Abstract
Biogrout is a new method for soil reinforcement, which is based on microbial-induced carbonate precipitation. Bacteria and reactants are flushed through the soil, resulting in calcium carbonate precipitation and consequent soil reinforcement. Bacteria are crucially important in the Biogrout process since they catalyse the reaction. Hence, to control the process, it is essential to know where the bacteria are located. The bacteria are possibly in suspension but can also be adsorbed or fixated on the matrix of the porous structure. In this article, a model is derived for the placement of bacteria. The model contains three phases of bacteria: bacteria in suspension, adsorbed bacteria and fixed bacteria. An analytical solution is derived for instantaneous reactions between these three phases. The analytical solution is compared to numerical simulations for finite reaction rates. For the numerical simulations the standard Galerkin Finite Element Method is used.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- C :
-
Normalized concentration of suspended bacteria [1]
- C adsorbed :
-
Normalized concentration of (temporarily and permanently) adsorbed bacteria [1]
- \({\overline{C}}\) :
-
Normalized concentration of temporarily adsorbed bacteria [1]
- S :
-
Normalized concentration of fixated bacteria [1]
- \({\Psi}\) :
-
Normalized total concentration of bacteria [1]
- c fix :
-
Concentration of the fixation fluid [kmol/m3]
- \({\theta}\) :
-
Porosity [1]
- q :
-
Darcy velocity [m/h]
- v :
-
Pore water velocity [m/h]
- D bac :
-
Dispersion/diffusion coefficient for bacteria [m2/h]
- D fix :
-
Dispersion/diffusion coefficient for the fixation fluid [m2/h]
- r ads :
-
Adsorption reaction rate [1/h]
- r des :
-
Desorption reaction rate [1/h]
- r fix :
-
Fixation reaction rate [1/h]
- k ads :
-
Adsorption rate constant [1/h]
- k des :
-
Desorption rate constant [1/h]
- k fix :
-
Fixation rate constant [1/h]
- \({\varphi}\) :
-
Adsorption isotherm
- β :
-
Factor that describes which part of the adsorbed bacteria are fixated [1]
- β 0 :
-
Factor that describes which part of the adsorbed bacteria are fixated [m 3/kmol]
- α :
-
Langmuir constant [1]
- \({\overline{C}_{\rm max}}\) :
-
Maximum adsorption capacity [1]
- L :
-
Length of the column [m]
- T 0 :
-
Time at which the injection of bacteria is stopped and the injection of fixation fluid is started [h]
- T 1 :
-
Time at which the front of the fixation fluid reaches the front of the pulse with bacteria [h]
- T 2 :
-
Time at which the shock speed changes [h]
References
Bachmeier K.L., Williams A.E., Warmington J.R., Bang S.S.: Urease activity in microbiologically-induced calcite precipitation. J. Biotechnol. 93, 171–181 (2002)
Bang S.S., Galinata J.K., Ramakrishnanb V.: Calcite precipitation induced by polyurethane-immobilized Bacillus pasteurii. Enzym. Microb. Technol. 28, 404–409 (2001)
DeJong J.T., Fritzges M.B., Nusslein K.: Microbially induced cementation to control sand response to undrained shear. J. Geotech. Geoenviron. Eng. 132(11), 1381–1392 (2006)
DeJong J.T., Mortensen B.M., Martinez B.C., Nelson D.C.: Bio-mediated soil improvement. Ecol. Eng. 36(2), 197–210 (2010)
Fontes D.E., Mills A.L., Hornberger G.M., Herman J.S.: Physical and chemical factors influencing transport of microorganisms through porous media. Appl. Environ. Microbiol. 57(9), 2473–2481 (1991)
Foppen J.W.A., Schijven J.F.: Evaluation of data from the literature on the transport and survival of Escherichia coli and thermotolerant coliforms in aquifers under saturated conditions. Water Res. 40, 401–426 (2006)
Harkes M.P., van Paassen L.A., Booster J.L., Whiffin V.S., Loosdrecht M.C.M.: Fixation and distribution of bacterial activity in sand to induce carbonate precipitation for ground reinforcement. Ecol. Eng. 36, 112–117 (2010)
Hornberger G.M., Mills A.L., Herman J.S.: Bacterial transport in porous media: evaluation of a model using laboratory observations. Water Resour. Res. 28(3), 915–923 (1992)
Ivanov I., Chu J.: Applications of microorganisms to geotechnical engineering for bioclogging and biocementation of soil in situ. Rev. Environ. Sci. Biotechnol. 7, 139–153 (2008)
Johnson W.P., Blue K.A., Logan B.E., Arnold R.G.: Modeling bacterial detachment during transport through porous media as a residence-time-dependent process. Water Resour. Res. 31(11), 2649–2658 (1995)
Matthess G., Pekdeger A.: Concepts of a survival and transport model of pathogenic bacteria and viruses in groundwater. Sci Total Environ 21, 149–159 (1981)
Matthess G., Pekdeger A., Schroeter J.: Persistence and transport of bacteria and viruses in groundwater—a conceptual evaluation. J. Contam. Hydrol. 2(2), 171–188 (1988)
Nemati M., Voordouw G.: Modification of porous media permeability, using calcium carbonate produced enzymatically in situ. Enzym. Microb. Technol. 33, 635–642 (2003)
Tan Y., Gannon J.T., Baveye P., Alexander M.: Transport of bacteria in an aquifer sand: experiments and model simulations. Water Resour. Res. 30(12), 3243–3252 (1994)
Van der Ruyt M., Van der Zon W.: Biological in situ reinforcement of sand in near-shore areas. Proc. Inst. Civil Eng. Geotech. Eng. 162, 81–83 (2009)
Van der Star, W.R.L., Van Wijngaarden, W.K., Van Paassen, L.A., Van Baalen, L.R., Van Zwieten, G.: Stabilization of gravel deposits using microorganisms. In: Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering, pp. 85–90 (2011)
Van Meurs, G.A., Van der Zon, W.H., Lambert, J.W.M., Van Ree, C.C.D., Whiffin, V.S., Molendijk, W.O.: The challenge to adapt soil properties. In: Thomas, H.R. (ed.) Proceedings of the 5th International Congress on Environmental Geotechnics: Opportunities, Challenges and Responsibilities for Environmental Geotechnics. Thomas Telford Ltd., Cardiff, Wales, pp. 1192–1199 (2006)
Van Paassen, L.A., Van Loosdrecht, M.C.M., Van den Eijnden, A.P., Mulder, A., Verwaal, W., Ngan-Tillard, D.J.M., Harkes, M.P., Bekendam, R.F.: Reinforcement of calcarenite room and pillar mines by microbially induced carbonate precipitation. In: EuroEngeo 2008, Escuela de Ingenieria de Obras Publicas Madrid, Madrid, pp. 1–6 (2008)
Van Paassen, L.A.: Biogrout, ground improvement by microbially induced carbonate precipitation. PhD thesis, Delft University of Technology, pp. 1–195 (2009)
Van Paassen, L.A., Harkes, M.P., van Zwieten, G.A., van der Zon, W.H., van der Star, W.R.L., van Loosdrecht, M.C.M.: Scale up of BioGrout: a biological ground reinforcement method. In: Hamza, M., et al. (eds.) Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering, pp. 2328–2333 (2009a)
Van Paassen, L.A., Pieron, M., Mulder, A., Van der Linden T.J.M., Van Loosdrecht, M.C.M., Ngan-Tillard, D.J.M.: Strength and deformation of biologically cemented sandstone. In: Vrkljan, I. (ed.) Proceedings of the ISRM Regional conference EUROCK 2009—Rock engineering in difficult ground conditions—Soft Rocks and Karst, pp. 405–410, Dubrovnik, Croatia, 29–31 October 2009 (2009b)
Van Paassen L.A., Ghose R., van der Linden T.J.M., van der Star W.R.L., van Loosdrecht M.C.M.: Quantifying biomediated ground improvement by ureolysis: large-scale Biogrout experiment. J. Geotech. Geoenviron. Eng. 136(12), 1721–1728 (2010)
Van Wijngaarden, W.K., Vermolen, F.J., van Meurs, G.A.M., Vuik, C.: Modelling the new soil improvement method Biogrout: extension to 3D. In: Kreiss, G., et al. (eds.) Numerical Mathematics and Advanced Applications. Springer, Berlin, pp. 893–900 (2010)
Van Wijngaarden W.K., Vermolen F.J., van Meurs G.A.M., Vuik C.: Modelling Biogrout: a new ground improvement method based on microbial-induced carbonate precipitation. Transp. Porous Med. 87, 397–420 (2011)
Whiffin, V.S.: Microbial CaCO3 precipitation for the production of biocement. Ph.D thesis, Murdoch University, Perth, Australia, pp. 1–154 (2004)
Whiffin V.S., van Paassen L.A., Harkes M.P.: Microbial carbonate precipitation as a soil improvement technique. Geomicrobiol. J. 24(5), 417–423 (2007)
Yavuz Corapcioglu M., Haridas A.: Transport and fate of microorganisms in porous media: a theoretical investigation. J. Hydrol. 72(1–2), 149–169 (1984)
Zheng C., Bennett G.D.: Applied Contaminant Transport Modeling. Van Nostrand Reinhold, New York (1995)
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
van Wijngaarden, W.K., Vermolen, F.J., van Meurs, G.A.M. et al. A Mathematical Model and Analytical Solution for the Fixation of Bacteria in Biogrout. Transp Porous Med 92, 847–866 (2012). https://doi.org/10.1007/s11242-011-9937-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-011-9937-0