Diversion in heterogeneous carbonate reservoirs plays the most important role to the success of acidizing. Without the use of diversion, more acid preferentially flows into the high-permeability region and leaves the low-permeability region underreacted. But a clear understanding of diverting agents, such as polymer-based in-situ-gelled acids, can help uniformly stimulate the near-wellbore region. In this paper, we correct the rheological model that was developed by Ratnakar et al. (2013) according to experimental data from Gomaa and Nasr-El-Din (2010b) by considering shear-rate effect in a two-scale continuum model. It is found that the rheology parameters and shear rate are influential parameters in diversion. In addition, the amount of acid required for the breakthrough is found to be strongly dependent on rheology parameters and permeability in single-coreflood simulation. In our study, the viscosity of the spent acid is found to be the key parameter for diversion efficiency. We have constructed a mechanistic model similar to that in Panga et al. (2005) that simulates the acid injection in two dimensions. Then, we extended our simulation to dual-core systems with different permeability contrasts. The results show that there exists an intermediate injection rate that develops a wormhole in low-permeability core. This intermediate injection rate increases with increasing the permeability contrast. The results suggest that the dissolution pattern in the high-permeability core is dependent on the permeability contrast. It changes from wormhole to uniform shape when the permeability contrast increases.