Pore-scale modeling of acid etching in a carbonate fracture

<p>Acid fracturing has been widely used in the oil and gas industry to increase permeability in carbonate reservoirs. In recent years this chemical stimulation technique has been borrowed from the oil and gas industry, employed in the enhanced geothermal systems at Gro&#223; Sch&#246;nebeck, Germany (Zimmermann et al., 2010), and at Soultz-sous-For&#234;ts, France (Portier et. al., 2009). In concept, acid fracturing utilizes strong acids that react with acid-soluble rock matrix in order to non-uniformly etch fracture surfaces. The permeability-enhancing effect depends upon the degree of surface irregularity after pore-scale acidizing which is affected by the compositional heterogeneity of the reacting rock matrix, fracture aperture heterogeneity, and flow and transport heterogeneity. In order to have an insight into these impacts on the acid etching process with the final goal of determining optimum operating conditions (e.g., acid type and acid injection rate), a pore-scale acid-fracturing model is needed. The core components of the pore-scale acid-fracturing model consist in tracking the motion of the fluid-matrix boundary surface induced by acid etching. To date, a number of front tracking approaches (e.g., local remeshing technique, embedded boundary method, immersed boundary method, and level-set method) have been proposed by many researchers in order for moving boundary problems. Each approach has its pros and cons. In this work, we propose employing the phase-field approach as an alternative to the existing front tracking approaches to capture the physically sharp concentration discontinuities across the liquid-solid interface. The developed pore-scale acid-fracturing model includes the Stokes-Brinkmann equations for fluid flow in the fracture-matrix system, the multi-component reactive transport equation for transport of solute species in the rough-walled fracture, and the phase-field equation for the reaction-driven motion of the fluid-matrix boundary surface. Through this numerical study, we demonstrate that the phase-field approach is viable to track recession of carbonate fracture surface by acid etching and to capture the solute concentration jump (w.r.t., Ca²⁺, H⁺, and HCO3^&#8722;) across the solid-liquid interface.</p><p>&#160;</p><p>Reference</p><p>Zimmermann, G., Moeck, I. and Bl&#246;cher, G., 2010. Cyclic waterfrac stimulation to develop an enhanced geothermal system (EGS) &#8212; conceptual design and experimental results. Geothermics, 39(1), pp.59-69.</p><p>Portier, S., Vuataz, F.D., Nami, P., Sanjuan, B. and G&#233;rard, A., 2009. Chemical stimulation techniques for geothermal wells: experiments on the three-well EGS system at Soultz-sous-For&#234;ts, France. Geothermics, 38(4), pp.349-359.</p>