Calculating iv from the Virial EOS SVNA 11'6

1
Calculating ?iv from the Virial EOS SVNA 11.6

• We have used the virial equation of state to
  calculate the fugacity and fugacity coefficient
  of pure, non-polar gases at moderate pressures.
• Under these conditions, it represents non-ideal
  PVT behaviour of pure gases quite accurately
• We will generalize the virial equation to allow
  the calculation of mixture fugacities.
• For mixtures, we use the truncated virial
  equation
• where B is a function of temperature and
  composition according to
• (11.57)11.61
• Bij characterizes binary interactions between i
  and j BijBji

2
Calculating ?iv from the Virial EOS

• Pure component coefficients (B11 B1, B22
  B2,etc) are calculated as previously and cross
  coefficients are found from
• (11.66)11.69b
• where,
• and
• (11.67-71)
• 11.70-73
• Bo and B1 for the binary pairs are calculated
  using the standard equations 3.503.65 and
  3.513.66at TrT/Tcij.

3
Calculating ?iv from the Virial EOS

• We now have an equation of state that represents
  non-ideal PVT behaviour of mixtures
• or
• We are equipped to calculate mixture fugacity
  coefficients from equation 11.60

4
Calculating ?iv from the Virial EOS

• The result of differentiation is
• (11.61)11.64
• with the auxilliary functions defined as
• In the binary case, we have
• (11.59)11.63a
• (11.60)11.63b

5
6. Calculating ?iv from the Virial EOS

• Method for calculating mixture fugacity
  coefficients
• 1. For each component in the mixture, look up
• Tc, Pc, Vc, Zc, ?
• 2. For each component, calculate the virial
  coefficient, B
• 3. For each pair of components, calculate
• Tcij, Pcij, Vcij, Zcij, ?ij
• and
• using Tcij, Pcij for Bo,B1
• 4. Calculate ?ik, ?ij and the fugacity
  coefficients from