Analytical Solution for Dissolution-Timescale Reactive Transport in Fluid-Saturated Porous Rocks

Abstract

Reactive transport, in which chemical dissolution reactions dissolve dissolvable materials in fluid-saturated porous rocks, is very common in groundwater pollution and geoenvironmental engineering. Because of coupled porosity evolution and mass transport processes on the dissolution time scale, analytical solutions for dissolution-timescale reactive-transport problems were unavailable to date. This paper presents an analytical solution for the dissolution-timescale reactive-transport problem in a special case in which the acid dissolution capacity approached zero and the porosity change of the rock was small. The presented analytical solution showed that (1) the increase of the Zh number (a dimensionless number to represent the characteristic of a reactive-transport system) caused faster propagation of the planar reference dissolution front in the dissolution-timescale reactive-transport system; (2) with an increase in the dimensionless longitudinal dispersivity, there was a remarkable decrease in the critical dimensionless time; (3) the Zh number of a dissolution-timescale reactive- transport system significantly affected the dimensionless acid concentration distribution; (4) with an increase in the Zh number, there was an increase in the acid concentration ratio at the planar reference dissolution front; and (5) the consideration of the porosity evolution process in a reactive-transport system resulted in greater values of the dimensionless acid concentration than when this process was neglected.