Verification of a Distillation Column Benchmark

Copyright © IFAC Dynamics and Control of Chemical Reactors (DYCORD+'95), Copenhagen, Denmark, 1995

VERIFICATION OF A DISTILLATION COLUMN BENCHMARK A. Koggersbol and S. Day Jorgensen

Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark.

Abstract: This paper presents the validation of an elaborate model of a semi industrial scale distillation column equipped with an indirect heat pump. The model is derived for ordinary operation within the designed operating window . The paper describes the basis assumptions of the model. From experimental data model parameters are found and the model is validated against static and dynarrtic experimental data. The performance of the model is generally good, however, it does not catch some of the more complex behaviour of the process . Keywords: Bendunark examples; Mathematical models; Process models; Process simulators.

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1. INTRODUCTION With the significantly increased utilisation of model based process design and optimization and especially of dynamic models for process simulation and control design there is a need for validated test cases or benchmarks of important process examples. Such test cases may be applied for development of simulation models and for development of new control structures and of new control designs.

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In the chemical industry unit operations are often tightly interconnected to minimize the load on energy and raw materials. Interconnections tend to give rise to complex dynamic behaviour and to more difficult control problems. The purpose of this work is to provide a benchmark for testing e.g . control designs on a plant with the above characteristics . The paper describes development of a dynamic model of an energy integrated distillation column. This is done by first describing and commenting the assumptions which were chosen as the platform of the model , and then presenting validation results. Model equations are not presented here since they are easily derived from the assumptions.

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Fig. 1. Distillation plant flowsheet.

arates a mixture of methanol and isopropanol with a low concentration water impurity. The heat pump has an expansion valve which throttles high pressure liquid freon (Rl14) to a lower pressure (PL) suitable for evaporation in the condenser. After the condenser there is a throttling valve (CV9) by which the freon vapour ftowrate can be manipulated . After superheating the vapour the compressor elevates the pressure to a high pressure (PH) suitable for condensation in the reboiler. A small part of the condensation takes place in a secondary condenser which by a cooling water circuit is connected to a set of air-fan coolers . The cooling rate can be manipulated by the control valve CV8, thus controlling PH. Through a storage tank (Rec) and the pre-compression

2. PLANT DESCRIPTION Figure 1 shows a schematic of the process . The column has 19 sieve trays, a thermosiphon reboiler, a total condenser and a reflux drum. It sep495

heat exchanger the freon circuit expansion valve.

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A. 6 Interphase transport assumptions: 1. The thermodynamic equillibrium IS described using UNIFAC . 2. The reboiler is assumed to provide an ideal equillibrium stage. 3. A (constant) Murphree stage efficiency describes the approach to equillibrium . A. 7 Heat pump vapour phase: 1. The vapour holdup is assumed quasistationary 2. Expansions over the expansion and the throttling valves are assumed isenthalpic . 3. Compression in the piston flow compressors is assumed adiabatic and reversible, i.e. isentropic. 4. Pressure changes are assumed concentrated to three locations: (a) Over the compressors, where pressure increases to PH. (b) Over the expansion valve , where pressure decreases from PH to PL (c) Over the throttling valve CV9 where pressure decreases to the compressor inlet pressure : Pi . A. 8 Heat pump Liquid phase: 1. Dynamic heat pump fluid hold up in Rec. and on heat pump side of the column condenser . Both volumes are assumed well mixed. 2. The apparent liquid level on the heat pump side of the condenser is controlled by a mechanical float which uses the expansion valve as actuator. The total volumetric hold-up is modelled assuming a bubble rise velocity. 3. Quasistationary temperature profiles in secondary condenser and compressor gas preheater . A. 9 A Redlich-Kwong equation of state is used for the heat transfer medium.

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3. MODELLIl\G ASSUI\IPTIONS A mathematical model is formulated from first engineering principles. The basis for the model development is a set of assumptions motivated by the desire to obtain a model which is suitable for understanding process dynamics with the aim of leading to simplified models for control design . The model should however not become unneccessarily complex. The basic assumptions deal first with the number of phases and balances. Additional assumptions treat the behavioural aspects within each phase and balance , first for the distillation column and then for the heat pump: A. 1 The number of flowing phases is limited to one liquid and one gas phase A . 2 Balances are formulated for components and energy. A. 3 Vapour phase assumptions: 1. Quasistationary and ideal vapour phase. 2. Constant molar vapour flow rate . 3. The tray pressure drop is the summed contributions from liquid weight and the dry hole pressure drop using correlations from Zuiderweg( 1982) . A. 4 Liquid phase assumptions: 1. Ideal liquid phase mixing is assumed on the trays, on both sides in the reboiler and on the coolant (heat pump) side of the column condenser and in the accumulator. 2. The column side of the condenser is assumed to consist of a sub cooled well mixed liquid and a well mixed vapour region at the bubble point temperature. Thus reflux is subcooled . 3. Tray hydraulics are modeled assuming spray flow regime using correlations from Zuiderweg( 1982) . 4. The feed is saturated liquid . 5. Liquid flows induced by pumps in volumetric units . 6. Constant heat of vapourisation. A . 5 Total energy balance assumptions: 1. Quasistationary energy balances around column ends. 2. Heatloss is negligible. 3. Negligible pressure drop due to friction in tubes and heat exchangers. 4. Liquid heat capacities are composition (but not temperature) dependent. 5. Dynamic energy balances in condenser and accumulator . 6. Linear correlations between heat transfer coefficients and freon flow rate and heat pump low pressure . 7. Infinite efficiency of the air-fan coolers .

The main differences between the developed model and standard distillation column model assumptions used in the litterature can be pinpointed to three points: • This column is closed to environment , therefore pressure dynamics are modelled. The vapour flow rate is determined implicitly from two energy balances around the column ends and the tray pressure drops . • Realistic non ideal thermodynamics. • Realistic tray hydraulics , thus flow dynamics are not instantaneous . This assumption reduce the liquid amount on the sieve trays compared to the standard assumption of emulsion flow regime. Thus leading to faster column dynamics both for the slow and fast time constants (Skogestad and Morari , 1988). This assumption also leads to a smaller contribution to the tray pressure drop. 496

2) Transients from changing an external flow in the production case . This will reveal the slowest time constant which is related to disturbance of the external material balance.

The major limitations of this model may be variations in tray efficiencies , which at present are not incorporated. An additional limitation may be that thermal delays in the heat pump heat exchangers are not included. However both these limitations can clearly quite easily be accomodated if experimental results prove this to be desirable .

4.1. Total reflux

An experiment with 13 step changes in PH, PL , and the number of active compressor cylinders is shown in figure 3. 8 steady state operating points were established. Reboiler , condenser, and accumulator levels and heat pump high and low pressures are under feedback control.

The assumption regarding constant molar vapour flowrate is reasonable because the molar heats of vapourization of the two main components differ from the mean value by only some 2% and the temperature dependence is insignificant within the relevant operating range (4 % change on a 20°C temperature change) (Smith and Van Ness , i975) . Reid, Prausnitz, and Poling (1987) illustrate that the heat capacity of a liquid is almost constant around and below the normal boiling point . Therefore the heat capacity of a mixture is assumed only to be concentration dependent.

The plots show the comparison between transients from the experiment and the results of a simulation where the same setpoints changes were applied as during the experiment . On the plots of the heat pump pressures it is seen that in the simulation the transients are generally faster than in the experiment. This indicates that the heat pump model doesn't fully encompass the constraints in the energy inputs and outputs which are present in reality. At times 5.3 and 11.4 hours the cooling valve CV8 controlling PH actually saturates which is why the decending and climbing rates of PH suddenly decrease during these large steps. The behaviour is nonlinear since it seems that reducing PH is easier than increasing it. The model does not catch this characteristic probably due to simplifications in the model of the compression (isentropic) and the model of the air coolers connected to the secondary condenser (infinite efficiency : cooling water return temperature equals temperature of the surroundings). The mismodelling of these characteristics is, however, only important for large step changes in the setpoints of PL and PH . The case which is usually of interest is the use of PH and PL for control purposes and in this case the increments of the pressure setpoints at each sampling instance are never as large as 50 kPa. The mismodelling should therefore have little significance for the control results.

The assumptions of isenthalpic expansions and adiabatic compression are basically assumptions of ideal behaviour . With the present instrumentation on the plant it is not possible to validate these assumptions experimentally. However, with respect to the dynamic behaviour of the system these assumptions have little significance. Static gains with respect to the heat pump pressures PL and Pi may on the other hand be affected significantly by e.g. non-ideal (non-adiabatic) compression, and a far better description may be obtained of the non-linear gain of the expansion valve CV9 which is of great importance for low-pressure control purposes, if the thermodynamics of the compressors were modelled with greater detail.

4. VALIDATION Three experimental runs comprising 15 steady states were used for estimation of model parameters. As an example the plots on figure 2 show estimation of stage efficiencies by comparing simulated temperature profiles to experimental data covering most of the operating region. The PTIOO-elements are more accurate and better calibrated than the thermocouple elements so in case of significant differences between the two the former is to be trusted. Clearly, by using a single constant stage efficiency for all trays it is not possible to obtain a perfect temperature-profile fit, however, it seems that the temperature profile is reasonably well estimated assuming a value of 5060% .

In a number of situations (at time 2.93 hr, 5.22 hr, and 11.36 hr) where P L was reduced or PH was increased the CV9 valve of the simulation saturated at fully open in an attempt to hold PL down to the setpoint. It seems as if the model of the compressors doesn't give them enough suction power compared to the live conditions. This inaccuracy of the model is probably due to the fact that the compression is modelled adiabatically and heatloss from tubes and from the column was set to zero in the simulation. Such heat loss would if all other conditions remained unchanged result in a decrease of PL. Nonadiabatic operation of the compressors would increase the slope of the com-

Using the estmated parameters transients from two experiments were simulated: 1) Transients from operation at total reflux. This may reveal all but the slowest time constant of the system . 497

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pression curve in a P,H-diagram with the result that the pressure drop across CV9 should be larger in order to fulfil the enthalpy balance for the compression circle.

Apart from these offsets and the overshoots caused by the overshoots of PH the dynamic behaviour of the experimental reflux rate seems to be reasonably well described by the model. The model seems to have too fast dynamics for the column pressures but the deviations from the experiment can all be related to the fast and overshooting be-

Estimation of heat transfer coefficients has proven to be encumbered with relatively large uncertainties, These affect the accuracy of the simulated column pressures and especially the simulated internal flowrates . The latter is clear as the simu498

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sures it seems that in the model the vapour flowrate affects the pressure drop across a tray more than in the experiment . At time 8.76 hours the setpoint for PL is reduced by 25 kPa with the result that the reflux rate is increased and the pressure on the top tray is decreased . In the experiment the pressure is decreased on all trays but in the simulation the increased vapour flow rate re-

haviour of PH . In situations where only PL is changed the speed of response of the column pressures does match that of PL both for the simulation and the experiment. So the model assumption that column pressure has no dynamics of its own seems to be justified. Combining the reflux rate and the column pres499

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estimated correctly resulting in faulty estimates of the temperature gains since these are closely correlated to the slope of the temperature profile.

suits in an increased pressure drop across the trays such that the pressure in the reboiler is actually increased. It appears that the exponent of Zuiderwegs (19S2) equation 10

5. CONCLUSIONS The main conclusions are that the model in general perform well by predicting the time constants of the actual plant and the approximate process gains. The accuracy of predicted steady state temperature profiles is somewhat limited by the assumption of constant stage efficiency. It has also become evident that for accurate simulation of a distillation column which is heat integrated and closed to environment modelling of heat transfer rates in heat exchangers is crucial. Furthermore, the assumption of ideal compression is seen to restrict the accuracy of steady state gains from the control valves CVS and CV9 to the heat pump pressures.

should be slitely less than 2 for our tray design (6mm holes in 15mm 6. pitch). In this equation t1Pdry is the pressure drop through the tray holes [Pa), pg is vapour density [kg/m3 ), Ug.h is hole vapour velocity [mls), and CD is a discharge coefficient.

4.2. Production case

From a production experiment transients following a single step change in the top-product flowrate from 1.30 to 1.22 Ilmin are recorded. The feed flow rate is 3 Ilmin and boil-up rate is lS.S I/min. Boil-up rate and top tray pressure are controlled in addition to the control loops implemented during the total reflux experiment. Being a disturbance to the external material balance, this excites the slowest time constant of the distillation column which is visible in the temperature plots on figure 4. The plots show that the model does encompass this slow dynamic element since the time constant of the simulated responses resemble that of the experimental ones. However, it is clear that the magnitude of temperature gains in the model are not accurate, and that the inaccuracy depends very much on the conditions on the actual tray. This is very likely to be a result of the "Constant stage efficiency"-assumption which from figure 2 is known to have only a limited validity. If the stage efficiency during this transient is different from the previously estimated value, and even more if it varies from tray to tray, then the shape of the temperature profile will not be

6. REFERENCES Reid, R .C.; Prausnitz, J.M.; Poling, B.E. (19S7); 'The Properties of Gases and Liquids '; Fourth edition, McGraw-Hill Book Company. Skogestad, S.; M. Morari; (19SS); 'Understanding the Dynamic Behaviour of Distillation Columns'; lud. Eng. Chem. Res, 27 (JO), p.1848. Smith, J .M.; Van Ness,H.C. (1975); 'Introduction to Chemical Engineermg Thermodynamics '; ~lcGraw-Hill Book Company, Third Edition. Zuiderweg, F.J . (19S2); 'Sieve trays: A view on the state of the art '; Chem. Eng. Sci.,37(JO), p.1441 .

500