A chemical reaction model in a porous medium

Chemical reactions in a porous medium are found in many natural phenomena and technological processes. Reactive substances dissolved in groundwater can significantly change the soil strength. The precipitate formed as a result of the reaction changes the porous medium structure and affects the porosity and permeability. A one-dimensional model of the reaction of two reagents in a homogeneous porous medium with a linear reaction function is considered. The model includes the mass balance equations of each reagent and precipitate, and the kinetic equation of precipitate growth. It is assumed that the precipitate is stationary and the growth rate of the precipitate is proportional to the reagents' concentration. A carrier fluid with constant concentration reagents is injected at the empty porous medium entrance. The reaction front moves in a porous medium at a constant speed. The exact solution to the problem is constructed by eliminating the unknown functions and lowering the equations' order. A Riemann invariant that relates the concentration of sediment and reagents to the system's characteristics was found. The reaction's numerical simulation is performed. It is shown that, for a long time, the reagents' concentrations and the precipitate tend to final limit values. Sediment profiles always decrease monotonously, and the type of the profiles' convexity changes.