Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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


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.


C urea :

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 :


θ 0 :

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)

R k :

Retardation factor of species k (1)

q i :

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

v i :

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

r :

Reaction rate (kmol/m3/s)

t :

Time (s)

v max :

Maximal reaction rate (kmol/m3/s)

t max :

Life time of the bacteria (s)

K m :

Saturation constant (kmol/m3)

ρ b :

Bulk density of the subsurface medium (kg/m3)

D :

Hydrodynamic dispersion coefficient tensor (m2/s)

α L :

Longitudinal dispersivity (m)

α T :

Transverse dispersivity (m)

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

Molecular mass of calcium carbonate (kg/kmol)

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

Density of calcium carbonate (kg/m3)

k i :

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

d m :

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


  1. Atkins H.L., Shu C.-W.: Quadrature-free implementation of discontinuous galerkin method for hyperbolic equations. AIAA J. 36(5), 2440–2463 (1998)

  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)

  3. Banga S.S., Galinata J.K., Ramakrishnan V.: Calcite precipitation induced by polyurethane-immobilized Bacillus pasteurii. Enzym. Microb. Technol. 28, 404–409 (2001)

  4. Bear J.: Dynamics of Fluids in Porous Media, pp. 119–194. Dover Publications, New York (1972)

  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)

  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)

  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)

  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

  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)

  10. DeJong J.T., Mortensen B.M., Martinez B.C., Nelson D.C.: Bio-mediated soil improvement. Ecol. Eng. 36(2), 197–210 (2010)

  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)

  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)

  13. Krivodonova L.: Limiters for high order DG methods. J. Comput. Phys. 226, 879–896 (2007)

  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)

  15. Lichtner P.C., Steefel C.I., Oelkers E.H.: Reactive transport in porous media. Rev. Mineral. 34, 83–125 (1996)

  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)

  17. Nemati M., Voordouw G.: Modification of porous media permeability, using calcium carbonate produced enzymatically in situ. Enzym. Microb. Technol. 33, 635–642 (2003)

  18. Stocks-Fischer S., Galinat J.K., Bang S.S.: Microbiological precipitation of CaCO3. Soil Biol. Biochem. 31, 1563–1571 (1999)

  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)

  20. Van Paassen, L.A.: Biogrout, ground improvement by microbially induced carbonate precipitation. PhD thesis, Delft University of Technology, pp. 1–195 (2009)

  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 2009

  22. Weast R.C.: 1980 Handbook of Chemistry and Physics, pp. D-229–D-276. CRC Press, Boca Raton (1980)

  23. Whiffin, V.S.: Microbial CaCO3 precipitation for the production of biocement. PhD thesis, Murdoch University, Perth, Australia, pp. 1–154, (2004)

  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)

  25. Zheng C., Bennett G.D.: Applied Contaminant Transport Modeling, pp. 3–79. Van Nostrand Reinhold, New York (1995)

  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)

Download references


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.

Author information

Correspondence to W. K. van Wijngaarden.

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.

Reprints and Permissions

About this article

Cite this article

van Wijngaarden, W.K., Vermolen, F.J., van Meurs, G.A.M. et al. Modelling Biogrout: A New Ground Improvement Method Based on Microbial-Induced Carbonate Precipitation. Transp Porous Med 87, 397–420 (2011). https://doi.org/10.1007/s11242-010-9691-8

Download citation


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