As our industry is tapping into tighter carbonate reservoirs than in the past, completion techniques need to be improved to stimulate the low-permeability carbonate formation. Multistage acid fracturing technique has been developed in recent years and proved to be successful in some carbonate reservoirs. A multistage acid fracturing job is to perform several stages of acid fracturing along a horizontal well. The goal of acid fracturing operations is to create enough fracture roughness through differential acid etching on fracture walls such that the acid fracture can keep open and sustain a high enough acid fracture conductivity under the closure stress. In multistage acid fracturing treatments, acid flow is in a radial flow scenario and the acid etching process can be different from acid fracturing in vertical wells. In order to accurately predict the acid-fracture conductivity, a detailed description of the rough acid-fracture surfaces is required. In this paper, we developed a 3D acid transport model to compute the geometry of acid fracture for multistage acid fracturing treatments. The developed model couples the acid fluid flow, reactive transport and rock dissolution in the fracture. We also included acid viscous fingering in our model since viscous fingering mechanism is commonly applied in multistage acid fracturing to achieve non-uniform acid etching. Our simulation results reproduced the acid viscous fingering phenomenon observed from experiments in the literature. During the process of acid viscous fingering, high-conductivity channels developed in the fingering regions. We modeled the acid etching process in multistage acid fracturing treatments and compared it with acid fracturing treatments in vertical wells. We found that due to the radial flow effect, it is more difficult to achieve non-uniform acid etching in multistage acid fracturing treatments than in vertical wells. We investigated the effects of perforation design and pad fluid viscosity on multistage acid fracturing treatments. We need to have an adequate number of perforations in order to develop non-uniform acid etching. We found that a higher viscosity pad fluid helps acid to penetrate deeper in the fracture and result in a longer and narrower etched channel.

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