Transport in Porous Media

, Volume 30, Issue 1, pp 1–23 | Cite as

Network Model of Flow, Transport and Biofilm Effects in Porous Media

  • Brian J. Suchomel
  • Benito M. Chen
  • Myron B. AllenIII


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.

biofilm network model permeability transport numerical diffusion 


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  1. Alexander, M.: 1994, Biodegradation and Bioremediation, Academic Press, New York.Google Scholar
  2. Brualdi, B. A. and Ryser, H. J.: 1991, Combinatorial Matrix Theory, Cambridge University Press.Google Scholar
  3. Christensen, B. E. and Characklis, W. G.: 1990, Physical and Chemical Properties of Biofilms, In: W. G. Characklis and K. C. Marshall (eds), Biofilms, Wiley-Interscience, New York, pp. 93-130.Google Scholar
  4. Hull, L. C. and Koslow, K. N.: 1986, Streamline routing through fracture junctions, Water Resour. Res. 22(12), 1731-1734.Google Scholar
  5. Imdakm, A. O. and Sahimi, M.: 1991, Computer simulation of particle transport processes in flow through porous media, Chem. Eng. Sci. 46(8), 1977-1993.Google Scholar
  6. Jerauld, G. R., Hatfield, J. C., Scriven, L. E. and Davis, H. T.: 1984a, Percolation and conduction on Voronoi and triangular networks: a case study in topological disorder, J. Phys. C: Solid State Phys. 17, 1519-1529.Google Scholar
  7. Jerauld, G. R., Scriven, L. E. and Davis, H. T.: 1984b, Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder, J. Phys. C: Solid State Phys. 17, 3429-3439.Google Scholar
  8. Kincaid, D. and Cheney, W.: 1991, Numerical Analysis, Brooks/Cole Publ. Co., Pacific Grove, Ca., p. 690.Google Scholar
  9. Koplik, J.: 1982, Creeping flow in two-dimensional networks, J. Fluid Mech. 119, 219-247.Google Scholar
  10. Koplik, J. and Lasseter, T.: 1982, Two-phase flow in random network models of porous media, Paper presented at 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME.Google Scholar
  11. Lindqvist, R., Cho, J. S. and Enfield, C. G.: 1994, A kinetic model for cell density dependent bacterial transport in porous media, Water Resour. Res. 30(12), 3291-3299.Google Scholar
  12. Philip, J. R.: 1988 The fluid mechanics of fracture and other junctions, Water Resour. Res. 24(2), 239-246.Google Scholar
  13. Rege, S. and Fogler, H.: 1987, Network model for straining dominated particle entrapment in porous media, Chem. Eng. Sci. 42(7), 1553-1564.Google Scholar
  14. Scheidegger, A. E.: 1957, The Physics of Flow Through Porous Media, University of Toronto Press.Google Scholar
  15. Simon, R. and Kelsey, F. J.: 1971, The use of capillary tube networks in reservoir performance studies: I. equal-viscosity miscible displacements, Soc. Petrol. Eng. J. 11, 99-112.Google Scholar
  16. Simon, R. and Kelsey, F. J.: 1971, The use of capillary tube networks in reservoir performance studies: II. effect of heterogeneity and mobility on miscible displacement efficiency, Soc. Petrol. Eng. J. 12, 345-351.Google Scholar
  17. Suchomel, B. J., Chen, B. M. and Allen, M. B.: 1998, Macro-scale properties in porous media from a network model, Transport in Porous Media (to appear).Google Scholar
  18. Sugita, F., Gillham, R. W. and Mase, C.: 1995, Pore scale variation in retardation factor as a cause of nonideal breakthrough curves: 2. Pore network analysis, Water Resour. Res. 31(1), 113-119.Google Scholar
  19. Tan, Y., Gannon, J. T., Baveye, R. and Alexander, M.: 1994, Transport of bacteria in an aquifer sand: experiments and model simulations, Water Resour. Res. 30(12), 3243-3252.Google Scholar
  20. Taylor, S. W. and Jaffé, P. R.: 1990a, Biofilm Growth and the related changes in the physical properties of a porous medium 1. Experimental investigation, Water Resour. Res. 26(9), 2153-2159.Google Scholar
  21. Taylor, S. W., Milly, P. C. D. and Jaffé, P. R.: 1990b, Biofilm growth and the related changes in the physical properties of a porous medium 2. Permeability, Water Resour. Res. 26(9), 2161-2169.Google Scholar
  22. Taylor, S. W. and Jaffé, P. R.: 1990c, Biofilm growth and the related changes in the physical properties of a porous medium 3. Dispersivity and model verification, Water Resour. Res. 26(9), 2171-2180.Google Scholar
  23. van Brakel, J.: 1975, Pore space models for transport phenomena in porous media, review and evaluation with special emphasis on capillary liquid transport, Powder Technol. 11, 205-236.Google Scholar
  24. Vandevivere, P. and Baveye, P.: 1992, Effect of bacterial extracellular polymers on the saturated hydraulic conductivity of sand columns, Appl. Environ. Microbiol. 58(5), 1690-1698.Google Scholar
  25. Young, D. M.: 1971, Iterative Solution of Large Linear Systems, Academic Press, New York, p. 570.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Brian J. Suchomel
    • 1
  • Benito M. Chen
    • 2
  • Myron B. AllenIII
    • 2
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisU.S.A.
  2. 2.Department of MathematicsUniversity of WyomingLaramieU.S.A.

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