Development of Miscibility in Four-Component CO2 Floods
- F.M. Orr Jr. (Stanford U.) | R.T. Johns (Stanford U.) | Birol Dindoruk (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- May 1993
- Document Type
- Journal Paper
- 135 - 142
- 1993. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 4.6 Natural Gas, 5.2.2 Fluid Modeling, Equations of State, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 5.4.2 Gas Injection Methods, 5.2 Reservoir Fluid Dynamics, 4.1.2 Separation and Treating, 5.6.4 Drillstem/Well Testing, 5.4 Enhanced Recovery, 5.3.1 Flow in Porous Media, 5.4.9 Miscible Methods, 4.1.5 Processing Equipment
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A rigorous tie-line extension criterion for the minimum miscibility pressure (MMP) is derived for dispersion-free, 1D displacements in four-component systems in which CO2 displaces oil containing dissolved methane. The key tie-lines required for application of the MMP criterion are obtained by a simple graphical construction. A simplified technique for construction of solutions is demonstrated for the CO2/methane/butane/decane system. The new technique makes solution of certain four-component problems not much more difficult than solution of a Buckley-Leverett displacement of oil by water.
Most analyses of the mechanisms of miscible floods have been based on the behavior of three-component systems. If only three components are present, miscibility develops if either the injection composition (condensing-gas drive) or the initial composition (vaporizing-gas drive) lies outside the region of tie-line extensions on a ternary phase diagram.1-3
Several investigators have argued that real miscible-flood systems show important behavior that cannot be represented adequately on ternary diagrams. For example, Zick4 and Stalkup5 used compositional simulations to show that multicomponent displacements have characteristics of both condensing and vaporizing gas drives. Jensen and Michelsen6 used four-component systems to demonstrate that direct application of the critical tie-line criterion from ternary systems leads to incorrect MMP estimates in some cases. Stalkup5 argued that quaternary phase diagrams were required in the analysis of displacements by N2 and methane (CH4). However, no investigator has developed a rigorous extension of the three-component tie-line criterion for miscibility to systems with more than three components.
In this paper, we use and significantly extend the solution technique described by Monroe et al.7 for 1D, dispersion-free flow of four-component mixtures. We show how analytical solutions by the method of characteristics can be found by geometric constructions not much more difficult than those performed in the Buckley-Leverett solution for displacement of oil by water. We demonstrate solutions for displacement of mixtures of CH4, butane (C4), and decane (C10) by CO2, and we derive a tie-line extension criterion for development of miscibility in these quaternary displacements.
We analyze 1D, dispersion-free flow of four-component mixtures under the assumptions stated by Monroe et al.7 To simplify the problem description, we also assume that components do not change volume as they transfer between phases. We emphasize, however, that the main results presented here also apply when the volume changes as components transfer between phases.8
The resulting material balance equations are
Equations 1a and 1b
Phase-equilibrium calculations were performed with the Peng-Robinson9 equation of state (PREOS) with the critical properties, acentric factors, and binary interaction parameters given in Table 1.
Component densities used to convert mole fractions to volume fractions also are given in Table 1. Phase viscosities were calculated with the Lohrenz et al.10 correlation with values of the critical volumes reported in Table 1. Under the assumption of no volume change on mixing, phase densities calculated with the PREOS were not used to calculate phase saturations, but the PREOS densities were used in phase-viscosity calculations. Volume-translation parameters in Table 1 were used to improve estimates of phase density for use in those phase-viscosity calculations. The fractional flow function was
where Sor=0.20, eo=2.0, and eg=2.0.
Eqs. 1 are a system of first-order hyperbolic equations. The solution is found by calculating the velocity at which each overall composition propagates through the porous medium.2 Because dispersion is absent, the mixture compositions that form during the displacement lie on a single composition route that connects the initial and injection compositions. The problem, then, is to find the appropriate route for given initial and injection compositions. Potential solution routes or paths are obtained by solving an eigenvalue problem.2 Path directions are given by eigenvectors and composition propagation rates (wave velocities) by eigenvalues. tielines, for example, are paths; also, two additional non-tie-line paths go through each composition point.2,7 The solution route then must be selected from the infinite set of composition paths subject to the additional "velocity constraint" that requires the propagation velocity for compositions in the two-phase region to increase monotonically as the solution route is traced from the injection composition to the initial composition.
The solution route that satisfies those constraints includes shocks (jumps from one composition to another), continuous variations (spreading waves) along a composition path, and constant-state zones, which arise when the solution route switches from one path to another. Shocks occur when it is impossible to satisfy the velocity constraint with continuous variations. A material balance for each component across a shock shows that the wave velocity of the shock is
where I and II refer to opposite sides of the shock.
Eq. 3 can be used to prove that the solution route can enter or leave a two-phase region only by a shock in which the single-phase composition lies on an extension of an equilibrium tie-line.2 That proof establishes that the solution route will avoid the two-phase region if either the injection or initial composition does not lie on any tie-line extension, and it applies to systems with any number of components. In other words, the displacement will be miscible in a multicontact sense.
In ternary systems, a displacement is multicontact miscible (MCM) only if either the initial or injection composition lies outside the region of tie-line extensions. Monroe et al.7 showed that addition of CH4 to a C4/C10 mixture induces two-phase flow, but they did not investigate how miscibility develops for the live oil.
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