Field-scale modeling of microbially induced calcite precipitation

  • A. B. Cunningham
  • H. Class
  • A. Ebigbo
  • R. Gerlach
  • A. J. Phillips
  • J. Hommel
Original Paper


The biogeochemical process known as microbially induced calcite precipitation (MICP) is being investigated for engineering and material science applications. To model MICP process behavior in porous media, computational simulators must couple flow, transport, and relevant biogeochemical reactions. Changes in media porosity and permeability due to biomass growth and calcite precipitation, as well as their effects on one another must be considered. A comprehensive Darcy-scale model has been developed by Ebigbo et al. (Water Resour. Res. 48(7), W07519, 2012) and Hommel et al. (Water Resour. Res. 51, 3695–3715, 2015) and validated at different scales of observation using laboratory experimental systems at the Center for Biofilm Engineering (CBE), Montana State University (MSU). This investigation clearly demonstrates that a close synergy between laboratory experimentation at different scales and corresponding simulation model development is necessary to advance MICP application to the field scale. Ultimately, model predictions of MICP sealing of a fractured sandstone formation, located 340.8 m below ground surface, were made and compared with corresponding field observations. Modeling MICP at the field scale poses special challenges, including choosing a reasonable model-domain size, initial and boundary conditions, and determining the initial distribution of porosity and permeability. In the presented study, model predictions of deposited calcite volume agree favorably with corresponding field observations of increased injection pressure during the MICP fracture sealing test in the field. Results indicate that the current status of our MICP model now allows its use for further subsurface engineering applications, including well-bore cement sealing and certain fracture-related applications in unconventional oil and gas production.


Microbially induced calcite precipitation (MICP) Permeability modification Field-scale modeling Reactive transport 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

The International Research Training Group NUPUS, funded by the German Research Foundation (DFG), is acknowledged for enabling the model development through funding between 2007 and 2016. Further, we acknowledge the DFG for funding ongoing research related to this study in the grants HO6055/1-1 and within the Collaborative Research Center 1313. Funding for the laboratory and field MICP experimental work was provided by two US Department of Energy grants DE-FE0004478, “Advanced CO2 Leakage Mitigation using Engineered Biomineralization Sealing Technologies” and DE-FE000959, “Field Test and Evaluation of Engineered Biomineralization Technology for Sealing Existing Wells” with matching support from Southern Company Generation and Shell International Exploration and Production B.V. Additional financial support was also provided by DOE DE-FG02-13ER86571 and NSF award no. DMS0934696. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the Department of Energy (DOE).


  1. 1.
    Bachmeier, K.L., Williams, A.E., Warmington, J.R., Bang, S.S.: Urease activity in microbiologically-induced calcite precipitation. J. Biotechnol. 93(2), 171–81 (2002)CrossRefGoogle Scholar
  2. 2.
    Barkouki, T.H., Martinez, B.C., Mortensen, B.M., Weathers, T.S., De Jong, J.D., Ginn, T.R., Spycher, N.F., Smith, R.W., Fujita, Y.: Forward and inverse bio-geochemical modeling of microbially induced calcite precipitation in half-meter column experiments. Transp. Porous Media 90(1), 23–39 (2011). CrossRefGoogle Scholar
  3. 3.
    Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing Part II: Implementation and tests in DUNE. Comput. (Vienna/New York) 82(2-3), 121–138 (2008a). CrossRefGoogle Scholar
  4. 4.
    Bastian, P., Blatt, M., Dedner, A., Engwer C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework. Comput. (Vienna/New York) 82(2-3), 103–119 (2008b). CrossRefGoogle Scholar
  5. 5.
    Batzle, M., Wang, Z.: Seismic Properties of Pore Fluids. Geophysics 57(11), 1396–1408 (1992). CrossRefGoogle Scholar
  6. 6.
    Birkhölzer, J.T., Zhou, Q., Tsang, C.F.: Large-scale impact of CO2 storage in deep saline aquifers: A sensitivity study on pressure response in stratified systems. Int. J. Greenh. Gas Control 3(2), 181–194 (2009)CrossRefGoogle Scholar
  7. 7.
    Bottero, S., Picioreanu, C., Enzien, M.V., Van Loosdrecht, M., Bruining, J., Heimovaara, T.: Formation Damage and Impact on Gas Flow Caused by Biofilms Growing Within Proppant Packing Used in Hydraulic Fracturing. Society of Petroleum Engineers, (2010)
  8. 8.
    Bottero, S., Storck, T., Heimovaara, T.J., van Loosdrecht, M.C., Enzien, M.V., Picioreanu, C.: Biofilm development and the dynamics of preferential flow paths in porous media. Biofouling 29(9), 1069–1086 (2013). CrossRefGoogle Scholar
  9. 9.
    Bringedal, C., Berre, I., Pop, I.S., Radu, F.A.: Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity. Transp. Porous Media 114(2), 371–393 (2016). CrossRefGoogle Scholar
  10. 10.
    Burbank, M.B., Weaver, T.J., Green, T.L., Williams, B.C., Crawford, R.L.: Precipitation of calcite by indigenous microorganisms to strengthen liquefiable soils. Geomicrobiol J. 28(4), 301–312 (2011). CrossRefGoogle Scholar
  11. 11.
    Burr, D.T., Sudicky, E.A., Naff, R.L.: Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty. Water Resour. Res. 30(3), 791–815 (1994). CrossRefGoogle Scholar
  12. 12.
    Carrayrou, J., Hoffmann, J., Knabner, P., Kräutle, S., de Dieuleveult, C., Erhel, J., Van der Lee, J., Lagneau, V., Mayer, K.U., MacQuarrie, K.T.B.: Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems?the MoMaS benchmark case. Comput. Geosci. 14 (3), 483–502 (2010). CrossRefGoogle Scholar
  13. 13.
    Chou, L., Garrels, R.M., Wollast, R.: Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals. Chem. Geol. 78, 269–282 (1989)CrossRefGoogle Scholar
  14. 14.
    Clegg, S.L., Whitfield, M.: A chemical model of seawater including dissolved ammonia and the stoichiometric dissociation constant of ammonia in estuarine water and seawater from -2 to 40c. Geochim. Cosmochim. Acta 59(12), 2403–2421 (1995)CrossRefGoogle Scholar
  15. 15.
    Connolly, J.M., Kaufman, M., Rothman, A., Gupta, R., Redden, G., Schuster, M., Colwell, F., Gerlach, R.: Construction of two ureolytic model organisms for the study of microbially induced calcium carbonate precipitation. J. Microbiol. Methods 94(3), 290–299 (2013). CrossRefGoogle Scholar
  16. 16.
    Cunningham, A.B., Phillips, A.J., Troyer, E., Lauchnor, E.G., Hiebert, R., Gerlach, R., Spangler, L.H.: Wellbore leakage mitigation using engineered biomineralization. Energy Procedia 63, 4612–4619 (2014). CrossRefGoogle Scholar
  17. 17.
    Cuthbert, M.O., McMillan, L.A., Handley-Sidhu, S., Riley, M.S., Tobler, D.J., Phoenix, V.R.: A field and modeling study of fractured rock permeability reduction using microbially induced calcite precipitation. Environ. Sci. Technol. 47(23), 13637–13643 (2013). CrossRefGoogle Scholar
  18. 18.
    Ebigbo, A., Helmig, R., Cunningham, A.B., Class, H., Gerlach, R.: Modelling biofilm growth in the presence of carbon dioxide and water flow in the subsurface. Adv. Water Resour. 33(7), 762–781 (2010). CrossRefGoogle Scholar
  19. 19.
    Ebigbo, A., Phillips, A.J., Gerlach, R., Helmig, R., Cunningham, A.B., Class, H., Spangler, L.H.: Darcy-scale modeling of microbially induced carbonate mineral precipitation in sand columns. Water Resour. Res. 48(7), W07519 (2012). CrossRefGoogle Scholar
  20. 20.
    Faigle, B., Helmig, R., Aavatsmark, I., Flemisch, B.: Efficient multiphysics modelling with adaptive grid refinement using a MPFA method. Comput. Geosci. 18(5), 625–636.
  21. 21.
    Faigle, B., Elfeel, M.A., Helmig, R., Becker, B., Flemisch, B., Geiger, S.: Multi-physics modeling of non-isothermal compositional flow on adaptive grids. Comput. Methods Appl. Mech. Eng. 292, 16–34 (2015). CrossRefGoogle Scholar
  22. 22.
    Ferris, F.G., Stehmeier, L.G., Kantzas, A., Mourits, F.M.: Bacteriogenic mineral plugging. J. Can. Pet. Technol. 35(8), 56–61 (1996). CrossRefGoogle Scholar
  23. 23.
    Fidaleo, M., Lavecchia, R.: Kinetic study of enzymatic urea hydrolysis in the pH range 4-9. Chem. Biochem. Eng. Q. 17, 311–318 (2003)Google Scholar
  24. 24.
    Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A, Mosthaf, K., Müthing, S, Nuske, P., Tatomir, A., Wolff, M., Helmig, R.: DumuX: DUNE for multi-{phase,component,scale,physics,...} flow and transport in porous media. Adv. Water Resour. 34(9), 1102–1112 (2011). CrossRefGoogle Scholar
  25. 25.
    Flukiger, F., Bernard, D.: A new numerical model for pore scale dissolution of calcite due to CO2 saturated water flow in 3D realistic geometry: Principles and first results. Chem. Geol. 265(1-2), 171–180 (2009). CrossRefGoogle Scholar
  26. 26.
    Frippiat, C.C., Pérez, P.C., Holeyman, A.E.: Estimation of laboratory-scale dispersivities using an annulus-and-core device. J. Hydrol. 362(1-2), 57–68 (2008). CrossRefGoogle Scholar
  27. 27.
    Fujita, Y., Taylor, J.L., Gresham, T.L.T., Delwiche, M.E., Colwell, F.S., McLing, T.L., Petzke, L.M., Smith, R.W.: Stimulation of microbial urea hydrolysis in groundwater to enhance calcite precipitation. Environ. Sci. Technol. 42(8), 3025–3032 (2008)CrossRefGoogle Scholar
  28. 28.
    Hajibeygi, H., Bonfigli, G., Hesse, M.A., Jenny, P.: Iterative multiscale finite-volume method. J. Comput. Phys. 227(19), 8604–8621 (2008). CrossRefGoogle Scholar
  29. 29.
    Hao, O.J., Richard, M.G., Jenkins, D., Blanch, H.W.: The half-saturation coefficient for dissolved oxygen: a dynamic method for its determination and its effect on dual species competition. Biotechnol. Bioeng. 25 (2), 403–16 (1983). CrossRefGoogle Scholar
  30. 30.
    Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface - A Contribution to the Modeling of Hydrosystems. Springer, Berlin (1997)CrossRefGoogle Scholar
  31. 31.
    Heße, F., Radu, F., Thullner, M., Attinger, S.: Upscaling of the advection-diffusion-reaction equation with Monod reaction. Adv. Water Resour. 32(8), 1336–1351 (2009). CrossRefGoogle Scholar
  32. 32.
    Hoffmann, J., Kräutle, S., Knabner, P.: A general reduction scheme for reactive transport in porous media. Comput. Geosci. 16 (4), 1081–1099 (2012). CrossRefGoogle Scholar
  33. 33.
    Hommel, J., Cunningham, A.B., Helmig, R., Ebigbo, A., Class, H.: Numerical investigation of microbially induced calcite precipitation as a leakage mitigation technology. Energy Procedia 40C, 392–397 (2013). CrossRefGoogle Scholar
  34. 34.
    Hommel, J., Lauchnor, E.G., Phillips, A.J., Gerlach, R., Cunningham, A.B., Helmig, R., Ebigbo, A., Class, H.: A revised model for microbially induced calcite precipitation: Improvements and new insights based on recent experiments. Water Resour. Res. 51(5), 3695–3715 (2015). CrossRefGoogle Scholar
  35. 35.
    Hommel, J., Lauchnor, E.G., Gerlach, R., Cunningham, A.B., Ebigbo, A., Helmig, R., Class, H.: Investigating the influence of the initial biomass distribution and injection strategies on Biofilm-Mediated calcite precipitation in porous media. Transp. Porous Media 114(2), 557–579 (2016). CrossRefGoogle Scholar
  36. 36.
    Hommel, J., Coltman, E., Class, H.: Porosity-Permeability Relations for Evolving Pore Space: A Review with a Focus on (Bio-)geochemically Altered Porous Media. Transport in Porous Media, (2018)CrossRefGoogle Scholar
  37. 37.
    Jacques, D., Šimu̇nek, J., Mallants, D., van Genuchten, M.: Modelling coupled water flow, solute transport and geochemical reactions affecting heavy metal migration in a podzol soil. Geoderma 145(3), 449–461 (2008). CrossRefGoogle Scholar
  38. 38.
    Jenny, P., Lee, S., Tchelepi, H.: Adaptive Multiscale finite-Volume Method for Multiphase Flow and Transport in Porous Media. Multiscale Model. Simul. 3(1), 50–64 (2005). CrossRefGoogle Scholar
  39. 39.
    Kim, D.S., Thomas, S., Fogler, H.S.: Effects of pH and trace minerals on long-term starvation of Leuconostoc mesenteroides. Appl. Environ. Microbiol. 66(3), 976–81 (2000)CrossRefGoogle Scholar
  40. 40.
    Krajewska B.: Urease-aided calcium carbonate mineralization for engineering applications: A review. Journal of Advanced Research, (2017)CrossRefGoogle Scholar
  41. 41.
    Kräutle, S., Knabner, P.: A new numerical reduction scheme for fully coupled multicomponent transport-reaction problems in porous media. Water Resour. Res. 41(9), W09414 (2005). CrossRefGoogle Scholar
  42. 42.
    Kräutle, S., Knabner, P.: A reduction scheme for coupled multicomponent transport-reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions. Water Resour. Res. 43(3), W03429 (2007). CrossRefGoogle Scholar
  43. 43.
    Kumar, K., van Noorden, T., Pop, I.: Effective dispersion equations for reactive flows involving free boundaries at the microscale. Multiscale Model. Simul. 9(1), 29–58 (2011). CrossRefGoogle Scholar
  44. 44.
    Landa-Marbán, D., Radu, F.A., Nordbotten, J.M.: Modeling and simulation of microbial enhanced oil recovery including interfacial area. Transp. Porous Media 120(2), 395–413 (2017). CrossRefGoogle Scholar
  45. 45.
    Lauchnor, E.G., Topp, D.M., Parker, A.E., Gerlach, R.: Whole cell kinetics of ureolysis by Sporosarcina pasteurii. J. Appl. Microbiol. 118(6), 1321–1332 (2015). CrossRefGoogle Scholar
  46. 46.
    Martinez, B., De Jong, J.T., Ginn, T.R.: Bio-geochemical reactive transport modeling of microbial induced calcite precipitation to predict the treatment of sand in one-dimensional flow. Comput. Geotech. 58, 1–13 (2014). CrossRefGoogle Scholar
  47. 47.
    Mateles, R.I.: Calculation of the oxygen required for cell production. Biotechnol. Bioeng. 13(4), 581–582 (1971). CrossRefGoogle Scholar
  48. 48.
    Millero, F.J., Milne, P.J., Thurmond, V.L.: The solubility of calcite, strontianite and witherite in NaCl solutions at 25c. Geochim. Cosmochim. Acta 48, 1141–1143 (1984). CrossRefGoogle Scholar
  49. 49.
    Minto, J.M., Tan, Q., Lunn, R.J., Mountassir, G.E., Guo, H., Cheng, X.: ‘Microbial mortar’-restoration of degraded marble structures with microbially induced carbonate precipitation. Constr. Build. Mater. 180, 44–54 (2018). CrossRefGoogle Scholar
  50. 50.
    Mitchell, A.C., Phillips, A.J., Schultz, L., Parks, S., Spangler, L.H., Cunningham, A.B., Gerlach, R.: Microbial CaCO3 mineral formation and stability in an experimentally simulated high pressure saline aquifer with supercritical CO2. Int. J. Greenh. Gas Control 15, 86–96 (2013). CrossRefGoogle Scholar
  51. 51.
    Nassar, M.K., Gurung, D., Bastani, M., Ginn, T.R., Shafei, B., Gomez, M.G., Graddy, C.M.R., Nelson, D.C., DeJong, J.T.: Large-Scale Experiments in microbially induced calcite precipitation (MICP): Reactive transport model development and prediction. Water Resour. Res. 54, 480–500 (2018). CrossRefGoogle Scholar
  52. 52.
    Nemati, M., Voordouw, G.: Modification of porous media permeability, using calcium carbonate produced enzymatically in situ. Enzyme Microb. Technol. 33(5), 635–642 (2003). CrossRefGoogle Scholar
  53. 53.
    Nielsen, S.M., Nesterov, I., Shapiro, A.A.: Simulations of microbial-enhanced oil recovery: Adsorption and filtration. Transp. Porous Media 102(2), 227–259 (2014). CrossRefGoogle Scholar
  54. 54.
    Nielsen, S.M., Nesterov, I., Shapiro, A.A.: Microbial enhanced oil recovery—a modeling study of the potential of spore-forming bacteria. Comput. Geosci. 20(3), 567–580 (2016). CrossRefGoogle Scholar
  55. 55.
    van Noorden, T.L., Pop, I.S., Ebigbo, A., Helmig, R.: An upscaled model for biofilm growth in a thin strip. Water Resour. Res. 46(6), W06505 (2010). Google Scholar
  56. 56.
    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. Geotechn. Geoenviron. Eng. 136(12), 1721–1728 (2010). CrossRefGoogle Scholar
  57. 57.
    Peszyńska, M., Wheeler, M.F., Yotov, I.: Mortar Upscaling for Multiphase Flow in Porous Media. Comput. Geosci. 6(1), 73–100 (2002). CrossRefGoogle Scholar
  58. 58.
    Peszyṅska, M., Trykozko, A., Iltis, G., Schlueter, S., Wildenschild, D.: Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscaling. Adv. Water Resour. 95, 288–301 (2016). CrossRefGoogle Scholar
  59. 59.
    Phillips, A.J., Gerlach, R., Lauchnor, E.G., Mitchell, A.C., Cunningham, A.B., Spangler, L.H.: Engineered applications of ureolytic biomineralization: a review. Biofouling 29(6), 715–733 (2013a). CrossRefGoogle Scholar
  60. 60.
    Phillips, A.J., Lauchnor, E.G., Eldring, J.J., Esposito, R., Mitchell, A.C., Gerlach, R., Cunningham, A.B., Spangler, L.H.: Potential CO2 leakage reduction through biofilm-induced calcium carbonate precipitation. Environ. Sci. Technol. 47, 142–149 (2013b). CrossRefGoogle Scholar
  61. 61.
    Phillips, A.J., Eldring, J., Hiebert, R., Lauchnor, E.G., Mitchell, A.C., Cunningham, A.B., Spangler, L.H., Gerlach, R.: Design of a meso-scale high pressure vessel for the laboratory examination of biogeochemical subsurface processes. J. Pet. Sci. Eng. 126, 55–62 (2015). CrossRefGoogle Scholar
  62. 62.
    Phillips, A.J., Cunningham, A.B., Gerlach, R., Hiebert, R., Hwang, C., Lomans, B.P., Westrich, J., Mantilla, C., Kirksey, J., Esposito, R., Spangler, L.H.: Fracture sealing with Microbially-Induced calcium carbonate precipitation: a field study. Environ. Sci. Technol. 50, 4111–4117 (2016). CrossRefGoogle Scholar
  63. 63.
    Prommer, H., Grassi, M.E., Davis, A.C., Patterson, B.M.: Modeling of microbial dynamics and geochemical changes in a metal bioprecipitation experiment. Environ. Sci. Technol. 41(24), 8433–8438 (2007). CrossRefGoogle Scholar
  64. 64.
    Qin, C., Hassanizadeh, S.M., Ebigbo, A.: Pore-scale network modeling of microbially induced calcium carbonate precipitation: Insight into scale dependence of biogeochemical reaction rates. Water Resour. Res. 52(11), 8794–8810 (2016). CrossRefGoogle Scholar
  65. 65.
    Riquelme, R., Lira, I., Pérez-López, C., Rayas, J.A., Rodríguez-vera, R.: Interferometric measurement of a diffusion coefficient: comparison of two methods and uncertainty analysis. J. Phys. D: Appl. Phys. 40(9), 2769–2776 (2007). CrossRefGoogle Scholar
  66. 66.
    Schäfer, F, Walter, L., Class, H., Müller, C.: The regional pressure impact of CO2 storage: a showcase study from the North German Basin. Environ. Earth Sci. 65(7), 2037–2049 (2012). CrossRefGoogle Scholar
  67. 67.
    Seto, M., Alexander, M.: Effect of bacterial density and substrate concentration on yield coefficients. Appl. Environ. Microbiol. 50(5), 1132–1136 (1985)Google Scholar
  68. 68.
    Taylor, S.W., Jaffé, P.R.: Substrate and biomass transport in a porous-medium. Water Resour. Res. 26 (9), 2181–2194 (1990). CrossRefGoogle Scholar
  69. 69.
    Tebes-Stevens, C., Valocchi, A.J., VanBriesen, J.M., Rittmann, B.E.: Multicomponent transport with coupled geochemical and microbiological reactions: model description and example simulations. J. Hydrol. 209(1), 8–26 (1998). CrossRefGoogle Scholar
  70. 70.
    Umar, M., Kassim, K.A., Chiet, K.T.P.: Biological process of soil improvement in civil engineering: a review. J. Rock Mechan. Geotechn. Eng. 8(5), 767–774 (2016). CrossRefGoogle Scholar
  71. 71.
    Verma, A., Pruess, K.: Thermohydrological conditions and silica redistribution near high-level nuclear wastes emplaced in saturated geological formations. J. Geophys. Res. Solid Earth 93(B2), 1159–1173 (1988). CrossRefGoogle Scholar
  72. 72.
    Vilcáez, J., Li, L., Wu, D., Hubbard, S.S.: Reactive transport modeling of induced selective plugging by leuconostoc mesenteroides in carbonate formations. Geomicrobiol J. 30(9), 813–828 (2013). CrossRefGoogle Scholar
  73. 73.
    van der Vorst, H.A.: BI-CGSTAB: A fast and smoothy converging variant of BI-CG for the solution of nansymmetric linear systems. SIAM J. Sci. Comput. 13(2), 631–644 (1992)CrossRefGoogle Scholar
  74. 74.
    Watson, I.a., Oswald, S.E., Mayer, K.U., Wu, Y., Banwart, Sa: Modeling kinetic processes controlling hydrogen and acetate concentrations in an aquifer-derived microcosm. Environ. Sci. Tech. 37(17), 3910–3919 (2003). CrossRefGoogle Scholar
  75. 75.
    Whiffin, V.S., La van, P., Harkes, M.P.: Microbial carbonate precipitation as a soil improvement technique. Geomicrobiol. J. 24(5), 417–423 (2007). CrossRefGoogle Scholar
  76. 76.
    van Wijngaarden, W.K., Vermolen, F.J., Meurs, G.A.M., Vuik, C.: Modelling Biogrout: A new ground improvement method based on microbial-induced carbonate precipitation. Transp. Porous Media 87(2), 397–420 (2011). CrossRefGoogle Scholar
  77. 77.
    van Wijngaarden, W.K., Vermolen, F.J., Meurs, G.A.M., Vuik, C.: A mathematical model for Biogrout. Comput. Geosci. 17(3), 463–478 (2013). CrossRefGoogle Scholar
  78. 78.
    van Wijngaarden, W.K., van Paassen, L.A., Vermolen, F.J., van Meurs, G.A.M., Vuik, C.: A reactive transport model for biogrout compared to experimental data. Transp. Porous Media 111(3), 627–648 (2016). CrossRefGoogle Scholar
  79. 79.
    Wolf, M., Breitkopf, O., Puk, R.: Solubility of calcite in different electrolytes at temperatures between 10 and 60C and at CO2 partial pressures of about 1 kPa. Geochem. J. 76, 291–301 (1989)Google Scholar
  80. 80.
    Zhang, T., Klapper, I.: Mathematical model of biofilm induced calcite precipitation. Water Sci. Technol. 61(11), 2957 (2010). CrossRefGoogle Scholar
  81. 81.
    Zhang, T., Klapper, I.: Mathematical model of the effect of electrodiffusion on biomineralization. Int. J. Non-Linear Mech. 46(4), 657–666 (2011). CrossRefGoogle Scholar
  82. 82.
    Zhang, T., Klapper, I.: Critical occlusion via biofilm induced calcite precipitation in porous media. J. Phys. 16(5), 055009 (2014). Google Scholar
  83. 83.
    Zhong, S., Mucci, A.: Calcite and aragonite precipitation from seawater solutions of various salinities: Precipitation rates and overgrowth compositions. Chem. Geol. 78, 283–299 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Center for Biofilm EngineeringMontana State UniversityBozemanUSA
  2. 2.Department of Hydromechanics and Modelling of HydrosystemsUniversity of StuttgartStuttgartGermany
  3. 3.Institute of GeophysicsSwiss Federal Institute of Technology ZurichZurichSwitzerland

Personalised recommendations