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Reaction Hysteresis A New Cause of Output Multiplicity in Reactive Distillation.

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Dev. Chem. Eng. Mineral Process., 7(1/2),pp.41-56, 1999.
Reaction Hysteresis: A New Cause of Output
Multiplicity in Reactive Distillation
M.G. Sneesby
Aspen Technology, Sheraton House, Castle Park, Cambridge, CB3
Ofl
UK
M.O. Tadd and T.N. Smith
School of Chemical Engineering, Curtin University of Technology,
Pevth, WesternAustralia 6845, AUSTAALIA
Jacobsen and Skogestad (1991) described two causes of multiple steady states in
binaly distillation via an anaIysis of the firndamental equations of the equilibrium
stage model for distillation processes. Later, Bekiaris and Morari (1993) described
multiple steady states in azeotropic distillation using a geometric analysis based on
the conditions of perfect fiactionation (infinite number of stages and infinite reflux
ratio). Commercial process simulators ( P r o / I P and Speedup-) were used to
investigate multiple steady states in reactive distillation via the construction of
bifirrcation diagrams (the locus of solutions obtained by varying a single continuation
parameter). These results indicate that the mechanisms described by Jacobsen and
Skogestad (1991) and Bekiaris and Morari (1993) are each pertinent to reactive
distillation processes. However, some aamples of multiple steady states cannot be
adequately explained with the available explanations and a fourth cause of output
multiplicity, applicable only to hybrid reactive distillation. was proposed.
Supplementary simulation studies indicate that the proposed explanation is sound.
Introduction
Reactive distillation is now widely used for the large-scale production of methyl tertbutyl ether (MTBE) and several specialty chemicals. The recent growth in reactive
dlstillation applications can be traced to a series of patents awarded in the early 1980s
(e.g. Smith, 1980) which described methods to support fme catalyst particles within a
distillation column such that adequate vapour-liquid capacity was maintained whlst
providing suitable reactive sites to promote a reversible reaction towards equilibrium.
Thls system permits very high reactant conversions in some applications since
unreacted reactants are continuously recycled to the reaction zone. MTBE is one such
case and higher reactant conversions are achievable using reactive distdlation
technology compared with traditional fixed bed processes.
There are clearly demonstrable advantages to the reactive &stillation process
where steady state conditions are compared. However, there is mounting evidence to
suggest that the full steady state potential might go unrealised in many installations
~~
~
Author to whom correspondence should be addressed (telephone: 618-9266-7704;
fax: 618-9266-3554; email: tadem@che.curtin.edu.au).
41
M.G.Sneesby, M.0.Tade' and T.N. Smith
due to the reduced operability and controllability afforded by the complexity of the
transient process (Sneesby et al., 1997). Reactive distillation is usually highly nonlinear, particularly near the optimal operating points, but the possibility for multiple
steady states to exist can have even greater implications for the operation of these
columns. It might be expected that a distillation column would yield only a single
steady state for every fully-defined and unique set of inputs (e.g. the feed rate and
composition, the column pressure and as many independent operating variables as
there exists products). Indeed, this applies in the vast majority of cases. However, in
some cases, the process outputs for a column are uncertain for a fully-defined, unique
set of inputs. This type of behaviour is well known in continuous stirred tank reactors
(CSTFki) where the process outputs are also dependent on the recent history of the
process. More recently, evidence has been presented to show that this phenomenon is
also possible in distillation, including reactive distillation.
The existence of multiple steady states in the reactive distillation of MTBE
has been demonstrated by simulation (Jacobs and Krishna, 1993; Nijhuis et al., 1993;
Schrans et al., 1996; Sneesby et al., 1998; and others) and although conclusive
experimental evidence has not yet been published, this evidence is anticipated shortly
as similar investigations have already been completed to experimentally confirm the
existence of multiple steady states in binary distillation (Kienle et al., 1995;
Koggersbnrl et al., 1996) and azeotropic distillation (Giittinger et al., 1997).
The phenomenon of multiple steady states in distillation has been studied by
several groups using a first principles approach (e.g. Jacobsen and Skogestad, 1991),
geometric analysis (e.g. Bekiaris and Morari, 1993; Giittinger and Morari, 1997) and,
less successfully, by a mechanistic analysis of simulation results (e.g. Hauan, 1995;
1997). The results of these studies can be categorised to elucidate and class@ the
various causes of output multiplicity according to Table 1. Jacobsen and Skogestad
(1991) speculated on two aspects of the distillation process which could (and
sometimes do) result in multiple steady states. Bekiaris and Morari (1993) and
subsequent co-workers advocate a third cause of output multiplicity which derives
directly from the vapour-liquid equilibrium (VLE). These two approaches are equally
valid and are not mutually exclusive.
The present work summarises the various mechanisms and provides an
example of each cause using simulations of the reactive distillation synthesis of
MTBE and ETBE. The simulation results were analysed to show that some examples
of output multiplicity are inadequately explained by prior research. The possibility of
a fourth cause of multiple steady states in distillation which pertains only to reactive
distillation has been identified here and speculation has been introduced regarding the
pertinent mechanism.
Multiple Steady States due to Unit Singularities
Jacobsen and Skogestad (1991) presented an example of an ideal distillation process
which yielded multiple steady states (i.e. it exhibited output multiplicity) when mass
units were used but only one steady state when molar units were used. They argued
that the change of units created the multiplicity as the partial derivative of the mass
flow with respect to the molar flow was not necessarily always positive. They
proposed the term input transfornation to describe this behaviour. Later, Guttinger
and Morari (1997) considered singularities in the mass-molar relationsbps with
42
Reaction hysteresis in reactive distillation
respect to output multiplicity in reactive distillation and proposed a geometrical
technique to analyse singularities which occur with external specifications (i.e.
product flow rates). However, they were unable to provide an example of a reactive
distillation system where multiplicity was directly attributable to a singularity.
Table 1. Proposed Causes of Multiple Steady States in Distillation.
Mechanism
Proposer
I Singularities in the mass-molar
Jacobsen and Skogestad
relationships for various input variables (1991)
The effect of the stage-to-stage energy Jacobsen and Skogestad
balances on compositions
(1991)
Bekiaris and Morari
Azeotropes in the VLE
(1993)
Sneesby et al. (19971
Reaction hysteresis
Designation
1
I1
III
Iv
A more general designation of this condition is proposed here: unit
singulun'ties, referring to any stationary point in an otherwise smooth relationship
between input variables. This description is preferred to others since it may pertain to
a singularity in dissimilar variables (e.g. the relationship between the molar boilup
and the reboiler duty). This is important since these singularities are equally capable
of causing multiplicity. A specific example of a singularity in the mass-molar
relationship causing an output multiplicity in a reactive &stillation column is also
provided.
A 30-stage ETBE reactive column with the configuration given by Figure 1
and Table 2 was analysed. Figure 2 is part of the bifurcation diagram for this system
and was constructed by finding the locus of steady state solutions for a given set of
inputs (i.e. Table 2) which differ by one parameter only - the independent variable (in
this case, the bottoms product mass draw rate). P r o P (Simulation Sciences, 1994)
was used to solve the column equations in each case. An output multiplicity is clearly
apparent since there are three separate steady state solutions for all bottoms velds
between 35.2% and 36.6% of the feed rate. The salient features of the upper and
lower branches of the bifurcation diagram are in&cated in Table 2 which pertain to
points A and B on Figure 2.
Table 2. Characteristics of 30 Stage ETBE Column.
Design Parameter
Value
8
Rectifjmg stages (including total condenser)
Reactive stages
7
15
Stripping stages (including partial reboiler)
Feed stage
uppermost stripping stage
Hydrocarbon feed composition (mol %)
25% isobutene, 75% n-butenes
0%
Stoichlometric ethanol excess (mol %)
100 kg/hr
Total feed rate (lanovhr)
Overhead pressure
700 Wa-g
Reflux rate
81.3 k g h
43
M.G.Sneesby,M.O. Tadi and T.N. Smith
CONDENSER
FEED
&
/I
BOILUP
-
1
BOlTOMS
REBOILER
Figure 1. Reactive Distillation Columnfor MTBE or ETBE Synthesis.
Table 3. High and Low Conversion Steady States for ETBE Column.
High Conversion
Low Conversion
Property
Steady State Value
Steady State
(Point A)
Value (Point B)
Overall isobutene conversion (mol %)
90.7
84.1
90.4
79.6
Bottoms ETBE purity (mol %)
144.7
135.7
Reboiler temperature (“C)
0.914
0.920
Reboiler duty
4.67
4.33
Boilup ratio (molar basis)
Bottoms yield (molar basis w.r.t. feed)
20.1%
21.1%
1.272
1.271
Reflux ratio
I
The cause of the output multiplicity in t h ~ scolumn is a singularity in the relationship
between the molar bottoms flow (B) and the mass bottoms flow (Bm),as shown in
Figure 3. The stationary points from this plot satisfy condition (1) whch is sufficient
for multiplicity. Equation (2) implies a unit singularity between the molar boilup rate
44
Reaction hysteresis in reactive distillation
1
33%
32%
34%
35%
36%
37%
38%
Bottoms Mass Yield
~~
~
Figure 2. Output Multiplicity due to a Unit Singularity in a Reactive ETBE Column.
(V) and the reboiler duty (QR) and, although not present in this column, such a
singularity is also sufficient for output multiplicity. Indeed, any singularity between a
molar input (i.e. molar reflux, boilup, distillate and bottoms rates) and the actual input
(i.e. volumetric or mass reflux, distillate and bottom rates, and the reboiler duty) will
cause an output multiplicity.
Multiple Steady States due to the Influence of the Energy Balance
Thls cause of multiplicity was also originally described by Jacobsen and Skogestad
(199 1) with respect to an ideal, binary, non-reactive distillation column. In certain
cases, multiple steady states were not observed when the energy balances around each
distillation stage were neglected (i.e. the constant molar overflow, CMO, solution was
considered). Although they only considered non-reactive distillation, ttus concept is
equally valid in other areas, including reactive distillation and hybrid columns.
Essentially, multiple steady states arise where the energy balances result in a
45
M.G. Sneesby, M.O. Tadi and T.N. Smith
24%
.
I
1
1
I
I
I
I
I
I
I
,
,
I
I
I
I
m
I
1
I
19%
32%
33%
I
I
I
I
I
I
I
I
I
I
I
34%
35%
I
36%
Bottoms Mass Yield
,
,
I
37%
38%
Figure 3. Singularities in the Bottoms Mass-Molar Relationship.
change in the product compositions that has an opposite and more substantial effect
on the product flows than the direct effect of the change in the internal liquid (or
vapour) flow. This is summarised by inequalities (3) and (4) which are necessary and
sufficient conditions for multiple steady states (Jacobsen and Skogestad, 1991).
Under these conditions, an increase in the reflux rate has an inverse effect on the
bottoms product draw rate or, similarly, an increase in the boilup rate decreases the
distillate draw rate. Thus, multiple values of the product rate (and, therefore, product
composition) can exist for a single value of the reflux or boilup rate.
The heat of reaction has been postulated as a possible cause for multiple
steady states in reactive distillation (Jacobs and Knshna, 1993). In light of the above
explanation for the effect of the energy balances in the distillation model (or,
conversely, the effect of ignoring the energy balances), the basis for the postulation
becomes clearer: the heat of reaction introduces another term to the energy balances
46
Reaction hysteresis in reactive disxillaxion
whch will create a difference between the molar flow rate entering and leaving a
stage. This effect may be directionally different fkom the normal effect of the internal
flow rate. For example, increasing the reflux rate may have a beneficial effect on the
net reaction rate that might result in an effective decrease in the liquid leaving a
reactive stage. If this effect is substantial enough, it will result in a change of sign of
(aB/
and, therefore, satisfy conhtion (3) and result in an output multiplicity.
Figure 4 shows a section of the bifurcation diagram for constant reflux rate
in the 17 stage MTBE column described in Table 4. This configuration is similar to
that which was analysed by Jabobs and Krishna (1 993), Nijhuis et al. (1993), Schrans
et al. (1996) and others. Multiple steady states exist for boilup rates of 80-82 lanoyhr
if the simulation model includes rigorous energy balances for each theoretical stage
but only one steady state if the results are obtained with a CMO model. The offset
between the two curves is also a result of the exclusion of energy balance as the heat
of reaction is not considered in the CMO case. The cause of the observed multiplicity
can be seen in Figure 4 which shows the influence of the energy balance on the
relationship between the boilup rate and the bottoms temperature for the same section
of the bifurcation dagram. Condition (4) is satisfied at boilup rates of 80-82 kmol/hr
with the energy balance model while
is always greater than zero with
the CMO model.
(ao/av>,
Table 4. MTBE Column Characteristics.
Design Parameter
Rectifying stages (including total condenser)
Reactive stages
Stripping stages (including partial reboiler)
Feed stage
Hydrocarbon feed composition (mol %)
Stoichiometric methanol excess (mol %)
Total feed rate
Overhead pressure
Reflux ratio
-
Value
3
8
6
lowest reactive stage
36% isobutene, 64%n-butane
10 %
2752 kmoVhr
1000 kPa-g
-7.0
Parallels Between the Energy Balance and the Unit Singularities Causes
The explanations for multiplicity caused by unit singularities and by energy balance
effects are fundamentally different but there are similarities between the two
mechanisms which suggest that a unified method of analysis might be available. In
fact, equations (1) and (2) (the conditions for multiplicity due to unit singularities) can
be combined with inequalities (3) and (4) (the conditions for multiplicity due to the
d u e n c e of the energy balance) according to equations (5) and (6). These equations
yield new, more general conditions for multiplicity (inequalities 7 and 8) and do not
include any molar flow terms.
47
M.G.Sneesby, M.0.Tadk and T.N. Smith
I
140
I
~
130
iE 120
g
S
e
Y
E
110
8!
Y)
g
100
5
90
75
80
85
90
95
100
Boilup (mol/min)
105
110
11:
Figure 4. Multiple Steady States Caused by the Energy Balance.
Any of the partial derivatives on the right hand sides of equations (5) and (6)
can be negative and, thereby, cause multiplicity. If two of the derivatives are negative
at the same time, the effects will cancel each other and the multiplicity will only be
observed for molar units. An example of this is provided by the MTBE column
< 0 and Figure 6 shows
described in Table 4. Figure 5 shows (a0
/av)
48
Reaction hysteresis in reactive distillation
I
I
12
75
80
85
95
100
Boilup (molimin)
90
105
110
1151
i
Figure 5. Effect of Molar Boilup on the Distillate Product Rate.
(aQRl a V ) < 0 . The two curves have the same shape so that (aD,/@,
)> 0
for all values of the boilup rate.
Unfortunately, conditions (7) and (8) can only realistically be evaluated
using a bifurcation analysis with a rigorous simulation model of the system under
study. This restricts the application of these equations but other tools (especially
those that rely on molar inputs) are not guaranteed to be accurate in all cases.
Multiple Steady States due to Azeotropes
Azeotropes in mixtures of three or more components can result in a completely
different type of dstillation multiplicity. In h s case, the multiplicity will be
observable in any type of unit (i.e. molar, volumetric, mass, duty, etc.) and can be
detected with a rigorous model or with a CMO model. Bekiaris and Morari (1993)
were the first to elucidate the link between azeotropes and multiplicity in non-reactive
distillation and were able to develop a geometrical tool to detect multiplicities without
a bifurcation diagram. The tool, m/m analysis, allows the product composition to be
predicted from the feed composition and a product rate specification, assuming the
column fractionation is sufficiently close to the ideal case (i.e. infinite stages and
infinite reflux ratio, hence mlo).
The m/co approach is an excellent tool but it still has several shortcomings:
the fractionation characteristics (i.e. the number of stages, etc.) required for the
predxtions to be accurate is uncertain so that the analysis is not always applicable for
49
M.G.Sneesby,M.0.Tadi and T.N. Smith
I
I
I
I
I
I
50 -.
E4
,--i-
-.
45
b
40.
b
e!
i
2
35-
30 -
75
80
85
90
95
100
105
Il(
Boilup (mol/min)
Figure 6. Singularities Between the Reboiler Duty and the Molar Boilup.
finite columns; to be applied, the system must be representable as a pseudo-ternary
mixture; only single-feed, dual-product columns can be analysed; and, no predictions
can be made for internal specifications (e.g. the reflux rate or ratio, or the reboiler
duty). However, co/m analysis can be applied to reactive columns if txansformed
composition co-ordinates are used (Guttinger and Morari, 1997). The transformations
required are the same as those proposed by Ung and Doherty (1 995) and others.
The principal result which is obtained from m/co analysis is the region in
composition space which will produce multiple steady states. The analysis is
independent of the column configuration and only requires basic VLE data on the
components and the azeotropes. Thus, an analysis that has been completed for the
MTBE system is adequate for all MTBE columns. Such an analysis has been consists
completed previously (Guttinger and Morari, 1997) and suggests that a feed which of
25% isobutene, 35% methanol and 40% n-butenes (40% stoichiometric excess of
methanol) will produce multiple steady states. According to the colco techaque, this
type of multiplicity can be detected more easily in the transformed composition coordinates.
The effectiveness of the colw analysis was evaluated here for two different
hybrid MTBE columns. Figure 7 was constructed using a bifurcation analysis of the
column configuration indicated in Table 4 with the given feed composition and a
constant reflux to feed ratio of 3.5. Figure 8 considers the same combination of feed
composition and reflux ratio in a 10 stage column with two rectifying stages
(including a total condenser), one reactive stage and seven stripping stages (including
50
Reaction hysteresis in reactive distillation
a partial reboiler). The feed to h s column is split between the stage immediately
above the reactive stage and the stage uppermost stripping stage. The transformed
flow and composition are defined as follows:
I
100%
90%
80%
--5
70%
ZI
a
60%
i 50%
0
U
a!
40%
,o
e
e-
30%
. 20%
i
i
10%
20%
i
I
i
I
30%
40%
50%
60%
Transformed Flow
i
i
I
-
80%
90%
10%
0%
0%
70%
100%
Figure 7. Bifurcation Resultsfor a I 7 Stage MTBE Reactive Distillation Column
with a Feed Composition Predicted to Produce Multiple Steady States by an oda,
Analysis.
The m/m analysis correctly predicts the multiplicity in the 17 stage column
but does not recognise that the multiplicity disappears in a shorter column. The
analysis of the 10 stage column is a stringent test for the m/cu technique as there are
several factors whch contradict the cu/m assumptions: the column contains both
reactive and non-reactive sections; there are two feed points; and the column is
relatively short (only 10 stages). It is, therefore, not surprising that the c o b
predictions are incorrect in h s case.
Since there is uncertainty regarding the predictions for finite columns,
perhaps the best application of the culm technique is for screening reactive distillation
systems and feed compositions for the possible existence of multiple steady states.
M.G.Sneesby,M.O. Tadi and T.N. Smith
I
,
90%
80%
5
70%
g
60%
5
0
50%
En
I
5!
10
'
1
e
40%
30%
l-
1
~
20%
10%
Lo
0%
Id%
26%
36%
i%,d%
SOYo
Transformed Flow
4696
7
l
!
%
gd%
,
1I
I
I
Figure 8. Bifirrcation Resultsfor a 10 Stage MTBE Reactive Distillation Column
with a Feed CompositionPredicted to Produce Multiple Steady States by an cda,
Analysis.
For example, the reactive residue curve diagram for ETBE, in transformed variables,
shows no azeotropes. Although an azeotrope exists between ETBE and ethanol, it is
not independent of the reaction. Therefore, azeotropic multiple steady states will not
be present in ETBE reactive distillation for any feed composition in any column
configuration. However, this does not preclude the possibility of another type of
multiplicity occurring!
Multiple Steady States due to Reaction Hysteresis
The basic configuration outlined in Table 4 was reanalysed for a feed rate of 100
lanol/hr and a constant reboiler duty of 1.42 MW using Pro/IITM and also Speedup'"
(Aspen Tech., 1993). Qualitatively, there was no difference between the two
simulators and this combination of operating configuration and conditions was also
found to yield multiple steady states. A section of the bifurcation diagram (generated
with Speedup? is shown in Figure 9. Point 'X' is indicative of the high conversion
branch while point 'Y' is indicative of the low conversion branch.
A new mulhplicity mechanism, reaction hysteresis, is proposed here to
explain the multiple steady states seen in Figure 9. A new explanation is required
since the multiplicity X-Y cannot be adequately accounted for by any of the known
causes discussed previously: it is not caused by singularities in any mass-molar
52
Reaction hysteresis in reactive distillation
110
i
I
14000
14500
15000
15500
16000
16500
7 7000
Reflux Rate (kghr)
Figure 9. Ou2put Multiplicity in a Hybrid M D E Column.
relationslup as the multiplicity persists if molar units are considered; neither is it
caused by energy balance effects since the multiplicity also persists if the energy
balance is ignored; and the azeotropic mechanism only applies to material-balance
specifications (e.g. constant distillate or bottoms product rate), and the feed
composition is outside the region which produces multiple steady states anyway (as
determined via an m/a, analysis). Giittinger and Morari (1997) suggested that
interactions between the reactive and non-reactive column sections could extend the
multiplicity feed region but provide only one column analysis as evidence for h s
speculation and do not suggest how azeotropes could account for multiplicity with an
energy-balance specification (e.g. constant reboiler duty or reflux rate). Thus, none of
the literature explanations (i.e. type 1, I1 and LII multiplicities) fit the observations and
the cause of the unusual behaviour remains unclear.
It is proposed that, in this case, the multiple steady states arise from
interactions between the reactive and non-reactive column sections via the effect that
the non-reactive sections have on the reaction zone condtions. Thls type of
multiplicity is applicable to any hybrid column with any type of specifications, and is
caused by a change in the reaction zone conditions that is propagated and remforced
by the fractionation changes that concurrently resulted from the original disturbance.
A very high process gain is possible from thls combination of effects but, more
importantly, the two effects may not remforce each other in the opposite direction.
Th~spattern describes a process hysteresis that is a sufficient condition for
multiplicity.
53
M.G.Sneesby, M.O.Tadi and T.N. Smith
To understand the proposed mechanism, it is important to consider necessary
and sufficient conditions for output multiplicity. Previous authors (e.g. Hauan et al.,
1995 and 1997) have discussed multiplicity in relation to strongly non-linear
behaviour but non-linearity is only necessary and not sufficient for output
multiplicity. Provided that a change in an operating condition is reversible, the
bifurcation diagram for that parameter will be smooth and only one steady state will
exist. A distinctive ‘S’shape is seen in the bifurcation diagram where there are
multiple steady states. The ‘S’shape effectively defines a process hysteresis (i.e. a
non-reversible change in operating conditions) which is both a necessary and
sufficient condition for output multiplicity. One bifurcation branch is accessible only
by increasing the bifurcation parameter while the other branch is accessible only by
decreasing the bifurcation parameter.
The application of reaction hysteresis to this hybrid MTE3E column is as
follows. Where the reactive section of the column is cool and lean in methanol,
increasing the boilup rate strips methanol from the bottoms product and promotes the
MTBE synthesis reaction on the reactive stages. This is facilitated by the minimumboiling azeotropes which form between methanol (the heaviest reactant) and the
various C, components. However, an increase in the boilup rate causes the phase
equilibrium temperature to rise, which tends to suppress the synthesis reaction due to
its exothermic nature.
The duality of effects continues in this way with increasing boilup until a
critical point is reached when the effect of the increasing temperature predominates
and the decomposition reaction is favoured. This produces more methanol which
propagates the trend of rising temperatures (the reactive residue curve terminates at
methanol and not MTBE) and escalates the MTBE decomposition rate. The column
profile then goes through a catastrophic change before stabilising to a new operating
point with higher concentration of methanol in the reaction zone (and upper stripping
section) and a lower overall conversion of reactants to MTBE. In reverse, a decrease
in the boilup rate has only a slight effect on the temperature and composition profiles
as the two effects no longer reinforce each other. The situation is somewhat
analogous to a reaction runaway although fiactionation effects trigger the runaway
rather than kinetic effects.
As with multiplicities due to the presence of azeotropes in the VLE, the
column configuration (i.e. the number of theoretical stages, and the internal vapour
and liquid flow rates) can affect the presence of a reaction hysteresis. With fewer
stages and lower internal flows (i.e. low reflux and boilup ratios), composition
differences between adjoining stages are lessened, and there is less scope for changes
in the stage-to-stage temperatures and compositionsto propagate and multiply.
Reaction hysteresis, as described above, is dependent on interactions
between the reactive and non-reactive column sections, and is independent of reaction
kinetics, the column energy balance and singularities in the mass-molarrelationshps.
This type of behaviour exactly fits the simulation observations and could be
responsible for the output multiplicity shown in Figure 9.
To check this hypothesis another series of simulations were completed.
Since the proposed mechanism relies on interactions between the reaction rate and the
reaction zone conditions provided by the internal feeds from the non-reactive
sections, the multiplicity should disappear if the dependent between reaction rate and
54
Reaction hysteresis in reactive distillation
reaction zone conditions is removed. Th~ssituation was simulated by assuming that
the reaction equilibrium constant (&) was independent of temperature and
composition. The resulting bifurcation diagram for the same column and conditions
as was used to produce Figure 9 is indicated in Figure 10. Clearly, there is only one
steady state for each value of the reflux rate. This confirms the importance of
interactions between fractionation and reaction. Without these interactions,
multiplicity was not observed.
160
150
3
E
E
b
n
130
120
8
110
100
14000
14500
15000
15500
16000
Fteflux Rate (kglhr)
16500
17000
Figure 10. Bifirrcation Resultsfor Constant Reaction Equilibrium Constant.
Conclusions
Three distinct and comprehensive explanations for multiple steady states in
distillation have been proposed previously. Importantly, each explanation pertains to
a real physical effect and are not the results of numerical techniques or the
assumptions made for the purposes of eflcient simulation. Each mechanism is
equally applicable to reactive distillation systems (including hybrid systems with both
reactive and non-reactive column sections). Separate examples of multiplicity caused
by all three mechanisms have been presented here using simulation data obtained
with Pro/IIm and Speedupm.
Some reactive distillation multiplicities in the synthesis of MTBE were also
detected that could not adequately be explained using only the previously described
mechanisms. A new cause of multiple steady states, reaction hysteresis, was
proposed to account for this discrepancy. It was proposed that reaction hysteresis is
only possible in columns which include both reactive and non-reactive sections and is
55
M.C.Sneesby, M.0.Tad& and T.N. Smith
caused by the interactions between fractionation and the reaction. These effects
compete in one duection and reinforce in another, creating a process hysteresis that is
a necessary and sufficient condition for multiplicity. If the interaction between
fractionation and reaction is removed (e.g. by assuming a constant reaction
equilibrium that is independent of temperature and composition), only one steady
state was observed in the column under study. This provides evidence of the
soundness of the proposed explanation.
References
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