Newton method for reactive solute transport with equilibrium sorption in porous media

Radu, Florin A.; Pop, Sorin

doi:10.1016/j.cam.2009.08.070

Cited by 27 publications

(18 citation statements)

References 16 publications

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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%

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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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Section: Introductionmentioning

confidence: 99%

“…In Radu et al (2013), the differential equation for the porosity is comparable to the one used in this article. In Radu and Pop (2010), , the Newton method is used to deal with the nonlinear equations and the convergence of this method is studied.…”

Section: Introductionmentioning

confidence: 99%

A Reactive Transport Model for Biogrout Compared to Experimental Data

et al. 2015

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“…The implicit scheme provides a set of coupled nonlinear equation for the triple (u n h , Q n h , v n h ). A Newton iteration is used to solve the resulting system (see [36,38], where the Newton method is applied to similar problems). The tests are applied to the case described before, and the results are presented in Tables 5.3 and 5.4.…”

Section: Case (B) Dissolution Frontsmentioning

confidence: 99%

“…Non-Lipschitz, but Hölder continuous rates are considered using conformal finite element method (FEM) schemes in [4,5]. Similarly, for Hölder continuous rates (including equilibrium and nonequilibrium cases), MFEMs are analyzed rigorously in [36,38], whereas [37] provides error estimates for the coupled system describing unsaturated flow and reactive transport. In all these cases, the continuity of the reaction rates allows error estimates to be obtained.…”

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confidence: 99%

Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Kumar¹,

Pop²,

Radu³

2013

SIAM J. Numer. Anal.

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“…Conformal FEM schemes for reactive porous media flow models are discussed in [1,2], where nonLipschitz, but Hölder continuous rates are considered. Similarly, for Hölder continuous rates (including equilibrium and non-equilibrium cases) mixed FEM methods are analyzed rigorously in [31,32], whereas [33] provides error estimates for the coupled system describing unsaturated flow and reactive transport. In all these cases, the continuity of the reaction rates allows obtaining error estimates.…”

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confidence: 99%