A general and efficient numerical solution of reactive transport with multirate mass transfer

The presence of low permeability regions within porous media impacts solute transport and the distribution of species concentrations. Therefore, (bio)chemical reactions are equally affected. Multirate Mass Transfer (MRMT) models can be used to represent this anomalous transport process. MRMT conceptualizes the medium as a set of multiple continua: one mobile zone and multiple immobile zones. It simulates species transport in mobile and immobile zones simultaneously, which are related by first-order mass exchange. Numerical modeling of reactive transport in this kind of multicontinua media is complex and demanding because of the high dimensionality of the problem. In this paper, we establish the governing equations of reactive transport in multicontinuum media incorporating chemical kinetics into the governing equations. We propose a general numerical solution of reactive transport with MRMT by applying direct substitution approach (DSA) based on Newton-Raphson method. The efficiency of the proposed algorithm benefits of the block structure of the system, which allows us to eliminate immobile zones equations and leads to significant savings in CPU time. We test the validity of the developed solution by comparison with other numerical and analytical solutions.

Automated summary

The presence of low permeability regions within porous media affects solute transport and species concentrations distribution. Multirate Mass Transfer (MRMT) models represent this anomalous transport process, which conceptualizes the medium as one mobile zone and multiple immobile zones. The numerical solution with MRMT for reactive transport is developed, incorporating chemical kinetics into the governing equations, and the efficiency of the proposed algorithm allows for significant savings in CPU time. The validity of the developed solution is tested by comparison with other numerical and analytical solutions.