A Single-Pole Approximation to Interfacial Mass Transfer in Porous Media Augmented with Bulk Reactions

Abstract

We study interfacial mass transfer between two immiscible fluids in porous media augmented with bulk reactions. A closed-form analytic approximation derived through Laplace transformation is represented for Darcy-Brinkman flow in the presence of firstorder bulk reactions represented by the Damköhler number (Da). By comparing the residues of all the singularities, it is shown that the main contributor to the solution is the simple pole of the equations. We show that the solution holds for a range of Da.Pe < 2.5 × 10 5 , where Pe is the Péclet number. By determining the bulk flow mass transfer coefficient, we verify our approximation compared to the previous studies and show acceptable conformity of the solutions. We find that the results are applicable for potential bulk reactions, such as biodegradation, in a typical groundwater system. List of symbolś

The Dynamics of Per- and Polyfluoroalkyl Substances (PFAS) at Interfaces in Porous Media: A Computational Roadmap from Nanoscale Molecular Dynamics Simulation to Macroscale Modeling

“…This is seen to be feasible through systematic upscaling of both experimental and computational studies from nano- to microscales. Indeed, similar to the momentum field for which the Darcy law has been amended by further terms for special cases (e.g., Darcy–Forchheimer and Darcy Brinkman for inertia and friction, respectively), it might be possible to include terms in the Darcy scale mass transport equation. Where NAPLs also coexist (including DNAPLs , ), this is particularly challenging, but such occurrences are common and warrant investigation.…”

A Screening Model to Predict Entrapped LNAPL Depletion

“…Teramoto and Chang [15], Mackay et al [23], Huntley and Beckett [24], and Thornton et al [25], among others, demonstrated that the continuous loss of water-soluble compounds leads to continuous depletion of LNAPL in the source zone. Actually, there are a large number of analytical and numerical approaches, varying in scale and complexity, to simulate NAPL dissolution into the aqueous phase [18,[26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Most of these approaches are based on empirical Sherwood-Gilland models that do not consider explicitly the NAPL/water interface area and were exclusively validated by lab-scale experiments.…”

New Perspectives on the Laminar Boundary Layer Physics in a Polarized Pressure Field with Temperature Gradient: an Analytical Approximation to Blasius Equation

“…Such spectrum is very broad ranging from the revelation of homotopy analysis (Liao, 1992;Liao, 1999;Bég et al, 2012;Malvandi et al, 2014;Hassan andRashidi, 2014 andMakukula andMotsa, 2014), differential transforms (Rashidi et al, 2013 andGanji et al, 2016) and Adomian decompositions (Adomian, 1994;Wang, 2004;Aski et al, 2014 andAkpan, 2015) to a combination of these and analogous techniques (e.g., coupled integral transform and functional analysis (Lari and Moeini, 2015) and the joined differential transform method with the Padè approximants (Rashidi et al, 2013 andThiagarajan andSenthilkumar, 2013). An important outcome was investigation into more complex physical problems.…”