Time‐space continuum description of fluid/rock interaction in permeable media

Abstract

The feasibility of integrating multicomponent mass transport equations over geologic time spans is demonstrated for the case of pure advection in a homogeneous porous medium. The mathematical formulation of the problem is based on the quasi‐stationary state approximation, or multiple reaction path description, in which the time evolution of a geochemical system is represented by a sequence of stationary states or reaction paths. The method is implemented in the computer code MPATH which solves the transport equations in a single spatial dimension taking into account irreversible mineral precipitation/dissolution reactions and local equilibrium of aqueous complexing reactions. An adaptive grid enables the positions of reaction zones, with widths which vary over many orders of magnitude and which move with greatly differing velocities, to be tracked simultaneously over geologic time spans. There appears to be virtually no limitation to the number of chemical species that can be included in the code without rendering the computational effort beyond the bounds of a high‐performance workstation. The numerical accuracy of the solution can be verified through global mass conservation equations and by comparing the asymptotic kinetic solution with the corresponding solution to algebraic equations representing local equilibrium conditions for pure advective transport, if such solutions exist. The code MPATH is applied to several examples including migration of redox fronts, weathering and hydrothermal alteration in a spatially varying temperature field. These examples demonstrate the absolute necessity of solving the governing transport equations for sufficiently long time spans in order to fully characterize the behavior of the system.