Please cite this article as: Malgorzata Peszynska, Anna Trykozko, Gabriel Iltis, Steffen Schlueter, Dorthe Wildenschild, Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscaling, Advances in Water Resources (2015), Highlights 1 • We use 3D imaging with a barium-based contrasting agent to obtain 2 porescale geometries filled with biofilm 3 • We simulate the flow in the porescale geometries with and without 4 biofilm, and upscale the results to the conductivities which compare 5 • well with the experimental values, and which show the dependence of 6 the degree of bioclogging on the flow rates 7 • We simulate biomass growth and transport coupled to the flow and 8 obtain morphologies similar to those in the experiment 9 • We show several reduced models for conductivities and their depen-10 dence on the biofilm growth Abstract 21 Biofilm growth changes many physical properties of porous media such 22 as porosity, permeability and mass transport parameters. The growth de-23 pends on various environmental conditions, and in particular, on flow rates. 24 Modeling the evolution of such properties is difficult both at the porescale 25 where the phase morphology can be distinguished, as well as during up-26 scaling to the corescale effective properties. Experimental data on biofilm 27 growth is also limited because its collection can interfere with the growth, 28 while imaging itself presents challenges. 29 In this paper we combine insight from imaging, experiments, and nu-30 merical simulations and visualization. The experimental dataset is based on 31 glass beads domain inoculated by biomass which is subjected to various flow 32 conditions promoting the growth of biomass and the appearance of a biofilm 33 phase. The domain is imaged and the imaging data is used directly by a 34 computational model for flow and transport. The results of the computa-35 tional flow model are upscaled to produce conductivities which compare well 36 with the experimentally obtained hydraulic properties of the medium. The 37 flow model is also coupled to a newly developed biomass-nutrient growth 38 model, and the model reproduces morphologies qualitatively similar to those 39 observed in the experiment.40 Keywords: 41 porescale modeling, imaging porous media, microtomography, reactive 42 transport, biomass and biofilm growth, parabolic variational inequality, 43 Lagrange multipliers, coupled nonlinear system, multicomponent 44 multiphase flow and transport in porous media 45 2

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SUMMARYTo be able to use a limited number of relatively large grid cells in numerical oil reservoir simulators and groundwater models, upscaling of the absolute permeability is frequently applied. The spatial ÿne-scale permeability distribution, which is generally obtained from geological and geostatistical models, is incorporated in the relatively large grid cells of the numerical model. If the porous medium may be approximated as a periodic medium, upscaling can be performed by the homogenization method. Numerical homogenization gives rise to an approximation error. The complementarity between the conformal-nodal ÿnite element method and the mixed-hybrid ÿnite element method has been used to quantify this error. The two methods yield, respectively, upper and lower bounds for the eigenvalues of the coarse-scale permeability tensor. Results of numerical experiments obtained using tetrahedral meshes are shown both in the far ÿeld and in the near well region.

Abstract. We propose algorithms for computational upscaling of flow from porescale (microscale) to lab scale (mesoscale). In particular, we solve Navier-Stokes equations in complex pore geometries and average their solutions to derive properties of flow relevant at lab scale such as permeability and inertia coefficients. We discuss two variants of traditional discretizations: a simple algorithm which works well in periodic isotropic media and can be used when coarse approximations are needed, and a more complex one which is well suited for nonisotropic geometries. Convergence of solutions and averaging techniques are major concerns but these can be relaxed if only mesoscopic parameters are needed. The project is a proof-of-concept computational laboratory for porous media which delivers data needed for mesoscale simulations by performing microscale computational simulations.