Proof of the Two-Phase Steady-State Theory for Flow Through Porous Media

Abstract

Summary A two-phase steady-state theory presented by O'Dell and Miller and modified later by Fussell predicts the performance of single-well gas condensate systems when there is liquid condensate dropout. The proof of this theory is developed with material-balance equations and phase equilibrium concepts. In this proof, dispersion, capillary, and gravity effects are neglected. We also show that this theory can be applied to any two-phase hydrocarbon system (e.g., black oil, volatile oil, or gas condensate) when steady-state conditions exist in the vicinity of a single producing well. Results obtained with this theory are compared with the producing well. Results obtained with this theory are compared with the simulation results obtained with a compositional model. A new procedure to compute the in-place composition profiles for systems under steady-state conditions greatly reduces the computation effort because only the phase equilibrium data for the original reservoir fluid are required. Composition profiles calculated with the proposed procedure are identical to the steady-state composition profiles generated with the compositional model. This theory's usefulness for unsteady flow is also illustrated. Introduction Condensate liquid accumulation occurs near a wellbore when the bottomhole pressure (BHP) fats below the saturation pressure of the reservoir fluid. As a result, the formation flow capacity to the gas phase becomes less than the formation flow capacity to single-phase gas flow. A two-phase steady-state theory presented by O'Dell and Miller and later modified by Fussell predicts performance when this phenomenon occurs. This theory predicts saturation and pressure distributions in the vicinity of a producing well and total fluid production rate as a function producing well and total fluid production rate as a function of the BHP. It was based on the assumption that, at any location within the two-phase region, the ratio of the volumetric flow rates of the two phases equals the ratio of the volume fractions of the two phases as given by constant-composition expansion (CCE) at the corresponding pressure. The theory has not been applied widely, pressure. The theory has not been applied widely, possibly because of unresolved questions about its validity. possibly because of unresolved questions about its validity. The objectives of this paper are to develop a rigorous proof of this theory, to extend the theory to compute the proof of this theory, to extend the theory to compute the in-place composition profiles in the vicinity of a single producing well, and to illustrate its usefulness for unsteady producing well, and to illustrate its usefulness for unsteady flows.