Compositional models are commonly used to simulate recovery processes in which injection gas and reservoir gases have distinctly different properties. Such processes include vapourising miscible drives, condensing miscible drives and low-pressure air injection. Recovery is typically enhanced by changes in fluid properties and a reduction in interfacial tension, leading to a variation of the relative permeability endpoints. These changes are due to mass transfer, in particular the solution of intermediate hydrocarbon components in the oil. Extensions of the black oil model such as that due to Todd and Longstaff can also treat such processes, although the mechanisms considered are rather different - in particular the amount of inter-phase mixing which occurs.
In this paper we attempt to unify these two approaches. The traditional black oil model is extended to multiple gases and property data constructed which yields a measure of the surface tension after mass transfer. Once the surface tension is known, a common end-point shift treatment can be used in both compositional and extended black oil treatments.
Traditional black oil numerical methods based on saturation variables have problems in treating the effect of partial pressure on the amount of dissolved gas when the gas saturation is low. This may be overcome using mass-based variables, but these have typically been less efficient due to the addition of an extra volume balance equation. A reduced mass variable formulation is described which retains the efficiency of the saturation-based approach whilst being easy to generalize to multiple gas components.
The multiple gas black oil and full compositional methods are assessed on some generic examples of gas injection processes.
A black oil model typically uses fluid flow equations that conserve surface oil, surface gas and water. The use of a single type of gas is limiting when attempting to model processes in which the nature of the injection gas and its equilibrium behavior in the presence of reservoir oil is different from that of the original reservoir gas. Zick (ref. 1) suggests that in practice miscible recoveries are obtained by enriched gas injection via a combined condensing/vapourising process. Gas flows into oil ahead of the front and condenses, yielding a lighter oil; whilst oil vaporizes behind the front, yielding a richer gas. In some cases this multi-contact process may yield a genuine single-phase state; alternatively the true miscible state is not reached, but the interfacial tension is reduced to such an extent that typical miscible class recoveries are obtained.
Such miscible processes may be modeled using a compositional simulator employing an equation of state (EoS) for phase equilibrium. The mass transfer occurs naturally as a result of the flash calculation, and the simulator can model direct oil-to-gas transitions (ref. 2). However, the higher calculational cost of using a compositional model and the potential instabilities introduced by IMPES and adaptive implicit formulations make it desirable to use an extended black oil model for such processes if possible.
Extended black oil models can address the miscible displacement process using a Todd and Longstaff model (ref. 3). This can be used in three or four-component form. In the latter case the components are oil, water, original reservoir gas and solvent. The Todd and Longstaff model also addresses the issue of fluid viscosity variation when phases are highly intermingled due to fingering. Gas condensation and surface tension effects are not usually included - the solvent is regarded as having a saturation and being miscible with the oil on first contact.