Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions

In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported

Modeling non-equilibrium mass transport in biologically reactive porous media.

We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection–dispersion–reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium

A model for reactive porous transport during re-wetting of hardened concrete

A mathematical model is developed that captures the transport of liquid water in hardened concrete, as well as the chemical reactions that occur between the imbibed water and the residual calcium silicate compounds residing in the porous concrete matrix. The main hypothesis in this model is that the reaction product -- calcium silicate hydrate gel -- clogs the pores within the concrete thereby hindering water transport. Numerical simulations are employed to determine the sensitivity of the model solution to changes in various physical parameters, and compare to experimental results available in the literature.Comment: 30 page

Mathematical modeling of bioremediation of trichloroethylene in aquifers

AbstractTrichloroethylene (TCE) is a very common contaminant of groundwater. It is used as an industrial solvent and is frequently poured into the soil. There exist bacteria that can degrade TCE. In contrast with most cases of bioremediation, the bacteria that degrade TCE do not use it as a carbon source. Instead the bacteria produce an enzyme to metabolize methane. This enzyme can degrade other organics including TCE. In this paper we model in situ bioremediation of TCE in an aquifer by using two species of bacteria: one that forms biobarriers to restrict the movement of TCE and the second one to reduce TCE. The model includes flow of water, transport of TCE and the nutrients, bacterial growth and degradation of TCE. Nonstandard numerical methods are used to discretize the equations. Some results are presented

スポンジ担体におけるバイオフィルムのマルチスケールモデル

本研究は、生物学的排水処理プロセスで多用される生物膜法について、生物膜内外の物質移動と生物反応を数学的に記述することを目的としたものである。北九州市立大

Effects of pore-scale velocity and pore-scale physical processes on contaminant biodegradation during transport in groundwater: modeling and experiments

Contamination of surface and ground water has emerged as one of the most important environmental issues in developed and developing countries. Bioremediation of groundwater takes advantage of bacteria present in the environment to transform toxic compounds to non-toxic metabolites. This biotechnology holds the potential for fast, inexpensive, and effective water decontamination. However, it is still poorly understood and usually not fully controlled due to the lack of information describing the natural phenomena involved. Therefore, a better understanding of the phenomena involved during bioremediation of groundwater could help in the design and implementation of more efficient technologies. The main objective of the present research is to assess how pore-scale physical factors, such as pore-scale velocity, affect the degradation potential of contaminants during transport in groundwater. The target chemicals studied were chlorinated ethenes because they are commonly found in contaminated groundwater sites. To achieve the research objective, the following were employed: a mathematical model that links pore scale processes to the macro-scale representation of contaminant transport; development of numerical tools to solve the mathematical model; and experimental elucidation of the influence of pore-scale flow velocity on the biodegradation of contaminants using column experiments. Results from the mathematical model and experiments were used to elucidate the inter-relationship between physical and biological phenomena at the micro scale. The influence of flow velocity through the porous media (a physical factor) on the biological structure (microbial community in the porous media) was assessed. The results of this investigation contribute to the bioremediation of contaminated groundwater understanding with new insights on the importance of physical transport factors on the biodegradation potential. For example, flow velocity is shown to have an important effect on the degradation potential of chlorinated ethenes. Additionally, the mathematical model and numerical tools have potential application to many other reactive transport problems, including: adsorption onto activated carbon, reaction in packed beds of catalyst, chemical transport in streambeds, and separation in chromatographic columns

Reactive transport: a review of basic concepts with emphasis on biochemical processes

Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advancement along the current frontier: biochemical reactions. To this end, we review the basic equations to indicate that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous challenges are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic eleven conceptual issues that we consider fundamental for any conceptually sound RT effort.This work is part of grants MEDISTRAES III funded by MCIN/AEI/ PID2019-110212RB-C22 and MCIN/AEI/PID2019-110311RB-C21 and Water JPI project MARadentro (PCI2019-103603), and by the Catalan Water Agency through the project RESTORA (CA210/18/00040). IDAEA-CSIC is a Center of Excellence Severo Ochoa (Grant CEX2018-000794-S funded by MCIN/AEI/ 10.13039/501100011033).Peer ReviewedPostprint (published version