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  • 1
    ISSN: 1573-1634
    Keywords: network model ; biofilm ; biobarrier ; permeability ; Monod kinetics ; adsorption
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We demonstrate how a network model can predict porosity and permeability changes in a porous medium as a result of biofilm buildup in the pore spaces. A biofilm consists of bacteria and extracellular polymeric substances (EPS) bonded together and attached to a surface. In this case, the surface consists of the walls of the porous medium, which we model as a random network of pipes. Our model contains five species. Four of these are bacteria and EPS in both fluid and adsorbed phases. The fifth species is nutrient, which we assume to reside in the fluid phase only. Bacteria and EPS transfer between the adsorbed and fluid phases through adsorption and erosion or sloughing. The adsorbed species influence the effective radii of the pipes in the network, which affect the porosity and permeability. We develop a technique for integrating the coupled system of ordinary and partial differential equations that govern transport of these species in the network. We examine ensemble averages of simulations using different arrays of pipe radii having identical statistics. These averages show how different rate parameters in the biofilm transport processes affect the concentration and permeability profiles.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0749-159X
    Keywords: convection-reaction equations ; Lagrangian methods ; convective flows ; reactive solute transport problems ; exact finite difference schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467-485, 1998
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biofilm forming microbes have complex effects on the flow properties of natural porous media. Subsurface biofilms have the potential for the formation of biobarriers to inhibit contaminant migration in groundwater. Another example of beneficial microbial effects is the biotransformation of organic contaminants to less harmful forms, thereby providing an in situ method for treatment of contaminated groundwater supplies. Mathematical models that describe contaminant transport with biodegradation involve a set of coupled convection-dispersion equations with non-linear reactions. The reactive solute transport equation is one for which numerical solution procedures continue to exhibit significant limitations for certain problems of groundwater hydrology interest. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. A new numerical method is developed for simulation of reactive bacterial transport in porous media. The non-standard numerical approach is based on the ideas of the ‘exact’ time-stepping scheme. It leads to solutions free from the numerical instabilities that arise from incorrect modeling of derivatives and reaction terms. Applications to different biofilm models are examined and numerical results are presented to demonstrate the performance of the proposed new method.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-1634
    Keywords: biofilm ; network model ; permeability ; transport ; numerical diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper, we develop a network model to determine porosity and permeability changes in a porous medium as a result of changes in the amount of biomass. The biomass is in the form of biofilms. Biofilms form when certain types of bacteria reproduce, bond to surfaces, and produce extracellular polymer (EPS) filaments that link together the bacteria. The pore spaces are modeled as a system of interconnected pipes in two and three dimensions. The radii of the pipes are given by a lognormal probability distribution. Volumetric flow rates through each of the pipes, and through the medium, are determined by solving a linear system of equations, with a symmetric and positive definite matrix. Transport through the medium is modeled by upwind, explicit finite difference approximations in the individual pipes. Methods for handling the boundary conditions between pipes and for visualizing the results of numerical simulations are developed. Increases in biomass, as a result of transport and reaction, decrease the pipe radii, which decreases the permeability of the medium. Relationships between biomass accumulation and permeability and porosity reduction are presented.
    Type of Medium: Electronic Resource
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  • 5
    Publication Date: 2017-01-12
    Description: Terrestrial ecosystems have absorbed roughly 30% of anthropogenic CO2 emissions over the past decades, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling and experimental and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under global change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, which is the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3-D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. In addition, the physical emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. Overall, this new mathematical framework offers new approaches to understanding, evaluating, diagnosing, and improving land C cycle models.
    Print ISSN: 1726-4170
    Electronic ISSN: 1726-4189
    Topics: Biology , Geosciences
    Published by Copernicus on behalf of European Geosciences Union (EGU).
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  • 6
    Publication Date: 2016-09-16
    Description: Terrestrial ecosystems absorb roughly 30 % of anthropogenic CO2 emissions since preindustrial era, but it is unclear whether this carbon (C) sink will endure into the future. Despite extensive modeling, experimental, and observational studies, what fundamentally determines transient dynamics of terrestrial C storage under climate change is still not very clear. Here we develop a new framework for understanding transient dynamics of terrestrial C storage through mathematical analysis and numerical experiments. Our analysis indicates that the ultimate force driving ecosystem C storage change is the C storage capacity, which is jointly determined by ecosystem C input (e.g., net primary production, NPP) and residence time. Since both C input and residence time vary with time, the C storage capacity is time-dependent and acts as a moving attractor that actual C storage chases. The rate of change in C storage is proportional to the C storage potential, the difference between the current storage and the storage capacity. The C storage capacity represents instantaneous responses of the land C cycle to external forcing, whereas the C storage potential represents the internal capability of the land C cycle to influence the C change trajectory in the next time step. The influence happens through redistribution of net C pool changes in a network of pools with different residence times. Moreover, this and our other studies have demonstrated that one matrix equation can exactly replicate simulations of most land C cycle models (i.e., physical emulators). As a result, simulation outputs of those models can be placed into a three-dimensional (3D) parameter space to measure their differences. The latter can be decomposed into traceable components to track the origins of model uncertainty. Moreover, the emulators make data assimilation computationally feasible so that both C flux- and pool-related datasets can be used to better constrain model predictions of land C sequestration. We also propose that the C storage potential be the targeted variable for research, market trading, and government negotiation for C credits.
    Print ISSN: 1810-6277
    Electronic ISSN: 1810-6285
    Topics: Biology , Geosciences
    Published by Copernicus on behalf of European Geosciences Union (EGU).
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