Diffusive mass transfer between fracture and matrix accompanied with sorption significantly influences the efficiency of natural attenuation in hard rocks. While these processes have extensively been studied in a fractured formation, limited information exists on the sorption nonlinearity. For this purpose, a numerical model is developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous solute source boundary condition. The influence of both favorable and unfavorable sorption intensities on solute mobility is investigated using the method of spatial moments. The differing capacities of available sorption sites between fracture surfaces at the fracture-matrix interface and the solid grain surfaces within the rock matrix result in a slower migration of solutes along the fracture, and a larger amount of diffusive mass transfer away from the high permeability fracture. © 2009 ASCE.

Govindarajan Suresh Kumar

Department of Ocean Engineering

Fracture

MASS TRANSFER

Mathematical models

Numerical methods

Rocks

Sorption

DIFFUSIVE MASS TRANSFERS

Fracture surfaces

FRACTURED FORMATIONS

HARD ROCKS

HIGH PERMEABILITIES

LIMITED INFORMATIONS

MATRIX DIFFUSIONS

MATRIX INTERFACES

NATURAL ATTENUATIONS

NONLINEAR SORPTIONS

Numerical models

ROCK MATRIXES

SINGLE FRACTURES

SOLID GRAINS

SORPTION NONLINEARITIES

SORPTION SITES

spatial analysis

SPATIAL MOMENTS

Method of moments

BOUNDARY CONDITION

FRACTURED MEDIUM

NATURAL ATTENUATION

numerical model

permeability

Porosity

rock

solute transport

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Influence of Sorption Intensity on Solute Mobility in a Fractured Formation

Journal of Environmental Engineering

A numerical model was applied to investigate sequential biodegradation of dissolved benzene, toluene, and xylene (BTX) within a fractured aquifer system under the presence of multiple electron acceptors and microbes. The present model differs from existing biodegradation models in fractures by adopting the dual-porosity conceptualization in the model formulation. The influence of fracture-matrix (F-M) interactions on the biodegradation rate of dissolved BTX within a fractured rock was examined. Aerobic, denitrifying, and sulfate reduction biodegradation reactions of BTX constituents were considered to occur within the fractured rock system. Model results suggested that the biodegradation greatly reduces the migration length of dissolved BTX along directions parallel and perpendicular to fracture length. The biodegradation rate of benzene in fracture and matrix was more influenced by the injection rate of dissolved oxygen and aerobic microbe at the fracture inlet. However, the biodegradation rate of toluene and xylene was more under anaerobic biodegradation conditions. A sensitivity analysis was conducted to analyze the sensitivity of flow, fracture, and matrix parameters on the concentration distribution of BTX, electron acceptors, and biomass within the F-M system.

Environmental Engineering Science

Multispecies Transport Modeling on Biodegradation of Benzene, Toluene, and Xylene in a Saturated Fracture-Matrix System with Multiple Electron Acceptors

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. © 2016, Springer International Publishing Switzerland.

Environmental Modeling and Assessment

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. © 2016, Springer International Publishing Switzerland.

Environmental Processes

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

A variable aperture model, instead of a conventional parallel plate model, is utilized to study the transport of radionuclides in a single coupled fracture-matrix system. A fully implicit finite difference model has been developed, which incorporates fracture aperture width variation in the numerical study of two species radionuclide transport. Two distinct geometric profiles namely, sinusoidal and logarithmic have been used to capture the variation of aperture width. The dependence of advection, hydrodynamic dispersion, linear sorption, and matrix diffusion on aperture width is considered in the analysis of radionuclides transport. Two species (parent and daughter) radioactive decay chain is also incorporated. There is a greater retardation of radionuclides in fracture for the variable aperture model than the parallel plate model. Sensitivity analysis on fracture surface sorption coefficient, longitudinal dispersivity, matrix porosity, and matrix diffusion coefficient shows that the conventional parallel plate model overestimate the radionuclide concentration in the fracture when compared to the variable aperture model. © 2016, The Association of Korean Geoscience Societies and Springer-Verlag Berlin Heidelberg.

Geosciences Journal

Numerical modeling of two species radionuclide transport in a single fracturematrix system with variable fracture aperture

A numerical model has been developed in this study for analysing the influence of Sips sorption isotherm on the contaminant transport mechanism in a coupled fracture matrix system. The implicit finite difference numerical technique has been used to solve the coupled non-linear governing equations. A varying grid is adopted at the fracture and rock matrix interface to capture the mass transfer at the interface. A constant continuous source of contaminants is assumed at the inlet of the fracture and the fracture is assumed to be saturated. Results suggest that the magnitude of the Sip’s equilibrium constant in the fracture is extremely sensitive in deciding the resultant transport behaviour within the high permeable fracture. The magnitude of the Sip’s model exponent within the high permeable fracture is highly sensitive in deciding the timing of zero concentration (exhaustion) within the high permeable fracture. © 2016, Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg.

KSCE Journal of Civil Engineering

Effect of sips sorption isotherm on contaminant transport mechanism in fractured porous media

Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay. © Springer-Verlag 2007.

Hydrogeology Journal

Effect of sorption intensities on dispersivity and macro-dispersion coefficient in a single fracture with matrix diffusion

Journal of Hydrologic Engineering

Numerical Modeling and Analysis of Solute Velocity and Macrodispersion for Linearly and Nonlinearly Sorbing Solutes in a Single Fracture with Matrix Diffusion

Journal of Contaminant Hydrology

A controlled field experiment on groundwater contamination by a multicomponent DNAPL: dissolved-plume retardation

Experimental determination of sorption in fractured flow systems

Water Resources Research

Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single-well injection-withdrawal tests

Influence of sorption intensity on solute mobility in a fractured formation