SPE Journal
Volume 15,
Number 2,
June 2010,
pp. 313-325
Summary
Flash calculations for use in compositional simulation are more difficult
and time-consuming as the number of equilibrium phases increases beyond two.
Because of its complexity many simulators do not even attempt to incorporate
three or more hydrocarbon phases even though such cases are important in many
low-temperature gas floods, or for high temperatures where hydrocarbons can
partition into water. Multiphase flash algorithms typically use successive
substitution (SS) followed by Newton's method. For NP-phase
flash calculations, (NP-1) Rachford-Rice (RR) equations are
solved in every iteration step in SS, and depending on the choice of
independent variables, in Newton's method. Solution of RR equations determines
both compositions and amounts of phases for a fixed overall composition and set
of K -values. A robust algorithm for RR is critical to obtain
convergence in multiphase compositional simulation, and has not been
satisfactorily developed unlike the traditional two-phase flash. In this paper,
we develop an algorithm for RR equations for multiphase compositional
simulation that is guaranteed to converge to the correct solution independent
of the number of phases for both positive and negative flash
calculations.
We derive a function, whose gradient vector consists of RR equations. This
correct solution to the RR equations is formulated as a minimization of the
non-monotonic convex function using the independent variables of
(NP-1) phase mole fractions. The key to obtaining a robust
algorithm is that we specify non-negative constraints for the resulting
equilibrium phase compositions, which are described by a very small region with
no poles. The minimization uses Newton's direction with a line search technique
to exhibit super-linear convergence. We show a case in which a previously
developed method cannot converge while our algorithm rapidly converges in a few
iterations. We implement the algorithm both in a stand-alone flash code and in
UTCOMP, a multiphase compositional simulator, and show that the algorithm is
guaranteed to converge when a multiphase region exists as indicated by
stability analysis.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
16 June 2009
- Revised manuscript received:
11 August 2009
- Manuscript approved:
19 August 2009
- Published online:
16 February 2010
- Version of record:
17 June 2010
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