Vapor‐liquid equilibria with the redlich‐kwong equation of state

Joffe, Joseph; Schroeder, George M.; Zudkevitch, David

doi:10.1002/aic.690160332

Cited by 70 publications

(18 citation statements)

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“…To establish ic, for polar compounds, two densities must be known while for nonpolar substances only one such value is needed. Despite the similarity of eq 3 and 7 , it was noted by Joffe and Zudkevitch (87) that parameter + + rarely has the same value as w , the acentric factor.…”

Section: (2)mentioning

confidence: 90%

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Saturated liquid densities of polar and nonpolar pure substances

Campbell¹,

Thodos²

1984

Ind. Eng. Chem. Fund.

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Experimental information available in the literature for the density behavior of the saturated liquid state of 46 nonpolar and polar substances has been modeled according to the expression, pR = 1 + a( 1 -T,)"' + p( 1 -T,)" , in which pR is the ratio of the density at reduced temperature T , to the critical density. This relationship has been found to apply over the complete range between the triple point and the critical point. Exponent rn is a universal constant (rn = I*). The critical constants and normal boiling points are needed to establish a, p, and n for nonpolar substances. For polar substances, the dipole moment is also required. Saturated liquid densities calculated with correlated values of a, p, and n have been compared with corresponding experimental measurements to yield an overall average deviation of 0.83% (4284 points) for the 46 substances used in this development. This generalized treatment has been applied to 16 additional substances to yield for them an average deviation of 1.14 % (669 points).The ability to predict saturated liquid densities for elements and compounds continues to play an important role in the treatment of thermodynamic properties. Although the calculation of such densities is possible through the use of an equation of state more often than not, the calculated saturated densities are not in good agreement with corresponding experimental measurements. Rather than relying on an equation of state to calculate saturated liquid densities, it is perhaps more expeditious to utilize a relationship that applies directly to the saturated liquid state. Early attempts express the dependence of density in the form of first, second, and third degree polynomials in temperature (82). Although the form of such relationships proves satisfadory for temperatures approaching the normal boiling point, it does not accommodate the density behavior at higher temperatures, particularly near the critical point.Riedel (161) presented a generalized relationship for the reduced saturated liquid density in terms of reduced temperature as follows PR = 1 + 0.85(1 -TR) + (0.53 + 0.2ac)(1 -TR)"3 (1) Equation 1 is applicable to nonpolar and nonassociating polar liquids between their triple points and critical points. The Riedel factor, a, = (d In PR/d In TR)TR=l.oo, has been shown by Reid and Sherwood (160) to relate to the Pitzer acentric factor, w , as follows (2)Thus, by substitution, eq 1 may be expressed in terms of w through the relationship w = 0.2O3(ac -7.00) + 0.242Equation 3 is somewhat more convenient to apply than eq 1, since values of w are more accessible than corresponding values of ac.Yen and Woods (222) investigated the density behavior of 62 pure compounds, whose critical compressibility factors range from z, = 0.21 to z, = 0.29, and proposed the relationship /JR = 1 + A(1 -TR)'I3 + B(1 -TRI2l3 + D(1 -TR)4'3where A , B, and D are given as third-order polynomials in 2,. These investigators reported an average deviation of 2.1% (693 points) for the 62 substances.

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Section: (2)mentioning

confidence: 90%

“…Joffe and Zudkevitch (87) extended the development of Riedel (161) given by eq 3 to express the dependence of densities for both polar and nonpolar substances between their triple points and their critical points as follows…”

Section: (2)mentioning

confidence: 99%

Saturated liquid densities of polar and nonpolar pure substances

Campbell¹,

Thodos²

1984

Ind. Eng. Chem. Fund.

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“…Out of many evolutions, as mentioned before, the Soave-Redlich-Kwong (SRK) [1] and the Peng-Robinson (PR) [2] versions have been the most successful in vapor-liquid equilibria calculations of conventional as well as non-conventional mixtures of fluids. The major modifications that have taken place are: modifications of the second or the attractive term and/or introduction of a temperature dependence to the parameter a as suggested by Zudkevitch and Joffe [14], Joffe et al [15] and Chang and Lu [16]. In Tab.…”

Section: The Peng-robinson and Soave-redlich-kwong Equations Of Statementioning

confidence: 96%

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Ghosh¹

1999

Chem. Eng. Technol.

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Knowledge of vapor-liquid equilibria is essential for chemical process design. Development of algebraically simple cubic equations of state, particularly Peng-Robinson and Soave-Redlich-Kwong equations of state has encouraged vapor-liquid equilibria calculation using the equation of state approach. To extend applicability to complex mixtures, several modifications to these equations of state were proposed. Also, many new mixing rules have been developed besides the already existing ones that incorporate excess free energy models. Some of these EoS/G E models are found to be applicable to complex systems in which the components can be highly polar, differ vastly in size or may be forming association. In spite of a large number of publications on this field, this subject is still open for further research. In this article, an overview on the work done using the most successful of the cubic equations of state, i.e., Peng-Robinson and Soave-Redlich-Kwong equations of state is presented. In the later part of this article, VLE predictions (using these two equations of state) of some interesting systems like water/hydrocarbon mixtures, polymer solutions, electrolyte solutions and refrigerant mixtures are discussed. The objective is to present the available information for ready reference that will prove to be useful from a designers point of view. It is seen from the existing literature that with a proper choice of equation of state and mixing rule based on the available knowledge on the properties of the system of interest, VLE of highly complex systems can be predicted with accuracy. Several comparative studies that are cited here (and discussed) will help the designer to pick-up the right combination for the system under investigation.

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“…In 1954, R i i l ( 2 ) considered only the saturated-liquid state and proposed the generalized relationship P R = 1 + 0.85(1 -TR) + (0.53 + O.2ac)(l -TR)l13 (3) where pR is the reduced density and the Riedel factor cy, = (d In P,/d In TR)TR=l.oo. Replacement of a, through the relationship w = 0.2O3(ac -7.90) + 0.242, given by Sherwood and Reid (3), transforms eq 3 to the expression pR = 1 + 0.85(1 -T,) + (1.6916 + 0.9846~)(1 -r,)lI3 (4) where the acentric factor w = -log PRITR=0.700 -1.000. Riedel's method expressed through eq 3 and 4 is claimed to predict reliable density values for both nonpolar and polar substances, but fails to accommodate polar associating liquids.…”

mentioning

confidence: 99%

“…Riedel's method expressed through eq 3 and 4 is claimed to predict reliable density values for both nonpolar and polar substances, but fails to accommodate polar associating liquids. To extend the method of Riedel to include polar associating liquids, Joffe and Zudkevitch (4) replace the factor w in eq 4 with the tem- peraturedependent function, $, to express reduced density as follows:…”

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confidence: 99%

Prediction of saturated-liquid densities and critical volumes for polar and nonpolar substances

Campbell¹,

Thodos²

1985

J. Chem. Eng. Data

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The parameter Z,, advanced by Spencer and Danner for the calculation of saturated-llquld densltles through the relatlonshlp p = ~P,/(RT~R*l+(l-TnP"), has been found to vary wHh temperature over the complete range between the trlple polnt and the crltlcal polnt. Thls dependence has been accounted for by replacing Z,. by the temperature-dependent function a + p(1 -TR), where a and p are constants unique to a substance. Data for 62 substances have been used to develop reiatlonships for cy and p which predlct saturated-liquid dermltles for quantum, nonpolar, polar, and assoclated polar llqulds with an overall average devlatlon of 1.32% (4942 polnts). Nlne additlonal polar and nonpolar compounds were employed to test the relablUty of thls method. When applied at the crltlcal point, thls development deflnes the crltlcal volume as Y, = aRT,/P,. Calculated crltlcal volumes ylelded an average devlatlon of 2.14% (68 substances), when compared to actual values available In the Ilterature.The prediction of densities for the saturated-liquid state continues to play an important role in the calculation of thermodynamic properties. Watson (1) in 1943 was the first to attempt a generalization of the density behavior for the liquid state by introducing the w factor through the relationshipwhere w = P,/(Z/?T,).For this development, Watson utilizes the PVT behavior of isopentane and presents a graphical relationship for this factor against T, for different parameters of P, . Unfortunately, this factor is not a truly generalized function of P , and T, since it can vary by as much as 20% between different compounds existing at identical reduced conditions. In order to predict density more accurately, Watson suggests the use of a single actual density p1 so that the ratioapplies. I n eq 2, the factor w1 corresponds to the pressure and temperature conditions associated with pl. In 1954, R i i l ( 2 ) considered only the saturated-liquid state and proposed the generalized relationshipwhere pR is the reduced density and the Riedel factor cy, = (d In P,/d In TR)TR=l.oo. Replacement of a, through the relationship w = 0.2O3(ac -7.90) + 0.242, given by Sherwood and Reid (3), transforms eq 3 to the expression pR = 1 + 0.85(1 -T,) + (1.6916 + 0.9846~)(1 -r,)lI3 (4) where the acentric factor w = -log PRITR=0.700 -1.000. Riedel's method expressed through eq 3 and 4 is claimed to predict reliable density values for both nonpolar and polar substances, but fails to accommodate polar associating liquids. To extend the method of Riedel to include polar associating liquids, Joffe and Zudkevitch (4) replace the factor w in eq 4 with the tem-0021-956818511730-0102$01.50/0 METHANE M.16.043 T,=190.555 K P,=45.36atm + Jenien and Kurata (141 1 API Prolect 44 191 4 Bloomer and Parent (101 a McClune (15) Cardom (Ill * Pan, Mady and Miller (I61 0 Goodwin and Rydr (12) 0 Rodosevich and Miller (17) 0 Terry,Lynch, Bunclark. Monsell and Slaveley (18) 0,301 + Hoyner and H m (13) peraturedependent function, $, to express reduced density as follows: p, = 1 + 0.85(1 -...

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Vapor‐liquid equilibria with the redlich‐kwong equation of state

Cited by 70 publications

References 9 publications

Saturated liquid densities of polar and nonpolar pure substances

Saturated liquid densities of polar and nonpolar pure substances

Prediction of Vapor-Liquid Equilibria Using Peng-Robinson and Soave-Redlich-Kwong Equations of State

Prediction of saturated-liquid densities and critical volumes for polar and nonpolar substances

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