experimental verification of dynamic operation of

EXPERIMENTAL VERIFICATION OF DYNAMIC OPERATION OF CONTINUOUS AND MULTIVESSEL BATCH DISTILLATION COLUMNS by Bernd Wittgens

A Thesis Submitted for the Degree of Dr. Ing.

The Norwegian University of Science and Technology Submitted September 1999

ERRATTA 22. November. 1999 Some results in Chapter 2 were unfortunately omitted in the final editing of the Chapter. The reader is referred to the paper “Evaluation of Dynamic Models of Distillation Columns with Emphasis on the Initial Response” by Bernd Wittgens and Sigurd Skogestad, presented at: DYCORD+’95, 7-9 June 1995, Helsingør, Danmark (see Appendix F). In sections three to six of the paper and also Appendix B and C of the thesis, methods to determine operational parameters from experiment are presented. Further results concerning the importance of linearized tray hydraulics which were omitted in the thesis are given.

In Table B.11, page 201, the coefficients of Equation B.53 are: Procedure D D2R D2S








-11.44 -24.17 -7.03

0.63 0.73 0.61

1.0 1.0 1.0

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Abstract Distillation is probably the most important unit operation in chemical industries for the separation of liquid mixtures into pure products. In a single batch distillation column, multicomponent mixtures can be separated into a number of product fractions, whereas in continuous distillation a sequence of columns is necessary to perform the same task. Batch distillation columns offer greater flexibility with respect to variations of feed mixtures, feed composition, relative volatilities and product specification. However, batch distillation columns in general require more energy input compared to a continuous distillation column. A newly developed batch distillation column, for the simultaneous separation of a multicomponent mixture might represent a process which combine the energy consumption of continuous distillation and the flexibility of conventional distillation. In recent years research on the dynamics of distillation column was focused on the development of models suitable for dynamic simulation of the composition dynamics. The purpose of research was on e.g. the selection of control structures. Few of these models were verified experimentally on distillation columns. A rigorous model based on first principles of a staged high purity continuous distillation column is presented and experiments are performed to verify the model. The importance of the tray hydraulics to obtain good agreement between simulation and experiment is demonstrated. Further, analytical expressions are derived for hydraulic time constants for the application in models with simplified liquid and vapor dynamics. Over the last centuries, chemical industries has more and more changed from conventional batch columns to continuous distillation columns, because of the lower energy demand. However, this trend is about to change especially in the production of fine chemicals or pharmaceuticals where batch distillation is recently becoming more important. The production of fine chemicals is characterized by small amounts of product and frequent changes with respect to feedstock and product specifications. With this renewed interest, investigations on the operation of batch distillation processes are needed or alternatively, new column configurations should be considered. The newly developed multivessel batch distillation column consists of a reboiler, intermediate vessels and a condenser vessel and provides a generalization of previously proposed batch distillation schemes. The total reflux operation of the multivessel batch distillation column was presented recently, a simple feedback control structure based on temperature measurements has been developed. The feasibility of this strategy is demonstrated by simulations and verified on a laboratory scale multivessel column. The experiments show very good agreement with the simulations, and confirm that the multivessel column can be easily operated with simple temperature controllers. A simple procedure to determine the setpoint of the temperature controller is presented and show that final product compositions are independent on the feed composition. The multivessel batch distillation column is compared to a conventional batch column, both operated under feedback control. It is found that the energy consumption for separation of a multicomponent mixtures into high purity product requires considerably less energy in a multivessel column compared to a conventional batch distillation column. Besides the reduction in energy consumption the much simpler operation of the new column is established.

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Acknowledgement I am grateful to my supervisor, Sigurd Skogestad, for his great encouragement and guiding me into the scientific world. The numerous discussions with him have always been fruitful and inspiring. Further, I am grateful for his patience and moral support throughout the work. Thanks to all present and past members of the staff of the Department of Chemical Engineering, especially the process control group at NTNU for a good time and many interesting discussions, both on research projects as well as on less serious matters. In particular, I would like to thank Eva Sørensen who endured me during the first years of this study. Many friends have been important to me over the years. In particular I have shared lots of good time with Jørn & Trude Skogø and Christian Steinebach who shared both ups and downs with me. Thanks also to all members of “Trondhjem’s Kajakk Klubb” of Trondheim for the mostly exciting and usually time consuming kajak-trips in Norway. Most of all I would like to thank the one which has suffered the most during the final “phase” of this work, Ann Elisabet Østvik, she gave me all the support I needed through this rather demanding time. My family has always been important to me. Nevertheless, I am most off all grateful to my very first teacher, who has always supported me and I therefore dedicate this thesis to my mother. Financial support from the Royal Norwegian Council for Scientific and Industrial Research (DEMINEX-Program) and the Norwegian University of Science and Technology is gradefully acknowledged.

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Contents 1

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Introduction and Literature Review 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Distillation dynamics and modeling . . . . . . . . . . . . . . 1.2.1 Rigorous Models . . . . . . . . . . . . . . . . . . . . 1.2.2 Simplified models . . . . . . . . . . . . . . . . . . . 1.2.3 Constant molar flow model . . . . . . . . . . . . . . . 1.2.4 Simplification of the liquid dynamics . . . . . . . . . 1.3 Continuous Distillation . . . . . . . . . . . . . . . . . . . . . 1.3.1 Initial response in Continuous distillation columns . . 1.3.2 Experimental determination of operational parameters 1.4 Batch Distillation . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Conventional batch column . . . . . . . . . . . . . . 1.4.2 Heat integrated batch columns . . . . . . . . . . . . . 1.4.3 Middle Vessel Column . . . . . . . . . . . . . . . . . 1.4.4 Multiple-effect Batch Distillation System . . . . . . . 1.4.5 Multivessel Batch Distillation Column . . . . . . . . . 1.5 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation of Dynamic Models of Distillation Columns with Emphasis on the Initial Response 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Rigorous Tray Model . . . . . . . . . . . . . . . 2.3 Simplified Model with Linearized Tray Hydraulics . . . 2.3.1 Tray Model . . . . . . . . . . . . . . . . . . . . 2.3.2 Linearized Tray Hydraulics . . . . . . . . . . . 2.4 Obtain operational parameters from experiment . . . . .   

and 2.4.1 Liquid holdup and distribution on tray  2.4.2 Liquid hydraulic time constant  . . . . . . . . . 2.4.3 Vapor constant . . . . . . . . . . . . . . . . . 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Holdup estimation . . . . . . . . . . . . . . . . 2.5.2 Hydraulic time constant . . . . . . . . . . . . .

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CONTENTS 2.5.3 Comparison of initial time constant of Experiment and Simulation 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Multivessel Batch Distillation 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . 3.2 Simulation model . . . . . . . . . . . . . . . . . . 3.3 Total reflux operation with constant vessel holdups 3.4 Feedback control of multivessel column . . . . . . 3.5 Achievable separation . . . . . . . . . . . . . . . . 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . .

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Closed Operation of Batch Distillation Experimental Verification 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Multivessel Batch Distillation Pilot Plant . . . . . . . . . . 4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . 4.3.1 Experiment 12: Feed initially in reboiler . . . . . . 4.3.2 Experiment 4: Feed initially distributed . . . . . . 4.3.3 Experiment 2: Product composition trajectory . . . 4.4 Simulation of experiment 12 . . . . . . . . . . . . . . . . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Main lessons from the experiments . . . . . . . . 4.5.2 Suggestions for controller tunings . . . . . . . . . 4.5.3 Justification for column temperature control . . . . 4.5.4 Alternative control variables . . . . . . . . . . . . 4.5.5 Optimal operation . . . . . . . . . . . . . . . . . 4.5.6 Closed operation of conventional batch distillation 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Alternative Control Structure of Multivessel Batch Distillation 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Total Reflux Operation . . . . . . . . . . . . . . . . . . . . 5.3 Composition control by feedback . . . . . . . . . . . . . . . 5.3.1 Feedback from vessel composition . . . . . . . . . 5.3.2 Feedback from control tray composition . . . . . . 5.3.3 Feedback control based on tray temperatures . . . .

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CONTENTS 5.4 Alternative Start-up Procedure 5.5 Discussion . . . . . . . . . . . 5.6 Conclusions . . . . . . . . . . Bibliography . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . 6

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Comparison of Multivessel and Conventional Batch Distillation 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Column configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Conventional batch distillation . . . . . . . . . . . . . . . . . . . 6.2.2 Multivessel batch distillation . . . . . . . . . . . . . . . . . . . . 6.3 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Operation policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Conventional batch distillation . . . . . . . . . . . . . . . . . . . 6.4.2 Multivessel batch distillation . . . . . . . . . . . . . . . . . . . . 6.4.3 Operation conditions . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Conventional batch distillation: Production rate . . . . . . . . . . 6.5.2 Multivessel batch distillation: Production rate . . . . . . . . . . . 6.5.3 Multivessel batch distillation: Achievable separation . . . . . . . 6.5.4 Multivessel batch distillation: Influence of the controller setpoint . 6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Discussion, Conclusions and Future Work 7.1 Discussion . . . . . . . . . . . . . . . 7.2 Conclusions . . . . . . . . . . . . . . 7.3 Future work . . . . . . . . . . . . . . 7.3.1 Continuous distillation . . . . 7.3.2 Multivessel batch distillation .

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A Experimental facilities A.1 Continuous distillation tower . . . . . . . A.1.1 Tray design . . . . . . . . . . . . A.1.2 Reboiler . . . . . . . . . . . . . . A.1.3 Total condenser and accumulator . A.1.4 Peripheral equipment . . . . . . . A.1.5 Instrumentation . . . . . . . . . . A.1.6 Data acquisition and control . . . A.1.7 Control of manipulated variables . A.2 Multivessel batch distillation unit . . . . .

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CONTENTS A.2.1 Instrumentation . . . . . . . A.2.2 Control structure . . . . . . A.2.3 Design and operation data . A.2.4 Data Acquisition and control A.3 Product composition analysis . . . . A.4 Distilled system . . . . . . . . . . .

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D Multivessel Batch Distillation, Modeling aspects D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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B Obtain operational parameters of a distillation column B.1 Initial temperature response . . . . . . . . . . . . . . . . . . . . . . . . . B.1.1 Definition of the initial time constant . . . . . . . . . . . . . . . B.1.2 Hydraulic time constant estimated from experiment . . . . . . . . B.1.3 Experimental procedure to obtain the initial temperature response B.1.4 Results inital temperature response . . . . . . . . . . . . . . . . B.1.5 Estimation of the tray holdup from initial temperature response . B.1.6 Results tray holdup estimation . . . . . . . . . . . . . . . . . . . B.2 Experiments to obtain the hydraulic time constant . . . . . . . . . . . . . B.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3 Experimental determination of the residence time . . . . . . . . . . . . . B.3.1 Experimental procedure of tracer injection experiments . . . . . . B.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3.3 Discussion of experimental procedure . . . . . . . . . . . . . . . B.3.4 Modeling of tracer experiment . . . . . . . . . . . . . . . . . . . B.4 Obtain column holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . B.4.1 Dumping of the column . . . . . . . . . . . . . . . . . . . . . . B.4.2 Modeling of the column pressure drop . . . . . . . . . . . . . . . B.4.3 Parameter Estimation for the simulation model . . . . . . . . . . B.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.4.5 Holdup prediction . . . . . . . . . . . . . . . . . . . . . . . . . B.4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.5 Summary of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C Linearized Tray Hydraulics C.1 Tray hydraulics . . . . . . . . . . . . . . . . . . . . . . . . . . C.2 Estimation of hydraulic time constants from column design data C.3 Linearization of hydraulics . . . . . . . . . . . . . . . . . . . . C.4 Summary: Hydraulic time constants . . . . . . . . . . . . . . . C.4.1 Comparison: Experiment - Simulation . . . . . . . . . .

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CONTENTS D.2 Simulation model . . . . . . . . . . . D.2.1 Mass and Component Balance D.2.2 Vapor Liquid Equilibrium . . D.2.3 Thermodynamic model . . . . D.3 Comparison simulation models . . . . D.4 Design of the experimental system . . D.5 Discussion . . . . . . . . . . . . . . . D.6 Conclusions . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . .

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E Experiments: Multivessel Batch Distillation E.1 Experiment 1 . . . . . . . . . . . . . . E.2 Experiment 2, 06.december.1995 . . . . E.3 Experiment 3, 22. march. 1996 . . . . . E.4 Experiment 4, 03. april. 1996 . . . . . . E.5 Experiment 7, 04. october. 1996 . . . . E.6 Operation with three components . . . .

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F Evaluation of Dynamic Models of Distillation Columns Initial Response F.1 Introduction . . . . . . . . . . . . . . . . . . . . . . F.2 Tray Modeling . . . . . . . . . . . . . . . . . . . . F.2.1 Rigorous Tray Model . . . . . . . . . . . . . F.2.2 Tray hydraulics . . . . . . . . . . . . . . . . F.3 Linear Tray Hydraulics . . . . . . . . . . . . . . . . F.3.1 Linear flow relationships for column sections F.4 Obtaining parameters from experiments . . . . . . . F.4.1 Liquid holdup . . . . . . . . . . . . . . . . .  F.4.2 Liquid hydraulic time constant  . . . . . . . F.4.3 Vapor constant . . . . . . . . . . . . . . . F.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . F.5.1 Pressure drop . . . . . . . . . . . . . . . . . F.5.2 Liquid holdup . . . . . . . . . . . . . . . . .  F.5.3 Liquid hydraulic time constant  . . . . . . . F.5.4 Vapor constant . . . . . . . . . . . . . . . F.6 Discussion and Conclusion . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2

CONTENTS

Chapter 1 Introduction and Literature Review Abstract This chapter give a brief description of the two types of distillation columns considered in this thesis. The remainder of this chapter is devided into two major parts; first an overview of the literature concerning modeling of the initial response of distillation columns, the second part is focused on the control of a newly developed distillation arrangement, the multivessel batch distillation column. The introductory chapter concludes with a description of the following chapters of the thesis.

1.1

Motivation

Distillation is an essential unit operation in chemical industries, e.g. for the purification of final products or for the recovery of components due to environmental aspects. The distillation of chemical mixtures can be performed both by means of batch or continuous operation. A schematic of a continuous distillation column including a control structure is shown to the left in Figure 1.1. A generalized batch distillation column (further called multivessel batch distillation column) with a feedback control structure is shown to the right of Figure 1.1. During the last decades, the academic research community have focused their activities more on the energy consumption of the process by improving the operation of this process in general and its design. In the chemical industries distillation columns are high energy consumers with up to 40 % of the total energy consumption of the plant. Continuous distillation columns are used for the separation of bulk chemicals where high througput and few feed or product changes are expected. The design of the processes concerns rather often one feed mixture which is about to be seperated, the unit is than optimized with respect to productivity and energy consumption. Batch distillation with its inherent flexibility becomes increasingly important in the production of fine chemicals and pharmaceuticals, where product is characterised by small amounts and high added value. Batch distillation is able to recover a number of different products from one multicomponent feed charge, a wide range of feed compositions and relative volatilites can be handled in one sin-

4

1. Introduction and Literature Review

gle column. In a conventional batch distillation, one component at a time is separated from the mixture when multicomponent mixtures are separated. Generally, batch distillation is applied for low throughput operations where the higher capital costs of a continuous distillation unit are not justified. A generalization of the conventional batch distillation column is the multivessel batch distillation column, in it’s most flexible form, a superstructure for batch distillation columns with an energy consumption comparable to a continuous distillation for a given separation. Qc

Qc

Mc M

V Dx

Tc

d

M1

L1

1

Tc1

6

11

V

L2

M2

12

F zF

Tc2 17

22

V

L3

M3

23

Tc3 28

Tc

33

V

L

Mc

V M4

Qb

Bx

b

Q

b

Figure 1.1: Flowsheet of a continuous (left) and multi vessel batch distillation column (right) Although distillation is one of the most intensively studied processes in the chemical industry, still it represents an interesting field for research:

The academic research in distillation is primarily directed towards the optimization of the operation and the process itself. Further, dynamic studies are performed concerning the control of this process, which is characterized by excessive control interaction of the manipulated variables. For this purpose models of different complexity are developed and applied with satisfactory accuracy for simulation studies, both with respect to the dynamic and steady state behavior of the process. However, few of these models are validated experimentally on distillation plants.

Batch distillation is probably the “oldest” unit operation in chemical industries. The operation policy of industrial installations is not fundamentally different from laboratory equipment, which means that rather simple operation policies are applied. Increasing demand for efficiency, both with respect to energy consumption and product

1.2. Distillation dynamics and modeling

5

recovery, opens for research focused on new operation policies. Further, the combination of several units to some kind of “superstructure” which combines flexibility with respect to feed mixtures, ease of operation and reduced energy consumption is an important research area.

1.2

Distillation dynamics and modeling

Review articles in the area of distillation column dynamics and control are published quite frequently and give a rather good insight in ongoing reasearch. Early articles consider mainly steady state operation of distillation columns, the introduction of digital computing enable the investigation of the dynamics in the erarly 1950’s. The pioneering work in distillation dynamics is reviewed in the work by Rosenbrok (1962). The book by Rademaker (1975) includes a detailed investigation on the material and energy balance of staged distillation column, further the influence of the flow dynamics on the composition dynamics is considered. Reviews on dynamics and control were published by Tolliver and Waggoner (1980), McAvoy and Wang (1986) and Skogestad (1997). Practical recommandations for the control of distillation columns are published by Shinskey (1984) and Luyben (1992) considering dual composition control, including the issue of control configurations selection. There is a continuous development of rigorous models of distillation columns for process control and dynamic studies. Nevertheless, few of these models solve the material and energy balance on each plate using models which incorporate plate hydraulics and the downcomer dynamic. Further, the performance of the process can seldom be predicted by models which exclude fluid hydraulics and change of physical properties. However, the application of highly complex models for control studies is not always necessary. The existence of a rigorous model of the system enables the study of the relative importance of different features and can verify simplifications of simplified models. The objective of a model is to describe a dynamic system as precise as necessary and the complexity of the model considered is strongly dependent on the intended use of the model. Models with neglected tray hydraulics are sufficient for the steady state optimization of an entire plant, while they are insufficient in the selection process of a new control system. For the development, validation and verification of a control system, the model has to represent the initial response of a given unit to step changes of the manipulated variables or disturbances correctly, since the control system is supposed to limit deviations from the intended point of operation. Further, the process of modeling has to consider the design data of a particular tray, the operation point of the plant and will often encounter the use of empirical functions to describe some phenomena. Correct modeling of e.g. the hydraulic time constant of the liquid flow is important in this respect. The liquid lag over a staged column decouples the composition response of the column, which is from a control point of view an advantage, since it opens for somewhat slower composition measurements. Low order dynamic models can be used for several purposes, for example for the derivation of analytical expressions to gain deeper insight into the dynamic behavior of a process. Further, low order model can be applied for simulation and controller design. However, the derivation of low order models from rigorous models by combining sub-models (one for the

6

1. Introduction and Literature Review

dominant composition dynamics, one for the holdups) may result in inconsistant models. Jacobsen et al. (1991) suggested to derive low order linear models from (numerical) linearizing the nonlinear rigorous model combined with subsequent model reduction.

1.2.1

Rigorous Models

Models are often classified as “rigorous” or “simplified” models. Rigorous models for equilibrium stages consist of mass and energy balance which include some kind of flow and pressure dynamic as well as the thermodynamic relations. The flow dynamic describe the changes in liquid holdup on a stage because of variations in liquid and vapor flow, while the pressure dynamic primary influence the vapor holdup on a stage. Considering the stage design (see Figure 1.2) of a column the liquid holdup has (sometimes) to be split into liquid on the tray and downcomer which result in twice as much states per stage. Nevertheless, even in the most rigorous model certain simplifications as thermal and mechanical equilibrium or assumption of perfect mixing in the phases are introduced. The thermodynamic equilibrium (vapor liquid equilibrium) can be corrected by introducing a simple Murphree tray efficiency for each component. Commonly, the effect of heat losses to the surroundings and the dynamic of the column structure are neglected. Vi yi

control volume vapor liquid

L i+1 x i+1

x Vi-1 yi-1

Li xi

Figure 1.2: Control volume on a stage Assumptions for an equilibrium based stage model: A1 perfect mixing in both liquid and vapor phase A2 thermodynamic and mechanical equilibrium (assume 100 % tray efficiency) A3 neglect heat loss and thermal capacity of column structure A4 consider only normal operation (e.g. no flooding, weeping)

1.2. Distillation dynamics and modeling

7

Assumptions A3 and A4 can be removed easily by extending the model. The differential-algebraic system of equations to describe a “staged” distillation column (see Figure 1.2) based on a UV-flash, consist of the component-mass balance:

     
  
 !         "$# &%
 ')( &% 
 ' #  )(    (1.1) *     " +   *   where with as component holdup of component , on stage - . This are  .0/ 21      independent component balances since 432576   .  represents the entire *+   liquid holdup (tray and downcomer) and the molar holdup of the vapor phase. Both liquid and vapor phase are subjected to some dynamics because of changes in liquid and vapor flow (flow dynamics, see Equations 1.3 and 1.4). The energy balance over the stage

98  =  
  C% + C%  +  :;@?  A  @?  "B# 
 '@? 
 # @?  (1.2) 8      9DE?    GFHJI &K " +   7DL? +   MFNH@I +K with . The flow dynamics of the liquid leav ing the tray and downcomer are described by algebraic and empirical equations which link hydraulic and stage design, determined by

  QP PVU QPXWZY)[]\^Y `_ ( K O D  #RTS F

(1.3)

#  2O D *+  QP #NRaS PVU F QPXWZY)[@\^Y `_ ( K

(1.4)

 and the vapor dynamic



These correlations consider the design of a stage and can be found in e.g. Bennett et al. (1983), Lockett (1986), Rademaker et al. (1975), or Stichlmair (1978). Additionally, thermodynamic relations to describe the flash relation (VLE) given by

D 8 P #RTS PVTKcb

Dd Q P ( QPXeNQP F E P ?   QP ? +  EPf   QPf+  TK

(1.5)

between liquid and vapor phase are necessary. Given the above assumption and the constant stage volume implies that a UV-flash has to #RTS be solved. The definition of a UV-flash is: Given the internal energy U, volume of a stage, *   and the component holdup    N,+ a  flash calculation is performed computing the ratio of vapor  and liquid on the stage ( or phase split), composition of vapor and liquid phase ( ( e and ), as well as pressure F and temperature . In a recent review paper on distillation (Skogestad, 1997) are almost no references listed which apply this approach. Papers by Gani et al. (1990) on design an simulation of complex chemical process and Flatby et al. (1994) seams to be the exception. An alternative model by Retzbach (1986), propose a rate based mass transfer correlation between phases, including hydraulic and pressure drop correlations. The rigorous model of Retzbach is primarily developed for the nonlinear simulation of a multi-component mixture in a distillation column with side stripper. The tray hydraulic models applied are extensively described by Stichlmair (1978), simplifications are introduced to simplify for application of the model in a control structure synthesis.

8

1. Introduction and Literature Review

1.2.2

Simplified models

Solving a dynamic distillation column with a that complicated model (see outline in section 1.2.1) often requires a considerable amount of both time and resources (computer power) to solve the set of differential-algebraic equations. Neglecting the vapor holdup  g  The most common simplification is to neglect the vapor holdup (  o?  "p# nDL?  o? 

(1.8)

1.2. Distillation dynamics and modeling

9

This simplification will be reasonable correct even for more extensive holdup changes, since   H : is considered in the energy balance (see Eq. 1.7). the term   :rq Further simplification of the energy balance is achieved by assumming ? H h and   ?  ? constant liquid enthalpy on all stages, . This assumption can be used by definition  of the correct reference state, which should be the pure component as saturated liquid at a given reference pressure. Applying this definition give different reference temperatures (components boiling points at e.g. column pressure).

  C %
nDL? +  C%
m?   aK "B#  nDE?    o? +  dK   ?  : l  `/ 

Úr w/ I  ? /a

 Ëë KMÒ  Ë ë Ú / Û+  I ? Ë ë

(2.31) (2.32) (2.33) (2.34)

2.3. Simplified Model with Linearized Tray Hydraulics

31



 EÍ Ï  KMÒ  ÍQÏ Úr `/ F ÍQÏ # D  O È 2  W * Ý  KGÒ   Ë RER Ú¬ `/ I  ø á `ù / 2O D  ËEÌfS  W

(2.35)

  ËRER

(2.36)

Ë

The clear liquid height is defined in Equation 2.19. The height over weir ? ë is obtained from Equation 2.20, finally the dry pressure drop is computed from Equation 2.25. Assuming constant molar flows over the tray we can express the hydraulic time constant +  of vapor  and liquid  of Equation 2.29 by changes in liquid holdup on the stage.



g





 ÍQÏ ì
g

v

  ËRER v ì



 /a " ì
g î v î v " ì

î g

 Ëë v

î g

(2.37)

(2.38)

Express the holdups with correlations 2.32 to 2.36 and linearize the nonlinear equations yields:

 /a K /T æ D  æ ù #  #  È  ÍQÏ  ÍEÏ Ä #  # È  ËRLR  ËRLR Ä ËL̊S    Ëë

Çh



É

 Ëë Ùh ñ ËL̊S 

(2.39)

(2.40)

(2.41)

(2.42)

Combining Equations 2.39 to 2.42 with 2.37 and 2.38 yields:

 ÍQÏ  /a æ