Surrogate modeling and global sensitivity analysis for biomineralization in porous media

We focus on the assessment of spatiotemporal distributions of precipitates in complex porous systems under a variety of sources of uncertainty. Our study specifically targets calcium carbonate (CaCO₃) biomineralizing techniques, that are of significant interest across a wide range of engineering applications. In this context, one can note that favoring mineralization can markedly alter the pore space structure as well as hydrodynamic parameters of porous materials. Otherwise, uncertainties surrounding our ability to assess hydraulic and biochemical parameters driving the dynamics of biomineralization treatments can influence the way we quantify the extent of mineral precipitation. Here, we start from a pore scale perspective and rest on a stochastic modeling approach. The latter leverages a combination of (i) a fully coupled biomineralization model based on a pore network model (PNM) and (ii) a surrogate model that enables one to perform numerical Monte Carlo simulations at a reduced computational cost. Our surrogate model relies on a classical polynomial chaos expansion approach. We consider the biomineralization model described by Qin et al. (2016) and perform geochemical speciation through the open-source PHREEQC module. The surrogate model is constructed on the basis of numerical results stemming from the full biomineralization model and is here employed to perform global sensitivity studies and uncertainty quantification analyses. Our results enable one to identify the relative importance of four design (or control) quantities (i.e., (i) injected biomass concentration, (ii) initial biofilm across the pore space, (iii) pressure difference between inlet and outlet of the porous medium, and (iv) injected urea concentration) and of the initial distribution of pore sizes across the domain on (a) volume fraction of precipitates within the host porous medium (in terms of total amount and preferential location within pores of given size) and (b) permeability reduction of the overall porous medium after biomineralization. Global sensitivity analyses reveal that the volume fraction of precipitates is strongly influenced by biomass and urea concentrations. These quantities are associated with a strong positive correlation with precipitate volumes. Our results can form the basis to inform model calibration under uncertainty, thus providing a robust foundation for optimizing biomineralization strategies in engineering applications. 

Reference:

Qin, C.-Z., Hassanizadeh, S. M., & Ebigbo, A. (2016). Pore-scale network modeling of microbially induced calcium carbonate precipitation: Insight into scale dependence of biogeochemical reaction rates: pore-scale network modeling of MICP. Water Resources Research, 52(11), 8794–8810. https://doi.org/10.1002/2016WR019128.