Chemical and Thermochemical Wave Behavior in Multiphase Fluid Flow Through Permeable Media: Wave-Wave Interactions

The flow of reactive fluids through permeable media creates regions of constant composition for purely reactive flow. These regions are separated by waves, which mark the change in composition from one region to the next. We develop a theory which elucidates the interactions of these chemical waves with those formed from other flowing phenomena. We consider the following interactions: 1.) the intersection of precipitation/dissolution waves with other precipitation/dissolution waves formed from the sequential injection of fluid of a different composition, from a change in the direction of fluid flow, or from finite changes in the initial composition of the rock; 2.) the interactions of precipitation/dissolution waves with ion exchange waves; 3.) the interaction of thermal waves with chemical precipitation/dissolution waves, considering coupled and uncoupled thermal/chemical effects. Waves of a nature not previously found under constant (Riemann) boundary conditions are formed. Through the nondimensionalization of the chemical-energy balance, we define six dimensionless parameters, and investigate the relative effects of these parameters on temperature and composition. One dimensionless number can indicate when heat effects are important. The interaction of a thermal wave with precipitation/dissolution waves for nonadiabatic cases results in the formation of stationary waves and precipitation/dissolution waves with varying velocity. We assume a MarxLangenheim formulation sufficiently describes the movement of a thermal wave with thermal losses to the under- and overburden. A sequence may develop which contains mineral entities different from either the low or high temperature mineral sequence. We also show important effects of one additional dimensionless number obtained from restating the traditional Marx-Langenheim equation. The location of this thermal wave with respect to the precipitation/dissolution waves has a profound influence on the resulting fluid composition, mineral sequence, and the manner in which these compositions propagate within the permeable media. We further elucidate the nature of the Riemann problem for precipitation/dissolution reactions. Multiple discontinuities are regions of zero width in purely convective flow but appear with nonzero width in convective-dispersive flow. We show two cases which indicate the nonuniversality of the direction-dependent solution technique.