Non-linear dynamic e ects in Reactive Distillation for · PDF file · 2006-07-26tillation process for the production of TAME is presented. ... dehydration of secondary butanol with

Katariya, Mahajani and Moudgalya, Ind. Eng. Chem. Res., August 05

Non-linear dynamic effects in Reactive

Distillation for synthesis of TAME

Amit M. Katariya, Sanjay M. Mahajani∗ and Kannan M. Moudgalya

Department of Chemical Engineering,

Indian Institute of Technology Bombay,

Mumbai-400076. INDIA

* Corresponding auther:

Prof. Sanjay M. Mahajani,

Department of Chemical Engineering, IIT Bombay

Mumbai-400076.

E-mail: [email protected]

Tel :- +91-22-25767246 Fax : +91-22-25726895.

1


Abstract

The liquid phase synthesis of octane enhancing ethers like, methyl tertiary butyl

ether (MTBE) or tertiary amyl methyl ether (TAME), can be advantageously per-

formed in a reactive distillation (RD) processes with ion exchange resin catalyst.

In the present contribution, a case study for dynamic simulation of reactive dis-

tillation process for the production of TAME is presented. Non-linear dynamic

effects such as oscillations, multiple steady states and internal state multiplic-

ity have been observed under certain conditions. Feed condition and Damkohler

number are the important parameters that have influence on the existence of these

effects. The presence of these effects has been confirmed through independent bi-

furcation analysis. The influence of various modeling parameters, reaction kinetics

and phase equilibrium models on this observation is studied.

Keywords: Reactive Distillation, Dynamic Simulation, Continuation analysis, Hopf

Bifurcation, Oscillations.

2


Introduction

A novel technology called reactive separations, combines chemical reaction and

the product separation in a single apparatus. Based on the applied separation

technology, reactive distillation, reactive extraction, reactive adsorption and other

combined processes have been distinguished. The combined simultaneous per-

formance of chemical reaction and a multicomponent distillation process is an

alternative, which has been increasingly used for the large-scale production of

relevant chemicals. The use of RD process can offer several advantages such as

reduced downstream processing, utilization of heat of reaction for evaporation

of liquid phase, simple temperature control of reactor, possibility of influencing

chemical equilibria by removal of products and limitations imposed by azeotropic

mixture. Several commercially important processes in reactive distillation have

been identified in some recent reviews1,2. Reactive distillation has been success-

fully applied for the etherification reaction to produce fuel ethers such as methyl

tert-butyl ether (MTBE), tert-amyl methyl ether(TAME) and ethyl tert-butyl

ether (ETBE). These have been the model reactions for the studies in reactive

distillation in the last two decades and studies on various aspects such as kinet-

ics, thermodynamics and conceptual design, and both steady state and dynamic

simulations have been reported in the literature.

A combination of the reaction and distillation also results in complex nonlin-

ear behaviors associated with individual processes, such as multiple steady states,

sustained oscillations and internal state multiplicity. Sustained oscillations or

limit cycles have been well recognized in chemical reactors, but occurrence of

such phenomena was not so common in the open loop distillation or reactive

distillation columns. Oscillations in distillation and reactive distillation systems

through simulation and experiments have been reported by few investigators in

the past. Under-damped oscillations in heterogeneous distillation by dynamic sim-

3


ulation were first observed by Widagdo et al.3. Here, dehydration of secondary

butanol with di-secondary butyl ether was carried out in 12 stage column with a

decanter. In an another study, oscillations of process variables have been observed

in the lab-scale packed reactive distillation column for MTBE synthesis as well as

non-reactive distillation of methanol and iso-butene4. Schrans et al.5 carried out

dynamic simulation of MTBE synthesis by reactive distillation. They observed

transition of one steady state to another steady state or to the state of sustained

oscillation. Morari et al.6 have demonstrated the presence of periodic solution in

an open loop distillation model through simulation for the azeotropic distillation

of methanol-methyl butyrate-toluene. Oscillatory behavior for azeotropic distilla-

tion of cyclohexane-isopropyl alcohol-water was experimentally detected by Wang

et al.7. However, they did not observe the same through dynamic simulations.

Oscillations in the simulation of ethylene glycol synthesis and methyl formate

synthesis by reactive distillation were reported by Kienle and Marquardt 8, but

the oscillations disappeared when energy balance was neglected. As reported by

Kienle and Marquardt8, in general, the potential cause of the oscillatory behavior

may be due to unwanted periodic forcing i.e. due to badly tuned controller, fluid

dynamic instabilities or concentration dynamic instabilities.

In the case of TAME synthesis by reactive distillation, Bravo et al.9 have reported

the occurrence of steady state multiplicity in the experimental column. Several au-

thors10,11,12,13,14,15 have examined and explained the existence of multiple steady

states for TAME synthesis in a reactive distillation column. The details of the

previous work on TAME synthesis and internal state multiplicity has been given

in the next section. To the best of our knowledge, sustained oscillations for the

TAME synthesis have not been reported before. The present work mainly deals

with the nonlinear dynamics of commercial scale column studied by Subawalla

and Fair16. Although rigorous design studies of this column by NEQ stage model

4


is carried out by Baur and Krishna17, the effect of various parameter by continu-

ation analysis has not been investigated for this column configuration. Also, the

influence of kinetic models and two different UNIQUAC parameters obtained from

different sources, on dynamics of the column has been studied in the present work.

Previous work

In this section the previous work on TAME synthesis by reactive distillation has

been reviewed.

Kinetics and Thermodynamics

Tertiary Amyl Methyl Ether(TAME) is synthesized by acid catalyzed equilibrium

reaction of isoamylenes and methanol. The reactions involved in the synthesis of

TAME are as follows:

MeOH + 2M1B ⇐⇒ TAME R1 = kf1(a2M1B

aMeOH

−1

Ka1

aTAME

a2MeOH

)

MeOH + 2M2B ⇐⇒ TAME R2 = kf2(a2M2B

aMeOH

−1

Ka2

aTAME

a2MeOH

)

2M1B ⇐⇒ 2M2B R3 = kf3(a2M1B

aMeOH

−1

Ka3

a2M2B

aMeOH

)

The reaction kinetics for TAME synthesis has been studied by various authors.

Hwang and Wu18 have reported a concentration based rate expression for com-

bined etherification reaction from two isoamylenes. Later rigorous kinetic study

has been performed by Oost and Hoffmann19, Christian et al.20 and Sundmacher

et al.21, all from Clausthal and Rihko and Krause22, Rihko et al.23, Paivi et al.24

and Paivi and Krause25, all from Helsinki. They reported activity based kinetic

models for lumped as well as separate etherification reactions. Investigators from

Clausthal used UNIFAC method, whereas the Helsinki group used UNIQUAC

method for calculating activities of the species involved. In most of the studies,

5


except a few at Helsinki, isomerization reaction has been ignored. Faisal et al. 26

have experimentally verified the previous kinetic models and reported individual

equilibrium constants for etherification and isomerization reactions. They used

UNIFAC method in the calculation of activities required in kinetic parameter

estimations. Subawalla and Fair16 have used UNIQUAC binary interaction pa-

rameters, which were obtained from ASPEN PLUS, to calculate activities. Rihko

et al.27 performed isobaric VLE experiments at 101.32KPa and reported the Wil-

son binary interaction parameters for the system of interest.

Experimental and Theoretical studies on column

Table 1 gives a summary of modeling, simulation and design studies performed

on the TAME synthesis in reactive distillation columns. Mohl et al.10 performed

rigorous bifurcation and stability analysis for a reactive distillation process in the

production of fuel ethers. Simulations were carried out for a pilot scale column at

Clausthal. A one meter tall column with approximately 10 theoretical stages op-

erating at 0.25MPa was used. A mixture of methanol, isoamylenes and n-pentane

was fed to the middle of the column between reactive and nonreactive sections.

The Wilson model was used to represent liquid phase non-ideality. Further rigor-

ous experimental verification of steady state multiplicity in the pilot plant reactive

distillation column was carried out by Mohl et al.11. The focus of the study was on

steady state multiplicity and rigorous bifurcation analysis for fuel ethers (MTBE

and TAME) production. Here, different sources and physical causes of existence of

MSS were discussed. Sundmacher et al.21 presented the comparative study of sev-

eral possible models of different complexity for the same pilot scale column, with

homogeneous and heterogeneous catalysis. The simulation results were experi-

mentally validated and it was concluded that consideration of side reactions and

modeling of internal catalyst phenomena play important roles in the interpretation

of experimental results. Baur et al.14 have developed a dynamic non-equilibrium

6


stage model for reactive distillation columns. Maxwell-Stefan equation was used

for describing mass transfer between fluid phases, and solid catalyzed reactions

were treated pseudo-homogeneously. Also, a comparison has been carried out

with experimental results of Mohl et al.11. Baur et al.13 presented bifurcation

analysis for the synthesis of TAME in reactive distillation column, for the above

pilot plant column, with pseudo-homogeneous and heterogeneous reaction kinetic

models. Similar nature of the bifurcation characteristics were found with both the

kinetic models and there was qualitative agreement of dynamic results with exper-

iments of Mohl et al.11. Subawalla and Fair16 have presented the design guidelines

for solid catalyzed reactive distillation systems. The design of the column used in

all the above studies is different from the one used by Subawalla and Fair16 and

that in the present study.

Although the above studies on simulation of RD have considered n-pentane as

representative of the inert components in C5 fraction obtained from refinery, iso-

pentane is expected to be present in large amount in some cases. Similarly, while

the literature on kinetics reports the use of UNIQUAC activity models for kinetic

parameter estimations, simulation experiments used the Wilson model. Hence,

in the present work the UNIQUAC activity model has been used and a compar-

ison of two different UNIQUAC parameters obtained from HYSYS (H-type) and

Subawalla and Fair16(A-type) is carried out. The present analysis covers a wide

range of input design and operating parameters and presents some interesting

observations which have not been reported in the literature.

Process Description

Light gasolene fraction (C5-cut) from fluidized catalytic cracking unit is the source

of isoamylenes. There are three isomers of amylene viz. 2-Methyl-1-Butene(2M1B),

2-Methyl-2-Butene(2M2B) which are reactive and 2-Methyl-3-Butene(2M3B) which

7


is a non-reactive one. The feedstock also contains inert components such as iso-

pentane, n-pentane, 1-pentene, 2-pentene etc. Iso-pentane is the major component

of the total inert fraction and there is not much difference in the boiling points of

these components, hence for simplicity all inert components have been represented

by a single component i.e. iso-pentane. Besides TAME synthesis, there are several

side reactions like isomerization of reactive amylenes, hydration of isoamylenes to

tertiary amyl alcohol etc. take place. In all the earlier studies on column sim-

ulations for TAME synthesis, both the isomers have been considered as equally

reactive and isomerization reaction have been neglected. In the present study,

etherification and isomerization reactions have been considered separately. As the

system consists of mixture of polar and non-polar components, it is highly non-

ideal and the use of activity based kinetics and thermodynamics is justifiable. The

UNIQUAC model has been used for describing non-ideality of liquid phases, with

binary interaction parameters taken from HYSYS and that reported by Subawalla

and Fair16 from ASPEN PLUS, hereafter we refer them as H-type and A-type

parameters respectively. Forward rate constants and equilibrium constants have

been obtained from different sources22,19,26. Detailed kinetic and thermodynamic

parameters used in the present study are given in appendix A.

In the present work, the column design as reported by Subawalla and Fair16 has

been considered. Figure 1 shows the column configuration along with operating

and design parameters used for the study. The column has 35 theoretical stages

with two feeds, one of which is pure methanol and the other is pre-reacted feed,

with 56-63 % conversion of amylenes to TAME in the pre-reactor.

Modeling

An equilibrium stage dynamic model of the reactive distillation column has been

formulated and solved. The assumptions involved are: constant molar liquid

8


holdups on each tray with negligible vapor holdup, perfect mixing of vapor and

liquid streams on each stage, streams leaving are at their boiling points, reaction

takes place in liquid phase only. Quasi-static energy balance has been consid-

ered. The column has a total condenser with reflux sent at its bubble point. The

mathematical model of this system is given below.

Stage equations:

0 = Vk+1 + Lk−1 + Fk − (Lk + SLk ) − (Vk + SV

k )

+ rf

r∑

m=1

C∑

i=1

(γi,mRm,kεk) (1)

Mk

dxi,k

dt= Vk+1yi,k+1 + Lk−1xi,k−1 + Fkzi,k − (Lk + SL

k )xi,k

− (Vk + SVk )yi,k + rf

r∑

m=1

(γi,mRm,kεk) (2)

0 = Vk+1Hk+1 + Lk−1hk−1 + Fkhfk − (Lk + SLk )hk

− (Vk + SVk )Hk + rf

r∑

m=1

(Rm,kεkHRm,k) − Qk (3)

yi,k = Ki,kxi,k (4)C∑

i=1

xi,k = 1 (5)

C∑

i=1

yi,k = 1 (6)

Here, rf is a multiplication factor which takes values equal to zero for non-reactive

and one for reactive stage. The Damkohler number, Da = kf1,refW/Ftotal, is the

ratio of characteristic liquid residence time to the characteristic reaction time.

Here, kf1,ref is the forward rate constant of the first reaction at reference temper-

ature.

9


Condenser equations:

0 = Vk+1 + Fk − (Lk + D) − Vk (7)

Mk

dxi,k

dt= Vk+1yi,k+1 + Fkzi,k − (Lk + D)xi,k − Vkyi,k (8)

0 = Vk+1Hk+1Fkhfk − (Lk + D)hk − VkHk − Qc (9)


i=1

xi,k = 1 (11)

C∑

i=1

yi,k = 1 (12)

For the case of total condenser, Vk = 0, which is an additional equation. Also

the reflux is returned to the column at its bubble point and hence the summation

condition of vapor phase compositions is used to determine the temperature of the

condenser stage.

Reboiler equations:

0 = Lk−1 + Fk − B − Vk + rf

r∑

m=1

C∑

i=1

(γi,mRm,kεk) (13)

Mk

dxi,k

dt= Lk−1xi,k−1 + Fkzi,k − Bxi,k − Vkyi,k + rf

r∑

m=1

(γi,mRm,kεk) (14)

0 = Lk−1hk−1 + Fkhfk − Bhk − VkHk

+ rf

r∑

m=1

(Rm,kεkHRm,k) + Qr (15)


i=1

xi,k = 1 (17)

C∑

i=1

yi,k = 1 (18)

10


The subscripted H’s and h’s are the enthalpies of vapor and liquid phases respec-

tively. Heat of formation is considered while calculating the enthalpies of streams

by means of which we can easily remove the heat of reaction term from the energy

balance equation.

Results and Discussion

Steady state Simulation

The steady state simulation of a 35-staged column with 19 reactive stages has

been carried out to get the initial values for dynamic simulations. The column

has two feeds: pure methanol at 305 K is introduced on the 24th stage while the

pre-reacted feed at 325 K is introduced on the 29th stage. The column has been

operated at 4.5 bar pressure and a molar reflux of 1.5 with 20.5 MW heat supplied

to the reboiler.

An attempt was made to solve all the resulting algebraic equations through New-

ton’s method. Unfortunately we could not converge to the steady state value.

The large dimensionality of the problem made the assignment of initial values a

difficult task. As a result, dynamic simulations were used to reach the steady state.

Because of the difference in the time scale of composition and holdup, the compo-

nent material balance equations have been modeled as ordinary differential equa-

tions (ODEs) and the remaining equations as algebraic equations. An attempt was

made to solve algebraic and differential equations separately in sequence. Even

after this simplification, there were difficulties in the choice of initial values and

convergence: some variables came out with unrealistic values, like negative flow-

rates. To overcome this difficulty a continuation type of approach was used. The

model equations were initially solved for the nonreactive case by setting Damkohler

11


number to zero. The Damkohler number was then gradually increased to achieve

the desired catalyst loading. This approach resulted in convergence to the steady

state value.

The steady state composition and temperature profiles along with column op-

erating parameters are shown in Figure 2. H-type thermodynamics and reaction

kinetic model-1 have been used for the simulation. The simulation results have

been validated for the design and operating parameters of Subawalla and Fair 16

and Baur and Krishna17 with A-type thermodynamics and hot feed conditions.

An excellent agreement has been found. The steady state results have also been

cross-checked using Newton based steady state solver. It will be shown later that

although the steady state results by both sets of VLE parameters agreed well, the

dynamics are significantly different.

Dynamic Simulation

In reality, the feed composition of the C5 cut is prone to variations depending on

the upstream conditions. Hence, the column dynamics have been studied for the

disturbance in amylene concentration in the feed under various conditions. Simu-

lations have been carried with cold feed condition, H-Type thermodynamics and

kinetic model described by Faisal et al.26 i.e model-1. Operating and design pa-

rameters used are: Reflux ratio=1.5, Reboiler duty=20.5 MW and Pressure=4.5

bar. Dynamic simulations have been carried out by solving algebraic and differen-

tial equations separately in sequence. The state of the art integrator LSODE has

been used for solving the ODEs.

The dynamic response of the column reboiler temperature and TAME purity in

bottoms has been studied for a step change in the 2M1B concentration in the

feed. The analysis has been done for two different values of Damkohler number

12


i.e Da = 1.0 and Da = 2.0 and the corresponding behaviors have been shown in

Figures 3(a) and 3(b) respectively. For Da = 1.0, the response is nearly first order

and the system reaches the corresponding steady state. However, for Da = 2.0, a

state of sustained oscillations have been observed in open loop simulation of the

column. The amplitude of the oscillations increases with an increase in the size of

the step change. Such oscillations have been observed in every state variable.

This oscillatory behavior has been confirmed by repeating the dynamic simula-

tion in the DIVA simulation environment28 . DIVA uses the equation oriented

approach for solving all the equations simultaneously as a set of differential al-

gebraic equations. DIVA incorporates a number of diverse methods to analyze

large systems of nonlinear differential and algebraic equations with highly efficient

numerical algorithms.

The Damkohler number determines the extent of reaction. At lower values of Da,

the reaction is relatively slow and the column performance is determined by the

kinetic parameters such as rate constant(s) and residence time. As the Da value

becomes large, the reaction becomes fast and reaction equilibrium is approached

on a given stage. The performance of the column in such a case is independent of

kinetic parameters. The steady state conversion at large values of Da is expected

to be insensitive to the further changes in Da. The absence and presence of the

oscillatory behavior at Da = 1.0 and Da = 2.0 respectively, suggests that a sys-

tematic analysis is required for predicting the effect of Damkohler number on the

system behavior. Such a kind of analysis can be done using continuation methods

combined with the concept of stability and bifurcation theory.

13


Bifurcation analysis of the column

The bifurcation diagram depicts the vector of state variables versus certain design

or operating parameters29. These diagrams are extremely useful as the solution

may form a continua, reflected by a continuous curve called as branches. There

may be emergence of new branches or termination of branches or even intersection

of two or more branches. It is useful in predicting multiple steady states for the

system of interest. In our study, the AUTO continuation software has been used

for bifurcation analysis. AUTO is a freely available software for continuation and

bifurcation problems in ODEs30. Although DIVA has a capability to carry out

continuation and bifurcation analysis, it has been found to be slower than AUTO

for large dimensional systems like the one in the present study. The advantage of

DIVA is that it can handle DAEs in addition to ODEs, while AUTO cannot. In

our analysis, AUTO has been used for steady state bifurcation analysis. To get

the set of ODEs for AUTO, algebraic and differential equations have been solved

separately in sequence.

Figure 4 shows two bifurcation diagrams for the H-type thermodynamics and cold

feed conditions, obtained with Damkohler number as a continuation parameter.

The steady state temperatures of 25th stage and reboiler have been plotted against

the Damkohler number. The dotted curve shows the branch of unstable steady

state and solid squares indicate the Hopf bifurcation points. As expected, the col-

umn performance is sensitive to Da at lower values. However, the solution remains

unchanged at higher values of Da. At Da = 4.6, the stable steady state branch

loses its stability and unstable branch emerges. At this point, a pair of complex

conjugate eigenvalues crosses the imaginary plane and the unstable steady state

branch associated with sustained oscillations has been observed. The solid cir-

cles shows the amplitude of oscillations as a function of Damkohler number. It

should be noted that even at sufficiently higher values of Da, the column dynamics

14


are dependent on Da. With a further increase in Da, two independent solution

branches have been observed, one of them being the original unstable solution

branch, while the other one is an independent stable solution branch over a small

range of Da values i.e. 22.72 to 25. It can be seen that the stable and unstable

solutions in Figure 4(b) overlap over this range, while in Figure 4(a), two sepa-

rate steady states are seen. In Figure 5(a), the unstable and stable steady state

solutions have been plotted corresponding to Da=25. These solutions have been

obtained directly from AUTO with stability described by eigenvalue analysis. It

has been observed that for the same conversion of amylene and TAME purity in

bottoms, composition and temperature profiles near the feed stage are different.

This is an unusual behavior and can be considered as a special case of internal

state multiplicity. Internal state multiplicity is defined as the case where two or

more steady state composition and temperature profiles are realized for the same

input with identical end compositions (xD and xB). Such a behavior has been

observed in sufficiently tall non-reactive distillation columns31. However, in such

cases normally all the multiple solutions obtained are stable. In the present case,

one of the solutions is unstable and is associated with limit cycles. In Figure 5(b),

dynamic response to a pulse of amylene concentration in feed at Da=25 is plotted

by supplying stable steady state results as initial values. It can be seen that the

pulse change in the feed composition results in sustained oscillations.

After having observed this peculiar behavior, it was considered essential to study

the effect of various parameters and model assumptions on the non-linear dynamic

behavior. A comparison with three different kinetic models, proposed by Faisal

et al.26, Christian et al.20 and Rihko and Krause22, referred to as models 1,2 and

3 respectively, has been carried out. Figure 6 shows the effect of kinetic models

and two different UNIQUAC parameters (H-type and A-type) for hot feed. Hopf

bifurcation is observed only in the case of H-type thermodynamics. Although this

15


points to the existence of oscillations, they could not be produced by dynamic sim-

ulation with model-1 and model-2 as the range of Da over which oscillation may

be observed is small. Nevertheless, oscillations through dynamic simulations have

been observed for the kinetic model-3. These results also indicate that the column

response is sensitive to feed conditions as the results shown in Figure 4 for the cold

feed are significantly different under otherwise similar conditions. For the hot feed

condition, we have seen in Figure 6 that there is a possibility of multiple steady

states (MSS), whereas in the case of cold feed, MSS is not present under similar

operating conditions and only oscillations have been seen. Hence, the choice of the

thermodynamic data and feed conditions are crucial in the prediction of nonlinear

dynamic effects.

Bifurcation analysis of reactor

Although we tried to identify the exact cause of above discussed behavior, we could

not succeed. As the first step towards finding the reason of the oscillatory behav-

ior, an attempt has been made to study the kinetics and VLE in smaller systems.

In view of this, we constructed and studied the following systems: isothermal and

adiabatic CSTR, a CSTR operated at bubble point and a reactive flash configu-

ration, in increasing order of similarity to a reactive distillation column.

Simulations and bifurcation analysis have been carried out independently for

isothermal as well as adiabatic CSTR. Kinetic model-1 is used in the analysis of

CSTR with activities calculated from H-type thermodynamics. α = (xmeoh)/(x2M1B+

x2M2B) and β = (x2M1B + x2M2B)/(x2M1B + x2M2B + xinert) are used as repre-

sentatives of the feed composition. Figure 7 shows the bifurcation diagrams for

isothermal and adiabatic CSTR. In these diagrams, methanol conversion is plot-

ted against Damkohler number as a parameter. Multiple steady states have been

observed in the case of isothermal CSTR, which is in agreement with results re-

16


ported by Baur et al.13. In the case of adiabatic CSTR, along-with multiple steady

states, the presence of Hopf bifurcation has also been observed. Similar analysis

is repeated using A-type thermodynamics for calculations of activities and similar

behavior has been observed.

The above explaied set of simulations have been repeated after adding the dis-

tillation effect to the reactor. The reaction described by model-1 is carried out

in a reactor, which is operated at its bubble point32, with constant molar holdup

of liquid. Vapor stream from the reactor is sent to the total condenser and the

entire condensed liquid is recycled to the reactor. we will refer to this as the

bubble point reactor. The holdup of the condenser is assumed to be negligible.

The energy balance equation is removed from the set of model equations as it is

used to calculate the vapor flow rate, which does not affect component material

balances. Figure 8(a) shows the bifurcation diagrams: reactor temperature versus

Damkohler number as the parameter. Although multiple steady states have been

observed in this case, the presence of Hopf bifurcation point is not evident.

The reactive flash could be assumed as a prototype of the reactive distillation

stage. Hence reactive flash has been studied with same reaction kinetics and ther-

modynamics. Constant molar holdup of liquid and pseudo-steady state energy

balance is assumed in modeling of the reactive flash. Figure 8(b) is the bifurca-

tion diagram for the reactive flash, where similar behavior as seen for bubble point

reactor is observed. In this case also the presence of Hopf point is not observed,

although MSS is present.

From these observations it can be concluded that the presence of energy balance

and non-linearity of the reaction kinetics has a possible impact on the observed

limit cycle behavior in the column. The presence of several state variables makes

17


it difficult to correlate the column performance based only on the CSTR analysis.

Also, the absence of oscillatory behavior in the case of reactive flash and bubble

point reactor shows that it will not be possible to correlate the behavior of the

column by condensing it to smaller systems.

To throw more light on the phenomena of the observed oscillations, bifurcation

analysis has been repeated for the column with reduced number of stages. It has

been observed that if the stripping section is reduced by one or more stages, the

oscillations disappear. However, oscillations continue to exist if rectifying stages

are reduced or even removed completely. We have found the following smallest

column that exhibits oscillatory behavior: two stages in reactive zone, 13-stages

in stripping section and no rectifying section, with pure methanol feed at the bot-

tom of reactive section and pre-reacted feed at 8th stage from top. It should be

noted that this analysis has been carried out in a parameter space close to optimal

conditions. Hence the observed behavior cannot be generalized over wide range

of parameters. We believe that the observed limit cycles are mainly due to the

interactions between a large number of state variables associated with the large

number of stages i.e. because of the large dimensionality of the system. Find-

ing out the exact cause of these effects remains a wide open problem for future

investigators.

Conclusion

Dynamic simulation of TAME synthesis by reactive distillation has been performed

using DIVA simulation environment as well as LSODE integrator. Dynamic sim-

ulations show instabilities in the column for certain disturbances in the feed con-

centration. Open loop oscillations and steady state multiplicity including inter-

nal state multiplicity have been confirmed with different solution approaches and

through continuation analysis of the column for different kinetic and thermody-

18


namic models and at different values of the input parameters. It is worth noting

that though all the kinetic and thermodynamic models predict the same steady

state behavior, the non-linear dynamic effects predicted by them are significantly

different. Various types of nonlinear dynamic effects have been observed over a

range of Da values. It has been seen that even at higher values of Damkohler

number dynamics is influenced by Da values. The step forward would be to find

the source of oscillations in RD systems and investigate the effect of modeling

assumptions on the unstable behavior of the column.

19


Pure Mthanol Feed215 kmol/hr

Pre reacted feed to column (kmol/hr)

isopentane 789.15TAME 157.02M2B 83.942M1B 9.55Methanol 156.0

Rectifying section4−theoretical sages

Reaction section19−theoretical stages

Stripping section10−theoretical stages

Column Pressure 4.5 barIsopentane +MeOH

Reflux ratio = 1.5

TAME

Figure 1: Reactive distillation column configuration used for simulation in present

work17

20


0 0.2 0.4

5

10

15

20

25

30

35

Sta

ge N

umbe

r

0 0.5 1

5

10

15

20

25

30

35340 360 380 400

5

10

15

20

25

30

35

TAMEi−pent

AmyleneMeOH

Liquid mole fraction Temperature (K)

Figure 2: Steady state composition and temperature profiles (P=4.5 bar, Qr=20.5

MW, conversion=77.78 %, TAME purity=83.97%)

0.84

0.85

0.86

TA

ME

pur

ity in

bot

tom

398

399

400

401

Bot

tom

Tem

p (K

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100007

8

9

10x 10

−3

Fee

d co

mpo

sitio

n

Dimensionless time

Da=1.0

(a)

390

400

410

420

Bot

tom

Tem

p (K

)

0.75

0.8

0.85

0.9

0.95

TA

ME

pur

ity in

bot

tom

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100007

8

9

10x 10

−3

Fee

d co

mpo

sitio

n

Dimensionless time

Da=2.0

(b)

Figure 3: (a) First order response to change in feed concentration, at Da=1 (b)

Oscillatory response to change in feed concentration, at Da=2

21


0 5 10 15 20 25345

346

347

348

349

350

351

352

353

Damkohler Number

Reb

oile

r T

empe

ratu

re

(a)

0 5 10 15 20 25360

365

370

375

380

385

390

395

400

405

410

Damkohler Number

Reb

oile

r T

empe

ratu

re

(b)

Figure 4: Bifurcation diagram, with Damkohler number as parameter (cold feed

and H-type thermodynamics)

0 0.2 0.4

5

10

15

20

25

30

35

Sta

ge n

umbe

r

0 0.5 1

5

10

15

20

25

30

35350 400

5

10

15

20

25

30

35

MeOH

Amylene

iPent

TAME

Stable solution−−−−− Unstable solution

LIquid mole fraction Temperature (K)

(a)

0.8

0.85

0.9

0.95

1

TA

ME

pur

ity in

bot

tom

395

400

405

410

415

Bot

tom

Tem

p (K

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100007

8

9

10x 10

−3

Fee

d co

mpo

sitio

n

Dimensionless time

Da = 25.0

(b)

Figure 5: Steady state and dynamic response at Da=25 (cold feed and H-type

thermodynamics); (a) Steady state composition and temperature profiles for stable

and unstable steady state; (b) Dynamic response of bottom temperature and

TAME purity in the bottoms to the pulse in feed composition

22


0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Damkohler number

TA

ME

pur

ity in

the

Bot

tom

s

H−type thermodynamics and kinetic model 1

(a)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Damkohler number

TA

ME

pur

ity in

the

Bot

tom

s

A−type thermodynamics and kinetic model−1

(b)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1H−type thermodynamics and kinetic model −2

Damkohler Number

TA

ME

pur

ity in

Bot

tom

s

(c)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Damkohler number

TA

ME

pur

ity in

the

Bot

tom

s


(d)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1H−type thermodynamics and kinetic model −3

Damkohler number

TA

ME

pur

ity in

Bot

tom

s

(e)

0 0.5 1 1.5 2 2.5 30.4

0.5

0.6

0.7

0.8

0.9

1

Damkohler number

TA

ME

pur

ity in

the

Bot

tom

s


(f)

Figure 6: Comparison showing effect of various kinetic and thermodynamic model

for the hot feed. Hopf bifurcation is present in only H-type thermodynamics i.e

first column of the figures. (P=4.5 bar, QR=19.281 MW, R=1.5)

23


0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Damkolhar number

Met

hano

l con

vers

ion

Isothermal CSTR, H−type thermodynamics, reaction model−1

α = 0.15 α = 0.20

α = 0.22

α = 0.25

(a)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6Adabatic CSTR, H−type thermodynamics. reaction model−1

Damkolhar Number

Met

hano

l con

vers

ion

Tf = 320K Tf = 310K

Tf = 300K

Tf = 305K Tf = 315K

(b)

Figure 7: Bifurcation diagrams for CSTR: (a) Isothermal CSTR, Tf=328 K and

T=335 K, β=0.45 (b) Adiabatic CSTR, α=1.25, β=0.2411

(a) (b)

Figure 8: Bifurcation diagrams : (a) Bubble point CSTR, Tf=330 K, β=0.45,

P=2.5 bar (b) Reactive flash, Tf=330 K, β=0.45, P=2.5 bar

24

Katariya,

Mah

ajan

ian

dM

oudgalya,

Ind.Eng.

Chem

.Res.,

August

05

Table 1: Summary of the literature on modeling, simulation and design studies on TAME synthesis by reactive distillation

(× : The study does not cover this aspect;√

: The study covers this aspect)

(Model-1 = Faisal et al.26, Model-2 = Christian et al.20, Model-3 = Rihko and Krause22)

Authors Simulation Experimental work Design Bifurcation analysis Kinetic Model VLE

Mohl et al.10 Dynamic × ×√

Model-2 Wilson

Sundmacher et al.21 Steady state√

× × Model-2 Wilson

Mohl et al.11 ×√

×√

Model-2 Wilson

Baur et al.14 Dynamic NEQ × ×√

Model-2 Wilson

Baur et al.13 EQ and NEQ × ×√

forward const=Model-2 Wilson

Equm constants=Model-3

Chen et al.15 × × ×√

forward const=Model-2 Wilson


Subawalla and Fair16 Steady state ×√

× Model-3 UNIQUAC

Baur and Krishna17 steady state ×√

× forward const=Model-2 UNIQUAC


Present Work Dynamic × ×√

Model-1/Model-2/Model-3 UNIQUAC

25


Appendix A

Kinetic models used in present study

Model-126

kf1 = 1.215835 × 1017exp(−13752.9

T)

kf2 = 9.40164 × 1014exp(−12488.5

T)

kf3 = 2.142878 × 1021exp(−17040.8

T)

ln(Ka1) = −39.065 +5018.61

T+ 4.686ln(T ) + 0.0077T

− 2.635 × 10−5T 2 + 1.547 × 10−8T 3

ln(Ka2) = −34.798 +3918.02

T+ 3.916ln(T ) + 0.0139T

− 3.121 × 10−5T 2 + 1.805 × 10−8T 3

Model-220

kf1 = 2.576exp(−10746(1

T−

1

333.15))

kf2 = 2.576Ka3exp(−10746(1

T−

1

333.15))

kf3 = 1.078 × 103exp(−10861(1

T−

1

333.15))

Ka1 = 1.057 × 10−4exp(4273.5

T)

Ka2 = 1.629 × 10−4exp(3374.4

T)

Ka3 =Ka1

Ka2

26


Table 2: Design and operating conditions of the column in the present work

Cold feed Hot feed

Number of theoretical stages

Rectifying section 4

Reactive section 19

Stripping section 10

Reflux ratio 1.5 1.5

Reboiler load 20.5 MW 19.0 MW

Operating pressure 4.5 bar 4.5 bar

Feed location and condition:

Pure methanol feed on stage 24 (305 K) 24 (377 K)

Pre-reacted feed on stage 29 (325 K) 29 (343 K)

Model-322

kf1 = 1.7054 × 1017 × exp(−100000.0

8.314×

1

T)

kf2 = 1.3282 × 1017 × exp(−95100.0

8.314×

1

T)

kf3 = 3.6 × 1.078 × 103exp(−10861(1

T−

1

333.15))

Ka1 = exp(−8.3881 +4041.2

T)

Ka2 = exp(−8.2473 +3225.3

T)

Ka3 = exp(−0.188 +833.3

T)

kt

km= 0.1283

27


Table 3: UNIQUAC binary interaction parameters

ASPEN PLUS HYSYS

component i component j bi,j[K−1] bi,j[K

−1] bi,j[cal/gmol] bi,j[cal/gmol]

Methanol 2M1B 54.4 -788.85 -3.3629 1427.23

Methanol 2M2B 28.82 -757.37 6.0199 1412.1475

Methanol TAME 75.15 -511.92 -154.7763 947.128

Methanol ipentane -9.34 -670.42 32.829 1385.481

Methanol n-pentane -30.05 -553.32 32.827 1385.453

Methanol 1-pentene -10.49 -612.24 -9.2854 1439.487

2M1B 2M2B -6.85 3.80 -46.442 46.8944

2M1B TAME -41.65 20.71 57.2099 -13.081

2M1B iso-pentane 82.98 -98.81 -26.628 37.666

2M1B n-pentane -6.81 -5.30 -26.586 37.616

2M1B 1-pentene 62.57 -69.18 -47.6049 48.125

2M2B TAME -16.61 1.042 104.296 -55.4663

2M2B iso-pentane 63.71 -81.44 3.4628 1.429

2M2B n-pentane -3.89 -6.752 3.5147 1.371

2M2B 1-pentene 52.74 -58.81 -48.1617 51.0291

TAME iso-pentane 107.92 -144.72 -4.6411 68.6812

TAME n-pentane -85.47 -60.35 -4.5902 61.482

TAME 1-pentene 18.98 -39.71 -8.5904 57.19025

iso-pentane n-pentane 98.07 -110.03 48.4045 -47.081

iso-pentane 1-pentene -48.75 40.45 -53.901 71.5658

n-pentane 1-pentene 59.39 -84.01 -53.879 71.5413

28


Nomenclature

Symbol Interpretation

Roman letters

rf Multiplication factor, 1 for reaction and 0

for non-reactive

kfm Forward rate constant of the mth reaction, mol/(eq.s)

kf1,ref Forward rate constant of 1st reaction at reference

temperature, mol/(eq. s)

Kam Reaction equilibrium constant of the mth reaction

ai Activity of the ith component

Vk, Lk, Fk Molar flow rates of vapor, liquid and feed

of kth stage respectively, mol/s

D, B Molar flow rates of distillate and bottom

xD, xB Mole fraction of distillate and bottom

SVk , SL

k Molar flow of vapor and liquid side streams

of kth stage, mol/s

Qk Heat loss from kthstage, J/s

Qr, Qc Reboiler and condenser duty, J/s

R Reflux ratio

W Weight of the catalyst, Kg or equivalents

Ftotal Sum of all the feed flows, mol/s

T Temperature, K

HRm,k Heat of reaction, for mth reaction and kth

stage, J/mol

Hk, hk, hfk Molar enthalpy of vapor, liquid and feed for

kth stage, J/mol

Rm,k Rate of mth reaction and kth stage, mol/s

29


Mk Molar holdup of kth stage, mol

εk Volume or weight of the catalyst for kth stage

γi,m Stoichiometric coefficient of ith component

and mth reaction

xi,k, yi,k Liquid and vapor mole fractions of ith

component and kth stage

zi,k Feed mole fraction of ith component and kth stage

Ki,k Vapor liquid equilibrium constant of ith component

and kth stage

ktkm

Ratio of adsorpion equilibrium constant

α Ratio of methanol to total C5 fraction

β Ratio of total reactive isoamylenes to total C5 fraction

Abbreviations

RD Reactive Distillation

MeOH Methanol

2M1B 2-Methyl 1-Butene

2M2B 2-Methyl 2-Butene

TAME Tertiary-Amyl Methyl Ether

i-PENT Isopentane

Da Damkohler Number

DAE Differential Algebraic Equation

ODE Ordinary Differential Equation

VLE Vapor liquid equilibrium

30

Katariya, Mahajani and Moudgalya, Ind. Eng. Chem. Res., August 05REFERENCES

References

[1] Sharma, M. M.; Mahajani, S. M., Industrial application of reac-

tive distillation. In reactive distillation: status and future direc-

tions Sundmacher, K., Kienle, A.,Eds, page 3. Wiley-Vch, Wein-

heim, Germany 2003.

[2] Hiwale, R. S.; Bhate, N. V.; Mahajan, Y. S.; Mahajani, S. M. In-

dustrial applications of reactive distillation: recent trends, Int. J.

Chem. React. Eng. 2004, 2, 1–52.

[3] Widagdo, S.; Seider, W. D.; Sebastian, D. H. Dynamic analysis of

heterogeneous azeotropic distillation, AIChE J 1992, 38, 1229.

[4] Sundmacher, K.; Hoffmann, U. Oscillatory vapor-liquid transport

phenomena in packed reactive distillation columns for fuel ether pro-

duction, Chemical Engineering Journal 1995, 57, 219.

[5] Schrans, S.; Wolf, S.; Baur, R. Dynamic simulation of reactive distil-

lation: An MTBE case study, Computer and Chemical Engineering

1996, 20, S1619–S1624.

[6] Morari, M.; Lee, M.; Dorn, C.; Meski, G. A. Limit cycles in ho-

mogeneous azeotropic distillation, Ind. Eng. Chem. Res. 1999, 38,

2021–2027.

[7] Wang, C. J.; Wong, D. S.; Chien, I. L.; Shih, R. F.; Wang, S. J.; Tsai,

C. S. Experimental investigation of multiple steady states and para-

metric sensitivity in azeotropic distillation, Computer and Chemical

Engineering 1997, 21, S535.

[8] Kienle, A.; Marquardt, W., Nonlinear dynamics and control of

reactive distillation proceses, In reactive distillation: status and

31


future directions Sundmacher, K., Kienle, A.,Eds, page 241. Wiley-

Vch, Weinheim, Germany 2003.

[9] Bravo, J.; Pyhalahti, A.; Jarvelin, H. Investigation in catalytic distil-

lation pilot plant: vapor/liquid equilibrium, kinetics and mass trans-

fer issues, Ind. Eng. Chem. Res. 1993, 32, 2220.

[10] Mohl, K. D.; Kienle, A.; Gilles, E. D.; Rapmound, P.; Sundmacher,

K.; Hoffmann, U. Nonlinear dynamics of reactive distillation pro-

cesses for the production of fuel ethers, Computer and Chemical

Engineering 1997, 21, S989–S994.

[11] Mohl, K. D.; Kienle, A.; Gilles, E. D.; Rapmound, P.; Sundmacher,

K.; Hoffmann, U. Steady state multiplicities in reactive distillation

columns for the production of fuel ethers MTBE and TAME: theo-

retical analysis and experimental verification, Chem. Eng. Sci. 1999,

54, 1029–1043.

[12] Baur, R.; Higler, A. P.; Taylor, R.; Krishna, R. Comparison of

equilibrium stage and nonequilibrium stage models for reactive dis-

tillation, Chemical Engineering Journal 2000, 76, 33–47.

[13] Baur, R.; Krishna, R.; Taylor, R. Bifurcation analysis for TAME

synthesis in reactive distillation column: comparison of pseudo-

homogeneous and heterogeneous reaction kinetics models, Chem.

Eng. Processing. 2003, 42, 211–221.

[14] Baur, R.; Taylor, R.; Krishna, R. Dynamic behavior of reactive dis-

tillation columns described by a nonequilibrium stage model, Chem.

Eng. Sci. 2001, 56, 2085–2102.

[15] Chen, F.; Huss, R. S.; Doherty, M. F.; Malone, M. F. Multiple

32


steady states in reactive distillation: kinetic effects, Computer and

Chemical Engineering 2002, 26, 81–93.

[16] Subawalla, H.; Fair, J. R. Design guidelines for solid catalysed

Reactive distillation systems, Ind. Eng. Chem. Res. 1999, 38, 3696–

3709.

[17] Baur, R.; Krishna, R. Hardware selection and design aspects for

reactive distillation columns. A case study on synthesis of TAME,

Chem. Eng. Processing. 2002, 41, 445–462.

[18] Hwang, W. S.; Wu, J. C. Kinetics and thermodynamics of synthesis

of tertiary amyl methyl ether catalysed by ion-exchange resin, J.

Chin. Chem. Soc. 1994, 41, 181–186.

[19] Oost, C.; Hoffmann, U. The synthesis of tertiary amyl methyl ether

(TAME): microkinetics of the reactions, Chem. Eng. Sci. 1996, 51,

329–340.

[20] Christian, T.; Sundmacher, K.; Hoffmann, U. Residue curve

maps for heterogeneously catalysed reactive distillation of fuel ethers

MTBE and TAME, Chem. Eng. Sci. 1997, 52, 993–1005.

[21] Sundmacher, K.; Uhde, G.; Hoffmann, U. Multiple reactions in cat-

alytic distillation processes for the production of the fuel oxygenates

MTBE and TAME: Analysis by rigorous model and experimental

validation, Chem. Eng. Sci. 1999, 54, 2839–2847.

[22] Rihko, L. K.; Krause, A. O. Kinetics of heterogeneously catalysed

tert-Amyl Methyl Ether reactions in liquid phase, Ind. Eng. Chem.

Res. 1995, 34, 1172.

33


[23] Rihko, L. K.; Paivi, K. K.; Krause, A. O. Kinetic model for ether-

ification of isoamylenes with methanol, Ind. Eng. Chem. Res. 1997,

36, 614–621.

[24] Paivi, K. K.; Struckmann, L.; Krause, A. O. Comparison of the

various kinetic models of TAME formation by simulation and param-

eter estimation, Chem. Eng. Technol. 1998, 21, 321–326.

[25] Paivi, K. P.; Krause, A. O. Simulteneous isomerisation and ether-

ification of isoamylenes with methanol, Chem. Eng. Technol. 2003,

26, 479–489.

[26] Faisal, H.; Syed, C. E.; Datta, R. TAME: thermodynamic analysis

of reaction equilibria in the liquid phase, J. of chem. eng. data 2000,

45, 319–323.

[27] Rihko, L. K.; Linnekoski, J. A.; Krause, A. O. Vapour-liquid

and chemical reaction equilibria in the synthesis of 2-Methoxy-2-

Methylbutane(TAME), J. of chem. eng. data 2000, 45, 1030–1035.

[28] Kroner, A.; Holl, P.; Marquardt, W.; Gilles, E. D. DIVA: An open

Architecture for Dynamic Simulation, Computer and Chemical En-

gineering 1990, 14(11), 1289–1295.

[29] Seydel, R., Practical bifurcation and stability analysis: from equi-

librium to chaos. Springer-Verlag, New York 1994.

[30] Doedel, E. J. AUTO: A program for the automatic bifurcation

analysis of autonomous systems, Cong. Num. 1981, 30, 265–284.

[31] Gani, R.; Jorgensen, S. B. Multiplicity in numerical solution of

non-linear models: seperation processes, Computer and Chemical

Engineering 1994, 18, S55–S61.

34


[32] Waschler, R.; Pushpvanam, S.; Kienle, A. Multiple steady states in

two-phase reactors under boiling conditions, Chem. Eng. Sci. 2003,

58, 2203–2214.

35

Documents

Non-linear dynamic e ects in Reactive Distillation for · PDF file · 2006-07-26tillation process for the production of TAME is presented. ... dehydration of secondary butanol with