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Applicability of averaged concentrations in determining geochemical reaction rates in heterogeneous porous media

Li Li^*,, Catherine A. Peters^** and Michael A. Celia^**

^* Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 90-1116, Berkeley, California 94720
^** Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey 08544

Corresponding author: Li Li, lili{at}lbl.gov

This work examines the applicability of averaged concentrations, a mathematical analog of field-measured solute concentrations averaged over a large number of pores, in determining mineral reaction rates in heterogeneous porous media. Pore-scale network models were used to represent sandstones with anorthite and kaolinite as reactive minerals that are heterogeneously distributed in space. Reaction rates calculated from averaged concentrations were compared to true reaction rates that take into account variabilities in individual pore properties. Simulations were run under the highly acidic conditions relevant to geological CO₂ sequestration in deep brine formations under various mineralogical and flow conditions. Results show that, under conditions where incomplete mixing arises, the averaged concentrations and analogously the field-measured concentrations, do not accurately reflect reaction progress. Over the length scale of several millimeters, the anorthite dissolution rates can be overestimated by a factor of three. For kaolinite, due to its highly nonlinear reaction rate law, even the reaction direction may be incorrectly determined, with precipitation predicted as dissolution. The extent of errors introduced depends on the extent of incomplete mixing. Conditions that homogenize the concentration fields, such as small reactive mineral clusters, abundant reactive minerals, and very fast or very slow flow rates, minimize errors introduced from averaging. These results indicate that the averaging scheme may partly contribute to the often-cited laboratory-field rate discrepancy and have important implications for the interpretation of concentration data obtained from field investigation.