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The thermal effectiveness and number of transfer units
methodology is ideally suited to the prediction of the performance of heat
exchangers and is used throughout this analysis. Basically, heat exchangers
are designed to operate at steady state conditions so that a specified outlet
temperature is obtained. Both outlet temperatures can be presented explicitly
by the rearrangement of the definition of the thermal effectiveness, shown in
equation (1):
 (1) |
to give expressions in terms of the inlet stream temperatures ( ), the system effectiveness ( ),
and the heat capacity rates ( ), as follows:
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(2) |
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(3)
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Equations (2) and (3) permit the calculation
of the steady state outlet temperatures for a two stream heat exchanger. Heat
exchangers do not always operate at the specified design conditions in real
industrial practice. The variation in process conditions causes changes in the
outlet temperatures of a two stream exchanger. The heat exchanger performance
will vary according to changes in process conditions. Therefore, by applying
the basic understanding of heat exchanger thermodynamics, the behavior of such
thermal systems can be verified. Later on, tackling any existing problems will
be an easy task.
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2. Deviations From The Design Level |
The incremental change in the process variables will be
given the sign ( ), and if
it is not stated as a positive or a negative change, then it could be either.
To investigate the effect temperature disturbances on the overall heat
transfer duty, it is better to carry out the heat exchanger analysis on an
incremental basis; for instance change in the outlet temperature of the hot
stream:
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(4) |
Equations (5) and (6) are the generalized response equations
(GREs)[1].
These developed equations accommodate all
possible individual and combinatorial effects.
(5) |
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(6) |
if only temperature disturbance occurs in heat exchanger
network, the loop and paths can cause additional inlet temperature
disturbances [2]
. Any disturbed process parameter can cause a
deviation in the design outlet stream temperature and a change in the overall
heat exchanger duty.
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3. Incremental Analysis Approach |
The analysis of disturbance using the
incremental approach has disclosed a dimension which exists between the design
and controlled levels, and has distinguished the importance of the control
parameters. It is totally clear now that temperature disturbances do not
change the system effectiveness. The work presented in this paper tries to
look at the effect of temperature disturbance propagation through different
heat exchanger arrangements connected in serial mode. Mathematical expressions
of outlet temperature disturbances for several heat exchanger arrangements are
developed in this paper, and these arrangements are:
1) Two identical counter current heat exchangers.
2) Two identical co-current heat exchangers.
3.1. Two Identical Counter- current Heat Exchangers
The following Figure 1, represents two identical heat exchangers in
series in counter-current arrangement.
Figure 1 Two Identical Counter- current
Heat Exchangers
If the above arrangement suffers from an
inlet temperature disturbance on the hot stream side ( )
of the first heat exchanger, the outlet stream temperatures will feel the
disturbance, but in different effect levels. At the outlet hot stream
temperature( ), the disturbance will equal to , and at the outlet cold stream temperature( ),the disturbance will equal to .
If this temperature disturbance propagates to the second heat exchanger, the
final disturbance at the outlet hot stream temperature ()
will be equal to , and
whereas the final disturbance at the outlet cold stream temperature()will
be equal to .
At later stage the first heat exchanger will suffer two temperature
disturbances from both inlet hot and cold streams( ). This will cause more complex disturbances at the outlet stream temperatures
of the first heat exchanger which will proceed affecting the second one. As
time passes, the disturbances will get more and more complex at the outlet
stream temperatures of the overall system
( ).The
following equations
(10) and (11) represent the mathematical expressions for
temperature disturbance propagation as it accumulates throughout the system:
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(8) |
3.2. Two Identical Co- current Heat Exchangers
The following Figure 2, represents two
identical heat exchangers in series in co-current arrangement.
Figure 2 Two Identical Co-current Heat
Exchangers
If the temperature disturbance occurs only
on the inlet hot stream, the outlet hot stream temperature()will
have a disturbance equal to,
and the outlet cold stream temperature( )will
have a disturbance equal to.
Whereas the final disturbances on the outlet streams()of
the second heat exchangers will have the following expressions:
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(9) |
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(10) |
On the other hand, if temperature
disturbances( )occur on both inlet streams, the final disturbances on the outlet streams of
the second heat exchangers will have the following expressions:
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(11) |
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 (12) |
The general response equations provide a
deeper insight, and a powerful tools on detecting the effect of temperature
disturbances on the outlet stream temperatures. The responses due to
disturbances in the inlet stream temperatures can be directly summed. The
developed mathematical expressions will definitely in tracking the disturbance
propagation through heat exchangers connected in series. It clear that the
heat exchanger arrangement plays an important role in knowing whether there
will be an accumulation of temperature disturbances on the outlet stream
temperatures or not. In addition, it is possible to be able to formulate the
expressions to describe for these disturbances which will provide a tool to
select a particular type of control strategy to be implemented to achieve
certain design outlet temperature. This is the first step in developing
further expressions for mass and fouling disturbances.
[1] Abu-Khader, M. M., 1997, "
Control Strategies For Steady State Operation of Two Stream Heat Exchangers",
PhD Thesis, UMIST.
[2] Picon-Nunez, M. and Polley, G. T. , January 1995, "
Determination of the Steady State Response of Heat Exchanger Networks
without Simulation" , Trans. IChemE., Vol. 73, part A, pp. 49-58.
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