Bimolecular reactive transport in a two-dimensional velocity field in disordered media. (25th September 2019)

• Record Type: Journal Article
• Authors: Ben-Zvi, Rami; Scher, Harvey; Berkowitz, Brian
• Is Part Of: Journal of physics. Volume 52:Number 42(2019)
• Publication Date: 2019-09-25
• Subjects: continuous time random walk (CTRW) -- anomalous transport -- bimolecular reactions -- modeling -- laboratory experiment; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab4077
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The nonlocal-in-time, integro-partial differential equation ( i PDE) describing the continuous time random walk (CTRW) is augmented by a nonlinear chemical-species term accounting for migrating bimolecular reactions in disordered media. This augmented form of the i PDE, previously shown to be in excellent agreement with a particle-tracking (CTRW-PT) version of reactive transport, is applied here to a reanalysis of recent experimental results to further establish its validity. The experimental set-up uses an injected solution of a pH indicator (Congo red) as both an inert tracer or a reactant, depending on the pH of the solution. A refraction index-matched, water-saturated porous medium allows tracking of the reacted concentration field, which is modeled by the solutions of the two-species coupled i PDE, whose nonlinear form precludes the use of a Laplace transform. The time-domain solutions are obtained with a finite element method (FEM) and a sum of exponentials representation of the kernel (memory function). The two-dimensional flow field subject to the macroscopic boundary conditions is calculated by solving the Darcy equation. The CTRW is well established for nonreactive transport in disordered media. The fit for the inert tracer in this case provides a reasonable match to these particular experimental data. The comparable, agreeable fit for the reactive case further establishes the validity of the i PDE augmented with a nonlinear, second-order reaction term.