An upscaled model for biofilm growth in a thin strip

Noorden, van Tl Tycho; Pop, Sorin; Ebigbo, Anozie; Helmig, Rainer

doi:10.1029/2009wr008217

Cited by 59 publications

(68 citation statements)

References 32 publications

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“…In these papers, the position of the interface between grain and void space is tracked, giving a problem with a free boundary. Similar models can also be obtained for biofilm growth (van Noorden et al 2010), for drug release from collagen matrices (Ray et al 2013), and on an evolving microstructure (Peter 2009). These models do not include any temperature dependence in the reaction rates nor any heat transfer.…”

Section: Introductionmentioning

confidence: 97%

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

Bringedal

Kumar

2017

Transp Porous Med

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For a non-isothermal reactive flow process, effective properties such as permeability and heat conductivity change as the underlying pore structure evolves. We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al (2016). In particular, we focus on the limit behavior near clogging. The effective heat conductivities are compared to common porosity-weighted volume averaging approximations and we find that geometric averages perform better than arithmetic and harmonic for isotropic media, while the optimal choice for anisotropic media depends on the degree and direction of the anisotropy. An approximate analytical expression is found to perform well for the isotropic effective heat conductivity. The permeability is compared to some commonly used approaches focusing on the limiting behavior near clogging, where a fitted power law is found to behave reasonably well. The resulting macroscale equations are tested on a case where the geochemical reactions cause pore clogging and a corresponding change in the flow and transport behavior at Darcy scale. As pores clog the flow paths shift away, while heat conduction increases in regions with lower porosity.

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Section: Introductionmentioning

confidence: 97%

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

Bringedal

Kumar

2017

Transp Porous Med

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“…Specifically, we let the fracture thickness ε go to zero and reduce the fracture model to a boundary condition. We refer to [9,25] for a general procedure applied to convection dominated regimes, and to [19,30,31] for more specific applications related to precipitation-dissolution models, or to biofilm growth in porous media. However, these papers refer strictly to the fracture region and do not consider the coupling with a porous block.…”

Section: Formal Upscalingmentioning

confidence: 99%

Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition

2016

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“…Combining these phenomena leads to a coupled reactive transport model. Some articles about modelling reactive flow and transport in porous media are Agosti et al (2015), Chilakapati et al (2000), Radu et al (2013), Radu and Pop (2010), ; Samper and Zhang (2006), van Noorden (2009), van Noorden et al (2010, Yang et al (2008), of which Agosti et al (2015), Radu et al (2013), van Noorden (2009) also consider a variable porosity. In van Noorden (2009), the level set function is used for the boundary of the crystals and a homogenization procedure is applied to obtain the upscaled equations.…”

Section: Introductionmentioning

confidence: 99%

A Reactive Transport Model for Biogrout Compared to Experimental Data

et al. 2015

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Biogrout is a method for reinforcement of granular soil. In the Biogrout process, calcium carbonate is produced. This solid connects the grains, and therefore the strength of the soil is increased. The calcium carbonate is formed with the use of micro-organisms. Experiments and numerical simulations have been performed to demonstrate the process under various conditions. In this paper, it has been examined whether a reactive transport model can be used to describe a Biogrout experiment that was performed in a column with a length of 5 m. Four different models for the course of the reaction rate are considered. The concentration of micro-organisms and the reaction rate are fine-tuned in order to find a description of the experiment that is a best fit for the particular model. This is done by minimizing the error between the experimental and numerical results for the concentration of calcium carbonate and the by-product of the reaction. List of symbolsInjected concentration of micro-organisms (normalized) (1) S bac Ratio of micro-organisms that is fixated (with respect to the injected concentration) (1)

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An upscaled model for biofilm growth in a thin strip

Cited by 59 publications

References 32 publications

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition

A Reactive Transport Model for Biogrout Compared to Experimental Data

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