Beyond hydraulic diffusion: reaction front propagation and timescales in metamorphic (de)volatilization processes

Abstract. Metamorphic (de)volatilization reactions play fundamental roles in many geodynamic processes and are frequently associated with propagating reaction fronts, yet the mechanisms controlling front propagation remain poorly constrained. Here, we derive new analytical solutions for fluid pressure-driven (de)volatilization reaction fronts in porous rocks. The solutions predict that reaction-zone width increases with the square root of time, a scaling that arises from mass conservation across the moving reaction front rather than from classical hydraulic pore-pressure diffusion. Front propagation is governed by an effective diffusivity that depends on both hydraulic and chemical parameters, including reaction-induced density changes. Unlike conventional hydraulic diffusivity, which neglects reaction-induced density variations and generally predicts much faster propagation, the effective diffusivity captures the retardation of reaction fronts caused by density changes, with larger reaction-induced density changes producing slower propagation. In addition to a single-front formulation, we derive an analytical solution for two simultaneously propagating, coupled reaction fronts. The fronts are dynamically linked through mass conservation, preventing independent propagation and causing the leading front to advance faster than the trailing front. Both the single- and two-front solutions closely match numerical simulations. Application of the two-front model to published gypsum dehydration experiments shows that accounting for pore-water to pore-vapor transitions yields more realistic permeability estimates than single-front models. Application to natural metamorphic reactions predicts permeabilities between 10^-18 and 10^-24 m², consistent with independent experimental, geophysical, and geological estimates. By analogy, the analytical framework can also be extended to chemically controlled reaction fronts governed solely by chemical diffusion. The analytical solutions provide a quantitative framework for estimating the timescales of natural and experimental (de)volatilization processes involving propagating reaction fronts.