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Calculating  i v from the Virial EOS SVNA 11.6

Calculating  i v 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

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Calculating  i v from the Virial EOS SVNA 11.6

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  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; Bij=Bji Lecture 17

  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 3.50[3.65] and 3.51[3.66]at Tr=T/Tcij. Lecture 17

  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 Lecture 17

  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] Lecture 17

  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: Lecture 17

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