Summary
A new IMPSAT model, with explicit solution of variables that are isochoric (i.e., complementary to volumes), is compared to the conventional IMPSAT model, which determines phase mole fractions explicitly. The compared properties are performance of the nonlinear iteration and numerical stability.
The use of complementary variables in the new IMPSAT model makes the nonlinear system better conditioned. Consequently, fewer nonlinear iteration steps are required. The resulting speedup more than compensates for the added costs of introducing and using the isochoric variables.
The stability criterion associated with the new IMPSAT model is in many cases significantly less conservative than the conventional criterion. However, for cases in which there is little or no saturation change between the hydrocarbon phases (e.g., for retrograde gas condensate cases or single hydrocarbon phase cases), the difference between the criteria is insignificant.
The timestep sizes for which instabilities occur are practically the same for the two models, and no oscillations have been observed unless both the new and the conventional criterion are violated. Consequently, the stability properties are similar, and the new criterion seems to apply to both models.
Our conclusions are supported by numerical results.
Introduction
An isothermal compositional model of Nc components involves the solution of Nc flow equations per gridblock (e.g., the mass balance equations):
(Eq. 1)
where ?ni is the change in the amount of component i during timestep ?t, while fi and qi are the component interblock flow and source rates. In addition, phase equilibrium between the oil and gas phases (e.g., equalities of fugacities),
(Eq. 2)
must be taken into account.
Because of the large number of equations and the complex thermodynamics, it is too demanding to determine all variables implicitly (i.e., simultaneously in all gridblocks). Instead, we use a partially explicit approach, where some variables are determined implicitly, while others are determined explicitly, gridblock by gridblock. The explicit solution relies on explicit treatment of variables (i.e., evaluating parts of the interblock flow with variables from the previous time level).
Newtonsche Aufheizung, Abelsche Integralgleichungen zweiter Art und Mittag-Leffler-Funktionen