Field-scale modeling of microbially induced calcite precipitation

Abstract

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.

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Funding

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).

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Appendix

Appendix

This appendix provides the reactive source and sink terms in the model for MICP used in this study. In the following tables, we refer to the components (water (w), inorganic carbon (ic), sodium (Na), chloride (Cl), calcium (Ca), urea (u), ammonium/ammonia (a), substrate (s), oxygen (O2), and suspended biomass(sb)) and solid phase (biofilm (b) and calcite (c)) with the respective super- or subscripts.

Sodium and chloride do not take part in any of the reactions directly, which is why qNa = qCl = 0. However, they represent the effect of the presence of ions in the aqueous phase on the fluid properties density and viscosity according to the salinity dependent relations given in [5] and on the activity coefficients of the reacting components calculated using Pitzer equations according to [14, 48, 79], as discussed in detail in [19]. Also calcium is considered to contribute to salinity and ionic strength. All ions are considered in the charge balance used to determine the pH and the dissociation of total inorganic carbon and ammonia/ammonium.

Table 2 Component-specific reactive source and sink terms of the model used in this study

Table 2 gives all reactive source and sink terms composed of the rates kinetics of the biogeochemical reactions considered in the model. The parameters used to calculated the source and sink terms and rate kinetics are the following (see also Table 3 for their values): Mκ is the molar mass of κ, Y the growth yield coefficient, F the ratio of oxygen to substrate used for growth, kurease the maximum activity of urease, kub the mass ratio of urease to biofilm, ρb the density of biofilm, mκ the molality of κ calculated from the mole fraction \(x^{\kappa }_{\mathrm {w}}\) and the water-phase properties, Ku the half-saturation coefficients for ureolysis, kprec and nprec are empirical precipitation parameters, kdiss,1, kdiss,2, and ndiss are dissolution parameters, Asw,0 the initial interfacial area of solid and water phase, ac the specific surface area of calcite, Ksp the calcite solubility product and γκ the activity coefficients of κ calculated using Pitzer equations [14, 48, 79] kμ the maximum specific growth rate, \(C_{\mathrm {w}}^{\mathrm {s}}\) and \(C_{\mathrm {w}}^{\mathrm {O_{2}}}\) the mass concentrations of substrate and oxygen, calculated from the mole fraction \(x^{\kappa }_{\mathrm {w}}\) and the water-phase properties, Ks and \(K_{\mathrm {O_{2}}}\) the half-saturation coefficients for substrate and oxygen, respectively, b0 is the endogenous decay rate, KpH an empirical constant accounting for increased bacterial inactivation at non-optimal pH, ca,1 a general first-order attachment coefficient, ca,2 a attachment coefficient for preferential attachment to existing biofilm, cd the first order coefficient for detachment due to shear stress, and |∇pwρwg| the absolute value of the potential gradient.

Table 3 Parameter values used for the simulations in 2014 and 2018

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Cunningham, A.B., Class, H., Ebigbo, A. et al. Field-scale modeling of microbially induced calcite precipitation. Comput Geosci 23, 399–414 (2019). https://doi.org/10.1007/s10596-018-9797-6

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Keywords

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