Integrated Acid Fracture Model with Reservoir Simulation Under Non-Isothermal Condition

Modeling of acid fracturing process is challenging because of the coupled complex effects of flow through porous media and fractures, chemical reaction in a geostatistical base, wormhole propagation, and reservoir heterogeneity. To avoid the complexity, decoupled approaches are commonly used; the reservoir effect is represented by leakoff with a constant leakoff coefficient, and analytical solutions for heat flux from a reservoir is used to avoid complexity. An acid fracturing numerical model is presented that is coupled with a single-phase black oil reservoir simulator for a vertical well in the carbonate reservoir. The coupled acid fracturing model considers fracture propagation, acid transport, and heat transfer. After simulating acid fracturing, the conductivity of the fracture is calculated using empirical correlations, and the productivity is computed by simulating the flow to the well. Non-isothermal condition is assumed to simulate the flow in both the fracture and reservoir because the acid reaction is temperature sensitive. Leakoff from fracture to reservoir is simulated with a reservoir flow model for pressure and leakoff velocity as functions of time and location. Wormhole propagation from the fracture is considered by using empirical equations for wormhole propagation based on leakoff velocity estimated from the reservoir simulation. The benefits of coupled modeling are evaluated by comparing the conventional acid fracturing model which uses a decoupled approach to the numerical acid fracturing model developed in this study. The results show that the coupling reservoir model improves the accuracy of estimated in fracture conductivity. It has been shown that the analytical equations for heat from a reservoir used in literature overestimates the final acid fracture conductivity. Thus, it is suggested to use fully numerically solve fluid flow and energy balance in a fracture and a reservoir. Complex leakoff due to pressure and temperature change with time and wormhole propagation was implemented in the simulator. The wormhole effect was added and the distribution of leakoff coefficient was reasonable. A comparison of simulation results with and without wormholes showed that the significant difference was not observed in acid concentration, but ideal width distribution was lower with wormholes. It is concluded based on the observation of the study that the leakoff from acid fracture represented by a reservoir model with wormhole propagation is important to correctly understand acid fracture efficiency. Simply using a constant leakoff coefficient can lead to significant error and misleading conclusions.