(629d) A New Approach to Heat Exchanger Network Synthesis Problem

Introduction

Heat exchanger networks (HENs) bring several fluid
streams into their desired temperatures by using available heat in the process.
Since water and energy that are wasted to produce utility streams such as
superheated steam and cooling water cause environmental and economic costs,
processing a fluid to be heated with the one to be cooled is better than
producing utility streams for efficient usage of energy.

In this study, we present a new solution approach for
HEN synthesis problem. Our aim is to provide a complete network design coupled
with a detailed equipment design for heat exchangers (HEs). We generate all
possible HE alternatives instead of structuring the HEN at the very beginning
as done in Yee and Grossmann (1990). Alternatives are generated by discretizing
the inlet and outlet temperatures for hot and cold stream pairs. A
mixed-integer nonlinear programming (MINLP) model is solved to design each HE
alternative in detail. The model decides on the number of shell-and-tube passes
and tubes, diameter of shell, inner/outer tube diameters, and tube pattern
while minimizing HE area or the total construction and operation cost. 

The Yee-Grossmann approach, based on developing a
MINLP formulation for a proposed superstructure of the design of network,
dominates the HEN design literature since 1990 (see Furman & Sahinidis, 2002; Morar & Agachi, 2010; and references therein). Related studies that
keep the superstructure mostly focus on reviewing viability of the
formulation assumptions, improving the methodology for solving the MINLP,
and/or extending the framework. Mizutani et al.
(2003), an example of those who extend the Yee-Grossmann approach, combine
detailed HE design with HEN superstructure. Our study is pretty different than all these studies
in the literature because we produce a detailed design for every network
alternative, abandon using a superstructure, and evaluate all possible
alternatives on a shortest-path network problem in which each path represents a
HEN design alternative. Considering all thermo-physical and transport
properties, the heat transfer coefficients are calculated for every stream at
the environment temperature and pressure. Plus, one can also control the
solution quality by deciding on the minimum temperature difference between
inlet and outlet streams as the main parameter.

Problem Formulation and Solution Approach

Our goal for the HEN synthesis problem is to achieve
maximum heat transfer between streams and to use utility streams minimally. The
decisions are:

-         
Which cold and hot streams meet in a HE?

-         
How much heat will transfer in HEs?

-         
What should be the design properties for every HE?

-         
How many HEs should be in the network?

-         
How should HEs be arranged in the network?

The main idea behind our problem formulation is to
generate all possible HE alternatives, each of which can be represented a node
on a network. We call a stream ?hot (cold) stream' if that would be cooled
(heated) during the process. ?System inlet (target) temperature' refers to the
temperature of a stream at the beginning (after being processed) in the system.
Start and end nodes of the network represent the initial and target status of
the streams, respectively. Arcs between nodes, having associated costs, are
generated by considering the inlet and outlet temperatures and energy
requirements of the streams. The minimum-cost path on the network gives the
final HEN design (Figure-1).

Figure-1. General representation of the whole network, where the
selected HEN is shown in bold.

Note that nodes (i.e. alternatives HE designs) are
generated for all hot and cold stream pairs and for every step change of their
temperatures. For example, assume that there are 3 hot (H1, H2, H3) and 2 cold
(C1, C2) streams and their system inlet and target temperatures are given. If
the minimum temperature difference α is selected as 10°C by discretization, the system inlet and target temperatures
are set as represented in Table-1. Table-2 shows some possible alternatives of
HEs for this example. At each node on the graph, we keep the temperature
information for all streams so that we can keep track of them along the
network. Figure-2 shows what data is stored at a node if there are m hot
streams (i=1,?,m) and n cold streams (j=1,?,n).

Table-1. Data
for a HEN synthesis problem

Table-2.
Several HE alternatives generated for the example

Figure-2.  Content of a node in the network.

 The solution approach consists of 5 steps summarized
below:

a)    Node
Enumeration: Generate all necessary nodes by enumerating all
possible inlet and outlet temperatures for every stream in the system. The
temperature enumeration would be performed as explained above. Note that at a
node (HE), the inlet temperature of a processed hot stream should be higher
than its outlet temperature, and inverse is also true for a processed cold
stream. For each unprocessed stream, the outlet temperature should be equal to
its inlet temperature.

b)    Eliminating
Nodes: Calculate the thermo-physical properties for every
processed stream for each HE. Eliminate the node if energy balance is not
satisfied. The heat load required by the cold fluid should be equal to the heat
load generated by the hot fluid.

c)    
Connecting Nodes

a. Dummy nodes: There are 2 dummy nodes (Start, End)
in the graph. Every node v should be directly connected to the starting and
ending dummy nodes.

b. Connecting HE Nodes: For any two nodes u and v, u
and v would be connected if the following condition holds:

- For all hot streams and cold streams:

outlet temperature of hot stream i in node v =
inlet temperature of hot stream i in node u 

AND

outlet
temperature of cold stream j in node v = inlet temperature of cold stream j in
node u 

d)    Individual
HE Design and Costs: For every node in the network, solve a cost-minimizing
MINLP model for the detailed design of shell-and-tube heat exchangers with TEMA
standards.  The MINLP model consists of necessary design (Geankoplis, 2003) and cost equations (Turton
et. al., 2003) for each HE (i.e. node), and gives the cost of each
incoming arc to that node. The costs on the arcs from the start to the end
nodes are calculated by solving a MINLP model for every stream that is not at
the system inlet temperature and has not reached its desired temperature,
respectively. Utilities such as cold water for cooling and superheated steam
for heating are assumed to be used. The utility costs are added to the cost of
that specific arc. If the streams are at the system inlet temperature, the cost
of an arc from the starting node to that node should be 0. Similarly, if the
streams have reached their target temperatures, then the cost of an arc from
that node to the ending node should be 0.

e)    Shortest
Path: Solve the shortest-path problem on the whole network
to find the best HEN with detailed design.

Computational Results and Conclusion

For implementation of our solution approach we use
MATLAB. For solving the MINLP models, MATLAB calls GAMS/BARON solver. We solve
the shortest-path problem by using the Dijkstra's
algorithm. Our approach is flexible and successfully finds the required number
of heat exchangers and their connections. Note that the decision maker can
change the parameter α to manage the HEN synthesis achieved at the end.

Several HEN examples from the literature are solved to
assess the performance of our approach and comparative results are obtained. We
observed that our approach outperform the superstructure approach.

References

Furman, K.C. & Sahinidis,
N.V. (2002). A critical review and annotated bibliography for heat exchanger
network synthesis in the 20^th century. Ind. Eng. Chem. Res.,
41, 2335-2370.

Geankoplis, C.J. (2003). Transport Processes and Separation
Process Principles (4^th ed.). New Jersey: Prentice Hall.

Mizutani, F.T., Pessoa, F.L.P., Queiroz,
E.M., Hauan, S. & Grossmann, I.E. (2003).
Mathematical programming model for heat exchanger network synthesis including
detailed heat-exchanger designs. 2. Network synthesis. Ind. Eng. Chem. Res.,
42, 4019-4027.

Morar,
M. & Agachi, P.S. (2010). Review: Important
contributions in development and improvement of the heat integration
techniques, Comput. Chem. Eng., 34,
1171-1179.

Turton,
R., Bailie, R.C., Whiting, W.B. & Shaeiwitz, J.A. (2003). Analysis, Synthesis, and Design of
Chemical Processes (2^nd ed.). New Jersey: Prentice Hall. 

Yee, T.F. & Grossmann, I.E. (1990). Simultaneous
optimization models for heat integration ? II. Heat exchanger network
synthesis. Comput. Chem. Eng., 14,
1165-1184.