Analytical solutions for chemical dissolution‐front instability problems involving radially divergent flow within fluid‐saturated porous media

Abstract

AbstractThrough using rigorously mathematical deductions, this article derives analytical solutions for chemical dissolution‐front instability (CDFI) problems, in which radially divergent flow is involved within fluid‐saturated porous media. Since the acid injection‐well to be considered is a circle of nonzero radius in the horizontal plane, a polar coordinate system is used to describe the coupled mathematical governing equations of the CDFI problem. To facilitate deriving analytical solutions, an appropriate mathematical transform is used to convert the coupled mathematical governing equations from a dimensional form into a dimensionless one. This enables the generalized linear stability approach to be utilized for deriving both analytical base and perturbation solutions for the CDFI problem involving radially divergent flow within a fluid‐saturated porous medium. Consequently, a theoretical criterion, which is usable for assessing the CDFI in the chemical dissolution system (CDS), is further established from the corresponding analytical perturbation solutions. The related theoretical results have demonstrated that: (1) the proposed theoretical criterion is useful and applicable for assessing the CDFI associated with radially divergent flow within fluid‐saturated porous media; (2) the permeability ratio between the downstream and upstream regions can affect significantly the critical Peclet number of a CDS associated with radially divergent flow; (3) the initial porosity can have remarkable effects on the critical Peclet number of a CDS associated with radially divergent flow; and (4) the difference between the final and initial porosities can also affect significantly the critical Peclet number of a CDS associated with radially divergent flow in the fluid‐saturated porous medium.