Some fundamental issues associated with theoretical analyses of reactive infiltration instability in fluid‐saturated porous media

• Published in: International journal for numerical and analytical methods in geomechanics 2023-06, Vol.47 (9), p.1596-1611
• Main Authors: Zhao, Chongbin, Hobbs, Bruce E., Ord, Alison
• Format: Article
• Language: English
• Subjects: chemical dissolution; Daily; Dissolution; Dissolving; front propagation; Fronts; Infiltration; Instability; instability criterion; Mathematical analysis; Minerals; Porosity; Porous media; Shape; spatial shape; Stability; Stability analysis; Stability criteria; theoretical analyses; Theoretical analysis; Time domain analysis
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.3530

This paper deals with three fundamental issues associated with theoretical analyses of reactive infiltration instability (RII) problems in fluid‐saturated porous media. The first fundamental issue is to determine the spatial shapes of chemical dissolution‐fronts in the limit case of the mineral dissolution ratio approaching zero in both conventional time (daily life time) and unconventional time ( time) domains. The chemical dissolution‐front is commonly represented by the spatial shape of the porosity profile. The second fundamental issue is to conduct theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through directly solving dimensional mathematical governing equations in the conventional time domain. The third fundamental issue is to carry out theoretical analyses of the RII problems associated with the mineral dissolution ratio approaching zero through solving dimensionless mathematical governing equations in the unconventional time domain. Through purely mathematical deductions, it has been proven that: (1) the spatially sharp shape of a chemical dissolution‐front, which is theoretically predicted either at a much smaller timescale than the dissolution timescale associated with the daily life time or at a much larger timescale than the dissolution timescale associated with the daily life time, can be observed in the daily life time domain; (2) the theoretical instability criterion of an RII problem can be established directly at three different length‐scales in the daily life time domain; and (3) although the spatial shape of a chemical dissolution‐front at the dissolution timescale associated with the daily life time cannot be observed in the daily life time domain, the theoretical instability criterion of an RII problem at the dissolution timescale associated with the daily life time can be established when a physically consistent mathematical transform is used in the theoretical analysis.