Practical evaluation of hold-up for passive decoupling in distillation column

PRACTICAL EVALUATION OF HOLD-UP FOR PASSIVE DECOUPLING IN DISTILLATION COLUMN

C. H.Sodré¹, J. A.Wilson ² and W Jones2

1Departamento de Engenharia Química, Universidade Federal de Alagoas, Br 104 -

Km 14, Maceió- Al, Brazil E-mail: [e-mail]

² School of Chemical, Environmental and Mining Engineering, University of Nottingham

University Park - Nottingham England -NG7-2RD

(Received: November 12, 1999 ; Accepted: May 18, 2000)

Abstract - Decisions made during the steady-state design of distillation columns have a large influence on the dynamic characteristics of the operating unit. Conventionally, steady-state design is often completed before dynamics and control issues are considered. Additional complexity in the active control system must as a result be used to compensate for any resulting shortcomings in dynamic performance. Here, our aim is to improve control system performance not through more complex active control but through passive improvements arising from more favourable equipment design. An extra liquid hold-up, the middle vessel, was placed in the middle of the column by connecting the feed to an external vessel via a circulating system. To exploit and demonstrate the potential performance of this new modified design, our study was focussed on an existing pilot scale distillation column at Nottingham University. This new design was shown to be very effective in rejecting both feed composition and feed flowrate step changes.

Keywords: Dual composition control, continuous distillation, liquid hold-up, Interactions,middle vessel

INTRODUCTION

The distillation field has a wide diversity of columns. These columns in nature have different types of operation and can process different feed conditions having different product specifications. The result of this diversity is that almost each column requires its own control system. However, general results have been established governing the inherent control limitations in distillation, mainly with respect to interaction. Change of the control configuration and use of decouplers are two possible ways to improve the distillation control in this direction. During the past 10 years significant results using different approach, modified design, have been appeared in the literature: in batch distillation design the use of the middle vessel was cited in papers by Hasebe et al.(1992); Mujtaba et al.(1995), Barolo et al.(1996, 1996a), Skogestad et al.(1997) and Farschman and Diwekar(1998). In continuous distillation column the modified design was cited in papers by Wachter and Andres (1989) and Kropholler and Guesalaga (1990).

The use of the middle vessel was originally proposed by Robinson and Gilliland(1950) for using in batch distillation. In this scheme the feed was added to the middle of the column and the heavy and lights components were withdrawn in the bottom and top simultaneously. Later Bortollini and Guarise(1970) analysed such column for the separation of binary and multicomponent mixtures. This combined operation for batch distillation columns gained renewed attention after the work of Hasebe et al.(1992), Figure 1. It was concluded that the complex column is more effective in removing light and heavy impurities from products than the ordinary batch distillation column.

Barolo et al. (1996) investigated the performance of a batch distillation column with a middle vessel. They used a different operating procedure from the one adopted by Hasebe et al.(1992). According to the simulation the feed vessel decouples the two sections of the column. Because the optimal reflux ratio was almost independent of the reboiler hold-up, and the reboil ratio does not depend significantly on the amount stored in the reflux drum.

The paper by Farschman and Diwekar (1998) investigated the performance of the middle vessel column in batch distillation with respect to interactions. Using variable reflux ratio/variable reboils ratio the authors evaluated degree of interaction between the two composition loops, the distillate composition was controlled by the reflux ratio and the reboiler composition was controlled by the reboil ratio. Simulation results showed that the interactions between the control loops were negligible. But as the hold-up in the middle vessel falls to the order of the hold-up on the trays, the decoupling effect was lost.

Skogestad et al. (1997) investigated the performance of batch distillation column using a the multivessel batch column. This arrangment consist of a reboiler, several mass transfer sections, intermediate vessels and a condenser vessel. The mass transfer sections and tanks are arranged so that all liquid flows by gravity. The authors cited two advantages of this design: the saving of energy and the simple operation of the multivessel column under total reflux. However the column itself is more complicated due to the number of vessels.

In the field of continuous distillation columns, Wachter and Andres (1989) proposed a modified design where two sidestreams where recycle from the column back to the feed in attempt to improve controlability.

Jacobsen and Skogestad (1991) analysed the effect of the overdesign by introducing extra trays in the column. One of the characteristics of this overdesign is that it has a pinch zone in the composition profile. Considering that one of the main reasons for the interaction in a distillation column is the interactions between compositions on all stages, based on this consideration the authors used the pinch zone in the overdesign column to reduce interaction between the sections above and below the pinch zone.

Kropholer and Guesala(1990) suggested to divert part of a reflux to a tray further down the column with the intention of achieving better performance of the derivative action of a feedback controller.

Khelassi (1991) performed a theoretical study of the effect of the feed tray and the reflux drum liquid hold-up on the system performance. The author suggested that as the reflux drum and the feed plate hold-up were increased the result was that both top and bottom loops where decoupled from interacting with each other. The bottom loop was almost unaffected by changes in the top loop by increasing the reflux drum hold-up, whereas, the bottom loop was insensitive to changes in the top loop by increasing the feed tray hold-up. According to the author the interaction in the R-V structure disappears by changing the liquid hold-up and the remaining disturbance was just propagated from one direction only.

All these work show the interplay between design and control in attempt to improve control system performance. The work presented here investigates the effect of increasing the feed tray hold-up in the dynamic performance of the column studied theoretically by Kelhassi(1991). This idea here was studied both theoretically by simulation and experimentally. This extra hold-up was allocated to the middle of the column and is introduced by placing a vessel in the middle of the column and recycling liquid from the feed tray to the middle vessel and back.

DYNAMIC MODELING

As an initial procedure a computer program was developed and validated against plant data. The dynamic behaviour of the distillation column is investigated using the nonlinear dynamic model described below.

The Column

The column contains n=10 real trays. The stages are numbered from the top with the condenser as stage 1 and the reboiler as stage 12. The liquid hold-up on each tray is M_n(moles) and has composition x_n(molar). The methanol-water mixture is fed to the column as a subcooled liquid, onto the feed tray, with molar flow rate F(mol/min) and mole fraction of methanol x_F. The overhead vapour stream is cooled and completely condensed, and then it flows into the reflux drum. The liquid from the reflux drum is partly pumped back to the column(top tray, n=2) as a subcooled reflux at flow rate R(moles/min) and is partly removed as the distillate product with a molar flow rate D(moles/min). The liquid holdup in the reflux drum is M₁ moles and is assumed to be perfectly mixed with mole fraction x₁. The pressure P is constant on each tray and throughout the column. The vapour is generated in a kettle reboiler and fed to the bottom tray. The bottom product is removed at rate B(mol/s) and mole fraction x₁₂(molar).

The distillation column is illustrated in Figure 2.

The Model

A dynamic model was developed such that the overall and component balance was solved for each tray. Additional algebraic model equations are needed for the steady-state energy balance, vapour-liquid equilibrium relationships and Francis weir formula for liquid flow in the reboiler and liquid flow relationship for each tray. The model assumptions are: constant pressure, constant molal overflow, negligible vapour hold-up, fast vapour flow dynamics and non-ideal equilibrium vapour-liquid. To describe the vapour-liquid equilibrium relationship for the more volatile component in a binary mixture, Dalton’s law is applied to the vapour phase and the liquid non-ideal deviation from Raoult’s law behaviour is accounted for by an activity coefficient. For a methanol-water mixture the two parameter can be fitted by the van Laar equations and the van Laar parameters used were from Kojima(1968).

The column equations are shown in Table 1

The Liquid flow leaving each tray is:

(17)

This model was based on experimental observations on the pilot plant column. Mo_n is the nominal tray holdup based on the column diameter and weir dimensions.

Experimental Equipment

The column has ten trays. Each tray has two bubble caps except the feed tray. The feed tray has four bubble-caps. The rig is well equipped with liquid sample points, thermowells and rotameters. Tray temperatures are used to infer the composition from a measurement of bubble point temperature on column trays. For temperature measurements the thermocouples used were ‘T’ type copper/copper constantan. All column trays and the reflux and feed lines were equipped with thermocouples. All column trays also have liquid sample points. Samples of liquid process were analysed using a gas chromatograph (GC).

Due to the limitation of channels of the Eurobeeb system, Eurobeeb system is a 6502 microprocessor that acts as an interface between the measured variable signals and a Personal Computer, only eight variables were record in real time. The on-line measurements from reflux flow, steam flow, top and tray bellow the feed tray temperatures, feed temperature and reflux temperature were logged into files on the hard disk of a personal computer. The others tray temperature were connected to a Cambridge multi-channel temperature indicator.

The feed tray has a different design from the others tray. Figure 3 shows the feed tray envelop, number four, which is composed by the feed tray, number 2, and a trap-out section, number 3. The liquid from the feed tray flows over a circular weir, via a liquid seal into the trap-out. The hold-up in the trap-out does not make contact with the vapour phase therefore it is assumed that the liquid in this section and the liquid on the feed tray are at the same composition.

The external circulation tank, Figure 3 number 6, the middle vessel, has the capacity of 20 litres and it is operated flooded. The tank has two distinct line one situated on the top of the tank admits liquid to the tank and the other one situated at the bottom of the tank is the return line that goes to the feed tray. There is one manual ball valve in the tank line and another one in the tank return line that connects to feed return line. These valves allow liquid to flow either through the tank or to circulate solely around the pump. The tank is provided with a stirwell mixed and avoid stagnant zones.

Liquid is pumped at a high circulation rate from the trap-out section through the external tank and back to the feed tray, through the circulation return line, using a centrifugal pump. A rotameter in the return line indicates the flow back to the column. Liquid circulation rate is 7 litres/min. This circulation rate is much higher than the internal flow in the column to promote good homogenisation in the middle vessel.

The liquid coming from the trap-out section can either go through the circulation tank before being sent back to the feed tray or goes direct to the feed tray without pass through the circulation tank. One of these operational condition is chosen simply changing the position of the valves in the tank circulation lines as mentioned earlier.

MODEL VALIDATION-OPEN LOOP RESPONSE

A computer program written in FORTRAN was developed to solve the system of equations. The program was validated against plant data. The results comparing open-loop response for experimental runs and computer simulation are presented here. The open-loop response, was taken to mean the data collected with both top and bottom tray temperatures in open-loop mode, i.e. without control. For the computer simulation, the reflux and reboiler levels are considered to be under perfect control. For the practical column, the liquid levels in the reboiler and reflux drum are controlled by bottom product flow and distillate flow respectively. Different operational conditions were analysed and the composition and temperature profiles obtained using the theoretical model were compared with the experimental results. The column was always brought close to the reference steady-state, in each run, Table 1. When the steady-state was reached the column was subjected to step change in one of the following variables: Reflux flow, feed composition or steam flow.

Step Change in Reflux Flow

Figure 4 a) and b)gives the dynamic response for (±)20 % step change in the reflux flow in the open-loop situation. The column was allowed to reach the steady-state when the step change in reflux flow was made. For the first part of the response, the positive step change in the reflux flow propagates from tray to tray down the column. When this change reaches a tray, the composition of the tray liquid will start to change and also the composition of vapour. This change will occur from tray to tray until the whole column is in the new steady-state. Looking towards the stripping section the initial composition changes will be bigger where the composition difference between adjacent trays is larger. This is seen in Figure 4 b) where the difference between the previous and the new steady-state for the top temperature is around 0.2 ⁰C while for the Tray 7the difference is around 0.7 ⁰C. After the new steady- state was reached, the system suffer again a step change back to the original reflux flow. Although there is a slightly difference in theoretical and experimental temperature response, the trend is the same.

Step Change in Feed Composition

This experiment was carried out for a step change in feed composition of (-20)%. Figure 5 a) and b) shows the transient behaviour for the top tray and the tray 7 temperature. The tray 7 temperature shows larger movement between the steady states than the top tray for this step change. And the methanol concentration for this tray has changed from a 0.58 mole fraction to 0.49 mole fraction. The amplitude of the simulated and experimental responses match well.

Step Change in the Vapour Flow

A step change of +15% was made in the vapour flow. The propagation of the vapour flow through the column is very fast. A positive step change in the reboiler heat input acts through the reboiler and a fast first order response is then impressed on all trays nearly simultaneously. The composition on the tray starts to decrease since the vapour leaving the tray is richer in more volatile component than the vapour coming from the tray below. This gives a higher temperature profile, Figure 6 a) and Figure 6 b). The vapour flow leaving the top of the column is higher and therefore the reflux drum level is increased and once this level is stabilised by the level controller, the distillate flow is increased also. With the new distillate and bottom flows and top tray temperature, the net flow of methanol out of the column is no longer balanced and the material balance is slowly re-established as the product composition changes.

Considering all results for different step changes, it is possible to conclude that for the open-loop response, the mathematical model has a very good agreement with the practical continuous distillation column behaviour. The program has been tested for different operating data and performed satisfactory in all cases.

MODEL VALIDATION- CLOSED LOOP RESPONSE

The problem of interaction in distillation columns has been subject of discussion in many papers, Shinskey (1977), McAvoy and Weischedel (1981) and Moutziaris and Georgiou (1988). To study the possibility of improving column response with respect to interaction using liquid hold-up, the R-V control configuration was used. This configuration is the one most commonly used in industry and has received great attention in the literature when discussing interaction. For this reason it was chosen to test the performance of this new approach. The middle vessel arrangement was shown in Figure 3. A change in the liquid hold-up is used in an attempt to reduce interactions between loops. An extra hold-up was allocated to the middle of the column by continuously recycling a stream of the liquid from the feed tray to an external 20 litre vessel and back to the feed. All experiments were made with the same circulation ratio. The idea is that the additional holdup serves to damp and attenuate compositions disturbance composition disturbances which would otherwise propagate quickly throughout the rectifying and stripping sections of column. The feed tray hold-up was increased by the factor of 12(twelve) Figure 3. Thus for the practical experiment the volume of the vessel is 12(twelve) times the hold-up in the feed tray.

For studying this configuration theoretically, the model developed before was used. The increased hold-up was accounted in the model only by increasing twelve times the value of the hold-up in the feed tray. In addition, the control equations shown below were implemented in the simulation program to represent the control loops. Both top and bottom temperature loops used PI controllers. The top tray temperature was controlled by the reflux flow and the bottom tray temperature was controlled by the vapour flow. The reflux drum and reboiler levels were assumed to be perfectly controlled.

For the bottom tray temperature

V₃= K_c1 * [ (T_11setpoint-T₁₁) + K _i1 *

( ò (T_11setpoint-T₁₁)dt)] + vo

(18)

For the top tray temperature:

R= K_c2 * [ (T_2setpoint-T₂) + K _i2 *

(( ò (T_2setpoint-T₂)dt)] + ro

(19)

Step Change in Feed Flowrate-Normal Hold-Up

The initial experiment was made using the laboratory column with normal feed tray hold-up the experiment was made. As before the column was brought close to the reference steady-state. The top and bottom temperature loops were then closed and time allowed for them to settle. A step change of (+) 20% in the feed flowrate was made. The heat supply to preheat the feed was also adjusted manually in order to keep close to feed saturation.

Figure 7 a) shows the top tray temperature response. For the top tray temperature the peak deviation was, approximately 0.3^oC. The simulated and practical results have a very good match.

Figure 7 b) shows the response for the bottom tray temperature. The transient deviation in the controlled temperature was comparatively large. But the simulation results follow the experimental one quite closely. The peak change in the bottom temperature is approximately 0.9 ⁰C.

Step Change in feed flowrate-Increased feed tray hold-up hold-up

The increased feed tray hold-up was included using the pump around through the middle vessel arrangement as previous described. The middle vessel is brought into operation by opening the relevant valves and starting the pump once the distillation column has started to warm up. The system is allowed to run until close to the reference steady-state when the top and bottom tray temperature loops were closed and allowed to settle. A step change of (+) 20% in the feed flow was made.

Figure 8 a) and b) shows the transient response for the bottom and top tray temperatures. As can be seen in Figure 8 a) no significant change in the temperature was observed. Comparing Figures 7 a) and 8a) it is possible to conclude that the extra hold-up in the feed tray reduced the transient deviation in the top tray temperature.

Figure 8 b) shows the practical result for the bottom tray temperature. For this transient response the middle vessel also has a positive contribution, decreasing the effect of the feed flow step change in the bottom temperature. The response is much smoother than the response without the middle vessel and the transient deviation in the controlled temperature is not as noticeable as it was for the experiment with the normal feed plate hold-up.

Step Change in Feed Composition - Normal Feed Tray Hold-Up

The practical temperature profile has been record for a negative step change in feed composition from 0.481 to 0.46 mole fraction for the column without the middle vessel. The graphs for this step response are shown in Figures 9 a) and b). Figure 9 a) shows the response for top tray temperature. After the step change was made at approximately t=5500s, the top temperature took about another 1000 seconds to respond. It appears that the most dynamic behaviour results from the changing composition hitting the bottom tray and the reboiler; and this occurs approximately after 1000 seconds. Changes in temperature at the bottom of the column activate the heat input change and consequent column vapour traffic, only then do significant changes appear at the column top, that is when the reflux flow starts to change. For the top temperature, Figure 9 a) the time that it took to recover the previous steady state was only 50 minutes. The agreement between practical and simulation results can barely seen.

Figure 9 b) shows the bottom tray temperature response. The first part of the response in this graph is partially due to the 1000 seconds transport lag in the feed pipeline. The measurements indicate that the bottom temperature stabilises 90 minutes after the step change was made. The theoretical and practical results have quite good agreement.

Step change in feed composition- Increased Feed Tray Hold-Up.

This experiment was performed using the same initial procedure as described in section 4.2 with the same circulation rate between the middle vessel and feed tray, 7 litres min^-1. Once the steady-state was reached, a negative step change in the feed composition was made from 0.481 to 0.46 mole fraction. Figures 10 a) and b) show the temperature responses for top and bottom trays. Comparing the top tray temperature responses in Figure 10 a) and 8 a), it is clear that the maximum deviation is much reduced showing no deviation from the set point when the bigger feed tray inventory is used. The simulation and theoretical results match quite well.

For the bottom temperature, comparing the graphs in Figure 9b) and 10 b) it is possible to see that the highest temperature reached was only 0.1 ^oC above the set point for the case using the extra inventory in the feed tray, Figure 10 b), while for the case without the middle vessel, Figure 9 b), the temperature went 0.2 ^oC above the set point. However the overall response for the bottom tray temperature, Figure 9 a), reaches the set point much earlier than the one in Figure 10 a). The comparison between the theoretical and practical results do not show very good agreement. The simulation results reached the steady-state much earlier than the experimental one.

DISCUSSION

The column dynamic model reproduces the true performance of the column with quite good accuracy for the step change in feed flowrate for the case both with and without the middle vessel. For the feed composition disturbances however, the agreement between the theoretical and practical results for the bottom tray temperature response were not very good when using the middle vessel. The model reached the steady-state much quicker than the practical experiment. The deviation between the simulated and practical responses takes roughly three hours to disappear. Because this is much longer than the response time of the column system, this is probably due to a background disturbance during the experiment.

The most important point to notice is that the use of the middle vessel reduces the size of the transient deviation in both controlled variables for both step changes. This is because the bigger hold-up absorbs the effects of the step change much more. However the effect with the feed flowrate step change was better absorbed than with the feed composition.

ACKNOWLEDGEMENTS

CNPq- Brazilian Government Agency for the Post Graduate Education, for the financial support received through a research grant.

NOMENCLATURE

F Feed flow (mole.s^-1) K_c1 Proportional parameter of the controller (^oC/mole. s^-1) K_i1 Integral parameter of the controller (s^-1) L_n Liquid flowrate (mole.s^-1) M_n Molar hold-up (mole) M_on Nominal molar hold-up Ro Reflux flowrate steady-state value (mole. s^-1) R Reflux flowrate (mole. s^-1) T_nsetpoint Temperature setpoint (^oC) Vo Vapour flow steady-state value (mole. s^-1) V_n Vapour flow leaving the stage (mole.s^-1) x Liquid phase composition (mole fraction) y Vapour phase composition (mole fraction) t Hidraulic constant (s)

Subscripts

F Feed n Tray number

*To whom correspondence should be addressed

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• Barolo, M. Guarise, B. G., Rienzi, S. A.; Trotta, A. "Running Batch Distillation in a Column With a Middle Vessel" Ind. Eng. Chem. Res., 35, pp. 4612-4618(1996a)
• Bortolini, P. and Guarise, G. B.) "Un Nuovo Metodo di Distillazione Discontinua" Quad. Ing. Chim. Ital., pp.150-159(1970)
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• Mujtaba, I. M., Stuart, G. and Macchietto, S. "Alambic- A Software Package for Optimising Design and Operation of Batch Distillation Columns" IFAC Dynamics and Control of Chemical Reactors(DYCORD+95), Copenhagen, Denmark(1995)
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• Sodré, C.H.(1999)"Practical Practical Evaluation of Hold-up For Passive Decoupling in Distillation Column" PhDThesis Dissertation, University of Nottingham, Nottingham, UK (1999)
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Publication Dates

• Publication in this collection
  16 Mar 2001
• Date of issue
  Dec 2000

History

• Received
  12 Nov 1999
• Accepted
  18 May 2000