EXPOSURE TIME FORMULATION FOR REACTIVE TRANSPORT

Deviyani Gurung

Reactive transport modeling is an important tool for the analysis of physical, chemical and biological processes encountered in many environmental systems. Several upscaled models, of natural or engineered porous media, are commonly used for such modeling and take advantage of standard advection dispersion reaction equations (ADREs). These simple models are however unable to account for physical processes that can heavily influence reactive transport in such media, such as pre-asymptotic flow fields and mixing limitations between transport and reaction processes. To account for these complexities, researchers have developed proportionally complex mathematical and simulation-based models. However, these complicated models have remained underutilized among most practitioners owing to their non-intuitive formulations and computationally intensive mathematics. In this thesis, we present a novel, intuitive and relatively less strenuous computational method for the simulation of homogenous chemical reactions through the use of age: defined as exposure-time to the flow field, structured ADREs. The utility of this method is demonstrated through the development of two models to quantify mixing processes and pre-asymptotic dispersion without the use of non-local models. Analysis of reactive transport in porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of different species and processes. Additionally, general use of solute age has been recently explored as a proxy for reaction extent. Pairing these two concepts we developed mixing ratio models, structured on age, that is cast into a 1D transport formulation and compared with conventional formulations of mixing ratio models. This modeling framework was applied to the problem of mixing-limited reactive transport in one-dimension by explicitly considering unmixed and mixed phases. To address mixing limitations under the entirety of transport, including the pre-asymptotic dispersion timeframe, I use age-dependent dispersion coefficient in a local-formulation of transport. This formulation addresses the divisive controversy surrounding the use of time-dependent dispersion coefficients within an ADRE framework. Our physically intuitive model matches the performance of a recently published complicated and computationally intensive model of transient dispersion in direct comparison. Furthermore, our solutions can be applied to other upscaled one-dimensional transport problems such as river corridor, pipe networks, groundwater flows.

EXPOSURE TIME FORMULATION FOR REACTIVE TRANSPORT

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