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8. Non-Ideal VLE to Moderate Pressure SVNA 14.1

8. Non-Ideal VLE to Moderate Pressure SVNA 14.1. We now have the tools required to describe and calculate vapour-liquid equilibrium conditions for even the most non-ideal systems. 1. Equilibrium Criteria: In terms of chemical potential In terms of mixture fugacity

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8. Non-Ideal VLE to Moderate Pressure SVNA 14.1

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  1. 8. Non-Ideal VLE to Moderate Pressure SVNA 14.1 • We now have the tools required to describe and calculate vapour-liquid equilibrium conditions for even the most non-ideal systems. • 1. Equilibrium Criteria: • In terms of chemical potential • In terms of mixture fugacity • 2. Fugacity of a component in a non-ideal gas mixture: • 3. Fugacity of a component in a non-ideal liquid mixture: Design Exercise Notes

  2. g, f Formulation of VLE Problems • To this point, Raoult’s Law was only description we had for VLE behaviour: • We have repeatedly observed that calculations based on Raoult’s Law do not predict actual phase behaviour due to over-simplifying assumptions. • Accurate treatment of non-ideal phase equilibrium requires the use of mixture fugacities. At equilibrium, the fugacity of each component is the same in all phases. Therefore, • or, • determines the VLE behaviour of non-ideal systems where Raoult’s Law fails. Design Exercise Notes

  3. Non-Ideal VLE to Moderate Pressures • A simpler expression for non-ideal VLE is created upon defining a lumped parameter, F. • The final expression becomes, • (i = 1,2,3,…,N) 14.1 • To perform VLE calculations we therefore require vapour pressure data (Pisat), vapour mixture and pure component fugacity correlations (i) and liquid phase activity coefficients (i). Design Exercise Notes

  4. Non-Ideal VLE to Moderate Pressures • Sources of Data: • 1. Vapour pressure: Antoine’s Equation (or similar correlations) • 14.3 • 2. Vapour Fugacity Coefficients: Viral EOS (or others) • 14.6 • 3. Liquid Activity Coefficients • Binary Systems - Margules,van Laar, Wilson, NRTL, Uniquac • Ternary (or higher) Systems - Wilson, NRTL, Uniquac Design Exercise Notes

  5. Non-Ideal VLE Calculations • The Pxy diagram to the right • is for the non-ideal system of • chloroform-dioxane. • Note the P-x1 line represents • a saturated liquid, and is commonly BUBL LINE • referred to as the bubble-line. • P-y1 represents a saturated • vapour, and is referred to as the • dew line (the point where a liquid DEW LINE • phase is incipient). Design Exercise Notes

  6. Non-Ideal BUBL P Calculations • The simplest VLE calculation of the five is the bubble-point pressure calculation. • Given: T, x1, x2,…, xn Calculate P, y1, y2,…, yn • To find P, we start with a material balance on the vapour phase: • Our equilibrium relationship provides: • 14.8 • which yields the Bubble Line equation when substituted into the material balance: • or • 14.10 Design Exercise Notes

  7. Non-Ideal BUBL P Calculations • Non-ideal BUBL P calculations are complicated by the dependence of our coefficients on pressure and composition. • Given: T, x1, x2,…, xn Calculate P, y1, y2,…, yn • To apply the Bubble Line Equation: • requires: • ? •  •  • Therefore, the procedure is: • calculate Pisat, and i from the information provided • assume i=1, calculate an approximate PBUBL • use this estimate to calculate an approximate i • repeat PBUBL and i calculations until solution converges. Design Exercise Notes

  8. Non-Ideal Dew P Calculations • The dew point pressure of a vapour is that pressure which the mixture generates an infinitesimal amount of liquid. The basic calculation is: • Given: T, y1, y2,…, yn Calculate P, x1, x2,…, xn • To solve for P, we use a material balance on the liquid phase: • Our equilibrium relationship provides: • 14.9 • From which the Dew Line expression needed to calculate P is generated: • 14.11 Design Exercise Notes

  9. Non-Ideal Dew P Calculations • In trying to solve this equation, we encounter difficulties in estimating thermodynamic parameters. • Given: T, y1, y2,…, yn Calculate P, x1, x2,…, xn • ? • ? •  • While the vapour pressures can be calculated, the unknown pressure is required to calculate i, and the liquid composition is needed to determine i • Assume both parameters equal one as a first estimate, calculate P and xi • Using these estimates, calculate i • Refine the estimate of xi (12.10) and estimate i • Refine the estimate of P • Iterate until pressure and composition converges. Design Exercise Notes

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