2007
DOI: 10.1029/2005wr004465
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A reduction scheme for coupled multicomponent transport‐reaction problems in porous media: Generalization to problems with heterogeneous equilibrium reactions

Abstract: 1] In this article a systematic approach for the efficient computation of the transport and reaction of a multispecies, multireaction system is proposed. The objective of this approach is to reformulate the given system of differential or differential-algebraic equations in such a way that the couplings and the nonlinearities are concentrated in a reduced number of equations (if compared to the original formulation), while some linear equations decouple from the system. The resulting system is handled in the s… Show more

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Cited by 59 publications
(55 citation statements)
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“…Starting with a reaction network of N reactions involving M species, each reaction can involve any number of species, one can write M species transport equations based on the principle of chemical kinetics [172]. Performing GaussJordan reduction of the reaction network [173][174][175], one obtains a system of M transport equations for M reaction extents, each of which is a linear combination of the M species concentrations [170,171]. A reaction extent is called a component when there is no reaction term appearing in its transport equation.…”
Section: Hydrogeochemmentioning
confidence: 99%
“…Starting with a reaction network of N reactions involving M species, each reaction can involve any number of species, one can write M species transport equations based on the principle of chemical kinetics [172]. Performing GaussJordan reduction of the reaction network [173][174][175], one obtains a system of M transport equations for M reaction extents, each of which is a linear combination of the M species concentrations [170,171]. A reaction extent is called a component when there is no reaction term appearing in its transport equation.…”
Section: Hydrogeochemmentioning
confidence: 99%
“…Chilakapathi [4] provides significant flexibility in handling any type of kinetic biogeochemical reaction coupled with transport, representing equilibrium processes as fast reversible kinetic reactions but requires problem-specific modifications to the code for new simulations to be run. Recently, these types of reaction-based paradigms capable of simulating any number of reactions incorporating both geochemical and biological processes have gained popularity and implemented in a number of codes (e.g., [14,15,54,55,58]). This paper describes the development and application of the latest versions of HYDROGEOCHEM [56][57][58], a mechanistically based numerical model for simulation of coupled fluid flow, thermal transport, and reactive chemical transport in variably saturated porous and fractured media.…”
Section: Introductionmentioning
confidence: 99%
“…Since these techniques are already known from [27,28] (but strictly needed for our subsequent analysis), we will keep this section as short as possible. First, we apply the decoupling technique proposed in [27,28] to the PDE-ODE system (3.14)-(3.15). This will lead to a decoupling of some linear PDEs.…”
Section: Transformation Of the Dynamic Systemmentioning
confidence: 99%
“…In Chapter 3 background information is given, the problem is formulated and its mathematical model is given. Afterwards an equivalence transformation is applied to the PDE-ODE-AE-CC system (going back to [27,28,25]). The motivation for this reformulation is a decoupling of some (linear) PDEs, leading to a smaller nonlinear system.…”
Section: Introductionmentioning
confidence: 99%