165. ULTRA-LONG TIME PREDICTION OF REACTIVE SOLUTE TRANSPORT IN GEOLOGIC FORMATIONS USING SPATIO-TEMPORAL UPSCALING: THEORY AND NUMERICAL EXPERIMENTS

Department: Mechanical & Aerospace Engineering
Faculty Advisor(s): Daniel M. Tartakovsky | Ilenia Battiato

Primary Student
Name: Farzaneh Rajabi
Email: frajabi@ucsd.edu
Phone: 858-291-2938
Grad Year: 2018

Abstract
Long-time predictions of reactive transport in porous media under time dependent boundary conditions and/or forcing factors require the formulation of continuum scale models for time-averages. Yet, as every macroscopic model, time-averaged models can loose predictivity and accuracy under certain conditions. This is true whenever lack of temporal and spatial scale separation occurs. In this work, we consider reactive transport of a solute undergoing a heterogeneous reaction and subject to time-varying boundary conditions in a periodic porous medium. By means of homogenization method, we derive macro-time continuum-scale equations and show that i) the dynamics at the macro-scale (Darcy-scale) is strongly influenced by the interplay between signal frequency at the boundary and transport processes at the pore level and ii) under which conditions space-time averaged equations accurately describe pore-scale processes. Finally, we test our theoretical results through numerical simulations of transport in a planar fracture with reacting walls and time-varying boundary conditions at the inlet. Our analysis shows a good match between numerical simulations and theoretical predictions.

Industry Application Area(s)
Energy/Clean technology | Environmental Engineering

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