Mixing Ratios With Age: Application to Preasymptotic One-Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media

Analysis of reactive transport in natural and engineered porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of transport and reactions processes. General use of solute age has also been recently explored as a way to describe solute mass transfer and/or as a proxy for reaction extent. Age here is defined as exposure time to the flow field. Pairing these concepts, we develop mixing ratio models that are structured on age. One-dimensional transport is cast in terms of age-structured mixing ratios in general and compared with conventional formulations of mixing ratio models, demonstrating that age is often a more natural independent variable than absolute time. Using this modeling framework, we then apply age-structured mixing ratios to the problem of mixing-limited reactive transport in one-dimension by explicitly considering unmixed and mixed phases. In order to address mixing limitations under the entirety of transport including the preasymptotic dispersion timeframe, we use the same age variable to define the dispersion coefficient value in a local formulation of transport. Establishing an age-dependent dispersion coefficient allows simulation of the whole transport time including both preasymptotic and asymptotic dispersion conditions with one model. In our application we explore use of this modeling approach to both synthetic preasymptotic data and experimental asymptotic data pertaining to one famous experiment.