| 15 Jun 2026
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.
The manuscript addresses the important problem of reaction front propagation that is, according to the authors, driven essentially by the conservation of mass in the quasi-static regime. The authors derive the governing equations of a single reaction front at a first stage, then they propose two reaction fronts that are coupled. Their derivations lead to a characteristic square-root-of-time scaling of the front propagation that is governed by the conservation of mass across the moving boundary rather than classical non-reactive hydraulic pore-pressure diffusion. Hence, the authors define "effective diffusivities" that incorporate both hydraulic variables (permeability, viscosity, pressure difference) and chemical parameters (variation of density within the front). This result is interesting because it explains why the reaction progress is orders of magnitudes slower than expected based on the intuitive pure hydraulic process. Comparisons with the data of Fusseis (2012) and Schmalholz (2020) seem to support the proposed model.
There are some minor changes that I would like to suggest to improve the readability of the paper:
1- The assumptions and limitations of the proposed model need to be stated clearly. For example, the model is only valid if the matrix is rigid. This assumption makes the model useful in the absence of mechanical loading only. This model may also fail if the front profile changes shape (the case where v_fron is dependent on space) or the reaction presents wave fingers.
2- In equation 9, the gradient is is unusual it should be Delta P/Delta x, because in the end, x-front and x-behind do move.
3- In Darcy law, why is k dependent on z_behind and not on z_front or z_average?
4- In many situations, the coupled two front seem to require that density, permeability and viscosity are all different. (see equations A19, A20 and A21 etc), but this is not required. In fact it sufficient that one of them changes. For example in the case of gypsum, the density and viscosity of water remain the same at room temperature but permeability may change significantly.
5- Please check the text for typos. For example, in page 16, "generate a reaction front with a witdth of 1 m...". Change this to width.
Overall, the manuscript is of good quality in my opinion, and I recommend it for publication.