Computer-based simulation method and system for thermal desorption, mass transfer, and heat transfer

Abstract

This application provides a computer simulation-based method and system for simulating thermal desorption, mass transfer, and heat transfer, relating to the field of computer simulation technology. This application obtains a constructed geometric model of a contaminated soil pile and acquires multiple sets of pore pressure gradients at different depths within the contaminated soil pile at different times, along with corresponding gas Darcy velocities. Support vector regression is used to perform regression analysis on these multiple sets of pore pressure gradients and gas Darcy velocities to calculate the permeability tensor. The Darcy resistance term in the momentum conservation equation is corrected based on the permeability tensor of each grid cell, generating a gas flow equation for each grid cell. The gas flow equations of all grid cells are then combined to obtain the gas velocity field. The velocity vector is used as a convection parameter and substituted into the pre-set heat transport equation and pollutant transport equation to obtain the simulation results of thermal desorption, mass transfer, and heat transfer, achieving accurate simulation of the dynamic permeability changes caused by the gas slippage effect under high vacuum extraction.

Description

Technical Field

[0001] This application relates to the field of computer simulation technology, and in particular to a computer simulation-based method and system for simulating thermal desorption, mass transfer, and heat transfer. Background Technology

[0002] Remediation of organically contaminated sites is receiving increasing attention, with ex-situ slope-pile thermal desorption combined with gas phase extraction technology becoming a mainstream remediation method due to its high efficiency and wide applicability. To optimize process parameters, reduce energy consumption, and ensure remediation compliance, computer-simulated mass and heat transfer methods are widely used to predict soil warming processes and pollutant removal efficiency, showing broad application prospects in guiding engineering design and construction.

[0003] Existing thermal desorption simulation methods typically construct porous media seepage models based on Darcy's law, assuming a linear relationship between fluid velocity and pressure gradient, and then couple heat conduction and component transport equations for numerical calculations. These methods perform reasonably well in simulating conventional low-pressure or highly permeable media, and some commercial software can already perform basic heat-fluid coupling simulations.

[0004] However, in actual high-vacuum extraction of low-permeability soils, the slippage effect generated by gas flow in micropores causes fluid motion to deviate from the linear Darcy's law, exhibiting strong nonlinear characteristics. Existing simulation methods based on the linear Darcy's law cannot describe this dynamic permeability change, leading to significant errors in simulating gas flow fields under high-vacuum conditions, and consequently causing severe distortion in the predictions of convective heat transfer and contaminant migration. Therefore, existing technologies suffer from the technical problem of being unable to accurately simulate the thermal desorption mass and heat transfer process under non-Darcy flow conditions. Summary of the Invention

[0005] The purpose of this application is to provide a computer simulation-based method and system for simulating thermal desorption mass transfer and heat transfer, in order to solve the technical problem in the prior art that it is impossible to accurately simulate the thermal desorption mass transfer and heat transfer process under non-Darcy flow conditions.

[0006] In a first aspect, this application provides a computer simulation-based method for simulating thermal desorption, mass transfer, and heat transfer, including:

[0007] Obtain the geometric model of the constructed contaminated soil pile, and obtain multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding Darcy flow velocities of the gas at those locations;

[0008] Multiple sets of pore pressure gradients and gas Darcy velocities were regressed using support vector regression. The kernel function of support vector regression was used to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations. The geometric model was discretized into multiple grid cells, and the permeability tensor of each grid cell was calculated according to the constitutive relations.

[0009] The gas flow equation for each grid cell is generated by correcting the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell.

[0010] The gas flow equations of all grid cells are combined to obtain the gas flow equation system. The gas velocity field is obtained by iteratively solving the gas flow equation system using the finite volume method. The gas velocity field includes velocity vector and pressure data.

[0011] By substituting the velocity vector as a convection term parameter into the preset heat transfer equation and pollutant transport equation, the convective heat transfer process of hot air and the migration process of gasified pollutants are simulated through multiphysics field coupling calculations, and the simulation results of thermal desorption mass transfer and heat transfer are obtained.

[0012] Optionally, support vector regression is used to perform regression analysis on multiple sets of pore pressure gradients and gas Darcy velocities. The kernel function of support vector regression is used to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations, including:

[0013] Multiple sets of pore pressure gradients are used as feature data, and multiple sets of gas Darcy velocities are used as label data. A regression training sample set is constructed based on the feature data and label data.

[0014] The regression training sample set is input into support vector regression to calculate the feature inner product of the feature data in the high-dimensional feature space using the kernel function of support vector regression, and a quadratic programming objective function is constructed based on the feature inner product.

[0015] The quadratic programming objective function is solved using the labeled data as constraints to obtain the optimal solution vector, and support vectors and Lagrange multipliers corresponding to the support vectors are extracted from the optimal solution vector.

[0016] A regression decision function is constructed using support vectors and Lagrange multipliers, and this regression decision function is used as a constitutive relation to represent the nonlinear relationship between pore pressure gradient and gas Darcy velocity.

[0017] Secondly, this application provides a computer-simulated thermal desorption mass transfer and heat transfer simulation system, including:

[0018] The acquisition module is used to acquire the geometric model of the constructed contaminated soil pile and to acquire multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding Darcy flow velocities of the gas.

[0019] The analysis module is used to perform regression analysis on multiple sets of pore pressure gradients and gas Darcy velocities using support vector regression. It uses the kernel function of support vector regression to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations, discretizes the geometric model into multiple grid cells, and calculates the permeability tensor of each grid cell according to the constitutive relations.

[0020] The correction module is used to correct the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell, and generate the gas flow equation for each grid cell.

[0021] The simultaneous equation module is used to combine the gas flow equations of all grid cells to obtain a gas flow equation set. The gas velocity field is obtained by iteratively solving the gas flow equation set using the finite volume method. The gas velocity field includes velocity vectors and pressure data.

[0022] The simulation module is used to substitute the velocity vector as a convection term parameter into the preset heat transfer equation and pollutant transport equation, respectively. Through multi-physics field coupling calculation, it simulates the convective heat transfer process of hot air and the migration process of gasified pollutants, and obtains the simulation results of thermal desorption mass transfer and heat transfer.

[0023] Thirdly, this application provides an electronic device, comprising:

[0024] Memory, used to store computer programs;

[0025] A processor is used to execute a computer program to implement the steps of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method as described in the first aspect above.

[0026] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method described in the first aspect above.

[0027] The computer simulation-based thermal desorption mass and heat transfer simulation method provided in this application overcomes the problem of inaccurate boundary condition settings caused by relying solely on theoretical assumptions by collecting multi-temporal and spatial pore pressure gradient and gas Darcy velocity data. It achieves dynamic permeability tensor calculation for each discrete grid cell, enabling the simulation model to accurately characterize the conductivity of the soil medium as pressure changes, solving the problem that existing technologies cannot describe non-Darcy flow characteristics due to the use of fixed permeability. It ensures mass and momentum conservation under nonlinear flow resistance conditions, thereby calculating a gas velocity field that accurately reflects non-Darcy flow characteristics, correcting the problem of large calculation errors in flow field distribution when simulating high vacuum conditions in existing technologies. It avoids errors in predicting convective heat transfer efficiency and pollutant migration paths due to flow field distortion, improving the credibility and engineering guidance value of simulations of ex-situ slope-pile thermal desorption combined with gas phase extraction processes.

[0028] Furthermore, this application constructs a regression training sample set by using multiple sets of pore pressure gradients as feature data and multiple sets of gas Darcy velocities as label data. This sample set is then input into support vector regression to calculate the inner product of features in the high-dimensional feature space using a kernel function, and to construct a quadratic programming objective function. The optimal solution vector is then obtained by using the label data as constraints, and support vectors and Lagrange multipliers are extracted. Finally, the support vectors and Lagrange multipliers are used to construct a regression decision function as a constitutive relation describing the nonlinear correspondence. This overcomes the technical barrier that existing linear simulation models cannot adapt to complex working conditions such as high vacuum and low permeability. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 A schematic flowchart of a computer simulation-based thermal desorption mass transfer and heat transfer simulation method provided in an embodiment of this application;

[0031] Figure 2 A flowchart illustrating a method for obtaining constitutive relations provided in an embodiment of this application;

[0032] Figure 3 A flowchart illustrating a method for obtaining the temperature distribution field and pollutant concentration distribution field at each time step, provided in an embodiment of this application;

[0033] Figure 4 A schematic diagram of the structure of a computer-simulated thermal desorption mass transfer and heat transfer simulation system provided in this application embodiment;

[0034] Figure 5 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0035] To address the technical problem that existing simulation methods based on linear Darcy's law cannot describe the nonlinear fluid motion characteristics of low-permeability soil under high vacuum extraction conditions caused by gas slippage, resulting in large simulation errors in gas flow field and distortion in the prediction of convective heat transfer and pollutant migration.

[0036] This application captures real nonlinear rheological characteristics by acquiring measured data of pore pressure gradients and gas Darcy velocity in multiple spatiotemporal dimensions. Then, it uses the kernel function mapping capability of support vector regression to construct a constitutive relation that can characterize the slip effect. Based on this, it calculates the permeability tensor that reflects the dynamic conductivity of the medium. The tensor is then used to physically correct the Darcy drag term in the momentum conservation equation. Finally, by combining the finite volume method with multiphysics coupling calculation, it achieves accurate simulation of heat transfer and pollutant migration processes under non-Darcy flow conditions.

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] The core of this application is to provide a computer simulation-based method for simulating thermal desorption mass and heat transfer, and a flowchart of one specific implementation is shown below. Figure 1 As shown, the method includes:

[0039] Step 101: Obtain the geometric model of the constructed contaminated soil pile and obtain multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding Darcy flow velocities.

[0040] In this step, the contaminated soil mound refers to a solid structure formed by piling up excavated organically contaminated soil at the treatment site according to a predetermined shape and volume. It typically contains heating electrodes and a gas extraction pipeline network. The geometric model refers to a virtual mathematical model constructed in computer simulation software to digitally characterize the three-dimensional spatial morphology, dimensions, and boundary conditions of the contaminated soil mound. It can be a cuboid, frustum, or other irregular polyhedral structure. The pore pressure gradient refers to the rate of change of pore fluid pressure per unit distance within the soil, reflecting the local dynamic intensity driving gas flow in minute pores; its physical unit is usually Pascals per meter. The Darcy velocity refers to the volumetric flow rate of gas through a unit cross-sectional area of ​​a porous medium, also known as the apparent velocity, used to macroscopically quantify the gas seepage rate; its physical unit is usually meters per second.

[0041] In this embodiment, computer-aided design software is first used to establish a three-dimensional geometric model consistent with the actual size of the contaminated soil pile based on the design drawings of the actual engineering site or laser scanning data of the soil pile on site, and the boundaries of the heating zone and the extraction zone are delineated. Next, during the actual ex-situ remediation operation, micro-differential pressure sensors pre-embedded at different depths within the contaminated soil pile, such as shallow layer A1, middle layer A2, and deep layer A3, are used to collect pressure difference data at each measuring point relative to atmospheric pressure or adjacent measuring points. The pore pressure gradient data at that location is calculated by combining the spatial distance between the measuring points, and denoted as G.

[0042] Simultaneously, high-precision thermal gas flow meters installed at each extraction wellhead or branch pipeline associated with the aforementioned measurement points are used to collect gas mass flow rate data at that moment. This data, combined with the cross-sectional area of ​​the extraction pipe and gas density parameters, is used to calculate the corresponding Darcy velocity data, denoted as V. To capture the nonlinear rheological characteristics of the soil medium under different working conditions, multiple sets of data pairs need to be collected continuously or intermittently at different times during the remediation process, such as T1, T2, and T3, forming a training dataset that includes both spatiotemporal dimensions.

[0043] For example, the pore pressure gradient G1 at depth A1 at time T1 and the corresponding gas Darcy velocity V1 can be obtained, as well as the pore pressure gradient G2 at depth A2 at time T2 and the corresponding gas Darcy velocity V2. These data directly reflect the macroscopic flow response generated by pressure driving forces of different intensities under the current soil structure and moisture content conditions.

[0044] Step 102: Perform regression analysis on multiple sets of pore pressure gradients and gas Darcy velocities using support vector regression. Use the kernel function of support vector regression to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations. Discretize the geometric model into multiple grid cells and calculate the permeability tensor of each grid cell according to the constitutive relations.

[0045] In this step, Support Vector Regression (SVR) is a machine learning algorithm based on statistical learning theory. It finds an optimal hyperplane to fit the nonlinear regression relationship of the data, exhibiting strong generalization ability. The kernel function in SVR is a mathematical function used to map a low-dimensional nonlinear problem to a high-dimensional space, making it linearly separable. It can be a radial basis function, a polynomial function, etc. The high-dimensional feature space refers to the abstract vector space in which the data resides after mapping by the kernel function; its dimension is typically much higher than the original data space.

[0046] Constitutive relations are mathematical models that describe the physical relationship between a material's response and excitation under stress or field conditions; here, they specifically refer to the nonlinear correspondence between pore pressure gradient and Darcy velocity of gas. A mesh element is the smallest computational domain formed by discretizing a continuous geometric model; it can be hexahedral, tetrahedral, or other shapes. The permeability tensor is a matrix of directional coefficients describing the conductivity of porous media, typically expressed as a diagonal matrix.

[0047] The training of the support vector regression model in this application is a systematic optimization process aimed at learning and establishing accurate mapping relationships from measured data including nonlinear features. This process follows the principle of minimizing structural risk to ensure that the model has good generalization ability while fitting the training data. The training process mainly includes the following stages:

[0048] Data preprocessing: First, the feature data, namely the pore pressure gradient and the label data, namely the gas Darcy velocity, in the regression training sample set are standardized.

[0049] Kernel function selection and parameter initialization: Based on the expected complex nonlinear relationship between the pore pressure gradient and the gas Darcy velocity, a Gaussian radial basis kernel function with strong nonlinear mapping capabilities is selected. Simultaneously, key hyperparameters of the model are initialized, including the penalty coefficient, the insensitive loss parameter, and the kernel function's bandwidth parameter. The initial values ​​of these parameters can be set according to the data characteristics and optimized in subsequent steps.

[0050] Problem Construction and Solution: Based on the selected kernel function and hyperparameters, the regression problem is transformed into a convex quadratic programming problem. The objective function of this problem aims to minimize structural risk, and its constraints ensure that the model prediction error is controlled within a pre-defined insensitivity band. Efficient algorithms such as sequential minimum optimization are employed to solve this quadratic programming problem. This algorithm iteratively updates the Lagrange multipliers until all conditions are satisfied, thereby obtaining the global optimum.

[0051] Model Construction: From the optimal Lagrange multiplier vectors obtained from the solution, support vectors are identified, i.e., those training samples that play a decisive role in the decision boundary. Using these support vectors and their corresponding multipliers, the bias term of the regression decision function is calculated. Finally, the support vectors, Lagrange multipliers, kernel function, and bias term are integrated to construct a complete regression decision function. Considering that both the pressure gradient and gas velocity are three-dimensional vectors, this application trains three independent support vector regression models, corresponding to the component prediction of velocity in the x, y, and z directions, respectively, or adopts a multi-output support vector regression architecture to establish a nonlinear constitutive relationship from the three-dimensional pressure gradient space to the three-dimensional velocity space.

[0052] Hyperparameter tuning and validation: To obtain optimal model performance, cross-validation was used to systematically tune the initially set hyperparameters. The model's performance metrics on the validation set were evaluated under multiple hyperparameter combinations, and the set of hyperparameters with the strongest generalization ability was selected. Finally, the model was retrained using all training samples and the optimal hyperparameters to obtain the final support vector regression model for subsequent simulation calculations.

[0053] like Figure 2 As shown, Figure 2 This is a flowchart illustrating a method for obtaining constitutive relations, provided as an embodiment of this application.

[0054] Step 201: Use multiple sets of pore pressure gradients as feature data and multiple sets of gas Darcy velocities as label data to construct a regression training sample set based on the feature data and label data.

[0055] In this step, feature data refers to the set of data used as input variables in the machine learning model. Label data refers to the set of data corresponding to the feature data and used as the learning target of the model in the supervised learning model. The regression training sample set refers to the dataset used to train the regression model, which consists of paired feature data and label data.

[0056] In this embodiment, all collected pore pressure gradient and gas Darcy velocity data are systematically processed. Each measured pore pressure gradient value is defined as an input feature of a sample, denoted as... The Darcy velocity value of the gas measured at the same time and space location is defined as the output label corresponding to the sample, denoted as . All These data pairs are combined to form a training sample set for machine learning regression analysis. For example, data collected from two depths (A1, A2) and two time points (T1, T2) can be used to construct a dataset containing four samples: ,in and These represent the measured pressure gradient and Darcy velocity at time T1 and depth A1, respectively.

[0057] Step 202: Input the regression training sample set into support vector regression, so as to use the kernel function of support vector regression to calculate the feature inner product of the feature data in the high-dimensional feature space, and construct a quadratic programming objective function based on the feature inner product.

[0058] In this step, the inner product of features refers to the result of performing an inner product operation on two feature vectors in a high-dimensional feature space, which is directly calculated using a kernel function. The objective function of a quadratic programming problem is an optimization function whose mathematical form is a quadratic function, and which seeks to minimize or maximize it under a series of linear equality or inequality constraints.

[0059] In this embodiment of the application, the constructed regression training sample set is... The input is then fed into the support vector regression algorithm model. First, a suitable kernel function is selected. For example, the Gaussian radial basis kernel function is shown in formula (1):

[0060] (1)

[0061] in The kernel parameter is used. This kernel function can directly calculate the inner product of any two sample features in a high-dimensional feature space. For example, calculation Based on this, we construct a system using Lagrange multipliers. and The objective function for optimizing the variables is a quadratic programming problem, as shown in formula (2):

[0062] (2)

[0063] in, This is a preset insensitive loss parameter used to control the regression model's tolerance to prediction errors; for example, it can be set to 0.01. To represent the label observation corresponding to the i-th sample, in regression involving three-dimensional vectors, regression equations can be established for the components of the three dimensions x, y, and z respectively.

[0064] Step 203: Solve the quadratic programming objective function using the label data as constraints to obtain the optimal solution vector, and extract the support vectors and the corresponding Lagrange multipliers from the optimal solution vector.

[0065] In this step, the optimal solution vector refers to the set of Lagrange multipliers that minimize the quadratic programming objective function under given constraints. Support vectors refer to the Lagrange multipliers in the training samples that correspond to the optimal solution. or Non-zero sample points play a decisive role in the construction of the final regression model.

[0066] In the embodiments of this application, under specific constraints, typically including , as well as ,in Let be the penalty coefficient, for example, set to 1.0. Solving the quadratic programming objective function yields a set of optimal Lagrange multiplier vectors. From this optimal solution vector, select those corresponding... or Non-zero sample points are called support vectors. For example, after solving, we might find that sample points 1, 2, and 4 correspond to... If the values ​​are not zero, then they constitute a support vector set, denoted by the set of indices. Their corresponding Lagrange multipliers are respectively , as well as .

[0067] Step 204: Construct a regression decision function using support vectors and Lagrange multipliers, and use the regression decision function as a constitutive relation to represent the nonlinear relationship between pore pressure gradient and gas Darcy velocity.

[0068] In this step, the regression decision function refers to the mathematical function used to predict the output of new input feature data after the support vector regression model has been trained.

[0069] In this embodiment, the final decision function for support vector regression is constructed using support vectors and their corresponding Lagrange multipliers. This function can handle any new pore pressure gradient input. The corresponding gas Darcy velocity is predicted as shown in formula (3):

[0070] (3)

[0071] in, This is the bias term, which can be calculated using support vectors. This decision function... This refers to the constitutive relation constructed in this invention. It quantitatively describes the pore pressure gradient. With gas Darcy velocity The complex nonlinear mapping relationship between them, i.e. For example, for a newly calculated pressure gradient The Darcy velocity of the gas under these conditions was predicted.

[0072] Step 211: Divide the geometric model into multiple indexed mesh elements by hexahedral meshing.

[0073] In this step, hexahedral meshing refers to dividing a three-dimensional geometry into a set of multiple hexahedral elements, which is a common method for spatial discretization in the finite element or finite volume method.

[0074] In this embodiment, during the numerical simulation preprocessing stage, the established three-dimensional geometric model of the contaminated soil pile is spatially discretized. A structured hexahedral mesh generation method is used to divide the entire continuous computational domain into... Each mesh element consists of non-overlapping hexahedral cells. Each mesh cell is assigned a globally unique index identifier. ,in This is used for accurate location and access in subsequent calculations. For example, a model of a mound measuring 10m × 5m × 3m can be uniformly divided into 150 hexahedral mesh elements.

[0075] Step 212: Substitute the pressure gradient value of each grid cell in the geometric model into the constitutive relation to calculate the predicted gas velocity of each grid cell.

[0076] In this step, predicting the gas velocity refers to the Darcy velocity value of the gas calculated and output by the model after inputting the pressure gradient value of the grid cell into the trained constitutive relation, i.e., the regression decision function.

[0077] In the embodiments of this application, during the iterative process of solving the flow field, for each grid cell... Based on the pressure field calculated in the current iteration step, the pressure gradient vector at the center of the cell can be obtained. Then, this pressure gradient vector Substitute the constitutive relation as input parameters The predicted Darcy velocity vector of the gas in this mesh cell under the current local pressure was obtained through calculation. ,Right now .

[0078] For example, if the calculated pressure gradient value of element 5 is Then through constitutive relations It can output the corresponding predicted flow rate. .

[0079] Step 213: Calculate the ratio of the modulus of the predicted gas velocity to the modulus of the pressure gradient value to obtain the apparent permeability coefficient of each grid cell, and multiply the apparent permeability coefficient by the preset gas dynamic viscosity parameter to obtain the scalar permeability of each grid cell.

[0080] In this step, the apparent permeability coefficient is a coefficient reflecting apparent conductivity, calculated based on the ratio of the predicted velocity to the modulus of the pressure gradient, using nonlinear flow relationships. Scalar permeability is a scalar parameter with standard permeability dimensions obtained by multiplying the apparent permeability coefficient by the fluid dynamic viscosity.

[0081] In this embodiment, in order to embed the nonlinear flow relationship into a numerical model based on Darcy's law, it is necessary to calculate an equivalent state-dependent permeability for each grid cell. First, the permeability of each grid cell is calculated. Apparent permeability coefficient This coefficient is defined as the ratio of the magnitude of the predicted gas velocity vector to the magnitude of the pressure gradient vector: .

[0082] For example, if Its model Pressure gradient mode ,but Then, considering the complete form of Westerner's law, the mesh element... Scalar penetration rate in the current state It can be calculated using the following formula: ,in It is the dynamic viscosity of a gas, that is, a known physical property parameter, such as air at room temperature. Substituting into the calculation, we get... .

[0083] Step 214: Construct a diagonal matrix based on the scalar permeability, and use the diagonal matrix as the permeability tensor of the corresponding grid cell.

[0084] In this step, a diagonal matrix refers to a square matrix whose elements are all zero except for the main diagonal elements. In this application, it is used to extend scalar permeability into a tensor form characterizing isotropic permeability.

[0085] In the embodiments of this application, although the simplified assumption of isotropic soil medium is used as an example for illustration, the dynamic scalar permeability is used. Constructing a structure with equal diagonal elements Diagonal matrix; however, in practical engineering, if the flow velocity vector predicted by the support vector regression model... Direction and pressure gradient The inconsistent directions indicate that the soil exhibits significant anisotropy. In this case, scalar permeability... The calculated permeability tensor It can be represented as a matrix with unequal diagonal elements, or even a non-diagonal matrix, to more precisely characterize the differences in permeability along different bedding directions. For example, a 3×3 diagonal matrix can be constructed where all elements on the main diagonal are equal. Off-diagonal elements are zero:

[0086]

[0087] For example, for unit 5, its permeability tensor is:

[0088]

[0089] this This will serve as a key parameter used in subsequent steps to correct the momentum conservation equation for this grid cell, thereby introducing non-Darcy flow effects into macroscopic fluid dynamics calculations.

[0090] Step 103: Correct the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell to generate the gas flow equation for each grid cell.

[0091] In this step, the momentum conservation equation is a partial differential equation describing the change of momentum in fluid motion. It can be a variant of the Navier-Stokes equation in porous media, used to describe the relationship between the fluid velocity field and the pressure field. The Darcy drag term is a mathematical term in the momentum conservation equation used to describe the viscous resistance experienced by the fluid as it flows through the porous medium. It is usually proportional to the flow velocity, and its coefficients include the fluid viscosity and the medium permeability. The gas seepage equation is a modified governing equation specifically used to describe the flow behavior of gas in porous media. It is similar in form to the momentum conservation equation, but uses drag coefficients corrected for the gas slippage effect.

[0092] Step 301: Replace the permeability coefficient of the Darcy drag term in the momentum conservation equation with the permeability tensor of each grid cell to obtain the corrected Darcy drag term for each grid cell.

[0093] In this step, the modified Darcy drag term refers to the new mathematical expression obtained by updating the traditional Darcy drag term with a dynamic tensor form of permeability parameter. Its coefficients are no longer fixed scalars, but tensors that change with the flow state.

[0094] In this embodiment of the application, for each grid cell i within the computational domain, the permeability tensor of its current iteration step is obtained. Taking an isotropic medium as an example, this tensor has diagonal elements equal to the scalar permeability. The diagonal matrix. In the traditional momentum conservation equation used for seepage in porous media, the Darcy drag term is usually expressed as... ,in This is a constant permeability coefficient. To introduce nonlinear effects, this coefficient is fixed. Replace with dynamic tensor .

[0095] The specific replacement method follows the generalized form of Darcy's law: because the relationship between velocity and pressure gradient is... Rewriting it in drag term form, we get the corrected Darcy drag term expression: .here It is the permeability tensor The inverse matrix of the given matrix is ​​also a diagonal matrix with diagonal elements of 1. For example, for grid cell 5, if its scalar permeability... Then its corrected Darcy drag coefficient is .

[0096] Step 302: Reconstruct the momentum conservation equation using the modified Darcy drag term to obtain the gas flow equation for each grid cell.

[0097] In this step, the gas seepage equation refers to the governing equation obtained after the above correction, which describes the seepage behavior of gas under conditions considering non-Darcy effect. It is the specific implementation of momentum conservation in this method.

[0098] In this embodiment of the application, the modified Darcy drag term is used. Substituting this into the general momentum conservation equation applicable to porous media flow, under the steady-state or quasi-steady-state assumptions of neglecting inertia terms and considering only the pressure gradient, viscous drag, and possible volume force balance, the core part of this equation can be expressed as the balance between the pressure gradient and Darcy drag. After reconstruction, the gas seepage equation for each grid cell i is obtained. Its core formula is shown in equation (4):

[0099] (4)

[0100] in, It is the pressure gradient of unit i. It is the density of the gas. It is the gravitational acceleration vector. This is the Darcy velocity vector of the gas. If the effect of gravity is ignored, the equation can be simplified to: For grid cell 5, based on the above example, its specific gas seepage equation is shown in formula (5):

[0101] (5)

[0102] This equation represents the controlling relationship for the local flow in this unit, where the permeability parameter... It changes dynamically with the pressure gradient, thus embedding the nonlinear constitutive relation into the macroscopic conservation law. After performing this operation on all mesh elements, a set of interrelated local governing equations with distinct coefficients is obtained.

[0103] Step 104: Combine the gas flow equations of all grid cells to obtain the gas flow equation set. Iterate the gas flow equation set using the finite volume method to obtain the gas velocity field, which includes velocity vectors and pressure data.

[0104] In this step, the gas flow equations refer to the set of algebraic equations consisting of the gas flow equations of all grid cells, typically expressed as a large sparse matrix. The finite volume method is a numerical computation method that solves for physical quantities by dividing the computational domain into control volumes and integrating the governing equations, thus ensuring conservation. The gas velocity field refers to the distribution of gas flow states throughout the computational domain, including the velocity vector and pressure data for each grid cell. The velocity vector describes the magnitude and direction of the gas flow velocity at a given point. The pressure data describes the magnitude of the gas pressure at a given point.

[0105] Step 401: Based on the topological connection relationship of the grid cells, map the pressure correlation coefficients in the gas seepage equations of all grid cells to the sparse coefficient matrix of the finite volume method, and use the sparse coefficient matrix as the coefficient matrix to construct the gas seepage equation set.

[0106] In this step, the pressure correlation coefficient refers to the coefficient associated with the unknown pressure of the cell itself and its neighboring cells after the gas flow equation for each grid cell is discretized. The sparse coefficient matrix is ​​a matrix whose vast majority of elements are zero. In the finite volume method, each non-zero row of this matrix is ​​typically associated with only a central grid cell and its directly adjacent cells.

[0107] In this embodiment, firstly, based on the hexahedral mesh division, an adjacency table for each mesh element i is established, clarifying the element indices j adjacent to its six faces. Then, for each gas flow equation, the finite volume method is applied to discretize it on the control volume of the corresponding mesh element. The discretization process transforms the differential equation into a function relating to the pressure value at the center of the mesh element. and neighboring pressure values The linear algebraic equation is in the form of formula (6):

[0108] (6)

[0109] Among them, the pressure correlation coefficient and The penetration tensor of the current iteration step The parameters such as mesh volume, interface area, and fluid viscosity μ are calculated. For example, for element 5, if its permeability... It shares a common interface area with its eastern neighbor, Unit 6. The distance is Then the coefficient Possibly with Proportional. Finally, based on the global index, all coefficients are... and Fill in a large matrix The i-th row, i-th column, and j-th column of the matrix. For a matrix consisting of 3 elements (e.g., element 1, 2, 3, where element 1 and element 3 are not directly adjacent), the assembled coefficient matrix should exhibit sparsity, and its form is as follows:

[0110]

[0111] in and Since unit 1 and unit 3 have no common interface, the value is 0. Meanwhile, the constant term... Combined into vectors Thus, a sparse linear system of equations is constructed. That is, the system of gas seepage equations to be solved, where .

[0112] Step 402: Set a preset pressure value for each grid cell, and combine the preset pressure values ​​of all grid cells to obtain initial pressure data. Substitute the initial pressure data into the algebraic multigrid to perform iterative calculations on the gas flow equations to obtain iterated pressure data.

[0113] In this step, the initial pressure data refers to a vector consisting of the initial guessed pressure values ​​of all grid cells arranged in index order. Algebraic multigrid is a fast iterative algorithm for solving large sparse linear systems of equations.

[0114] In this embodiment, an initial pressure field is first set for the entire computational domain. For example, the initial pressure of all internal mesh cells is preset to atmospheric pressure. The boundary elements are set according to the negative pressure conditions of the extraction well. These values ​​are then combined into an initial pressure vector based on the grid index. For the 3-unit example above, the initial pressure vector is... system of equations Input an algebraic multigrid solver. The solver efficiently eliminates errors of different frequencies by constructing a series of coarsened grids and alternating between coarse and fine grids for relaxation smoothing and error correction.

[0115] After a preset number of iterations, a pressure vector that more closely approximates the true solution is output. This vector represents the pressure data after this nonlinear iteration.

[0116] Step 403: Calculate the residual between the pressure data after iteration and the initial pressure data. If the residual is greater than or equal to the preset convergence threshold, use the pressure data after iteration as the initial pressure data, recalculate the permeability tensor of each grid cell and update the gas flow equations until the residual is less than the convergence threshold.

[0117] In this step, the residual is a scalar that measures the degree of change in the pressure field between two nonlinear iterations. The convergence threshold is a preset criterion for determining whether the nonlinear iteration has terminated.

[0118] In this embodiment of the application, iterative pressure data is obtained. Then, its initial pressure data is compared with the previous data. The residuals between The L2 norm is typically used for calculation. This residual With the preset convergence threshold Compare. If This indicates that the solution is not yet stable. For example, if and In contrast, the pressure at each node fluctuated by several Pascals, and the calculated residuals... Still above the convergence threshold If so, further iterations are needed.

[0119] Based on this new pressure field = Repeat steps 212 to 302: Calculate the new pressure gradient for each cell. Through constitutive relations The new predicted flow rate is obtained, and then the new scalar permeability is calculated. and permeability tensor Subsequently, using the updated Re-discrete to generate new pressure correlation coefficients and assemble them into a new sparse matrix. and right end item The updated system of equations is obtained. Then return to step 402, using the updated system of equations and the new... The solution is solved again. This process is repeated until the residual is found after a certain iteration. Assuming convergence after the third iteration, the final convergent pressure field would be: .

[0120] Step 404: Calculate the velocity vector of each grid cell based on the iterated pressure data and the gas flow equation, and combine the velocity vectors of all grid cells with the iterated pressure data to obtain the gas velocity field.

[0121] In this step, the final pressure field data is obtained after the nonlinear iteration converges. ,For example For each grid cell i, according to The pressure gradient of the unit and its adjacent units is calculated using a central difference scheme. Simultaneously, the permeability tensor determined for this unit in the last iteration is obtained. Substituting both into the generalized Darcy's law formula, as shown in formula (7):

[0122] (7)

[0123] The gas Darcy velocity vector of this unit can be directly calculated. For example, for unit 1, if its final pressure gradient is calculated as... The final penetration tensor is:

[0124]

[0125] Then its velocity vector After performing this calculation on all mesh elements, the velocity vector for each element is... Its pressure value By combining the indices, a complete gas velocity field, including velocity and pressure distributions, is obtained. This flow field accurately reflects the seepage state under non-Darcy effect conditions.

[0126] Step 105: Substitute the velocity vector as a convection term parameter into the preset heat transfer equation and pollutant transport equation respectively, and simulate the convective heat transfer process of hot air and the migration process of gasified pollutants through multi-physics field coupling calculation to obtain the simulation results of thermal desorption mass transfer and heat transfer.

[0127] In this step, the convection term parameter refers to the coefficients used in the transport equation to describe the migration of matter or energy with fluid movement; it is usually the fluid velocity. The pre-defined heat transport equation refers to the pre-set mathematical equations describing the conduction and convection of heat in the medium; it is usually the energy conservation equation. The pollutant transport equation refers to the pre-set mathematical equations describing the migration and transformation of pollutants in the medium, such as diffusion, adsorption, degradation, and phase change; it is usually the component transport equation. Multiphysics coupling refers to the computational technique that correlates and solves multiple physical processes such as flow field, temperature field, and concentration field simultaneously. The thermal desorption mass and heat transfer simulation results refer to the final set of spatiotemporal evolution data reflecting soil temperature changes and the pollutant removal process obtained through simulation calculations.

[0128] Step 501: Map the velocity vector of each grid cell in the gas velocity field as a convection term parameter to the convection velocity term in the preset heat transfer equation and the advection velocity term in the preset pollutant transport equation, respectively. The heat transfer equation is used to represent the convective heat transfer process of hot air driven by the flow velocity, and the pollutant transport equation is used to represent the migration process of gasified pollutants driven by the flow velocity.

[0129] In this step, the convection velocity term refers to the term in the heat transport equation that describes the heat transfer caused by the macroscopic motion of the fluid, and its core parameter is the fluid velocity. The advection velocity term refers to the term in the contaminant transport equation that describes the migration of contaminants along with the overall motion of the fluid, and its core parameter is also the fluid velocity.

[0130] In this embodiment, steady-state or quasi-steady-state gas velocity field data is first read. This flow field provides a corresponding velocity vector for each grid cell i. Taking unit 5 as an example, assume its velocity vector is... Next, in the transient solver, this velocity field is imported as known conditions. For the heat transport equation, its transient convection term is in the form of: When discretizing element 5 using the finite volume method, it is necessary to calculate the convective flux through each of its faces.

[0131] For example, when calculating the convective flux at its eastern interface, the normal velocity at that interface is required, which is determined by the velocity of element 5. The velocity of its eastern adjacent unit, such as unit 6 The velocity interpolation was obtained through a specific interpolation method. The same velocity interpolation process was applied to the advection term of the pollutant transport equation. In the discrete form. By , Once the specific velocity values ​​are mapped into the discrete format of these two equations, the heat and pollutant transport process is coupled with the precise non-Darcy seepage field.

[0132] Step 502: Set the total simulation duration and divide it into multiple consecutive time steps. Solve the heat transfer equation and pollutant transport equation for each time step separately to obtain the temperature distribution field and pollutant concentration distribution field for each time step.

[0133] In this step, the total simulation duration refers to the physical time span required to simulate the entire thermal desorption process. The time step refers to the physical time interval represented by each computational step after discretizing the total simulation duration. Separate solution is a coupled-field solution strategy, which involves solving different physical field governing equations sequentially within a single time step. The temperature distribution field refers to the spatial distribution set of temperature values ​​for all grid cells within the computational domain at a specific moment. The pollutant concentration distribution field refers to the spatial distribution set of gaseous pollutant mass concentrations in all grid cells within the computational domain at a specific moment.

[0134] like Figure 3 As shown, Figure 3 This is a flowchart illustrating a method for obtaining the temperature distribution field and pollutant concentration distribution field at each time step, as provided in an embodiment of this application.

[0135] Step 5021: Solve the heat transfer equation for each time step to obtain the temperature distribution field for each time step.

[0136] In this step, for the first time step Given the current gas flow field and the temperature field at the previous moment Under these conditions, the pre-set heat transfer equation is solved. The general form of this equation is shown in formula (8):

[0137] (8)

[0138] in, These are the equivalent density, specific heat capacity, and thermal conductivity of the soil and gas mixture, respectively. For the density and specific heat capacity of the gas; The term represents the heat source. During the solution process, a fully implicit time-discretion scheme is employed to ensure numerical stability, and the finite volume method is used for spatial discretization. For each grid cell i, discrete algebraic equations are established regarding its own temperature and the temperatures of its adjacent cells, forming a system of linear equations.

[0139] For example, for unit 5, its discrete equation might be: , where the coefficient and With flow rate Physical property parameters and This is relevant. By solving this system of equations, the new time can be obtained. Temperature values ​​of all grid cells This constitutes the temperature distribution field at that moment. For example, the temperature of element 5 might be obtained after solving the problem. ,compared to The temperature has increased, which is consistent with the typical operating conditions during the thermal desorption heating stage.

[0140] Step 5022: Extract the temperature data of each grid cell from the temperature distribution field, and calculate the thermal desorption rate of each grid cell based on the preset pollutant saturated vapor pressure and temperature function, and in combination with the pollutant concentration data of the pollutant concentration distribution field of each grid cell in the previous time step.

[0141] In this step, the temperature distribution field is first... Read the temperature value of each unit, for example, the temperature of unit 5 is At the same time, retrieve the previous time step from storage. Pollutant concentration distribution field For example, the concentration of unit 5 is For each grid cell i, its thermal desorption rate The calculation consists of two steps. The first step is to calculate the current temperature using a preset function. Saturated vapor pressure of pollutants The function is in the form of formula (9):

[0142] (9)

[0143] in This is a physical property constant. The second step is to calculate the thermal desorption rate based on the mass transfer kinetics model. A commonly used linear driving force model is shown in equation (10):

[0144] (10)

[0145] in, It is the local mass transfer coefficient of unit i. It is determined by saturated vapor pressure The equilibrium gas phase concentration is obtained by conversion using the ideal gas law. For unit 5, the equilibrium concentration at 405 K is calculated using the above function. If its mass transfer coefficient Then the thermal desorption rate .

[0146] Step 5023: Based on the thermal desorption rate, update the generation source term in the pollutant transport equation to obtain the updated pollutant transport equation.

[0147] In this embodiment of the application, the thermal desorption rate of each grid cell i is obtained. Then, it is directly assigned to the corresponding source term in the pollutant transport equation. The original pollutant transport equation is shown in equation (11):

[0148] (11)

[0149] in, Representing source and sink terms. The update operation involves... (The sentence is incomplete and requires more context to translate accurately.) Concretized at unit i For example, the calculation results of Unit 5 Substituting this value, the constant term in the discrete equation corresponding to that unit is updated to this value. After performing this operation on all units, we obtain the pollutant transport equation with the source term updated by the current temperature field and the concentration field at the previous time step. For example, the source term of the equation for unit 5 is updated from a previous value to 0.1. This equation accurately reflects the intensity of the pollutant transformation from the soil phase to the gas phase due to the temperature rise in the current time step.

[0150] Step 5024: Solve the updated pollutant transport equation to obtain the pollutant concentration distribution field at each time step.

[0151] In this step, the source item was updated. The subsequent pollutant transport equation is then solved. This equation is also solved using fully implicit time discretization and finite volume spatial discretization. Given the current gas velocity field... Concentration field at the previous moment and the updated source item Under these conditions, a new concentration at a new time is formed. A system of linear equations.

[0152] For example, for unit 5, its discrete equation can be shown as formula (12):

[0153] (12)

[0154] The right-hand item Includes Flow rate, flux and source terms The contribution of this equation system. Solving this system of equations will yield the new time step. Gaseous pollutant concentrations in all grid cells This constitutes the pollutant concentration distribution field at that moment. For example, the concentration of element 5 is obtained after solving. This indicates that, under the combined effect of thermal desorption and extraction, its concentration was higher than that of the previous time step. It has declined somewhat.

[0155] Step 503: According to the time sequence, stitch together the temperature distribution field and pollutant concentration distribution field of all time steps to obtain the thermal desorption mass transfer and heat transfer simulation results.

[0156] In the embodiments of this application, at each time step After the solution is completed, the physical time at this moment will be... Temperature field data and concentration field data With time tags They are stored together in a serialized data structure.

[0157] For example, time step ,exist Time-stored dataset Time step ,exist Time-stored dataset And so on. When the simulation is complete, a total of [number] data points have been stored. There are several such datasets. Finally, they are sorted by time label. All datasets in ascending order Logically link or integrate the data into a unified data object to form a complete spatiotemporal evolution result of the thermal desorption process. This result can be directly used to generate animations of temperature and pollutant concentration changes over time, or to extract temperature and time curves at any location. Concentration and time curves This allows for a comprehensive demonstration and analysis of the heat and mass transfer dynamics during the repair process.

[0158] This application overcomes the problem of inaccurate boundary condition settings caused by relying solely on theoretical assumptions by collecting pore pressure gradient and gas Darcy velocity data in multiple spatiotemporal dimensions. It achieves dynamic permeability tensor calculation for each discrete grid cell, enabling the simulation model to accurately characterize the conductivity of the soil medium as pressure changes, solving the problem that existing technologies cannot describe non-Darcy flow characteristics due to the use of fixed permeability. It ensures mass and momentum conservation under nonlinear flow resistance conditions, thereby calculating a gas velocity field that accurately reflects non-Darcy flow characteristics, correcting the problem of large calculation errors in flow field distribution when simulating high vacuum conditions in existing technologies. It avoids errors in predicting convective heat transfer efficiency and pollutant migration paths due to flow field distortion, improving the credibility and engineering guidance value of the simulation of ex-situ slope-pile thermal desorption synergistic gas phase extraction process.

[0159] Figure 4 This is a schematic diagram of a specific implementation of the computer-simulated thermal desorption mass transfer and heat transfer simulation system provided in this application. (Refer to...) Figure 4 The system may include:

[0160] The acquisition module 21 is used to acquire the geometric model of the constructed contaminated soil pile and to acquire multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding gas Darcy velocity.

[0161] Analysis module 22 is used to perform regression analysis on multiple sets of pore pressure gradients and gas Darcy velocities through support vector regression. It uses the kernel function of support vector regression to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations, discretizes the geometric model into multiple grid cells, and calculates the permeability tensor of each grid cell according to the constitutive relations.

[0162] The correction module 23 is used to correct the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell, and generate the gas flow equation for each grid cell.

[0163] The simultaneous equation module 24 is used to combine the gas flow equations of all grid cells to obtain the gas flow equation set. The gas velocity field is obtained by iteratively solving the gas flow equation set using the finite volume method. The gas velocity field includes velocity vector and pressure data.

[0164] The simulation module 25 is used to substitute the velocity vector as a convection term parameter into the preset heat transfer equation and pollutant transport equation, respectively, and simulate the convective heat transfer process of hot air and the migration process of gasified pollutants through multi-physics field coupling calculation to obtain the simulation results of thermal desorption mass transfer and heat transfer.

[0165] The computer-simulated thermal desorption mass transfer and heat transfer simulation system of this application is used to implement the aforementioned computer-simulated thermal desorption mass transfer and heat transfer simulation method. Therefore, the specific implementation of the computer-simulated thermal desorption mass transfer and heat transfer simulation system can be found in the embodiment section of the computer-simulated thermal desorption mass transfer and heat transfer simulation method above. The specific implementation can be referred to the description of the corresponding embodiments, which will not be repeated here.

[0166] Figure 5 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0167] This application also provides an electronic device, including: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method described above.

[0168] The electronic device may include a processor 510 and a memory 520 storing computer program instructions.

[0169] Specifically, the processor 510 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0170] Memory 520 may include mass storage for data or instructions. For example, and not limitingly, memory 520 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 520 may include removable or non-removable (or fixed) media. Where appropriate, memory 520 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 520 is non-volatile solid-state memory.

[0171] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to the first aspect of this disclosure.

[0172] The processor 510 reads and executes computer program instructions stored in the memory 520 to implement any of the computer simulation-based thermal desorption mass transfer and heat transfer simulation methods in the above embodiments.

[0173] In one example, the electronic device may also include a communication interface 530 and a bus 540. Wherein, such as Figure 5 As shown, the processor 510, memory 520, and communication interface 530 are connected through bus 540 and complete communication with each other.

[0174] The communication interface 530 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0175] Bus 540 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 540 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0176] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-described computer simulation-based thermal desorption mass transfer and heat transfer simulation methods.

[0177] In one exemplary embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as USB flash drives, read-only memory, random access memory, portable hard drives, magnetic disks, or optical disks.

[0178] Embodiments of the present invention also provide a computer program product, which includes a computer program that, when executed by a processor, implements the steps in any of the embodiments of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method.

[0179] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0180] The above provides a detailed description of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method and system provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A computer simulation-based method for simulating thermal desorption, mass transfer, and heat transfer, characterized in that: include: Obtain the geometric model of the constructed contaminated soil pile, and obtain multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding gas Darcy velocities at the locations. The pore pressure gradient and the gas Darcy velocity are regressed by support vector regression. The kernel function of the support vector regression is used to map the pore pressure gradient and the gas Darcy velocity to a high-dimensional feature space to construct a constitutive relation. The geometric model is discretized into multiple grid cells, and the permeability tensor of each grid cell is calculated according to the constitutive relation. The gas flow equation for each grid cell is generated by correcting the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell. The gas flow equations of all grid cells are combined to obtain a gas flow equation set. The gas velocity field is obtained by iteratively solving the gas flow equation set using the finite volume method. The gas velocity field includes velocity vectors and pressure data. The velocity vector is substituted as a convection term parameter into the preset heat transfer equation and pollutant transport equation, respectively. The convective heat transfer process of hot air and the migration process of gasified pollutants are simulated by multi-physics field coupling calculation to obtain the simulation results of thermal desorption mass transfer and heat transfer. Based on the permeability tensor of each grid cell, the Darcy drag term in the momentum conservation equation is corrected, and the gas flow equation for each grid cell is generated, including: By replacing the permeability coefficient of the Darcy drag term in the momentum conservation equation with the permeability tensor of each grid cell, the corrected Darcy drag term for each grid cell is obtained. The momentum conservation equation is reconstructed using the modified Darcy drag term to obtain the gas flow equation for each grid cell.

2. The method according to claim 1, characterized in that, Multiple sets of pore pressure gradients and gas Darcy velocities are analyzed using support vector regression. The kernel function of the support vector regression is used to map the pore pressure gradients and gas Darcy velocities to a high-dimensional feature space to construct constitutive relations, including: Multiple sets of pore pressure gradients are used as feature data, and multiple sets of gas Darcy velocities are used as label data. A regression training sample set is constructed based on the feature data and the label data. The regression training sample set is input into support vector regression to calculate the feature inner product of the feature data in the high-dimensional feature space using the kernel function of support vector regression, and a quadratic programming objective function is constructed based on the feature inner product. The quadratic programming objective function is solved using the labeled data as constraints to obtain the optimal solution vector, and support vectors and Lagrange multipliers corresponding to the support vectors are extracted from the optimal solution vector. A regression decision function is constructed using the support vectors and the Lagrange multipliers, and the regression decision function is used as a constitutive relation to represent the nonlinear correspondence between the pore pressure gradient and the gas Darcy velocity.

3. The method according to claim 2, characterized in that, The geometric model is discretized into multiple grid cells, and the permeability tensor of each grid cell is calculated according to the constitutive relation, including: The geometric model is divided into multiple indexed mesh units by hexahedral meshing; Substituting the pressure gradient value of each grid cell in the geometric model into the constitutive relation, the predicted gas velocity of each grid cell is calculated. The ratio of the modulus of the predicted gas flow rate to the modulus of the pressure gradient value is calculated to obtain the apparent permeability coefficient of each grid cell. The apparent permeability coefficient is then multiplied by a preset gas dynamic viscosity parameter to obtain the scalar permeability of each grid cell. Construct a diagonal matrix based on the scalar permeability, and use the diagonal matrix as the permeability tensor of the corresponding grid cell.

4. The method according to claim 1, characterized in that, The gas flow equations for all grid cells are combined to obtain a system of gas flow equations. The gas velocity field is then obtained by iteratively solving this system of equations using the finite volume method, including: Based on the topological connection relationship of the grid cells, the pressure correlation coefficients in the gas seepage equations of all grid cells are mapped to the sparse coefficient matrix of the finite volume method, and the sparse coefficient matrix is ​​used as the coefficient matrix to construct the gas seepage equation set. A preset pressure value is set for each grid cell, and the preset pressure values ​​of all grid cells are combined to obtain initial pressure data. The initial pressure data is then substituted into an algebraic multigrid to iteratively calculate the gas flow equations to obtain iterated pressure data. Calculate the residual between the pressure data after iteration and the initial pressure data. If the residual is greater than or equal to a preset convergence threshold, then use the pressure data after iteration as the initial pressure data, recalculate the permeability tensor of each grid cell and update the gas flow equations until the residual is less than the convergence threshold. The velocity vector of each grid cell is calculated based on the iterated pressure data and the gas flow equation, and the velocity vectors of all grid cells are combined with the iterated pressure data to obtain the gas velocity field.

5. The method according to claim 4, characterized in that, The velocity vector is substituted as a convection term parameter into the preset heat transport equation and pollutant transport equation, respectively. Through multiphysics coupling calculations, the convective heat transfer process of hot air and the migration process of vaporized pollutants are simulated to obtain the thermal desorption, mass transfer, and heat transfer simulation results, including: The velocity vector of each grid cell in the gas velocity field is used as a convection term parameter and mapped to the convection velocity term in the preset heat transfer equation and the advection velocity term in the preset pollutant transport equation, respectively. The heat transfer equation is used to represent the convective heat transfer process of hot air driven by the flow velocity, and the pollutant transport equation is used to represent the migration process of gasified pollutants driven by the flow velocity. Set the total simulation duration and divide it into multiple consecutive time steps. Solve the heat transfer equation and pollutant transport equation for each time step separately using a separate solution method to obtain the temperature distribution field and pollutant concentration distribution field for each time step. Based on the time sequence, the temperature distribution field and pollutant concentration distribution field of all time steps are spliced ​​together to obtain the simulation results of thermal desorption mass transfer and heat transfer.

6. The method according to claim 5, characterized in that, By solving the heat transport equation and pollutant transport equation separately for each time step, the temperature distribution field and pollutant concentration distribution field for each time step are obtained, including: Solve the heat transfer equation for each time step to obtain the temperature distribution field for each time step; Temperature data of each grid cell is extracted from the temperature distribution field. Based on the preset pollutant saturated vapor pressure and temperature function, and combined with the pollutant concentration data of each grid cell in the pollutant concentration distribution field of the previous time step, the thermal desorption rate of each grid cell is calculated. Based on the thermal desorption rate, the generation source term in the pollutant transport equation is updated to obtain the updated pollutant transport equation. The updated pollutant transport equation is solved to obtain the pollutant concentration distribution field at each time step.

7. A computer-simulated thermal desorption mass transfer and heat transfer simulation system, characterized in that, include: The acquisition module is used to acquire the geometric model of the constructed contaminated soil pile and to acquire multiple sets of pore pressure gradients at different depths inside the contaminated soil pile at different times and the corresponding gas Darcy velocity. The analysis module is used to perform regression analysis on multiple sets of the pore pressure gradient and the gas Darcy velocity through support vector regression. The kernel function of the support vector regression is used to map the pore pressure gradient and the gas Darcy velocity to a high-dimensional feature space to construct a constitutive relation. The geometric model is discretized into multiple grid cells, and the permeability tensor of each grid cell is calculated according to the constitutive relation. The correction module is used to correct the Darcy drag term in the momentum conservation equation based on the permeability tensor of each grid cell, and generate the gas flow equation for each grid cell. The simultaneous equation module is used to combine the gas flow equations of all grid cells to obtain a gas flow equation set. The gas velocity field is obtained by iteratively solving the gas flow equation set using the finite volume method. The gas velocity field includes velocity vectors and pressure data. The simulation module is used to substitute the velocity vector as a convection term parameter into the preset heat transfer equation and pollutant transport equation, respectively, and simulate the convective heat transfer process of hot air and the migration process of gasified pollutants through multi-physics field coupling calculation to obtain the simulation results of thermal desorption mass transfer and heat transfer. Based on the permeability tensor of each grid cell, the Darcy drag term in the momentum conservation equation is corrected, and the gas flow equation for each grid cell is generated, including: By replacing the permeability coefficient of the Darcy drag term in the momentum conservation equation with the permeability tensor of each grid cell, the corrected Darcy drag term for each grid cell is obtained. The momentum conservation equation is reconstructed using the modified Darcy drag term to obtain the gas flow equation for each grid cell.

8. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the computer simulation-based thermal desorption mass transfer and heat transfer simulation method as described in any one of claims 1 to 6.

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