7. Excess Gibbs Energy Models

1
7. Excess Gibbs Energy Models

• Practicing engineers find most of the
  liquid-phase information needed for equilibrium
  calculations in the form of excess Gibbs Energy
  models. These models
• reduce vast quantities of experimental data into
  a few empirical parameters,
• provide information an equation format that can
  be used in thermodynamic simulation packages
  (Provision)
• Simple empirical models
• Symmetric, Margules, vanLaar
• No fundamental basis but easy to use
• Parameters apply to a given temperature, and the
  models usually cannot be extended beyond binary
  systems.
• Local composition models
• Wilsons, NRTL, Uniquac
• Some fundamental basis
• Parameters are temperature dependent, and
  multi-component behaviour can be predicted from
  binary data.

2
Excess Gibbs Energy Models

• Our objectives are to learn how to fit Excess
  Gibbs Energy models to experimental data, and to
  learn how to use these models to calculate
  activity coefficients.

3
Margules Equations

• While the simplest Redlich/Kister-type expansion
  is the Symmetric Equation, a more accurate model
  is the Margules expression
• (12.9a)
• Note that as x1 goes to zero,
• and from Lhopitals rule we know
• therefore,
• and similarly

4
Margules Equations

• If you have Margules parameters, the activity
  coefficients are easily derived from the excess
  Gibbs energy expression
• (12.9a)
• to yield
• (12.10ab)
• These empirical equations are widely used to
  describe binary solutions. A knowledge of A12
  and A21 at the given T is all we require to
  calculate activity coefficients for a given
  solution composition.

5
van Laar Equations

• Another two-parameter excess Gibbs energy model
  is developed from an expansion of (RTx1x2)/GE
  instead of GE/RTx1x2. The end results are
• (12.16)
• for the excess Gibbs energy and
• (12.17a)
• (12.17b)
• for the activity coefficients.
• Note that as x1?0, ln?1? ? A12
• and as x2 ? 0, ln?2? ? A21

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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

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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.

8
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).

9
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