The success of matrix acidizing in carbonates is often dependent on the efficiency of diversion agents, especially for treatments on wells with thick formations or multiple zones, or horizontal wells with long and heterogeneous intervals. Viscoelastic-surfactant (VES) -based self-diversion acid has been used successfully in fields because of its negligible damage to the formation and good diversion ability. Although the diversion ability of VES acid was studied experimentally with small core plugs, the diversion conditions of VES acid under in-situ radial conditions need to be studied. In this paper, we develop a VES radial-acidizing model that simulates VES acid flow, acid/rock reaction, porosity variation, viscosifying, wormholing, and acid diversion in multiple zones. On the basis of the model, extensive numerical simulations are conducted to investigate wormholing behavior of the VES acid, the factors that affect the diversion ability of VES acid, and the diversion conditions of VES acid. This study shows that the VES acid-dissolution patterns depend on the injection rate, and there is an optimum injection rate under which the dominant wormholes are formed. Compared with regular acid, the VES acid provides better acid placement for heterogeneous intervals. The intervals with separation shorter than approximately 150 m can be acidized together with VES acid if the two intervals have a close permeability with no perforation between them. The permeability ratio of the two intervals has remarkable influence on the diversion performance of VES acid. Even though the viscosified fluid acts as a temporary barrier to prevent the fluid flowing into the higher-permeability formation, the VES acid reduces diversion effectiveness for large permeability contrast. We also investigated the combined effect of permeability contrast and separation of the two intervals on diversion performance. This study provides a basis to select diversion technology and a method to evaluate diversion performance of VES acid for field-acidizing treatments.