Simplified Method for Calculation of Minimum Miscibility Pressure or Enrichment
- Hua Yuan (PetroTel Inc.) | Russell T. Johns (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2005
- Document Type
- Journal Paper
- 416 - 425
- 2005. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 4.6 Natural Gas, 5.3.2 Multiphase Flow, 5.5.7 Streamline Simulation, 5.2 Fluid Characterization, 5.2.2 Fluid Modeling, Equations of State, 5.4.2 Gas Injection Methods, 5.2.1 Phase Behavior and PVT Measurements, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.5 Reservoir Simulation
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Local displacement efficiency from gas injection is highly dependent on theminimum miscibility pressure (MMP) or minimum miscibility enrichment (MME).Analytical methods, which are inexpensive and quick to use, have been developedto estimate MMPs for complex fluid characterizations. Published methods,1-3however, often require estimation of numerous parameters and little has beenwritten with regard to method robustness. This paper presents a simplified androbust method for MMP or MME calculation.
The approach relies on finding key crossover tie lines for a dispersion-freedisplacement using method of characteristic theory (MOC). The new method,however, differs from published methods by significantly reducing the number ofequations and unknown parameters, and by providing a fast and robust methodthat can avoid trivial and false solutions. We demonstrate the improvements bycalculation of the MMP and MME for a variety of gas/oil systems and also givenew analytical solutions for constant K-value systems that give insight intothe nature of false solutions.The number of potential false solutionsincreases greatly with the number of components in the fluid characterization.Thus, any proposed method must ensure convergence to the physical MMP/MME.
Gas enrichment is an important optimization parameter in enriched gasfloods. Recoveries from slim tube experiments often give a sharp bend at theMME. Above the MME, slim-tube recoveries (or local displacement efficiencies)do not increase significantly with enrichment. This is also true for slim-tuberecoveries as a function of pressure above the MMP. Thus, the accuratedetermination of MME or MMP is important in gas flood design.
Pseudoternary diagrams have traditionally been used to explain the behaviorof multicontact miscible (MCM) gas drive processes.4 Both qualitative mixingcell arguments and more rigorous mathematical approaches show that a ternarydisplacement can be MCM only if either the oil composition (vaporizing gasdrive) or the injection gas composition (condensing gas drive) lies outside theregion of tie-line extensions on a ternary phase diagram.5,6 For ternarysystems, the MMP is the pressure at which the oil lies on a critical tie-lineextension, whereas the MME is found when the gas lies on a critical tie-lineextension. Thus, a ternary displacement can be either condensing or vaporizingbut not both.
Zick7 and Stalkup8 found that real oil displacements could have features ofboth vaporizing and condensing drives (CV). They also found that MMPs and MMEsestimated by ternary methods were different than those observed for combined CVdrives. Thus, new methods were needed to estimate MMPs and MMEs for realsystems.
Four primary methods have been used in recent years to calculate MMPs andMMEs for real systems: slim tube experiments, compositional simulation,8mixing-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 resultsdepending on the small level of physical dispersion present.10 Fine-gridcompositional simulations and mixing-cell models can suffer from numericaldispersion effects and are also time-consuming to perform. Dispersion-freeanalytical methods are often very fast, but like simulation and mixing-cellmodels, they rely on an accurate fluid characterization by an equation-of-state(EOS). Because of their improved speed, however, analytical methods offersignificant promise for developing improved fluid correlations11 and for use incompositional streamline simulations.
Monroe et al.12 first examined the analytical theory for quaternary systemsand showed that there exists a third key tie line in the displacement path,called the crossover tie line. Johns et al.13 also considered quaternarysystems and analytically proved the existence of the combined CV mechanism.They showed that the crossover tie line controls the development of miscibilityfor such systems. They also provided a simple geometric construction to locatethe crossover tie line; the crossover tie-line extension must intersect the oiland gas tie lines.
Later, Johns and Orr1 showed that the displacement path for dispersion-freeflow is controlled by nc-1 key tie lines, which include the oil tie line, gastie line, and nc-3 crossover tie lines.They extended the simple geometricconstruction to show that successive key tie lines must intersect and that anyone of those key tie lines could control the development of miscibility. Johnsand Orr showed that MCM flow is obtained when any one of the key tie linesintersects the critical locus as pressure (MMP) or enrichment (MME) isincreased. Furthermore, they showed that the displacement is purely vaporizingwhen the oil tie line becomes a critical tie line first as pressure isincreased. Otherwise, miscibility is controlled by one of the crossover tielines and the displacement exhibits a combined CV mechanism. Johns and Orr gavethe first multicomponent example calculation of MMP for a displacement of11-component oil by pure CO2.
Wang and Orr2 gave calculations of MMP for oils displaced by amulticomponent gas. They used a multidimensional Newton-Raphson scheme tolocate the crossover tie lines based on the geometric construction approach ofJohns and Orr.1 They reported convergence difficulties for cases when twosuccessive key tie lines were nearly parallel. They also stated that falsesolutions were obtained in some cases and that the method often convergedslowly. Jessen et al.3 modified Wang and Orr's method to improve speed androbustness. Their main achievement was the inclusion of fugacity equations inthe Newton-Raphson iterations that significantly increased the calculationspeed.
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