Page 129 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

126 Chapter 5 Heat exchanger network analysis

In large process systems, e.g. in refinery crude preheat trains, there exist several options to match
the heat duties of the hot and the cold streams and the composite curves can be used to set capital cost
targets as well as energy targets to obtain an optimum value of ðDT min Þ.
The minimum overall surface area (A min ) is computed by considering the area requirement in each
interval.
" #
1
X X q i;k
(5.12a)
A min ¼
DT LMTD;k h i;k
k i
where q i,k and h i.k are the heat duty and heat transfer coefficient for stream i in the kth interval.
Eq. (5.12a) relies on estimates of heat transfer coefficients for individual streams. It is based on the
assumption of (i) heat exchange between the overlapping hot and the cold composite curves across the
entire enthalpy range (ii) negligible wall and fouling resistances in exchanger(s). This arrangement,
equivalent to pure counter-current flow within the overall network, gives the minimum total surface
area. However, employing multi-pass exchangers would result in “non-vertical” heat exchange be-
tween the streams. This is handled by incorporating LMTD correction factor (ðF T Þ) resulting in the
following expression

" #

X 1 X q i;k
(5.12b)
A min ¼
F T;k DT LMTD;k h i;k
k i
The minimum number of heat exchanger units (N min ) in a process with total (S) numbers of process
and utility streams involved in heat exchange is given by
(5.13)
N min ¼ðS 1Þ
It is important to note that Eq. (5.13) does not give the minimum number of units for (i) a trivial
case of no heat recovery, i.e. each stream is exchanging heat with a utility (hot/cold) and (ii) exact
matching of duties between hot and cold stream(s). However both these cases hardly occur in practice.
Minimising the network capital cost looks for minimising the total surface area as well as the
number of units in the network.
The capital cost of heat exchangers typically correlates with exchanger area in the power law form
with a bias as shown below
c
(5.14)
C ex ¼ a þ bðA ex Þ
where a, b and c are constants for a given type of heat exchanger and A ex is the heat transfer area of the
exchanger. The minimum capital cost of the network, using average heat transfer area per shell for N s
shells in N min exchangers may be expressed using Eq. (5.14).
The minimum operating cost can be considered to be the minimum annual utility cost that can be
estimated for a minimum utility design. The capital and the operating cost can be combined as
annualised cost by using a capital cost recovery factor. This cost can be minimised with respect to
DT min to obtain the minimum total cost target and the optimum ðDT min Þ within the feasible range ahead
of design. This is represented in Fig. 5.5. One may note that this is a generalised representation of the
two-stream case already discussed earlier and depicted in Fig. 5.3.