Stochastic Model And Numerical Simulation Of Reactive Transport Processes In Porous Media

The global shortage of freshwater resources,the idea of protecting freshwater resources runs through our daily life.The rapid development of urbanization and industrialization in our country has made the problem of water pollution increasingly serious.In order to prevent more serious environmental problems,the governance of water resources is imminent.Irreversible bimolecular reactions in porous media are an important problem in the study of contaminant transfer during groundwater transport.Currently,the commonly used mathematical models are based on a class of deterministic convection-dispersion-reaction equations,that is,groundwater seepage in the model equations.The velocity is taken as a fixed value,but such models overpredict the peak concentration of reaction products.To better simulate irreversible bimolecular reactions in porous media,a new stochastic model is proposed in this thesis,which is composed of convection-dispersion-The system of reaction equations（ADREs）is obtained by coupling the stochastic Darcy equation,in which the stochastic Darcy equation is used to describe the motion state of porous media flow,and the seepage velocity field in the model is obtained by this equation.The numerical simulation method of this model is carried out in this thesis.A more in-depth study was carried out to discuss its applicability to the problem of reaction transport in porous media.When numerical simulation of ADREs is performed,it is possible that the numerical solution is difficult due to the dominance of convection.To solve this problem,this thesis compares the classical finite element method and the streamlined upwind Petrov-Galerkin（SUPG）method to deal with the dominance of convection.The numerical results show that when the above two discrete methods are used to solve such problems numerically,the numerical results of the classic finite element method are large.However,the error convergence of the numerical results obtained by using the SUPG method is O（h²）.This thesis uses a stochastic model to simulate a numerical simulation of a type of irreversible biomolecular reaction.Select the appropriate numerical discrete method to simulate the concentration of the reaction product.In addition,this article has the diffuse coefficient D and the chemical reaction coefficient K_r in the model equation.The influence of the size changes on the numerical results was explored.Research found that the reduction of the chemical reaction coefficient K_r will cause the ripple shape of the reaction product Cu EDTA^2-concentration predictive image to be rounded,the ripple position to the right,the peak of the reaction product decreases.Increasing the shape of the predictive image of the product concentration,the effect of the prediction effect of the concentration of the reaction product decreases.In the end,the appropriate parameter is selected for numerical simulation.Compared with the Gramling experimental data,the concentration image of the stochastic model prediction is compared with the Gramling experiment data,and the excessive prediction of the concentration peak has been reduced from 39.9% to 2.43%.