Abstract Matrix acidizing is one of the most effective stimulation techniques to achieve industrial development of carbonate reservoirs. In this work, a two-scale continuum model is modified to consider mass conversion between liquid and solid phases. The results show that the mass conversion between liquid and solid phases is very important and nonnegligible. Compared to modified model, original model overestimates amount of acid required for core breakthrough. A series of numerical cases based on modified model are presented for sensitivity studies on acid injection conditions, core geometries, acid, and rock properties. The modified model can well capture optimum acid injection velocity and typical dissolution patterns observed in experimental studies. Pore volume to breakthrough (PVBT) is very sensitive to acid injection concentration and acid surface reaction rate. Increasing injected acid concentration substantially reduces the amount of solute required but acid injection mass does not change significantly. Strong acid can effectively reduce least pore volume to breakthrough (PVBT) but meanwhile optimum acid injection velocity obviously increases. The simulation results are compared with available experimental and numerical data and found to attain a consistent match.