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cost of the exchanger. The total cost consists of five components:
the capital cost of the exchanger, the capital costs for two pumps,
and the operating (power) costs of the pumps. The expression for
the total annual cost is of the form
TAC ¼ Af ðCexc þ Cpump;T þ Cpump;SÞþ Cpow
HY
g
_ mtDPT
qt
þ
_ msDPS
qs
ð12Þ
where Cexc, Cpump,T and Cpump,S are the capital cost for the exchanger,
tube-side and shell-side pumps, respectively. The capital costs for
the pumps are given by the following equations:
Cpump;T ¼ Ce þ Cf
_ mtDPT
qt
e
ð13Þ
Cpump;S ¼ Ce þ Cf
_ mSDPS
qs
e
ð14Þ
The capital cost for the heat exchanger is typically calculated by an
equation of the form
Cexc ¼ Ca þ C0
bAc
ð15Þ
Alternatively, one can incorporate a more detailed estimation by
splitting the capital cost into the cost of component parts and man-
ufacturing costs. Purohit [11] suggested the following expression
for that purpose:
Cexc ¼ Cts þ Csh þ Cb þ Ctd þ Ctb þ Cba ð16Þ
where Cts is the tube-sheet cost based on weight, including cutting
but not drilling; Csh is the shell cost including fabrication, based on
weight; Cb is the baffle cost assuming 1/2-in thickness, based on
weight; Ctd is the tube-sheet, baffle drilling and bundle tubing cost,
based on number of tubes; Ctb is the cost of tubes, based on outside
heat transfer surface; and Cba is the base cost to cover overhead and
labor costs, which is independent on the type of material.
2.4. Search variables
A vector x of search variables was manipulated as part of the
optimization algorithm. The vector contains 10 components,
according to the degrees of freedom of the problem; the definition
of variables is given in Table 1. Once the search vector is defined,
the algorithm by Serna and Jimenez [10] is used to obtain the de-
sign of the exchanger. It should be clear that a major difficulty is
the selection of design values that satisfy all of the geometric
and operational constraints.
3. Optimization model using genetic algorithms
To generate an efficient optimization method, genetic algo-
rithms are used. Genetic algorithms search for an optimum solu-
tion based on the mechanics of natural selection and genetic
[12,13].
Table 1
Search optimization variables
Variable Definition
x1 Tube-side pressure drop
x2 Shell-side pressures drop
x3 Baffle cut (between 15% and 45%)
x4 Number of tube passes (1, 2, 4, 6 or 8)
x5 Standard inside, outside tube diameters and pitch (80 standard
possible combinations given by the TEMA)
x6 Tube pattern arrangement (triangular, square or rotated square)
x7 Hot fluid allocation (tubes or shell)
x8 Number of sealing strings (0, 1, 2, 3 or 4)
x9 Tube bundle type (fixed-tube plate, packed-tube plate, floating head,
pull-through floating head or U-tube bundle)
x10 Ratio inlet and outlet baffle spacingwas found in 121 generations, which required the simulation of
12,100 heat exchangers, and consumed 51 s of CPU time. One can
notice that the design obtained with the proposed algorithm has a
lower total annual cost than the one obtained byMizutani et al. [9].
This observation seems to indicate that the solution obtained by
Mizutani et al. [9] got trapped into a local optimal point within
their search algorithm. The main difference between both results is
in the pumping costs. Our solution shows a reduction in pumping
costs of about 60% that, in spite of an increment in the area cost of