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Highlights • An effective method for simulating wormhole in fractured formation was proposed. • The effects of three typical fractures on wormhole propagation were studied. • The local control domain around the fracture was found. • A step-by-step calculation method was proposed in this paper. Abstract Wormholes can effectively connect the fracture system as the dominant channels when carbonate matrix is acidified, thereby increasing the distance of acidification. It is critical to clarify the wormhole propagation law in carbonate reservoirs so as to optimize the acidification design. Previous studies highlight the influences of matrix as well as single simple fracture on wormhole propagation. However, the works characterizing impacts of single and multiple fractures with different geometry are insufficient. In this paper, the two-scale continuum model and pseudo-fracture model were combined to study the wormhole with different fractures. It was found that the fractures parallel to injection direction can concentrate fluids and thus accelerate the acid penetrating the formation, while the perpendicular ones will disperse fluids, thereby slowing down the breakthrough. The effect of straight fractures and arc fractures on wormholes are similar. When the inclination angle is less than 60°, straight fracture and arc fracture can be regarded as parallel fracture of corresponding length. When the inclination angle is greater than 60°, they can be regarded as superposition of parallel fracture and perpendicular fracture. As for the circular and polygonal fractures, only the parts near the outlet impact the subsequent wormhole propagation trajectories. The analysis of flow field shows that there is a control domain of about 3· L ·cos(θ) around the fractures. When there is no intersection of control domains of multiple fractures, there is no interference between them. There is no need to consider all fractures in the formation. Based on this, the step-by-step calculation method proposed in this paper is suitable for acidizing large-scale formation with complex fracture network. [ABSTRACT FROM AUTHOR]

• The reason for the poor effect of acid fracturing with retarded acid in dolomite reservoir was found. • The correlation between the acid-rock reaction control mode and etching morphology was analyzed. • The effects of different factors on the conductivity of fractures were studied. • Two uneven acid injection approaches were discussed. Retarded acids are often used for acid fracturing in carbonate reservoirs to reduce acid leakoff. Compared with limestone reservoirs, dolomite reservoirs are seen with lower fracture conductivity using retarded acid. This study focuses on the acid etching morphology of fracture, and investigates influential factors and improvement methods of fracture conductivity. Our analysis shows the etching morphology has no direct dependency upon the controlling regime of acid-rock reaction. It is determined by reaction rates. Low conductivity is caused by the slow reaction between dolomite and retarded acid, and difficulties in creating irregular etched grooves on fracture surfaces. A small amount of dolomite in reservoirs does not impact conductivity, and yet dolomitic contents over 80% will lead to tremendous reduction of conductivity. It is feasible to form the irregular etching morphology by reducing the flow rate and the thickening agent concentration while alternately injecting two types of acid solutions into reservoirs. [ABSTRACT FROM AUTHOR]