Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1576-1593 |
| Number of pages | 18 |
| Journal | International Journal for Numerical and Analytical Methods in Geomechanics |
| Volume | 43 |
| Issue number | 8 |
| Early online date | 20 Mar 2019 |
| DOIs | |
| Publication status | Published - 10 Jun 2019 |
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An interface-condition substitution strategy for theoretical study of dissolution-timescale reactive infiltration instability in fluid-saturated porous rocks. / Zhao, Chongbin; Hobbs, Bruce E.; Ord, Alison.
In: International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, No. 8, 10.06.2019, p. 1576-1593.Research output: Contribution to journal › Article
TY - JOUR
T1 - An interface-condition substitution strategy for theoretical study of dissolution-timescale reactive infiltration instability in fluid-saturated porous rocks
AU - Zhao, Chongbin
AU - Hobbs, Bruce E.
AU - Ord, Alison
PY - 2019/6/10
Y1 - 2019/6/10
N2 - 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.
AB - 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.
KW - chemical dissolution
KW - dissolution timescale
KW - infiltration instability
KW - porous rocks
KW - substitution strategy
KW - theoretical study
UR - http://www.scopus.com/inward/record.url?scp=85063129751&partnerID=8YFLogxK
U2 - 10.1002/nag.2907
DO - 10.1002/nag.2907
M3 - Article
VL - 43
SP - 1576
EP - 1593
JO - International Journal of Numerical and Analytical Methods in Geomechanics
JF - International Journal of Numerical and Analytical Methods in Geomechanics
SN - 0363-9061
IS - 8
ER -