Equilibrium-Approximated Solutions to the Reactive Lauwerier Problem: Thermal Fronts as Controls on Reactive Fronts in Earth Systems

Abstract. Rates of subsurface rock alteration by reactive flows are often essentially independent of kinetic rates and governed solely by solute transport to and from reactive mineral surfaces. This allows for a major simplification, making models tractable in complex kinetic systems through the widely applied local equilibrium assumption. Here, this assumption is applied to the Reactive Lauwerier Problem (RLP), which describes non-isothermal fluid injection into a confined aquifer, driving thermally induced solubility changes and reactions. Specifically, depending on the solubility nature of a given mineral, the thermally induced solubility changes can lead to either undersaturation and dissolution or supersaturation and precipitation. Using this framework, solutions for reaction rate and porosity evolution are developed and analyzed, leading to a functional time-dependent criterion that incorporates thermal parameters. A key feature – coalescence of thermal and reactive fronts – is then analyzed under various conditions. Finally, the applicability of the equilibrium model for important fluid-rock interaction processes is then discussed and examined, including sedimentary reservoir development, mineral carbonation in peridotite, and ore deposit formation. The findings highlight that such thermally driven reactive fronts near equilibrium often become essentially stationary after a relatively short period. As a result, their spatial evolution is governed solely by geological processes operating on much longer timescales.