Modeling multiphase non-isothermal fluid flow and reactive geochemical transport in variably saturated fractured rocks: 1. Methodology

Reactive fluid flow and geochemical transport in unsaturated fractured rocks have received increasing attention for studies of contaminant transport, ground-water quality, waste disposal, acid mine drainage remediation, mineral deposits, sedimentary diagenesis, and fluid-rock interactions in hydrothermal systems, This paper presents methods for modeling geochemical systems that emphasize: (1) involvement of the gas phase in addition to liquid and solid phases m fluid flow, mass transport, and chemical reactions; (2) treatment of physically and chemically heterogeneous and fractured rocks, (3) the effect of heat on fluid flow and reaction properties and processes, and (4) the kinetics of fluid-rock interaction. The physical and chemical process model is embodied in a system of partial differential equations for flow and transport, coupled to algebraic equations and ordinary differential equations for chemical interactions. For numerical solution, the continuum equations are discretized in space and time. Space discretization is based on a flexible integral finite difference approach that can use irregular gridding to model geologic structure; time is discretized fully implicitly as a first-order finite difference. Heterogeneous and fractured media are treated with a general multiple interacting continua method that includes double-porosity, dual-permeability, and multi-region models as special cases, A sequential iteration approach is used to treat the coupling between fluid flow and mass transport on the one hand, chemical reactions on the other. Applications of the methods developed here to variably saturated geochemical systems are presented in a companion paper (part 2, this issue).