Numerical simulation of power-law acid flow in rough fractures of carbonate rocks

Acid fracturing is the most widely applied technology for stimulating carbonate reservoirs. Meanwhile, the effectiveness of this method largely depends on factors such as acid penetration distance, fracture morphology and conductivity, all of which are closely governed by acid flow behavior. A wealth of numerical simulations have been conducted to characterize acid flow during fracturing, whereas the coupled effects of acid rheological properties and fracture surface roughness on the acid flow behavior remain underexplored. In this work, a three-dimensional numerical model of acid etching fracture was developed by coupling an acid-rock reaction model with computational fluid dynamics methods, which comprehensively incorporates the rheological property of acid and fracture surface roughness. Validation against experimental data showed a deviation of 11.15% in dissolved mass, with errors within 10.00% for most roughness parameters, confirming the numerical model's accuracy. Furthermore, the numerical model was employed to investigate the quantitative effect of the rheological index on acid transport and the spatiotemporal evolution of acid flow and dissolution. The results revealed significant interdependencies among flow velocity, shear rate, acid-rock reaction rate, and fracture width, all of which evolve dynamically over time and space. Moreover, it was found that the non-uniform distribution of flow velocity, shear rate, acid-rock reaction rate is caused by fracture surface roughness, and the degree of non-uniformity is enhanced as the shear-thinning capacity of the acid increases. This work provides a robust numerical framework for the simulation of the transport and reaction of acids with power-law characteristics in three-dimensional rough fractures, thus offers valuable theoretical insights for guiding the optimization of acid fracturing parameters and enhancing reservoir stimulation efficiency.