Modeling Study of Temperature and Fracture-Propagation Effects on the Fracture-Surface Dissolution Patterns and Fractured-Well Productivity in Acid Fracturing

Abstract

Summary The acid–fracturing operations in carbonate formations are modeled to evaluate possible improvements in well productivity. Models are developed mainly to estimate the acid–penetration length and fracture–surface etched–width profiles. Variable combinations of these two parameters produce significant differences in fracture productivity. To estimate these parameters better, a reliable fracture–propagation model should be coupled with an acid reaction/transport model. Simulating weak acids or dolomite–formation reactivity requires the inclusion of a heat–transfer model. The model provided in this study couples these factors as fractures propagate to obtain the fracture–conductivity distribution along the length. The fracture–propagation model was created to update the domain of the acid model continuously. In the process, a transient acid convection and diffusion equation is solved and the fracture's etched–width profile is calculated. An iterative procedure is then implemented in a temperature–dependent kinetic model that stops when both the temperature and the acid solutions converge. When the injection stops, the acid etching and fluid temperatures are updated as the fracture closes. As the final etching profile is drawn, conductivity is calculated using a correlation that considers formation heterogeneity. The conductivity distribution along the fracture surface can be used to predict the fractured–well productivity for given reservoir properties. Coupling of the fracture propagation shows a significant difference in the acid–model solutions, as compared to those assuming a constant–fracture geometry. For an extremely high Péclet number that represents a very retarded acid system, a constant drop in the etched–width value until reaching zero at the fracture tip is theoretically obtainable. For lower Péclet numbers, the etching profile sharply declines toward the fracture end. This is in contrast to the noncoupled approach, from which a uniform etching profile is obtained at moderate–to–high Péclet numbers. In this research, it was observed that the simulation of acid injection in a noncoupled, constant–fracture geometry always overestimates the acid–penetration distance. The etched–width distribution and acid–penetration length are temperature sensitive, especially in dolomite formations. Temperature coupling shows that the maximum etching in dolomite formations occurs away from the fracture entrance, as acid reactivity increases. It also shows that the cooling effects of the first–stage pad fluid on improving the acid–penetration distance are limited. This work illustrates that the impact of fracture propagation, heat transfer, and simulation of fracture after shut–in on productivity prediction is substantial. Simulating acid–fracturing operations, assuming a constant final fracture geometry and average single temperature, is time efficient but results in inaccurate solutions. This research quantifies the effects of integrating fracture–propagation and heat–transfer models on the acid–etching pattern. It also emphasizes the significance of simulating acid fracture during the closure, especially for dolomite formations or weak–acid cases, from which a better estimation of the fracture's productivity can be expected. A simplified analytical solution for multiple–fluid simulation is also introduced in this work.