Fluid flow and solute transport in a 3D rough-walled fracture–matrix system were simulated by directly solving the Navier–Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture–matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture–matrix systems and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behaviors caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture–matrix systems. Such analysis is helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.

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Modeling of Solute Transport in a 3D Rough-Walled Fracture–Matrix System

The present paper addresses critical issues that describe the transient transfer of stored rock-matrix flow into high-permeable fractures and rate-limited diffusive solute flux into low-permeable rock matrix using a typical dual-porosity approach. An improved mathematical model is suggested that better describes fluid flow through a coupled fracture-matrix system using a dual-porosity approach. The suggested model differs from a conventional model as the fracture flow equation contains a hyperbolic term in addition to the conventional dispersive term. The matrix flow equation contains the coupling term that controls the transient nature of fluid exchange from the stored rock matrix into the hydraulic conductors. The Langmuir sorption isotherm is suggested to describe the limited sorption sites available on fracture walls, while the Freundlich sorption isotherm is recommended to describe the unlimited sorption sites available within the rock matrix. The dispersion mechanism in a coupled fracture-ma...

Mathematical Modeling of Groundwater Flow and Solute Transport in Saturated Fractured Rock Using a Dual-Porosity Approach

Mechanics of jointed and faulted rock

Modeling of radionuclide transport in porous media: A review of recent studies

A numerical study on the effect of complex fracture aperture geometry on propagation of thermal front in a coupled single fracture–matrix system has been carried out. Sinusoidal and logarithmic functions have been used to capture the variation in fracture aperture. Modifications have been made to existing coupled partial differential governing equations to consider the variation of fracture aperture. Effect of temperature on the thermal and physical properties of rock have been incorporated. A fully implicit finite difference scheme has been used to discretize the coupled governing equations. Thermal convection, dispersion and conduction are the major transport processes within fracture, while conduction is the major transport process within rock matrix. The results suggest that variation of fracture aperture increases the heat transfer rate at the fracture–matrix interface. Sensitivity analysis on rock thermal conductivity and fracture aperture have been carried out. The results suggest that the heat transfer from rock matrix to fracture for the case of the parallel plate model is greatly dependent on the rock thermal conductivity (λ
 m) as compared to variable aperture model. Further, the thermal front propagation for both parallel plate model and variable aperture model is sensitive to changes in fracture aperture. The heat transfer rate at the interface is greater at smaller fracture apertures and decreases with increase in aperture.

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Thermal front propagation in variable aperture fracture–matrix system: A numerical study

This study deals with transport of solutes through a saturated sub-surface rock formation with well-defined horizontal parallel fractures. For this purpose, a simplified conceptual model consisting of a single fracture and its associated rock-matrix is considered in the presence of a fracture-skin in order to study the mobility and mixing of solutes along the fracture. In this paper, a coupled fracture-skin-matrix system is modeled numerically using finite difference method in a pseudo two-dimensional domain with a constant continuous source at fracture inlet. Flow and transport processes are considered parallel to the fracture axis, while the transport processes in fracture-skin as well as in rock-matrix are considered perpendicular to the fracture axis. Having obtained the concentration distribution along the fracture, method of spatial moments is employed to study the mobility and spreading of solutes. Sensitivity analyses have been done to understand the effect of various fracture-skin parameters like porosity, thickness, and diffusion coefficient. Further, the influence of non-linear sorption and radioactive decaying of solutes are carried out for different sorption intensities and decay constants. Results suggest that the presence of fracture-skin significantly influences the mobility and spreading of solutes along the fracture in comparison with a coupled fracture-matrix system without fracture-skin.

Numerical Modeling and Spatial Moment Analysis of Solute Mobility and Spreading in a Coupled Fracture-Skin-Matrix System

In the present study, method of temporal moments has been used to analyse the transport characteristics of reactive solute along fracture in a coupled fracture-skin-matrix system. In order to obtain the concentration distribution within the fracture, a system of coupled partial differential equations for fracture, fracture-skin and rock-matrix has been solved numerically in a pseudo two-dimensional domain using implicit finite difference method. Subsequently, lower order temporal moments of solute have been computed from the concentration distribution to analyse the transport characteristics of solutes in the fracture. This study has been done by considering an inlet boundary condition of constant continuous source in a single fracture. The effect of various fracture-skin parameters like porosity, thickness and diffusion coefficient on the transport of solutes have been studied by doing sensitivity analyses. The effect of nonlinear sorption and radioactive decay of solutes have also been analysed by carrying out simulations for different sorption intensities and decay constants. Numerical results suggested that the presence of fracture-skin significantly influences the transport characteristics of reactive solutes along the fracture.

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Temporal moment analysis of solute transport in a coupled fracture-skin-matrix system

This paper presents an analysis using temporal moments to study multi-species radionuclide transport along a single fracture with variable fracture aperture in a fracture-skin-matrix system. In the present study, a decay chain having three elements is considered and transport of each member in the decay chain is modeled by solving a coupled system of partial differential equations for fracture, fracture-skin, and rock matrix using explicit finite difference method. Having obtained the concentration distribution, lower order temporal moments of radionuclide distribution are computed to analyze the effective velocity and macro-dispersion coefficient of radionuclides in the fracture. In the present study, effect of varying fracture aperture on transport characteristics of radionuclides is also analyzed. It is found that the fracture aperture variation profile has significant impact on radionuclide distribution along the fracture. Sensitivity analysis is carried out in a fracture-skin-matrix system with sinusoidal fracture aperture to study the effect of various parameters like fracture aperture thickness, fracture-skin porosity, fracture-skin diffusion coefficient, flow rate, radioactive decay constant, and Freundlich sorption isotherm exponent on transport characteristics of radionuclide. The results suggest that the above mentioned parameters significantly influence concentration, distribution, mobility, and effective macro-dispersion coefficient of radionuclides along the fracture.

Temporal Moment Analysis of Multi-Species Radionuclide Transport in a Coupled Fracture-Skin-Matrix System with a Variable Fracture Aperture

Dissolution from residual source zones of benzene poses serious threat to the groundwater quality. Proper understanding of fate and migration of dissolved benzene is a prerequisite for planning remediation strategies to reduce groundwater contamination. In the present study, an attempt has been made to numerically model the dissolution of benzene and to investigate the transport of aqueous phase benzene in a saturated fracture-matrix system under steady-state flow condition. In addition to dissolution mass transfer, advection, dispersion and matrix diffusion of aqueous benzene has been considered along the fracture. In the present numerical model, residual phase benzene is considered to be present along the entire length of the fracture and residual phase benzene is assumed to be immobile for the flow conditions considered in the analysis. Transport equations for fracture and rock-matrix are solved using implicit finite difference method. Transport equation for aqueous benzene within the fracture has been solved in a one-dimensional domain and transport equation for aqueous benzene within rock-matrix has been solved in a pseudo-two-dimensional domain. Sensitivity studies have been conducted to investigate the impact of variation of flow velocity, dispersivity, fracture aperture, inlet benzene concentration, rock-matrix diffusion coefficient, and half fracture spacing on transport of aqueous benzene concentration within the fracture. From the present study, it can be concluded that the addition of slow liquid benzene dissolution into aqueous phase influences the benzene breakthrough curves/profiles at different velocity, fracture aperture, initial benzene concentration, mass transfer rate, rock dispersivity and half fracture spacing.

Numerical Modeling on Benzene Dissolution into Groundwater and Transport of Dissolved Benzene in a Saturated Fracture-Matrix System

Flow and transport studies in fractured aquifers have been widely carried out by adopting the parallel plate approximation for fracture walls. However, the fractures existing in the field scenario may not always possess parallel walls and may have spatially varying fracture widths. Hence, the parallel plate conceptualization of a real fracture may be highly idealistic in some cases. The principal aim of this work is to numerically investigate the coupled dissolution and transport of benzene along a sinusoidal fracture under non-uniform flow conditions, and to compare the simulation results with the results obtained using the parallel fracture model. Results from the simulation study indicate that the parallel plate approximation of a sinusoidal fracture may lead to incorrect prediction of dissolved benzene concentration along the fracture. A sensitivity analysis is carried out to investigate the sensitivity of sinusoidal fracture parameters, such as amplitude, wavelength and average fracture aperture on the dissolution and transport of benzene within the fracture. Simulation results obtained using the parallel plate idealization of sinusoidal fractures with high amplitudes and low wavelength is found to deviate more from the real field scenario. Sensitivity of the inlet fracture pressure on concentration distribution of benzene is also analyzed. Transport of dissolved benzene is found to be significantly sensitive to fluid pressure at the fracture inlet.

V. Renu

Papers

Numerical Modeling and Spatial Moment Analysis of Solute Mobility and Spreading in a Coupled Fracture-Skin-Matrix System

Temporal moment analysis of solute transport in a coupled fracture-skin-matrix system

Temporal Moment Analysis of Multi-Species Radionuclide Transport in a Coupled Fracture-Skin-Matrix System with a Variable Fracture Aperture

Numerical Modeling on Benzene Dissolution into Groundwater and Transport of Dissolved Benzene in a Saturated Fracture-Matrix System

Benzene Dissolution and Transport in a Saturated Sinusoidal Fracture with non-uniform Flow: Numerical Investigation and Sensitivity Analysis