Page 64 - Separation process principles 2

2.1 Energy, Entropy, and Availability Balances 29

of coolant associated with the processing plant being is the lost work, LW, which is also called the loss of avail-
analyzed. This might be the average temperature of cooling ability (or exergy), and is defined by
water, air, or a nearby river, lake, or ocean. Heat transfer as-
sociated with this surrounding coolant and transferred from
(or to) the process is termed Qo. Thus, in both (1) and (2) in Lost work is always a positive quantity. The greater its
Table 2.1, the Q and Q/Ts terms include contributions from value, the greater is the energy inefficiency. In the lower
Q, ,d Qo/To, respectively. limit, as a reversible process is approached, lost work tends
The derivation of (3) in Table 2.1 can be made, as shown to zero. The lost work has the same units as energy, thus
by de Nevers and Seader [31, by combining (1) and (2) to making it easy to attach significance to its numerical value.
eliminate Qo. The resulting equation is referred to as an In words, the steady-state availability balance is
availability (or exergy) balance, where the term availability
means "available for complete conversion to shaft work." (Stream availability flows + availability of heat
,,,,,,
+ shaft ~ork)~~,~,~, (stream availability flows
-
ne stream availability function, b, as defined by
+availability of heat + shaft ,,,,,,
= loss of availability (lost work)
is a measure of the maximum amount of stream energy that
For any separation process, lost work can be computed
can be converted into shaft work if the stream is taken to
from (3) in Table 2.1. Its magnitude depends on the extent of
the reference state. It is similar to Gibbs free energy,
process irreversibilities, which include fluid friction, heat
= h - Ts, but differs in that the infinite surroundings tem-
transfer due to finite temperature-driving forces, mass trans-
perature, To, appears in the equation instead of the stream
fer due to finite concentration or activity-driving forces,
temperature, T. Terms in (3) in Table 2.1 containing Q are
chemical reactions proceeding at finite displacements from
multiplied by (1 - To/T,), which, as shown in Figure 2.2, is chemical equilibrium, mixing of streams at differing condi-
the reversible Carnot heat-engine cycle efficiency, represent-
tions of temperature, pressure, and/or composition, and so
ing the maximum amount of shaft work that can be produced
on. Thus, to reduce the lost work, driving forces for momen-
from Q at T,, where the residual amount of energy (Q - W,)
tum transfer, heat transfer, mass transfer, and chemical reac-
is transferred as heat to a sink at To. Shaft work, W,, remains
tion must be reduced. Practical limits to this reduction exist
at its full value in (3). Thus, although Q and W, have the
because, as driving forces are decreased, equipment sizes
same thermodynamic worth in (1) of Table 2.1, heat transfer
increase, tending to infinitely large sizes as driving forces
has less worth in (3). This is because shaft work can be con-
approach zero.
verted completely to heat (by friction), but heat cannot be
For a separation process that occurs without chemical re-
converted completely to shaft work unless the heat is avail-
action, the summation of the stream availability functions
able at an infinite temperature.
leaving the process is usually greater than the same summa-
Availability, like entropy, is not conserved in a real, irre-
versible process. The total availability (i.e., ability to pro- tion for streams entering the process. In the limit for a re-
versible process (LW = O), (3) of Table 2.1 reduces to (4),
duce shaft work) passing into a system is always greater than
where Wdn is the minimum shaft work required to conduct
the total availability leaving a process. Thus (3) in Table 2.1
the separation and is equivalent to the difference in the heat
is written with the "into system" terms first. The difference
transfer and shaft work terms in (3). This minimum work is
independent of the nature (or path) of the separation process.
The work of separation for an actual irreversible process is
First law: T= T,
always greater than the minimum value computed from (4).
Qin = w, Qout From (3) of Table 2.1, it is seen that as a separation
+
process becomes more irreversible, and thus more energy
t
Second law: inefficient, the increasing LW causes the required equivalent
Qin Qout work of separation to increase by the same amount. Thus,
Reversible
Ts To heat 1 = the equivalent work of separation for an irreversible process
engine ws is given by the sum of lost work and minimum work of
Combined first and (ASirr = 0) separation. The second-law eficiency, therefore, can be
second laws (to defined as
eliminate Qout):
(fractional second-law efficiency)
minimum work of separation
T= To
= (equivalent actual work of separation
Q = Q0"t
Figure 2.2 Carnot heat engine cycle for converting heat to shaft In terms of symbols, the efficiency is given by (5) in Table 2.1.
work.