Physical and Chemical Dissolution Front Instability in Porous Media

Instability of nonlinear systems is a common phenomenon in nature. This phenomenon is the direct consequence of a nonlinear system when it reaches a qualitative change state (i.e. an unstable state) from a quantitative change state (i.e. a stable state). If a nonlinear system is in a stable state, then any small perturbation applied to the system does not cause any change in the basic characteristic of the dynamic response of the system. However, if a nonlinear system is in an unstable state, then any small perturbation applied to the system can cause a qualitative change in the basic characteristic of the dynamic response of the system. For this reason, the study of nonlinear system instability has become an important topic in many scientific and engineering fields over the past few decades.

When fresh pore-fluid enters a solute-saturated porous medium, where the concentration of the solute (i.e. aqueous mineral) reaches its equilibrium concentration, 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.

Particle shapes and arrangements within a porous medium can significantly affect the porosity and permeability of the porous medium.

Consideration of mineral dissolution due to chemical reactions plays an important role in the computational simulation of reactive transport problems involving fluid-saturated porous media (Steefel and Lasage 1990, 1994; Yeh and Tripathi 1991; Raffensperger and Garven 1995; Shafter et al. 1998a, b; Xu et al. 1999; Ormond and Ortoleva 2000; Alt-Epping and Smith 2001; Chen and Liu 2002; Zhao et al. 1998, 2001; 2003, 2005, 2006).

The instability of a chemical dissolution front is an important scientific problem associated with reactive transport processes in fluid-saturated porous media (Chadam et al. 1986, 1988; Ortoleva et al. 1987; Imhoff and Miller 1996; Renard et al. 1998; Imhoff et al. 2003; Chen and Liu 2002; Chen et al. 2009; Zhao et al. 2008a, b, 2010).

In the previous studies, mathematical analyses were conducted to establish a theoretical criterion, which is used to judge whether or not a planar chemical-dissolution front can become unstable during its propagation in the fluid-saturated porous medium (Chadam et al. 1986, 1988; Zhao et al. 2008a, 2009).

Both medium and pore-fluid compressibility was neglected in the previous study of the classical reactive infiltration instability problem within a fluid-saturated porous medium (Chadam et al. 1986, 1988; Ortoleva et al. 1987). Due to this simplification, the critical condition, which is used to assess whether or not the fully-coupled nonlinear system between porosity, pore-fluid pressure and reactive chemical-species transport within the fluid-saturated porous medium can become unstable, was rigorously derived in a pure mathematical manner.

Numerical simulation of chemical dissolution-front instability in fluid-saturated porous media is an important topic in the field of computational geosciences, which is a beautiful marriage between the contemporary computational mechanics and traditional geosciences. If fresh water is injected into a fluid-saturated porous medium with the solute (i.e. chemical-species) being in an equilibrium state, it can break the equilibrium state of the solute so that the whole system becomes chemically far from equilibrium. To drive the system towards a new chemical equilibrium state, the solid part of the solute is dissolved within the porous medium. This process causes an increase in the porosity of the porous medium. The resulting porosity increase can cause a corresponding increase in the permeability of the medium so that the pore-fluid flow can be enhanced within the porous medium. This means that both permeability and diffusivity are dependent on the porosity of a porous medium (Bear 1972). When the injected fresh water flow is relatively weak, the chemical dissolution front is stable so that a planar chemical dissolution-front remains the planar shape during its propagation within the porous medium. However, when the injected fresh water flow is strong enough, the chemical dissolution front becomes unstable. In this case, a planar chemical dissolution-front can be changed into a complicated and complex morphology during its propagation within the porous medium. This is the scientific problem, known as the chemical dissolution-front instability problem in the fluid-saturated porous medium, to be considered in this investigation. It is noted that there is another mechanism that can also cause pore-fluid channeling instability due to the rheological asymmetry associated with compaction and decompaction in ductile rocks (Connolly and Podladchikov 2007). This instability is closely associated with porosity waves and can be referred to as the mechanical instability. Owing to a significant mechanism difference between a chemical dissolution instability problem and a mechanical instability one, this chapter focuses on the consideration of chemical dissolution instability problems. However, a possible interaction between these two different mechanisms may need to be considered in a future investigation.

The transport of nonaqueous phase liquids (NAPLs) in contaminated subsurface is an important problem in geoenvironmental engineering.

In the field of contaminant hydrology, both land contamination and land remediation problems are often encountered. Land contamination is known as the distribution of chemical and pollutants on land sites, while land remediation is known as the cleanup of chemical and pollutants on land sites that causes health concerns to the humans and the environment. When nonaqueous phase liquids (NAPLs), such as trichloroethylene, ethylene dibromide, benzene, toluene and so forth (Miller et al. 1990), are released to groundwater, they can reside in the form of disconnected ganglia or blobs as residual saturations within the pores of porous media. This process belongs to the land contamination problem

Instability of acidization dissolution fronts in carbonate rocks is an important mechanism of the karst formation that is commonly observed in nature.