REACTIVE TRANSPORT AND IMMISCIBLE FLOW IN GEOLOGICAL MEDIA .1. GENERAL-THEORY

Steady flow of incompressible fluid takes place in geological formatio ns of spatially variable permeability. The permeability is regarded as a stationary random space function (RSF) of given statistical moments . The fluid carries reactive solutes and we consider, for illustration purposes, two types of reactions: nonlinear equilibrium sorption of a single species and mineral dissolution (linear kinetics). In addition , we analyse the nonlinear problem of horizontal flow of two immiscibl e fluids (the Buckley-Leverett flow). We consider injection at constan t concentration in a semiinfinite domain at constant initial concentra tion and we neglect the effect of pore scale dispersion. The field-sca le transport problem consists of characterizing an erratic plume, or d isplacement front, emanating from a given source area along distinct r andom flow paths. Reactive transport along three-dimensional flow path s is transformed to a one-dimensional Lagrangian-Eulerian domain (tau, t), where tau is the fluid residence time and t is the real time. Due to nonlinearity, discontinuities (shock waves) along a flow path may develop. Close form solutions are obtained for the expected values of the spatial and temporal moments of a nonlinearly reacting solute plum e, or of two immiscible fluids. These results generalize the previous results for linearly reacting solute (Cvetkovic & Dagan 1994). The gen eral results are illustrated and discussed in part II.