Summary
Equations of state (EOSs) are typically tuned to black-oil
pressure/volume/temperature (PVT) data such as constant volume-depletion,
constant-composition-expansion, differential-liberation, and separator tests.
Other PVT data more appropriate for gas injection could include multicontact
and swelling tests and slimtube tests. The standard method of tuning, however,
does not typically incorporate important displacement parameters, such as the
minimum miscibility pressure (MMP), minimum miscibility enrichment (MME), or
the likely compositions that result in a reservoir from condensing-vaporizing
(CV) displacements.
This paper demonstrates an improved reservoir-fluid-characterization
procedure for miscible gas floods that can represent the interaction of flow
and phase behavior more accurately. We demonstrate the approach for two
displacements, an 11-component CO2 flood and a 12-component
enriched-gas flood. The method-of-characteristic (MOC) theory is used to
determine the MME (or MMP) of both lumped and unlumped models. The results show
that by tuning to the calculated MME/MMP, fewer pseudocomponents are required
to characterize the fluid than with conventional tuning methods. For the cases
studied, fluids lumped to as few as four or five pseudocomponents can provide a
good match to the composition profiles and oil recoveries of the unlumped
models.
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 modeled best by compositional simulation.
A significant disadvantage of compositional simulation, however, is that it
is 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 EOSs. The use of fewer pseudocomponents could reduce
the flash computation time, but fewer components results in poor fluid
characterizations and reduced accuracy.
Reservoir oils typically are subjected to standard black-oil PVT experiments
that give volumetric behavior for recovery predictions from conventional
methods, such as waterflooding. These experiments include
constant-volume-depletion, differential-liberation,
constant-composition-expansion, and separator tests. Standard PVT experiments,
however, do not provide sufficient phase-behavior data in the range of
compositions that result from mixing of gas with resident oil.
For gas floods, multicontact experiments, along with swelling tests and
slimtube experiments, are sometimes performed (Pedersen et al. 1989). Most
gasfloods, such as those with CO2 and enriched-gas injection,
however, have features of both condensing and vaporizing drives (Zick 1986;
Stalkup 1987; Johns et al. 1993). Miscibility in these CV drives is developed
in the transition zone between the condensing and vaporizing regions at an
equilibrium tie line, known as the crossover tie line (Johns et al. 1993, 2002;
Johns and Orr 1996). Multicontact tests attempt to mimic the composition paths
that result from either vaporizing or condensing drives, but not both. Thus,
these tests do not provide sufficient PVT data in the compositional range of
interest, especially in the transition zone near the critical region in which
miscibility is developed in CV drives.
Slimtube tests can and should be used to tune an EOS by matching the
experimental recoveries with 1D compositional simulations (Shanin and Kremesec
1992). Slimtube tests, however, are expensive and time-consuming to obtain, and
their recoveries can be affected by dispersion and relative permeabilities
(Johns et al. 1994; Solano et al. 2001). Slimtube tests are not always
available, and even if they are, it would be helpful to have a method that is
not dependent on the level of dispersion or relative permeability parameters,
and one that is very fast so that regression of the MMP/MME is possible. Recent
research has shown how to calculate the dispersion-free MMP/MME from an EOS by
MOC (Jessen et al. 1998; Wang and Orr 2002; Yuan 2003; Yuan and Johns
2005).
EOS are used to predict the compositions and volumetric behavior that result
when oil and gas mix in the reservoir. These EOS fluid characterizations must
be tuned to match the PVT behavior of the original reservoir fluid. The process
of tuning an EOS involves: (1) selection of the pseudocomponents, (2)
determination of EOS properties for the pseudocomponents, and (3) adjustment of
pseudocomponent EOS properties by regression to the PVT data.
The fluid characterizations that result from the lumping and tuning process
are dependent on the method used and the experimental PVT data available
(Pedersen et al. 1989). Often the tuning process involves iteration and
subjectivity concerning which parameters to regress and the number of
pseudocomponents to use. The usual approach is first to lump the original fluid
analysis to as few as 12 to 15 components and pseudocomponents. This EOS model
is tuned to match the available PVT data, and it can be lumped into fewer
pseudocomponents as needed.
There are several methods for lumping components into pseudocomponents and
determining their EOS properties (Danesh 1998; Pedersen and Christensen 2006).
The simplest methods assign pseudocomponents on the basis of component mole
fractions (Cotterman and Prausnitz 1985), mass fractions (Pedersen et al.
1985), ranges in molecular weights (Whitson 1983), and K -values (Li et
al. 1985; Newley and Merrill 1991) pore-complex methods include the statistical
approach of Mehra et al. (1982). The method used in this research is that of
Newley and Merrill (1991), which is based on K-values at some selected
feed composition. We use this method because analytical theory has demonstrated
that components within the reservoir are chromatographically separated by their
K-values (Orr 2007).
Several regression procedures have been suggested for tuning EOS
characterizations (Hong 1982; Fong et al. 1992; Khan et al. 1992; Liu 1999;
Zurrita and McCain 2002). The selection of parameters to tune to match a set of
PVT data is more of an art than an exact science. Adjusting too many parameters
could result in poor PVT predictions away from the range of the measured PVT
data. Jhaveri and Youngren (1984) recommend classifying PVT experimental data
into volumetric and compositional data. Preselected EOS parameters are adjusted
to match the compositional data first, and, then, volumetric data are matched
by adjusting the volumetric-shift parameters. Pedersen and Christensen (2006)
showed that fluid characterizations can predict fluid properties better when
most binary-interaction parameters (BIPs) between hydrocarbon components are
zero. Typically, the parameters associated with the heaviest pseudocomponents
are adjusted by up to 10% to match the compositional data because these
components have properties with the largest measurement uncertainties (Danesh
1998; Christensen 1999; Pedersen and Christensen 2006).
This paper presents a method to improve fluid characterizations that can
account for the complex composition paths that result from a CV process. Such a
method can be used to reduce the number of required pseudocomponents for use in
compositional simulation. The proposed method is based on matching all
available PVT data and the analytical calculation of MMP/MME from the lumped
EOS models to the original unlumped fluid characterizations. The lumping and
tuning procedure is demonstrated for 11-component and 12-component oil
displacements by gas using the Peng-Robinson EOS (Peng and Robinson 1976).
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
22 March 2005
- Meeting paper published:
13 June 2005
- Revised manuscript received:
3 March 2008
- Manuscript approved:
19 March 2008
- Version of record:
20 August 2008
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