A conceptual model of subsurface contaminant transport with biodegradation is presented. This model incorporates both aerobic and anaerobic reactions, with several models of differing complexity presented for the anaerobic case. Nutrient uptake is described using Michaelis‐Menten expressions, which are incorporated into a multiple nutrient uptake model. Several uptake inhibition factors are also included in the model. The mathematical model that results takes the form of a series of reactive transport equations. These equations are coupled nonlinearly through the reaction terms, which are themselves coupled to growth equations for subsurface bacterial populations. Example simulations are presented for a variety of cases, ranging from one‐substrate, one‐population aerobic degradation to multisubstrate, multipopulation anaerobic consortium degradation.

A new numerical solution procedure is presented for simulation of reactive transport in porous media. The new procedure, which is referred to as an optimal test function (OTF) method, is formulated so that it systematically adapts to the changing character of the governing partial differential equation. Relative importance of diffusion, advection, and reaction are directly incorporated into the numerical approximation by judicious choice of the test, or weight, function that appears in the weak form of the equation. Specific algorithms are presented to solve a general class of nonlinear, multispecies transport equations. This includes a variety of models of subsurface contaminant transport with biodegradation.

A new numerical solution procedure is presented for the one-dimensional, transient advective-diffusive transport equation. The new method applies Herrera's algebraic theory of numerical methods to the spatial derivatives to produce a semi-discrete approximation. The semi-discrete system is then solved by standard time marching algorithms. The algebraic theory, which involves careful choice of test functions in a weak form statement of the problem, leads to a numerical approximation that inherently accommodates different degrees of advection domination. Algorithms are presented that provide either nodal values of the unknown function or nodal values of both the function and its spatial derivative. Numerical solution of several test problems demonstrates the behavior of the method. LNTRODUCTIONNumerical solution of the advective-diffusive transport equation is of great importance in many fields of engineering and science. When the diffusive process dominates, the transport equation is relatively easy to solve by virtually any standard numerical scheme. However, when the problem is dominated by advection, standard numerical approximations become problematic. Either nonphysical oscillations appear in the vicinity of sharp fronts, or excessive numerical diffusion is introduced and the ability to capture a sharp front is precluded.Considerable effort has been expended in developing discretization formulas for the advective-diffusive transport equation. Most formulations involve some sort of upstream weighting to accommodate the advective nature of the transport. These include classical upstream weighted finite differences [20], highorder upstream finite differences [21], collocation methods [ l , 221, and a variety of finite element, or Petrov-Galerkin methods [3,8, 10,[16][17][18]. A fundamental

The borehole permeameter (BP) method was developed in the 1950s by the United States Bureau of Reclamation to estimate saturated soil hydraulic conductivity (K S) in shallow boreholes completed above the water table. The approach has been improved over the years, and now accounts for flow due to pressure, gravity and soil capillarity. However, the BP method is calibrated only for normally consolidated soils and ponding depth (H) versus borehole radius (r) ratios (H/r) ≤ 22. The primary objective of this study was to recalibrate the BP method for use in glacially over-consolidated soils with H/r ranging from 0.05 to 200. Recalibration consisted of using numerically simulated steady BP flow for five representative glacially over-consolidated soils to update the BP shape function fitting parameters (Z 1 , Z 2 , Z 3) for nine specified K S values and 15 test pit and borehole configurations. Four sets of fitting parameters were determined, which apply for H/r ≤ 20, H/r ≥ 20, soil with <12% silt content, and soil with >12% silt content. Relative to specified K S , the updated shape function parameters yielded BP estimates of K S with a maximum error of 13% and an average error of 3%, whereas the original shape function parameters (developed for normally consolidated soils and H/r ≤ 22) produced a maximum K S error of 94% and an average error of 23%. The numerical simulations were also used to develop criteria for estimating time required to achieve steady BP flow, and for correcting BP estimates of K S where steady flow was not achieved.

This paper -Develops a discrete fracture approach to flow analysis of dual-porosity systems. The well-established methods of analyzing dual-porosity flow in fractures deal primarily with matrix blocks having idealized sha s, suc, pe n as slabs, blocks, and spheres. While these geometric simplification allow analytical solution of difficult flow problems, they @) neglect the geometric complexities Of real fracture systenis. The discrete-fracture, dual-porosity approach present@ here is an enhancement of discrete-fracture network model which associates a volume of storative material .with each fracture surface. The flow interactions betwec!n the storative volume and the fracture may be either steaijy-state or transient.Two applir-ations are presented. Thit first uses a s . single horizontal fracture as a test case. The second employs a small number of vertical fractures to investigate local effects on drawdown behavior INTRODUCTION The analysis of flow in fractures has followed two broad approaches over the past several years. On one hand, there has bctn the discrete fracture approach which has attempted to study the flow in individually-identified fracture conduits. Among these have been the approaches of Long, et al: (19:32), and Dershowitz (1984) which model 120-1 flow in discrete fracture networks generated by stochastic simulators. On the other hand, there have been numerous methods which idealize the fracture systems as porous co . ntinua . with special attributes such as being an anisotropic continuum (Hsieh, 1983) or heterogeneous (stochastic) continuum (e.g., Smith and Freeze, 1979). In these methods it is assumed that the fracture system behaves as a continuum at scales larger than a representative elementary volume.As Moench (1984) points out, the theory of dual-porosity flow is a continuum approach in which there are two rei)resentative elementary volumes (REV's). One REV represents the fracture system, the other the matrix. As in all continuum approaches, the details of the fracture-system geometry are lumped into the properties of the continuum. Potentially important details on interconnection among fractures and between boundaries are lost.This paper presents the extension of dual porosity concepts from continuum-flow analysis to discrete fracture-flow . analysis. The paper begins with a discussion of dual-porosity continuum methods, concentrating on the description of flow between the matrix blocks and the fracture continuum.A dual-porosity model of discrete fracture flow is developed by associating a generic matrix block with each fracture segment in the discrete-fracture