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A strategy is presented for describing all the solid–fluid phase equilibria of a binary mixture, by combining a classical equation-of-state with a general mathematical artifice for the fugacity of the solid phase. As a case study, the strategy is applied to predict the solid–fluid phase equilibria of the binary mixture methane + carbon dioxide using the Soave–Redlich–Kwong equation-of-state to represent all real and hypothetical fluid phases. A system stability criterion is used to identify the slg locus, which is the intersection of the sl and sg equilibrium regions.

This paper demonstrates that the use of quadrature to designate pseudocomponents of continuous systems in solid−fluid phase equilibrium computations can lead to results that would be inconsistent with what one would expect from actual (more continuous) descriptions. Differential distillation (liquid + vapor) and differential crystallization (liquid + solid) computations are performed using two compositional representations: (1) a 94-component integer mixture of n-paraffinic species and (2) a 12-component quadrature representation of the same n-paraffinic mixture. Results for the differential distillation process do not vary significantly between the two representations; however, corresponding results for the differential crystallization process are dramatically different. Computations suggest that strong nonideality in a mixture phase can render its pseudocomponent description inadequate, leading to unrealistic results when that phase equilibrates with another.

The liquid–liquid–vapor (llg) partial miscibility behavior of the ternary mixtures carbon dioxide+1-methylnaphthalene+methanol was experimentally studied by use of a visual cell (stoichiometric) technique. Phase compositions and molar volumes of the two liquid phases in equilibrium are reported as functions of temperature and pressure within the llg region. In contrast to an earlier study using acetone as a cosolvent, the cosolvent methanol does not enhance the amount of the solute 1-methylnaphthalene taken up by the second (carbon dioxide-rich) liquid phase. Additional llg isotherms of the mixtures carbon dioxide+1-methylnaphthalene+n-hexane, and carbon dioxide+n-tetradecane+n-hexane were studied in order to elucidate the role that molecular similarity vis-a-vis dipole moment has on solute solubility enhancement in the second liquid phase l2.

The solid−fluid phase equilibrium problem is solved for an n-paraffinic C7+ model fluid whose pseudocomponent compositional characterization is determined by finite Laguerre−Gauss quadrature, under the assumption that the initial solid phase formed is a “pure” pseudocomponent. Of interest is how rapidly the crystal point temperature result converges with an increase in the level of quadrature. It is concluded that the highly nonlinear nature of the fluid phase's Gibbs energy of mixing presents a serious challenge to obtaining a satisfactory asymptotic result. Furthermore, it is suggested that the convergence of fluid-phase equilibrium results with increasing quadrature level may likewise be affected, though probably to a lesser extent.

Liquid-liquid-vapor (llg) loci for the binary mixtures xenon + 1-hexanol and xenon + methanol are studied experimentally using a visual cell (stoichiometric) technique. The pressure, temperature, phase compositions and molar volumes of the two liquid phases are reported for all the xenon + 1-alkanol mixtures from ethanol to 1-tetradecanol, which with methanol are all the members of this homologous series of binary mixtures that display llg behavior. The llg behavior of this homologous series of mixtures is compared to that of the homologous series of 1-alkanol mixtures with the solvent gases ethane, carbon dioxide, and nitrous oxide.

Hong, S.-P., Green, K.A. and Luks, K.D., 1994. Solubility and volumetric behavior of methane and carbon dioxide plus C 7+ pseudocomponents of an oil. Fluid Phase Equilibria , 95: 267-280. Liquid-vapor (1g) phase equilibria for the binary mixtures methane + five Prudhoe Bay oil cuts and CO 2 + five Prudhoe Bay oil cuts were studied at 360.93 K to pressures of 80 bar, using a stoichiometric (visual cell) technique. Liquid phase composition and molar volume data are reported. The liquid phase composition data are correlated using the Soave-Redlich-Kwong and Peng-Robinson equations of state, with the objective of identifying whether useful patterns exist in the gas + oil cut binary interaction parameters.

Green, K.A., Zhou, S. and Luks, K.D., 1993. The fractal response of robust solution techniques to the stationary point problem. Fluid Phase Equilibria 84: 49-78. The mathematical nature and physical significance of the stationary point problem, as related to the computation of phase equilibria, is reviewed. Robust (Newton) techniques are used to compute stationary points in composition space for three ternary systems: (1) a simple model of excess Gibbs energy; (2) a Type I van der Waals mixture at a temperature and pressure which does not have any real-root multiplicity when solving the cubic equation-of-state; (3) the same Type I van der Waals mixture at a temperature and pressure which has real-root multiplicity when solving the cubic equation-of-state. All three examples can exhibit fractal behavior with respect to the points of initiation of the robust solution technique. The occurrence and nature of the fractal patterns are a function of the location of the reference point of the solution search in the composition space.

Hong S.-P. and Luks K.D., 1992. Multiphase equilibria of the mixture carbon dioxide + toluene + naphthalene. Fluid Phase Equilibria, 74: 133-144. Solid-liquid-vapor (slg) phase equilibria for the ternary mixture CO2 + toluene + naphthalene are measured at temperatures below the binary slg locus of CO2 + naphthalene using a stoichiometric (visual cell) technique. Conjugate slg runs are performed so that the compositions and molar volumes of both fluid phases in the presence of the solid phase can be determined. These data can be useful for evaluating the equation-of-state parameters for CO2 + naphthalene as a component pair at temperatures below the latter species' melting point. The boundaries of the liquid-liquid-vapor region are also reported for the ternary mixture.

Solid-liquid-vapor (SLV) phase equilibria for the ternary mixture C0 2 + n -hexane + n -hexatriacontane ( n -C 36 H 74 ) are measured at temperatures below the SLV locus of C0 2 + n -hexatriacontane using a stoichiometric (visual cell) technique. Conjugate runs are performed so that the compositions and molar volumes of both the fluid phases in the presence of the solid phase can be determined. These data can be useful for evaluating the equation-of-state parameters of the n-hexatriacontane as a fluid component at temperatures below its melting point.

The liquid-liquid-vapor (LLV) phase equilibria of the ternary mixture ethane + methanol + 1-decanol were experimentally studied by using a visual cell (stoichlometric) technique with pressure discrimination of ±0.01 bar, achieved by coupling a dead-weight gauge to the cell pressure transducer. The pressure, phase compositions, and molar volumes of the two liquid phases of the ternary LLV system are reported at 295.15 K

Liquid-liquid-vapor (LLV) loci for the binary mixtures ethane + n-propanol, ethane + n-butanol, ethane + n-octanol and ethane + n-decanol are studied experimentally using a visual cell (stoichiometric) technique. The pressure, temperature, phase compositions and molar volumes of the two liquid phases are reported for all the mixtures. The vapor phase compositions and molar volumes of the mixtures ethane + n-propanol and ethane + n-butanol are also reported. LLV locus end points are reported for all the ethane + n-alkanol mixtures from ethanol to n-pentadecanol. A transition in the nature of the LLV locus occurs in the homologous series between n-decanol and n-undecanol. For n-undecanol and higher n-alkanols, the lower terminus of the LLV locus is a four-phase solid-liquid-liquid-vapor (SLLV) point, with the termination of LLV immiscibility occurring with n-pentadecanol. For n-decanol and lower n-alkanols to ethanol, the lower terminus is a lower critical end point, with the two liquid phases being critical.

Liquid—liquid—vapor (LLV) and solid—liquid—vapor (SLV) phase equilibria for the binary mixtures nitrous oxide+n-nonadecane and nitrous oxide+n-tetracosane were experimentally studied using a visual cell (stoichiometric) technique. The pressure, temperature, compositions and molar volumes of the liquid phases in all the multiphase systems are reported. For the homologous series of nitrous oxide+n-paraffin binary mixtures, the topographical nature of the LLV loci is similar to that of the ethane+n-paraffin homologous series. n-Octadecane was found to be the first member of the series to exhibit LLV immiscibility with nitrous oxide. A transition in the nature of the LLV locus occurs in the series between n-docosane and n-tricosane. The termination of LLV immiscibility occurs with n-penta-cosane.

In a previous study, Zarah et al. (1974) reported on the three-phase liquid—liquid—vapor phase equilibria of the ternary mixture CO 2 +n -butylbenzene+n-eicosane, using a combination of stoichiometric and sampling experiments. In addition to identifying some of the boundaries of the three-phase surface and measuring the selectivity of the hydrocarbons between the two liquid phases, they reported the rather unusual phenomenon of density inversion of the two liquid phases at ambient temperatures for systems rich in n-butylbenzene vis-a-vis n-eicosane. In this present study, performed using only stoichiometric means but with visual cell pressure discrimination of ± 70 Pa, achieved by coupling a dead weight gauge to a differential pressure transducer, we (1) complete the identification of all the boundaries of the three-phase surface extending from the CO 2 +n-eicosane binary liquid—liquid—vapor locus, (2) report the liquid phase compositions of all the components, not just the hydrocarbon liquid—liquid selectivity, and (3) show that the apparent “density inversion” is instead a switch of the system from one type of consolute point locus to another, these loci being separated by a lower critical end point (LCEP).

The ability of CO/sub 2/ to induce partial miscibility in hydrocarbons suggests separation processes with liquid CO/sub 2/ as a selective solvent. Its potential utility in this respect is attractive because of its availability and other desirable properties like low toxicity and noncorrosiveness. The phase-equilibria behavior of the binary system CO/sub 2/-2-methylnaphthalene was studied for liquid-vapor, solid-liquid-vapor, and liquid-liquid-vapor systems. The liquid-liquid-vapor equilibria of the ternary system CO/sub 2/-2-methylnaphthalene-n-decane were studied in detail. (17 refs.)

This study proposes a process for extracting high-molecular-weight hydrocarbons from a solid phase in equilibrium with a liquid hydrocarbon phase using methane pressurization. An application for this process could be the removal of high-molecular-weight hydrocarbons from a reservoir on which primary and secondary recovery procedures have been performed. The presence of methane under pressure will not only increase dissolution of solid n-dotriacontane, but also reduce the viscosity of the liquid phase substantially through its dissolution in the liquid phase. With methane as the extractive agent in this process, the process is further aided by the fact that the methane in solution can be easily outgassed and recovered once the liquid phase is removed from the system. (21 refs.)

The three-phase liquid-liquid-vapor (L/sub 1/-L/sub 2/-V) phase equilibria behavior of the ternary mixture nitrogen + methane + n-heptane is presented, with special attention directed toward identifying the boundaries of the three-phase region. This ternary system has a constituent binary mixture, methane + n-heptane, which exhibits L/sub 1/-L/sub 2/-V immiscibility. The presence of nitrogen creates a three-sided L/sub 1/-L/sub 2/-V region extending in pressure-temperature space down in temperature, over a range of 169-192 {Kappa}, from the binary L/sub 1/-L/sub 2/-V locus. The other two boundaries of the three-phase region are type {Kappa} point (L/sub 1/-L/sub 2/=V) and Q point (S-L/sub 1/-L/sub 2/-V) loci. Liquid-phase compositions and molar volumes are reported as a function of temperature and pressure within the three-phase region and along the boundaries.

The 3-phase liquid-liquid-vapor loci of 4 binary CO/sub 2/-n-paraffin systems (n-dodecane, n-tridecane, n-tetradecane, n-pentadecane) are studied, and temperature, pressure, and molar volumes and composition of both liquid phases are reported. It is within this group of n-paraffins that the nature of the upper critical end point for the CO/sub 2/-containing binary systems changes with increasing carbon number from an upper critical solution (temperature) point where L/sub 1/ and L/sub 2/ phases become critical in presence of vapor phase to a K point, where L/sub 2/ and vapor phases become critical in the presence of L/sub 1/ phase. These 4 loci are compared with earlier obtained loci on CO/sub 2/-n-decane and CO/sub 2/-n-elcosane.

Pressure, temperature, liquid-phase molar volumes, and liquid-phase compositions are presented aong the solid--liquid--vapor loci for binary systems of the solvent ethane with the solutes 2-methylnaphthalene and naphthalene and propane with the solutes n-decane and n-dodecane. The data were taken employing cryoscopic techniques over a liquid compositional range from solute-rich solutions to very dilute solute solutions. The liquid compositional data when represented as a logarithm of solute composition vs. T/sub R//T are smooth curves exhibiting three distinct types of solid--liquid--vapor phase behavior, the type depending on the solute. The curves become quite linear in the lower temperature range. The standard deviations of the liquid composition data are 2.95% for the ethane--2-methylnaphthalene system, 1.52% for the ethane--naphthalene system, 1.95% for the propane--n-decane system, and 1.85% for the propane--n-dodecane system. 2 figures, 4 tables.

This study presents data on the binary system CO/sub 2/-n-eicosane and the ternary system CO/sub 2/-n-decane-n-eicosane as an extractive agent. The initial choice of a paraffinic mixture in the ternary system was based on the desire to understand better the phase behavior of CO/sub 2/-paraffin systems: the long-range plan is to study diverse hydrocarbon mixtures, e.g., aromatic-paraffinic, with CO/sub 2/ to establish broad selectivity criteria which would aid in separational process design for petroleum fractions in general.

The authors have for some time been conducting an extensive study of the solid-liquid-vapor phase equilibria behavior of binary and ternary prototype systems pertinent to the problem of solids formation in LNG vapor-liquid systems. The formation of solids during the liquefaction processing of natural gas can form coatings on surfaces of heat exchangers and foul expansion devices, requiring the unit to be shut down for cleaning and/or repair.