Chemical dissolution-front instability associated with water-rock reactions in groundwater hydrology: Analyses of porosity-permeability relationship effects

Because dissolution of rocks may create and enhance groundwater flow channels, the chemical dissolution-front instability (CDFI) can control the quality of groundwater. This paper presents the theoretical analyses of porosity-permeability relationship effects on the CDFI in water-saturated porous rocks. Since the CDFI in a water-rock reaction system can be assessed by comparing the comprehensive dimensionless dynamic characteristic (CDDC) number with the corresponding critical CDDC number of the geochemical dissolution system, it is necessary to investigate theoretically how different porosity-permeability relationships can affect the CDDC number and critical CDDC number of a water-rock reaction system. With the commonly-used Kozeny-Carman (KC) formula taken as a reference porosity-permeability formula, the permeability variation indicator (PVI), which is defined as the ratio of the permeability obtained from any porosity-permeability formula to that obtained from the KC formula, is proposed to reflect the effect of the porosity-permeability formula on the CDFI in a water-rock reaction system. The theoretical results demonstrated that: (1) since the porosity-permeability formula with a higher PVI can result in a stronger Darcy flow velocity, it may have a significant influence on the CDFI in the water-rock reaction system. (2) With an increase in the PVI of a porosity-permeability formula, there is a decrease in the critical CDDC number of the water-rock reaction system. This means that the porous rock with a higher PVI can enable the CDFI to take place much easier in the water-rock reaction system. (3) The use of the porosity-permeability formula with a higher PVI can also cause an increase in both the dimensionless growth rate of a perturbation and the propagation speed of the chemical dissolution front in the water-rock reaction system.