Numerical and physical simulations of the displacement of synthetic oil mixtures
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Numerical simulation and experiments are often used to study the mixing phenomenon of the fluids during an unstable displacement process. One of the deficiencies of the conventional compositional reservoir simulators for predicting the unstable displacement process is that these simulators all involve the use of the assumption that fluids in each grid block are in a state of thermodynamic equilibrium. In reality, the different fluid phases coexisting in each grid block may not be in equilibrium with each other because of insufficient contact time. The main objective of this study is to develop a non-equilibrium phase behaviour model for compositional simulation of the unstable displacement process and is to verify the simulation results with experimental data. Physical simulations of the displacement process were carried out in a slim-tube apparatus. Four synthetic oil mixtures were used as displaced fluids and four gases were used as displacing fluids. A total of fifteen experiments were performed at displacement pressures ranging from 2390 psia to 3430 psia and with injection rates varying from 0.048 to 0.127 PV/hr. The results of the experiments are presented. A model has been developed to calculate the non-equilibrium phase behaviour of the fluids under displacement process conditions. The model is based on the mixing parameter model proposed by Todd and Longstaff (1972) and the concept of Murphree efficiency commonly used in multicomponent, multistage separation calculations. Phase behaviour calculations are performed for the fluids over the entire grid block under non-equilibrium conditions. The deviation from equilibrium in respect of each component is considered a function of the equilibrium K-value and the effective mobility ratio of the in-situ fluids. Efficient algorithms for phase behaviour calculations (e.g., flash calculations and saturation pressure calculations) generally used in the numerical simulations are presented. An acceleration scheme based on the dominant eigenvalue method coupled with Newton's method is developed for two-phase flash calculations. Effective switching criteria are suggested for the switch over of the acceleration scheme to Newton's method. The proposed method is robust and fast for flash calculations when the specifications are near the critical state values of the fluid mixtures. The performance of the proposed method is compared with those of other improved methods for flash calculations. An algorithm is developed to accelerate the convergence of phase-boundary calculations using Newton's method. The algorithm takes advantage of the history of the iterates and uses the derivative of the iterates to further improve the iterates after three Newton steps. The performance of the proposed algorithm shows its superiority over that of Newton's method particularly when the specifications are near the critical state values of the fluid mixtures. Comparisons of the performance of the proposed algorithm with that of Newton's method and other acceleration algorithms for Newton's method are presented. Comparisons of the numerical simulation results based on the proposed non-equilibrium phase behaviour model with the experimental data obtained from the slim-tube displacement tests for well-defined hydrocarbon systems and with simulation results based on conventional equilibrium phase behaviour model are presented.