Advertisement

Transport in Porous Media

, Volume 87, Issue 2, pp 397–420 | Cite as

Modelling Biogrout: A New Ground Improvement Method Based on Microbial-Induced Carbonate Precipitation

  • W. K. van WijngaardenEmail author
  • F. J. Vermolen
  • G. A. M. van Meurs
  • C. Vuik
Open Access
Article

Abstract

Biogrout is a new soil reinforcement method based on microbial-induced carbonate precipitation. Bacteria are placed and reactants are flushed through the soil, resulting in calcium carbonate precipitation, causing an increase in strength and stiffness of the soil. Due to this precipitation, the porosity of the soil decreases. The decreasing porosity influences the permeability and therefore the flow. To analyse the Biogrout process, a model was created that describes the process. The model contains the concentrations of the dissolved species that are present in the biochemical reaction. These concentrations can be solved from a advection–dispersion–reaction equation with a variable porosity. Other model equations involve the bacteria, the solid calcium carbonate concentration, the (decreasing) porosity, the flow and the density of the fluid. The density of the fluid changes due to the biochemical reactions, which results in density driven flow. The partial differential equations are solved by the Standard Galerkin finite-element method. Simulations are done for some 1D and 2D configurations. A 1D configuration can be used to model a column experiment and a 2D configuration may correspond to a sheet or a cross section of a 3D configuration.

Keywords

Biogrout Microbial-induced carbonate precipitation Density flow Finite-element method Decreasing porosity 

List of Symbols

Curea

Concentration of dissolved urea molecules (kmol/m3)

\({C^{\rm Ca^{2+}}}\)

Concentration of dissolved calcium ions (kmol/m3)

\({C^{\rm NH_4^{\,+}}}\)

Concentration of dissolved ammonium ions (kmol/m3)

\({C^{\rm CaCO_3}}\)

Concentration of calcium carbonate molecules (kg/m3)

\({\bar{C}^{k}}\)

Sorbed concentration of species k (kmol/kg)

θ

Porosity

θ0

Initial porosity

\({q_{\rm s}^{k}}\)

Volumetric flow rate per unit volume of aquifer of species k (1/s)

\({C_{\rm s}^{k}}\)

Concentration of species k in the source or sink (kmol/m3)

Rk

Retardation factor of species k (1)

qi

Darcy velocity in the respective coordinate directions (i = x, y, z) (m/s)

vi

Pore water velocity in the respective coordinate directions (i = x, y, z) (m/s)

r

Reaction rate (kmol/m3/s)

t

Time (s)

vmax

Maximal reaction rate (kmol/m3/s)

tmax

Life time of the bacteria (s)

Km

Saturation constant (kmol/m3)

ρb

Bulk density of the subsurface medium (kg/m3)

D

Hydrodynamic dispersion coefficient tensor (m2/s)

αL

Longitudinal dispersivity (m)

αT

Transverse dispersivity (m)

\({m_{\rm CaCO_3}}\)

Molecular mass of calcium carbonate (kg/kmol)

\({\rho_{\rm CaCO_3}}\)

Density of calcium carbonate (kg/m3)

ki

Intrinsic permeability in the respective coordinate directions (i = x, y, z) (m2)

dm

Mean particle size of the subsurface medium (m)

μ

Dynamic viscosity of the fluid (Pa s)

p

Pressure (Pa)

g

Gravitation constant (m/s2)

ρ

Density of the fluid (kg/m3)

L

Length of the domain (m)

M

Width or height of the domain (m)

N

Number of elements

Notes

Acknowledgments

Special thanks to Jitse Pruiksma (Deltares) and Leon van Paassen (Delft University of Technology) for partly deriving the differential equations.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Atkins H.L., Shu C.-W.: Quadrature-free implementation of discontinuous galerkin method for hyperbolic equations. AIAA J. 36(5), 2440–2463 (1998)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. Banga S.S., Galinata J.K., Ramakrishnan V.: Calcite precipitation induced by polyurethane-immobilized Bacillus pasteurii. Enzym. Microb. Technol. 28, 404–409 (2001)CrossRefGoogle Scholar
  4. Bear J.: Dynamics of Fluids in Porous Media, pp. 119–194. Dover Publications, New York (1972)Google Scholar
  5. Celia M.A., Kindred J.S., Herrera I.: Contaminant transport and biodegradation, a numerical model for reactive transport in porous media. Water Resour. Res. 25(6), 1141–1148 (1989)CrossRefGoogle Scholar
  6. Cockburn, B.: An Introduction to the Discontinuous Galerkin Method for Convection Dominated Problems. School of Mathematics, University of Minnesota, Minneapolis, pp. 151–268 (1998)Google Scholar
  7. Cockburn B., Shu C.-W.: The local discontinuous Galerkin method for time-dependent convection–diffusion systems. SIAM J. Numer. Anal. 35(6), 2440–2463 (1998)CrossRefGoogle Scholar
  8. Costa A.: Permeability–porosity relationship: a reexamination of the Kozeny–Carman equation based on a fractal pore-space geometry assumption. Geophys. Res. Lett. 33, L02318 (2006). doi: 10.1029/2005GL025134 CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. DeJong J.T., Mortensen B.M., Martinez B.C., Nelson D.C.: Bio-mediated soil improvement. Ecol. Eng. 36(2), 197–210 (2010)CrossRefGoogle Scholar
  11. Ewing R.E., Wang H.: A summary of numerical methods for time-dependent advection-dominated partial differential equations. J. Comput. Appl. Math. 128, 423–445 (2001)CrossRefGoogle Scholar
  12. Heinrich J.C., Huyakorn P.S., Zienkiewicz O.C.: An ‘upwind’ finite element method for two-dimensional convective transport equation. Int. J. Numer. Methods Eng. 11, 131–143 (1977)CrossRefGoogle Scholar
  13. Krivodonova L.: Limiters for high order DG methods. J. Comput. Phys. 226, 879–896 (2007)CrossRefGoogle Scholar
  14. Le Beau G.J., Tezduyar T.E.: Finite element computation of compressible flows with the SUPG formulation. In: Engleman, M.S., Reddy, J.N. (eds) Advances in Finite Element Analysis in Fluid Dynamics, FED-vol. 123, pp. 21–27. ASME, New York (1991)Google Scholar
  15. Lichtner P.C., Steefel C.I., Oelkers E.H.: Reactive transport in porous media. Rev. Mineral. 34, 83–125 (1996)Google Scholar
  16. Lohner R., Morgan K., Zienkiewicz O.C.: The solution of non-linear hyperbolic equation systems by the finite element method. Int. J. Numer. Methods Fluids 4, 1043–1063 (1984)CrossRefGoogle Scholar
  17. Nemati M., Voordouw G.: Modification of porous media permeability, using calcium carbonate produced enzymatically in situ. Enzym. Microb. Technol. 33, 635–642 (2003)CrossRefGoogle Scholar
  18. Stocks-Fischer S., Galinat J.K., Bang S.S.: Microbiological precipitation of CaCO3. Soil Biol. Biochem. 31, 1563–1571 (1999)CrossRefGoogle Scholar
  19. 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)Google Scholar
  20. Van Paassen, L.A.: Biogrout, ground improvement by microbially induced carbonate precipitation. PhD thesis, Delft University of Technology, pp. 1–195 (2009)Google Scholar
  21. 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 (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 2009Google Scholar
  22. Weast R.C.: 1980 Handbook of Chemistry and Physics, pp. D-229–D-276. CRC Press, Boca Raton (1980)Google Scholar
  23. Whiffin, V.S.: Microbial CaCO3 precipitation for the production of biocement. PhD thesis, Murdoch University, Perth, Australia, pp. 1–154, (2004)Google Scholar
  24. 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)CrossRefGoogle Scholar
  25. Zheng C., Bennett G.D.: Applied Contaminant Transport Modeling, pp. 3–79. Van Nostrand Reinhold, New York (1995)Google Scholar
  26. Zienkiewicz O.C., Taylor R.L., Taylor R.L.: The Finite Element Method for Solid and Structural Mechanics, pp. 1–596. Butterworth-Heinemann, Oxford (2005)Google Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  • W. K. van Wijngaarden
    • 1
    • 2
    Email author
  • F. J. Vermolen
    • 1
  • G. A. M. van Meurs
    • 2
  • C. Vuik
    • 1
  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Deltares, Unit Geo EngineeringDelftThe Netherlands

Personalised recommendations