The reaction order plays a crucial role in evaluating the response rate of acid-rock. However, the conventional two-scale model typically assumes that the reaction order is constant as one, which can lead to significant deviations from reality. To address this issue, this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation. Through numerical simulations, this model allows for the investigation of the impact of acidification conditions on different orders of reaction, thereby providing valuable insights for on-site construction. The analysis reveals that higher response orders require higher optimal acid liquid flow rates, and lower optimal H⁺diffusion coefficients, and demonstrate no significant correlation with acid concentration. Consequently, it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content, while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.