An efficient finite element technique for modeling transport in fractured porous media: 1. Single species transport

Abstract

A mathematical model is presented for numerical simulation of solute transport in naturally fractured porous media. The model is based on the dual-porosity conceptual approach and is capable of simulating interactions between porous rock matrix and fractures. Unlike earlier dual-porosity transport models, which rely on l•arallel fracture assumptions, the present model is a unified model tha represent blocky fractured systems (i.e., systems with suborthogonal fractures) by using a spherical idealization of matrix blocks. Two governing, partial differential equations are written for solute transport in the fractures and diffusion in the porous matrix blocks. These equations are coupled by mass flux terms (leakages). An efficient numerical scheme is presented for approximating the governing transport equations. The scheme effectively combines a two-dimensional, upstream-weighted, finite-element approximation for transport in the fractures with a one-dimensional Galerkin approximation for diffusion within the individual matrix blocks. Coupling of the two approximations is performed implicitly. The systems of algebraic equations resulting from both finite-element approximations are solved by using sequential solution algorithms designed especially for this type of problem. Stability and accuracy of the numerical scheme are checked by applying the model to a number of test problems and comparing results with available analytical solutions. In all cases the numerical scheme is found to be highly stable and capable of producing reliable results with the use of relatively coarse spatial and temporal discretizations. Finally, the utility of the model is demonstrated by applying it to a hypothetical, yet realistic, problem. INTRODUCTIONProblems involving fluid flow and solute transport in fractured porous media have received rapidly increasing attention. Recent motivation for their solution is due to the necessity of evaluating the suitability of geologic sites for nuclear waste repositories and the concern over contamination of fractured aquifers. The objective of this paper is to present the development, verification, and application of an efficient numerical model for simulation of two-and three-dimensional transport of a single-species solute in a fractured system. Naturally fractured systems contain extreme discontinuities in porosity and permeability, with most of the fluid being located in low-permeability, disjointed matrix blocks. In contrast, most of the fluid mobility is in a small volume of highpermeability, interconnected fractures. When solute transport occurs in such a system, advection and dispersion are the dominant processes within the fractures, whereas diffusion is the dominant process in the matrix. This diffusion has been termed 'matrix diffusion' and is discussed by Neretnieks [1980] and Grisak and Pickens I-1980]. Matrix diffusion is important as a retarding process, and in the case of a reacting solute, matrix diffusion is a mechanism for further retardation because of the existence of additional ...

Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant

“…Thus, the brine aquifer boundary may coincide with the topographic surface elevations of Nash Draw. Drilling associated with the WIPP hydrogeologic studies in the northern half of Nash Draw support this theory (p. 50, Mercer 1983).…”

“…Second-order central differencing is used to approximate the spatial derivatives, and a first-order backwards differencing is used to approximate temporal derivatives. The implicit coupling is accomplished using a technique developed by Huyakorn et al (1983). A detailed description of this technique and its implementation in the 1996 WIPP PA is given in the SECOTP2D user's manual (App.…”

Effective matrix diffusion in kilometer‐scale transport in fractured crystalline rock

“…At the kilometer scale, diffusion of dissolved constituents from groundwater moving in fractures t0 a less permeable rock matr• plays a large role in the attenuation of migrating constituents [Neretnieks, 1981;Maloszewski andZuber, 1985, 1991]. A variety of mathematical models have been proposed to describe matrix diffusion in fractured rock [see, e.g., Tang et al, 1981;Huyakorn et al, 1983;Bear, 1993]; however, heterogeneity and sparse hydraulic and geochemical data at the kilometer scale do not necessarily lend themselves to the evaluation of these models. Furthermore, most investigations of kilometer-scale transport in fractured rock have used estimates of the matrix diffusion from centimeter-scale experiments on rock cores [see, e.g., Maloszewski and Zuber, 1984;Maloszewski, 1994], again, because sparse geochemical data are not amenable to inferring this parameter.…”

Characterization of preferential flow paths between boreholes in fractured rock using a nanoscale zero-valent iron tracer test

“…11). Such a similar duration of the conductivity changes in the two wells suggested the dominance of advection in the transport of the nZVI slurry through the connected fracture between wells A and C. Hydrodynamic dispersion of the nZVI slurry was not significant, possibly due to the short migration distance and less tortuosity in the permeable fracture (Grisak and Pickens 1980;Huyakorn et al 1983).…”