Abstract
This paper describes an implicit, three-dimensional formulation for simulating compositional-type reservoir problems. The model treats three-phase flow in Cartesian (x-y-z) or cylindrical (r-theta-z) geometries. Applicability ranges from depletion or cycling of volatile oil and gas condensate to miscible flooding operations involving either outright or multicontact-miscibility.The formulation uses an equation of state for phase equilibrium and property calculations. The equation of state provides consistency and smoothness as gas- and oil-phase compositions and properties converge near a critical point. This avoids computational problems near a critical point associated with use of different correlations for K values as opposed to phase densities. Computational testing with example multicontact-miscibility (MCM) problems indicates stable convergence of this formulation as phase properties converge at a critical point. Results for these MCM problems show significant numerical dispersion, primarily affecting the calculated velocity of the miscible-front advance. Our continuing effort is directed toward reduction of this numerical disperson and comparison of model results with laboratory experiments for both MCM and outright-miscibility cases.We feel that the implicit nature of the model enhances efficiency as well as reliability for most compositional-type problems. However, while we report detailed problem results and associated computing times, we lack similar reported times to compare the overall efficiency of an implicit compositional formulation with that of a semi-implicit formulation.
Introduction
Many papers have treated increasingly sophisticated or efficient methods for numerical modeling of black-oil reservoir performance. That type of reservoir allows an assumption that reservoir gas and oil have different but fixed compositions, with the solubility of gas in oil being dependent on pressure alone.A smaller number of papers have presented numerical models for simulating isothermal "compositional" reservoirs, where oil and gas equilibrium compositions vary considerably with spatial position and time. With some simplification, the reservoir problems requiring compositional treatment can be divided into two types. The first type is depletion and/or cycling of volatile oil and gas condensate reservoirs. The second type is miscible flooding with MCM generated in situ.A distinction between these types is that the first usually involves phase compositions removed from the critical point, while the second type generally requires calculation of phase compositions and properties converging at the critical point. A compositional model should be capable of treating the additional problem of outright miscibility where the original oil and injected fluid are miscible on first contact.A difficulty in modeling the MCM process is achievement of consistent, stable convergence of gas-and oil-phase compositions, densities, and viscosities as the critical point is approached. A number of studies have reported models that use different correlations for equilibrium K-values as opposed to phase densities. Use of an equation of state offers the advantage of a single, consistent source of calculated K-values, phase densities, and their densities near a critical point.
SPEJ
P. 363＾
Fundamental equation of state developed on basis of Migdal’s phenomenological theory of critical point
