Scholarly article on topic 'Modeling, Design and Control of Cyclic Distillation Systems'

Modeling, Design and Control of Cyclic Distillation Systems Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — I. Liţă, C. Sorin Bîldea, A.A. Kiss

Abstract Cyclic distillation can bring new life in old distillation columns, by using a cyclic operation mode that leads to key benefits, such as: increased column throughput, lower energy requirements and higher separation performance. The literature reveals experimental and theoretical studies carried out so far, including several models for simulating cyclic distillation. However, the accuracy of these models is limited due to the linear equilibrium assumption. Moreover, these models can be used for rating studies only and no design method exists up to now, for the general case of nonlinear equilibrium. This paper fills this gap by presenting a novel approach for the design of cyclic distillation systems and an insightful comparison against conventional distillation. The complete model, an innovative graphical design method, and a case study proving the good controllability of cyclic distillation are also presented.

Academic research paper on topic "Modeling, Design and Control of Cyclic Distillation Systems"

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Engineering

Procedía

ELSEVIER

Procedía Engineering 42 (2012) 1311 - 1322

www.elsevier.com/locate/procedia

20th International Congress of Chemical and Process Engineering CHISA 2012 25 - 29 August 2012, Prague, Czech Republic

Modeling, design and control of cyclic distillation systems

aUniversity Politehnica of Bucharest, Department of Chemical Engineering, Str. Polizu 1-7, 011061 Bucharest, Romania bWeb: www.tonykiss.com, E-mail: tonykiss@gmail.com

Cyclic distillation can bring new life in old distillation columns, by using a cyclic operation mode that leads to key benefits, such as: increased column throughput, lower energy requirements and higher separation performance. The literature reveals experimental and theoretical studies carried out so far, including several models for simulating cyclic distillation. However, the accuracy of these models is limited due to the linear equilibrium assumption. Moreover, these models can be used for rating studies only and no design method exists up to now, for the general case of nonlinear equilibrium. This paper fills this gap by presenting a novel approach for the design of cyclic distillation systems and an insightful comparison against conventional distillation. The complete model, an innovative graphical design method, and a case study proving the good controllability of cyclic distillation are also presented.

©2012 Published by Elsevier Ltd. Selection under responsibility of the Congress Scientific Committee (Petr Kluson)

Keywords: Cyclic distillation; design method; non-linear equilibrium; operating lines; comparison with classic distillation

1. Introduction

Process intensification in distillation systems received much attention during the last decades, with the aim of increasing energy and separation efficiency. Various techniques, such as internal heat-integrated distillation, dividing-wall columns and reactive distillation were studied [1,2]. Cyclic operation is considered as an innovative method for operating existing distillation columns, leading to increased throughput, lower energy requirements and higher separation performance.

a* Corresponding author. Tel.: +40 21 402 3903 E-mail addresses: s_bildea@upb.ro, tonykiss@gmail.com

I. Litäa, C. Sorin Bîlde3 a*, A. A. Kissb

Abstract

1877-7058 © 2012 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.07.512

Nomenclature

B bottoms (kmol/cycle)

D distillate (kmol/cycle)

L reflux (kmol/cycle)

F feed (kmol/cycle)

M holdup (kmol)

NF feed stage

NT total number of stages

t time

¿vap duration of the vapor-flow periond

V vapor flow rate

X mole fraction, liquid phase

y mole fraction, vapor phase

Superscripts

(V) end of the vapor-flow period (L) end of the liquid-flow period

Subscripts

k stage number (1- condenser, NT - reboiler) F feed D distillate B bottoms

The cyclic operating mode consists of two parts: (1) a vapor-flow period, when vapor flows upward through the column, while liquid remains stationary on each plate, and (2) a liquid-flow period, when vapor flow is stopped, reflux and feed are supplied to the column, while the liquid holdup is dropped from each tray to the tray below . This mode of operation can be easily achieved by using perforated trays, without downcomers, combined with sluice chambers located under each tray. If the vapor velocity exceeds the flooding limit, the liquid does not overflow from tray to tray during the vapor-flow period. When the vapor supply is interrupted, the liquid drops down by gravitation to the sluice chamber. When the vapor supply is started again, the sluice chambers open and the liquid is transferred to the tray below. The principle of cyclic operation is schematically illustrated in Fig. 1.

Although the advantages of cyclic operation have been demonstrated experimentally, the information about modelling and designing cyclic distillation columns is rather limited. The idea of cyclic operation in the fields of distillation, liquid-liquid extraction and particle separation was introduced by Cannon and tested in tray and packed columns . Afterward, Sommerfeld et al. used computer simulation to investigate the theoretical effects of various parameters on the separating ability of a controlled cycling column. Analytical results were also presented for certain simplified cases assuming constant composition in the reboiler, and a linear equilibrium relationship. Moreover, an analogy with classic distillation was developed. Analytical expressions describing the dynamics of a distillation column operated in controlled cyclic fashion were derived for linear equilibrium assumption and considering an average value for the liquid composition during one operating cycle. Also, an iterative procedure was proposed to handle the case of nonlinear equilibrium . Based on a model assuming linear equilibrium and straight operating line, Robinson and Engel suggest replacing the distance-axis composition profiles found in a conventional column with a composition profile along the time axis.

Vapour-flow period Liquid-flow period

to condenser

to condenser

Liquid

Vapour

to reboiler

to reboiler

Fig. 1. Schematics illustrating the working principle of cyclic distillation

Schrodt et al. describes a plant-scale cyclic column (19 in. diameter) for separation of water-acetone mixture, proving that a 240% capacity increase is possible. Gel'perin et al. created a cyclic regime using electromagnetic valves. A 200% efficiency increase proved again the beneficial effect of cycling regime An empirical model was used to predict the performance. Soon after, Rivas derived simple analytical equations that can be used to calculate the ideal number of trays for cyclic counter-current processes such as cyclic distillation, absorption, and stripping. However, this applies better to absorption than to distillation, due to the linear-equilibrium assumption. For a benzene-toluene mixture and 95% product purity, a 50% reduction in number of stages compared to conventional distillation was observed. The importance of liquid plug-flow down the column was emphasized by Baron et al. . An analytical solution of balance equations in cycling operation was obtained , under the assumptions - among others - of constant vapor concentration entering the bottom stage, condenser without holdup and again linear equilibrium. This was used for studying the effect of feed tray location, reboiler volume, relative volatility, stage efficiency, number of trays and reflux number on the separation performance. The assumption of linear equilibrium was relaxed. Matsubara et al. [15,17] used cycling operation as an example to emphasize the advantages of relay feedback periodic control compared to the forced oscillation scheme. Further energy saving was achieved by combining cycling and stepwise operation modes [16,17]. The cycling operating mode was demonstrated experimentally on a five-stage watermethanol mixture. Up to 50% energy reduction was observed, compared to conventional continuous column.

An efficient algorithm for dynamic simulation of cyclic processes, without the need of repeatedly evaluating a large number of steps, was applied to cyclic distillation. Dynamic optimization was used to find the optimal profiles of flow rates of feed, product streams, reflux and vapor in order to reduce the energy demand.

A more recent study gives an overview of previous work on cyclic distillation and presents a novel model of a theoretical stage with perfect displacement. Equilibrium and operating lines (assuming linear equilibrium) diagrams are used to illustrate the principle of cyclic operation. Two relevant case-studies illustrate the theoretical findings and applications. Application of cyclic operation to batch distillation was recently reviewed by Flodman and Timm .

The literature review clearly proves the advantages of cyclic operation as compared to conventional, steady state operation of distillation. Several models are available to simulate the behaviour of the cyclic distillation columns. When the assumption of linear equilibrium is employed, it is indeed possible to derive analytical solutions of the model equations. However, although these analytical expressions could be used to design cyclic operation columns, the accuracy of the results is limited due to the linear equilibrium assumption. Moreover, these models can be used for rating studies only and no design method exists up to now, for the general case of nonlinear equilibrium. This paper fills this gap by presenting a novel approach for the design of cyclic distillation systems and an insightful comparison against conventional distillation. The complete model and an innovative graphical method similar to the McCabe-Thiele diagram are also presented hereafter. Finally, the good controllability of cyclic distillation columns is demonstrated.

2. Modelling approach

2.1.Assumptions

The model of the cyclic distillation column is derived under the following assumptions:

Binary (mixture) distillation

Ideal stages (vapor-liquid equilibrium is reached)

Equal heat of vaporization (this implies constant molar holdup and vapor flow rate) Perfect mixing on each stage Negligible vapor holdup Saturated liquid feed

Note that in contrast to the previously cited papers, no assumptions are made here with regard to the linearity of vapor-liquid equilibrium, infinite reboiler holdup or zero condenser holdup.

2.2. Operationalconstraints

From the condenser and reboiler mass balance, written for one operating cycle:

V- Kv ~-D +L L +F - V-tvap +B

the following feasibility condition follows:

L <V-tvap <L +F

2.3.Model of the vapor-flowperiod

The following equations describe the evolution in time of stage holdup and composition, during the vapor-flow period:

dM, dx. , ,

Condenser: -1 = V ; Ml —- = V (y2 - xi

dM, dx, , ,

Trays: - 0; =V ({+, - )

Reboiler: ^ --V ; -V ({ - yNT)

Initial conditions: AU=0, (M,x) - (m(î),x(l]

Integration from t=0 to t = gives the state of the system at the end of the vapor How period,

M[v\ xM

2.4.Model of the liquid-flowperiod

The following equations give the stage holdup and composition at the end of the liquid-phase period: Condenser: M[lL] - mIv) - D- L ; xj1' - x^1

Trays, rectifying section: M[M - L ; xM) - x^-J

Feed tray: MM)t, - L + F ; , - ^ +

M + b )

Trays, stripping section: M(l) - L + F ; xM1 - x^J

Reboiler: mM-1 - M^1 - B + m(}_ j

M[v] - B)xM + MM x[v]

v NT ^J^NT r NT -1ANT -1

2.5. Solution method

Equations - and - can be written in the following condensed form, where $ M) and $ {i) are mappings relating the state at the start and the end of the vapor- and liquid-flow periods, respectively.

(M'v), x'v))-$(v)(M , x )

(mM\x(i))- $M](M,x)

Periodicity condition requires:

(m(i>, xw)-0{i)o $m{m(il, xw)

A straightforward solution of equation can be obtained by considering an initial state and applying relationships and until the difference between two iterations becomes small. However, the convergence can be accelerated by applying algebraic equations numerical methods (for example Newton or Broyden). The model can be conveniently solved in Mathworks Matlab or any other similar software.

3. Comparison with classic distillation

Fig. 2. compares the vapor / feed ratio versus the product purity (xD = 1 - xB) in conventional distillation and cyclic distillation employing different number of trays: 24 trays for conventional distillation and 12-24 trays for the cyclic distillation. Separation of an equimolar mixture benzene -toluene was considered.

It can be observed that the energy requirements - which are directly proportional with the vapor How rate - are greatly reduced, especially for high purity products. Moreover, the number of trays required by cyclic distillation is almost half as compared to the conventional distillation, when the same purity is obtained with the same vapor flow rate.

1.8 1.6 1.4 1.2

0.0001

\ \ \ \ 14\\ \l2

Classic distillation

NT = 24

^20 v, \

1 -X D

Fig. 2. Comparison of energy requirements in cyclic distillation vs conventional distillation

4. Design of cyclic distillation

4.1. Design methodology

Initial data. Given the feed (F, xF) and the required performance (xD, xB) solve the mass balance over one operating cycle, to find the product flow rates (D, B):

F = D + B

F ■ xF = D ■ xD + B ■ xB

Hydrodynamics. Specify the vapor flow rate Fand the duration of the vapor-flow period, /vap, and calculate the amount of liquid transferred from condesnser to the top tray:

L = V-tvap -D

Tray holdups areMk = L (rectifying section) and Mk = L + F (stripping section). Check the hydrodynamics (column diameter, vapor velocity, pressure drop) The state of the reboiler at the end of the vapor-How period, specified as follows:

- holdup, Mmity,.?). The result of the design procedure is independent of this value, whose specification is nevertheless necessary.

- composition, XNT(ivap) = xB. At the end of vapor-flow period, the reboiler is richer in the heavy component, therefore this is the moment to take out the bottom product.

Integrate the reboiler equations , from t = /vap to / = 0, to find the holdup and reboiler composition at the beginning of the vapor-flow period,MNT(0), xNT(0).

Find the state of the last tray (stage NT-1) at the end of the vapor-flow period, using the mass balance for the liquid-flow period:

^vr -1 (()~-L +F

XNT - 1 I Kc.

MNT (0).Xnt ( 0 ) - ( Mm (tvap )-B ) [tvap] L + F

Find the state of reboiler and last tray at the beginning of the vapor flow period by integrating equations and from t = tvsp to / = 0

Add one more tray, whose state at the end of the vapor-flow period is

Mm - 2 (M )--L +F

XNT-2 ( Kvap ) " XNT-1 ( ^)

and integrate the resulting set of equations from t = t^pto t = 0. Repeat until the feed composition is reached for the tray NF+1.

Find the state of the feed tray at the end of the vapor-flow period:

MNF (tvap ) L

XNF ( Kvap J

MNF +!'XNF +1 M)- F'XF

and integrate the resulting set of equations from t = tViVtot = 0.

Similarly, repeat addition of one tray, finding its state at the end of vapor-flow period and integration of the resulting equations until the distillate composition is reached.

The first three steps of the design procedure are illustrated in Fig. 3.

xiLphz— -v Tray

^vaph;-

„-» Tray

Reboiler

Reboiler

vap> _

„-» Tray

x(0) ./ x(/vap|

Reboiler

Fig. 3. First steps of the design procedure

4.2. Results of case study

The following model system is used to demonstrate the procedure:

- Ideal binary mixture, relative volatility =3.5 (the large volatility is chosen for a clear graphical illustration of the results)

- Feed: F = 0.375 kmol/cycle; xF = 0.5

- Distillate: D = 0.1875 kmol/cycle; xD = 0.995

- Bottoms: B = 0.1875 kmol/cycle; xB = 0.005

- Vapor flow: V= 2.21 kmol/min; /vap= 0.2 min (0.442kmol/cycle)

0 0.25 0.5 0.75 1

t/ [min]

Fig. 4. Evolution of liquid-phase mole fraction over four operating cycles. Tray number are indicated on the right side (condenser not shown). The coloring of the lines indicate the flow of the liquid from one tray to another.

Fig. 4 shows the evolution of the liquid phase composition over four vapor flow - liquid flow cycles, for the model system. Tray numbers are indicated on the right, while the line coloring suggests the flow of the liquid from tray to tray (the liquid-flow period). The feed is on the tray NT-4, as the composition at the end of vapor-flow period / beginning of the liquid-How period matches the feed composition, xF = 0.5. If the vapor flow rate is set to 2.21 kmol/min, nine separation stages are needed to perform the required separation (reboiler, 7 trays, condenser). The bottom mole fraction is xB = 0.005, while the distillate purity xd=0.9993 exceeds the specification.

It is useful to present the results in a plot similar to the McCabe-Thiele diagram (Fig. 5). The diagram contains the equilibrium line and the operating line. The coordinates of the points on the operating line are the liquid mole fraction on the tray k, xk(t), and the vapour mole fraction on the tray below, yk+i(t). As the time varies between 0 and /vap, one segment corresponds to each tray k. Additionally, these segments are connected because, at the end of the vapour-flow period, liquid from tray k is moved to tray k+1, therefore:

** (°) = ** +1 () y*+1 (0) = y* ()

The dotted lines represent the operating lines for the classic distillation corresponding to the same reflux and vapor flow. Clearly, fewer trays are required in cyclic operation. Moreover, Fig. 5 illustrates the existence of a minimum vapor-flow rate - corresponding to an infinite number of trays - and also a minimum number of trays, corresponding to an infinite vapor flow.

After the number of trays is found, the cyclic operation mode is simulated and the vapor flow rate is adjusted such that the purity specifications are exactly matched. For the test case, the new vapor flow rate is V =2.12 kmol/min.

Fig. 5. Representation of the cyclic operation mode using equilibrium and operating lines

i .5 1

time / [min] stage 4

i .5 1

time / [min] stage 8

i .5 1

time / [min]

0.5 0.4 -0.3 -

°.V fr

5 .5 • 5 -4 .5,-

) .5 1

time / [min] stage 6

) .5 1

time / [min] R e b o ile r

time / [min]

c o n d e n s e r

stage 2

Fig. 6. Evolution of liquid composition in condenser, reboiler and selectedtrays, over several operation cycles

Fig. 6 shows the evolution of liquid mole fraction in condenser, reboiler and selected trays over several operating cycles. It should be observed that a stationary periodic state is reached. Moreover, at the end of vapour-flow period, the reboiler and condenser mole fractions are equal to the bottoms and distillate specifications.

5. Control considerations

The design procedure described in the previous section was applied for separation of an equimolar mixture of benzene and toluene. The feed flow rate was set to 0.375 kmol/cycle, while the distillate and bottoms composition were set to 0.995 and 0.005, respectively. The cyclic distillation column has 14 stages in total, with the feed located on stage 7. The required vapor and liquid flows were set to V= 0.496 kmol/cycle andZ = 0.312 kmol/cycle, respectively.

The control strategy measures the reboiler and condenser compositions at the end of the vapor-flow period and uses the discrete PI-algorithm to adjust the values of the vapor and reflux, according to:

Kttl =ut +a ■ ettl + $ ■ £k

where u and are the manipulated and control errors, respectively, while and are the control tuning parameters.

In addition, the bottoms and distillate amounts are used to control the reboiler and condenser holdups (e.g. level control). The performance of the control system was tested for a 10% increase of the feed flow rate, as well as for a change of the feed composition from xF = 0.5 to xF = 0.6. The results presented in Fig. 7 and Fig. 8 show that the product purities can be indeed kept to their set points. Remarkable, the disturbances in the feed flowrate and composition are rejected successfully with short settling times and low overshooting - this proving indeed the good controllability of cyclic distillation.

Fig. 7. Performance of the control system for a 10% increase of the feed amount

Fig. 8. Performance of the control system for a change of the feed composition from xF = 0.5 to xF = 0.6

6. Conclusions

Cyclic distillation can bring new life in old distillation columns, providing key benefits, such as: high column throughput, low energy requirements and high separation performance. However, the cyclic distillation models reported in literature can be used for rating studies only and no design method exists up to now, for the general case of nonlinear equilibrium. This study successfully fills this gap by proposing a novel approach for the design of cyclic distillation systems, and presenting an insightful comparison against conventional distillation. The key findings of this work are the following:

The energy requirements for cyclic distillation are greatly reduced especially for high purity products. Moreover, the number of trays required by cyclic distillation is almost half as compared to the conventional distillation, when the same purity is obtained with the same vapor flow rate.

In cyclic distillation, a minimum vapor-flow rate exists - corresponding to an infinite number of trays - as well as a minimum number of trays, corresponding to an infinite vapor How.

Cyclic distillation columns can be easily controlled by adjusting the reflux and the vapor flow rate, in order to keep the required product purities. Remarkable, disturbances in the feed flowrate and composition are successfully rejected with low settling times and low overshooting.

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