Composition Routes for Three-Phase Partially Miscible Flow in Ternary Systems
- Tara C. LaForce (U. of Texas at Austin) | Russell T. Johns (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2005
- Document Type
- Journal Paper
- 161 - 174
- 2005. Society of Petroleum Engineers
- 5.4 Enhanced Recovery, 5.4.1 Waterflooding, 5.4.2 Gas Injection Methods, 4.1.2 Separation and Treating, 4.3.4 Scale, 5.3.1 Flow in Porous Media, 5.3.2 Multiphase Flow, 5.2.1 Phase Behavior and PVT Measurements, 4.1.5 Processing Equipment, 5.5 Reservoir Simulation, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 1.6.9 Coring, Fishing, 4.5.7 Controls and Umbilicals, 5.6.4 Drillstem/Well Testing
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Three-phase flow often occurs in reservoirs, particularly for secondary ortertiary oil recovery methods such as miscible gas or chemical flooding. Inthese cases, there is often significant mutual solubility of components in thephases. Unfortunately, there is insufficient understanding of how threepartially miscible phases can affect flow. Furthermore, there are currently nobenchmark analytical solutions available to validate numerical simulations forthis complex flow regime.
In this research, compositional solution routes are developed by the methodof characteristics (MOC) for 1D, dispersion-free flow wherein up to threepartially miscible flowing phases may be present. The method is applied to awater/alcohol/oil system that exhibits a large three-phase region in laboratoryexperiments. Unique solutions are found based on continuity arguments,shock-jump conditions, entropy constraints, and velocity constraints. Theanalytical solutions are compared to fine-grid finite-difference simulations toverify that they converge to the same dispersion-free limit.
The results show that composition routes within the three-phase region oftenexhibit one phase below its residual saturation so that only two phases areflowing. As miscibility is approached, cumulative oil recovery initiallydeclines because of the development of constant states in the solution, whichcause the leading shock to speed up. We show that multicontact miscibility isdeveloped at the critical point of one two-phase region and along the boundaryof the three-phase region where all shocks and waves flow at a dimensionlessvelocity of one. Last, we show that injectivity changes by a factor of two forthe specific relative permeabilities and injection compositions used.
Flow in a reservoir often consists of three or more flowing phases. Forexample, injection of CO 2 can form three hydrocarbon phases under realisticreservoir temperature and pressure conditions. 1 Three hydrocarbon phases arebelieved to occur in many west Texas CO 2 floods, and the numerous phases canhave an adverse effect on wellbore injectivity. 2 Although three-phase flow isbelieved to occur often, many fundamental questions remain about the effect ofthree-phase flow on oil recovery, particularly its effect on the miscible gasprocess.
Helfferich 3 first presented a general analytical theory using the MOC formulticomponent multiphase displacements. Construction of solutions to specificgas displacements has been ongoing ever since. For example, the analyticaltheory for two-phase partially miscible gas displacements has been studiedextensively for floods with an arbitrary number of components. 4--6
Many researchers have also studied immiscible three-phase three-componentMOC displacements. 7--14 In three-phase immiscible systems the mass-balanceequations governing flow may be elliptic, hyperbolic, or nonstrictly hyperbolicdepending on the relative permeability model used. 7 Gonzales and Araujo 11 andSahni et al. 12 have studied the effect of relative permeabilities oncomposition routes. Recently Juanes and Patzek 13,1.proposed new relativepermeabilities for which the mass-balance equation is hyperbolic at everyinterior point of the three-phase region. The elliptic and strictly hyperboliccases are beyond the scope of this paper; however, displacements with ellipticregions in the mass-balance equation have been studied extensively. 7
There has been considerable mathematical research dedicated to understandingnonunique solutions in three-phase immiscible flow. 15--18 Nonuniquenessresults from the introduction of transitional shocks when Lax and Liu entropyconditions fail to provide a composition route. 7 In the example cases studiedhere, no transitional shocks were encountered.
Several researchers have examined the numerical simulation of three-phasepartially miscible flow. Orr, 19 for example, outlined a numerical simulatorthat allows for partially miscible flow of up to four components and fourphases. Pongpitak 20 used this simulator to model three-phase waterflooding forcores saturated with the alcohol n-butanol (NBA) and C 16. The simulationssignificantly underestimated the oil recovery compared with core experiments.Fanchi 21 showed the relative unimportance of small three-phase regions using asimilar simulator on pseudoternary representations of CO 2 injection with crudeand synthetic oils. Gardner et al. 22 obtained an excellent match to slim-tubeexperiments with numerical simulation using pseudoternary representations of CO2 injected into Wasson crude. Moreover, Gardner et al. 22 showed that thenumerical composition route is dependent upon the level of numericaldispersion.
There is very little in the literature on the development of MOC solutionsto three-phase partially miscible flow. Giordano and Salter 23 comparednumerical simulations, corefloods, and one MOC solution for a partiallymiscible three-phase water/NPA/DMP system. The MOC and simulated compositionroutes agreed well, although the match to corefloods was only qualitative. Thedevelopment of this one MOC solution was not thoroughly explained in theirpaper.
In this paper, the analytical theory using MOC is extended tothree-component, three-phase partially miscible flow for a variety of injectioncompositions. Unique solutions are found for a three-phase partially miscibleflow problem with a large three-phase region. The MOC solutions are comparedwith fine-grid finite-difference solutions. Changes in injectivity andcumulative oil recovery with alcohol enrichment are also studied.
|File Size||1 MB||Number of Pages||14|
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