Three-Dimensional Transport in Acid Fracturing Treatments: Theoretical Development and Consequences for Hydrocarbon Production

Abstract

Abstract While the effect of two-dimensional (2D) proppant transport during hydraulic fracturing has been extensively studied and frequently debated, relatively little attention has been given to a similar consideration for acid fracturing treatments. In addition to fluid density differences and gravity-driven segregation, spatial variation of the acid temperature and of the rock chemical properties result in more complicated physical phenomena for acid fracturing. In addition, the acid diffusion in the fracture has been estimated empirically with no considerations being made to correctly model the acid flow across the fracture width. The etched width profile resulting from three-dimensional (3D) flow could be significantly different from that predicted by the one-dimensional (1 D), piston-like displacement normally included in acid fracture simulators. An important consequence of this variation in the etched pattern is a substantially different prediction of the fracture conductivity, and hence the post-stimulation hydrocarbon production. The acid flow in the fracture thus can affect the outcome of reservoir stimulation and must be considered when designing acid fracturing treatments. The equations governing fluid flow are initially developed for a 2D pressure profile. These equations are coupled with the formulations for acid wall reaction, heat transfer and diffusion within the framework of a pseudo-3D hydraulic fracturing simulator. The theoretical formulation for acid transport across the fracture width is then presented and coupled with the equations for 2D acid flow. The equation of acid diffusion is then solved across the fracture width, hence solving the equations of fluid flow for three dimensions in the fracture. The resulting fracture geometry and conductivity are subsequently used with a reservoir simulator to illustrate the consequences of the 3D acid formulation on hydrocarbon production. P. 475