Page 125 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

122 Chapter 5 Heat exchanger network analysis

Without any heat exchange between the hot and the cold streams, the annual cost of utility requirement
(C op,annual ) is computed from the unit cost of the hot and cold utility i.e. C h , and C c , respectively
multiplied by the hours of operation per annum (t ann )
(5.3)
C op;annual ¼ðq h C h þ q c C c Þ t ann
When the hot stream is used to preheat the cold stream, the corresponding energy savings in the
recovery heat exchanger (q rec ) is obtained at the expense of an investment (C ex ) which is a function of
the heat exchanger area (A ex ) computed for a counterflow exchanger as
q rec
(5.4)
A ex ¼
U ex DT LMTDcounterflow
The above expression considers the LMTD correction factor (multiplier to DT LMTDcounterflow )tobe
close to unity. However the same may be incorporated, if multipass exchangers are used.
Following the nomenclature depicted in Fig. 5.2,

TS h T c;rec T h;rec TS c

TS h T c;rec (5.5)
DT LMTDcounterflow ¼
ln
T h;rec TS c
where T c,rec and T h,rec refer to the respective exit temperatures of the cold and the hot streams from the
recovery exchanger.
Overall heat transfer coefficient (U ex ) can be obtained from the convective heat transfer coefficient
for the cold (h c ) and the hot fluid (h h ) as discussed in Chapters 2e4.
The heat recovery (q rec )in Eq. 5.4 is limited by the approach temperature ðDT min Þ, the temperature
difference between the hot and the cold stream in the exchanger. For constant heat load (q h and q c )of
the hot and cold streams, the energy savings of the hot utility is equal to the energy saving of the cold
utility and the maximum heat recovered is
(5.6)
q rec ¼ CP h ½TS h ðTS c þ DT min ފ
From Eq (5.6), a higher ðDT min Þ results in a smaller (q rec ) and (A ex ) and a higher (q ) and (q ). This

þ
is well evidenced from Fig. 5.2 as lower overlap (q rec ) of the curves lead to greater extension of the
curves in the hot and the cold utilities regions.
Mathematically, the optimal ðDT min Þ is obtained by adding the annual operating cost due to utilities
C op, annual over a yearly operating time (t ann ).
C op;annual ¼½C h ðq h q rec Þþ C c ðq c q rec ފ t ann (5.7)
Optimal DT min
to the annualised investment (C ex ) estimate based on annual interest rate fraction
i over the expected lifetime of the plant in years (n ex )

n ex
b ex (5.8)
ið1 þ iÞ
n ex 1
C ex ¼ a ex ½A ex Š
ð1 þ iÞ
The installed cost of heat exchanger is related to heat transfer area (A ex ) by a power law relation
b ex (5.9)
C ¼ a ex ðA ex Þ