(210f) Wormholing in Radial Flow

Matrix Stimulation in carbonates using an acidic fluid is an oft-employed enhanced oil recovery process to increase productivity of reservoir. Acid is injected into the porous medium where it dissolves the carbonaceous material, thereby increasing permeability. The heterogeneous reaction between the acid and the carbonate rock can be either kinetic or mass transfer controlled at the pore scale and is influenced by the presence of heterogeneities in addition to the competition between flow, dispersion and inter-phase mass transfer. As a result characteristic patterns arise depending upon the injection rate. For instance, at low injection velocities of the acid, transverse dispersion is the dominant mechanism and most of the acid is spent before it can penetrate into the medium. This gives rise to compact dissolution where most of the medium is dissolved behind the reaction front and remains unreacted beyond it. On the other hand, when acid is injected at a fast rate, convection is the dominant mechanism. In this case, even though the acid penetrates deep into the medium, the residence time is small, and hence unspent acid leaves the medium leading to a relatively uniform dissolution of the medium. In between these two extremes, at intermediate flow rates where both convection and transverse dispersion are comparable in magnitude, long channels called wormholes are formed. These channels are recognized as the most efficient means of increasing the permeability of the rock surrounding the wellbore. Several experimental studies have noted this dependence of wormhole formation on injection rate of acid. Modeling efforts have attempted to reproduce and explain the formation of these patterns at lab-scale but very few have been successful in accounting for all the mechanisms associated with reactive dissolution. Also, not much work has been reported on pattern formation in radial flow using a model that explains the correct dynamics of the process. In this work, a two-scale continuum model that accounts for all the phenomena occurring at both the pore-scale and Darcy scales, is numerically simulated and analyzed for radial flow of acid into the medium. The influence of key dimensionless parameters of the model such as the macroscale Damköhler number (Da), pore scale Thiele modulus (phi^2), macroscopic Thiele Modulus (Phi^2), Peclet number (PeL), acid capacity number (Nac), and the magnitude and length scale of heterogeneity on wormhole formation is investigated. In addition to determining the parameter range where wormholes are generated, a detailed study is done to understand the effect of these parameters on pore volumes to breakthrough, PVBT. Finally, the difference in acidization response for linear and radial flow is highlighted and conditions under which radial flow approximates linear flow is presented.