Author: admin
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Summary
The essence of the equation of state approach to mixtures is that the equation of state for mixtures is the same as the equation of state for pure fluids. The expressions for Z, A, and U are exactly the same. The only difference is that the parameters (e.g., a and b of the Peng-Robinson equation) are dependent on the composition. That should…
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Strategies for Applying VLE Routines
For some problems, such as generation of a phase diagram, the examples in this chapter can be followed directly. Often, however, it takes some thought to decide which type of VLE routine is appropriate to apply in a given situation. Do not discount this step in the problem solution strategy. Part of the objective of…
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VLE Calculations by an Equation of State
At the end of Section 15.2, the bubble-pressure method was briefly introduced to show how the fugacity coefficients are incorporated into a VLE calculation, without concentrating on the details of the iterations. Section 15.3 offered derivations of formulas for the fugacity coefficients that were presented without proof at the beginning of the chapter. Now, it is time to…
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Differentiation of Mixing Rules
Since a compositional derivative is necessary to obtain the partial molar quantities, and the compositions are present in summation terms, we must understand the procedures for differentiation of the sums. Since all of the compositional dependence is embedded in these terms, if we understand how these terms are handled, we can then apply the results to any equation of…
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Fugacity and Chemical Potential from an EOS
We begin with a reminder that for phase equilibria calculations, that the fugacities of components are needed. The tool that we need for VLE calculations is the K-ratio and an expression for the component fugacity. In Section 10.9 we demonstrated that the component fugacity for an ideal gas component is equal to the partial pressure. In this chapter…
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Mixing Rules for Equations of State
Virial Equation of State The virial equation was introduced for pure fluids in Section 7.4. Previously, we have also given a strategy for relating parameters to composition in Section 12.1. If we extend this mixing rule to the virial equation, which for a binary mixture becomes Similar to our previous discussion, it is understood that B12 is equivalent to B21. The…
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Practice Problems
P14.1. It has been suggested that the phase diagram of the hexane + furfural system can be adequately represented by the Margules one-parameter equation, where ln γi = xj2 · 800/T (K). Estimate the liquid-liquid mutual solubilities of each component in each liquid phase at 298 K. (ANS. ~10% each, by symmetry) P14.2. Suppose the solubility of water in ethyl…
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Solid-Liquid Equilibria
Solid-liquid equilibria (SLE) calculations begin just as VLE and LLE calculations, by equating fugacities. From Eqn. 11.13, . The next step is to equate and derive an equation to solve for temperature or composition depending on the problem statement. We have deliberately avoided substituting , however, as we did for VLE and LLE. This is because pure components below…
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Numerical Procedures for Binary, Ternary LLE
Numerical procedures using Excel and MATLAB are provided in online supplements. The Excel procedure extends Actcoeff.xlsx and explains details on setting up the macro or circular reference for binary or ternary mixtures. The MATLAB Rachford-Rice procedure can be extended more easily to multicomponent mixtures.
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Critical Points in Binary Liquid Mixtures
Referring back to Fig. 14.1, we may wish to find the combination of x1 and A12 where the system just begins to phase-split. This is known as a liquid-liquid critical point. If it is the highest T where two phases exist (called the UCST, upper critical solution temperature), then we must seek x1 where the concavity is equal to zero at only one composition…