Theoretical Study And Numerical Simulation Of Solute Transport In Fracture-matrix System

Study of solute transport in fractured rock has important significance for prevention and control of groundwater pollution.In fractured media,the influence of matrix diffusion on solute transport process could not be ignored.The solute transport model in the previous studies cannot describe the different reaction rates in fracture and matrix,or often ignore the matrix diffusion process.In view of some gaps in the current studies of solute transport in fractured rocks,analytical solutions and numerical simulation methods are used in this paper to deal with solute transport problems in smooth parallel fracturematric system and rough wall fracture-matrix system.The effects of matrix diffusion on solute transport process are discussed in different systems.Thus,to provide a powerful theoretical basis for the design of tracer experiments in fractured rocks and solving the problems of groundwater flow and water quality faced in the evaluation and construction of underground engineering.The main contents and findings of this study are as follows.Mathematical models coupled of solute transport in the fracture and matrix are developed considering different first-order reaction rates in the two media.The problem includes advection along the fracture,transverse diffusion in the matrix,with linear sorption as well as first-order reactions operative in both the fracture and the matrix.Analytical solutions are derived for a constant-concentration boundary condition and a decay source boundary condition in the fracture.The analytical and semi-analytical solutions are in excellent agreement with the numerical simulation results using COMSOL Multiphysics software.Sensitivity analysis is conducted to assess the relative importance of matrix diffusion coefficient,fracture aperture,and matrix porosity.The analytical solution obtained in this study could be applied to a parallel fracture system thus quantitatively evaluate the spatiotemporal distribution of solute in a parallel fracturematrix system.Analytical solutions are obtained in this study to quantify the conservative and reactive solute transport processes in an asymmetric fracture-matrix system.Numerical simulations are performed using Hydro Geo Sphere to test the solutions.Well matched curves of the numerical results and the closed-form solutions and semi-analytical solutions indicate that the analytical solutions are robust.Penetration depth into the matrix and fracture as well as the mass stored in the matrix could be calculated based on the analytical models.A dimensionless number is defined to quantify the maximal penetration depth into the matrix.Influence of different physical parameters on transport process are analyzed.The matrix porosity and retardation factor appear to significantly affect the spatiotemporal distribution of solute in a fracture-matrix system.The solutions obtained can act as an effective tool for risk assessment of contaminated fractured rock.Meanwhile,the analytical model is also applicable to advection-dominated solute or heat transport in a thin aquifer bounded by two different aquitards.An electrical correction term is formulated to correct the effective diffusion coefficient in low permeability porous media.Based on the modified parameter,the analytical models for solute transport in fracture-matrix system are applied to solve the solute transport problem in a coupled three-layer system.The modified analytical model is used to fit the previous tracer test and analyze the difference between the previous theoretical model and the experimental data.In addition,a semi-analytical solution considering longitudinal dispersion in the high permeability layer is developed to find out the role of longitudinal dispersion on solute transport in the coupled system.Our model provides a significant improvement in fit between simulated and measured breakthrough curves,demonstrating that tracer electrical properties play an important role in controlling the molecular diffusion process and transport in multi-domain systems.Meanwhile,it proves that the fracture-matrix transport model has good applicability in laboratory scale.Two-dimensional numerical models of seepage and solute transport are established in the rough wall fracture-matrix system.Navier Stokes equation and Advection-diffusion equation which control flow and solute transport process are solved with COMSOL Multiphysics directly.The characteristics of flow and solute transport under different hydraulic conditions are analyzed based on the numerical simulation results.At the same time,the model results of considering matrix diffusion and neglecting matrix diffusion are compared to evaluate the influence of matrix diffusion on solute transport in rough fractures.The ways of solute exchange between the main fracture channel,the immobile zone and the matrix under different hydraulic conditions are also discussed.It appears that the influences of matrix diffusion on solute transport in rough fractures are not obvious under high hydraulic conditions,but the effects will increase with the decrease of hydraulic gradient.With a same hydraulic gradient,the influence of matrix diffusion on solute transport increases as the fracture roughness growth.