Pore‐scale modeling of biological clogging due to aggregate expansion: A material mechanics approach

Whereas most previous studies of biomass growth and biological clogging consider continuous biofilms, we investigate how the growth of biomass in the form of aggregates affects the permeability and the transport properties of porous media. This paper presents modeling of processes in a single pore, and a companion paper [Dupin et al., this issue] describes modeling over a network of pores. Each pore (channel) is seeded with initial biomass that consumes an electron donor and an electron acceptor according to dual Monod kinetics. Biomass is modeled as a continuous uniform isotropic hyperelastic material, whose expansion and deformation are governed by material mechanics stress-strain relations, unlike traditional approaches that use ad hoc empirical schemes. The Stokes flow, the advection-diffusion-reaction mass transport, and the biomass deformation partial differential equations are solved using finite elements. The solute transport problem is made more computationally efficient by controlling the time step discretization. Results from a simulation illustrate the methodology.

[1]  Cristian Picioreanu,et al.  Constrained discounted Markov decision processes and Hamiltonian cycles , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[2]  T. P. Clement,et al.  Macroscopic Models for Predicting Changes in Saturated Porous Media Properties Caused by Microbial Growth , 1996 .

[3]  Philippe C. Baveye,et al.  Microbial Clogging of Saturated Soils and Aquifer Materials: Evaluation of Mathematical Models , 1995 .

[4]  Alfred B. Cunningham,et al.  Influence of Biofilm Accumulation on Porous Media Hydrodynamics , 1991 .

[5]  Stewart W. Taylor,et al.  Biofilm growth and the related changes in the physical properties of a porous medium: 1. Experimental investigation , 1990 .

[6]  M. Shephard,et al.  A stabilized mixed finite element method for finite elasticity.: Formulation for linear displacement and pressure interpolation , 1999 .

[7]  F. Molz,et al.  Simulation of Microbial Growth Dynamics Coupled to Nutrient and Oxygen Transport in Porous Media , 1986 .

[8]  Rune Bakke,et al.  Biofilm morphology in porous media, a study with microscopic and image techniques , 1997 .

[9]  Evaluation of a coupled mass transport-biofilm process model using dissolved oxygen microsensors , 1995 .

[10]  Wing Kam Liu,et al.  Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures , 1996 .

[11]  R. C. Weast CRC Handbook of Chemistry and Physics , 1973 .

[12]  P. Mccarty,et al.  Model of steady-state-biofilm kinetics. , 1980, Biotechnology and bioengineering.

[13]  Peter K. Kitanidis,et al.  Simulations of two‐dimensional modeling of biomass aggregate growth in network models , 2001 .

[14]  P L McCarty,et al.  Utilization rates of trace halogenated organic compounds in acetate‐grown biofilms , 1985, Biotechnology and bioengineering.

[15]  Brian Berkowitz,et al.  Percolation Theory and Network Modeling Applications in Soil Physics , 1998 .

[16]  Brian J. Suchomel,et al.  Network Model of Flow, Transport and Biofilm Effects in Porous Media , 1998 .

[17]  Stewart W. Taylor,et al.  ENHANCED IN-SITU BIODEGRADATION AND AQUIFER PERMEABILITY REDUCTION , 1991 .

[18]  Philippe C. Baveye,et al.  An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers , 1989 .

[19]  I. Fatt The Network Model of Porous Media , 1956 .

[20]  James E. Anderson,et al.  Model for Treatment of Trichloroethylene by Methanotrophic Biofilms , 1994 .

[21]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[22]  John H. Montgomery,et al.  Groundwater Chemicals Desk Reference , 1989 .

[23]  Walter Hayduk,et al.  Prediction of diffusion coefficients for nonelectrolytes in dilute aqueous solutions , 1974 .

[24]  Perry L. McCarty,et al.  Impact of colony morphologies and disinfection on biological clogging in porous media , 2000 .

[25]  G. Parkin,et al.  Biotransformation of trichloroethylene by a phenol-induced mixed culture , 1996 .

[26]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[27]  Thomas J. R. Hughes,et al.  The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces , 1987 .

[28]  P. Wilderer,et al.  Fractal structure of biofilms: new tools for investigation of morphology , 1995 .

[29]  Perry L. McCarty,et al.  Mesoscale and Microscale Observations of Biological Growth in a Silicon Pore Imaging Element , 1999 .

[30]  Bruce E. Rittmann,et al.  The significance of biofilms in porous media , 1993 .

[31]  J J Heijnen,et al.  Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. , 1998, Biotechnology and bioengineering.

[32]  Perry L. McCarty,et al.  Substrate Flux into Biofilms of Any Thickness , 1981 .

[33]  Stewart W. Taylor,et al.  Biofilm growth and the related changes in the physical properties of a porous medium: 2. Permeability , 1990 .

[34]  Lewis Semprini,et al.  Comparison Between Model Simulations and Field Results for In‐Situ Biorestoration of Chlorinated Aliphatics: Part 1. Biostimulation of Methanotrophic Bacteria , 1991 .

[35]  Philippe C. Baveye,et al.  Saturated Hydraulic Conductivity Reduction Caused by Aerobic Bacteria in Sand Columns , 1992 .

[36]  D. Nicholson,et al.  Theory of thermohyperelasticity for near-incompressible elastomers , 1996 .

[37]  Stewart W. Taylor,et al.  Substrate and biomass transport in a porous medium , 1990 .

[38]  P L McCarty,et al.  A model of substrate utilization by bacterial films. , 1976, Journal - Water Pollution Control Federation.

[39]  P. Bishop,et al.  A method for describing biofilm surface roughness using geostatistical techniques , 1995 .

[40]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[41]  Jun Cao Estimations d'erreur a posteriori et techniques d'adaptation en elements finis pour la simulation numerique d'ecoulements de fluides visqueux , 1995 .

[42]  Thomas J. R. Hughes,et al.  Fast projection algorithm for unstructured meshes , 1992 .

[43]  Richard E. Ewing,et al.  Two‐dimensional modeling of microscale transport and biotransformation in porous media , 1994 .

[44]  P Vandevivere,et al.  Effect of bacterial extracellular polymers on the saturated hydraulic conductivity of sand columns , 1992, Applied and environmental microbiology.

[45]  Perry L. McCarty,et al.  Full-Scale Evaluation of In Situ Cometabolic Degradation of Trichloroethylene in Groundwater through Toluene Injection , 1998 .