Physicochemical Phenomena of Diffusion Relaxation: Experimental Results and Application for Acid Stimulation Operations

Abstract

Accurate prediction of the rock dissolution process is crucial for designing efficient acid stimulation treatments. At typical conditions, the dissolution of carbonates in most acids is limited by the rate of convective diffusion of reactive species to the surface of the rock. The experimental techniques used to determine the acid-diffusion coefficient are comparably well-understood by the research and engineering community. However, one important physicochemical phenomenon termed diffusion relaxation has not been studied in detail and accounted for in all the existing acid fracturing and matrix acidizing modeling software programs. The objective of this work is to address these gaps in research and optimize acid treatment designs. Diffusion relaxation occurs downstream of an inert or less reactive rock layer and results in higher mass transfer, i.e., dissolution rate of the rock located immediately downstream of an inert layer. To study the process of diffusion relaxation, 15 wt% hydrochloric acid at a temperature of 150°F was injected through a composite acid fracture model. This model was prepared by inserting 0.5 and 0.25 in.-long sandstone layers into a standard 7 in.-long fracture model made of Indiana limestone. Laser profilometry of the fracture surfaces after the experiment revealed the presence of 0.1 in.-deep channels of more etched limestone downstream of inert layers, as compared to the upstream of inert layers. The zone of an enhanced dissolution rate—termed diffusion relaxation zone—extends to a distance comparable to the length of an inert layer and appears because of the following. As soon as the acid flow encounters inert areas, the concentration of reactive species at the fracture surface starts to accumulate since there is no dissolution reaction. Right downstream the inert areas, the limestone surface contacts with the acid that has not been spent by the diffusion of reactive species. Because of that and an impact of tangential mass transfer in the diffusion boundary layer, downstream of inert areas the diffusional mass transfer significantly—often more than two times—exceeds the limiting mass transfer established upstream of the inert areas. Etched channels formed in diffusion relaxation zones contribute to the fracture conductivity, which is not considered in existing modeling software programs. Results indicate that the observed phenomenon is universal, i.e, it also occurs during dissolution of rocks with different reactivities. This research innovatively discusses the impact of physicochemical phenomena of diffusion relaxation on the dissolution of carbonate rocks, and formation of conductive flow channels. Presented results are integral for designing acid stimulation operations.