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 ...

A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual-porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual-porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one-dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element-convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture-matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models. INTRODUCTION Literature ReviewFlow in fractured porous media has been and still continues to be an important concern in areas such as petroleum and mining engineering and karst hydrology. Increased interest in fractured porous media has resulted from terminal waste storage programs, especially those associated with high-level radioactive waste. Characterization of the media, as well as development of related methodologies for predicting flow behavior, are of primary importance to these programs. This paper, the first in a series of three, deals with the latter problem of predicting flow behavior. In particular, we focus attention on areal flow in fractured aquifers and discuss four alternative conceptual models, as well as present the mathematical formulation and finite element solution algorithms. The second paper makes use of results from the first paper and extends our predictive capabilities by incorporating singlespecies solute transport. In the final paper of the series, multiple-species solute transport with chain reactions is discus...

Although based on exact analytical solutions, semi-analytical solute transport models can have significant numerical error in applications with high frequency oscillatory source terms and when parameter value combinations cause series solution approximations to converge slowly. Methods for correcting these numerical errors are presented and implemented in the AT123D code, which employs Green's functions to represent point, linear, and rectangular prismatic source zones. In order to increase its computational accuracy, a Romberg numerical integration scheme was added to AT123D with prespecified error criteria, variable time stepping, and partitioning of the integral to handle rapidly changing source terms. More rapidly converging series solution approximations for the Green's functions were also incorporated to improve both accuracy and computational efficiency for finite-depth aquifers. AT123D also has been modified to eliminate redundant calculations at points where approximate steady-state conditions have been reached to improve computational efficiency during numerical integration. These modifications help to decrease computer run times that can be excessive for three-dimensional problems with large numbers of computational points, small time steps, and/or long simulation time periods. Errors in the original AT123D code also were corrected in this modified version, AT123D-AT, in order to accurately simulate finite-duration (pulse) source releases.

A finite element model is presented for simulation of nuclide decay chain transport in a naturally fractured porous medium system. The model is capable of representing the physical system using a dual‐porosity approach, a discrete fracture approach, or a combination of these two approaches. Advection and hydrodynamic dispersion in the fractures, as well as diffusion in the porous matrix and chain reactions of solute species, can be taken into account simultaneously. An efficient finite element solution technique has been developed to solve a coupled system of governing partial differential equations. Via this technique, spatial discretizations and solutions of systems of algebraic equations for nodal concentration values in fracture and porous matrix domains can be performed separately. The present finite element model has been verified against analytical solutions. Two test problems involving transport of a chain of three components in unfractured and fractured porous media are presented to demonstrate the accuracy and efficiency of the proposed finite element technique. Results indicate that the present numerical model is capable of producing good predictions of breakthrough curves using relatively coarse spatial and temporal discretizations. A major advantage of the present transport model over previous transport models is that the latter are based on a numerical approach that employs overall discretization and simultaneous solution of the entire set of algebraic equations for concentration values in the fracture and porous matrix block domains. Such an approach is not computationally efficient when compared with the present numerical approach, which employs not only separate discretizations of the fracture and porous matrix domains but also direct sequential solutions of much smaller subsets of algebraic equations. Another important practical aspect is that the present model enables more complex problems, involving transverse diffusion into porous matrix and two‐dimensional transport in the fracture flow plane, to be handled without resorting to a fully three‐dimensional grid. In practical applications, CPU time and cost involved in performing a fully three‐dimensional analysis of multiple species transport may be prohibitive.

Volusia County, in east central Florida, comprises approximately 1,200 square miles situated between the St. Johns River and the Atlantic Ocean. Most of the County is underlain by a threeaquifer system. Population centers in Volusia County, which create a large water demand, are located near the coast. Saltwater intrusion into the ground water near these population centers has led to relocation of public water supply wells further inland. Regional management of the county's water resources commissioned construction of a three-dimensional computer model of the county. Predevelopment simulation results were used as initial conditions for the development simulations, which included well discharge data. The predevelopment model calibration consisted of reproducing field-determined potentiometric surfaces. As part of the calibration process, sensitivity analyses were performed on boundary conditions, recharge rates, permeability, and leakage properties. Results of the model study indicate the utility of computer models as a management tool for the complex ground-water system in Volusia County. (KEY TERMS: ground-water management; saltwater intrusion; finitedifference model.)