An interface‐condition substitution strategy for theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 43; no. 8; pp. 1576 - 1593
• Main Authors: Zhao, Chongbin, Hobbs, Bruce E., Ord, Alison
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.06.2019
• Subjects: Bridges; chemical dissolution; Dissolution; dissolution timescale; Dissolving; Exact solutions; Growth rate; Infiltration; infiltration instability; Instability; Mathematical analysis; Organic chemistry; Perturbation; porous rocks; Rock; Rocks; Stability; Strategy; Substitutes; substitution strategy; theoretical study; Time; Upstream
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2907

Summary A theoretical study of reactive infiltration instability is conducted on the dissolution timescale. In the present theoretical study, the transient behavior of a dissolution‐timescale reactive infiltration system needs to be considered, so that the upstream region of the chemical dissolution front should be finite. In addition, the chemical dissolution front of finite thickness should be considered on the dissolution timescale. Owing to these different considerations, it is very difficult, even in some special cases, to derive the first‐order perturbation solutions of the reactive infiltration system on the dissolution timescale. To overcome this difficulty, an interface‐condition substitution strategy is proposed in this paper. The basic idea behind the proposed strategy is that although the first‐order perturbation equations in the downstream region cannot be directly solved in a purely mathematical manner, they should hold at the planar reference front, which is the interface between the upstream region and the downstream region. This can lead to two new equations at the interface. The main advantage of using the proposed interface‐condition substitution strategy is that through using the original interface conditions as a bridge, the perturbation solutions for the dimensionless acid concentration, dimensionless Darcy velocity, and their derivatives involved in the two new equations at the interface can be evaluated just by using the obtained analytical solutions in the upstream region. The proposed strategy has been successfully used to derive the dimensionless growth rate, which is the key issue associated with the theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks.