Page 107 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Chapter 5
A Segregated Algorithm for Simulating

Chemical Dissolution Front Instabilities
in Fluid-Saturated Porous Rocks

When fresh pore-fluid flow enters a solute-saturated porous medium, where the
concentration of the solute (i.e. aqueous mineral) reaches its equilibrium concen-
tration, the concentration of the aqueous mineral is diluted so that the solid part of
the solute (i.e. solid mineral) is dissolved to maintain the equilibrium state of the
solution. This chemical dissolution process can result in the propagation of a disso-
lution front within the fluid-saturated porous medium. Due to the dissolution of the
solid mineral, the porosity of the porous medium is increased behind the dissolution
front. Since a change in porosity can cause a remarkable change in permeability,
there is a feedback effect of the porosity change on the pore-fluid flow, according to
Darcy’s law. It is well known that because pore-fluid flow plays an important role in
the process of reactive chemical-species transport, a change in pore-fluid flow can
cause a considerable change in the chemical-species concentration within the porous
medium (Steefel and Lasaga 1990, 1994, Yeh and Tripathi 1991, Raffensperger and
Garven 1995, Shafter et al. 1998a, b, Xu et al. 1999, 2004, Ormond and Ortoleva
2000, Chen and Liu 2002, Zhao et al. 2005a, 2006c). This means that the problem
associated with the propagation of a dissolution front is a fully coupled nonlinear
problem between porosity, pore-fluid pressure and reactive chemical-species trans-
port within the fluid-saturated porous medium. If the fresh pore-fluid flow is slow,
the feedback effect of the porosity change is weak so that the dissolution front is
stable. However, if the fresh pore-fluid flow is fast enough, the feedback effect of
the porosity change becomes strong so that the dissolution front becomes unstable.
In this case, a new morphology (i.e. dissipative structure) of the dissolution front can
emerge due to the self-organization of this coupled nonlinear system. This leads to
an important scientific problem, known as the reactive infiltration instability prob-
lem (Chadam et al. 1986, 1988, Ortoleva et al. 1987), which is closely associated
with mineral dissolution in a fluid-saturated porous medium.
This kind of chemical-dissolution-front instability problem exists ubiquitously
in many scientific and engineering fields. For example, in geo-environmental engi-
neering, the rehabilitation of contaminated sites using fresh water to wash the
sites involves the propagation problem of the removed contaminant material front
in water-saturated porous medium. In mineral mining engineering, the extraction
of minerals in the deep Earth using the in-situ leaching technique may result in

C. Zhao et al., Fundamentals of Computational Geoscience, 95
Lecture Notes in Earth Sciences 122, DOI 10.1007/978-3-540-89743-9 5,
C Springer-Verlag Berlin Heidelberg 2009