Numerical simulators are often used to aid the study of the factors influencing the unstable miscible displacement processes. 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 the 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.
A procedure has been developed to calculate the non-equilibrium phase behaviour of the fluids under displacement process conditions. The procedure is based on the mixing parameter model proposed by Todd and Longstaff (1972) and the concept of Murphree efficiency. 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.
Comparisons of the simulation results based on the proposed model with the experimental data obtained from slim-tube displacement tests for well-defined hydrocarbon systems and with simulation results based on conventional equilibrium phase behaviour model are presented.
The formulations used in conventional compositional reservoir simulators for calculating the distribution of reservoir fluids under stable miscible displacement process conditions are generally based on the assumption that the fluid mixture contained in each grid block is in a state of equilibrium. This assumption is valid if, as a result of Sufficient contact time and suitably specified reservoir parameters, complete mixing takes place everywhere at which the displaced fluid is contacted by the displacing fluid.
Unfortunately, not all displacement processes are stable. For example, viscous fingering can develop in the flow path of the fluids if the viscosities of the fluids at a certain point are of such magnitudes that they result in a large value for the viscosity ratio µo/ µg Where µo is the viscosity of the oil in place and µg that of the gas, which is in contact with the oil. In situations like this, there is insufficient time for interphase mass transfer to reach an equil ibriurn rate at that point in the reservoir, and consequently, a state of complete mixing will not be a valid assumption to use in making numerical simulation of an unstable displacement process.
It has long been recognized that the major factors that affect the stability of a displacement process are the mobility ratio for the reservoir fluids and the heterogeneity of the reservoir formation, which is essentially a large porous medium. Most of the models that have been proposed for use in numerical simulations of the unstable displacement processes are based on the use of some empirical parameters to account for the effects of mass transfer occurring at the interface on the properties of the adjoining fluids. Some of the theories and models relevant to this study are briefly mentioned in the next section.