Wellbore-Scale Matrix Acidizing with a Two-Scale Continuum Model: Breakthrough and Performance Analysis

Summary Matrix acidizing is a widely applied stimulation method in carbonate reservoirs; however, accurate prediction of acid/rock interactions at the wellbore scale remains challenging. The two-scale continuum (TSC) model has proved effective at the core scale, but its application to field-relevant conditions is limited by scale-dependent phenomena and computational complexity. In this work, we develop a wellbore-scale TSC model that incorporates realistic boundary conditions and accounts for radial wormhole growth, flow/reaction/transport coupling, and field-scale injection scenarios. A key advancement is the introduction of a breakthrough criterion based on pressure response differences between reactive and nonreactive injections, providing a practical and measurable definition of breakthrough at the wellbore scale. Using this criterion, an acid performance curve is constructed to quantify the relationship between injection rate and wormhole efficiency. Sensitivity analysis further reveals that optimal wormhole formation occurs when the mass transfer rate matches the surface reaction rate, confirming the transition from reaction-limited to mass transfer-limited regimes as the controlling factor in wormhole development. The proposed framework enables more reliable prediction of acidizing performance at the wellbore scale, offering practical guidance for optimizing stimulation design and operational parameters in carbonate reservoirs.