Integrated design and control of glycerol etherification processes

Abstract

The feasibility of an industrial-scale, acid-catalyzed process for etherification of glycerol with i-butene is analyzed. A simplified mass balance of the process is derived using a kinetic model for the reactor and black-box model for the separation section. Degree of freedom analysis is used to suggest plantwide control structures. Sensitivity analysis of the steady state model shows that the system exhibits both state multiplicity and regions where no solution exists. The nominal operating point is chosen to avoid high sensitivity to disturbances and to guarantee feasibility when operation and design parameters change or are uncertain. Detailed design is performed using AspenPlus. The stability and robustness in operation are checked by rigorous dynamic simulation in AspenDynamics.

Full text

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
Publicat de
Universitatea Tehnică „Gheorghe Asachi” din Iaşi
Tomul LVI (LX), Fasc. 4, 2010
SecŃia
CHIMIE şi INGINERIE CHIMICĂ
INTEGRATED DESIGN AND CONTROL OF GLYCEROL
ETHERIFICATION PROCESSES
BY
ELENA VLAD, COSTIN SORIN BILDEA and GRIGORE BOZGA
Abstract. The feasibility of an industrial-scale, acid-catalyzed process for
etherification of glycerol with i-butene is analyzed. A simplified mass balance of the
process is derived using a kinetic model for the reactor and black-box model for the
separation section. Degree of freedom analysis is used to suggest plantwide control
structures. Sensitivity analysis of the steady state model shows that the system exhibits
both state multiplicity and regions where no solution exists. The nominal operating point
is chosen to avoid high sensitivity to disturbances and to guarantee feasibility when
operation and design parameters change or are uncertain. Detailed design is performed
using AspenPlus. The stability and robustness in operation are checked by rigorous
dynamic simulation in AspenDynamics
.
Key words: glycerol ethers, process design, process control, nonlinear behavior.
1. Introduction
A recent European Union directive 0 requires that, by the end of the
year 2010, traffic fuels should contain 5.25% of components produced from
renewables. The amount of glycerol obtained as by-product in biodiesel
production is equivalent to about 10% wt. of the total product. As a result to the
increasing availability, the market price of glycerol has dropped rapidly.
Therefore, new uses for glycerol need to be found. Although glycerol could be
burnt as a fuel, it could also be processed into more valuable components.
Di- and tri-ethers of glycerol are compounds soluble in diesel and
biodiesel, improving the quality of the fuel 0. They diminish the emissions of
particulate matter, carbon oxide and carbonyl compounds. Moreover, they
decrease the cloud point of the fuel when combined with biodiesel. Therefore,

140
Elena Vlad, Costin Sorin Bildea and Grigore Bozga
ethers of glycerol are interesting alternatives to commercial oxygenate additives
such as MTBE, ETBE or TAME. Ethers of glycerol can be obtained by
etherification with olefins and alcohols (Fig. 1) such as i-butene and i-butanol or
by trans-esterification with another ether such as methyl-tert-butyl ether.
H
2
C OH
HC OH
H
2
C OH
G
+ O
DE
+
O
H
2
C OH
HC OH
H
2
C O R
H
2
C O
R
HC OH
H
2
C O R
+ O
H
2
C O R
HC O R
H
2
C O R
ME TE
Fig. 1 – Etherification of Glycerol with Olefines. G – glycerol; O – olefin;
ME – mono-ether; DE – di-ether; TE – tri-ether.
Reaction of i-butene with glycerol in presence of homogeneous 0 or
heterogeneous 0, 0 acid catalysts yields a mixture of mono-, di-, and tri-tert-
butyl glycerol ethers. Conceptual processes which could be used to perform this
transformation are described in references 0, 0,…,0.
In this article, we present the detailed design of a glycerol etherification
plant processing a nominal flow rate of 2 kmol/h of glycerol, assumed to be the
by-product of a 15000 tone/year biodiesel plant. We focus on operating
conditions leading to high selectivity in di-ether, 0.9 being a typical value.
2. Mathematical Model
A simplified model of the plant is used to choose a nominal operating
point together with the plantwide control structure. Fig. 2 presents the Reactor –
Separation – Recycle structure of the plant 0. After the reaction takes place, the
reactor effluent enters the Separation section. Here, the di- and tri- ethers are
removed from the plant while the glycerol, i-butene and mono-ether are
recycled to the reactor, after mixing with fresh reactants.
Reactor Separation
i-Butene
Glycerol
Mono-Ether recycle
i-Butene recycle
Glycerol recycle
0
0
1
1
2
3
3
3
4
di-Ethers
tri-Ether
Fig. 2 – Reactor - Separation – Recycle structure of the glycerol etherification plant.

Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 4, 2010 141
The CSTR is operated at 90ºC. The model of the reactor consists of
mass balance equations (1), where the reaction rates are taken from reference 0.
Moreover, ideal separation and mixing are assumed.
(1) ,2 ,1 ,
1,3
0 , , , ,
k k k j j
j
F F V r k G I M D T
ν
=
 
− + ⋅ ⋅ = =
 
 
 
∑
The design degrees of freedom represent the variables that must be
specified to completely define the process. The control degrees of freedom
are the variables that can be manipulated, namely the control valves in the
process. For most processes, the number of design degrees of freedom is
equal to the number of control degrees of freedom 0. The model of the
glycerol etherification plant consists of 23 equations and contains 25
variables (17 flow rates, 5 concentrations and 3 reaction rates). Therefore, 2
degrees of freedom must be fulfilled. This is in agreement with Fig. 2, where
two valves must be used for level control, leaving 2 valves available for
manipulating flow rates.
3. Steady State Behaviour
The aim of this section is to investigate the steady state behaviour the
etherification plant. Three control structures will be considered (Fig. 3). In all
control structures the flow rate of fresh glycerol is set to the value FG,0. Control
structures CS1, CS2 and CS3 differ by the second flow specification: fresh i-
butene (FI,0), ratio r0 = FI,0/FG,0 and i-butene at reactor inlet (FI,1), respectively.
For each control structure, the mathematical model is solved using Matlab 0.
The conversions of glycerol and i-butene (XG and XI, respectively) are plotted
versus the flow rate of fresh glycerol (FG,0) and conclusion are drawn
concerning the sensitivity of the desired operating point when variable flow
rates of glycerol must be processed.
i-Butene
LC
FCFC
Glycerol
LC
FCFC
0
0
1
1
3
3
CS1
i-Butene recycle
to Reactor
Glycerol recycle
to Reactor
i-Butene
LC
FCFC
Glycerol
LC
FCFC
0
0
1
1
3
3
CS2
i-Butene recycle
to Reactor
Glycerol recycle
to Reactor
xr
0
i-Butene
FC
LCLC
Glycerol
LC
FCFC
0
0
1
1
3
3
CS3
i-Butene recycle
to Reactor
Glycerol recycle
to Reactor
Fig. 3 − Plantwide control structures.

142
Elena Vlad, Costin Sorin Bildea and Grigore Bozga
When the control structure CS1 is applied, a closed form solution is
available for the product flow rates:
(2)
,4 ,0 ,0
3
D G I
F F F
= −
;
,4 ,0 ,0
2
T I G
F F F
= −
If follows that, for a fixed value of the fresh i-butene flow rate FI,0, the
model has a feasible solution (positive flow rates) only for a certain range of the
fresh glycerol flow rate FG,0.
(3)
,0 ,0
min max
,0 ,0 ,0
3 2
I I
G G G
F F
F F F< < < =
It should be noted that selectivity of the glycerol transformation into di-
ether is high when the fresh glycerol flow rate approaches the maximum
allowed flow rate
max
,0
G
F
.
Fig. 4 displays the results obtained when control structure CS1 is applied
to two etherification plants employing reactors of volume 1 m3 and 4 m3,
respectively. When the flow rate FG,0 is set to the upper limit
max
,0
G
F
, only di-ether
is obtained as product. However, both glycerol and i-butene conversions
approach zero and the recycle rates become infinite. This limit is independent of
the reactor volume. The lower admissible value
min
,0
G
F
approaches the theoretical
value FI,0/3 when the reactor volume V approaches infinity.
0
0.2
0.4
0.6
0.8
1
1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
G
V = 1 m
3
F
I,0
/ [kmol/h]=4.2 4.6 5
0
0.2
0.4
0.6
0.8
1
1.5 2 2.5 3
FG,0 / [kmol/h]
XI
V
= 1 m
3
F
I,0
/ [kmol/h]= 4.2 4.6 5
0
0.2
0.4
0.6
0.8
1
1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
G
V = 4 m
3
F
I,0
/ [kmol/h] = 4.2 4.6 5
0
0.2
0.4
0.6
0.8
1
1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
I
V=4 m
3
F
I,0
/ [kmol/h] = 4.2 4.6 5
Fig. 4 – Control structure CS1: glycerol and i-butene conversions vs.
fresh glycerol flow rate, for different values of the fresh
i-butene flow rate and reactor volume.

Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 4, 2010 143
Fig. 4 shows that, for given values of the model parameters, either zero
or two steady states are possible. When they exist, the two states are
characterized by similar values for the glycerol conversion, but very different
values for the conversion of i-butene. Moreover, a very high sensitivity of the i-
butene conversion with respect to glycerol flow rate is observed when high
selectivity in di-ether is required (FG,0 close to
max
,0
G
F
). This implies that small
disturbances will lead to large changes of the i-butene recycle rate, known as the
“snowball effect” 0, 0. In conclusion, control structure CS1 offers the advantage
of easily setting the ratio between the di- and tri-ethers by manipulating the
reactants flow rates. However, the operating points of high di-ether selectivity
exhibits high sensitivity to disturbances and are dangerously close to the
feasibility limit
max
,0
G
F
.
Fig. 5 presents the conversions versus the fresh glycerol flow rate, for
different reactor volumes, when control structure CS2 is used. The system
exhibits multiple steady states and a region of unfeasibility. On the two solution
branches, the values of glycerol conversion are very close to each other. The
two steady states extend to zero glycerol flow rate. Compared to control
structure CS1, much larger glycerol flow rates can be processed. The same
selectivity in di-ether, namely / ,0 ,0
3 0.9
D G I G
F F
σ
= − =
is obtained at all
operating points depicted in Fig. 5. It appears that the 1 m3 reactor allows
increasing the amount of processed glycerol by 50%.
0.4
0.42
0.44
0.46
0.48
0.5
0 2 4 6 8 10 12 14
F
G,0
/ [kmol/h]
X
G
F
I,0
/F
G,0
=2.1
V / [m
3
] = 1 2 4
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14
F
G,0
/ [kmol/h]
X
I
V / [m
3
] = 1 2 4
F
I,0
/F
G,0
=2.1
Fig. 5 – Control structure CS2: glycerol and i-butene conversions vs. fresh
glycerol flow rate, for different values of the reactor volume.
Fig. 6 presents results obtained when the control structure CS3 is
used. Again, irrespective of the reactor volume and of the fixed value for the
i-butene flow rate at reactor inlet, multiple steady states exist. The high-
selectivity operating points are located near the turning points of the
conversion – flow rate diagram and, therefore, are dangerously close to the
region of unfeasibility. Moreover, a direct relationship between the flow rate
FI,1 and the selectivity
σ
D/G does not exist. We conclude that control structure
CS3 appears to be unsuitable.

144
Elena Vlad, Costin Sorin Bildea and Grigore Bozga
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
G
V
= 1 m
3
F
I,1
/[kmol/h] = 5 67
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
I
F
I,1
/ [kmol/h] = 5 67
V= 1 m
3
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
I
V= 4 m
3
F
I,1
/ [kmol/h] = 5 6 7
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
F
G,0
/ [kmol/h]
X
G
V= 4 m
3
FI,1
/ [kmol/h] = 5 67
Fig. 6 – Control structure CS3: glycerol and i-butene conversions vs. fresh glycerol flow
rate, for different values of the reactor-inlet i-butene flow rate and reactor volume.
4. Detailed Design
This section presents the detailed design of glycerol etherification
process. The flowsheeting software ASPEN Plus version V7.0 0 was used as a
computer aided process engineering tool. Fig. 7 presents the flowsheet. A
detailed stream report is presented in Table 1. In the rest of this section, details
concerning the processing units will be given.
G1+M1
IB1
2
9
M+D+T
IB3B
G0
IB3A
G1+M1A
6
M1-B
D+T
IB0
CSTR
C1
SEP-GLL
B3
B4
C2
MIX-IB
I0
G0
I1
I3a
I3b
2
4
M1b
G1+M1a
G1+M1
2a 2b
MIX-IB
CSTR
SEP-GLL
C1
C2
Fig. 7 – Flowsheet of the glycerol etherification plant.

Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 4, 2010 145
Table 1
Stream Report
G0 I0 I1 G1+M1
2 I3a G1+M1a
2a 4 I3b 2b M1b
Flow, [kmol/hr]
2.057
4.063
6.333 8.284 10.55
0.247
7.940 4.429
2.061
2.023
2.406
0.345
Flow, [kg/hr] 189.4
228 355.347
971.8 1327.2
13.876
920.3 582.5
417.4
113.5
469.0
51.6
Temp., [ºC] 90.0
20.0
62.919
61.567
90.0 50.0 50.0 50.0
165.2
−6.6 243.1
244.2
Pressure, [bar] 14.0
14.0
14.0 14.0 14.0 1.0 1.0 1.0 0.2 1.0 1.12
0.73
Vapor Fraction 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0
Flow, [kmol/hr]
Glycerol 2.057
0.0 0.0 4.625 2.701
0.0 4.625 0.133
0.133
0.0 0.133
0.0
i-Butene 0.0 4.063
6.333 0.265 2.539
0.247
0.265 2.027
0.004
2.023
0.004
0.0
MTBG 0.0 0.0 0.0 2.947 2.947
0.0 2.611 0.336
0.000
0.0 0.336
0.336
DTBG 0.0 0.0 0.0 0.394 2.106
0.0 0.385 1.721
1.712
0.0 1.721
0.009
TTBG 0.0 0.0 0.0 0.053 0.265
0.0 0.053 0.212
0.212
0.0 0.212
0.0
WATER 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
The physical properties of glycerol, i-butene and water are available in
AspenPlus databank. The properties of the ethers were calculated using group
contribution methods. The behaviour of the liquid phase was described by the
NRTL activity model. The interaction parameters of pairs involving ethers and
glycerol or i-butene were taken from 0. The other unknown interaction
parameters were estimated using UNIFAC. Ideal mixing was assumed.
Glycerol etherification. The etherification of glycerol with i-butene
takes place in a CSTR of 1 m3. The reaction temperature and pressure are set to
90ºC and 14 bar, respectively, when the reaction mixture is liquid. When the
same reactor-inlet flow rates were specified to Matlab and Aspen models,
identical results for the reactor-outlet stream were obtained.
G-L-L separation. Depending on the temperature and composition, a
mixture of glycerol, i-butene and glycerol ethers can exist in a single or two
different liquid phases. The composition of the reactor-outlet stream falls in the
single-phase region. In order to exploit the immiscibility for separating the
reactants from products, the fresh glycerol is fed in the G-L-L separator. The
temperature is reduced to 50ºC and the pressure is set to 1 bar. The cooling duty
is 27.8 kW. 10% of i-butene is found in the vapour stream “I3a” and recycled.
The stream “G1+M1a” contains glycerol and mono-ether and is recycled. The
liquid stream “2a” contains i-butene and ethers.
Column C1 separates the i-butene. It has 9 theoretical stages with the
feed on stage 3. The column has a partial condenser and is operated at
atmospheric pressure. The column diameter is 0.2 m. The reflux ratio is set to 2.
The reboiler duty is 79.6 kW and the condenser duty is 25 kW. The entire
amount of i-butene is recovered in stream “I3b”.

146
Elena Vlad, Costin Sorin Bildea and Grigore Bozga
Column C2 separates di- and tri-ether from mono-ether. It has 50
theoretical stages with the feed on stage 25. The column has a total condenser
and is operated under vacuum to avoid high temperature in the bottom of the
column. The column diameter is 0.8 m. The reflux ratio is set to 4. The reboiler
duty is 191 kW and the condenser duty is 209 kW. Stream “M1b” contains 97%
mole fraction mono-ether and some of di-ether. Stream “4” contains 83% di-
ether and 10.2% tri-ether (mole fractions).
5. Dynamics and Control
From the viewpoint of steady state behaviour, the design performed in
the previous sections together with control structure CS2 allow processing the
nominal flow rate of glycerol and tolerate rather large disturbances. However,
the analysis showed two co-existing steady states, which cannot be
simultaneously stable. Moreover, the simplified model used in previous section
assumed perfect separation of the products from the un-consumed reactants,
which certainly is not the case. Therefore, the dynamics of the plant must be
considered in order to prove the stability of the operating point and the
resiliency with respect to disturbances. To reach this goal, a dynamic model of
the plant was built in AspenDynamics. Besides the control loops of CS2,
standard control of the G-L-L separator and distillation columns was used. The
controllers were tuned by a simple version of the direct synthesis method 0.
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10
t / [h]
F / [kmol/h]
0
2
4
6
8
10
I3a
4
I3b
G1+M1
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10
t / [h]
F / [kmol/h]
0
2
4
6
8
10
I3a
4
I3b
G1+M1
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10
t / [h]
F / [kmol/h]
0
2
4
6
8
10
I3a
4
I3b
G1+M1
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10
t / [h]
F / [kmol/h]
0
2
4
6
8
10
I3a
4
I3b
G1+M1
(a)
(b)
(c)
(d)
Fig. 8 – Dynamic simulation results.
Fig. 8 presents results of dynamic simulation. Starting from the steady
state, several disturbances were introduced at time = 1 h: in simulations a) and

Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 4, 2010 147
b), the glycerol flow rate was changed from 2 kmol/h to 2.2 kmol/h and 1.8
kmol/h, respectively. In simulations c) and d) the ratio between reactants was
changed from the nominal value of 1.2 kg/kg to 1.3 kg/kg and 1.1 kg/kg,
respectively. It can be seen that the nominal operating point is stable, and the
plant achieves stable operation when disturbances are introduced.
6. Conclusions
Production of glycerol ethers by etherification of glycerol with i-butene
catalyzed by homogeneous acid catalysts, such as p-toluene sulfonic acid, is
feasible. For a typical glycerol flow rate of 2 kmol/h, the reaction can be carried
on in a CSTR of 1 m3. The reactants conversion is high and small recycles are
needed. The separation products - unconsumed reactants can be achieved by a
combination of a 3-phase flash and two distillation columns.
When one of the control structures considered in this work is applied,
multiple steady states are possible and the flow rate of glycerol that can be
processed is limited. For this reason, the behaviour of the plant was investigated by
steady state sensitivity analysis. This allowed selecting a robust control structure.
Finally, rigorous dynamic simulation was performed in order to prove
that the chosen control structure ensure stable operation when operation and
design parameters change or are uncertain.
A c k n o w l e d g e m e n t s. The work has been funded by the Sectoral
Operational Programme Human Resources Development 2007-2013 of the Romanian
Ministry of Labour, Family and Social Protection through the Financial
Agreement POSDRU/88/1.5/S/61178 and by project IDEI 1545/2008 – “Advanced
modeling and simulation of catalytic distillation for biodiesel synthesis and glycerol
transformation”.
Received: November 10, 2010 University POLITEHNICA Bucharest,
Department of Chemical Engineering
e-mails: e_vlad@chim.upb.ro
s_bildea@upb.ro
g_bozga@chim.upb.ro
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INTEGRAREA PROIECTĂRII ŞI REGLĂRII PROCESULUI
DE ETERIFICARE A GLICERINEI
(Rezumat)
Fezabilitatea unui proces industrial de eterificare a glicerinei cu i-butenă, în
cataliză omogenă acidă, este investigată. Un model simplificat al bilanŃului de masă al
procesului este dedus folosind un model cinetic pentru reactor, secŃia de separare fiind
descrisă printr-un model de tip cutie-neagră. Analiza gradelor de libertate este folosită
pentru a dezvolta structuri de reglare a instalaŃiei. Analiza de senzitivitate a modelului
de regim staŃionar arată că sistemul prezintă stări multiple şi regiuni în care nu există
soluŃii. Punctul nominal de operare este ales astfel încât senzitivitatea faŃă de perturbaŃii
să fie evitată. În plus, fezabilitatea este garantată chiar dacă parametrii de operare se
modifică sau sunt incerŃi. Proiectarea detaliată a instalaŃiei este efectuată folosind
AspenPlus. Stabilitatea şi robusteŃea în operare sunt verificate prin simulare dinamică
riguroasă în AspenDynamics.