Zhao, Chongbin; Hobbs, B. E.; Mühlhaus, H. B. Finite element modelling of reactive mass transport problems in fluid-saturated porous media. (English) Zbl 0955.76053 Commun. Numer. Methods Eng. 15, No. 7, 501-513 (1999). Summary: We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression for chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions, especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of \(H^+\)) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Cited in 9 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76V05 Reaction effects in flows 76S05 Flows in porous media; filtration; seepage 86A05 Hydrology, hydrography, oceanography Keywords:isothermal non-equilibrium chemical reaction; finite element method; reactive mass transport; fluid-saturated porous media; Arrhenius law; distributions of PH; contaminant transport problems; groundwater systems Software:FIDAP PDFBibTeX XMLCite \textit{C. Zhao} et al., Commun. Numer. Methods Eng. 15, No. 7, 501--513 (1999; Zbl 0955.76053) Full Text: DOI References: [1] Zhao, Comput. Struct. 53 pp 849– (1993) [2] Zhao, Int. J. Water Resour. Eng. 1 pp 33– (1993) · doi:10.5188/ijsmer.1.33 [3] Zhao, Int. J. Numer. Methods Eng. 37 pp 1143– (1994) [4] Zhao, Int. J. Numer. Anal. Methods Geomech. 18 pp 523– (1994) [5] Zhao, Int. J. Numer. Anal. Methods Geomech. 18 pp 543– (1994) [6] Nithiarasu, Commun. Numer. Methods Eng. 14 pp 241– (1998) [7] Zhao, Comput. Methods Appl. Mech. Eng. 165 pp 175– (1998) [8] Fluid Dynamics International Fluid Dynamics Analysis Package: FIDAP, Fluid Dynamics International Inc., Illinois, 1997. [9] Arrhenius Equation and Non-equilibrium Kinetics: 100 Years Arrhenius Equation, BSB B. G. Teubner, Leipzig, 1989. [10] Zhao, Int. J. Numer. Anal. Methods Geomech. 21 pp 863– (1997) [11] Zhao, Int. J. Comput. Methodol.: Numer. Heat Transf. 33 pp 415– (1998) · doi:10.1080/10407789808913947 [12] The Finite Element Method, McGraw-Hill, London, 1977. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.