Dimension Reduction Method for Pore-Scale Reactive Transport Models

In the recent years pore-scale models emerged as a powerful tool to study reactive transport in porous media. The pore-scale models can employ varies numerical methods for solving conservation laws governing flow and transport on the pore-scale but they have a common feature: their discrete approximations are systems of ordinary differential equations (ODEs) which can contain an enormous number of unknowns ( >10¹⁰) when applied to a computational domain on the scale of REV. A direct solution of these ODEs can be extremely expensive. This necessitates development of advanced algorithms for model (or dimension) reduction. We developed a novel dimension reduction method for large size ODE systems. The method can significant accelerate pore-scale simulations regardless of the nature of a numerical solver. The method relies on a computational closure of averaged evolution balance equations. The computational closure is achieved via short bursts of a pore-scale model conducted in small portions of the computational domain. The dimension reduction model was used to simulate flow and transport with mixing controlled reactions and mineral precipitation. The good agreement with micro-fluidic experiments and analytical solutions confirms the accuracy and computational efficiency of the dimension reduction model.