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Two Different Computational Schemes for Solving Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media

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Abstract

This paper deals with how to solve chemical dissolution-front instability problems, which are nonlinearly coupled by subsurface pore-fluid flow, reactive mass transport and porosity evolution processes in fluid-saturated porous media, through using two different computational schemes. In the first computational scheme, porosity, pressure of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PPC scheme. In the second computational scheme, porosity, velocity of the pore-fluid and concentration of the solute are used as fundamental unknown variables to describe a chemical dissolution system, so that it can be named as the PVC scheme. Since the finite element equations of a chemical dissolution-front instability problem on the basis of using the PPC scheme is available, the main focus of this study is on deriving the finite element equations of a chemical dissolution-front instability problem on the basis of using the PVC scheme. In particular, analytical solutions for the property matrices of a four-node rectangular element have been derived and used in both the PVC scheme and the PPC scheme. Through comparing the computational simulation results obtained from using both the PPC scheme and the PVC scheme, it has demonstrated that: (1) if the chemical dissolution system is in a stable state, then the PPC scheme is superior to the PVC scheme because the PPC scheme uses less computational efforts than the PVC scheme; (2) if the chemical dissolution system is in an unstable state, then the PVC scheme is superior to the PPC scheme because the PVC scheme yields more accurate computational simulation results than the PPC scheme.

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Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (Grant Nos: 42030809 and 72088101). The authors express sincere thanks to the anonymous referees for their valuable comments, which led to a significant improvement over an early version of the paper.

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Authors and Affiliations

  1. Computational Geosciences Research Centre, Central South University, Changsha, 410083, China

    Chongbin Zhao

  2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha, 410083, China

    Chongbin Zhao

  3. School of Earth and Environment, The University of Western Australia, Crawley, WA, 6009, Australia

    B. E. Hobbs & A. Ord

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  1. Chongbin Zhao
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  2. B. E. Hobbs
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  3. A. Ord
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Correspondence to Chongbin Zhao.

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Zhao, C., Hobbs, B.E. & Ord, A. Two Different Computational Schemes for Solving Chemical Dissolution-Front Instability Problems in Fluid-Saturated Porous Media. Transp Porous Med 145, 323–346 (2022). https://doi.org/10.1007/s11242-022-01851-y

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