Numerical Simulation of Acid Flow in Rough Fractures

Summary Acid fracturing is a crucial technique for enhancing the productivity of carbonate rock reservoirs. Understanding the flow behavior and dissolution characteristics of acid within fractures is essential for optimizing acid fracturing operations. Previous studies primarily focused on investigating acid flow in acid-fractured fractures through physical experiments. However, the fracture models used often exhibited significant discrepancies from actual fractures, and the influence of fracture roughness on acid flow was seldom addressed. In this paper, we develop a rough fracture model using the “diamond-square” algorithm from random fractal theory, and formulate an acid-rock reaction rate equation based on the H+ mass transfer theory. The flow behavior and dissolution characteristics of acid within fractures are simulated and analyzed utilizing computational fluid dynamics under varying conditions of roughness, fracture width, and acid viscosity. The fluid flow velocity equation within the fracture considering the injection pressure gradient, fracture roughness, fracture width, and acid viscosity is established. The research findings indicate the following: (1) The fractal dimension of the fracture surface increases following acid etching, suggesting that acid treatment enhances the complexity of the fracture surface. (2) Under conditions of constant pressure injection, the average flow velocity at the center of the fracture and the width of the dissolution fracture exhibit an inverse relationship with roughness, a direct relationship with fracture width, and a power series decreasing relationship with acid viscosity. (3) An increase in roughness and fracture width results in greater heterogeneity in the flow velocity distribution within the fracture, whereas the opposite effect is observed with acid viscosity. (4) The characteristics of flow velocity distribution within the fracture significantly influence the dissolution characteristics of the fracture surface; specifically, a more complex flow velocity distribution correlates with more pronounced nonuniform dissolution characteristics of the fracture surface. (5) Among the factors examined, fracture width exerts the most substantial influence on the average flow velocity, while acid viscosity has the most significant impact on the width of the dissolution fracture and the entropy of the velocity distribution.