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

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.

n

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

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

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

\ '

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

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

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

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

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

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

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

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

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

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

0,, Input phase angle of the n'*' frequency component

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

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

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.

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).

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

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