A prediction and simulation method for the adsorption of a nanoparticle fluid in a porous medium

Abstract

The present invention discloses a prediction simulation method for the adsorption of nanoparticle fluid in porous media. First, the structure of the porous medium is obtained based on scanning electron microscopy, CT or simulated filling, and then the pore network of the porous medium is extracted based on the pore network extraction algorithm; the diameter of the particles in the porous medium to be measured is estimated, the adsorption rate of a single collector particle is obtained according to the colloid filtration theory, and an adsorption source term is established based on the first-order adsorption kinetic equation; a mass conservation equation is established for the pore bodies in the pore network of the porous medium, a component transport equation for the pore bodies is established based on the adsorption source term and the convective-diffusion equation, and the coupling of adsorption and flow is realized through an adsorption equivalent model; the decoupling of adsorption and flow is realized through a prediction-correction algorithm, and the prediction of the adsorption of particles in the porous medium is achieved. This method solves the problems of poor robustness and small applicable range of the existing particle adsorption prediction model, and improves the convergence and reliability of the prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering nanoparticle fluids, and particularly to a prediction and simulation method for the adsorption of nanoparticle fluids in porous media. Background Art

[0002] The process of engineering nanoparticle fluids flowing through porous media widely exists in fields such as chemical production, oil exploitation, and energy power. Nanoparticles are adsorbed on the surface of porous media under the interaction of colloids, causing the nanoparticles to be retained in the porous media. On the one hand, the particle adsorption phenomenon will change the porous media matrix, resulting in an increase in the maintenance cost of chemical equipment and damage to geological reservoirs. On the other hand, particle adsorption will affect the recycling of nanoparticles, leading to nanoparticle pollution of the ecosystem. Therefore, it is necessary to predict and calculate the particle adsorption phenomenon in porous media. After the particles are adsorbed, the porous media will be changed, thus changing the pore-scale flow. Since the particles are carried by the fluid, this will result in the coupling of particle adsorption and fluid flow. The prediction and calculation methods of particle adsorption phenomena generally include the macroscopic scale and the pore scale. Since particle adsorption occurs at the pore scale, the macroscopic scale method has failed, and it is necessary to simulate this phenomenon at the pore scale.

[0003] The pore-scale calculation methods commonly used for particle adsorption include the Euler-Lagrange method, the lattice Boltzmann method, the pore network model, etc. Among them, the Euler-Lagrange method and the lattice Boltzmann method both track particle particles. Since the calculation resources required for particle tracking are relatively large, the complexity of the calculation and the required calculation resources will further increase with the running of the calculation. This not only places high demands on the storage capacity of the computer, but also greatly increases the calculation time. Therefore, it is not applicable to long-term and high-concentration nanoparticle fluid systems; while the pore network model has not yet combined particle adsorption, porous media matrix, and pore-scale flow. Summary of the Invention

[0004] The purpose of the present invention is to provide a prediction and simulation method for the adsorption of nanoparticle fluids in porous media, which solves the problems of poor robustness and small application range of existing particle adsorption prediction models. By realizing the decoupled calculation of flow and adsorption, the error accumulation is effectively reduced, and the convergence and reliability of the prediction are improved.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A prediction and simulation method for the adsorption of nanoparticle fluids in porous media, and the method is executed by a computer terminal according to the following process:

[0007] Step 1: First, obtain the porous media structure based on scanning electron microscopy, CT, or simulation filling, and then extract the porous media pore network based on the pore network extraction algorithm;

[0008] Step 2: Estimate the diameter of the porous medium particles to be measured, obtain the contact efficiency of a single collector particle according to the colloid filtration theory, and establish an adsorption source term based on the first-order adsorption kinetic equation;

[0009] Step 3: Establish a mass conservation equation for the pore bodies in the pore network of the porous medium extracted in Step 1, establish a component transport equation for the pore bodies based on the adsorption source term in Step 2 and the convective-diffusion equation, and realize the coupling of adsorption and flow through an adsorption equivalent model;

[0010] Step 4: Decouple the adsorption and flow through a prediction-correction algorithm, so as to realize the prediction of the adsorption of the porous medium particles.

[0011] It can be seen from the technical solutions provided by the present invention described above that the above method solves the problems of poor robustness and small application range of the existing particle adsorption prediction model, effectively reduces the error accumulation by realizing the decoupled calculation of flow and adsorption, and improves the convergence and reliability of the prediction. Description of the Drawings

[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0013] Figure 1 It is a schematic flow chart of the prediction simulation method for the adsorption of nanoparticles in a porous medium provided by the embodiment of the present invention;

[0014] Figure 2 It is a schematic diagram of the conversion relationship between the adsorption volume and the throat diameter of the adsorption equivalent model described in the embodiment of the present invention;

[0015] Figure 3 It is a schematic diagram of the pore network obtained from the example of the present invention;

[0016] Figure 4 It is a schematic diagram of the porosity and permeability changing with time obtained from the example of the present invention;

[0017] Figure 5 It is a schematic diagram of the relative concentration field distribution of the numerical experiment at 1000 s obtained from the example of the present invention. Detailed Embodiments

[0018] The following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments, which does not constitute a limitation to the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0019] As Figure 1 shown in the schematic flow chart of the prediction simulation method for the adsorption of nanoparticle fluid in porous media provided by the embodiments of the present invention, the method is executed by a computer terminal according to the following process:

[0020] Step 1: First, obtain the porous medium structure based on scanning electron microscopy, CT, or simulation filling, and then extract the porous medium pore network based on the pore network extraction algorithm;

[0021] In this step, for the packed particle porous medium, the porous medium structure is constructed by simulation filling;

[0022] For the non-packed particle porous medium, obtain the pictures of different cross-sections of the porous medium by scanning electron microscopy or CT, and then obtain the digital file of the geometric structure of the porous medium through picture binarization and pixel matrix processing;

[0023] Then use the pore network extraction algorithm to extract the porous medium pore network; among them, the pore network extraction algorithm includes the largest ball algorithm and the watershed algorithm.

[0024] The pore network extraction algorithm takes the image binarization as the data set of pores and solid phases as the input; uses the connected component labeling method to identify individual pores, detects the connectivity between pores and establishes a topological connection network; in addition, it also extracts the one-dimensional thin wire network skeleton of the pores to simplify the complex structure and reduce the calculation amount. On this basis, a variety of quantitative features are calculated and output, including pore size distribution (volume, diameter, area, aspect ratio, etc.), connectivity, and connection relationship.

[0025] Step 2: Estimate the diameter of the particles in the porous medium to be measured, obtain the contact efficiency of a single collector particle according to the colloid filtration theory, and establish an adsorption source term based on the first-order adsorption kinetic equation;

[0026] In this step, for the porous medium formed by fillers, determine the particle diameter according to the material situation; for the porous medium formed by non-fillers, perform pore network extraction on the matrix and statistically analyze the equivalent particle diameter of the matrix;

[0027] The colloid filtration theory fits the correlation formula of the contact efficiency of a single collector particle through a method combining theoretical analysis and experiments. Generally, an appropriate correlation formula can be selected according to the actual problems of nanoparticles and porous media. If there are relevant column-scale experiments, the experimental data of the contact efficiency of a single collector particle can also be used. The contact efficiency η of a single collector particle obtained according to the colloid filtration theory is expressed as:

[0028]

[0029] Among them, A S is a porosity-related parameter, and the expression is:

[0030] A S = 2(1 - γ 5 ) / (2 - 3γ + 3γ 5 - 2γ 6 ), γ = (1 - θ) 1 / 3 ;

[0031] N R is the diameter ratio, and the expression is

[0032] N Pe is the Péclet number, and the expression is

[0033] N vdw is the van der Waals number, and the expression is A / k b T;

[0034] N A is the gravitational number, and the expression is

[0035] N G is the gravity number, and the expression is

[0036] In the formula, θ is the porosity; d p is the diameter of the nanoparticle, m; d c is the diameter of the collector particle, m; U is the throat velocity, m / s; D ∞ is the diffusion coefficient of the nanoparticle, m 2 / s; A is the Hamaker constant, J; k b is the Boltzmann constant, 1.38*10 -23 m 2 ·kg·s -2 ·K; T is the temperature, K; μ is the fluid viscosity Pa·S; a p is the radius of the nanoparticle, m; ρ p is the density of the nanoparticle, kg / m 3 ; ρ f is the density of the fluid, kg / m3 ; g is the acceleration due to gravity, m / s 2 ;

[0037] In a specific implementation, if the contact efficiency of a single collector particle is obtained through experiments, such as η = 0.8, the above formula does not need to be used for calculation.

[0038] The adsorption rate k of a single collector particle f The relationship with the contact efficiency η of a single collector particle is shown in the following formula:

[0039]

[0040] Then, substitute the adsorption rate k of a single collector particle f into the first-order adsorption kinetic equation to establish an adsorption source term. Taking the first-order irreversible adsorption as an example, it is expressed as:

[0041]

[0042] In the formula, C is the concentration of pore body nanoparticles, 1 / m 3 .

[0043] Step 3: Establish a mass conservation equation for the pore bodies in the pore network of the porous medium extracted in Step 1, establish a component transport equation for the pore bodies based on the adsorption source term in Step 2 and the convective diffusion equation, and realize the coupling of adsorption and flow through an adsorption equivalent model;

[0044] In this step, the mass conservation equation for the pore bodies in the pore network of the porous medium is realized based on the pore bodies and throats. Each pore body in the pore network of the porous medium conforms to the mass conservation equation, and the flow between the pores is an incompressible flow of Newtonian fluid. For each pore body, there is:

[0045]

[0046] In the formula, p i is the pressure to be solved for pore i, Pa; n i is the pore adjacent to pore i; N p is all the pores in the pore network; is the hydraulic conductivity between pore i and pore j, m 3 / (Pa·s);

[0047] Establish a component transport equation for the pore bodies to calculate the transport and adsorption of nanoparticles between the pores. For each pore body, there is:

[0048]

[0049]

[0050] where ΔV is the pore volume, m 3 ; Δt is the computational time step; Q ij is the volumetric flow rate, m 3 / s; is the adsorption source term, 1 / (s·m 3 );

[0051] The adsorption equivalent model converts the adsorption source term into an adsorption volume, transfers the local adsorption volume to the whole throat, and updates the throat diameter and the transport conductivity coefficient. The conversion relationship between the adsorption volume and the throat diameter of the adsorption equivalent model is as Figure 2 shown, that is: the particles adsorbed locally are uniformly calculated as the adsorption volume; then the adsorption volume is averaged over the whole throat; the throat diameter is reduced, and the transport conductivity coefficient is recalculated.

[0052] Step 4. Decouple adsorption and flow through the predictor-corrector algorithm, so as to realize the prediction of particle adsorption in porous media

[0053] In this step, specifically, a computational time step and a termination time are set. The computational time step is Δt in the component transport equation established in Step 3, and the termination time can be a fixed value or the time corresponding to a certain condition;

[0054] First, based on the pore network of the porous medium obtained in Step 1, it is divided into two cases:

[0055] If it is the zero time layer, initialize the mass conservation equation established in Step 3, initialize the component transport equation established in Step 3, and calculate the component transport equation according to the pressure-flow distribution obtained from the initialized mass conservation equation;

[0056] If it is a non-zero time layer, calculate the component transport equation according to the pressure-flow distribution of the previous time layer; then, based on the calculation results of the component transport equation, calculate the adsorption volume, the throat topology change amount, and the transport conductivity coefficient, and complete the prediction of the transport conductivity coefficient of this time layer;

[0057] Then, transfer the predicted transport conductivity coefficient to the correction module. The correction module calculates the mass conservation equation and the component transport equation of this time layer in turn, and updates the adsorption volume, the throat topology change amount, and the transport conductivity coefficient to complete the correction of the transport conductivity coefficient of this time layer;

[0058] Subsequently, it is judged whether the set termination time is reached. If so, the program ends; if not, the predictor-corrector of the next computational time layer is performed to realize the prediction of particle adsorption in porous media.

[0059] It should be noted that the content not described in detail in the embodiments of the present invention belongs to the prior art well known to those skilled in the art.

[0060] The method of the present invention will be illustrated by a specific example below. The packed column is a common porous medium, which is widely used in the fields of environmental ecology, chemical engineering, etc. It is formed by filling a specified packed column area with packed particles of a fixed shape. This example takes the adsorption test of packed column nanoparticles as an example:

[0061] Table 1 Numerical test conditions of the packed column

[0062] Injection velocity of nanoparticles (m / s) 1e-3 Volume fraction of nanoparticles 0.48％ Size of nanoparticles (nm) 2000 Simulation time (s) 2000

[0063] Step 1: A porous medium is generated by using a simulation filling method. The packed column is formed by packing spherical particles. The properties of the packed column are shown in Table 2 below:

[0064] Table 2 Properties of the packed column

[0065]

[0066] Subsequently, the watershed algorithm is used to extract the pore network of the packed column, and the obtained pore network is as Figure 3 shown.

[0067] Step 2: This is the filling of regular particles. The diameter of the material is 1.3e-3. The contact efficiency of a single collector particle is calculated according to the following formula:

[0068]

[0069] The relationship between the adsorption rate of a single collector particle and the contact efficiency of a single collector particle is shown in the following formula:

[0070]

[0071] After calculation, the adsorption rates of the pores numbered [1001 - 1010] are

[0072]

[0073] This numerical test is an irreversible adsorption. The first-order adsorption kinetic equation is used to establish the adsorption source term, which is expressed as:

[0074]

[0075] After calculation, the adsorption source terms of the pores numbered [1001 - 1010] are

[0076]

[0077] Step 3: A mass conservation equation is established for the pore bodies in the extracted pore network. Based on Step 2 and the convective-diffusion equation, a component transport equation for the pore bodies is established, and the coupling of adsorption and flow is realized through an adsorption equivalent model.

[0078] The mass conservation equation of pore bodies in the pore network model is based on pore bodies and throats. Each pore body in the pore network conforms to the mass conservation equation, and the flow between pores is an incompressible flow of Newtonian fluid. For each pore body, there is:

[0079]

[0080] After calculation, the pressure of the pores numbered [1001 - 1010] is

[0081]

[0082] Establish a component transport equation in the pore body to calculate the transport and adsorption of nanoparticles between pores. For each pore body, there is:

[0083]

[0084]

[0085] After calculation, the relative concentration of the pores numbered [1001 - 1010] is

[0086]

[0087] The adsorption equivalent model converts the adsorption source term into an adsorption volume, transfers the local adsorption volume to the whole throat, and then updates the throat diameter and transport conductivity coefficient. That is, the particles adsorbed locally are uniformly calculated as an adsorption volume, and then this adsorption volume is averaged over the whole throat. The throat diameter decreases, and the transport conductivity coefficient is recalculated.

[0088] Step 4: Decouple the flow and adsorption through the predictor-corrector algorithm to achieve the prediction of particle adsorption in porous media.

[0089] Specifically, first initialize the pore network of the computational domain, initialize the mass conservation equation, and initialize the component transport equation;

[0090] Then calculate the component transport equation to obtain the adsorption volume and pore geometry. The adsorption volume and pore geometry are only provided to the transport conductivity coefficient and do not need to be updated in the calculation storage module; calculate and update the transport conductivity coefficient according to the adsorption volume and pore geometry. This process is called prediction;

[0091] Subsequently, calculate the mass conservation equation and the component transport equation according to the predicted transport conductivity coefficient, update the adsorption volume and pore geometry, and recalculate and update the transport conductivity coefficient. This process is called correction;

[0092] In this numerical experiment, the simulation time, i.e., the termination time, is 2000 s, and the time step is taken as 1 s for simulation. As Figure 4The following is a schematic diagram showing the changes in porosity and permeability over time in an example of the present invention. The porosity is on the left side and the permeability is on the right side. From Figure 4 it can be seen that as the simulation time increases, nanoparticles adsorb, the pore volume gradually decreases, and the porosity decreases. Due to the decrease in porosity, the fluidity of the porous medium decreases, and the permeability also decreases.

[0093] The following uses a specific example to illustrate the method of the present invention. This example can be used to clarify the research on the influence law between nanoparticle adsorption and pore-scale flow. Taking a two-dimensional regular ball-and-stick pore network model as an example, a pore network model with a size of 50×50 in the x and y directions is given. The pore bodies and throats are generated using a normal distribution; the distance from pore body to pore body is 433 μm; the average diameter of the pore bodies is 165 μm, and the standard deviation is 66 μm; the average diameter of the throats is 121 μm, and the standard deviation is 62 μm;

[0094] Table 3 Numerical test conditions for the two-dimensional regular ball-and-stick pore network model

[0095] Injection velocity of nanoparticles (m / s) 1e-3 Volume fraction of nanoparticles 0.31％ Size of nanoparticles (nm) 1000 Simulation time (s) 1000

[0096] The ball-and-stick pore network has been given, so step one can be omitted. Steps two to four are the same as the corresponding parts in Example 1.

[0097] As Figure 5 shown is a schematic diagram of the relative concentration field distribution in the numerical test at 1000 s in an example of the present invention. From Figure 5 it can be seen that there is uneven adsorption of nanoparticles in the direction, highlighting the heterogeneity of the porous medium. The concentration is high at the left inlet and gradually decreases due to gradual adsorption.

[0098] In summary, the method described in the embodiments of the present invention realizes the simulation of nanoparticle retention phenomena at the pore scale, can explore and reveal the mechanism of retention phenomena at the pore scale, and clarify the influence law between nanoparticle adsorption and pore-scale flow; this method reasonably simplifies the geometric model, greatly shortens the calculation time for predicting particle retention phenomena in porous media, and has important engineering application value.

[0099] In addition, those of ordinary skill in the art can understand that all or part of the steps in implementing the above method embodiments can be completed by instructing relevant hardware through a program, and the corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk, an optical disc, etc.

[0100] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims. The information disclosed in the background art part of this article is only intended to deepen the understanding of the overall background art of the present invention, and should not be regarded as an admission or imply in any form that this information constitutes the prior art known to those skilled in the art.

Claims

1. A method for predicting and simulating the adsorption of nanoparticle fluid in porous media, characterized in that: The method is performed by a computer terminal according to the following process: Step 1: First, the porous medium structure is obtained based on scanning electron microscopy, CT or simulated filling, and then the porous medium pore network is extracted based on the pore network extraction algorithm; Step 2: Estimate the diameter of the porous medium particles to be tested, obtain the contact efficiency of a single collector particle according to the colloidal filtration theory, and establish the adsorption source term based on the first-order adsorption kinetic equation; Step 3: Establish a mass conservation equation for the pores in the porous medium pore network extracted in step 1, establish a component transport equation for the pores based on the adsorption source term and convection-diffusion equation in step 2, and realize the coupling of adsorption and flow through an adsorption equivalent model; Step 4: Decoupling adsorption and flow is achieved through the prediction and correction algorithm, thereby realizing the prediction of porous medium particle adsorption; the process of step 4 is specifically as follows: Set a calculation time step and end time. The calculation time step is Δt in the component transport equation established in step 3. The end time is a fixed value or the time corresponding to a certain condition. First, based on the porous media pore network obtained in step 1, it is divided into two cases: If it is a zero-time layer, initialize the mass conservation equation established in step 3, initialize the component transport equation established in step 3, and calculate the component transport equation based on the pressure flow distribution obtained by initializing the mass conservation equation; If it is a non-zero time layer, the component transport equation is calculated based on the pressure-flow distribution of the previous time layer; Then, based on the calculation results of the component transport equation, the adsorption volume, throat topology change, and transport conductivity are calculated to estimate the transport conductivity of the current layer; Then the estimated transport conductivity coefficient is passed to the correction module, which calculates the mass conservation equation and component transport equation of the current time layer in turn, and updates the adsorption volume, throat topology change and transport conductivity coefficient to complete the correction of the transport conductivity coefficient of the current time layer; Then it is determined whether the set end time has been reached. If so, the program ends; if not, an estimated correction is performed for the next calculation layer, thereby realizing the prediction of porous medium particle adsorption.

2. The method for predicting and simulating adsorption of nanoparticle fluid in porous media according to claim 1, characterized in that: In step 1, for a porous medium filled with particles, a porous medium structure is constructed by simulating filling; For non-filled particle porous media, images of different cross sections of the porous media are obtained by scanning electron microscopy and CT, and then the digital files of the geometric structure of the porous media are obtained by binarization and pixel matrix processing; Then, the pore network of the porous medium is extracted using a pore network extraction algorithm; wherein the pore network extraction algorithm includes a maximum sphere algorithm and a watershed algorithm; The pore network extraction algorithm uses a data set of pores and solid phases obtained by binarizing an image as input; uses a connected domain labeling method to identify individual pores, detects the connectivity between pores and establishes a topological connection network; and calculates and outputs a variety of quantitative features, including pore size distribution, connectivity, and connection relationships.

3. The method for predicting and simulating adsorption of nanoparticle fluid in porous media according to claim 1, characterized in that: In step 2, for porous media formed by fillers, the particle diameter is determined according to the material conditions; for porous media formed by non-fillers, the pore network of the matrix is ​​extracted and the equivalent particle diameter of the matrix is ​​calculated; According to the colloidal filtration theory, the contact efficiency η of a single collector particle is expressed as: Among them, A S is a porosity-related parameter, and its expression is: A S =2(1-γ 5 ) / (2-3c+3c 5 -2c 6 ),γ=(1-θ) 13 ; N R is the diameter ratio, and the expression is N Pe is the Pellet number, expressed as N vdw is the van der Waals number, expressed as A / k b T; N A is the gravitational number, and the expression is N G is the gravity number, and the expression is Where θ is the porosity; d p is the nanoparticle diameter; d c is the collector particle diameter; U is the throat velocity; D ∞ is the nanoparticle diffusion coefficient; A is the Hamaker constant; k b is the Boltzmann constant; T is the temperature; μ is the fluid viscosity; a p is the nanoparticle radius; ρ p is the nanoparticle density; ρ f is the fluid density; g is the acceleration due to gravity; Single collector particle adsorption rate k f The relationship with the contact efficiency η of a single collector particle is shown as follows: Then the adsorption rate of a single collector particle k f Substitute the first-order adsorption kinetics equation to establish the adsorption source term. Taking the first-order irreversible adsorption as an example, it is expressed as: Where C is the concentration of porous nanoparticles.

4. The method for predicting and simulating adsorption of nanoparticle fluid in porous media according to claim 1, characterized in that: In step 3, the established pore mass conservation equation in the porous media pore network is implemented based on the pores and throats. Each pore in the porous media pore network conforms to the mass conservation equation, and the flow between pores is an incompressible flow of Newtonian fluid. For each pore, there is: In the formula, p i is the pressure to be solved for pore i; n i is the pores adjacent to pore i; N p is all the pores in the pore network; is the hydraulic conductivity coefficient between pore i and pore j; The component transport equation is established in the pores to calculate the transport and adsorption of nanoparticles between pores. For each pore, there is: Where ΔV is the pore volume; Δt is the calculation time step; Q ij is the volume flow rate; is the adsorption source term; The adsorption equivalent model converts the adsorption source term into the adsorption volume, converts the local adsorption volume to the entire throat, and updates the throat diameter and transport conductivity. Specifically, the conversion relationship between the adsorption volume and the throat diameter of the adsorption equivalent model is: The locally adsorbed particles are uniformly calculated as the adsorption volume; this adsorption volume is then averaged over the entire throat; the throat diameter is reduced and the transport conductivity is recalculated.

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