Fluid flow, reaction progress and solid solution in lithologically layered porous media

Numerical modeling of the reactive fluid flow in natural porous media like rock and soil is not a trivial task. The governing system of coupled partial differential and non-linear equations that describe the mass transport, reaction stoichiometry, and mineral-fluid equilibrium is large and cumbersome. It is only within the last decade or so that theoretical models based on the equations of mass transport and reaction progress were developed. Proper modeling, however, has rarely met the challenge of considering the effects of solid solutions on reaction progress. Many current models of reactive fluid flow fail to consider that the minerals involved in the reactions are solid solutions. This is problematic because in nature most solids have compositions that can vary in space and time and the compositional variations can strongly effect reaction progress.;The system of non-linear equations that couples reaction progress to solid solution can, however, be simplified, and well approximated by a smaller system of quadratic functions. These quadratic functions can be used to greatly reduce the cost and complexity of modeling coupled transport and reaction progress. A theory that combines mass transport, reaction progress, as well as compositional variations was developed and implemented in a numerical model that specifically considers the reaction of a CO2-H2O fluid solution with olivine solid solution to form talc and magnesite. The reaction was chosen both to understand reactive metamorphic fluid flow in the Central Swiss Alps and as a simple analog for geological carbon sequestration. An analysis of the theory and its implementation is given along with some numerical results that demonstrate that the model can reproduce the seemingly disparate variety of distributions of mineral reactants and products observed in the field.