Page 65 - Separation process principles 2

30 Chapter 2 Thermodynamics of Separation Operations

EXAMPLE 2.1 Alternatively, compute lost work from an availability balance
around the entire distillation system. From (3), Table 2.1,
For the propylene-propane separation of Figure 1.12, using the fol- where the availability function, b, is defined near the bottom of
lowing thermodynamic properties for certain streams, as estimated Table 2.1,
from the Soave-Redlich-Kwong equation of state discussed in Sec-
tion 2.5, and the relations given in Table 2.1, compute in SI units: LW = n ~ + bQR(~ - To/TR)
~
b
~
(a) The condenser duty, Qc - n ~ - n~bs - Qc(l - To/Tc)
= 272.2[13,338 - (303)(-4.1683)]
(b) The reboiler duty, QR + 29,789,000(1 - 3031378)
(c) The irreversible entropy production, assuming 303 K for the - 159.2[12,243 - (303)(-13.8068)]
condenser cooling-water sink and 378 K for the reboiler steam - 113[14,687 - (303)(-2.3886)]
source - 29,811,000(1 - 3031303)
= 5,529,000 kJih (same result)
(d) The lost work, assuming To = 303 K
(e) The minimum work of separation
(e) Compute the minimum work of separation for the entire distil-
(f) The second-law efficiency lation system. From (4), Table 2.1,
Phase Enthalpy (h), Entropy (s),
Stream Condition kJ/kmol kT/kmol-K
Feed (F) Liquid 13,338 -4.1683
Overhead vapor (OV) Vapor 24,400 24.2609
Distillate (D) and reflux (R) Liquid 12,243 -13.8068
Bottoms (B) Liquid 14,687 -2.3886
(f) Compute the second-law efficiency for the entire distillation
SOLUTION system. From (5), Table 2.1,
Place the condenser (C) cooling water and the reboiler (R) steam
outside the distillation system. Thus, Qc and QR cross the boundary
of the system. The following calculations are made using the
stream flow rates in Figure 1.12 and properties above.
(a) Compute condenser duty from an energy balance around the
condenser. From (1), Table 2.1, noting that the overhead-vapor
molar flow rate is given by nov = nR + nD and hR = hD, the This low second-law efficiency is typical of a difficult distilla-
condenser duty is tion separation, which in this case requires 150 theoretical
stages with a reflux ratio of almost 15 times the distillate rate.

2.2 PHASE EQUILIBRIA
(b) Compute reboiler duty from an energy balance around the en-
tire distillation operation. (An energy balance around the re- Analysis of separations equipment frequently involves the
boiler cannot be made because data are not given for the boilup assumption of phase equilibria as expressed in terms of
rate.) From (I), Table 2.1, Gibbs free energy, chemical potentials, fugacities, or activi-
ties. For each phase in a multiphase, multicomponent sys-
tem, the total Gibbs free energy is

(c) Compute the production of entropy from an entropy balance where Ni = moles of species i. At equilibrium, the total G for
around the entire distillation system. From Eq. (2), Table 2.1,
all phases is a minimum, and methods for determining this
minimum are referred to as free-energy miniinization tech-
As,, = ~DSD + nBsB + QcITc - nFsF - QRITR
= 159.2(-13.8068) + 113(-2.3886) + 29,811,000/303 niques. Gibbs free energy is also the starting point for the
- 272.2(-4.1683) - 29,789,0001378 derivation of commonly used equations for expressing
= 18,246 kJih-K phase equilibria. From classical thermodynamics, the total
differential of G is given by
(d) Compute lost work from its definition at the bottom of Table 2.1:
C
LW = To AS,, dG = -SdT + VdP + Pid~i (2-3)
= 303(18,246) = 5,529,000 kJ/h i=l