Numerical Simulation of Acid Diversion and Wormhole Propagation Mechanism of Nanoparticle VES Acid in High-Temperature Carbonate Reservoirs

Uniform acid distribution is a critical challenge and a key factor for the successful acidizing of carbonate reservoirs. Previous experimental studies have shown that nanoparticles can enhance the viscosity and thermal resistance of viscoelastic surfactant (VES) fracturing fluids. However, there has been limited research on the effects of nanoparticles on the wormhole propagation and diversion performance of VES acid. This paper establishes a nanoparticle VES acid rheological model based on rheology experiments, and introduces a porous medium temperature field and nanoparticle adsorption model into a two-scale continuum model to establish a mathematical model for the expansion of wormholes in nanoparticle VES acid. The accuracy of the wormhole model is verified through laboratory experiments. The effects of permeability contrast, initial acid temperature, and nanoparticle adsorption on the diversion performance and wormhole propagation of nanoparticle VES acid are analyzed. The results indicate that nanoparticle VES acid differs from conventional VES acid, with its invaded zone divided into high-viscosity and low-viscosity zones. The presence of the high-viscosity zone allows nanoparticle VES acid to improve wormhole propagation in low-permeability cores by 16.2% compared to conventional VES acid. At 393 K, nanoparticle VES acid has a better diversion effect in carbonate cores with permeability contrast of 10, as the acid fluid flows faster in high-permeability cores, resulting in wormhole shapes with more branches. Numerical model results show that when the permeability contrast is 8, increasing the injection temperature of the acid solution from 293 K to 368 K improves the ability of low-permeability cores by 33.3%. This study establishes a mathematical model for nanoparticle VES acid based on laboratory experiments and numerical simulations, investigates the effects of nanoparticles on VES rheological properties under acidic conditions, and clarifies the wormhole propagation and acid diversion behavior of nanoparticle VES acid, providing guidance for future field applications of this acid.