Iteratively coupled reservoir simulation for multiphase flow in porous media
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Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or ef- ficient, given the increasing size and degree of complexity of highly heterogeneous reservoirs. In this dissertation, an iterative coupling approach is proposed and developed to solve multiphase flow problems targeting the efficient, robust and accurate simulation of the hydrocarbon recovery process. In the iterative coupling approach, the pressure equation is solved implicitly, followed by the saturation equation, which is solved semi-implicitly. These two stages are iteratively coupled at the end of each time step by evaluating material balance, both locally and globally, to check the convergence of each iteration. Additional iterations are conducted, if necessary; otherwise the simulation proceeds to the next time step. Several numerical techniques are incorporated to speed up the program convergence and cut down the number of iterations per time step, thus greatly improving iterative model performance. The iterative air-water model, the oil-water model, and the black oil model are all developed in this work. Several numerical examples have been tested using the iterative approach, the fully implicit method, and the IMPES method. Results show that with the iterative method, about 20%-40% of simulation time is saved when compared to the fully implicit method with similar accuracy. As compared to the IMPES method, the iterative method shows better stability, allowing larger time steps in simulation. The iterative method also produces better mass balance than IMPES over the same time. The iterative method is developed for parallel implementation, and several test cases have been run on parallel clusters with large numbers of processors. Good parallel scalability enables the iterative method to solve large problems with millions of elements and highly heterogeneous reservoir properties. Linear solvers take the greatest portion of CPU time in reservoir simulations. This dissertation investigates advanced linear solvers for high performance computers (HPC) for reservoir simulation. Their performance is compared and discussed.