Solute transport predicts scaling of surface reaction rates in porous media: Applications to silicate weathering

TL;DR

This paper demonstrates that a theory of conservative solute transport, based on percolation concepts, can predict surface reaction rate scaling in porous media, linking lab and field data for silicate weathering over vast scales.

Contribution

The study extends a conservative solute transport theory to reactive transport, successfully predicting weathering rates across multiple scales and unifying laboratory and field observations.

Findings

Transport velocities limit reaction rates.

Predicted temporal dependence matches weathering data.

Length dependence agrees with observed reaction rate scaling.

Abstract

We apply our theory of conservative solute transport, based on concepts from percolation theory, directly and without modification to reactive solute transport. This theory has previously been shown to predict the observed range of dispersivity values for conservative solute transport over ten orders of magnitude of length scale. We now show that the temporal dependence derived for the solute velocity accurately predicts the time-dependence for the weathering of silicate minerals over nine orders of magnitude of time scale, while its predicted length dependence agrees with data obtained for reaction rates over five orders of magnitude of length scale. In both cases, it is possible to unify lab and field results. Thus, net reaction rates appear to be limited by solute transport velocities. We suggest the possible relevance of our results to landscape evolution of the earth's terrestrial surface.