New Two-Parameter Local-Composition Equation Capable of Correlating Partial Miscibility

Palmer, Donald A.; Smith, Buford D.

doi:10.1021/i260041a022

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…Tractable equations for the excess thermodynamic functions that are suitable for a good representation of partial miscibilities include those by Bruin and Prausnitz (1971), Palmer and Smith (1972), and Renon and Prausnitz (1968). Reliable computing methods for the determination of the parameters involved in these equations are therefore essential to profit fully from the available solubility data which, as a rule, are sparse.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the Free Energy Equation Parameters from Ternary Liquid-Liquid Equilibrium Data

Várhegyi¹,

Eon²

1977

Ind. Eng. Chem. Fund.

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Section: Introductionmentioning

confidence: 99%

Calculation of the Free Energy Equation Parameters from Ternary Liquid-Liquid Equilibrium Data

Várhegyi¹,

Eon²

1977

Ind. Eng. Chem. Fund.

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“…where we take x = 8 and Y and R are given by equations (11) and (12). The value of COMM, has been therefore chosen by best fit of the experimental values of ~ by equation (14) over the whole range of 0_< X M _< 1.…”

Section: Binary Activity Factormentioning

confidence: 99%

“…An important feature of Wilson's and the NRTL equations is that they use only parameters which can be obtained from binary mixture data (Van Laar's equation requires in addition a ternary interaction parameter). Many modifications of these two equations have been suggested [8][9][10][11][12][13] in order to minimize the number of parameters (at least two) to be determined from each binary system. Indeed, the determination of these parameters by best fit procedures is very time consuming and gives rise to different solutions [14][15][16] depending upon the initial guess when a search method is used.…”

Section: Introductionmentioning

confidence: 99%

A stochastic theory of non-ideal behaviour

Termonia

1979

Molecular Physics

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The stochastic theory described in Part I is extended here to the case of a ternary system [A, B, C] at equilibrium. Using the microenvironment and the quasi-chemical (QC) approximations, we derive equations to estimate the differences in chemical potentials in terms of the three pair interaction parameters O)AB , mAC and OgBc. Alternative equations for calculating these differences have been derived by Bell, using the QC approximation alone. We show that, within the framework of the QC approximation, these estimations are essentially unaffected by our additional microenvironment approximation. Furthermore, the results are in excellent agreement with values obtained with the help of exact equations using computer simulation of ternary lattices at equilibrium.The capability of the theory to predict liquid-liquid equilibria in real ternary systems is examined. Experimental data on binary systems permit us to evaluate the values of the pair interaction parameters 09Aa, mAC and O)Bc. The theory is capable of describing a variety of phenomena encountered in the experiment. The eruption of an island curve with a two-phase region is accounted for by the theory without requiring the addition of a ternary interaction parameter. In all the cases reported, our results are in better agreement with experiment than those obtained from the widely used Van Laar or NRTL equations, which have moreover the weakness of dealing with a relatively large number of parameters. In this connection, it is worth stressing that the three pair interaction parameters o9, used in our theory, represent the reduced interaction energies between molecules of different type. Therefore, if experiments could provide a complete set of values for these interaction energies, our description of a ternary system would constitute a ' zero parameter ' theory.

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“…Sir: Bruin-Prausnitz (1971) and Palmer-Smith (1972) equations have, in comparison with classical NRTL equation, the following advantage: Certain restraining conditions between constants of NRTL equation must be fulfilled if the expressions for threeand more-component systems are to be consistent with Renon-Prausnitz model.…”

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confidence: 99%

Note to Bruin-Prausnitz One-Parameter and Palmer-Smith Two-Parameter Local Composition Equation

Hála¹

1972

Ind. Eng. Chem. Proc. Des. Dev.

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weigh a line drawn through the data very heavily toward the higher end without any consideration of the behavior of the lower end. Examination of the data on Figure 1 shows that the experimental data available for positive (&h/h0) fall reasonably well within the ±20% limits on h. Perhaps Danziger's concern about zero and negative values of (Ah/h0) is exaggerated.Sadek's correlation (Figure 1) was developed in an attempt to establish the major operating parameters affecting heat transfer under transport and to provide some guidance, heretofore unavailable to engineers, for estimating transport line heat transfer rates. It is believed that a step was taken toward achieving that goal by developing the use of the parameter nd2D. Undoubtedly, as in any area of learning, further information will serve to establish the quantitative dependencies more accurately.Literature Cited

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New Two-Parameter Local-Composition Equation Capable of Correlating Partial Miscibility

Cited by 10 publications

References 6 publications

Calculation of the Free Energy Equation Parameters from Ternary Liquid-Liquid Equilibrium Data

Calculation of the Free Energy Equation Parameters from Ternary Liquid-Liquid Equilibrium Data

A stochastic theory of non-ideal behaviour

Note to Bruin-Prausnitz One-Parameter and Palmer-Smith Two-Parameter Local Composition Equation

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