Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advancement along the current frontier: biochemical reactions. To this end, we review the basic equations to indicate that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous challenges are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic eleven conceptual issues that we consider fundamental for any conceptually sound RT effort.

Biofilm growth in porous media changes not only the hydrodynamic properties of the medium (reduction in porosity and permeability, and increase in dispersivity), but also the transport itself (breakthrough curves display increasingly fast first arrivals and long tails). These features are well reproduced by multicontinuum models (Multi‐Rate Mass Transfer, MRMT) which can be used to describe reactive transport in heterogeneous porous media and facilitate the simulation of reactions that are localized within biofilms. Here, we present a conceptual and numerical model of biochemical reactive transport with dynamic biofilm growth based on MRMT formulations. Mass exchange between mobile water and immobile biofilm aggregates is represented by a memory function, which simplifies definition of MRMT parameters. We successfully tested this model on two sets of laboratory data and found that (a) a basic model based on the growth of uniformly sized biofilm aggregates fails to reproduce laboratory tracer tests and rate of biofilm growth, while a fractal growth model, which we obtain by integrating the memory functions of biofilm aggregates with a power law distribution, does; (b) the biofilm memory function evolves as the biofilm grows; and (c) the early time portion of eluted volume tracer breakthrough curves are independent of flow rate, whereas the tail becomes heavier when the flow rate is decreased, which implies that both advection controlled and diffusion controlled mass exchange coexist in biofilms. These findings imply that porous media biofilms are essentially different from those developing in human tissues or open spaces.

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.

Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advance along the current frontier: biochemical reactions. To this end, we review the basic equations to point that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous frontiers are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic 10 issues that we consider fundamental for any conceptually sound RT effort.