Now we introduce a new concept: fugacity

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Presentation transcript:

Now we introduce a new concept: fugacity When we try to model “real” systems, the expression for the chemical potential that we used for ideal systems is no longer valid We introduce the concept of fugacity that for a pure component is the analogous (but is not equal) to the pressure

We showed that: Pure component i, ideal gas Component i in a mixture of ideal gases Let’s define: For a real fluid, we define Fugacity of pure species i

Residual Gibbs free energy Valid for species i in any phase and any condition

Since we know how to calculate residual properties… (section 6.2) Eqn. 6.49) Zi from an EOS, Virial, van der Waals, etc

examples From Virial EOS From van der Waals EOS General form, see eqn. 11.37 for cubic EOS. First solve for Zi in the vapor or in the liquid phase

For cubic EOS For the vapor phase: 3.52 For the liquid phase: 3.56 See Table 3.1 for parameters

Page 98

Fugacities of a 2-phase system One component, two phases: saturated liquid and saturated vapor at Pisat and Tisat What are the equilibrium conditions for a pure component?

Fugacity of a pure liquid at P and T

Fugacity of a pure liquid at P and T

example For water at 300oC and for P up to 10,000 kPa (100 bar) calculate values of fi and fi from data in the steam tables and plot them vs. P At low P, steam is an ideal gas => fi* =P* Get Hi* and Si* from the steam tables at 300oC and the lowest P, 1 kPa Then get values of Hi and Si at 300oC and at other pressures P and calculate fi (P)

Problem For SO2 at 600 K and 300 bar, determine good estimates of the fugacity and of GR/RT. SO2 is a gas, what equations can we use to calculate f = f/P Find Tc, Pc, and acentric factor, w, Table B1, p. 680 Calculate reduced properties: Tr, Pr Tr=1.393 and Pr=3.805

What equations can we use to determine fi (gas phase)

Generalized correlations: fugacity coefficient Tables E13 to E16 Lee-Kessler

High P, high T, gas: use Lee-Kessler correlation From tables E15 and E16 find f0 and f1 f0 = 0.672; f1 = 1.354 f = f0 f1w = 0.724 f = f P = 0.724 x 300 bar = 217.14 bar GR/RT = ln f = -0.323

Problem Estimate the fugacity of cyclopentane at 110oC and 275 bar. At 110 oC the vapor pressure of cyclopentane is 5.267 bar. At those conditions, cyclopentane is a high P liquid

Find Tc, Pc, Zc,, Vc and acentric factor, w, Table B1, p. 680 Calculate reduced properties: Tr, Prsat Tr = 0.7486 and Prsat = 0.117 At P = Psat we can use the virial EOS to calculate fisat Eqn. 11.68 Eqns. 3.65 and 3.66

Get the volume of the saturated liquid phase, Rackett equation fisat = 0.9 P-correction term: Get the volume of the saturated liquid phase, Rackett equation Eqn. 3.72, p. 109 Vsat = 107.55 cm3/mol f = 11.78 bar