Summary Closed-fracture acidizing (CFA) is a well-stimulation technique that can be applied to stimulate carbonate reservoirs at the end of acid-fracturing treatments. In CFA, acid is injected into the closed fracture at rates lower than the fracturing pressure to enhance the fracture conductivity. The objective of this study is to develop a robust model that can capture the dissolution process and wormhole-propagation phenomena that occur during CFA. This work develops a CFA model using computational-fluid-dynamics (CFD) techniques coupled with a two-scale continuum model that can predict accurately the reactive-flow mechanisms of hydrochloric acid (HCl) in carbonate formations. The developed CFA model is constructed and populated with the actual porosity-distribution profiles of tight carbonates. The model was tested against the experimental work performed on a fracture-conductivity apparatus. Sensitivity analysis is performed for several parameters that affect the performance of CFA in tight-carbonate formations. The developed model has successfully captured the dissolution patterns and wormhole-propagation phenomena that occur during CFA. In calcite formations, high temperatures promote acid leakoff into the formation, resulting in inefficient fracture stimulation. On the contrary, low temperatures reduce the overall reaction kinetics and attenuate the HCl reaction with calcite. Also, simulation results show that high acid concentration is favorable in treating low-conductivity fractures. In dolomite formations, it is essential to adapt a strong-acid system with an extended treatment duration to ensure efficient acid stimulation to the closed fractures. This paper provides a simulation study of the CFA process in a carbonates formation by establishing a 3D CFD model using the two-scale continuum approach. Fracture-surface etching and the associated acid-wormhole behavior during CFA are experimentally validated. This study optimizes the acid volumes and injection rates that can be used in conducting CFA.

Closed-fracture acidizing (CFA) technique has been proved to be a successful practice in stimulating tight carbonate formations. Acid is injected at rates lower than fracturing pressure to enhance the fracture conductivity and productivity. CFA operations are often associated with acid wormholing, promoted by acid leak-off in the formation. The objective of this study is to develop a model that represents these wormholes demonstrating their performance in enhancing the acid fracturing treatment in tight naturally fractured dolomite reservoirs under field conditions and investigate the effect of different parameters on acid wormholing during CFA. The wormholes propagation is modeled by the two-scale continuum model by developing a 3D computational fluid dynamics (CFD) model including the fracture geometry, conductivity of the fracture and the reaction kinetics between the acid system and the formation. The formation that is utilized in this study is tight naturally fractured dolomite formation exhibits low transmissibility and a considerable degree of heterogeneity. Well geometry was investigated to analyze the effect of injection area in the closed fracture on acid wormholing. Sensitivity analysis was conducted to cover the effect of several factors including acid concentration, injection rate, formation permeability and fracture conductivity to depict the actual flow in the formation. The presence of natural fractures was studied with the emphasis on their orientation and direction with respect to the hydraulic fracture whether it is parallel or perpendicular. Model upscaling was investigated to come up with a qualitative relationship between the acid volumes used in CFA model and the acid volumes used in actual field scale. Acid injection rates in the closed-fracture in CFA operations follow a similar trend as the acid performance curve in matrix acidizing in term of dissolution patterns where a face dissolution pattern at the injection inlet of fracture occurs at low and high injection rates. Higher acid concentration accelerates the reaction between the acid and rock matrix and yields faster results than the lower concentrations. Vertical wells exhibit larger injection area in contact with the closed-fracture than the horizontal wells, which promote larger propagation of these wormholes with less total inject volumes of acid during CFA. Formation permeability coupled with acid fracture conductivity have significant role in the acid volumes used in CFA that are required to deliver the acid certain distance in the formation, and it affect the wormholing density significantly. The presence of natural fractures in the parallel or transversal direction with respect to hydraulic fracture play a key role in generating flow networks between hydraulic fracture and natural fractures that are induced by the acid leakoff in the formation regardless of the intersected natural fractures with hydraulic fracture. Model upscaling demonstrates the relationship that clarifies the total acid volumes injected in actual field applications that have to be used in the design of optimum acid fracture stages in multistage acid fracturing and to estimate the optimum spacing between the stages which will maximize the performance of this completion.