Page 199 - Distillation theory

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6.2 Columns with Intermediate Inputs and Outputs of Heat: “Pinch Method” 173

D D
a) L
x Q
D con
N int
1 T r
Q int
con
S
r
F
F
Q int
reb
N int
s
Q reb
x L
B B B

2
ad
s S
S s
b) t
S r x rev

int
r N x B

x D x
F

1 + 3
N int
s s N
Figure 6.2. (a) A liquid profile for a column with direct split 1:
2,3 with intermediate heat input and heat output (solid line),
and for partially reversible column (dotted line). (b) Section
trajectories for a column with intermediate heat input and heat
output.

Liquid flows saltatory increases or decreases in the points of intermediate output
int
int
or input of heat at the temperature T con and T . The minimum possible value
reb
of liquid flows at parts from column ends to the points of intermediate input and
output of heat is equal to the value of liquid flow at partially reversible process in
int
those cross-sections, where T rev = T int and T rev = T . Calculation of reversible
con reb
distillation trajectory at parts from column ends to points S r and S s determines the
function L rev = f (1/T) for these parts and then determines such optimal values opt
int
T int and opt T , at which summary cost of inputs and outputs energy is minimum.
con reb
Such an approach was introduced in the work (Terranova & Westerberg, 1989;
Dhole & Linnhoff, 1993) and was named “pinch method.”
If it is accepted that the price for input heat is proportional to the value (1/T 0 −
int
1/T ) and the price for output heat is proportional to the values (1/T int − 1/T 0 ),
reb con
where T 0 is the ambient temperature, and amount of input or output heat is pro-
portional to liquid flow, then the cost of energy consumption in the main and
intermediate reboilers will turn out to be proportional to the hatched area in