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A numerical model is developed for studying the transport of bacterial facilitated contaminants in a coupled fracture-matrix system. The contaminants and bacteria are assumed to sorb onto the fracture surface, the contaminants are assumed to diffuse into the rock-matrix. Bacteria are assumed not to diffuse into the rock-matrix. The sorption of the contaminants onto the mobile and immobile bacteria within the fracture is assumed to be linear. The governing equations describing the bacterial transport and contaminant transport along the fracture as well as rock-matrix are coupled with each other. The coupled non-linear equations are solved numerically with fully implicit finite difference method. Constant concentration is assumed at the inlet of the fracture for both contaminants and bacteria. A varying grid is adopted at the fracture and rock-matrix interface to capture the flux transfer to ensure fluid mass transfer. Sensitivity analysis is performed to investigate the effects of various bacterial transport properties on the contaminant concentration in the fracture-matrix coupled system. Results suggest that for the contaminant and bacterial transport parameters that have been analysed, the bacterial concentration increases nearer to the fracture inlet due to consumption of contaminant substrate and consequently the contaminant concentration drastically reduces at the in the vicinity of fracture inlet. When the bacterial cells completely decay, the dead bacterial cells release the contaminants into the aqueous phase resulting in instantaneous increase in the contaminant concentration further away from the fracture inlet. For low matrix porosity and high half fracture aperture, bacterial concentration is consistent for a large portion of the fracture. There is significant bacterial concentration throughout the length of the fracture when the sorption coefficient of bacteria on the fracture wall surface is very low. When specific growth rate of bacteria is very high, an exponential growth pattern is observed nearer to the fracture inlet. � 2011 Elsevier B.V.

This paper presents a stress-induced variable aperture model to characterise the effect of polyaxial stress conditions on the fluid flow in three-dimensional (3D) persistent fracture networks. Geomechanical modelling of the fractured rock is achieved by the finite-discrete element method (FEMDEM), which can capture deformability of matrix blocks, heterogeneity of stress fields as well as sliding and opening of pre-existing fractures. Propagation of new cracks is not required for this study of persistent fracture systems. The deformed fracture network topologies include details of dilation, opening and closing of fracture apertures, from which the local variations in hydraulic apertures are derived. Stress-controlled distribution of fracture apertures is modelled with both fracture-scale and network-scale effects considered. Under a geomechanical condition with low differential stress ratio, fracture porosity is dominated by the fracture-scale roughness. However, with the increase of stress ratio, some favourably oriented fractures are reactivated for shearing, and matrix blocks are promoted to rotate and generate large openings along their boundaries, which tend to be the key contributors to the aperture field in such persistent systems. The flow behaviour is then considered for these stressed but static solid skeletons and is investigated using a finite element solution to the Laplace problem of single-phase fluid flow. The equivalent permeability tensor of each cube-shaped rock mass is computed based on a series of flow simulations under a macroscopic pressure differential applied at opposite model boundaries with no-flow conditions on the remaining boundaries. Components of the permeability tensor are found to vary more than three orders of magnitude with respect to the change of stress ratio. Large aperture channels formed under a critical stress state accommodate significant localisation features in the flow structure of the network. The results of this study have important implications for upscaling permeability to grid block properties for reservoir flow simulation.

A numerical model using finite volume QUICK scheme has been developed for simulating the transport behavior of solutes in a coupled fracture-matrix system for pulse-type boundary condition as against the conventional constant continuous source-type boundary condition, which essentially reflects the reality better, as it is practically not feasible for any source type to discharge it continuously with the same magnitude for a very long period. The sensitivity of fracture and rock matrix parameters, namely fracture aperture thickness, matrix porosity, and matrix diffusion coefficient have been analyzed under this complex boundary condition. In addition, the role of nonlinear sorption as well as decay has also been investigated. Numerical results suggest that the reduction in relative concentration within the fracture resulting from pulse-type boundary condition should always not be mistaken for matrix diffusion. It has been concluded from the present numerical study that segregating and quantifying the role on individual components, namely (a) source exhaustion (pulse-type boundary condition), (b) matrix diffusion, (c) sorption, and (d) decay in characterizing the resultant transport behavior of solutes in a single fracture with matrix diffusion under a pulse-type boundary condition remains challenging and needs further research. � 2014 � 2014 Indian Society for Hydraulics.

The contaminant transport mechanism in fractured clay porous media has been analysed using numerical modelling. Implicit finite difference has been used to develop the numerical model. A constant continuous source of contaminants has been assumed at the inlet of the fracture. The domain is considered to be saturated. A varying grid is considered in the fracture skin to account for the flux transfer at the interface of the fracture and the skin. The effect of constant dispersion as well as distance-dependent dispersion on the contaminant transport mechanism has been analysed in the presence of fracture skin. The contaminants are assumed to follow Freundlich non-linear sorption isotherm. Sensitivity analysis has been conducted to study the effect of different fracture-skin porosities, skin diffusion coefficients, half fracture apertures, fluid velocities and skin thicknesses on the solute transport mechanism within the fractured clay porous media. Results suggest that amount of solute diffusion into the clay matrix is directly proportional to the fracture-skin porosity and fracture-skin diffusion coefficient and inversely proportional to thickness of the half fracture aperture and the fluid velocity. The role of non-linear sorption is insignificant and scale-dependent dispersivity results in enhanced mass diffusion from the fracture. � 2014 Indian Society for Hydraulics.

In this study, the behavior of thermal fronts along the fracture is studied in the presence of fracture-skin in a coupled fracture-matrix system. Cold water is injected into the fracture, which advances gradually towards production well, while extracting heat from the surrounding reservoir matrix. The heat conduction into the fracture-skin and the rock-matrix from the high permeability fracture is assumed to be one dimensional perpendicular to the axis of fluid flow along the fracture. Constant temperature cold water is injected through an injection well at the fracture inlet. The fluid flow takes place along the horizontal fracture which ensures connectivity between the injection and production wells. Since the rock-matrix is assumed to be tight, the permeability of fracture-skin as well as the rock-matrix is neglected. The present study focuses on the heat flux transfer at the fracture-skin interface as against the earlier studies on fracture-matrix interface, and the sensitivity of additional heterogeneity in the form of fracture skin in a conventional fracture-matrix coupled system is studied. The behavior of thermal fronts for various thermal conductivity values of the fracture-skin and rock-matrix is analyzed. Spatial moment analysis is performed on the thermal distribution profiles resulting from numerical studies in order to investigate the impact on mobility and dispersion behavior of the fluid in the presence of fracture-skin. The presence of fracture skin affects the heat transfer significantly in the coupled fracture-matrix system. The lower order spatial moments indicate that the effective thermal velocity increases with increase in skin thermal conductivity and a significant thermal dispersion is observed at the inlet of the fracture owing to the high thermal conductivity of the fracture-skin at the early stages. Furthermore the higher spatial moments indicate that the asymmetricity increases with decrease in skin thermal conductivity unlike the case with half fracture aperture and fluid velocity and the kurtosis is maximum with higher skin thermal conductivity which implies enhanced heat extraction from the fracture-skin into the fracture. Results suggest that the amount of heat extraction by the circulating fluid within the fracture from the reservoir not only depends on the rock-matrix module of the reservoir characteristics but also the fracture-skin characteristics of the system and subsequently influence the reservoir efficiency. � 2011 Springer Science+Business Media B.V.

A mathematical model to account for non-laminar terms, during simulated transports in fractured rocks has been developed. The relevant conceptual model consists of a two dimensional grid block equivalent to a variable fracture plane. The block aperture variability is expressed by means of stochastic procedures, based upon some characteristics of fractured media. One of them, e.g. the equivalent hydraulic aperture, may be estimated by means of the results of field tests. The solution of Navier-Stokes and Darcy-Weisbach's equation for steady state flow between two parallel plates with constant aperture allows the systems of equations under respetively, laminar and non-laminar conditions, to be wirtten. The flow model is a standard finite-difference method with a modified version of Darcy's equation to account for non-laminar terms that are important at high water velocity. To simulate solute transports, the particle tracking technique was applied. q1999 Elsevier Science Ltd. All rights reserved