Design and Control of Glycerol-tert-Butyl Alcohol Etherification Process

Abstract

Design, economics, and plantwide control of a glycerol-
tert
-butyl alcohol (TBA) etherification plant are presented. The reaction takes place in liquid phase, in a plug flow reactor, using Amberlyst 15 as a catalyst. The products' separation is achieved by two distillation columns where high-purity ethers are obtained and a section involving extractive distillation with 1,4-butanediol as solvent, which separates TBA from the TBA/water azeotrope. Details of design performed in AspenPlus and an economic evaluation of the process are given. Three plantwide control structures are examined using a mass balance model of the plant. The preferred control structure fixes the fresh glycerol flow rate and the ratio glycerol + monoether : TBA at reactor-inlet. The stability and robustness in the operation are checked by rigorous dynamic simulation in AspenDynamics.

Full text

The Scientific World Journal
Volume 2012, Article ID 180617, 11 pages
doi:10.1100/2012/180617
The cientificWorldJOURNA
L
Research Article
Design and Control of Glycerol-
tert
-Butyl Alcohol
Etherification Process
Elena Vlad, Costin Sorin Bildea, and Grigore Bozga
Department of Chemical Engineering, University Politehnica of Bucharest, Street Gh. Polizu 1-7, 011061 Bucharest, Romania
Correspondence should be addressed to Costin Sorin Bildea, sbildea@upb.ro
Received 7 September 2012; Accepted 5 November 2012
Academic Editors: G. Morales and O. A. Scelza
Copyright © 2012 Elena Vlad et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Design, economics, and plantwide control of a glycerol-tert-butyl alcohol (TBA) etherification plant are presented. The reaction
takes place in liquid phase, in a plug flow reactor, using Amberlyst 15 as a catalyst. The products’ separation is achieved by two
distillation columns where high-purity ethers are obtained and a section involving extractive distillation with 1,4-butanediol
as solvent, which separates TBA from the TBA/water azeotrope. Details of design performed in AspenPlus and an economic
evaluation of the process are given. Three plantwide control structures are examined using a mass balance model of the plant.
The preferred control structure fixes the fresh glycerol flow rate and the ratio glycerol + monoether :TBA at reactor-inlet. The
stability and robustness in the operation are checked by rigorous dynamic simulation in AspenDynamics.
1. Introduction
As byproduct of biodiesel production, one mole of glycerol
(G) is produced for every three moles of methyl esters, which
is equivalent to approximately 10% wt. of the total product.
As a result of the increased 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
[1,2].
Di- and triethers of glycerol are compounds soluble in
diesel and biodiesel, improving the quality of the fuel [3].
They diminish the emissions of particulate matter, carbon
oxide, and carbonyl compounds. Moreover, they provide
a 5 K reduction in cloud point and an 8% reduction in
viscosity when combined with biodiesel [4]. Therefore,
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 such
as i-butene (IB), alcohols such as tert-butyl alcohol (TBA) or
ethanol [5]orbytrans-esterification with another ester such
as methyl-t-butyl ether.
Reaction of i-butene with glycerol in presence of homo-
geneous [6] or heterogeneous [7,8] acid catalysts yields
a mixture of mono-, di-, and tri-tert-butyl glycerol ethers
(ME, DE, and TE, resp.). Several processes were proposed to
perform this transformation [6,9–12]. In all these processes,
the reaction takes place at 14 bar, necessary for keeping
the i-butene in liquid phase. Moreover, from the reactor
outlet, i-butene is separated as a vapour stream and must
be recompressed before being recycled, which is another
drawback of the process.
The etherification reaction could be performed at
lower pressure using tert-butyl alcohol as reactant and
ion exchange resins as catalyst [13,14], according to the
following reactions:
G+TBAME + H2O
ME + TBA DE + H2O
DE + TBA TE + H2O
(1)
Small amounts of i-butene are formed due to TBA dehydra-
tion:
TBA IB + H2O(2)
Yusof et al. [15] report glycerol conversions exceeding
64% and mono- to diether ratio in the range 4 : 1–6 : 1,
obtained using Amberlyst 15, Amberlite IR-120, Montmo-
rillonite K10, p-toluenesulfonic acid, and sulfuric acid as

2The Scientific World Journal
Reactor Separation
TBA
Glycerol
TBA recycle
Glycerol and
monoether recycle
0
0
1b
1a
2
3a
4a
Diether
Triether
MIX-TBA
MIX-GE
4b
Water
3b
Figure 1: Reactor-separation-recycle structure of the glycerol-TBA etherification plant.
catalysts. Frusteri et al. [16] studied the etherification of
glycerol with tert-butyl alcohol in presence of lab-made silica
supported acid catalysts. Experiments were carried out in
batch mode at temperature ranging from 303 to 363 K. Ozbay
et al. [17] compared various solid acid catalysts, such as
Amberlyst-15 (A-15), Amberlyst-16 (A-16) and Amberlyst-
35 (A-35), Nafion-SAC-13, and gamma-alumina. Amberlyst
15 showed the highest activity at about 110 degrees C,
while A-16 gave higher diether selectivity values. Chang and
Chen [18] present a systematic optimization of the glycerol
etherification with alcohol-tert-butylic based on the small-
scale experimental data. The reaction conditions (reacting
temperature, catalyst loading, solvent loading) leading to
maximum glycerol ethers concentration were investigated.
Kiatkittipong et al. [19] present several kinetic models for
glycerol etherification with TBA, with parameters obtained
by regressing measured data from an autoclave reactor.
Experiments were performed in a reactive distillation col-
umn, the results being compared with AspenPlus simulation
predictions. It should be remarked that the column worked
as a series of CSTRs (the trays) where the reactants were fed
in countercurrent. Therefore, the distillate stream contained
a mixture of water and TBA, while the bottom stream
contained TBA, glycerol, and mono-, di-, and triether. As
a result, separation of reactants and products from the
column-outlet streams was still necessary. In a recent paper
[20], the liquid phase etherification of glycerol with tert-
butyl alcohol was investigated in a continuous-flow reactor
using Amberlyst-15 as catalyst.
In a different reaction pathway, Al-Lal et al. [21]suggest
dehydration to epichlorohydrin followed be etherification
with TBA.
Although the feasibility of glycerol etherification with
TBA was proved by experimental results, no design, eco-
nomic evaluation, and controllability analysis of the entire
processhavebeenreported.Thegoalofthisworkistofill
this gap. The paper is organized as follows. Next section
presents the conceptual design of the plant, using a steady
state mass-balance model which includes a rigorous model
of the chemical reactor and ideal models for the separation
section. Following the degree of freedom analysis, plantwide
control structures are suggested. For each control structure,
the model is solved and the influence of operating parameters
on the reactants conversion is analyzed. Thus, a control
structure is selected, allowing processing of variable amounts
of glycerol and ensuring a unique, steady stable state. Then,
detailed design of the separation section is performed and
an economic evaluation of the process is accomplished. The
performance of the plantwide control (ability to process
impure glycerol and to change the production rate) is proved
by means of rigorous dynamic simulation performed in
AspenDynamics.
2. Conceptual Design and Plantwide Control
2.1. Reactor-Separation-Recycle Model. In this section, a
simplified model of the plant will be used to assess the
feasibility of the process and to perform a preliminary mass
balance of the plant. Based on this model, several plantwide
controlstructureswillbesuggestedandevaluated.Figure 1
presents the Reactor-Separation-Recycle structure of the
plant [22]. After the reaction takes place, the reactor effluent
enters the separation section. Here, the di-, triethers and
water are removed from the plant, while the monoether and
unconverted reactants (glycerol and TBA) are recycled to the
reactor, after being mixed with fresh reactants. The notations
used here will follow Figure 1.Fk,jwill denote the mole flow
rate of species kin stream j.SubscriptsG,TBA,ME,DE,TE,
and W will be used for glycerol, tert-butyl alcohol, mono-,

The Scientific World Journal 3
di-,triethers,andwater,respectively.Subscripts0,1,2,3and
4 will denote the feed, reactor-inlet, reactor-outlet, recycle,
and product streams, respectively. For example, FG,1 stands
for the flow rate of glycerol at reactor inlet.
The model of the plant assumes a plug-flow reactor
(PFR) operated at a fixed temperature (70◦C) and perfect
separation. The etherification reactions leading to mono-, di-
, and triethers were considered, while TBA dehydration was
neglected (this assumption will be relaxed when designing
the whole plant). It was assumed that TBA, glycerol, and
monoether are recovered from the reactor outlet stream and
recycled. The model consists of (3) describing the reactor
and from (4)to(9) which describe the separation and
recycle:
dFj
dm =vR,j,j=G, TBA, ME, DE, TE, W
at m=0Fj=Fj,1 ,m∈(0, mcat),
(3)
FG,0 +FG,2−FG,1 =0, (4)
FTBA,0 +F
TBA,2−FTBA,1 =0, (5)
FME,1 −FME,2 =0, (6)
FDE,1 =0, FDE,4 =FDE,2,(7)
FTE,1 =0, FTE,4 =FTE,2,(8)
FW,1 =0, FW,4 =FW,2,(9)
The reaction rates are calculated by (10)to(13), where νis
the matrix of stoichiometric coefficients. The reaction rate
constants follow Arrhenius temperature dependence with
parameters given in Tabl e 1 [19]:
vR,j=
k
νk,jrk,(10)
r1=k1xGxTBA −1
Keq,1
xMExW, (11)
r2=k2xMExTBA −1
Keq,2
xDExW, (12)
r3=k3xDExTBA −1
Keq,3
xTExW, (13)
r4=k4xTBA.(14)
2.2. Plantwide Control Structures. The design degrees of
freedom represent the variables that must be specified
to completely define the process. Their number can be
calculated by subtracting the number of equations from the
number of variables. 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 [23]. The model of the glycerol etherification
plant consists of 15 equations and contains 17 variables
Tab le 1: Equilibrium constants and rate constants [19].
Equilibrium constant Rate constant/(mol s−1kg−1)
Keq1 =exp(2.581 −754.8/T)k1=exp(17342 −6835/T)
Keq2 =exp(1.228 −942.1/T)k2=exp(26953 −10382/T)
Keq3 =exp(1.779 −2212/T)k3=exp(26953 −10382/T)
—k4=exp(23.358 −12480/T)
(6 reactor-inlet, 6 reactor-outlet, 2 fresh reactants, and 3
product flow rates). Therefore, 2 degrees of freedom must be
fulfilled. This is in agreement with Figure 1, where two valves
must be used for level control, leaving 2 valves available for
manipulating flow rates.
2.3. Steady State Behavior. Theaimofthissectionisto
investigate the steady state behavior of an etherification plant
when different plantwide control structures are applied. We
will assume that the nominal flow rate of fresh glycerol
is 2.15 kmol/h, which is the typical output of a 15,000
tones/year biodiesel plant.
It should be remarked that the main task of plantwide
control system is controlling the inventory of reactants,
products, and impurities. Controlling the inventory of
reactants within the plant can be performed in two ways
[24]: (a) by evaluating, directly or indirectly, the inventory
of each reactant and controlling it by feedback using the
corresponding fresh feed as manipulated variable; (b) by
fixing the fresh feed rate and using the self-regulation
property of the mass balance [25]. The latter assumes that
the entire amount of reactant brought into the process is
converted into products, which are subsequently separated
and removed from the plant. Consequently, three control
structures will be further considered. Control structure CS1
attempts controlling the inventory of reactants by the use of
feedback [24]. Thus, the flow rates of TBA (F1b =FTBA,1)and
glycerol + ethers (F1a =FG,1 +FME,1) at reactor-inlet are fixed.
The amount of reactants in the buffer vessels are used as
indirect indications of inventories. Therefore, accumulation
or depletion of reactants is avoided by adjusting the fresh
reactant feed rates.
Control structures CS2 and CS3 make use of the self-
regulating property of the mass balance [25]. In both control
structures the flow rate of fresh glycerol is set to the value
FG,0. Control structures CS2 and CS3 differ by the second
flow specification: TBA at reactor inlet (F1b =FTBA,1)and
ratio r1=F1b/F1a, respectively. It should be remarked that,
for all control structures, the amount of product obtained
equals the amount of glycerol fed in the process, F4a =FG,0.
2.3.1. Control Structure CS1: Glycerol and TBA Inventories
Controlled by Feedback. Figure 2 presents the principle of
control structure CS1 and results concerning the behavior
of the plant when this control structure is applied. The
reactor uses 400 kg of catalyst. The top diagram shows
the amount of glycerol that is processed (FG,0) versus the
glycerol-ethers reactor-inlet flow rate (F1a), at different values
of the reactor-inlet TBA flow rate (FTBA,1). It can be observed

4The Scientific World Journal
TBA
FC
LC
Glycerol
0
0
1b
1a
3b
3a
TBA recycle
Glycerol and
ethers recycle
FC
LC
To reactor
To reactor
FTBA, 1
F1a
(a)
0
1
2
3
4
0246810
20 15
mcat =400 kg
FTBA, 1/(kmol/h) =25
FG,0/(kmol/h)
F1a/(kmol/h)
(b)
0.2
0.4
0.6
0.8
1
0246810
20
15
FTBA, 1/(kmol/h) =15
XG
F1a/(kmol/h)
mcat =400 kg
(c)
0
0.1
0.2
0.3
0.4
0246810
20 15
mcat =400 kg
FTBA, 1/(kmol/h) =25
F1a/(kmol/h)
XTBA
(d)
Figure 2: Control structure CS1. Processed glycerol and reactants conversion versus reactor-inlet glycerol + ethers flow rate.
that the nominal capacity of 2.15 kmol/h could be increased
by changing the flow rate F1a or by modifying the TBA flow
at reactor inlet FTBA,1.
The lower diagrams show the dependence of the glycerol
and TBA conversions, XG=1−FG,2/FG,1,andXTBA,1 =
1−FTBA,2/FTBA,1 versus the flow F1a.ForeachF1a value,
a single steady state exists, which is an advantage of this
control structure. However, because the fresh glycerol is
used to control the buffer-vessel level, this control structure
cannot be applied when the flow rate of glycerol is set by the
upstream biodiesel plant.
2.3.2. Control Structures CS2-CS3: Self-Regulating Glycerol
Inventory. In control structures CS2 and CS3 the flowrate
of fresh glycerol FG,0 is set, which is a very convenient,
direct way to change the production rate. In addition, control
structure CS2 fixes the reactor-inlet TBA flow rate, while the
ratio TBA: glycerol + ME is fixed in CS3.
Figure 3 presents results obtained when CS2 is applied.
The top diagram shows glycerol conversion (XG) plotted
versus the flow rate of fresh glycerol (FG,0), for different
amounts of catalyst used in the reactor. The system exhibits
two steady states—at small FG,0, or no steady state at
all—at large FG,0. This behavior is a major disadvantage
of this control structure. It can be observed that an
amount of 200 kg of Amberlyst is sufficient to process
2.15 kmol/h of glycerol, but does not allow a large increase
of this value. However, 400 kg of catalyst ensures enough
flexibility.
The bottom diagrams present the conversion of the
glycerol and TBA versus the fresh glycerol flow rate, for
different values of reactor-inlet TBA flow rate and 400kg of
catalyst. The extent of the feasibility region increases with
the reactor-inlet TBA flow rate. It can be observed that TBA
conversion has (almost) the same value on both branches.
Moreover, TBA conversion is independent of the amount of
catalyst used:
XTBA ≈2FG,0
FTBA,1
.(15)
Figure 4 presents results obtained when the control struc-
ture CS3 is used. Glycerol conversion versus fresh glycerol
flow rate is plotted for different amounts of catalyst. Inde-
pendently on the catalyst mass and ratio between reactor-
inlet flow rates, a unique steady states exists. Compared
to CS1, different amounts of glycerol can be processed.
However, there is a maximum flow rate of glycerol that can
be processed, which increases with the catalyst amount. It can
be seen that 400 kg of catalyst allows doubling the production
rate. For 400 kg of catalyst, the lower diagrams show that the
glycerol and TBA conversions have small sensitivity to the
production rate or the ratio between reactor-inlet flowrates.

The Scientific World Journal 5
TBA
FC
LC
Glycerol
LC
FC
0
0
1b
1a
3b
3a
TBA recycle
Glycerol and ethers
recycle
To reactor
To reactor
FTBA,1
FG,0
(a)
0
0.2
0.4
0.6
0.8
1
012345
300 400
XG
FG,0/(kmol/h)
mcat/(kg) =200
FTBA, 1 =20 (kmol/h)
(b)
0
0.2
0.4
0.6
0.8
1
012345
20
25
XG
FG,0/(kmol/h)
mcat =400 kg
FTBA, 1/(kmol/h) =15
(c)
0
0.2
0.4
0.6
0.8
1
012345
20 25
FG,0/(kmol/h)
mcat =400 kg
FTBA, 1/(kmol/h) =15
XTBA
(d)
Figure 3: Control structure CS2. Reactants conversions versus fresh glycerol flow rate, for different values of catalyst mass and reactor-inlet
TBA flow rate.
In conclusion, control structure CS3 offers the advantage
of a unique steady state together with easily setting the fresh
glycerol flow rate.
2.4. Separation Section. Liquid-liquid and vapor-liquid equi-
libria were analyzed using AspenPlus. Glycerol and TBA are
present in AspenPlus database, from where their physical
properties were taken. After defining the molecular structure
of the ethers, their properties were estimated using group
contribution methods. The behavior of the liquid phase
was described by the NRTL activity model. The interac-
tion parameters were taken from Aspen Plus database or
were estimated using UNIFAC Dortmund modified method
[26].
Tab l e 2 presents the boiling points of the main compo-
nents and their azeotropes. Small amounts of i-butene that
are formed by TBA dehydration can be easily removed due
to lower boiling point. The separation of TBA and water
from glycerol-ethers mixtures appear to be easy and will be
handled by distillation (column C1).
Also, glycerol and monoether which are recycled can
be obtained as a bottom product of a distillation column
(column C2). Obtaining high purity DE product seems
difficult due to the low-boiling G-DE azeotrope. However,
the residue curve map (Figure 5) of the DE-ME-G mixture
shows only one distillation region where ME acts as a solvent
for glycerol, allowing therefore high-purity diether to be
obtained in one distillation unit.
TBA and water form a low-boiling homogeneous
azeotrope. This can be broken by using a suitable solvent, for
example, 1,4-butanediol.
Figure 6 shows the residue curve map of the TBA-Water-
1,4-butanediol mixture.
The water-TBA mixture is firstly separated to TBA and
azeotrope (column C3). The azeotrope enters in the lower
part of the extractive distillation column (EX), while the
solvent is fed at the top. The distillate contains water, while
the bottom stream consists of solvent and TBA, which is
further separated in column C4.
3. Plant Flowsheet
Figure 7 presents the flowsheet, while Figure 8 details the
azeotrope separation section. The control loops are also
depicted. A detailed stream report of each section is pre-
sented in Tables 3and 4. The etherification of glycerol with
TBA takes place in a plug flow reactor in the presence of
400 kg Amberlyst. The reaction temperature and pressure are
set to 70◦C and 5 bar, respectively, when the reaction mixture
is liquid. The reactor-outlet stream is routed to Column C1.
TBA and water are separated as top product, while a mixture
of glycerol and ethers leaves the column as bottom product.

6The Scientific World Journal
TBA
LC
Glycerol
LC
FC
0
0
1b
1a
3b
3a
TBA recycle
Glycerol and ethers
recycle
To reactor
To reactor
x
FC
FC
(a)
0
0.2
0.4
0.6
0.8
1
012345
300
400
XG
FG,0/(kmol/h)
mcat/(kg) =200
r1=4
(b)
0
0.2
0.4
0.6
0.8
1
012345
3
4
XG
FG,0/(kmol/h)
mcat/(kg) =400
r1=2
(c)
0
0.1
0.2
0.3
0.4
012345
3
4
FG,0/(kmol/h)
mcat/(kg) =400
r1=2
XTBA
(d)
Figure 4: Control structure CS3. Reactants conversions versus fresh glycerol flow rate, for different values of catalyst mass and ratio between
reactor-inlet flow rates.
The column is operated under vacuum (0.1 bar) to avoid
high temperature in the bottom of the column. Column
C2 separates the mixture of di- and triethers. The bottom
product, containing glycerol and monoether, is recycled. The
column is operated under vacuum (0.1 bar) to avoid product
degradation.
Column C3 separates the TBA/water azeotrope from
TBA which is mixed with fresh TBA and recycled. The
extractive distillation column (EX) is fed on bottom with
TBA/water azeotrope and on top with 1,4-butanediol, which
is the solvent. The solvent extracts TBA and is eliminated
on the bottom of the column, while the water is removed
as liquid on the top. The column has partial condenser in
order to eliminate isobutene traces. Column C4 recovers the
solvent. TBA is removed on the top of the column, is mixed
with TBA stream from column C1 and with fresh TBA and is
recycled.
An economic evaluation of the process was performed.
A payback period of 10 years was considered and the
total annual cost of the plant (TAC) was calculated as the
following:
TAC =capital cost
payback period +energycost.(16)
The capital cost, including the costs of reactor, distillation
columns, and extractive distillation column, was calcu-
lated using well-known relationships [27]. The energy cost
Tab le 2: Boiling point for pure components and azeotropes at P=
1bar.
Component/azeotrope T/(◦C) Destination
IB −6.25 Byproduct
TBA (0.6209)/W (0.3791) 79.97 —
TBA 82.42 Recycle
W 100 Byproduct
G (0.1951)/DE (0.8049) 233.5 —
DE 240.4 Product
ME 256.61 Recycle
G 287.85 Recycle
includes the costs of cooling water (0.08 US$/m3)and
electricity (8·10−6US$/kJ). Tab l e 5 summarizes the results.
4. Dynamics and Control
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.
For control structure CS3, a dynamic model of the
plant was built in AspenDynamics [28]. The controllers
were tuned by a simple version of the direct synthesis
method. According to this method, the desired closed-
loop response for a given input is specified. Then, with
the model of the process known, the required form and

The Scientific World Journal 7
(DE)
(G)
(ME)
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.05
Figure 5: Residue curve map of the glycerol-monoether-diether mixture.
TBA
Solvent
Water
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
C3
C4
EX
Figure 6: Residue curve map of the TBA-water-1,4-butanediol mixture.

8The Scientific World Journal
1
TBA1
GM1
2
3a
3b
TBA0
G0
W
Azeotrope
separation
C1
C2
PFR
x
r1
LC FC
FC
PC
FC
LC
PC
LC
XCTC
TC
TC
LC
LC
D
+
T
Figure 7: Flowsheet and control loops of the reaction section.
X
3a
S0
S
TBA1b
TBA1a
AZ
W
IB
PC
PC
LC
LC
TC
TC
TC
LC
PC
LC
TC
TC
TC
XC
XC
TC
LC
C3
EX
C4
TBA
+
S
Figure 8: Flowsheet and control loops of the azeotrope separation section.

The Scientific World Journal 9
Tab le 3: Stream results for the reaction section (Figure 7).
Stream name G0 TBA1 TBA0 GM1 1 2 3a 3b W D + T
Flow/(kmol/hr) 2.15 26.5 4.37 6.23 32.75 32.8 26.47 6.32 4.35 2.24
Flow/(kg/hr) 198 1883 324 759 2642 2642 1635 1006.6 80.8 445.6
Tem p / (◦C) 20 79.8 25 140.9 70 70 29.3 177 25 139.5
Pressure/(bar) 1 5 1 5 5 4.95 1.2 0.15 1 0.1
Flow/(kmol/hr)
G 2.15 Trace 0 2.94 2.94 0.8 Trace 0.81 0 0.01
TBA 0 24.9 4.37 Trace 24.9 20.6 20.6 0.002 0.04 0.003
ME 0 Trace 0 3.27 3.27 3.27 Trace 3.27 0 0.007
DE 0 Trace 0 0.01 0.01 2.14 Trace 2.14 0 2.13
TE 0 Trace 0 Trace Trace 0.002 Trace 0.002 0 0.0019
Water 0 1.5 0 Trace 1.5 5.81 5.81 0.005 4.31 0.005
S 0 0.1 0 0 0.1 0.1 Trace 0.1 Trace 0.1
IB 0 0 0 0 Trace 0.04 0.04 Trace 0 Trace
Tab le 4: Stream results for the azeotrope separation section (Figure 8).
Stream name 3a TBA1a AZ S0 W TBA + S IB TBA1b S
Flow/(kmol/hr) 26.46 11.7 14.7 90.6 4.35 100.9 0.04 10.38 90.5
Flow/(kg/hr) 1635 858.5 776.6 8164.5 80.8 8858 2.22 700.1 8158
Tem p . / (◦C) 29.3 97.8 76 30 25 156 25 80 231
Pressure/(bar) 1.2 1.8 1.0 1.2 1 1.5 1 1.0 1.13
Flow/(kmol/hr)
TBA 20.61 11.5 9.1 0 0.04 9.05 Trace 9.03 Trace
IB 0.04 Trace 0.04 0 0.003 Trace 0.039 Trace Trace
S 0 0.0 Trace 90.6 Trace 90.6 0 0.1 90.5
Water 5.8 0.2 5.57 0 4.31 1.2 0.001 1.2 Trace
Tab le 5: Economic evaluation.
Reactor Column C1 Column C2 Column C3 Column EX Column C4
Diameter (m) 0.35
Reflux ratio 0.32 1.83 4 1.5 2
Diameter (m) 0.85 0.55 0.7 0.5 0.55
No of trays 6 15 41 30 7
Height (m) 2 Reboiler duty (kW) 343 170 716.2 525 563.3
Condenser duty (kW) 348.7 168.6 654 170 324.4
Cost ($) 9296 Cost ($) 297 966 221 775 589 424 759 704 338 157
Energy Cost =291 663$/year
Equipment Cost =2 440 746$
TAC =535 738$/year (10 years payback)
the tuning of the feedback controller are back-calculated.
For all controllers, the acceptable control error, Δεmax ,
and the maximum available control action, Δumax,were
specified. Then the controller gain, expressed in engineering
units, was calculated as Kc=Δumax/Δεmax and translated
into percentage units. First-order open-loop models were
assumed in order to calculate the integral time of the pressure
and temperature control loops. As rough evaluations of the
process time constants τ, 12min and 20min were used,
respectively. It can be shown that the direct synthesis method
requires that the reset time of a PI controller is equal to the
time constant of the process, τi=τ. For the level controllers,
a large reset time τi=60 min was chosen as no tight control
is required.
Figure 9 presents results of dynamic simulation. Molar
and mass flow rates together with mass fractions are
shown. Starting from the steady state (fresh glycerol:
198 kg/h), two disturbances were introduced. At time of
2 h, a 10% wt. water impurity in the fresh glycerol was
introduced. Later (time =40 h), the flow rate of fresh
glycerol (90% wt. purity) was increased to 220 kg/h. It can
be seen that the nominal operating point is stable, and
the plant achieves stable operation when disturbances are
introduced.

10 The Scientific World Journal
0
200
400
600
800
1000
0 20406080100
500
1000
1500
2000
2500
F/(kg/h)
F/(kg/h)
FTBA
FGM1
FTBA0
t/(h)
FG0
(a)
50
200
350
500
0 20 40 60 80 100
0.95
0.96
0.97
0.98
0.99
1
Mass fraction
F/(kg/h)
FW
FD+T
XD+T
XD
Xw
t/(h)
(b)
0
5
10
15
20
0 20406080100
0
10
20
30
40
F/(kmol/h)
F/(kmol/h)
FG0
t/(h)
FAZ
FGM1
FTBA0
FTBA1
FW
FD+T
(c)
0
500
1000
1500
0 20406080100
0.95
0.96
0.97
0.98
0.99
1
Mass fraction
F/(kg/h)
t/(h)
FAZ
FTBA1b
XAZ
XTBA1b
(d)
Figure 9: Dynamic simulation results. Refer to Figures 7and 8for nomenclature of various streams. xTBA1b and xAZ are mass fractions of
TBA in streams TBA1b and AZ. xDis the mass fraction of diether in the product stream D + T.
5. Conclusions
Production of glycerol ethers by etherification of glycerol
with tert-butyl alcohol catalyzed by heterogeneous acid
catalysts, such as Amberlyst 15, is feasible. For a typical
glycerol flow rate of 2.15kmol/h, the reaction can be carried
on in a PFR using 400 kg of catalyst. The glycerol conversion
is high. However, recycle of the monoether byproduct is
necessary. The separation products-unconsumed reactants,
are difficult due to formation of the water-TBA azeotrope,
which can be broken using a suitable solvent. The TAC of the
plant is rather high, 536 000 USD/year. The recommended
control structure sets the fresh glycerol feed rate and the ratio
G + ME :TBA at reactor inlet.
Acknowledgments
The work has been funded by the Sectoral Operational Pro-
gramme 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 CNCSIS-UEFISCSU, Project IDEI 1545/2008-
“Advanced modeling and simulation of catalytic distillation
for biodiesel synthesis and glycerol transformation.”
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