Recent changes in fracturing technologies have had a strong impact on the economic and political life, all over the world. In the United States, these technologies have increased the hydrocarbon reserves year-after-year by more than 15 percent. The oil and gas productions are substantially increased by creating new fractures that go deeply underground in different directions. Although this technology has been known for decades, many challenging problems had prevented it from being implemented. There is still a lack of fundamental knowledge about the long term impact of man-made fractures, not only on the environment in general, but also on basic human needs. Society needs robust, unbiased knowledge on the impacts of this technology, and our industry needs rigorous tools for predicting and controlling the geometrical and mechanical characteristics of the fractures underground. Algorithms and scientific tools that will be developed under this proposal can be used in many other areas of biochemical and biomedical research. The proposed research will be integrated within several educational programs, which include graduate and undergraduate courses. Junior and senior undergraduates, as well as graduate students, will participate in various stages of the proposed research. Associated industrial problems will stimulate engineering majors to learn fundamental mathematical topics, and will attract mathematics majors toward applied mathematics problems. Senior personnel will disseminate the results of this project, not only through professional meetings and journal publications, but also through a network of collaborations and partnerships with industry.
This proposal addresses fundamental issues related to modeling and computer simulation of strongly coupled systems in fractured reservoirs. The main challenges arise from the fact that the natural underground systems and substances that are utilized to produce fractures are subjected to coupled physical processes, such as stresses in solid rocks and flows of multiphase fluids in the multiscale system. This system is essentially a three-dimensional porous medium characterized by an extremely high ratio between the horizontal and vertical length of the fractures, and respectively, their width. In this investigation, main hydrodynamic features, observed in real life by reservoir engineers, will be modeled by using different sets of nonlinear partial differential equations in the porous regions and in the fractures. These systems of equations have not been studied before. The flow in the fractures does not follow the classical law (linear Darcy), and the inertial forces can no longer be neglected. Moreover, the dissipative effects due to the interaction between the fluid flows in the different regions must be taken into account. The proposal is focused on the combination of novel ideas in multigrid and domain decomposition algorithms, oriented to parallel architectures with the aim of achieving the best computational performance. In order to improve the retrieval of hydrocarbon resources, the proposal will also address the solution of optimization problems.
