8' NonIdeal VLE to Moderate Pressure SVNA 14'1

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

2
g, f Formulation of VLE Problems

• To this point, Raoults Law was only description
  we had for VLE behaviour
• We have repeatedly observed that calculations
  based on Raoults 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 Raoults Law fails.

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).

4
Non-Ideal VLE to Moderate Pressures

• Sources of Data
• 1. Vapour pressure Antoines 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

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).

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

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 ?i1, calculate an approximate PBUBL
• use this estimate to calculate an approximate ?i
• repeat PBUBL and ?i calculations until solution
  converges.

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

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.