lecture1-notes-2009 - 28420 Separation Processes Chapter 1...

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1 28420 Separation Processes 1 gives an introductory discussion of separations processes. Chapter 2 of S&H summarizes a great number of thermodynamic models and property relationships. The following pages are thought to be a supplement emphasizing practice - in addition to reading the text. I have tried to be consistent with the notation employed by S&H whenever possible. If I have not succeeded, let me know. Thermodynamics of Separation Processes An essential task in the design and evaluation of separation units is the calculation of phase equilibrium. In calculating the equilibrium compositions of phases at equilibrium we encounter two main categories of calculations Saturation points . Particularly bubble points and dew points, where we determine either the boiling pressure/temperature of a liquid or the condensation temperature/pressure of a vapor PT-flash calculations, where the amounts and compositions of phases at equilibrium at a given temperature and pressure are calculated Appendix A gives an overview of saturation point calculations and the PT-flash problem is summarized in a subsequent section. Essential aspects of the calculations is that we need a thermodynamic model to predict the non-ideality of the fluid (pure or mixture) to obtain a good result. Traditionally chemical engineers have taken two approaches to calculating phase equilibria: 1. The equation of state (EOS) approach, also called the ( , )-approach, and 2. The activity coefficient approach, or ( , )-approach Both have advantages and disadvantages. We will briefly reacquaint ourselves with these two methods by means of a few exercises. 1 Seader J.D., Henley E.J., 2006. “Separation Process Principles”. 2 nd ed., Wiley.
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2 Activity Coefficient Approach The activity coefficient approach - or ( , )-approach – is an approach to calculating VLE using an excess Gibbs free energy model for the liquid phase (Figure 1) and an EOS for the vapour phase. It is based on the equilibrium equations 2 i s i s i s i i i iV i iL iV POY ) T , P ( ) T ( P ) , T ( x P ) , P , T ( y ) , P , T ( f ) , P , T ( f : i φ γ = φ = 2200 x y x y or in a slightly more compact notation - - φ φ = Φ = γ = Φ RT ) P P ( V exp where ) C , 1 i ( P x P y s i L i s i iV i s i i i i i These equations have many factors. Application of this formulation requires assumptions about fluid behavior. The three most common sets of assumptions are captured by the model hierarchy outlined in Table 1. Table 1 . Model Hierarchy Model i i Inherent assumptions Raoult’s law = 1 = 1 Liquid phases: Incompressible Ideal solution Vapor phases: Ideal gas Modified Raoult’s law = 1 1 Liquid phases: Incompressible Vapor phases: Ideal gas Full rigorous 1 1 None 2 Bold x and y is short notation for mole fractions: x ~ [x 1 , x 2 , x 3 , …, x C ] EOS : Vapor l e d o m G : Liquid E - Figure 1 . The gamma-phi approach.
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3 Modified Raoult’s law is the most frequently applied version. That version requires a model for the
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lecture1-notes-2009 - 28420 Separation Processes Chapter 1...

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