Page 63 - Separation process principles 2

28 Chapter 2 Thermodynamics of Separation Operations

Heat transfer in and out or out of the system are denoted by Q, and shaft work cross-
Qin, T, Qou, ing the boundary of the system is denoted by Ws. At steady
state, if lunetic, potential, and surface energy changes are
neglected, the first law of thermodynamics (also referred to
as the conservation of energy or the energy balance), states
n, zi, T, P, h, s, b,U that the sum of all forms of energy flowing into the system
Separation
equals the sum of the energy flows leaving the system:
(system)
(stream enthalpy flows + heat transfer
Streams out + shaft ~ork)~,,,,, - (stream enthalpy flows
ASi,,. LW n, zi, T, P, h, s, b,u
+ heat transfer + shaft system

In terms of symbols, the energy balance is given by Eq. (1) in
Table 2.1, where all flow rate, heat transfer, and shaft work
(Ws)in (WJout terms are positive. Molar enthalpies may be positive or neg-
Shaft work in and out ative depending on the reference state.
Figure 2.1 General separation system. All separation processes must satisfy the energy balance.
Inefficient separation processes require large transfers of
heat andlor shaft work both into and out of the process; effi-
more product streams that flow out of the system. For all cient processes require smaller levels of heat transfer and/or
these streams, we denote the molar flow rates by n, the com- shaft work. The first law of thermodynamics provides no
ponent mole fractions by zi, the temperature by T, the pres- information on energy efficiency, but the second law of ther-
sure by P, the molar enthalpies by h, the molar entropies by modynamics (also referred to as the entropy balance), given
s, and the molar availabilities by b. If chemical reactions by Eq. (2) in Table 2.1, does. In words, the steady-state
occur in the process, enthalpies and entropies are referred to entropy balance is
the elements, as discussed by Felder and Rousseau [2]; oth- 1
(Stream entropy flows
erwise they can be referred to the compounds. Heat flows in
+ entropy flows by heat transfer),,,;,, system
- (stream entropy flows
+ entropy flows by heat
Table 2.1 Universal Thermodynamic Laws for a Continuous, = production of entropy by the process
Steady-State, Flow System
I11 the entropy balance equation, the heat sources and
Energy balance:
sinks in Figure 2.1 are at absolute temperatures T,. For ex-
(1) (nh + Q + W,) - (nh + Q + W,) = 0 ample, if condensing steam at 150°C supplies heat, Q, to the
out of in to
system system reboiler of a distillation column, Ts = 150 + 273 = 423 K.
Entropy balance: If cooling water at an average temperature of 30°C removes
heat, Q, in a condenser, T, = 30 + 273 = 303 K. Unlike the
(2) (ns + g) - (ns + g) =
energy balance, which states that energy is conserved, the
out of in to
system system entropy balance predicts the production of entropy, ASi,,
Availability balance: which is the irreversible increase in the entropy of the uni-
verse. This term, which must be a positive quantity, is a
quantitative measure of the thermodynamic inefficiency of a
system process. In the limit, as a reversible process is approached,
- [nb+ Q (1 - $) +ws] =LW ASi, tends to zero. Note that the entropy balance contains
out of no terms related to shaft work.
system
Although AS;, is a measure of energy inefficiency, it is
Minimum work of separation:
difficult to relate to this measure because it does not have the
units of energyltime (power). A more useful measure or
out of I" to
system system process inefficiency can be derived by combining (1) and (2)
Second-law efficiency: in Table 2.1 to obtain a combined statement of the first and
second laws of thermodynamics, which is given as (3) in
Table 2.1. To perform this derivation, it is first necessary to
define an infinite source of or sink for heat transfer at the ab-
where b = h - Tos = availability function
solute temperature, T, = To, of the surroundings. This tem-
LW = ToASix = lost work
perature is typically about 300 K and represents the largest