<p>Carbonate reservoirs acidizing is complex operation and and acid tends to penetrate more readily into layers with higher permeability, leading to uneven stimulation. To counteract this, acid diversion techniques are employed. Eccentric acidizing can be implemented through either mechanical or chemical methods. In the chemical approach, additives such as polymers, in-situ acid gels, and viscoelastic surfactants (VES) are introduced into the acid to enhance viscosity and redirect acid flow towards less permeable layers. This study investigates the impact of non-Newtonian acid injection and the presence of a hydrocarbon phase in acid diversion when VES is used as an additive. The rheological properties and viscosity of the injection fluid are influenced by the concentration of VES, calcium ion concentration, and acid pH. Upon injection, VES particles infiltrate both layers, yet due to the higher permeability in one layer, particle penetration occurs more rapidly there. Some VES particles also enter the less permeable layer, increasing viscosity in that layer and subsequently reducing acid penetration. To optimize penetration distribution, periodic injection of acid and VES is employed. Notably, this study pioneers the application of a two-phase continuum porous media model (TPTSC) to simulate the flow of acid and VES in porous media. Through periodic injection of viscoelastic surfactant, breakthrough is achieved in the less permeable layer, thereby enhancing the efficiency of the eccentric acidizing process. Under two-phase conditions, factors such as fluid saturation, capillary pressure, and oil properties require that the concentration of viscoelastic surfactant be increased at least threefold to effectively divert acid to the less permeable layer. Additionally, the surfactant injection should commence only after a minimum of one pore volume of acid has been injected.</p> Graphical abstract <p></p>