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Pure and Applied Chemistry

The Scientific Journal of IUPAC

Ed. by Burrows, Hugh / Stohner, Jürgen

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IMPACT FACTOR 2017: 5.294

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Volume 89, Issue 5

Issues

An overview of computational methods for chemical equilibrium and kinetic calculations for geochemical and reactive transport modeling

Allan M. M. LealORCID iD: http://orcid.org/0000-0003-4340-610X / Dmitrii A. Kulik
  • Laboratory for Waste Management, Nuclear Energy and Safety Research Department, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ William R. Smith
  • Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario NIG2 WI, Canada
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Martin O. Saar
  • Geothermal Energy and Geofluids Group, Department of Earth Sciences, ETH Zürich, Switzerland
  • Department of Earth Sciences, University of Minnesota, Minneapolis, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-04-29 | DOI: https://doi.org/10.1515/pac-2016-1107

Abstract

We present an overview of novel numerical methods for chemical equilibrium and kinetic calculations for complex non-ideal multiphase systems. The methods we present for equilibrium calculations are based either on Gibbs energy minimization (GEM) calculations or on solving the system of extended law of mass-action (xLMA) equations. In both methods, no a posteriori phase stability tests, and thus no tentative addition or removal of phases during or at the end of the calculations, are necessary. All potentially stable phases are considered from the beginning of the calculation, and stability indices are immediately available at the end of the computation to determine which phases are actually stable at equilibrium. Both GEM and xLMA equilibrium methods are tailored for computationally demanding applications that require many rapid local equilibrium calculations, such as reactive transport modeling. The numerical method for chemical kinetic calculations we present supports both closed and open systems, and it considers a partial equilibrium simplification for fast reactions. The method employs an implicit integration scheme that improves stability and speed when solving the often stiff differential equations in kinetic calculations. As such, it requires compositional derivatives of the reaction rates to assemble the Jacobian matrix of the resultant implicit algebraic equations that are solved at every time step. We present a detailed procedure to calculate these derivatives, and we show how the partial equilibrium assumption affects their computation. These numerical methods have been implemented in Reaktoro (reaktoro.org), an open-source software for modeling chemically reactive systems. We finish with a discussion on the comparison of these methods with others in the literature.

Keywords: chemical equilibrium; chemical kinetics; geochemical modeling; ISSP-17; numerical methods; reactive transport

Article note:

A collection of invited papers based on presentations at the International Symposium on Solubility Phenomena and Related Equilibrium Processes (ISSP-17), Geneva, 24–29 July 2016.

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About the article

Published Online: 2017-04-29

Published in Print: 2017-05-01


Citation Information: Pure and Applied Chemistry, Volume 89, Issue 5, Pages 597–643, ISSN (Online) 1365-3075, ISSN (Print) 0033-4545, DOI: https://doi.org/10.1515/pac-2016-1107.

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