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Summary Matrix acidizing is a common technique for carbonate reservoir stimulation. In this work, a new two-scale continuum model is developed to study the 2D acidizing process. The Navier-Stokes-Darcy equation is used instead of the Darcy’s-law equation to describe fluid flow. The continuity equation is also modified to consider the mass-exchange term between fluid and solid phases. The comparison results show that neglecting the solid-matrix-dissolution source term results in overestimation of pore volume (PV) to breakthrough (PVBT). The Darcy’s-law equation does not well-capture physical behaviors of fluid phase with low acid-injection velocity compared with the Navier-Stokes-Darcy equation. On the basis of this model, we discuss different processes influencing matrix acidizing, including convection, diffusion, and reaction, and different models, including classical and new two-scale continuum models. Besides, a comprehensive parametric study is also conducted to study the effect of parameters with respect to acid and rock physical parameters on the matrix-acidizing process. The typical dissolution patterns and optimal acid-injection rate presented in experimental studies can be well-observed by the new two-scale continuum model. Increasing the acid-injection concentration has a limited effect on the amount of acid mass but substantially reduces the amount of solute required. The acidizing curve is very sensitive to the dispersity coefficient, acid-surface-reaction rate, and porosity/permeability relationship.