This paper describes reactive flow in permeable media based on a numerical model that assumes local thermodynamic equilibrium. The model simulates single-phase, one-dimensional flow with greater generality than any model in the current literature. The mathematical foundation for the formulation is discussed in some detail. Results for hypothetical examples demonstrate that ion exchange and precipitation/dissolution of solids can interact to produce wave behavior not possible with either phenomenon alone. An important application involving both ion exchange and precipitation/dissolution is alkaline flooding. Model predictions for several laboratory alkaline floods indicate that the assumption of equilibrium is justified for these experiments. Simple calculations based on the equilibrium theory provide estimates of pH loss and hydroxide penetration distance.