Calculation of Minimum Miscibility Pressure
- K.D. Luks (U. of Tulsa) | E.A. Turek (Amoco Production Co.) | L.E. Baker (Amoco Production Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1987
- Document Type
- Journal Paper
- 501 - 506
- 1987. Society of Petroleum Engineers
- 5.4.2 Gas Injection Methods, 5.2.2 Fluid Modeling, Equations of State, 5.2.1 Phase Behavior and PVT Measurements
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Summary. An algorithm is presented for the calculation of the thermodynamic minimum miscibility pressure (TMMP) consistent with an equation-of-state (EOS) -based fluid description. This algorithm handles both condensing an vaporizing miscibility mechanisms. TMMP calculations are included for a ternary mixture of pure components, as well as a reservoir-oil/CO2 system.
For EOR processes involving gas injection, miscibility can be developed through one of two multiple-contact mechanisms at pressures where first-contact phase equilibria measurements show two-phase behavior. To model such processes with an EOS-based compositional simulator properly, fluid descriptions consistent with multiple-contact miscibility development are required. One measure of this consistency is agreement between the MMP determined from slim-tube displacements and the TMMP calculated from the fluid description. In this paper, an efficient algorithm for the calculation of TMMP is documented.
Hutchinson and Braun described miscible processes using ternary (triangular) compositional diagrams for conceptual analysis. The concept of a TMMP is offered again briefly to support the development of the new algorithm and the presentation of some of the computational results. While we use ternary diagrams to illustrate the concepts, the calculation method is implemented in ndimensional compositional space, where n is the number of components (three or greater) in the reservoir-oil/injection-gas system.
There are two common idealizations of the way in which a two-phase gas/liquid system achieves miscibility through multiple contacting. In the vaporizing mechanism, fresh (original) liquid phase is contacted with a vapor phase whose composition is altered by repeated equilibration with the liquid. In the condensing mechanism, the composition of the liquid phase is altered by equilibration with fresh vapor phase. The generally accepted definition of TMMP is that pressure (at a fixed temperature) above which miscibility occurs for a given feed (i.e., liquid or oil) and pressurizing gas solely through the multiple-contact equilibrium process. A pressure boundary below which miscibility does not occur can be calculated with the algorithm described for either of the two miscibility mechanisms. The TMMP is assumed to be the lower of the boundaries calculated for the two mechanisms, while the upper boundary corresponds to the first-contact miscibility pressure (i.e., the maximum two-phase pressure at the specified temperature).
Fig. 1 illustrates ternary gas and liquid systems at a fixed temperature and pressure. First consider the vaporizing mechanism fotwo initial gas and liquid streams, G and L, respectively. The vaporphase composition is altered by multiple contacting, its composition moving from G to the saturated vapor curve a-c, eventually approaching the composition d asymptotically. No further alteration of the gas phase occurs because the tie-line through d is coincident with the composition L; the conclusion is that miscibility cannot be achieved for the system G and L by thermodynamic multiple contacting alone at this temperature and pressure.
If the two initial streams had been G and L', a single phase, or miscible state, would have eventually occurred. The gas phase would have moved along the ac curve until the line connecting the gas phase with L' would no longer pass through the two-phase region. This limiting gas-phase composition associated with L' is denoted by d'. At this temperature and pressure, miscibility is achieved for the system G+L'.
Given G, the limiting initial liquid-stream composition for achieving miscibility, L", can be located by extending a tangent to the two-phase region from the critical point, c. For an initial mixture of G+L", this pressure at this temperature is the TMMP for the vaporizing mechanism. If one assumes that the extent of the two-phase region shrinks with increasing pressure, one can envision the eventual intersection of the vapor/liquid critical tangent with L; i.e., the TMMP for L is greater than that for L " (and L') at this temperature for the vaporizing mechanism.
One can make similar observations about the condensing mechanism. The conclusion is that all three systems (G+L, L', and L') are thermodynamically immiscible by the condensing mechanism at this pressure because there is a tie-line whose extension intersects G. Consequently, for the G+L (or L', or L') system, the TMMP is determined by the vaporizing mechanism because the condensing mechanism requires a considerably higher pressure at this temperature to be miscible. The pressure denoting the boundary between miscibility and immiscibility for the condensing mechanism will be that one at which the tangent to the phase envelope at the critical point, c, intersects G. Variation in the location of G causes a change in the value of the TMMP as determined by the condensing mechanism in the same manner that it is altered for the vaporizing mechanism by a change in the location of the liquid composition, L.
Calculation of TMMP
The preceding illustration suggests a methodology, cast in geometric terms, for the computation of TMMP. Specifically, for a given mechanism, one is below the TMMP if there is a tie-line (connecting equilibrium liquid and vapor compositions) that is collinear (coincident) with the original unaltered feed. The pressure at which the length of this coincident tie-line goes to zero is the pressure at which a tangent to the phase envelope at a critical point is collinear with the original unaltered feed. The lower of the two TMMP's for the vaporizing and condensing mechanisms is assumed to be that of the "preferred" miscibility mechanism and thus the appropriate computed TMMP.
Previous investigators have used EOS's to determine the vapor/ liquid equilibrium tie-line behavior combined with a strategy to locate the limiting (critical) coincident tie-line. Hagoort and Dumor and Kuo both initially chose a pressure for the given temperature below the TMMP. An iterative procedure is invoked to locate the coincident tie-line at this pressure, usually a stepping procedure of the type shown in Fig. 2 for a vaporizing mechanism. Streams G and L are mixed, say at a bubblepoint state B1, with which G1, is the equilibrium vapor.
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