3D transport in acid-fracturing treatments: Theoretical development and consequences for hydrocarbon production

While the effect of 2D proppant transport during hydraulic fracturing has b een studied extensively and debated frequently, relatively little attention has been given to 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 results in more complicated physical phenomena for acid fracturing. Acid diffusion in the fracture has been estimated empirically with no considerations made to model correctly the acid flow across the fracture width. The etched-width profile resulting from 3D flow could differ significantly from that predicted by the 1D, pis ton-like displacement normally included in acid-fracture simulators. An imp ortant consequence of this variation in the etched pattern is a substantial ly different prediction of the fracture conductivity, and hence the post-st imulation hydrocarbon production. Acid flow in the fracture can affect the outcome of reservoir stimulation and must be considered when designing acid -fracturing treatments. The equations governing fluid flow are developed initially for a 2D pressur e profile. These equations are coupled with the formulations for acid wall reaction, heat transfer, and diffusion within the framework of a P3D hydrau lic fracturing simulator. The theoretical formulation for acid transport ac ross the fracture width is presented then and coupled with the equations fo r 2D acid flow. The equation of acid diffusion is solved across the fractur e width, hence solving the equations of fluid flow for three dimensions in the fracture. The resulting fracture geometry and conductivity are used sub sequently with a reservoir simulator to illustrate the consequences of the 3D acid formulation on hydrocarbon production. Simulated and field examples are presented to illustrate the effects of 3D acid flow on the etched-widt h distribution and post-stimulation production.