THE QUASI-STATIONARY STATE APPROXIMATION TO COUPLED MASS TRANSPORT AND FLUID-ROCK INTERACTION IN A POROUS MEDIUM

Abstract

The quasi-stationary state approximation to mass transport and fluid-rock interaction provides a quantitative description of metasomatic processes over geologically significant time spans. Each stationary state describes the fluid composition and rates of reacting minerals as a function of distance corresponding to a particular state of alteration of the host rock. Because time steps separating stationary states are not restricted by stability and accuracy requirements as apply to conventional finite difference algorithms, geologic time spans are attainable for complex geochemical systems. The approximation is valid if mineral reaction zone boundaries, surface area, porosity and permeability change slowly compared to the time required to establish a stationary state. The propagation in time of mineral alteration zones can be predicted without any additional assumptions of the functional relationship of the zone boundaries on time. The validity of the quasi-stationary state approximation is examined for reaction of the minerals calcite and quartz. An exact expression is obtained for the velocity and position of the dissolution front formed in a single component system for a linear kinetic rate law. Numerical and analytical examples for the dissolution of quartz at 550/sup 0/C and 1 kb are in excellent agreement with numerical finite difference calculations based on exact transient mass conservation equations. Finally, the quasi-stationary state approximation is applied to the hydrochemical weathering of K-feldspar resulting from infiltrating rainwater. Product minerals gibbsite, kaolinite and muscovite form alteration zones which propagate with time in response to the reduction in surface area and, eventually, complete reaction of the dissolving K-feldspar mineral grains. During the initial stages of alteration gibbsite forms directly from K-feldspar, but in later stages forms indirectly from kaolinite.