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


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.


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

List of Symbols


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)


Sorbed concentration of species k (kmol/kg)




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)


Retardation factor of species k (1)


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


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


Reaction rate (kmol/m3/s)


Time (s)


Maximal reaction rate (kmol/m3/s)


Life time of the bacteria (s)


Saturation constant (kmol/m3)


Bulk density of the subsurface medium (kg/m3)


Hydrodynamic dispersion coefficient tensor (m2/s)


Longitudinal dispersivity (m)


Transverse dispersivity (m)

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

Molecular mass of calcium carbonate (kg/kmol)

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

Density of calcium carbonate (kg/m3)


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


Mean particle size of the subsurface medium (m)


Dynamic viscosity of the fluid (Pa s)


Pressure (Pa)


Gravitation constant (m/s2)


Density of the fluid (kg/m3)


Length of the domain (m)


Width or height of the domain (m)


Number of elements



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.


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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

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