Summary
The computational time for conventional flash calculations increases
significantly with the number of components, making it impractical for use in
many fine-grid compositional simulations and other applications. Previous
research to increase flash-calculation speed has been limited to those with
zero binary interaction parameters (BIPs) or approximate methods based on an
eigenvalue analysis of the binary interaction matrix. Practical flash
calculations, however, nearly always have some nonzero BIPs. Further, the
accuracy and speed of the eigenvalue methods varies depending on the choice and
number of the dominant eigenvalues.
This paper presents a new and simple method for significantly increasing the
speed of flash calculations for any number of nonzero BIPs. The approach
requires the solution of up to six reduced parameters regardless of fluid
complexity or the number of components and is based on decomposing the BIPs
into two parameters using a simple quadratic expression. The new approach is
exact in that the equilibrium-phase compositions for the same BIPs are
identical to those with the conventional flash calculation; no eigenvalue
analysis is required. Further, the new approach eliminates the Rachford-Rice
procedure (1952) and is more robust than the conventional flash-calculation
procedure. We demonstrate the new approach for several example fluids and show
that speedup by a factor of approximately 3 to 20 is obtained over conventional
flash calculations, depending on the number of components.
Introduction
Gas injection into oil reservoirs results in complex interactions of flow
with phase behavior that often are not modeled accurately by black-oil
simulation. This is especially true for miscible or nearly miscible floods in
which significant mass transfer occurs between the hydrocarbon phases. Such
floods are best modeled by compositional simulation.
A significant disadvantage of compositional simulation, however, is that it
is much more computationally intensive than black-oil simulation. The primary
reason for the increased computational time is the result of solving repeated
flash calculations with cubic equations of state (EOS). Research has shown that
EOS flash calculations can occupy 50 to 70% of total computational time in
compositional simulations (Stenby and Wang 1993; Chang 1990). This is also true
for other applications, such as multiphase flow in pipelines.
The use of fewer pseudocomponents can reduce the flash computation time, but
fewer components results in less accuracy (Hong 1982; Liu 2001; Egwuenu et al.
2005). This is especially true in multicontact miscible displacements, in which
miscibility is developed by a combined condensing/vaporizing drive process
(Zick 1986; Johns et al. 1993; Egwuenu et al. 2005). Fluid characterization by
pseudocomponent models can be improved by tuning to the analytical minimum
miscibility enrichment or minimum miscibility pressure (Johns et al. 1994), but
those models still require significant computational time, even for fewer
pseudocomponents.
Another way to reduce computation time is to reduce the number of
gridblocks. With coarse grids, however, numerical dispersion is large, which
may cloud the results (Solano et al. 2001). Ideally, fine grids should be used
that better match the level of dispersion found at the field scale.
More recently, methods have been examined to find reduced parameters for
flash calculations. Michelsen (1982a, 1982b, 1986) significantly increased
flash-calculation speed by finding three reduced parameters, regardless of the
number of components. His method, however, assumes zero BIPs, which is too
restrictive for real fluid characterization. Michelsen also gave a practical
method for stability calculations using the tangent plane distance (TPD)
(Michelsen 1982b).
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
13 April 2006
- Revised manuscript received:
25 May 2006
- Manuscript approved:
31 July 2006
- Version of record:
20 October 2006
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