Near-field performance of chemical dissolution-front instability around a circular acid-injection-well in fluid-saturated porous media

This paper investigates the near-field performance of chemical dissolution-front instability (CDFI) around a circular acid-injection-well in fluid-saturated porous media (FSPM) through using purely mathematical deductions. After the mathematical governing equations of the CDFI problem involving radially divergent flow are briefly described, both analytical base solutions and perturbation solutions for the considered problem are mathematically derived These analytical solutions lead to the theoretical expression of the perturbation induced dimensionless growth-rate and the following two new findings. The first new finding is that the critical Peclet number of a chemical dissolution system (CDS) associated with radially divergent flow in FSPM is not only a function of the permeability ratio between the undissolved and dissolved regions as well as the dimensionless wavenumber, but also a function of the circular chemical dissolution-front location relative to the circular acid-injection-well in FSPM. The second new finding is that as the direct result of considering a nonzero radius of the circular acid-injection-well, there exits a critical closeness number, which may be used to assess where the circular chemical dissolution-front starts becoming unstable in the CDS associated with radially divergent flow. Based on these two new findings, a theoretical criterion of two parts has been established. The first part of the established theoretical criterion answers the scientific question when a circular chemical dissolution-front can become unstable, while the second part of the established theoretical criterion answers the scientific question where a circular chemical dissolution-front can become unstable. Through applying the established theoretical criterion, a long-term existing mystery why the wormhole pattern of fractal nature and the compact pattern of fingering nature are formed at different locations away from the circular acid-injection-well circumference in fluid-saturated carbonate rocks has been successfully revealed.