The success of viscoelastic-surfactant (VES) acid in heterogeneous carbonate reservoirs depends on the wormholes propagation and diverting performance of acid. However, with the continuous propagation of wormholes in the high-permeability zone, the highly viscous spent acid enters the low-permeability zone under the pressure difference, thus affecting the wormholes propagation and diverting performance of acid in the low-permeability zone, which has been neglected in recent studies. Therefore, in this paper, the rheological model of acid is modified by considering the velocity of VES acid viscosity increase, and a two-scale continuous model was established. Based on this model, the diverting process is described, and reservoir connectivity, permeability contrast, and velocity of acid viscosity increase are used to investigate the influence of spent acid on wormholes propagation and diverting performance of acid in the low-permeability zone. The results show that the formation of wormholes in the high-permeability zone makes a pressure difference between the high-permeability zone and the low-permeability zone. The high viscous spent acid flows from the high permeability layer to the low permeability layer under the pressure difference, thus inhibiting the wormholes propagation and diverting performance of acid in the low-permeability zone of heterogeneous carbonate reservoirs. The influence degree of spent acid is 30.6% when the permeability contrast is 3, and the influence degree decreases with the enhancement of heterogeneity. At permeability contrasts greater than 10, there is almost no effect. The velocity of acid viscosity increase affects the diverting performance of acid, and the faster the viscosity increase, the farther the highly viscous zone formed in a short time, the better its diverting performance. In the VES acid system commonly used in carbonate acidizing, the maximum difference of diverting performance is 4.25 times. The parallel coreflood experiments overestimate the diverting performance of VES acid by about 20%. When selecting the diverting technology for acidizing treatment, the diverting acid system with higher diverting performance in the laboratory experiments or diverting technology with stronger diverting performance can be appropriately selected. In addition, the velocity of spent VES acid viscosity increase is a significant parameter affecting the acid diverting performance. In the low calcite content reservoir or dolomite reservoir, the spent acid viscosity increases relatively slowly due to the slower reaction rate, which will reduce the diverting performance in the reservoir.
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