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Heat Exchanger Network Dynamic Analysis.

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Dev. Chem. Eng. Mineral Process. 14(3/4), pp. 505-514, 2006.
Heat Exchanger Network Dynamic
Analysis
Brent R. Young*’, Denis L. Westphalen’ and
William Y. Svrcek3
Chemical and Materials Engineering, The University of Auckland,
Private Bag 92019, Auckland City, New Zealand
I
2
Jacobs Canada Inc., Calgary, Alberta, Canada
Chemical and Petroleum Engineering, University of Calgary,
Calgary, Alberta, Canada
The continued high cost of energy has mandated that the Chemical Process
Industries reduce operational and capital costs through process heat integration.
However, the heat integration of process streams can lead to process structures
that are di3cult to operate and control. This paper addresses the control of heat
exchanger networks and it shows the importance of dynamic simulations in the
synthesis of workable control structures. Steady-state simulations were used to
delineate the trade-off between flexibility and capital costs of networks. Dynamic
simulations were used to assess the placement of the by-pass on the process-toprocess heat exchangers. Steady-state and dynamic simulations showed that the use
of stream splitting should be avoided as a control scheme. The analysis of several
simple case studies allowed the proposal of heuristic rules to identifL the best
control strategy for a heat exchanger network.
Introduction
Heat exchanger networks are widely employed in the chemical processing
industries to recover energy, resulting in reduced operating costs. Several
methodologies can be found in the literature for the optimal design of heat
exchanger networks. Typical optimal criteria are maximum energy recovery [ 11 and
minimum heat transfer area [23. However, the heat integration of process streams
can lead to process structures that are difficult to control. Luyben et al. [3] present
a general procedure for plant wide control, where it is emphasized that energy
integration profoundly alters the dynamic behaviour of the plant and therefore
special attention must be paid to process-to-process heat exchangers, particularly if
* Authorfor correspondence (b.young@auckland.ac.nz).
505
B. R. Young, D.L. Westphalen and W.Y.Svrcek
they are used for heat removal from exothermic reactors. Kotjabasakis and Linnhoff
[4] introduced the concept of sensitivity tables and described how heat exchanger
areas should be increased with the aim of increasing the network's flexibility.
Glemmestad and Gundersen [S] and Glemmestad et al. [6] showed that after a
detailed degrees of freedom analysis, a control structure can be designed to satisfy
target temperatures at steady state, minimize utility costs at steady state, and ensure
a satisfactory closed-loop dynamic performance. Westphalen et al. [7]revised this
degrees of freedom analysis and proposed a set of heuristic rules for the synthesis of
control schemes for heat exchanger networks, and subsequently proposed a
controllability index as a measure of heat exchanger controllability [8]. In this
paper, the role of dynamic simulations in this synthesis is analysed.
Case Study Definition
Table 1 shows stream data for the case study used in this paper. Rigorous process
simulations were developed using the commercial simulator, HYSYS. For this
reason, detailed information was required to define process streams. The PengRobinson property package was employed. Both streams of Table 1 are at 1500 kPa
(and both streams are liquid for all the temperatures of Table l), contain 50 mole%
of benzene and 50 mole% of toluene, and the flow rates are 190.1 and 322.5 kmolh
for streams HI and C1, respectively.
Table 1. Case Study: Process streams.
Stream
Supply temperature
H1
c1
T
Target temperature
("c)
(sc)
190
80
150
160
Flow rate
capacity (k W/K)
10.0
15.0
'i"
Figure 1. Case study: (A) By-pass stream on cold stream; (B) By-pass on hot
stream.
506
Heat Exchanger Network Dynamic Analysis
Figure 1 depicts the process configuration studied in this work. As the heat duty
required by stream C1 is greater than the rejected heat from stream H1, a heater is
necessary. As stream C1 uses steam to attain its target temperature, any disturbance
to the process can be easily absorbed by the utility system. In other words, steam
flow rate can be manipulated to control the final temperature. On the other hand,
there is no utility stream attached to stream H1, and for that reason a bypass should
be employed to control its target temperature.
Steady State Analysis
Mathisen et al. [9] analysed the placement of a by-pass stream on a heat exchanger
for control purposes. Basically, when the flow rate through the by-pass stream is
changed, the heat exchanger duty is affected. If, for instance, the flow rate through
the by-pass stream is increased, the temperature differences are decreased and
therefore the heat exchanger duty is decreased. Moreover, it can be concluded that
such a heat exchanger cannot be designed with a nominal by-pass flow rate equal to
zero. In order to handle any kind of disturbance or process upset, the heat exchanger
duty must be able to be increased or decreased, that is, the control valve on the bypass stream can be opened or closed depending on the controller requirements.
However, given a nominal by-pass flow rate, how much of a disturbance can be
accommodated by manipulating this flow rate? Flexibility in handling both positive
and negative disturbances can be improved if the nominal by-pass flow rate is
increased, but at what cost? In order to address those points, the overall heat transfer
coefficient (v) of the process-to-process heat exchanger will be assumed as
1000 kJ/hm2K. The cost of the heat exchanger will be calculated using the Guthrie
correlations [lo], using a Marshall and Swift Equipment Cost Index equal to 1056.8
as per Equation (1):
101.3A0.65(2.29+F,)
...(1)
where M & S = Marshall and Swift Cost Index; A = heat transfer area (ft’); F, =
(FkF,,)F,; Fd = 0.80 (fixed tube sheet design type); Fp = 0. I (design pressure); and
F,,, = 1 .OO (carbon steel shell-and-tube material).
Tables 2 and 3 present the results of the steady-state simulations. Nominal bypass ratio (by-pass stream flow rate divided by inlet stream flow rate) was varied
from 0 to 0.6. Using a constant “UA” value for each by-pass ratio, the network was
simulated for the following situations: by-pass control valve closed and by-pass
control valve fully open (by-pass ratio equal to 2 times the nominal value). For
those situations, the inlet temperatures and flow rates of streams HI and C1 were
calculated in order to restore the set point temperature of stream H1 (150OC). The
results reflect the maximum or minimum disturbances of the inlet temperatures and
flow rates that can occur by manipulating the by-pass ratio. For a by-pass ratio of
zero, the by-pass ratio equal to 0.1 was specified for the situation of fully open
control valve.
507
B. R. Young, D.L. Westphalen and W.Y. Svrcek
Table 2. Results of steady-state simulations: by-pass on the hot stream.
Nominal by-pass ratio
0
0.1
0.2
0.3
0.4
0.5
Product UA (kJ/h”K)
19724 20536 21740 23678 27954 38665
19.72 20.54 21.74 23.68 27.95 38.66
A (mZ)
39698 40753 42290 44704 49798 61486
cost ($)
Min temp. H1 (“C)
188.5 188.1 184.5 177.3 164.3 150.0
(4)
191.6 193.8 197.4 204.4 220.5
Max temp. HI (“C)
Min flow H1 (kmol/h) 183.9 181.6 159.5
(2)
(2)
(2)
Max flow H1 (kmol/h)
(4)
196.6 206.1 220.9 247.5 315.8
Min temp. C1 (“C)
77.1
76.2
67.7
42.7
(3)
(3)
Max temp. C1 (“C)
(4)
82.9
86.8
92.1
101.2 114.6
Min flow C1 (kmol/h)
(4)
273.2 228.5 187.2 149.3 114.8
Max flow C1 (kmoVh) 393.1 421.7 1437.0
(I)
(1)
(1)
~~
(1) The enthalpy - temperature curve of the cold stream in the heat exchanger is almost flat. Any increase on
stream Cl’s flow rate can be accommodated manipulating the by-pass stream flow rate. (2) Convergence was
not obtained in the heat exchanger because of non-reliable values of FT correction factor. (3) Unrealistic low
temperatureswere obtained. (4) No disturbance can be accommodated by the system.
Table 3. Results of steady-state simulations: by-pass on the cold stream.
~
Product UA (kJ/h”K)
A (mZ)
cost ($)
Min temp. HI (“C)
Max temp. H1 (“C)
Min flow H1
(kmol/h)
Max flow H1
(kmoWh)
Min temp. C1 (“C)
Max temp. C1 (“C)
Min flow C1
(kmol/h)
Max flow Cl
(kmol/h)
~
Nominal by-pass ratio
0
0.1
0.2
0.3
0.4
0.5
19723 20221 20892 21838 23300 25863
19.72 20.22 20.89 21.84 23.30 25.86
39697 40346 41210 42414 44239 47345
189.1 188.8 186.7 182.1 171.5 150.0
(4)
190.9 192.2 194.0 196.7 201.4
0.6
31789
31.79
54139
150.0
211.6
186.3
185.3
176.2
156.7
109.2
(2)
(2)
(4)
193.8
199.3
206.7
217.6
235.8
275.2
78.2
77.8
81.8
72.9
84.1
60.5
87.1
6.1
91.2
(3)
(3)
(4)
97.2
106.9
(4)
286.4
259.5
226.0
193.7
161.3
130.2
355.8
362.2
428.2
563.8
960.8
(1)
(1)
(1) The enthalpy - temperature curve of the cold stream in the heat exchanger is almost flat. Any increase on
stream Cl’s flow rate can be accommodated manipulating the by-pass stream flow rate. (2) Convergence was
not obtained in the heat exchanger because of non-reliable values of FT correction factor. (3) Unrealistic low
temperatures were obtained. (4) No disturbance can be accommodated by the system.
508
Heat Exchanger Network Dynamic Analysis
The cases marked as (11, (2) and (3) in Tables 2 and 3 correspond to conditions
where the corresponding disturbances can be easily controlled by manipulating the
by-pass ratio (maximum flexibility). However, cases marked as (4) correspond to
conditions where the disturbances cannot be corrected by the manipulated variable
(no flexibility). As expected, this last condition happens when the nominal by-pass
ratio is zero, that is, only those disturbances that require opening the control valve
can be controlled by the process. Beyond the nominal by-pass ratio of 0.6, infeasible
designs were obtained because of too-low FT values, or temperature crosses inside
the heat exchanger.
Tables 2 and 3 show the disturbance ranges that can be handled by the control
structure as a function of additional costs, that is, flexibility can be improved by
means of expenditure on heat transfer area. The additional cost can be calculated as
the cost of heat exchange for each nominal by-pass ratio minus the cost for zero
nominal by-pass ratio. The disturbance range can be calculated as the maximum or
minimum variable at each nominal by-pass ratio minus its value at steady-state
conditions. However, simple cost analysis does not provide a tool for establishing
an “optimal” nominal by-pass ratio and specific process knowledge and experience
should be used instead.
In order to compare the two process structures (by-pass on hot stream or by-pass
on cold stream) the maximum disturbances of each input variable were calculated
for a 10% increase of the process-to-process heat exchanger cost. The results are
shown in Table 4.
From Table 4 it can be noted that any disturbances in steam HI supply
temperature (Min temp. HI and Max temp. HI) and negative disturbances in stream
C1 supply temperature (Min temp. C1) can be better controlled using the by-pass on
the cold stream. On the other hand, negative disturbances in stream HI flow rate
(Min flow HI) and positive disturbances in stream CI flow rate (Max flow C1) can
be better controlled using the by-pass on the hot stream. Positive disturbances in
stream HI flow rate, stream C1 supply temperature, and negative disturbances in
stream C1 flow rate can be controlled by either location of the by-pass stream.
Table 4. Allowable disturbancesfor a 10% increase in capital cost.
Process variable
Min. temp. H1 (YO)
Max. temp. HI (%)
Min. flow HI (YO)
Max. flow HI (%)
Min. temp. C1 (%)
Max. temp. C1 (%)
Min. flow CI (YO)
Max. flow CI (%)
By-pass on hot stream
-5.1
3.1
-46.0
12.9
-33.2
12.3
-36.5
any flow
Bypass on cold stream
-8 .0
8.3
-34.7
12.7
-71.1
12.3
-36.8
159.3
~~
509
B.R. Young, D.L. Westphalen and W.Y. Svrcek
The information presented in Table 4 could also be used to calculate a parameter
that would then measure and compare the controllability of the heat exchanger via a
by-pass on either the hot or the cold side. At a first glance, one could suggest the use
of a simple arithmetic average calculated from the maximum and minimum
allowable disturbance for a given capital increase. However, squared values of these
disturbances should be used because there are positive and negative values.
Moreover, manipulating the hot stream by-pass flow rate can control any value of
maximum flow rate of stream C1. In order to include this result in a numerical
analysis, the average should be calculated from the inverse of squared disturbances,
using an infinite value (inverse is equal to zero) for this maximum flow rate. Using
this result as a controllability index for this heat exchanger example, a better value
is obtained as this index approaches zero. The controllability indexes thus defined
for the by-pass located on the hot and cold streams are 199 and 56, respectively.
Tables 2 and 3 also show that for a given additional capital cost, larger nominal
by-pass ratios can be used when the by-pass stream is located on the cold stream
than on the hot stream. For the data presented, larger nominal by-pass ratios
suggest better controllability and as confirmed by the simple controllability index
calculated above.
The better controllability obtained with a by-pass located on the cold stream can
also be explained by the different heat flow rate capacities. Since the cold stream
has a larger heat flow rate capacity, changes in its flow rate have a large impact on
the temperatures of the hot stream. From steady-state analysis, it can be concluded
that the by-pass stream should be placed on the side of the heat exchanger with
larger heat flow rate capacity.
Dynamic Analysis
Dynamic simulations of the two process configurations were performed using
HYSYS. For both shell and tube sides of the heat exchanger, a residence time of
10 minutes was specified. Nominal by-pass ratios values of 0.26 and 0.37 were used
for the configurations using hot stream by-pass and cold stream by-pass,
respectively. These values correspond to an additional cost of 10% in relation to the
equipment with no by-pass stream.
The first step of the dynamic investigation was the development of open-loop
simulations. These simulations can provide a better understanding of the dynamic
behaviour of the process and, therefore, they can give some insight into the best
control strategy.
For both configurations,the process response was studied when the control valve
located on the by-pass stream was closed from 50% to 20%. Figure 2 shows the
outlet temperature of stream HI as a function of time, after the step change of the
by-pass flow rate. In both cases, this temperature changed from its initial value
(15OoC) to the same new steady-state value (148OC), however with a completely
different dynamic behaviour.
When the by-pass stream is located on the hot stream, any change in the by-pass
flow rate immediately affects the hot stream outlet temperature. It can be seen that
stream HI outlet temperature decreases in a few seconds to 142.7OC because after
510
Heat Exchanger Network Dynamic Analysis
the disturbance, the amount of this stream that is cooled in the heat exchanger has
been increased. This quick response is a result of the direct mixture of the streams to
a new condition, where no time delay exists. The new flow rate that goes through
the heat exchanger causes an increase in the hot stream outlet temperature and the
equipment capacitance defines the rate of this change. The resulting driving force in
the heat exchanger is responsible for the final steady-state temperature.
When the by-pass stream is located on the cold stream, there is no direct
connection between the manipulated and controlled variable. The curve shown in
Figure 2 (Cold side) is a typical step response of a first-order process [ 111 where the
time constant and process gain are defined by the heat exchanger characteristics.
Seborg et al. [ 1 I ] present some guidelines for selection of manipulated variables
in a process. From these guidelines, it can be concluded that the use of the by-pass
stream on the hot side should be preferred, because in this situation the manipulated
variable rapidly and directly affects the controlled variable. However, steady-state
analysis suggests the use of the by-pass on the cold stream. Yet, dynamic
simulations show a better performance when the by-pass is placed on the hot
stream. It is concluded that dynamic simulations should be used in parallel to
steady-state simulations during process design, because the dynamic behaviour of
the process might suggest different process structures.
__
151
150
149
E2 147
a
!
146
E
e
145
144
143
142
4
0
500
1000
1500
l i m e (s)
Figure 2. Step response of the open-loop process.
2000
2500
3000
B.R. Young, D.L. Westphalen and W.Y. Svrcek
151.0
-
E
1
150.5
e
*
iE
t-
150.0
149.5
4
0
500
1000
1500
2000
Tim
2500
3000
(6)
(A) Disturbance in stream HI
s
f
Y
150.1
e
150.0
by-pass on
hot 51re.em
(B) Disturbance in stream CI.
Figure 3. Step response for the closed loop process.
512
3500
4000
Heat Exchanger Network Dynamic Analysis
The next step is the simulation of the closed-loop responses. All controllers were
tuned by trial and error. When the by-pass stream was placed on the hot side of the
heat exchanger, controller values of K, = 3, z, = 0.05 minutes and z-d = 0.01 minutes
were obtained. For the by-pass on the cold side, controller values of K, = 5 , z, = 6
minutes and rd = 0.01 minutes were obtained.
Figure 3 shows the dynamic response of the process when the inlet temperature
of streams H1 and C1 were changed by +5"C. It can be seen that in both cases a
better performance was obtained when the by-pass was located on the hot stream.
Moreover, during the dynamic simulations, it was observed that the structure with
by-pass on cold stream is more prone to instability, depending on the controller
parameters.
Alternative Control Configurations
Some alternative control configurations such as cascade control and stream splitting
were analysed. A cascade control scheme was designed to take advantage of the
large heat flow rate capacity of the cold stream. However, since both primary and
secondary loops have response periods of the same order of magnitude, a cascade
control scheme should not be employed [12]. Stream splitting should not be used as
a control strategy because in some cases the controlled variable (outlet temperature)
does not change monotonically with the manipulated variable (flow rate of a
branch).
Conclusions
In a typical heat exchanger network, not all streams are connected to a utility
stream. For those streams in this situation, a by-pass should be employed on
process-to-process heat exchangers. The use of by-pass streams in a heat exchanger
results in additional flexibility and also an increased capital cost. The relationship
between flexibility and capital cost was examined in this work and considering
economic factors; the by-pass stream should be placed on the stream with larger
heat flow rate capacity. Dynamic simulation is a powerful tool that must be used in
process design. In this work, it was concluded that the best process structure from a
steady-state point of view is not necessarily the best one from a dynamic point of
view. For a process-to-process heat exchanger, a by-pass stream should be used on
the stream where the final temperature will be controlled. Other alternative control
configurations (cascade control and stream splitting) were also analyzed and
discarded.
References
Linnhoff, B., Townsend, D.W.,Boland, D., Hewitt, G.F.,Thomas, B.E.A., Guy, A.R., and
Marsland, R.H. 1982. A User Guide on Process Integration for the Eflcient Use of Energy. The
Institute of Chemical Engineers, Rugby, UK.
2. Linnhoff, B., and Ahmad, S. 1990. Cost Optimum Heat Exchanger Networks-]. Minimum Energy and
Capital Using Simple Models for Capital Cost. Compuf. Chem. Eng., 14(7), 729-750.
I.
513
B.R. Young, D.L. Westphalen and W.Y. Svrcek
and Luyben, W.L. 1997. Plantwide Control Design Procedure. AIChE
3. Luyben, M.L., Tyreus, B.D.,
J.,43(12), 3161-3174.
4. Kotjabasabis, E., and Linnhoff, B. 1986. Sensitivity Tables for the Design of Flexible Processes (1)
- How Much Contingency in Heat Exchanger Networks is Cost-Effective. Chem. Eng. Res. Des.,
64, 199-2 II.
5. Glemmestad, B., and Gundersen, T.A. 1998. Systematic Procedure for Optimal Operations of Heat
Exchanger Networks. Third International Conference of Foundations of Computer Aided Process
Operations, AlChE Symposium Series, 320(94), Snowbird, USA.
6. Glemmestad, B., Mathisen, K.W., and Gundersen, T. 1996. Optimal Operation of Heat Exchanger
Networks Based on Structural Information. Comput. Chem. Eng., 20, S8234828.
7. Westphalen, D.L., Young, B.R., Svrcek, W.Y., and Broussard, M. 2003. Strategies for the Operation
and Control of Heat Exchanger Networks. Proceedings of Foundafions of Computer-Aided Process
Operations - FOCAPO, Coral Springs, USA.
8. Westphalen, D.L., Young, B.R., and Svrcek, W.Y. 2003. A Controllability Index for Heat
Exchanger Networks, Ind. Eng. Chem. Res., 42,4659-4667.
9. Mathisen, K.W., Skogestad, S., and Wolff, E.A. 1992. Bypass Selection for Control of Heat
Exchanger Networks. Proceedings of European Symposium on Computer Aided Process
Engineering - ESCAPE I , Ellsinore, Denmark.
10. Douglas, J.M. 1988. Conceptual Design of Chemical Processes, McGraw-Hill Book Co., New York.
11. Seborg, D.E., Edgar T.F., and Mellichamp, D.A. 1989. Process Dynamics and Control. John Wiley
& Sons, Inc., New York.
12. Svrcek, W.Y., Mahoney, D.P., and Young, B.R. 2000.A Real-Time Approach to Process Control.
John Wiley & Sons Ltd., Chichester, UK.
Received: 28 February 2005; Accepted afier revision: 22 November 2005.
514
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