Page 278 - Design and Operation of Heat Exchangers and their Networks

264 Design and operation of heat exchangers and their networks

variable. The heat exchanger area depends on the heat load or inlet and out-
let temperatures of hot and cold streams; however, such a relation is not lin-
ear. Therefore, the mathematical model belongs to a mixed-integer
nonlinear programming (MINLP) problem. The third step is to find out
the solution of the MINLP model to reach the heat exchanger network fea-
turing the optimal total annual cost and operability. Thus, the tasks of math-
ematical programming method include setting up the proper MINLP model
and finding out its optimal solution with computer-based algorithms.
Based on pinch technology, the first mathematical programming model
is the transshipment model proposed by Papoulias and Grossmann (1983b)
and Floudas et al. (1986). The transshipment model has the hot streams and
heating utilities as commodity sources, the temperature intervals as interme-
diate nodes and cold streams, and cooling utilities as destinations. Heat is
regarded as a commodity that is shipped from hot streams to cold streams
through temperature intervals that account for thermodynamic constraints
in the transfer of heat. By transshipment model, the search for the optimal
network was decomposed into three major tasks. The first one involves the
solution of a linear programming (LP) problem to target the process utility.
In the next task, a mixed-integer linear programming (MILP) problem is
solved to find the minimum number of matches needed to achieve maxi-
mum heat recovery (MHR target). To minimize the number of units,
the authors normally apply the notion of process pinch to decompose the
problem into two independent networks. By doing so, constrained utility
targets implying a finite heat flow across the pinch can no longer be consid-
ered. Finally, a nonlinear nonconvex mathematical programming (NLP)
model based on a network superstructure is tackled to search for the config-
uration featuring the lowest total area cost among those ones performing the
set of heat matches and heat loads already selected through the MILP for-
mulation, that is, the heat exchanger network at the level of structure.
Yee and Grossmann (1990) proposed a MINLP mathematical formation
where all the design decisions can be optimized simultaneously. The model
is based on a superstructure resulting from a stagewise representation of heat
exchanger networks where a match between any pair of hot and cold streams
may take place at every stage. The number of stage is a model parameter to
be adopted by the user in such a way that all possible network designs are
taken into account. More stages will generally be required when the search
is restricted to series configurations. A feature of the model is the linearity of
the constraint set defining the problem feasible space. Such a linearity is
achieved by assuming (a) isothermal mixing of streams, (b) no split stream