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DISTILLATION VARIABILITY PREDICTION
by
SATISH ENAGANDULA, B.Tech.
A THESIS
IN
CHEMICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University
in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
CHEMICAL ENGINEERING
Approved
-r^ Chairperson of the ConplWttee
Accepted
InterimDean of the Graduate Schfco
December, 2000
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ACKNOWLEDGEMENTS
I would like to take this opportunity to sincerely thank my
advisor. Dr. James B. Riggs for his constant support and
encouragement throughout the project. I have thoroughly enjoyed
working on this project. I am highly indebted to him for his timely
guidance and direction without which this project could not have
been realized. I also appreciate the financial support provided by
the Texas Tech Process Control and Optimization Consortium members.
I would also like to thank Dr. Karlene A. Hoo for being a part of
my thesis committee. I also want to thank Marshall Duvall for his
help.
Personally, I would like to thank all my friends, Mukund, Namit,
Kishor, Alpesh, Govindhakannan, and Rohit for making my stay in
Lubbock a memorable one. I will miss you all. I also want to thank
Matt, Erik, Daguang, Meisong, Andrei, Xuan Li, and Rodney Thompson
for transforming the department office into a fun place to work in.
Finally, I would like to thank my parents, my sister, Vedashree and
my brother, Vineet for their love and support, which has kept me
going throughout these years.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii ABSTRACT vii
LIST OF TABLES viii LIST OF HGURES x
LIST OF NOMENCLATURE xiv 1. INTRODUCTION 1 2. LITERATURE REVIEW
4
2.1 Distillation 4
2.1.1 Distillation Dynamics 4
2.1.2 Dual-Ended Composition Control 5 2.1.3 Configuration
Selection 5 2.1.4 Decentralized PI Controller Tuning 6 2.1.5
Inferential Composition Control 7
2.2 Product Variability 8 2.3 Signal Processing 9
3. PRODUCT VARIABILITY PREDICTION APPROACH 10 3.1 Why a
Disturbance Test? 12
4. LINEAR DYNAMIC MODEL DEVELOPMENT 14 4.1 C3 Splitter-Binary
Distillation Column 14
4.1.1 Modeling Assumptions 14 4.1.2 Vapor Liquid Equilibrium 15
4.1.3 Steady State Designs 17 4.1.4 Linear Dynamic Modeling 17
4.1.4.1 Invariant Structure 20
4.1.4.2 Interior Trays of the Distillation Column 20
4.1.4.3 Accumulator 23 4.1.4.4 Reboiler 23
4.1.5 Level Controllers 24 iii
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4.1.6 Dynamic Simulation Development 26 4.1.7 Linear Model
Benchmarking 27
4.2 Depropanizer - Multicomponent distillation column 30
4.2.1 Modeling Assumptions 30
4.2.2 Vapor Liquid Equilibrium 31 4.2.3 Depropanizer Steady
State Designs 33 4.2.4 Linear Modeling 35
4.2.4.1 Interior Trays of distillation column 35 4.2.4.2
Accumulator 37
4.2.4.3 Reboiler 38 4.2.5 Depropanizer Level Controllers 38
4.2.6 Inferential Composition Control 39 4.2.7 Dynamic Simulation
Development 40 4.2.8 Linear Model Benchmarking 41
5. DUAL-ENDED COMPOSITION CONTROL 44 5.1 Configuration Selection
44 5.2 Invariant Structure of a Distillation Column 45 5.3
Composition Controller Tuning Criteria 46 5.4 Composition Control
Results 48
5.4.1 Base Case C3 Splitter 48 5.4.1.1 Setpoint Control Results
50 5.4.1.2 Closed-Loop Bode Plots 52
5.4.2 High Purity C3 SpUtter 57 5.4.2.1 Setpoint Control Results
57 5.4.2.2 Closed-Loop Bode Plots 60
5.4.3 Low Purity C3 Splitter 65 5.4.3.1 Setpoint Control Results
65
5.4.3.2 Closed-Loop Bode Plots 68 5.4.4 Inverted Purity C3
SpUtter 73
5.4.4.1 Setpoint Control Results 73
IV
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5.4.4.2 Closed-Loop Bode Plots 76 5.4.5 Base Case Depropanizer
77
5.4.5.1 Setpoint Control Results 81 5.4.5.2 Closed-Loop Bode
Plots 84
5.4.6 High Purity Depropanizer 89 5.4.6.1 Setpoint Control
Results 89 5.4.6.2 Closed-Loop Bode Plots 91
5.4.7 Low Purity Depropanizer 96 5.4.7.1 Setpoint Control
Results 98 5.4.7.2 Closed-Loop Bode Plots 98
5.4.8 Asymmetric Purity Depropanizer 103 5.4.8.1 Setpoint
Control Results 104 5.4.8.2 Closed-Loop Bode Plots 106
6. SIGNAL PROCESSING TECHNIQUES 111 6.1 Discrete Fourier
Transforms 112 6.2 The Sampling Theorem and Signal Aliasing 114 6.3
Digital Filtering in Time Domain 115 6.4 Treatment of End Effects
by Zero Padding 116 6.5 Industrial Feed Composition Signal 117 6.5
Results of Signal Processing Analysis 118
7. PRODUCT VARIABILFFY PREDICTION 122 7.1 Prediction Technique
122 7.2 Closed-Loop Product Variability Prediction 124
7.2.1 Base Case C3 Splitter 125 7.2.1.1 Results 125 7.2.1.2
Discussion 130
7.2.2 High Purity C3 Splitter 131 7.2.2.1 Results 131
7.2.2.2 Discussion 136 7.2.3 Low Purity C3 Splitter 137
\ '
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7.2.3.1 Results 137
7.2.3.2 Discussion 141
7.2.4 Inverted Purity C3 Splitter 143 7.2.4.1 Results 143
7.2.4.2 Discussion 147
7.2.5 Base Case Depropanizer 148 7.2.5.1 Results 148 7.2.5.2
Discussion 153
7.2.6 High Purity Depropanizer 154 7.2.6.1 Results 154 7.2.6.2
Discussion 155
7.2.7 Low Purity Depropanizer 159 7.2.7.1 Results 159 7.2.7.2
Discussion 164
7.2.8 Asymmetric Purity Depropanizer 165 7.2.8.1 Results 165
7.2.8.2 Discussion 166
7.3 Summary 171
8. CONCLUSIONS AND RECOMMENDATIONS 173 8.1 Conclusions 173
8.2 Recommendations 176 LFFERATURE CITED 177
VI
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ABSTRACT
A novel technique is proposed to predict product variabilities
for distillation columns. The technique uses industrial disturbance
data and applies signal processing techniques to extract its
amplitude and frequency information. This information is combined
with the closed-loop Bode plot for the same disturbance as a
function of frequency to predict closed-loop product variabilities
for the column. The closed-loop Bode plot is obtained using a
linear dynamic model of the process. The approach is demonstrated
using a binary distillation colunm, a C3 splitter and a
multicomponent distillation column, a depropanizer. Four different
designs of both columns were considered. A thorough study of the
approach is carried out to verify the accuracy and the shortcomings
of the approach. The potential of the approach as a quantitative
tool for
configuration selection was also explored. For this purpose,
nine different distillation configurations were analyzed which
indicated that this approach can be successfully used for
distillation configuration selection.
Vll
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LIST OF TABLES
3.1 Steady state and dynamic characteristics of a typical
distillation column 12
4.1 C3 Splitter Steady State Design Parameters 18
4.2 ALmax and ^ chosen for calculating the level controller
tuning parameters
for C3 splitter 26
4.3 Depropanizer Steady State Design Parameters 34
4.4 ALmax and ^ chosen for calculating the level controller
tuning parameters for Depropanizer 40
5.1 Controlled and Manipulated Variable pairings for dual PI
composition control 45 5.2 Base case C3 splitter dual PI
composition controller tuning parameters 49 5.3 Base case C3
Splitter lAE indices for overhead impurity setpoint control 51 5.4
High Purity C3 splitter dual PI composition controller tuning
parameters 58 5.5 High Purity C3 splitter lAE indices for overhead
impurity setpoint control 60 5.6 Low Purity C3 splitter dual PI
composition controller tuning parameters 66 5.7 Low Purity C3
splitter LAE indices for overhead impurity setpoint control 68 5.8
Inverted Purity C3 splitter dual PI composition controller tuning
parameters 74 5.9 Inverted Purity C3 splitter LAE indices for
overhead impurity setpoint control 76 5.10 Base case Depropanizer
dual PI composition controller tuning parameters 82 5.11 Base case
Depropanizer lAE indices for overhead impurity setpoint control 84
5.12 High Purity Depropanizer dual PI composition controller tuning
parameters 91 5.13 High Purity Depropanizer LAE indices for
overhead impurity setpoint control 91 5.14 Low Purity Depropanizer
dual PI composition controller tuning parameters 96 5.15 Low Purity
Depropanizer LAE indices for overhead impurity setpoint control 99
5.16 Asymmetric Purity Depropanizer dual PI composition controller
tuning
parameters 104 5.17 Asymmetric Purity Depropanizer LAE indices
for overhead impurity setpoint
control 106 7.1 Base case C3 Splitter LAE indices for Product
Variability Prediction 130
7.2 High Purity C3 Splitter lAE indices for Product Variability
Prediction 136 7.3 Low Purity C3 Splitter lAE indices for Product
Variability Prediction 142
viii
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7.4 Inverted Purity C3 splitter lAE indices for Product
Variability Prediction 147
7.5 Base case Depropanizer lAE indices for Product Variability
Prediction 153
7.6 High Purity Depropanizer lAE indices for Product Variability
Prediction 159 7.7 Low Purity Depropanizer lAE indices for Product
Variability Prediction 164
7.8 Asymmetric Purity Depropanizer LAE indices for Product
Variability Prediction 167
IX
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LIST OF HGURES
1.1 Schematic of proposed approach for predicting product
variability 11
4.1 Relative volatility variation of the propylene-propane
system at 211 psia 16 4.2 Typical Structure of a distillation
column 19 4.3 Invariant Structure of a distillation column 21 4.4
Distillation Tray Schematic 21
4.5 Comparison of open loop responses for C3 splitter 28 4.6
Comparison of open loop responses for depropanizer 42 5.1
Comparison between the closed-loop responses of the linear and
non-linear
model for setpoint tracking of the [D,V] configuration of the
Base case C3 Splitter 50'
5.2 Base case C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L,B] configuration 52
5.3 Base case C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V] configuration 53
5.4 Base case C3 Splitter Overhead Impurity Amplitude ratio
plots for feed composition disturbance rejection 55
5.5 Base case C3 splitter Bottoms Impurity Amplitude ratio plots
for feed composition disturbance rejection 56
5.6 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of the [D,V]
configuration of the High Purity C3 Splitter 59
5.7 High Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L,V] configuration 62
5.8 High Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V/B] configuration
62
5.9 High Purity C3 Splitter Overhead Impurity Amplitude ratio
plots for feed composition disturbance rejection 63
5.10 High Purity C3 Splitter Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection
5.11 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of the PD,V]
configuration of the Low Purity C3 Splitter 67
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5.12 Low Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L,V] configuration 70
5.13 Low Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V/B1 configuration
70
5.14 Low Purity C3 Splitter Overhead Impurity Amplitude ratio
plots for feed composition disturbance rejection 71
5.15 Low Purity C3 Splitter Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection 72
5.16 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of the [D,V]
configuration of the Low Purity C3 Splitter 75
5.17 Inverted Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L,V] configuration 78
5.18 Inverted Purity C3 Splitter Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V/B] configuration
78
5.19 Inverted Purity C3 Splitter Overhead Impurity Amplitude
ratio plots for feed composition disturbance rejection 79
5.20 Inverted Purity C3 Splitter Bottoms Impurity Amplitude
ratio plots for feed composition disturbance rejection 80
5.21 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of [L/D,V/B]
configuration of base case depropanizer 83
5.22 Base case Depropanizer Closed-Loop Bode plot for feed
composition disturbance rejection for [L,V] configuration 86
5.23 Base case Depropanizer Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V/B] configuration
86
5.24 Base case Depropanizer Overhead Impurity Amplitude ratio
plots for feed composition disturbance rejection 87
5.25 Base case Depropanizer Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection 88
5.26 Comparison between the closed-loop responses of the hnear
and non-linear model for setpoint tracking of [L/D,V/B]
configuration of high purity
depropanizer 90 5.27 High Purity Depropanizer Closed-Loop Bode
plot for feed composition
disturbance rejection for [L,V] configuration 93 5.28 High
Purity Depropanizer Closed-Loop Bode plot for feed composition
disturbance rejection for [L/D,V/B] configuration 93 xi
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5.29 High Purity Depropanizer Overhead Impurity Amplitude ratio
plots for feed composifion disturbance rejection 94
5.30 High Purity Depropanizer Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection 95
5.31 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of [L/D,V/B]
configuration of low purity
depropanizer 97
5.32 Low Purity Depropanizer Closed-Loop Bode plot for feed
composition disturbance rejection for [L,V] configuration 100
5.33 Low Purity Depropanizer Closed-Loop Bode plot for feed
composition disturbance rejection for [L/D,V/B1 configuration
100
5.34 Low Purity Depropanizer Overhead Impurity Amplitude ratio
plots for feed composition disturbance rejection 101^
5.35 Low Purity Depropanizer Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection 102
5.36 Comparison between the closed-loop responses of the linear
and non-linear model for setpoint tracking of |L/D,V/B]
configuration of high purity
depropanizer 105 5.37 Asymmetric Purity Depropanizer Closed-Loop
Bode plot for feed
composition disturbance rejection for [L,V] configuration 108
5.38 Asymmetric Purity Depropanizer Closed-Loop Bode plot for
feed
composition disturbance rejection for [L/D,V/B] configuration
108 5.39 Asymmetric Purity Depropanizer Overhead Impurity Amplitude
ratio
plots for feed composition disturbance rejection 109 5.40
Asymmetric Purity Depropanizer Bottoms Impurity Amplitude ratio
plots for feed composition disturbance rejection 110 6.1 Signal
representation of feed disturbance entering a linear model 112 6.2
Signal Processing Procedure 117 6.3 C3 Splitter Feed Composition
Signal 118 6.4 Depropanizer Feed Composition Signal 118 6.5 Signal
Processing for C3 Splitter Signal 120 6.6 Signal Processing for
Depropanizer Signal 121 7.1 Closed-Loop Rejection of disturbance of
the Base case C3 Splitter 127 7.2 Closed-Loop Rejection of
disturbance of the High Purity C3 Splitter 132 7.3 Closed-Loop
Rejection of disturbance of the Low Purity C3 Splitter 138
xii
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7.4 Closed-Loop Rejection of disturbance of the Inverted Purity
C3 Splitter 144 7.5 Closed-Loop Rejection of disturbance of the
Base case Depropanizer 150 7.6 Closed-Loop Rejection of disturbance
of the High Purity Depropanizer 156 7.7 Closed-Loop Rejection of
disturbance of the Low Purity Depropanizer 160 7.8 Closed-Loop
Rejection of disturbance of the Asymmetric Purity
Depropanizer 168
Xll l
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LIST OF NOMENCLATURE
a Lower cutoff frequency for bandpass filter An Input Amplitude
of signal n
A n Output Amplitude of signal n AR(w) Amplitude Ratio for
frequency w b Upper cutoff frequency for bandpass filter B Bottoms
Flowrate
D Distillate Flowrate
EMV Murphree Tray Efficiency
F Feed Flowrate / Frequency fc Nyquist critical frequency / / .
Fugacity of component j in the vapor leaving tray i
f^\ Fugacity of component j in the liquid leaving tray i
(i, . Liquid enthalpy of component j at tray i
/J
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MACC Holdup of the accumulator Mi Holdup of tray i
MREB Holdup of the reboiler
N Number of sample measurements P Pressure, psia
Pu Ultimate Period from ATV test
PSDn Power Spectral Density for n ^ frequency component Q
Reboiler Heat Duty Rn Real part of n^ *' frequency component of
DFT
XACC Liquid composition at the accumulator Xij Liquid
composition of component j at tray i XREB Liquid composition at the
reboiler yij Vapor composition of component j at tray i EMV
Murphree Tray Efficiency
T Temperature
TBJ Bubble temperature at tray i V Vapor Flowrate
Vi Vapor flowrate of stream leaving tray i
var(t) Product Variability Prediction w,j Angular frequency of
n^ component ZFJ Feed Composition of component j
Greek Letters a . ^ Relative volatility of component h to
component j at tray i A T Sampling interval
6 (CO,,) Phase Shift for the n^ frequency component A / Fugacity
coefficient of component j in the vapor leaving tray i Yi.j
A V Fugacity coefficient of component j in the liquid leaving
tray i
XV
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0,, Input phase angle of the n'*' frequency component
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CHAPTER 1
INTRODUCTION
Distillation is one of the most widely used processes in the
chemical processing industries worldwide. Its use ranges from
separation of heavy crudes to separation of liquefied air. In the
U.S alone, 40,000 distillation columns are used and they comprise
95% of the separation processes throughout the chemical processing
industries (CPI) (Degolyer & McNaughton, 1989). Producing
products with low variability and with minimal energy consumption
are the most crucial factors for the success of companies in
the CPI. For cases, where the column product is a high value
added product (e.g., feedstock for polymers) low variability may be
a primary customer application and as a result, upper product
variability limits are many times product specifications. Reduction
in product variability can easily translate into reduction in
energy/utility usage and increased production rates. It will also
help in reducing the variability in the downstream units and can
provide safety advantages too.
Distillation is an energy intensive process. Energy must be
supplied to the reboiler and removed from the condenser. It is
estimated that U.S consumes 80 quads ^ of energy annually, of which
7.25% is consumed by the CPI. Separation processes, mostly
distillation, in the CPI account for 43% of energy consumption in
the CPI. (U.S Dept. of Energy, 1988; U.S Dept. of Energy, 1989;
Chemical Manufacturer's Association, 1989). Humphrey et al. (1991)
showed for various distillation applications such as
ethylbenzene-styrene, propylene-propane, and methanol-water that
excess energy in the range of 10-15% is typically consumed during
the column operation. Most of this consumption resulted from manual
operation of the column, or operations at greater than specified
purities as a safety margin. Improper control strategies largely
accounted for increased variability in products and increased
utility usages. It may be concluded that the potential for economic
savings from even a small increase in efficiency of operation of
distillation columns, is great.
' 1 quad = lO'"* BTU, or 170 million bbl. of oil.
1
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Distillation control has a dominant effect on the economic
performance of a plant (Degolyer and McNaughton, 1989). It is a
challenging problem due to non-linearity, coupling between
manipulated variables, severe disturbances, and non-stationary
behavior. Single ended composition control has been shown to result
in higher energy consumption as it allows composition at one end of
the column to float. Dual ended composition control on the other
hand has been able to reduce energy consumption but results in
dynamic stability and interaction problems (Chiang and Luyben,
1985). These problems may be reduced by selection of proper
pairings between manipulated and control variables, i.e.,
configuration selection. The correct configurations are shown to
have a more profound effect on distillation control performance
than conventional or advanced control strategies. In fact, Duvall
(1999), Anderson (1998), and Hurowitz (1998) have shown that a
reasonable control configuration can result in product
variabilities that are an order of magnitude worse than the optimum
configuration. Distillation configuration selection is not
straightforward; it generally requires control studies based on
rigorous non-linear tray-to-tray column simulations, which is a
lengthy procedure.
The objective of this research is to address the distillation
configuration selection problem using an approach based on product
variability to compare different configurations. The approach is
demonstrated on two distillation columns, namely, C3 splitter and
depropanizer. This approach is an extension of the work by Hurowitz
(1998). In that work, it was demonstrated that it accurately
predicted product variability for an [L,B] configuration of a C3
splitter.
The C3 splitter represents a class of columns known as
superfractionators
(Luyben, 1992). These columns, generally binary, separate close
boiling mixtures such as propane-propylene, ethylbenzene-styrene
etc. Since the column products represent final products, frequent
upstream disturbances need to be minimized to maintain high product
quality. C3 splitters are characterized by low relative volatility
(less than 1.2), high reflux ratios, and a large number of trays.
They typically have long open loop response times in the range of
5-30 hours. Superfractionators typically have flat temperature
profiles, thereby hmiting the usage of tray temperature for
inferential composition control. As a
9
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result, only direct composition measurements can be taken which
introduce sampling time and transport delay problem. These factors
account for the difficulties encountered in the superfractionator
composition control (Luyben, 1992).
The depropanizer is in the class of high relative volatility
distillation columns, (greater than 1.5). Any disturbances in the
column are passed to the downstream units. These columns are
generally multicomponent columns and have fast dynamics and are
highly non-linear. To compensate for fast dynamics, inferential
composition control using tray temperatures is used to speed up
composition control. This may also address the deadtime and
sampling times associated with composition measurements (Carling
and Wood, 1986; Duvall, 1999).
The objective of this research addresses the issue of
configuration selection. For this purpose a novel approach of
predicting product variability is proposed. The approach identifies
a linear dynamic model and predicts product variability. The
procedure is carried out in the fi-equency domain. The approach
extracts frequency information from the feed disturbances and
combines it with the information in a closed-loop Bode plot for the
same feed disturbance generated using the linear dynamic model to
predict product variability. This research demonstrates that this
approach can be successfully used to identify the optimum
configuration for a distillation column. To accomplish these
objectives, the following stages are followed: (I) develop linear
dynamic models for the C3 splitter and the depropanizer, (2)
analyze signal processing techniques to extract frequency
information, and finally (3) compare product variabilities
predicted by different configurations to select the best
configuration based on the product variabilities.
Reviews on distillation, C3 splitter, depropanizer and signal
processing are provided in Chapter 2. The description of the
proposed approach to predict product variability is presented in
Chapter 3. Linear dynamic models of the C3 splitter and the
depropanizer needed for implementing the approach are developed in
Chapter 4. Chapter 5 describes the signal processing techniques
used to extract the frequency content from industrial feed
composition signals; Chapter 6 contains the results of the product
variability prediction and the impact on configuration selection.
Lastly, Chapter 7 summarizes the results and proposes future
research in this area.
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CHAPTER 2
LFTERATURE REVIEW
Since distillation is one of the most common processes used in
the chemical processing industries, a large body of knowledge
describing its dynamics, operation and control can be found in the
open literature (Luyben, 1992; Kister, 1992, 1990; Buckley et al.,
1985; Shinsky, 1984, Rademaker et al., 1975, Nissenfled and Seeman,
1981; Deshpande, 1985).
In this chapter, the literature about the dynamics and control
of distillation columns are reviewed especially as it concerns C3
splitter and depropanizer. This is followed by a discussion on
dual-ended composition control, configuration selection and
controller tuning as they are relevant to this research. Section 3
contains some signal processing information germane to the
understanding of this research.
2.1 Distillation
2.1.1 Distillation Dynamics
Fuentes and Luyben (1983) first studied dynamics of high purity
distillation columns. They studied the impact of relative
volatility on these columns. They found that with higher relative
volatility the dynamics becomes faster and non-linear and hence,
difficult to control. They recommend using faster composition
measurements using inferential measurements such as tray
compositions for high relative volatility columns.
Skogestad and Morari (1988) studied the dynamic behavior of
distillation columns by developing simple and analytical models.
They found that high purity columns with large reflux rates would
be most difficult to control. They proposed using logarithmic
compositions in the model to reduce the non-linearity of the
column. Carling and Wood (1986) and Wang and Wood (1985) studied
the behavior of multicomponent columns such as the depropanizer and
observed that they exhibit non-minimum phase behavior (inverse
responses) in the light key (propane) and heavy key (iso-butane).
Non-minimum phase behavior further contributes to the difficulties
encountered during multicomponent distillation control (Carling and
Wood, 1986).
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2.1.2 Dual-Ended Composition Control
Distillation accounts for a large percentage of energy used in
the chemical processing industries. Hence a reduction in energy
consumption could mean significant economic savings. Luyben (1975)
and Chiang and Luyben (1985) based on steady state calculations
showed that dual composition control considerably reduces energy
consumption as compared to single ended control. They, however,
pointed out the dynamic stability and interaction problems posed by
dual composition control. Ryskamp (1980) and Stanley and McAvoy
(1985) reported industrial energy savings of 10-30% on the use of
dual composition control. They observed that dynamic simulations
showed much larger energy savings as compared to those predicted by
steady state analysis.
However, Freuhauf and Mahoney (1994) recommended usage of single
composition control because of the difficulty involved in
implementing and maintaining dual composition control. For heat
integrated distillation columns, Hansen et al. (1998) showed that
dual-ended composition control provided better results than
single-ended control.
2.1.3 Configuration Selection Plenty of literature has been
published addressing the issue of configuration
selection. It is widely accepted that no particular
configuration is the best for all distillation columns.
Skogestad and Morari (1987), Skogestad (1990) and Shinsky (1984)
proposed a set of guidelines to identify the best configuration for
a distillation column. Shinsky (1984) approached the configuration
selection problem using a steady state relative gain array (RGA).
Skogestad and Morari (1987) also recommended an RGA analysis for
choosing the best configuration but based their studies on a linear
model of the distillation column. Skogestad (1990) highlighted the
usefulness of frequency dependent RGA for configuration selection
especially with respect to the [D,B] configuration.
In general, it has been found that P^/D,V/B] configuration was
the most favored control configuration for distillation control
(Skogestad and Morari, 1987; Shinsky, 1984; Skogestad, 1990).
Skogestad and Morari (1987) recommended avoiding configurations
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with large values of the entries of the RGA matrix because it
may signal ill-conditioning. They found that material balance
configurations resulted in poor dynamic response and poor
disturbance rejection if one of the loops was not functional. This
is consistent with Shinsky's (1984) recommendation of avoiding
material balance configurations.
Skogestad (1990) and Skogestand and Morari (1988) studied the
same seven distillation columns for configuration selection. For
dual-ended composition control, the [L/D,V/B] was found to be the
best configuration for all seven columns. This agreed with Finco
(1987) and Finco et al. (1989) on the performance of the [D,B]
configuration for columns with high purity and/or large reflux
rate.
Finco (1987) and Finco et al. (1989) carried out an extensive
study of a C3 spHtter and concluded that [L/D,V/B] and [D,B]
structures were the best configurations. They based their analysis
on a non-linear dynamic model of an industrial C3 splitter. They
also pointed out that the [D,B] configuration lacked integrity and
needed restructuring in the case of valve saturation and sensor
failures. They also recommended that tight level control be
maintained when using [D,B] configuration.
Gokhale et al. (1994) also studied an industrially benchmarked
non-linear C3 splitter model using decoupled PI controllers. They
concluded that the [L,B] configuration and [D,B] with tight level
control were the best configurations. Hurowitz (1998) carried out
an extensive analysis of an industrially benchmarked C3 splitter
and found [L,B], [D,B] with tight level control and IL,V/B]
configurations to be the most suitable configurations for their C3
splitter.
Carling and Wood (1986) and Freitas et al. (1994) found the
[L,V] to perform better than the [L,B1 configuration for a
depropanizer. Duvall (1999) reconmiended [L/D,V/B] and [L,V/B]
configurations based on his analysis using an industrially
benchmarked non-linear tray to tray depropanizer model. He also
found [L,V] to provide a reasonable control performance.
2.1.4 DecentraUzed PI Controller Tuning A distillation column
typically has two level control loops for controlling levels in
the reboiler and accumulator and two composition control loops
for controlling overhead
-
and bottom compositions. Tuning of both level and composition
control loops is crucial for good distillation control. Since the
level control loops are much faster than composition control loops,
the level control loops are tuned first followed by composition
control. Rademaker et al. (1975) recommend using tight level
control for energy balance configurations and detuned level control
for material balance configurations. Marlin (1995) has provided a
detailed study of level control dynamics and tuning. For
distillation columns, he recommended sluggish and detuned level
control. He observed that overshoot or oscillatory behavior of
level control loops might have an adverse effect on composition
control loops.
For tuning composition control loops, the interaction between
the two loops should be considered. Luyben (1986) demonstrated a
procedure of tuning composition loops using Ziegler and Nichols
settings (Ziegler and Nichols, 1942). The initial tuning parameters
for both composition loops are obtained by treating both loops as
independent loops and obtaining Ziegler and Nichols tuning
parameters for each based on transfer function model of the
process. The two loops are then detuned using a common detuning
factor determined by the Biggest Log Modulus Testing (BLT) method.
A drawback with the BLT method is that it requires all transfer
functions in the models which may be difficult to estimate using
the pulse testing method (Moudgalya, 1987). Finco (1987), in fact,
showed that these identified transfer functions could be in error
with the actual process. Instead of transfer function models of the
process, Astrom and Hagglund (1984) suggested using a relay
feedback technique, Autotone Variation (ATV) method.
Recently, Tyreus and Luyben (1992) proposed a new set of tuning
rules for processes with large time constants. They used the ATV
method to find the Tyreus and Luyben tuning parameters which they
promptly detuned using a modified version of the BLT method. They
concluded that the new tuning settings offered better results than
Ziegler and Nichols settings.
2.1.5 Inferential Composition Control Fuentes and Luyben (1983)
showed that high relative volatility columns exhibit
fast dynamics and recommended the use of inferential
measurements, such as tray
-
temperatures, to infer compositions. The relative volatility for
a depropanizer ranges between 1.5 and 2.0. Hence, tray temperatures
were used to estimate compositions. Inferential control can be
accomplished using a single control loop or a cascaded loop. Marlin
(1995) and Riggs (1998,1999) provide a detailed description about
inferential measurement and control. Riggs (1998) also provided a
simple procedure to identify the best trays for inferring
compositions. Wolf and Skogestad (1996) considered a cascade
implementation and described several effects that should be taken
into consideration for selection of trays.
Shen and Lee (1998) successfully applied multivariable adaptive
inferential control to the Berry and Wood column to improve product
quality. Joseph and Brosilow (1978) carried out a thorough analysis
of inferential control systems and demonstrated the concepts using
an industrial debutanizer. They reported improvements in steady
state performance by as much as 400% and reported that an
inferential control systems response to various disturbances were
superior to that of tuned composition feedback systems. McAvoy et
al. (1996) considered a non-linear inferential control scheme by
applying a non-hnear inferential parallel cascade control (NIPCC)
to the Tennesse Eastman Challenge problem. For random feed
fluctuations, they found the variance in product flow and
composition reduced significantly by using NIPCC.
2.2 Product Variability Instrumentation such as transmitters and
valves are recognized as key elements to
reducing product variability (Nelson, 1997; Weldon, 1999;
Pyotsia et al., 1996; Blevins et al., 1995). Few researchers have
proposed novel tools to study process variability. CoUani et al.
(1989) first proposed a procedure to monitor and control process
variability using standard deviation control charts. They proposed
process designs based on the economics of cost inspection,
collecting and analyzing data, and the cost and profit of renewals
in process design. A controllability index was developed by Zheng
et al. (1999) based on economic and product variability
considerations to identify the best process design and control
structure. They demonstrated the concept on a binary distillation
column. Tseng et al. (1999) proposed a quantitative design tool
based on frequency response of
8
-
individual parallel paths between inputs and outputs of a
process to identify sources of
product variabihty and to make necessary design changes.
2.3 Signal Processing A large body of material has been written
describing different signal processing
techniques such as sampling, filtering, integral transforms,
spectral analysis, etc. (Press et al., 1991; Kamen, 1990). Walker
(1991) has provided a good detailed description on fast Fourier
transforms such as radix-2-fast Fourier transform. Press et al.
(1992) has provided codes in Fortran 77 for implemention procedures
for the radi?c2-fast Fourier transform. Hurowitz (1998) has
provided a detailed description of employing signal processing
techniques on discrete signals.
-
CHAPTER 3
PRODUCT VARIABILITY PREDICTION APPROACH
Product variability is a concern for many industries. Thus
success relies on their ability to minimize the variability in the
products and to maintain the product quality within the specified
limits. Since distillation columns represent 95% of the separation
processes using in the chemical processing industries (CPI), the
variability introduced by distillation processes plays a major role
in the ultimate product quality. This work proposes to address
product variability for distillation columns. The approach is
described below.
The approach to predict product variability in distillation
columns is shown schematically in Figure 3.1. The main idea is to
address the problem in the frequency domain rather than in the time
domain. The process to be studied is characterized by its steady
state and dynamic process conditions. These characteristics are
used to generate a linear model for the process. The steady state
and dynamic operating conditions characterizing a typical
distillation column are summarized in Table 3.1. Based on a user
selected controller tuning criteria, the controller tuning
parameters are identified and tuned online. Using these tuning
parameters, the linear model is executed under closed-loop
conditions at different frequencies of the feed disturbances. From
the resulting responses at these various frequencies, amplitude
ratios and phase angle shifts are calculated to develop a
closed-loop Bode plot for the feed disturbance. Industrial
disturbance data can be processed to extract the amplitude and
frequency components of the signal. These are combined with the
closed-loop Bode plot to predict product variability.
This research is an extension to the previous work by Hurowitz
et al. (1998). There it was demonstrated for product variability
prediction for [L,B] configuration on a C3 splitter. The schematic
of that approach is analogous to the approach shown in Figure
3.1 except that the current approach uses a linear dynamic
model. The signal processing
techniques were improvement to the signal processing techniques
used (Hurowitz, 1998).
10
-
bX)
cd Q (U
c3 X) V i P +-
o U
^ i:J 3
O
u
C/0
I
W)
Q
C/5
o -H
teris
t
o cd
^ u
C3
O O H
c
73 O o-LH
Xi o O O H
ci 1 3
o C/5
11
-
Table 3.1 Steady state and dynamic characteristics of a typical
distillation column
State
Steady State Characteristics
Total Number of Trays Feed Tray location Murphree Tray
Efficiency
Column pressure Reflux Ratio
Boilup ratio
Feed Row Rate Feed condition Feed composition Distillate Flow
Rate
Distillate Composition Bottoms Flow Rate
Bottoms Composition
Dynamic Accumulator and Reboiler Residence Time Tray Hydraulic
Time Constant Composition Analyzer Deadtime Composition Analyzer
Sampling Rate
3.1 Why a Disturbance Test? A disturbance test is one of the
most severe tests for any controller with fixed
parameters. In the case of a distillation column, a feed
composition disturbance is not uncommon and usually has a
significant impact on the column's performance. Hence a change in
feed composition can be used to evaluate the performance of
different control configurations. Moreover, feed compositions can
sometimes be measured online.
The approach shown in Figure 3.1 is demonstrated using two
distillation columns namely, a C3 spHtter and a depropanizer. The
potential of the approach as a quantitative
12
-
tool for configuration selection is also evaluated. The C3
spHtter can be classified as a binary distillation column, which
separates a mixture of predominantly propane and propylene. It
represents a class of columns known as superfractionators, which
separate
close boiling mixtures (Luyben, 1992). They are characterized by
low relative volatility (less than 1.2), high reflux ratios and a
large number of trays. The depropanizer is a multicomponent
distillation column separating a mixture of propane, ethane,
n-butane, hexane, i-butane, and pentane. The mixture has a high
relative volatility (greater than 1.5) and is usually an
intermediate separation process in an industrial plant. The
depropanizer and the C3 splitter represent two very different
column types and can be used to demonstrate the approach. Linear
dynamic tray-to-tray simulators under dual PI composition control
are developed for both distillation columns based on their steady
state and dynamic operating conditions (Gokhale et al., 1995;
Duvall, 1999). The composition and level controllers are tuned
based on a preset tuning criteria and arc used to generate a
closed-loop Bode plot for feed composition disturbances. Industrial
feed composition disturbance data for the two columns are used to
generate the required frequency information. This frequency
information is then combined with closed-loop Bode plot information
of the disturbance to predict product variability. The results will
be compared with rigorous non-linear tray-to-tray simulations.
13
-
CHAPTER 4
LINEAR DYNAMIC MODEL DEVELOPMENT
In this chapter, we study two distillation columns namely the C3
splitter and the depropanizer. The C3 spUtter is a binary
distillation column whereas the depropanizer is a multicomponent
distillation column. The models for the C3 splitter and the
depropanizer considered here are adopted from Hurowitz (1998) and
Duvall (1999), respectively. They developed rigorous non-linear
dynamic models for these columns and benchmarked them against
industrial data. These rigorous non-linear models are linearized
around their steady state operating conditions to obtain linear
dynamic models. The linear models are tested by comparing their
open-loop responses to that of the rigorous non-linear models.
Throughout the chapter, the condenser and accumulator refer to as
the combined system of condenser and accumulator.
4.1 C3 Splitter-Binary Distillation Column 4.1.1 Modeling
Assumptions
The C3 splitter is one of the most important and widely used
distillation columns in the industry. The assumptions made in the
development of this model are as follows: 1. The input feed stream
is a binary system of propane and propylene. 2. The column has a
single feed stream and two product streams, the bottoms and the
distillate. 3. Pressure remains constant throughout the
column.
4. Since propane and propylene have identical molecular weights
and heats of vaporization, an equimolal overflow assumption is
valid.
5. Vapor-holdup is negligible. 6. At each tray of the column,
the vapor is in equilibrium with the liquid. The same is
true at the reboiler. 7. Vapor-liquid equilibrium (VLE) is
represented by a relative volatility model. The
relative volatility is a function of pressure and liquid phase
propylene mole fraction.
14
-
8. The trays are non-ideal and can be described by incorporating
a single Murphree tray
efficiency (Murphree, 1925) for all trays except the reboiler.
The reboiler is treated as an ideal stage.
9. The column uses a reboiler and a total condenser.
10. Tray Hquid hydrauHcs is calculated using the hydraulic time
constant approach
presented by Franks (1972) and Luyben (1990). 11. Heat-transfer
dynamics in the reboiler and condenser are not considered in the
model.
12. The liquid levels and compositions at the reboiler and
accumulator are controlled
using PI controllers.
4.1.2 Vapor Liquid Equilibrium
Propane and propylene form a binary mixture. The vapor liquid
equilibrium between these components can be described using a
relative volatility model. For a binary system, it can be
represented using the following equation,
y, = -^ (4.1) l + {a^,-i)x^
where yi, the vapor composition of component 1 is represented as
a function of jci, the liquid composition of component 1 and a , ,
, the relative volatility of component 1 to
component 2. In general, the relative volatility could be a
function of composition, and pressure or temperature. The
correlation for relative volatility for propane-propylene
mixture was developed by Finco (1987), using the thermodynamic
data provided by Hill (1959). The correlation treated the relative
volatility as a function of liquid composition and pressure and is
given as,
a^ = 1.285500 - 0.00044600P (4.3a) a^ = 0.008008-0.00010350P
(4.3b) a._ = 0.052215 - 0.00014607? (4.3c)
where P is the pressure in psia, x is Uie hquid phase propylene
mole fraction and a is the
relative volatility of propylene to propane. The relative
volatility is a measure of the
15
-
degree of separation, higher relative volatility (> 2)
implies an easier separation. The closer the value of the relative
volatility to I, the more difficult the separation. The
relative volatility predicted by the above equation. Figure 4.1
shows that that the relative
volatihty for propane-propylene mixture at 211 psia lies between
1.1 and 1.2 indicating
that the separation is very difficult.
0 0.2 0.4 0.6 0.8
Liquid Phase Propylene Mole Fraction
Figure 4.1 Relative volatility variation of the
propylene-propane system at 211 psia
In the dynamic model of the C3 splitter, VLE equations are
solved on each tray.
Hence, in order to generate a linear dynamic model, the VLE
equations need to be
hnearized at each tray. That is. /
yu = 1.2./ +
da \ 1.2./ dx,
(l-h(a,.,,-l)x,.,)
V
' 1 . / (4.4)
Jss
da., \ 1.2.1 dx \.i
= - ( ! . / + 2 f l , , . A-,,,) 55 (4.5) /55
where, tiie subscript / refers to tiie i^ tray, around whose
steady state (SS) tiiese equations are computed. The variables with
a bar represent deviations from their steady
state. This convention will be used throughout this chapter.
16
-
4.1.3 Steady State Designs
Five different C3 splitter steady state designs developed by
Hurowitz (1998) were studied. These designs differed from each
other with respect to product purity
specifications. The basic procedure followed for developing
these designs can be
summarized as:
1. The minimum number of theoretical trays required for the
desired separation were
calculated using Fenske's equation (Fenske, 1932). 2. The
minimum reflux ratio was calculated using Underwood's (1948)
equation. 3. The actual reflux ratio was taken as 1.2 times the
minimum reflux ratio.
4. The number of theoretical trays was determined using
Eduljee's equation (1975). 5. The actual number of total trays was
determinedusing Lockett's (1986) equation. 6. Finally, the feed
tray location was determined by minimizing the operating reflux
ratio.
The design parameters for the five different designs are
sunmiarized in Table 4.1
4.1.4 Linear Dynamic Modeling
The structure of a typical distillation column, such as a C3
splitter, is shown in Figure 4.2. A saturated Hquid feed stream
with flowrate F and propylene mole fraction ZF is introduced into
the distillation column at tray Np. The exit liquid stream from the
bottom tray of the column is partially recycled back to the column
through the reboiler. The remaining stream represents the bottoms
product B, rich in heavier component propane. The overhead vapor
from the top tray is condensed in the condenser. Part of the
condensed Hquid is recycled to the column and is called the reflux,
R. The remaining Hquid is the distillate product D, rich in the
lighter component propylene. The reflux combined with the liquid
feed stream and the vapor generated by the reboiler creates the
vapor/Hquid traffic throughout the column.
17
-
c 3
OH T3
^ ^
u,
> ( o
d>
^ Tf Tj--^
ON VO d
o r-d
; ^
.1 .H 4 - '
T3 OS (U Q O N
C <
c o
O cx
o
U
c
^ 4>
C3
.
00 VH
'vi O O H
o
u
-
Feed (F, Zp)
N
Condenser
Duty (Qc)
Accumulator
Reflux (LR) Distillate (D)
Vapor Boilup (V)
Reboiler
Reboiler Duty (QR)
Bottoms (B)
Figure 4.2 Typical Structure of a Distillation Column
19
-
From a process control viewpoint, the independent variables for
the process are feed flowrate, F, propylene feed composition, zp,
bottoms flowrate, B, distillate flowrate, D, reflux flowrate, LR,
vapor flowrate, V, from the reboiler and the constant pressure, P
throughout the column. For the C3 spHtter, the F, zp and P form the
disturbances to the system whereas the remaining variables, namely
B, D, R and V can be used as manipulated variables. It should be
realized that the steam used in the reboiler and the cooHng water
used in the condenser are not modeled for in the process. Instead,
the reflux R and vapor flowrate V are treated as direct inputs.
Luyben (1972) has provided a detailed non-Hnear model of an ideal
binary distillation column. The C3 spUtter model is developed along
the similar lines.
4.1.4.1 Invariant Structure
For a distillation column, choosing which manipulated variable
to control each controlled variable is called configuration
selection. It is one of the most important assessments associated
with distiUation control. Figure 4.3 represents a particular
invariant structure of distillation column, which faciHtates in
addressing this issue. In this structure, we assume that the
distillation column is made up of three separate entities namely,
the accumulator, reboiler and the interior trays of the
distillation column. These entities remain the same irrespective of
which configuration is used; only the mode of interaction between
them will differ from configuration to configuration. As a result,
the same model can be used for any configuration. The advantages of
having such a structure to assess various configurations are
explained in the next chapter.
4.1.4.2 Interior Trays of the Distillation Column
Let's consider a schematic of a tray in Figure 4.4. For the C3
spHtter, since the
latent heats of vaporization of propane and propylene are almost
equal, the equimolal
overflow assumption is found to be a good approximation. This
assumption means that
we need not consider the energy balance equation for each tray.
Thus,
V=Vi=constant i = 0,l,...N (4.6)
20
-
A material balance on each tray results in (Luyben, 1972), dM:
dt ^ = A>.-A
j ^ = Xi^i^M-x.L. + V(y._, - y.)
(4.7)
(4.8)
Accumulator
Feed
1
1 .
Distillate
Bottoms
Reboiler
Figure 4.3 Invariant Structure of a distillation column
-i+l Vi
Li Vi
Figure 4.4 Distillation Tray Schematic
21
-
Each tray is treated as a non-ideal tray with a Murphree tray
efficiency EMV (Murphree, 1925). Hence,
y> = y>-. + E^(yr-y
-
dt -^,>|-^/
K^'jss
A>.+ /55 V^'A.
-\',>1-1 /:,x - k; ,x , 1 N*^/ ^ / - i - ^ / - i
M: V-
Jss
L., + F ) "i+l
M:
( V ^ X- -
Jss M. ,
V ' JSS yi
yi-i+iZr-Xi)ssF + (E)ss^^
y, =y,_,+^(y; '^-y._ , ) (4.19) (4.20)
4.1.4.3 Accumulator
For the accumulator, the material balance equations are
dM ACC dt = V-L,-D
-l.^^-^l = y^,V-(L,+D)x at ACC
(4.21)
(4.22)
The accumulator is treated as a well-mixed vessel. Since the
cooling water is not considered a part of the distillation column,
the energy balance equation is not considered. To generate a linear
model for the accumulator, the above equations are linearized
around the steady state operating conditions of the accumulator
dM ACC dt
d(x.rc) ^
= V-L,-D
dt V \
M ACC yN
( V ^
y55 M ACC ^ACC
Jss
(4.23)
(4.24)
4.1.4.4 Reboiler
For the reboiler the material balance equations are given
as.
dt
^y-^REB'^ REB / _
dt A'jL, yREB^ -^REB^
(4.25)
(4.26)
The energy balance equation is not needed for the reboiler since
the vapor
flowrate is set independentiy by a controller. The Hnear model
for the reboiler is
23
-
dM -^^ = L,-V -B dt ' (4.27)
dt ^1 -^REB
\
y ^REB Jss
( L.-H
\
yJ^REB JSS
y REB ^REB
V M REB
r V-
Jss
L,-V y ^REB Jss
"REB
/ V \
M REB yREB
Jss
(4.28)
4.1.5 Level Controllers
The C3 splitter has two level control loops. PI controllers are
employed in both loops. The level controllers are actuaUy treated
as part of the distillation column model as this would facilitate
in isolating the impact of composition control. In addition the
level control loops perform much faster than composition control
loops.
Industrially, a hot wastewater stream is used as a heating
medium for C3 splitter. The hot wastewater stream experiences
frequent, intermittent organic liquid contamination, which
adversely affects the reboiHng heat transfer, even if the
wastewater flowrate remains constant. This results in signinficant
fluctuations in the reboiler which can be dampened through loose
level control. Hence, loose level control is a requirement for C3
splitter (Gokhale, 1994). The level control loops can be tuned
onHne but this would consume considerable computation time. To
enable faster tuning, analytical expressions derived by Marlin
(1995) for level controller parameters are used straightaway. These
equations are,
AF, K^ = -0.736
AL max
T = A*f-
(4.29)
(4.30)
where AFuix represents the maximum expected flowrate change in
the streams
entering/leaving, ALj^ the resulting expected maximum level
change, and ^ the damping ratio for the desired level control
response. The above tuning parameters are
applied separately to each level control loop by assuming they
are independent. The
24
-
level control loops are tuned for overdamped behavior. Hence, ^
was chosen in the range
of 2.5-15.
The levels in the reboiler and accumulator are directly affected
by the variations
in the vapor Hquid traffic throughout the column. The vapor
Hquid traffic in a column
varies around its reflux flowrate. A distiUation column in
general witnesses a disturbance
of around 5-10% in the vapor liquid traffic during normal
operation. Hence, it can be reasonably assumed that a flowrate
disturbance of around 5-10% of reflux flowrate affects the levels
in the reboiler and accumulator. Hence, for both level control
loops,
AFmax is arbitrarily chosen as 5% of the reflux flowrate.
For the two level control loops, different ALmax and t, are
chosen for different
configurations by taking into consideration the degree of
coupHng between the two loops
and the dynamics expected. As an example, consider level
controller tuning for the [L,B] configuration. In this
configuration, the distiUate flowrate is used to control the
accumulator level and the vapor flowrate is used to control the
reboiler level. The
bottoms loop is independent, whereas, the overhead loop is
coupled with the bottoms
loop. Changing the vapor flowrate in the bottoms loop would
directiy affect the
accumulator level but changing the distillate flowrate in the
overhead loop would not
affect the reboiler level. Thus, we may tune the bottom loop
independently but the
overhead loop needs to be tuned in such a way so as to counter
the interactions
introduced by the bottoms loop. This may be achieved by making
the overhead loop more
sluggish as compared to the bottoms loop, i.e., by choosing
larger AL,nax and
-
Table 4.2 A Lmax and ^ chosen for calculating the level
controller tuning parameters for C3 spHtter
Configuration Level Controller AL^ax ^ Level Controller
Accumulator
Reboiler
Accumulator
Reboiler
Accumulator
Reboiler
Accumulator
Reboiler
Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler
AL
13%
7%
7%
7%
12%
7%
10%
10% 7%
13% 7%
10% 10% 7% 7% 12%
9% 9% 1%
1%
L,B Accumulator 13% 7
4 L,V Accumulator 7% 4
4 L,V/B Accumulator 12% 7
4 D,B Accumulator 10% 7
7 D,V Accumulator 7% 4
7 D,V/B Accumulator 7% 7
7 L/D,B Accumulator 10% 7
7 L/D,V Accumulator 7% 4
7
I7D,V/B Accumulator 9% 6 6
D,B Tight Accumulator 1% 2.5 2.5
4.1.6 Dynamic Simulation Development The linear differential
equations comprising the C3 splitter model are integrated
using an Explicit Euler Integrator. The time interval for the
integration was chosen as 0.3
seconds. The small integration step did not lead to numerical
instabiHty and provided
accuracy. The computational time to execute on a 450 MHz PII was
around 5 minutes of CPU time corresponding to the simulation time
of approximately 5000 minutes.
26
-
4.1.7 Linear Model Benchmarking
The Hnear model developed for the C3 spHtter is derived from a
rigorous non-linear model developed by Hurowitz (1998). He
validated his C3 spHtter model using steady state and dynamic data
from industrial C3 spHtters, operating with the [L,B] control
configuration. Hence, the Hnear dynamic model for C3 spHtter
developed in this work is benchmarked against the non-Hnear
simulator of Hurowitz (1998).
The open-loop responses of the linear model are compared with
the open-loop responses of the non-linear simulator using [L,B]
configuration. The open-loop responses considered are (a) 0.1% step
increase in feed flowrate and (b) 0.1% step increase in feed
composition. Figures 4.5 (a) and 4.5(b) show the comparisons of the
open-loop responses of the linear model and the non-linear model.
It can be seen that the linear model's responses match well with
that of the non-Hnear model. For the feed flowrate step increase,
the linear model and non-linear model show a little mismatch at
steady state.
27
-
-^ 0.306
"o 0.305 H
.-^ 0.304
E 0.303 H
1^ 0.302 i o
T3 CD (U
>
o
0.301 -
0.3
0.299 0 1000 3000 2000
T i m e ^ m i n i i t a Q ^
Non-l inear Model Linear Model
4000
o E
2.02
1.98 3 Q. E ^ 1.96 Q . O
^ CO
E o
o
1.94
1.92 -
1.9 0 1000 2000 3000
Time (minutes) Non-l inear Model ^ ^ " " L i n e a r Mode l
4000
Figure 4.5. Comparison of open-loop responses for C3 SpHtter.
(a) For 0.1% step increase in feed flowrate between linear and
non-linear model for [L,B] configuration.
28
-
_ 0.302
0.294 0 1000 3000 2000
Time (minutes) Non-l inear Model Linear Model
4000
m 1.96 0 1000 2000 3000
Time (minutes) Non- l inear Model " " " " " L i n e a r
Model
4000
Figure 4.5. Continued, (b) For 0.1% step increase in feed
composition between Hnear and non-Hnear model for [L,B]
configuration.
29
-
4.2 Depropanizer - Multicomponent distillation column 4.2.1
ModeHng Assumptions
Depropanizer is also one of the widely used multicomponent
distiUation columns in the industry. The depropanizer distillation
column is structurally identical to the C3 splitter. The
assumptions used to develop a model of the depropanizer are:
1. The feed stream is comprised of six components: ethane,
propane, /-butane, -butane, pentane, and hexane.
2. The column is composed of a single-feed stream and two
product streams, an overhead and bottoms product
3. The column pressure is assumed to remain constant at each
tray but varies Hnearly throughout the column.
4. The vapor holdup is negligible.
5. At each tray of the column, the vapor is in equiHbrium with
the liquid. The same is assumed at the reboiler.
6. The vapor Hquid equiHbrium is represented by the
Soave-Redlich-Kwong (SRK) equation of state (Duvall, 1999).
7. Enthalpies are estimated using ideal enthalpy data and
enthalpy departure functions obtained from the SRK equation of
state (Duvall, 1999).
8. Trays are assumed to be non-ideal and are modeled using a
Murphree tray efficiency (Murphree, 1925) for all trays except the
reboiler. The reboiler is treated as an ideal stage.
9. The column has a partial reboiler and a total condenser. 10.
Tray liquid dynamics are treated using the hydraulic time constant
approach
presented by Franks (1972) and Luyben (1990). 11. The heat
transfer dynamics of the condenser are not considered. The reboiler
heat
transfer dynamics are treated using a first-order lag.
12. Row rates are modeled with first-order lags to represent
valve dynamics. 13. Holdup in the reboiler and condenser are
designed for 5 minute residence time. 14. Tray temperatures are
used to infer overhead and bottom compositions for control.
30
-
15. The heat transfer dynamics of the tray temperature
measurements are modeled using first-order lags.
16. Sensible heat change at each tray of the column is assumed
to be small enough to be neglected.
17. The liquid levels and compositions at the reboiler and
accumulator are controUed
using PI controllers.
4.2.2 Vapor Liquid Equilibrium
The depropanizer separates a multicomponent mixture of ethane,
propane, /-
butane, n-butane, pentane and hexane. The vapor Hquid equiHbrium
between these
components can be represented as (Smith et al., 1987),
r>.j=f'i.j (4.31)
where f^'. represents the fugacity of vapor of component j in
the vapor stream leaving
tray i and / . j represents the fugacity of component j in the
Hquid stream at tray i. Expressing the fugacity in terms of a
fugacity coefficient, the above equation becomes,
yi.jfi-j = xj'i.j (4.32)
where 0/. represents the fugacity coefficient of component j in
the vapor stream leaving
tray i, yij represents the corresponding vapor mole fraction, 0.
^ represents the fugacity coefficient of component j in the Hquid
stream at tray i and Xij represents the corresponding liquid mole
fraction.
The Hquid and vapor fugacity coefficients are estimated using
SRK equation of state. The expressions for fugacity coefficients
obtained using an SRK equation of state are provided by Walas
(1985). Thus, Equation (4.32) can be convenientiy represented
as,
yi.j = K^,x,^j (4.33) where Ki.j represents the vaporization
equilibrium ratio and is defined as,
K..=^. 4.34)
31
-
For multicomponent systems, relative volatility is defined
as.
^iM, = ^i.h
f^.J (4.35)
where a.^^j represents the relative volatihty of component h to
component j at tray i. Relative volatility is a measure of the
degree of separation. For the depropanizer, the relative volatility
lies in the range of 1.5-2.0, indicating a fairiy moderate degree
of separation (Duvall, 1999).
The above VLE equations are solved on each tray. Hence, to
obtain a Hnear dynamic model, these equations are linearized at
each tray around its steady state operating condition. Since the
SRK equation of state is non-linear and involves many parameters,
analytical Hnearization techniques result in large dimensional
equations. Hence, numerical techniques are used instead which
provide linear equations and are easily employed. The resulting
equations can be written as.
yij = ( .^;l .^;+I / dK
V " ' ^ a ^
'i .^.+x
/
A-,. ,.
y55 ';
9^M1 - J ' ^y. Jss
X: dK,, \ \
'J dT T Jss J
(4.36) where the partial derivatives are calculated using
numerical techniques. The above resulting equations are linear but
solving these equations for each tray requires considerable amount
of computational time (Duvall, 1999). To reduce the amount of
computational time, an inside-out algorithm is used (Boston and
SulHvan, 1974). The inside-out algorithm represents a stable
efficient algorithm to solve VLE for multicomponent distiUation
columns. The inside-out algorithm is a modified version of the KB
method. An exponential temperature dependence is assumed for
KB.
\n(K,^) = A. (4.37) B.i
Using the basic rules of vapor-liquid equiHbrium for a given
tray j and i components, it can be shown that KB is given by,
MK,,) = J^y,j\n(K,j) (4.38)
32
-
To estimate the parameters A and B, the linear vapor-Hquid
equilibrium equations
are solved at two temperatures close to the tray temperature, T
and T-H AT, AT being
small. For the depropanizer AT was chosen as 0.2PC. Thus, using
the above two
equations, the parameters are estimated as,
S) 'Mln(/f , ; . r .Ar)-Iy, . ; ln(^MT) B, = ; r^ (4.39) /
A
I 1 T T + AT
4.40)
The KB model approximation is assumed to be valid for small
changes in tray temperature. Hence, if the tray temperatures do not
vary much, the above equations may be used to represent the VLE. It
was found that for a change of at most 1C, the KB model may be
assumed accurate to represent the rigorous VLE equations. To keep
the KB model accurate, it is updated periodically every 10 seconds
and when any of the tray temperature rises above lC (Duvall,
1999).
4.2.3 Depropanizer Steady State Designs Four different
depropanizer steady state designs developed by Duvall (1999)
were studied. These designs differed from each other with
respect to product purities namely, low, asymmetric, base case, and
high purity. The procedure followed to design these columns can be
summarized as:
1. The minimum number of trays, feed tray location and minimum
reflux ratio were
obtained using Fenske-Underwood-GilHland procedure (Holland,
1991). 2. The reflux ratio was taken as 1.2 times the minimum
reflux (Holland, 1991). 3. A rigorous column design is used to
identify the column pressure drop, sub-cooHng
on reflux, Murphree efficiency (Murphree, 1925), and desired
product purities. 4. The feed tray location and number of trays
were adjusted to minimize the energy
requirements for the reboiler and accumulator.
5. The design parameters for the four different depropanizer
columns are shown in
Table 4.3.
33
-
(/3
ea
OH 3 top
D G 41
4>
OO > ^
cd D
41
00 Ui (U N 'c OH
o V-i
Q CO
H
c 3 x: too
c 4>
< a.
0, o
ID
u (U on C3
PQ
ON ^
-"^
C3 O
tin
00
Vi 3
Vi
>
O
o
o
o
00
O PQ
^
o
3 f 1I
00
O PQ
(U
o 3
-
4.2.4 Linear Modeling
4.2.4.1 Interior Trays of distillation column
Franks (1972) has provided a description about modeling of
multicomponent columns. While a model of depropanizer is similar to
the C3 spHtter, the equimolal overflow assumption cannot be
assumed.
The material balance on each tray is given as,
dM ^ = A>.+V;_,-L, -V, (4.41)
flf(A-,.M,) J^ = ^ , > . . ; ^ , > I - ^ M A + K - , >
' / - U -Viyi.j- 4.42)
While the energy balance is,
^ ^ ! ^ = I,,,,L,,-h,L, +V,_,H,_, -V,H,. 4.43)
Expanding the derivative amounts to,
^ W , +h,^ = h.,,,L.-h,L, + V,_,//,_, -V,H,. 4.44)
The first term of this above equation on the left hand side
represents the sensible heat change on each tray. For the
depropanizer, the sensible heat change at each tray is negHgible
and substituting Equation (4.41) into Equation (4.44) yields,
,, L.., (ft,.,-/,) + l^,(g,-/.,-) / / .-ft , / /
Each tray is treated as a non-ideal tray with a Murphree tray
efficiency (Murphree, 1925). y>,=y>-^, + E(yZ-y:-^.,)
(4-46)
Each tray is assumed to be a CST with a hydraulic time constant,
T.^ , . Hence Equation
(4.41) gives,
^ ^ ^ - " ^ - ' - ^ - ^ (4.47)
The trays in the stripping and rectifying section have different
hydraulic time
constants (Duvall, 1999). For the rectifying section, the
hydrauHc time constant is 3.5 seconds whereas in the stripping
section it is 5.25 seconds.
35
-
The liquid and vapor enthalpies are obtained from ideal enthalpy
data using departure functions (Duvall, 1999). These departure
functions are estimated using SRK equation of state (Walas, 1985).
Thus the enthalpy equations for each component in Hquid and vapor
are given by
ft,,=ft,0+Aft,,.
//,,,=//,+AW,,
(4.48)
(4.49)
where h^ . is the ideal liquid enthalpy component j and A/z,.^
represents the departure of liquid enthalpy of component j at tray
i from an ideal solution. Similar statements can be made about
vapor enthalpy. It should be noted that the multicomponent liquid
and vapor streams are assumed to be ideal solutions. Hence the
Hquid and vapor stream enthalpies, respectively are given by
Hi=J,yi,H,.. 4.51)
To obtain a Hnear model for the depropanizer, the non-linear
equations at each tray are linearized around the steady state
operating conditions on each tray. The linearization gives
dL. _L,.,+V,_,-Li-V. dt r.^^j
(4.52)
dx. i-j
^x -x ^
dt M,
^L ^
y^'jss
,^>.+ Jss
(L ^
\ ^ ' JSS ^i+1.;
^v, ^ ^M-
V ^ ' JSS y>.i +
^Vi-.' I Mi ,cc V ' JSS
yi.j-^' i-j M,
yi-Lj
K. + ^y. , . - A ^
y55 M.. V. ;- l
Jss
(4.53)
V. = v ^ ' - ^ ' y 5 5
r J \
A>i + ^H,_,-h^
H.-h h:-
H,-h
( v.. ^,-1 +
Jss ^H,-h,
i Jss \ _
H.
L \ v+i "^-^jss
( K, +
v.. \ ; - l yli.-K
H i-\ Jss
Jss (4.54)
36
-
y,i = y,-.,+E(jZ-y:-uy 4.55) In the case of the feed tray the
non-linear material and energy balance equations are.
dt tray,I
d{x,jM,) dt = XMjEM-^i,j^ +K-l3^/-W - ^ / X . ; +^^F.y
V: = A..(Kx -hi) + Vj.,(//,_. - / t , ) + F(h, -h^)
H^-k
(4.56)
(4.57)
yi.j = y,-ij + EMv(yLj-yi-iJ-Correspondingly, linearizing these
equations gives
JL.. li^i+V ,-li-V,+J 1-1 dt
dl. ( >-j
dt ^i+\.i ^i.j
tray
\
,^>.+ (L ^
Jss y^'^jss
M..
( ^/.y -
v.. =
755
^Kri^ H.-K
V. \
V ^ ' JSS yi.j +
^i+l.j
y'^'jss
4.58)
(4.59)
M. v..-h
755
-x..\ v..
y55
yi-Lj+i^F.j - ^ ' , . y ) 5 5 ^ + ( ^ ) 5 5 ^ ^ -
(4.60)
A>i +
/^ - I-
K 755
/ / . , - / z ^ r 1-1 " i //.-ft. ,^-, + Jss
h^ - h. \ ( F +
/-I
V ' ' JSS H:-k ^ , - 1 -
yHi-hijss h:-
yHi-h^jss
\ "i+l
y">-hips
K"'-''-JSS h i+\
//.+ . tli - h: , V ' 'JSS
/ i ,
>'/.; => ' / - l , ;+^w(K!-> ' / - l . ; )
(4.61) 4.62)
4.2.4.2 Accumulator
For the accumulator, the material balance equations are
dM ^'^^ =V -L -D
^ N ^R ^ dt
dix^cc^ACc) _ dt
= VA^;, - (L,, + D)x^^^.
(4.63)
4.64)
37
-
The accumulator is assumed to be an ideal stage. Since the
cooling water is not
considered a part of the distillation column, the energy balance
equation is not
considered. The linear model for the accumulator is given
by,
dM ACC dt = V,-L,-D
d(^,cc) ( y^ ^ dt
N
M .rr V ^^^ JSS
( yN-
N
M ACC 'ACC
Jss
(4.65)
4.66)
4.2.4.3 Reboiler
For the reboiler, the material and energy balance equations
are
by
dM REB _ dt
L,-V,-B
dJ^REB^REB) dt ^ IM yREB*^0 -^REB"
dh, Q + L,{h,-h^^)-M "REB REB ^ 0 =
dt H -h ^^ REB ''^REB
(4.67)
(4.68)
(4.69)
The reboiler is assumed to be an ideal stage. The resulting
Hnear model is given
dM REB dt
" \XREB )
= L,-V,-B (4.70)
dt -^1 XREB
\
M REB L,M
^ L ^
755 y^REB JSS A,H
yREB -^REB
M REB K-
Jss y "^ REB
\
Jss "REB
M REB yREB
Jss
(4.71)
4.2.5 Depropanizer Level Controllers
The level controllers are addressed in the same way as the C3
spHtter. The level
control loops are tuned for overdamped behavior (MarHn, 1995).
Equations (4.29) and (4.30) are used for estimating the controller
tuning parameters. AFmax is chosen as 5% of
38
-
the reflux flowrate. Different ALmax and ^ are chosen
heuristically for different
configurations by taking into consideration the interactions
between the two loops. Table
4.4 shows the values of A Lmax and ^ selected for the reboiler
and accumulator level
control for different configurations in the four depropanizer
designs. For the asymmetric
purity design A Lmax was chosen as twice that shown in the
table. Since the depropanizer
is more non-linear as compared to C3 splitter, composition
control is more difficult.
Hence larger values of ^ were chosen for depropanizer to dampen
the level control loops
and reduce the interaction with composition control loops. The
results obtained for
various values of ALmax and ^ are compared with the results
obtained by Duvall (1999).
4.2.6 Inferential Composition Control The analyzer sampling
period for depropanizer was one minute. To improve
composition control, infkerential control was used, i.e., the
composition is inferred using a particular tray temperature. Riggs
(1998) has provided a simple technique to identify the best tray
for estimating product composition. The different trays used for
inferring product compositions are provided in Table 4.3 for each
design. The basic correlation used for inferring compositions from
tray temperature is
ln(A) = A + T
(4.72)
where x is product composition estimated using tray temperature
measurement T. For implementing inferential composition control,
on-line analyzers were used to
update the parameters used in Equation (4.72) based on previous
analyzer readings and temperature measurements. Parameter updates
were carried out at each sampHng time. Using these updated
parameters, past analyzer measurement and past temperature
measurement, the composition is inferred as
Ax = X old exp /
B 1 1 T T old
> - l
x = x^+Ax
(4.73)
(4.74)
39
-
where Xoid and Tdd are analyzer and temperature measurements at
recent past sampling
times.
Table 4.4 ALmax and ^ chosen for calculating the level
controller tuning parameters for C3 spHtter Configuration Level
Controller A Lmax ^
L,B Accumulator 25% 15
10 L,V Accumulator 10% 10
10 L,V/B Accumulator 20% 15
10 D,B Accumulator 15% 15
15 D,V Accumulator 10% 10
15 D,V/B Accumulator 10% 15
15
L/D,B Accumulator 15% 15
15
L/D,V Accumulator 10% 10 15
L/D,V/B Accumulator 13% 13 13
Accumulator Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler Accumulator
Reboiler
25% 10%
10% 10% 20%
10%
15% 15% 10%
25% 10% 15% 15% 10% 10% 20%
13% 13%
4.2.7 Dynamic Simulation Development The Hnear differential
equations comprising the depropanizer model are
integrated using an expHcit Euler Integrator. The time interval
for integration was chosen
as 0.5 seconds. A small integration step was chosen to achieve
numerical stabiHty and
40
-
accuracy. The computational time on a 450MHz PII was
approximately 30 seconds of real time corresponding to a simulation
time of 400 minutes.
4.2.8 Linear Model Benchmarking
Analogous to the C3 spHtter, the Hnear model for the
depropanizer was adopted from Duvall (1999). In that work, a
rigorous non-linear model was developed for depropanizer based on
industrial depropanizers operating with an [L,B] configuration. He
benchmarked his non-Hnear model against the steady state and
dynamic data of the industrial columns by adjusting the efficiency
of the trays and the hydraulic time constant for the stripping and
rectifying sections. To obtain an industrially benchmarked linear
model of the depropanizer, this Hnear dynamic model is benchmarked
against this non-Hnear model. This is accompHshed by comparing the
open loop responses of the non-linear and Hnear models. The open
loop tests considered are (a) 0.1% step increase in feed flowrate
and (b) 0.1% step increase in the propane feed composition. These
responses are shown in Figure 4.6. From the responses it is
observed that the dynamics between the non-linear and Hnear model
are identical. However there is some mismatch between the Hnear and
non-Hnear models at steady state.
41
-
0.58
0.48 300
Time (m inutes) Non- l inear M o d e l "
400
'Linear Model
500
0 200 300 T ime (minutes)
Non- l inear Mode l " "
500
'Linear Model
Figure 4.6. Comparison of open-loop responses for depropanizer.
(a) For 0.1% step increase in feed flowrate between Hnear and
non-linear model for [L,B] configuration.
42
-
^ 0.51
0 100 200 300 400 T i m a / m in ii t
-
CHAPTER 5
DUAL-ENDED COMPOSITION CONTROL
Research (Luyben, 1975; Chiang and Luyben, 1985; Ryskamp, 1980;
Stanley and McAvoy, 1985) has shown that dual-ended composition
control provides significant reduction in energy consumption and
better control as compared to single ended control.
Hence, for analyzing distillation column operation, dual-ended
composition control is
considered. Closed-loop Bode plots for feed composition
disturbance are generated for
the C3 splitter and the depropanizer. The Bode plots are
obtained from simulations of the
linear dynamic models of the C3 spHtter and the
depropanizer.
In section 1, different configurations for distillation control
are discussed and the issue of configuration selection is
described. The utiHties of using an invariant structure of a
distillation column are presented in section 2. The tuning criteria
used to tune the composition controllers is discussed in section 3.
Comparison of the results for dual-ended composition control
between the Hnear model and non-Hnear model is carried out in
section 4. The closed-loop Bode plots for feed composition
disturbance for various configurations are also shown in section
4.
5.1 Configuration Selection From a process control perspective,
a distillation column essentially needs five
variables to be controlled to maintain continued operation.
These variables are: pressure, reboiler level, accumulator level,
overhead composition, and botto ms composition. These variables can
be controlled by choosing any of the following independent
variables: reflux, distiUate, bottoms, and vapor boilup (reboiler
duty) flow rates and condenser duty. Thus, it makes the
distillation problem a [5x5] control problem (Duvall, 1999;
Hurowitz, 1998). For C3 spHtter and depropanizer, the column
pressure is usually allowed to float, thereby cHminating one
controlled variable and hence one manipulated variable (condenser
duty). This reduces the distillation problem to just two
composition control loops and two level control loops. In addition,
reflux ratio and boilup ratios can be used to replace any of the
overhead and bottoms manipulated variables.
44
-
The procedure of pairing controlled variables to manipulated
variables is called
loop pairing. Assuming that the top manipulated variables are
not used to control bottom
controlled variables and vice versa, only nine configurations
are left possible. These nine
configurations are Hsted in Table 5.1. The ratio configurations
are implemented using Ryskamp (1980) ratio control arrangement.
Configuration selection is very crucial for achieving good
distillation control. Configuration selection problem inherently
addresses
the problem of coupHng between the loops.
Table 5.1 Controlled and Manipulated Variable pairings for dual
PI composition control
Configuration
L,B
L,V
L,V/B
D,B
D,V
D,V/B
L/D,B L/D,V
L/D,V/B
Overhead Composition
L
L
L
D
D
D
L/D L/D L/D
Bottoms Composition
B
V
V/B
B
V
V/B
B
V
V/B
Accumulator Level
D
D
D
L
L
L
L-hD
L-hD
L-t-D
Reboiler Level
V
B
V+B
V
B
V-HB
V
B
V-fB
Several researchers (Shinsky, 1984; Skogestad and Morari, 1987;
Skogestad et al., 1990a) have proposed guidcHnes to faciHtate
indentification of the best configuration. In regards to C3
spHtter, Gokhale (1994), Finco et al. (1989), and Hurowitz (1998),
compared the different configurations and analyzed tiieir control
performance. In the case
of the depropanizer, Duvall (1999) carried out an extensive
analysis of its different control configurations.
5.2 Invariant Structure of a DistiUation Column One of the most
important problems associated with distillation conU-ol is
configuration selection. It has been shown that choosing a
reasonable but inferior 45
-
configuration can result in an order of magnitude higher
variabihty in products for distillation columns (Anderson, 1998;
Hurowitz, 1998). The use of the relative gain array and other
configuration selection statistics has been shown not to correlate
well with configuration control performance, even if accurate Hnear
models of the column are available and they are not generally
available (CarHng and Wood, 1988; Anderson, 1998; Hurowitz, 1998;
Duvall, 1999). It seems reasonable to use the method proposed in
Chapter 3 for calculating product variabihty to identify the
optimum control configuration.
Figure 4.3 shows an invariant structure for a distillation
column that can facilitate these calculations. In this structure,
we assume that the distillation column is made up of three separate
entities namely, the accumulator, reboiler and the interior trays
of the distillation column (Yang et al., 1990). Note that
regardless of which configuration is used, the same model will
apply. For example, the (L,V) configuration would use the
distillate and bottoms flowrates to control the accumulator and
reboiler levels, respectively, while the reflux and boilup would be
used to control the product compositions. For the (L/D, B)
configuration, the sum of (L-HD) and vapor boilup would be used to
control the accumulator and reboiler levels respectively, while L/D
and B would be manipulated to control the product compositions. As
a result, the same Hnearized model could be used regardless of the
configuration chosen which greatly simpHfies the modcHng problem.
This invariant structure was utilized in developing the Hnear
dynamic models of C3 spHtter and depropanizer.
5.3 Composition ControUer Tuning Criteria The aim of tuning the
controllers is to achieve stable conttol with minimum
variation from setpoint. A common tuning approach is developed
for both the Q spHtter and the depropanizer to compare results
among different configurations. C3 spHtter and depropanizer are
slow response loops. Traditional open-loop tuning methods such as
step tests cannot be appHed on the depropanizer and C3 spHtter
because tiiey have very long response times. In addition, since
tiiese step tests are lengthy, they may be significantiy affected
by unmeasured disturbances and asymmetric dynamics of the process.
Hence,
46
-
an ATV test is used to identify the process parameters, which
can be run online without
significantiy varying the process.
The initial tuning parameters for the composition control loops
are obtained by
treating both loops to be independent of one another. First the
ultimate gain and period of
both loops are obtained independently using ATV tests (Astrom
and Hagglund, 1991) Tyreus and Luyben (TL) settings are then used
to derive initial tuning settings, which are given as
^^ ^''''~ 0.45 ^^ ^ '^^" 0.45 ^ ^ ^ ^ where the subscripts TOP
and BOT correspond to the top and bottom composition loops,
superscript TL refers to TL settings and Ku and Pu correspond to
ultimate gain and period.
Applying the above settings may result in suboptimal control
because they do not account for the coupling between the two loops.
Hence, the tuning parameters need to be detuned. This is achieved
by using a common on-line detuning factor for both loops. Thus the
new tuning settings are given by
(Kc)roR =^^4^ ^^OBOT = ^ ^ 4 ^ ^^'^'^^
(h )TOP = (r'')TOpXFo (h )BOT = (h'')BOT ^^O (5-2.2)
where FD represents the detuning factor. The detuning factor is
determined on-Hne by repeated simulation in a similar
approach to the one used by Finco (1987). The detuning factor is
tuned for minimum integral of the absolute value of error (lAE) in
controller response for overhead and bottoms impurity setpoint
changes.
47
-
5.4 Composition Control Results 5.4.1 Base Case C3 SpHtter
The base case design of the C3 spHtter was analyzed for dual PI
composition control for nine configurations listed in Table 5.1.
The level controller tuning parameters for the base case C3 spHtter
were obtained using Equations (4.29) and (4.30) and Table 4.2. The
TL tuning settings were obtained independently for overhead and
bottoms composition loops using an ATV test. These settings were
then detuned using a common detuning factor as given by Equations
(4.29) and (4.30). The detuning factor was tuned for minimum
integral of the absolute value of error (LAE) in controller
response for setpoint changes. For the base case C3 spHtter, since
the overhead product is more important than the bottoms product,
the detuning factor is tuned for minimum LAE in the overhead
impurity response for an overhead impurity setpoint change. The
overhead impurity setpoint change was carried out from 0.3% to
0.25% at t = 100 minutes and from 0.25% to 0.35% at t = 1000
minutes and the simulation stopped at t = 2000 minutes. The above
procedure was repeated for the nine configurations. The TL settings
and detuning factors obtained for the different configurations in
the base case design of C3 splitter are shown in Table 5.2
Previously dual PI composition control of the base case C3
spHtter has been carried out by Hurowitz et al. (1998). He used a
non-Hnear dynamic tray-to-tray model for his analysis. He tuned the
composition control loops for minimum lAE for setpoint changes in a
similar manner to the one adopted here. The TL settings obtained in
Table 5.2 compared well with those obtained by Hurowitz (1998).
However the detuning factors did not match well with those
generated by Hurowitz. The tuning factors obtained here were
aggressive as compared to those obtained by Hurowitz. The
difference between the tuning used here and