Deep tight-gas carbonate reservoirs have huge reserves, with the advantages of having clean and low-carbon characteristics in addition to being a sustainable and stable supply which leads to very high-quality green energy, despite its difficult extraction. The reservoirs are usually modified using acid fracturing before exploitation, but due to acid erosion, the continuous alteration of the mechanical properties of the reservoir rocks complicates the process of predicting the crack initiation pressure. This paper aims to address the difficulties in predicting the crack initiation pressure by conducting a series of acid-etching experiments on carbonate rock samples subjected to splitting and uniaxial compression tests. By examining the variations in the elastic modulus, Poisson’s ratio, tensile strength under distinct acid systems, and acid-etching durations and temperatures, a quantified mathematical model was developed. This model was integrated into a fracture-initiation pressure prediction framework, resulting in a practical and user-friendly tool for the acid fracture-initiation pressure prediction model, which was further demonstrated through field engineering validation. The findings reveal that the elastic modulus, Poisson’s ratio, and tensile strength of carbonate rocks exhibit an inverse relationship with acid-etching time and temperature. Extended acid fracturing durations and high reservoir temperatures are conducive to acid-fracturing transformations. The fracture-initiation pressure-prediction-model analysis disclosed that, compared to the gelled acid, the diverting acid demonstrates a more pronounced reduction in the reservoir fracture pressure under high-temperature and short-duration conditions. An acid system preference diagram was constructed to provide a theoretical foundation for practical engineering applications, delivering valuable insights for optimizing acid fracturing treatments in carbonate reservoirs to provide a boost for the green energy extraction of tight gas.