Summary
Local displacement efficiency from gas injection is highly dependent on the
minimum miscibility pressure (MMP) or minimum miscibility enrichment (MME).
Analytical methods, which are inexpensive and quick to use, have been developed
to estimate MMPs for complex fluid characterizations. Published methods,1–3
however, often require estimation of numerous parameters and little has been
written with regard to method robustness. This paper presents a simplified and
robust method for MMP or MME calculation.
The approach relies on finding key crossover tie lines for a dispersion-free
displacement using method of characteristic theory (MOC). The new method,
however, differs from published methods by significantly reducing the number of
equations and unknown parameters, and by providing a fast and robust method
that can avoid trivial and false solutions. We demonstrate the improvements by
calculation of the MMP and MME for a variety of gas/oil systems and also give
new analytical solutions for constant K-value systems that give insight into
the nature of false solutions. The number of potential false solutions
increases greatly with the number of components in the fluid characterization.
Thus, any proposed method must ensure convergence to the physical MMP/MME.
Introduction
Gas enrichment is an important optimization parameter in enriched gas
floods. Recoveries from slim tube experiments often give a sharp bend at the
MME. Above the MME, slim-tube recoveries (or local displacement efficiencies)
do not increase significantly with enrichment. This is also true for slim-tube
recoveries as a function of pressure above the MMP. Thus, the accurate
determination of MME or MMP is important in gas flood design.
Pseudoternary diagrams have traditionally been used to explain the behavior
of multicontact miscible (MCM) gas drive processes.4 Both qualitative mixing
cell arguments and more rigorous mathematical approaches show that a ternary
displacement can be MCM only if either the oil composition (vaporizing gas
drive) or the injection gas composition (condensing gas drive) lies outside the
region of tie-line extensions on a ternary phase diagram.5,6 For ternary
systems, the MMP is the pressure at which the oil lies on a critical tie-line
extension, whereas the MME is found when the gas lies on a critical tie-line
extension. Thus, a ternary displacement can be either condensing or vaporizing
but not both.
Zick7 and Stalkup8 found that real oil displacements could have features of
both vaporizing and condensing drives (CV). They also found that MMPs and MMEs
estimated by ternary methods were different than those observed for combined CV
drives. Thus, new methods were needed to estimate MMPs and MMEs for real
systems.
Four primary methods have been used in recent years to calculate MMPs and
MMEs for real systems: slim tube experiments, compositional simulation,8
mixing-cell models,9 and analytical models.1–3 Each of these methods, however,
has advantages and disadvantages. Slim tube experiments, which use real fluids,
are expensive and time-consuming to perform and can give misleading results
depending on the small level of physical dispersion present.10 Fine-grid
compositional simulations and mixing-cell models can suffer from numerical
dispersion effects and are also time-consuming to perform. Dispersion-free
analytical methods are often very fast, but like simulation and mixing-cell
models, they rely on an accurate fluid characterization by an equation-of-state
(EOS). Because of their improved speed, however, analytical methods offer
significant promise for developing improved fluid correlations11 and for use in
compositional streamline simulations.
Monroe et al.12 first examined the analytical theory for quaternary systems
and showed that there exists a third key tie line in the displacement path,
called the crossover tie line. Johns et al.13 also considered quaternary
systems and analytically proved the existence of the combined CV mechanism.
They showed that the crossover tie line controls the development of miscibility
for such systems. They also provided a simple geometric construction to locate
the crossover tie line; the crossover tie-line extension must intersect the oil
and gas tie lines.
Later, Johns and Orr1 showed that the displacement path for dispersion-free
flow is controlled by nc–1 key tie lines, which include the oil tie line, gas
tie line, and nc–3 crossover tie lines. They extended the simple geometric
construction to show that successive key tie lines must intersect and that any
one of those key tie lines could control the development of miscibility. Johns
and Orr showed that MCM flow is obtained when any one of the key tie lines
intersects the critical locus as pressure (MMP) or enrichment (MME) is
increased. Furthermore, they showed that the displacement is purely vaporizing
when the oil tie line becomes a critical tie line first as pressure is
increased. Otherwise, miscibility is controlled by one of the crossover tie
lines and the displacement exhibits a combined CV mechanism. Johns and Orr gave
the first multicomponent example calculation of MMP for a displacement of
11-component oil by pure CO2.
Wang and Orr2 gave calculations of MMP for oils displaced by a
multicomponent gas. They used a multidimensional Newton-Raphson scheme to
locate the crossover tie lines based on the geometric construction approach of
Johns and Orr.1 They reported convergence difficulties for cases when two
successive key tie lines were nearly parallel. They also stated that false
solutions were obtained in some cases and that the method often converged
slowly. Jessen et al.3 modified Wang and Orr’s method to improve speed and
robustness. Their main achievement was the inclusion of fugacity equations in
the Newton-Raphson iterations that significantly increased the calculation
speed.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
9 January 2003
- Revised manuscript received:
1 April 2005
- Manuscript approved:
4 April 2005
- Version of record:
15 December 2005
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