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The significant amount of oil and gas resources in the Taha oilfield is stored in natural holes. Acid-fracturing can establish fluid communication pathways between natural holes and wellbores, which can increase the development of carbonate reservoirs. An extended adaptive meshing technique was developed in this paper. The multi-physics coupling model for acid-fracture propagation was established using the phase-field method. The interaction between acid fractures and natural holes was simulated. The effects of in-situ stress, hole structure, and acid-rock reactions on acid-fracture propagation were analyzed. Two communication modes between acid-fractures and natural holes, direct communication and indirect communication, were summarized. The simulation results reveal the following conclusions: 1. the acid fracture model based on the phase field method solves the fracture propagation path based on the principle of energy minimization, which can simulate the acid fracture initiation and propagation under multi-field coupling conditions. 2. In-situ stress plays a dominant role in acid-fracture propagation. Natural holes affect the propagation of acid fracturing, and acid rock reaction assists in the propagation of acid fracturing. 3. The acid diffusion and etching capabilities result in indirect communication between acid fractures and surrounding holes, The oil and gas resources in the holes can enter the acid fracture through the acid-etched matrix. The identification of the holes distribution is the basis of improving the acid fracturing result. It is believed that this finding can offer information for acid-fracturing study in deep carbonate reservoirs.