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 Δni is the change in the amount of component
i during timestep Δt, 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).
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
5 January 2006
- Revised manuscript received:
23 August 2006
- Manuscript approved:
26 August 2006
- Version of record:
20 March 2007
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