formula:

[0071] C(r,t)=C(0,t)·expect[-(r / t) 1.5 ]

[0072] Where r = D ij +R ij , R ij =2a i a j / (a i +a j )

[0073] Where C(r, t) is the particle concentration at radius r at time t, dimensionless; C(0, t) is the center particle concentration, dimensionless; D ij is the equilibrium distance between particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; R ij is the harmonic mean radius of particles i and j, m; expect[-(r / t) 1.5 ] refers to the natural constant e -(r / t) 1.5 Power, dimensionless;

[0074] The vector order parameter of particle i is: is the angle between a pair of adjacent particles i and j and the x-axis. Adjacent particles are defined as particles within the friction interaction distance, i.e., the center-to-center distance is less than r = D ij +R ij ; The order parameter is pre-averaged over all particles in the grid, the order parameter is mapped to the spin vector on the regular square lattice, and the spin-spin correlation function of all lattice sites is averaged to obtain: By fitting, we can get the relationship between the correlation function and time and the correlation length: C(r,t)=C(0,t)exp[-(r / ξ(t)) 1.5 ], which is used to determine the influence of particles in each grid on the structure;

[0075] Furthermore, the porosity of each grid is determined by the following formula:

[0076]

[0077] In the formula, is the porosity, dimensionless; C(r, t) is the particle concentration at radius r at time t, dimensionless; PDI is the polydispersity index of the particles in the grid, dimensionless; V 颗粒 is the volume of a single particle, m 3 ; V 网格 is the grid volume, m 3 .

[0078] In one embodiment, in step 103, the flow field velocity in a certain grid is determined based on the following formula:

[0079]

[0080] Among them, S f =∑ i F gi +∑ i F Di +∑ i F Li

[0081]

[0082] Where t is time, s; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; τ is the flow field stress distribution, Pa; S f is the force on the particles in the grid, N; g is the acceleration due to gravity, m / s 2 ; α is the liquid volume fraction, dimensionless; F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 ; F Di is the drag force on particle i, N; d i is the diameter of particle i, m; u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless; F Li is the lift force on particle i, N; C L is the lift coefficient, dimensionless;

[0083] Based on the liquid volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid and the stress generated by the flow field in each grid, the flow field velocity in each grid can be determined using the above formula by using the discrete element solution method.

[0084] In one embodiment, in step 104, the combined force of gravity and buoyancy on a particle is determined based on the following formula:

[0085]

[0086] In the formula, F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 .

[0087] In one embodiment, in step 104, the drag force on a particle is determined based on the following formula:

[0088]

[0089] In the formula, F Di is the drag force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless.

[0090] In one embodiment, in step 104, the lift force of a particle is determined based on the following formula:

[0091]

[0092] In the formula, F Li is the lift force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C L is the lift coefficient, dimensionless.

[0093] In one embodiment, in step 105, the velocity and position of a particle in the next time step are determined based on the following formula:

[0094]

[0095] In the formula, m i is the mass of particle i, kg; u i is the velocity of particle i, m / s; t is time, s; F ai is the sum of the attractive forces between particle i and the rest of the particles (i.e., the total attractive force on particle i), N; F ri is the sum of the repulsive forces between particle i and the rest of the particles (i.e., the total repulsive force on particle i), N; is the sum of the friction forces between particle i and the rest of the particles (i.e. the total friction force on particle i), N; is the sum of the radial Brownian forces between particle i and the rest of the particles (i.e. the total radial Brownian force on particle i), N; F gi is the combined force of gravity and buoyancy on particle i, N; F Di is the drag force on particle i, N; F Li is the lift force on particle i, N.

[0096] In one embodiment, in step 106, the mechanical strength of the particle system is determined based on the following formula:

[0097] F=F a +F r +F f +F b +F g +F D +F L

[0098] In the formula, F a is the sum of the attractive forces on each particle, N; F r is the sum of the repulsive forces on each particle, N; F f is the sum of the friction forces on each particle, N; F b is the sum of the radial Brownian forces acting on each particle, N; F g is the sum of the combined force of gravity and buoyancy on each particle, N; F D is the sum of the drag forces on each particle, N; F L is the sum of the lift forces on each particle, N.

[0099] An embodiment of the present invention provides a method for optimizing the particle size distribution of foam-stabilizing particles, the method comprising the following steps:

[0100] Step 201, respectively determining the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models; using the method for determining the packing strength of the foam surface particles provided in the above embodiment, respectively determining the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determining the optimal continuous particle size model; wherein the particle size upper limit, particle size lower limit, and average particle size of each continuous particle size distribution model are the same;

[0101] Step 202, respectively determine the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model; use the method for determining the packing strength of the foam surface particles provided in the above embodiment to respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model, and then determine the optimal characteristic parameter value under the optimal continuous particle size model.

[0102] In one embodiment, in step 201, the different continuous particle size distribution models include at least two of: a Gaudin-Schuhmann model, an Alfred model, a Rosin-Rammler model, a normal distribution model, a lognormal distribution model, and a Weibull distribution model.

[0103] In one embodiment, in step 202, different characteristic parameter values ​​may be designed in a manner of, but not limited to, orthogonal experiment.

[0104] The present invention also provides a device for determining the stacking strength of foam surface particles, as described in the following embodiments. Since the principle of the device to solve the problem is similar to the method for determining the stacking strength of foam surface particles, the implementation of the device can refer to the implementation of the method for determining the stacking strength of foam surface particles, and the repeated parts will not be repeated.

[0105] The embodiment of the present invention provides a device for determining the stacking strength of particles on the surface of foam, which may specifically include:

[0106] The first module 301 is used to obtain the particle size distribution of the target surface particles, and construct the particles according to the particle size distribution of the target surface particles; at the initial moment, the constructed particles are evenly distributed in the gridded target area and an initial velocity is assigned to each constructed particle;

[0107] The second module 302 is used to determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid based on the position of each particle and the speed of each particle in the gridded target area, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid;

[0108] The third module 303 is used to determine the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force and stress generated by the flow field in each grid on each particle in each grid;

[0109] The fourth module 304 is used to determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid based on the flow field velocity in each grid;

[0110] The fifth module 305 is used to determine the velocity and position of the particles in the next time step based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0111] The sixth module 306 is used to repeatedly use the second module 302, the third module 303, the fourth module 304, and the fifth module 305 to determine the speed and position of the particles in each time step until the simulation time requirement is met, and then determine the mechanical strength of the particle system based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

[0112] In one embodiment, in the first module 301, when assigning an initial velocity to each constructed particle, the initial velocity is randomly selected between [-1, 1], and the positive and negative values ​​represent the direction of movement.

[0113] In one embodiment, in the second module 302, the repulsive force exerted on a particle by another particle is determined by the following formula:

[0114] When ij <D ij When (the distance between the two particles is less than the equilibrium distance), in,

[0115] When ij ≥D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F rij =0;

[0116] In the formula, r ij is the center distance between particles i and j, m, r ij =r j -r i , r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; Dij is the equilibrium distance between particles i and j, m; F rij is the repulsive force between particles i and j, N.

[0117] In one embodiment, in the second module 302, the attraction force exerted on a particle by another particle is determined by the following formula:

[0118] When ij >D ij When (the distance between the two particles is greater than the equilibrium distance), in, b=a i a j sinθ / D ij ,

[0119] When ij ≤D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F aij =0;

[0120] In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, r j is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; F aij is the attraction between particles i and j, N; δ ij is the range of the attractive interaction between particles i and j relative to the average diameter, m; ε ij is the range of the interaction force between particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ; b is the radius of the interface between particles i and j, m.

[0121] In one embodiment, in the second module 303, the friction force exerted on a particle by another particle is determined by the following formula:

[0122]

[0123] Among them, R ij =2a i a j / (a i+a j )

[0124] In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 is 1; R ij is the harmonic mean radius of particles i and j; a i is the radius of particle i, m; a j is the radius of particle j, m; is the friction force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; v ij is the relative velocity between particles i and j, m / s; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ij is the unit vector pointing from particle i to particle j, dimensionless.

[0125] In one embodiment, in the second module 302, the radial Brownian force exerted on a particle by another particle is determined by the following formula:

[0126]

[0127] Among them, R ij =2a i a j / (a i +a j )

[0128] In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 =1; ij (t) is a random number with unit variance, ranging from 0 to 1; R ij is the harmonic mean radius of particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; is the radial Brownian force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ijis the unit vector pointing from particle i to particle j, dimensionless; δt is the time step adopted, s; ​​k is the Boltzmann constant, J / K; T is the temperature, K.

[0129] In one embodiment, in the second module 302, the stress generated by the flow field is determined by the following formula:

[0130] τ i =a i r ij F i s / D ij

[0131] τ j =a j r ij F i s / D ij

[0132] in, b=a i a j sinθ / D ij

[0133] In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; is the shear force at the center of particle i, N; is the shear force at the center of particle j, N; b is the radius of the interface between particles i and j, m; u ij is the vertical displacement of particles i and j relative to the contact point, m; τ i is the component of shear stress in the i direction, Pa; τ j is the component of shear stress in the j direction, Pa.

[0134] In one embodiment, in the second module 302, determining the liquid volume fraction of each grid may specifically include:

[0135] Based on the positions of each particle in the gridded target area, determining the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure;

[0136] Based on the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure, the porosity of each grid is determined to be the liquid phase volume fraction of each grid;

[0137] Furthermore, the polydispersity index of particles within a grid is determined by the following formula:

[0138]

[0139] Where PDI is the polydispersity index of the particles in the grid; M w is the weight average molecular weight of the particles in the grid; M n is the number average molecular weight of the particles in the grid; M i is the relative molecular mass of the i-th particle in the grid; N is the total number of particles in the grid;

[0140] Furthermore, the influence of particles in each grid on the structure is determined by the following formula:

[0141] C(r,t)=C(0,t)·expect[-(r / t) 1.5 ]

[0142] Where r = D ij +R ij , R ij =2a i a j / (a i +a j )

[0143] In the formula, r = D ij +R ij , R ij =2a i a j / (a i +a j )

[0144] Where C(r, t) is the particle concentration at radius r at time t; C(0, t) is the center particle concentration; D ij is the equilibrium distance between particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; R ij is the harmonic mean radius of particles i and j, m; expect[-(r / t) 1.5 ] refers to the natural constant e -(r / t) 1.5 Power, dimensionless;

[0145] Furthermore, the porosity of each grid is determined by the following formula:

[0146]

[0147] In the formula, is the porosity, dimensionless; C(r, t) is the particle concentration at radius r at time t, dimensionless; PDI is the polydispersity index of the particles in the grid, dimensionless; V 颗粒 is the volume of a single particle, m 3 ; V 网格 is the grid volume, m 3 .

[0148] In one embodiment, in the third module 303, the flow field velocity in a certain grid is determined based on the following formula:

[0149]

[0150] Among them, S f =∑ i F gi +∑ i F Di +∑ i F Li

[0151] Where t is time, s; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; τ is the flow field stress distribution, Pa; S f is the force on the particles in the grid, N; g is the acceleration due to gravity, m / s 2 ; α is the liquid volume fraction, dimensionless; where F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 ; F Di is the drag force on particle i, N; d i is the diameter of particle i, m; u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless; F Li is the lift force on particle i, N; C L is the lift coefficient, dimensionless;

[0152] Based on the liquid volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid and the stress generated by the flow field in each grid, the flow field velocity in each grid can be determined using the above formula by using the discrete element solution method.

[0153] In one embodiment, in the fourth module 304, the combined force of gravity and buoyancy on a particle is determined based on the following formula:

[0154]

[0155] In the formula, F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 .

[0156] In one embodiment, in step 104, the drag force on a particle is determined based on the following formula:

[0157]

[0158] In the formula, F Di is the drag force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless.

[0159] In one embodiment, in step 104, the lift force of a particle is determined based on the following formula:

[0160]

[0161] In the formula, F Li is the lift force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C L is the lift coefficient, dimensionless.

[0162] In one embodiment, in the fifth module 305, the velocity and position of a particle in the next time step are determined based on the following formula:

[0163]

[0164] In the formula, m i is the mass of particle i, kg; u i is the velocity of particle i, m / s; t is time, s; F ai is the sum of the attractive forces between particle i and the rest of the particles (i.e., the total attractive force on particle i), N; F ri is the sum of the repulsive forces between particle i and the rest of the particles (i.e., the total repulsive force on particle i), N; is the sum of the friction forces between particle i and the rest of the particles (i.e. the total friction force on particle i), N; is the sum of the radial Brownian forces between particle i and the rest of the particles (i.e. the total radial Brownian force on particle i), N; F gi is the combined force of gravity and buoyancy on particle i, N; F Di is the drag force on particle i, N; F Li is the lift force on particle i, N.

[0165] In one embodiment, in the sixth module 306, the mechanical strength of the particle system is determined based on the following formula:

[0166] F=F a +F r +F f +F b +F g +F D +F L

[0167] In the formula, F a is the sum of the attractive forces on each particle, N; F r is the sum of the repulsive forces on each particle, N; F f is the sum of the friction forces on each particle, N; F b is the sum of the radial Brownian forces acting on each particle, N; F g is the sum of the combined force of gravity and buoyancy on each particle, N; F D is the sum of the drag forces on each particle, N; F L is the sum of the lift forces on each particle, N.

[0168] The present invention also provides a device for optimizing the particle size distribution of foam-stabilizing particles, as described in the following embodiments. Since the principle of the device to solve the problem is similar to the method for optimizing the particle size distribution of foam-stabilizing particles, the implementation of the device can refer to the implementation of the method for optimizing the particle size distribution of foam-stabilizing particles, and the repeated parts will not be repeated.

[0169] An embodiment of the present invention provides a device for optimizing the particle size distribution of foam-stabilizing particles, which may specifically include:

[0170] The first unit 401 is used to respectively determine the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models; using the apparatus for determining the packing strength of the foam surface particles provided in the above embodiment, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determine the optimal continuous particle size model; wherein the particle size upper limit, particle size lower limit and average particle size of each continuous particle size distribution model are the same;

[0171] The second unit 402 is used to respectively determine the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model; using the device for determining the packing strength of the foam surface particles provided in the above embodiment, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model, and then determine the optimal characteristic parameter value under the optimal continuous particle size model.

[0172] In one embodiment, in the first unit 401, the different continuous particle size distribution models include at least two of: a Gaudin-Schuhmann model, an Alfred model, a Rosin-Rammler model, a normal distribution model, a lognormal distribution model, and a Weibull distribution model.

[0173] In one embodiment, in the second unit 402, different characteristic parameter values ​​may be designed in a manner of, but not limited to, orthogonal experiment.

[0174] An embodiment of the present invention also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the above-mentioned method for determining the stacking strength of foam surface particles when executing the computer program.

[0175] An embodiment of the present invention also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned particle size distribution optimization method of the foam stabilizing particles when executing the computer program.

[0176] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for determining the stacking strength of particles on the surface of foam is implemented.

[0177] An embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the particle size distribution optimization method of the foam-stabilizing particles is implemented.

[0178] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the method for determining the stacking strength of particles on the surface of the foam is implemented.

[0179] An embodiment of the present invention further provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the particle size distribution optimization method of the foam-stabilizing particles is implemented.

[0180] Embodiment 1:

[0181] This embodiment provides a method for optimizing the particle size distribution of foam-stabilizing particles. In this embodiment, nano-silicon dioxide particles are used as foam-stabilizing particles (the average particle size is 100 nm, the lower limit of the particle size is 1 nm, the upper limit of the particle size is 300 nm, and the density is 2.4 g / cm 3 ), including:

[0182] 1. Determine the particle size distribution of stable foam particles under different continuous particle size distribution models respectively; wherein the different continuous particle size distribution models include: GS model (i.e. Gaudin-Schuhmann model), RR model (i.e. Rosin-Rammler model), normal distribution model, lognormal distribution model and Weibull distribution model.

[0183] 2. Determine the packing strength of foam surface particles under the particle size distribution of foam stabilizing particles corresponding to different continuous particle size models; wherein the packing strength of foam surface particles under each particle size distribution of foam stabilizing particles is determined by the following steps:

[0184] 2.1. Obtain the particle size distribution of the target surface particles, and construct the particles according to the particle size distribution of the target surface particles; at the initial moment, evenly distribute the constructed particles in the gridded target area and assign an initial velocity to each constructed particle. The initial velocity is randomly selected between [-1, 1], and the positive and negative values ​​indicate the direction of movement;

[0185] 2.2. Based on the position and velocity of each particle in the gridded target area, determine the conservative force (including repulsive force and attractive force), friction force, radial force Brownian force on each particle in each grid, determine the stress generated by the flow field in each grid, determine the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure; based on the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure, determine the porosity of each grid, that is, determine the liquid phase volume fraction of each grid;

[0186] The repulsive force exerted on a particle by another particle is determined by the following formula:

[0187] When ij <D ij When (the distance between the two particles is less than the equilibrium distance),

[0188] When ij ≥D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F rij =0;

[0189] The attractive force exerted on a particle by another particle is determined by the following formula:

[0190] When ij >D ij When (the distance between the two particles is greater than the equilibrium distance), in,

[0191] When ij ≤D ij When (the distance between the two particles is greater than or equal to the equilibrium distance), F aij =0;

[0192] The friction force exerted on a particle by another particle is determined by the following formula:

[0193]

[0194] The radial Brownian force exerted on a particle by another particle is determined by the following formula:

[0195]

[0196] The stress generated by the flow field is determined by the following formula:

[0197] τ i =a i r ij F i s / D ij

[0198] τj =a j r ij F i s / D ij

[0199] The polydispersity index of the particles within the grid is determined by the following formula:

[0200]

[0201] The influence of particles in each grid on the structure is determined by the following formula:

[0202] C(r,t)=C(0,t)·expect[-(r / t) 1.5 ]

[0203] Where r = D ij +R ij , b=a i a j sinθ / D ij , R ij =2a i a j / (a i +a j ),

[0204] In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, which is 200 MPa in this embodiment; a i is the radius of particle i; a j is the radius of particle j; θ is the angle between the tangent lines of particle i and particle j at the overlap; D ij is the equilibrium distance between particles i and j; F rij is the repulsive force between particles i and j; F aij is the attraction between particles i and j; δ ij is the range of the attractive interaction between particles i and j relative to the average diameter; ε ij is the amplitude of the interaction force between particles i and j; γ is the surface energy of the interface between particles and solution, which is 100 mJ / m in this embodiment. 2 ; b is the radius of the interface between particles i and j; For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 is 1; R ij is the harmonic mean radius of particles i and j; is the friction force between particles i and j; h ij is the gap width between the surfaces of particles i and j; v ij is the relative velocity between particles i and j; γ is the surface energy of the interface between particles and solution; e ij is the unit vector from particle i to particle j; ij (t) is a random number with unit variance, ranging from 0 to 1; is the radial Brownian force between particles i and j; δt is the time step used, which is 0.001s in this embodiment; k is the Boltzmann constant, which is 1.380649×10 -23 J / K; T is temperature, which is 273.15K in this embodiment; is the shear force at the center of particle i; is the shear force at the center of particle j; u ij is the vertical displacement of particles i and j relative to the contact point; τ i is the component of shear stress in the i direction; τ j is the component of shear stress in the j direction; PDI is the polydispersity index of the particles in the grid; M w is the weight average molecular weight of the particles in the grid; M n is the number average molecular weight of the particles in the grid; M i is the relative molecular mass of the ith particle in the grid; N is the total number of particles in the grid; C(r, t) is the particle concentration at radius r at time t; C(0, t) is the center particle concentration; expect[-(r / t) 1.5 ] refers to the natural constant e -(r / t) 1.5 Power; is the porosity; V 颗粒 is the volume of a single particle; V 网格 is the grid volume.

[0205] 2.3. Based on the liquid volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid and the stress generated by the flow field in each grid, the flow field velocity in each grid is determined based on the following formula:

[0206]

[0207] Among them, Sf =∑ i F gi +∑ i F Di +∑ i F Li

[0208]

[0209] Where t is time; ρ f is the fluid density, which is 1000 kg / m 3 ;u f is the flow field velocity; τ is the flow field stress distribution; S f is the force on the particles in the grid; g is the acceleration of gravity; α is the volume fraction of the liquid phase; F gi is the combined force of gravity and buoyancy on particle i; m i is the mass of particle i; ρ f is the fluid density; ρ p is the particle density; g is the gravitational acceleration; F Di is the drag force on particle i; d i is the diameter of particle i; u f is the flow field velocity; C D is the drag force coefficient; F Li is the lift force on particle i; C L is the lift coefficient;

[0210] 2.4. Based on the flow field velocity in each grid, determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid;

[0211] The combined force of gravity and buoyancy on a particle is determined based on the following formula:

[0212]

[0213] The drag force on a particle is determined based on the following formula:

[0214]

[0215] The lift of a particle is determined based on the following formula:

[0216]

[0217] In the formula, F gi is the combined force of gravity and buoyancy on particle i; m i is the mass of particle i; ρ f is the fluid density; ρ p is the particle density, kg / m 3; g is the acceleration due to gravity; F Di is the drag force on particle i; d i is the diameter of particle i; u f is the flow field velocity; C D is the drag force coefficient, which is 0.2 in this embodiment; F Li is the lift force on particle i; C L is the lift coefficient, which is 0.3 in this embodiment.

[0218] 2.5. Based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid, the velocity and position of each particle in the next time step are determined based on the following formula:

[0219]

[0220] In the formula, m i is the mass of particle i; u i is the velocity of particle i; t is time; F ai is the sum of the attractive forces between particle i and the rest of the particles (i.e., the total attractive force on particle i); F ri is the sum of the repulsive forces between particle i and the rest of the particles (i.e., the total repulsive force on particle i); is the sum of the friction forces between particle i and the rest of the particles (i.e. the total friction force on particle i); is the sum of the radial Brownian forces between particle i and the rest of the particles (i.e. the total radial Brownian force on particle i); F gi is the combined force of gravity and buoyancy on particle i; F Di is the drag force on particle i; F Li is the lift force on particle i.

[0221] 2.6. Repeat steps 2.2 to 2.5 until the simulation time requirement is met (i.e., 10 seconds). Then, based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid, the mechanical strength of the particle system is determined using the following formula:

[0222] F=F a +F r +F f +F b +F g +F D +F L

[0223] In the formula, F a is the sum of the attractive forces on each particle; F r is the sum of the repulsive forces on each particle; Ff is the sum of the friction forces on each particle; F b is the sum of the radial Brownian forces acting on each particle; F g is the sum of the combined force of gravity and buoyancy on each particle; F D is the sum of the drag forces on each particle; F L is the sum of the lift forces on each particle.

[0224] The results are shown in Table 1.

[0225] Table 1 Packing strength of foam surface particles under different continuous particle size models corresponding to the particle size distribution of stable foam particles

[0226] Model The stacking strength of foam surface particles / N GS 2.7 RR 4.1 normal distribution 5.2 Lognormal distribution 9.4 Weibull distribution 6.8

[0227] 3. Determine the optimal continuous particle size model based on the packing strength of the foam surface particles under the foam stabilizing particle size distribution corresponding to different continuous particle size models. In this embodiment, the optimal particle size distribution criterion is the normal distribution.

[0228] 4. Determine the particle size distribution of the foam-stabilizing particles corresponding to different characteristic parameter values ​​under the normal distribution model; use the methods provided in steps 2.1 to 2.6 to determine the packing strength of the foam surface particles under the particle size distribution of the foam-stabilizing particles corresponding to different characteristic parameter values ​​under the normal distribution model; wherein, the orthogonal test is designed for different characteristic parameter values, and the values ​​of each characteristic parameter are shown in Table 2; the results are shown in Table 2.

[0229] Table 2 Feature parameter optimization results

[0230]

[0231] Note: When d 50 It is the median particle size, which is the particle size corresponding to when the cumulative particle size distribution percentage reaches 50%.

[0232] 5. Based on the stacking strength of the foam surface particles under the foam stabilizing particle size distribution corresponding to different characteristic parameter values ​​under the normal distribution model, determine the optimal characteristic parameter value under the normal distribution model. In this embodiment, the optimal characteristic parameter value under the logarithmic normal distribution model is: the mean is 0.9d 50 , with a variance of 0.3d 50 , particle size range is 0.4d 50 -1.2d 50 .

[0233] Example 2

[0234] This embodiment provides a method for optimizing the particle size distribution of foam-stabilizing particles. In this embodiment, nano calcium carbonate particles are used as foam-stabilizing particles (with an average particle size of 500 nm, a lower particle size limit of 100 nm, an upper particle size limit of 800 nm, and a density of 2.9 g / cm 3 ), including:

[0235] 1. Determine the particle size distribution of stable foam particles under different continuous particle size distribution models; wherein the different continuous particle size distribution models include: GS model (i.e. Gaudin-Schuhmann model), RR model (i.e. Rosin-Rammler model), normal distribution model, lognormal distribution model and Weibull distribution model. 100-800nm

[0236] 2. Determine the packing strength of foam surface particles under the foam stabilizing particle size distribution corresponding to different continuous particle size models;

[0237] The packing strength of the foam surface particles under each foam stabilizing particle size distribution is respectively carried out by the method provided in step 2.1 to step 2.6 of Example 1; wherein the linear elastic modulus E, the surface energy γ of the interface between the particle and the solution, the time step δt used, the Boltzmann constant k, the temperature T, the fluid density ρ f , drag force coefficient C D , lift coefficient C L , the simulation time requirements are the same as those in Example 1.

[0238] The results are shown in Table 3.

[0239] Table 3 Packing strength of foam surface particles under different continuous particle size models corresponding to the particle size distribution of stable foam particles

[0240] Model The stacking strength of foam surface particles / N GS 3.6 RR 5.1 normal distribution 8.4 Lognormal distribution 6.9 Weibull distribution 5.3

[0241] 3. Determine the optimal continuous particle size model based on the packing strength of the foam surface particles under the foam stabilizing particle size distribution corresponding to different continuous particle size models. In this embodiment, the optimal particle size distribution criterion is the log-normal distribution.

[0242] 4. Determine the particle size distribution of the foam-stabilizing particles corresponding to different characteristic parameter values ​​under the log-normal distribution model; use the method provided in steps 2.1 to 2.6 in Example 1 to determine the packing strength of the foam surface particles under the particle size distribution of the foam-stabilizing particles corresponding to different characteristic parameter values ​​under the log-normal distribution model; wherein, the orthogonal test is used to design the different characteristic parameter values, and the values ​​of each characteristic parameter are shown in Table 4; the results are shown in Table 4.

[0243] Table 4 Feature parameter optimization results

[0244]

[0245]

[0246] Note: When d 50 It is the median particle size, which is the particle size corresponding to when the cumulative particle size distribution percentage reaches 50%.

[0247] 5. Based on the stacking strength of foam surface particles under the foam stabilizing particle size distribution corresponding to different characteristic parameter values ​​under the lognormal distribution model, determine the optimal characteristic parameter value under the lognormal distribution model. In this embodiment, the optimal characteristic parameter value under the lognormal distribution model is: the mean is 1.0d 50 , with a variance of 0.3d 50 , particle size range is 0.8d 50 -1.2d 50 .

[0248] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0249] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the stacking strength of foam surface particles, the method comprising the following steps: 1) Obtain the particle size distribution of the target surface particles, and construct the particles according to the particle size distribution of the target surface particles; At the initial moment, the constructed particles are evenly distributed in the gridded target area and an initial velocity is assigned to each constructed particle; 2) Based on the position and velocity of each particle in the gridded target area, determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid; 3) Determine the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force and stress generated by the flow field in each grid on each particle in each grid; 4) Based on the flow field velocity in each grid, determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid; 5) Determine the velocity and position of the particles in the next time step based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid; 6) Repeat steps 2) to 5) until the simulation time requirement is met, and then determine the mechanical strength of the particle system based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

2. The method according to claim 1, wherein: When assigning an initial velocity to each constructed particle, the initial velocity is randomly selected between [-1, 1], and the positive and negative values ​​indicate the direction of movement.

3. The method according to claim 1, wherein: The repulsive force exerted on a particle by another particle is determined by the following formula: When ij <D ij hour, in, When ij ≥D ij When F rij =0; In the formula, r ij is the center distance between particles i and j, m, r ij =r j -r i , r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; F rij is the repulsive force between particles i and j, N.

4. The method according to claim 1, wherein: The attractive force exerted on a particle by another particle is determined by the following formula: When ij >D ij hour, in, b=a i a j sinθ / D ij , When ij ≤D ij When F aij =0; In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, r j is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; F aij is the attraction between particles i and j, N; δ ij is the range of the attractive interaction between particles i and j relative to the average diameter, m; ε ij is the range of the interaction force between particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ; b is the radius of the interface between particles i and j, m.

5. The method according to claim 1, wherein: The friction force exerted on a particle by another particle is determined by the following formula: Among them, R ij = 2a i a j / (a i +a j ) In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 is 1; R ij is the harmonic mean radius of particles i and j; a i is the radius of particle i, m; a j is the radius of particle j, m; is the friction force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; v ij is the relative velocity between particles i and j, m / s; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ij is the unit vector pointing from particle i to particle j, dimensionless.

6. The method according to claim 1, wherein: The radial Brownian force exerted on a particle by another particle is determined by the following formula: Among them, R ij = 2a i a j / (a i +a j ) In the formula, For is the Heaviside step function of the independent variable, When less than or equal to 0 is 0, the independent variable When greater than 0 =1; ij (t) is a random number with unit variance, ranging from 0 to 1; R ij is the harmonic mean radius of particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; is the radial Brownian force between particles i and j, N; h ij is the gap width between the surfaces of particles i and j, m; γ is the surface energy of the interface between particles and solution, J / m 2 ;e ij is the unit vector pointing from particle i to particle j, dimensionless; δt is the time step adopted, s; ​​k is the Boltzmann constant, J / K; T is the temperature, K.

7. The method according to claim 1, wherein: The stress generated by the flow field is determined by the following formula: t i =a i r ij F i s / D ij t j =a j r ij F i s / D ij Among them, b=a i a j sinθ / D ij In the formula, r ij is the center distance between particles i and j, r ij =r j -r i , m; r i is the position of the center of particle i, rj is the position of the center of particle j; E is the linear elastic modulus, Pa; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; D ij is the equilibrium distance between particles i and j, m; is the shear force at the center of particle i, N; is the shear force at the center of particle j, N; b is the radius of the interface between particles i and j, m; u ij is the vertical displacement of particles i and j relative to the contact point, m; τ i is the component of shear stress in the i direction, Pa; τ j is the component of shear stress in the j direction, Pa.

8. The method according to claim 1, wherein: Determining the liquid volume fraction of each grid includes: Based on the positions of each particle in the gridded target area, determining the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure; Based on the polydispersity index of the particles in each grid and the influence of the particles in each grid on the structure, the porosity of each grid is determined to be the liquid phase volume fraction of each grid; Preferably, the polydispersity index of particles within a grid is determined by the following formula: Where PDI is the polydispersity index of the particles in the grid; M w is the weight average molecular weight of the particles in the grid; M n is the number average molecular weight of the particles in the grid; M i is the relative molecular mass of the i-th particle in the grid; N is the total number of particles in the grid; Preferably, the influence of particles in each grid on the structure is determined by the following formula: C(r,t)=C(0,t)·expect[-(r / t) 1.5 ] Where r = D ij +R ij , R ij =2a i a j / (a i +a j ) Where C(r, t) is the particle concentration at radius r at time t; C(0, t) is the center particle concentration; D ij is the equilibrium distance between particles i and j, m; a i is the radius of particle i, m; a j is the radius of particle j, m; θ is the angle between the tangent lines of particle i and particle j at the overlap, °; R ij is the harmonic mean radius of particles i and j, m; expect[-(r / t) 1.5 ] refers to the natural constant e -(r / t) 1.5 Power, dimensionless; Preferably, further, the porosity of each grid is determined by the following formula: In the formula, is the porosity, dimensionless; C(r, t) is the particle concentration at radius r at time t, dimensionless; PDI is the polydispersity index of the particles in the grid, dimensionless; V 颗粒 is the volume of a single particle, m 3 ; V 网格 is the grid volume, m 3 .

9. The method according to claim 1, wherein: The flow field velocity in a grid is determined based on the following formula: Among them, S f =∑ i F gi +∑ i F Di +∑ i F Li Where t is time, s; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; τ is the flow field stress distribution, Pa; S f is the force on the particles in the grid, N; g is the acceleration due to gravity, m / s 2 ; α is the liquid volume fraction, dimensionless; F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 ; F Di is the drag force on particle i, N; d i is the diameter of particle i, m; u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless; F Li is the lift force on particle i, N; C L is the lift coefficient, dimensionless.

10. The method according to claim 1, wherein: The combined force of gravity and buoyancy on a particle is determined based on the following formula: In the formula, F gi is the combined force of gravity and buoyancy on particle i, N; m i is the mass of particle i, kg; ρ f is the fluid density, kg / m 3 ; ρ p is the particle density, kg / m 3 ; g is the acceleration due to gravity, m / s 2 .

11. The method according to claim 1, wherein: The drag force on a particle is determined based on the following formula: In the formula, F Di is the drag force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C D is the drag force coefficient, dimensionless.

12. The method according to claim 1, wherein: The lift force of a particle is determined based on the following formula: In the formula, F Li is the lift force on particle i, N; d i is the diameter of particle i, m; ρ f is the fluid density, kg / m 3 ;u f is the flow field velocity, m / s; C L is the lift coefficient, dimensionless.

13. The method according to claim 1, wherein: The velocity and position of a particle in the next time step are determined based on the following formula: In the formula, m i is the mass of particle i, kg; u i is the velocity of particle i, m / s; t is time, s; F ai is the sum of the attractive forces between particle i and the rest of the particles, N; F ri is the sum of the repulsive forces between particle i and the rest of the particles, N; is the sum of the friction forces between particle i and the rest of the particles, N; is the sum of the radial Brownian forces between particle i and the rest of the particles, N; F gi is the combined force of gravity and buoyancy on particle i, N; F Di is the drag force on particle i, N; F Li is the lift force on particle i, N.

14. The method according to claim 1, wherein: The mechanical strength of the particle system is determined based on the following formula: F=F a +F r +F f +F b +F g +F D +F L In the formula, F a is the sum of the attractive forces on each particle, N; F r is the sum of the repulsive forces on each particle, N; F f is the sum of the friction forces on each particle, N; F b is the sum of the radial Brownian forces acting on each particle, N; F g is the sum of the combined force of gravity and buoyancy on each particle, N; F D is the sum of the drag forces on each particle, N; F L is the sum of the lift forces on each particle, N.

15. A method for optimizing the particle size distribution of foam-stabilizing particles, the method comprising the following steps: Determine the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models respectively; adopt the method for determining the packing strength of the foam surface particles according to any one of claims 1 to 14 to determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determine the optimal continuous particle size model; wherein the upper limit of the particle size, the lower limit of the particle size, and the average particle size of each continuous particle size distribution model are the same; Determine respectively the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model; adopt the method for determining the packing strength of foam surface particles described in any one of claims 1 to 14 to determine respectively the packing strength of foam surface particles under the foam stabilizing particle size distribution corresponding to different characteristic parameter values ​​under the optimal continuous particle size model, and then determine the optimal characteristic parameter value under the optimal continuous particle size model.

16. A device for determining the stacking strength of particles on a foam surface, the device comprising: The first module is used to obtain the particle size distribution of the target surface particles and construct the particles according to the particle size distribution of the target surface particles; At the initial moment, the constructed particles are evenly distributed in the gridded target area and an initial velocity is assigned to each constructed particle; The second module is used to determine the repulsive force, attractive force, friction force, radial force Brownian force on each particle in each grid based on the position and velocity of each particle in the gridded target area, determine the stress generated by the flow field in each grid, and determine the liquid phase volume fraction of each grid; The third module is used to determine the flow field velocity in each grid based on the liquid phase volume fraction of each grid and the repulsive force, attractive force, friction force, radial force Brownian force and stress generated by the flow field in each grid on each particle in each grid; The fourth module is used to determine the combined force of gravity and buoyancy, drag force and lift force on each particle in each grid based on the flow field velocity in each grid; The fifth module is used to determine the velocity and position of the particles in the next time step based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid; The sixth module is used to repeatedly use the second module, the third module, the fourth module and the fifth module to determine the speed and position of the particles in each time step until the simulation time requirement is met, and then the mechanical strength of the particle system is determined based on the repulsive force, attractive force, friction force, radial force Brownian force, combined force of gravity and buoyancy, drag force and lift force on each particle in each grid.

17. A device for optimizing the particle size distribution of foam-stabilizing particles, the device comprising: The first unit is used to respectively determine the particle size distribution of the foam stabilizing particles under different continuous particle size distribution models; using the device for determining the packing strength of the foam surface particles according to claim 16, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different continuous particle size models, and then determine the optimal continuous particle size model; wherein the upper limit of the particle size, the lower limit of the particle size, and the average particle size of each continuous particle size distribution model are the same; The second unit is used to respectively determine the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model; using the device for determining the packing strength of the foam surface particles described in claim 16, respectively determine the packing strength of the foam surface particles under the particle size distribution of the foam stabilizing particles corresponding to different characteristic parameter values ​​under the optimal continuous particle size model, and then determine the optimal characteristic parameter value under the optimal continuous particle size model.

18. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 14 and / or the method according to claim 15 when executing the computer program.

19. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the method according to any one of claims 1 to 14 and / or the method according to claim 15.

20. A computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements the method according to any one of claims 1 to 14 and / or the method according to claim 15.

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