| dc.description.abstract | Acid fracturing in heterogeneous carbonate formations is extremely challenging to model. To obtain an acceptable acid penetration distance and fracture surface etched-width profile, a reliable fracture propagation model must be incorporated. Fracture fluid and formation temperatures have an impact on the acid concentration profile, particularly when using weak acids or injecting into dolomite formations. The model provided in this study considers these factors as fractures propagate, in order to obtain the fracture conductivity distribution and evaluate the improvement in well productivity.
The pseudo three-dimensional fracture model developed here is able to provide the domains for the acid dissolution at each time step. A transient acid convection and diffusion equation is solved and the fracture etched-width profile is calculated. An iterative procedure is implemented in a temperature-dependent kinetic model, which stops when both the temperature and acid solutions converge. The model includes an injection of multiple fluid systems that can be either reactive (e.g., straight, emulsified, and gelled acid) or non-reactive (e.g., pad fluid and flush). The model incorporates multiple layer formations with different rock and kinetic properties. Leakoff is calculated for each layer and the wormhole effect is included if reaction takes place. When injection stops, the acid concentration and etching are solved as the fracture closes. As the final etching profile is generated, conductivity is calculated using a correlation that considered formation heterogeneity. Finally, the well productivity is numerically calculated by simulating the reservoir fluid flow and considering the obtained fracture with variable conductivity.
Coupling the fracture geometry and acid models has a significant impact on the final solution. Simulations of acid injection on a non-coupled, constant fracture geometry always overestimate the acid penetration distance and provide inaccurate etched-width profiles. The temperature-dependent kinetic model has a noticeable effect on the etched-width distribution and acid penetration distance for dolomite formations, both are directly related to fracture performance.
The model illustrated here is computationally efficient, which allows for optimizing the design parameters to create a fracture with maximum productivity for a given acid treatment size. More importantly, the optimum acid treatment size for a certain simulated reservoir volume can be determined. | en |
