Question

# n-butane vapor and liquid are in equilibrium (boiling) at 18.66 bars. Use the Peng Robinson EOS...

n-butane vapor and liquid are in equilibrium (boiling) at 18.66 bars. Use the Peng Robinson EOS to determine the saturated liquid and saturated vapor molar volumes. Also determine the saturated liquid molar volume using the Rachett equation. In addition, use the Pitzer correlation for the Virial EOS to estimate the saturated vapor molar volume.

Antoine coefficients for: log10(Psat[mmHg])=A-B/(T[oC]+C)

Antoine constants are A=6.80776 B=935.77 C=238.789

For the given P=18.66 bar=18.66*760 mm Hg=14181.6 mm hg

T sat calculated from Antoine equation =113 oC=273+113=386 K

The physical properties of n-butane are Tc=425 K,Pc=37.96 bar Vc=255 cm3/mol Zc=.274, acentric factor(w)=0.2

a) Peng-Robinson (P-R) equation of state has the following form:

R T                             a(T)

P       =    -----------      -    -------------------------------                                                          (1)

v - b                v (v + b) + b (v - b)

Here, R is the gas constant, P is the absolute pressure, T is the absolute temperature, v is the molar volume, and b and a(T) are given by:

R Tc

b       =    0.07780 ----------                                                                                        (2)

Pc

R 2Tc 2

a(T) =    0.45724 ------------- a(T)                                                                            (3)

Pc

a(T) =    [1 + k (1 - ( T/Tc ) 0.5) ]2                                                                       (4)

k                   =    0.37464   +   1.54226 w   -   0.26992 w2                                                              (5)

Here, Tc is the critical (absolute) temperature, Pc is the critical (absolute) pressure, and w is the Pitzer acentric factor

​a(T)=21797395 k=.6723 b=72.42

Substituting these in equation 1 we get which require iterative procedure

We get sat voume of gas= 1185 cm3/mol

Sat liquid volume =136.2 cm3/mol

b) Rachett equation:

Vsat=Vc Zc (1-Tr)2/7

Tr=T/Tc= 386/425=0.9082

= 255*0.274(1-0.9082)2/7= 35.31 cm3/mol

c)

Pitzer type correlations:

Z=Z0+wZ1

Pr= 18.66/37.96=0.4915 ,Tr= 0.9082

At these reduced conditions Z0+wZ1 from Lee kesseler tables we have

Z0=0.5384   Z1= -0.1161 and

Z=0.5384+(0.2*-0.1161)=0.51518

Z=PV/RT=V=RTZ/P=83.14*386*0.51518/18.66=886 cm3/mol

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