Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Car...Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Carlo simulations of water flow through DFNs to identify non-Darcian flow and non-Fickian pressure propagation in field-scale DFNs, by adjusting fracture density, matrix hydraulic conductivity, and the general hydraulic gradient. Numerical simulations and analyses show that interactions of the fracture architecture with the hydraulic gradient affect non-Darcian flow in DFNs, by generating and adjusting complex pathways for water. The fracture density affects significantly the propagation of hydraulic head/pressure in the DFN, likely due to fracture connectivity and flow channeling. The non-Darcian flow pattern may not be directly correlated to the non-Fickian pressure propagation process in the regional-scale DFNs, because they refer to different states of water flow and their controlling factors may not be the same. Findings of this study improve our understanding of the nature of flow in DFNs.展开更多
Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the reme...Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the remediation of contaminated groundwater.Aquifer heterogeneity usually leads to a distinct feature,the so-called“anomalous transport”in groundwater,which deviates from the phenomenon described by the classical advection-dispersion equation(ADE)based on Fick’s Law.Anomalous transport,also known as non-Fickian dispersion or“anomalous dispersion”in a broad sense,can explain the hydrogeological mechanism that leads to the temporally continuous deterioration of water quality and rapid spatial expansion of pollutant plumes.Contaminants enter and then are retained in the low-permeability matrix from the high-permeability zone via molecular diffusion,chemical adsorption,and other mass exchange effects.This process can be reversed when the concentration of pollutants in high-permeability zones is relatively low.The contaminants slowly return to the high-permeability zones through reverse molecular diffusion,resulting in sub-dispersive anomalous transport leading to the chronic gradual deterioration of water quality.Meanwhile,some contaminants are rapidly transported along the interconnected preferential flow paths,resulting in super-dispersive anomalous transport,which leads to the rapid spread of contaminants.Aquifer heterogeneity is also an important factor that constrains the efficacy of groundwater remediation,while the development,application,and evaluation of groundwater remediation technologies are usually based on the Fickian dispersion process predicted by the ADE equation.Comprehensive studies of the impacts of non-Fickian dispersion on contaminant transport and remediation are still needed.This article reviews the non-Fickian dispersion phenomenon caused by the heterogeneity of geological media,summarizes the processes and current understanding of contaminant migration and transformation in highly heterogeneous aquifers,and evaluates mathematical methods describing the main non-Fickian dispersion features.This critical review also discusses the limitations of existing research and outlines potential future research areas to advance the understanding of mechanisms and modeling of non-Fickian dispersion in heterogeneous media.展开更多
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodi...Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.展开更多
A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the siz...A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the size of the calcium spark produced by the new dynamic model was larger than that of Fick diffusion and was in more agreement with experimental results. In addition, the time lags of the calcium spark in cardiac myocytes were about 0.1—0.8 ms. These results can be used to understand the mechanism of calcium spark diffusion in cardiac myocytes.展开更多
文摘Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Carlo simulations of water flow through DFNs to identify non-Darcian flow and non-Fickian pressure propagation in field-scale DFNs, by adjusting fracture density, matrix hydraulic conductivity, and the general hydraulic gradient. Numerical simulations and analyses show that interactions of the fracture architecture with the hydraulic gradient affect non-Darcian flow in DFNs, by generating and adjusting complex pathways for water. The fracture density affects significantly the propagation of hydraulic head/pressure in the DFN, likely due to fracture connectivity and flow channeling. The non-Darcian flow pattern may not be directly correlated to the non-Fickian pressure propagation process in the regional-scale DFNs, because they refer to different states of water flow and their controlling factors may not be the same. Findings of this study improve our understanding of the nature of flow in DFNs.
基金supported by the National Key R&D Program of China(Grant No.2016YFC0402806)the National Natural Science Foundation of China(Grant Nos.41931292,42007162&41722208)the Natural Science Foundation of Guangdong Province(CN)(Grant No.2020A1515010891).
文摘Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the remediation of contaminated groundwater.Aquifer heterogeneity usually leads to a distinct feature,the so-called“anomalous transport”in groundwater,which deviates from the phenomenon described by the classical advection-dispersion equation(ADE)based on Fick’s Law.Anomalous transport,also known as non-Fickian dispersion or“anomalous dispersion”in a broad sense,can explain the hydrogeological mechanism that leads to the temporally continuous deterioration of water quality and rapid spatial expansion of pollutant plumes.Contaminants enter and then are retained in the low-permeability matrix from the high-permeability zone via molecular diffusion,chemical adsorption,and other mass exchange effects.This process can be reversed when the concentration of pollutants in high-permeability zones is relatively low.The contaminants slowly return to the high-permeability zones through reverse molecular diffusion,resulting in sub-dispersive anomalous transport leading to the chronic gradual deterioration of water quality.Meanwhile,some contaminants are rapidly transported along the interconnected preferential flow paths,resulting in super-dispersive anomalous transport,which leads to the rapid spread of contaminants.Aquifer heterogeneity is also an important factor that constrains the efficacy of groundwater remediation,while the development,application,and evaluation of groundwater remediation technologies are usually based on the Fickian dispersion process predicted by the ADE equation.Comprehensive studies of the impacts of non-Fickian dispersion on contaminant transport and remediation are still needed.This article reviews the non-Fickian dispersion phenomenon caused by the heterogeneity of geological media,summarizes the processes and current understanding of contaminant migration and transformation in highly heterogeneous aquifers,and evaluates mathematical methods describing the main non-Fickian dispersion features.This critical review also discusses the limitations of existing research and outlines potential future research areas to advance the understanding of mechanisms and modeling of non-Fickian dispersion in heterogeneous media.
基金supported by the research project UTAustin/MAT/066/2008.
文摘Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.
基金supported by the National Natural Science Foundation of China(Grant No.10372007)Bio-x center of Peking University and Japan Society for the Promotion of Science(PO2325).
文摘A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the size of the calcium spark produced by the new dynamic model was larger than that of Fick diffusion and was in more agreement with experimental results. In addition, the time lags of the calcium spark in cardiac myocytes were about 0.1—0.8 ms. These results can be used to understand the mechanism of calcium spark diffusion in cardiac myocytes.
