Non-isothermal modeling of glycerol oxidation reaction and estimation of thermodynamic parameters

Article abstract of DOI:10.1134/S1070363214110310

The paper presents determination of adiabatic temperature rise during the oxidation of glycerol to glyceraldehyde with hydrogen peroxide in order for estimating its potential hazardous behavior. Estimation of enthalpy of the reaction was carried out by using thermodynamic tables and the bond energy method. The Non-isothermal reaction system for glycerol oxidation was described on the basis of a dynamic modeling proposal, considering the energy balance in the reactor to describe the final stage in the process of glycerol oxidation. The objectives of the present study were determination of the physic-mathematical model for glycerol oxidation, performance of the linearization of the proposed model and determination of transfer function for control purposes.

Full text of DOI:10.1134/S1070363214110310

ISSN 1070-3632, Russian Journal of General Chemistry, 2014, Vol. 84, No. 11, pp. 2228–2233. © Pleiades Publishing, Ltd., 2014.
Non-Isothermal Modeling of Glycerol Oxidation Reaction
and Estimation of Thermodynamic Parameters1
J. C. Beltrán-Prietoa, K. Kolomazníka, and R. Slavíkb
a Department of Automation and Control Engineering, Faculty of Applied Informatics,
Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01 Zlín, Czech Republic
e-mail: prieto@fai.utb.cz
b Department of Environmental Engineering Protection, Faculty of Technology,
Tomas Bata University in Zlín, nám. T. G. Masaryka 275, 762 72 Zlín, Czech Republic
Received October 2, 2014
Abstract—The paper presents determination of adiabatic temperature rise during the oxidation of glycerol to
glyceraldehyde with hydrogen peroxide in order for estimating its potential hazardous behavior. Estimation of
enthalpy of the reaction was carried out by using thermodynamic tables and the bond energy method. The Non-
isothermal reaction system for glycerol oxidation was described on the basis of a dynamic modeling proposal,
considering the energy balance in the reactor to describe the final stage in the process of glycerol oxidation.
The objectives of the present study were determination of the physic-mathematical model for glycerol
oxidation, performance of the linearization of the proposed model and determination of transfer function for
control purposes.
Keywords: bond energy, enthalpy of reaction, adiabatic temperature rise, non-isothermal reactor
DOI: 10.1134/S1070363214110310
INTRODUCTION
whether the considered system is a lumped parameter
model. This means that the state values are functions
of time and thus the process is described by a system
of total differential equations and a distributed
parameter model in which the state values are not only
functions of time, but also position. In the latter case
the thermodynamic system is described by a system of
partial differential equations [3]. Taking into account
the practical aspect, it is necessary to determine the
inputs, outputs and state values.
Optimization of glycerol utilization is of con-
siderable importance for efficient processing of surplus
glycerol generated by the biodiesel industry. Glycerol
oxidation is one of the alternatives of glycerol
processing because it leads to the diversity of fine
chemicals [1]. Given the considerable quantities of
glycerol produced in biodiesel manufacturing techno-
logies, formation of contaminating by-products can be
avoided by the use of electrodes (Pt, Au) or oxidation
agents (N2O, O2, H2O2).
Such approach is important for designing a simple
and effective control scheme of the process and
maximizing the output.
The efficient glycerol oxidation reaction can be
performed only on the basis of deep knowledge of the
process thermodynamic and kinetic parameters as well
as heat release and transfer at laboratory and industrial
level [2]. In the case of partial oxidation of glycerol it
is necessary to carry out a chemical-engineering
analysis for the particular reaction, formulate a
quantitative reaction kinetics model based on the
estimation of the reaction mechanism and determine
This paper is devoted to analysis of oxidation of
glycerol to glyceraldehyde by H2O2 and calculation of
the adiabatic temperature rise and enthalpy of the reac-
tion by two different methods in order to determine its
potential hazardous behavior. Modeling of the dynamic
system of glycerol oxidation under non-isothermal
conditions was performed on the basis of energy balance
in the reactor. The physico-mathematical model that
describes the oxidation of glycerol and determination
of transfer function for control purposes was reached.
1 The text was submitted by the authors in English.
2228

NON-ISOTHERMAL MODELING OF GLYCEROL OXIDATION REACTION
Table 1. Bond enthalpies for glycerol, H2O2, glyceraldehyde and H2O [8–11]
2229
Number
of bonds
Bond enthalpy
per bond, kJ/mol
Sum of bond enthalpies,
kJ/mol
Net change,
Compound
Glycerol
Bond
kJ/mol
C–H
C–O
O–H
C–C
H–O
O–O
C–H
C–O
O–H
C–C
C=O
H–O
5
3
3
2
2
1
4
2
2
2
1
2
414
351
460
347
460
142
414
351
460
347
740
460
2070
1053
1380
694
5197
H2O2
920
1062
4712
142
Glyceraldehyde
1656
702
920
694
740
H2O
920
920
Thermodynamics parameters calculation. Estima-
tion of enthalpy of the reaction by thermodynamic
tables using Eq. (38) (see Experimental) is presented in
Eq. (1).
The estimation of the adiabatic temperature rise in
the course of glycerol oxidation reaction demonstrates
the highly exothermic behavior and as a result, the risk
aspect and danger of explosion. For this reason,
estimation of the above value, mass and energy
balance along with economic evaluation are essential
in the design of a pilot plant.
ΔHr, kJ/mol = [–598.312– 2(285.83)]
– (–668.43 – 187.8) = –313.742.
(1)
Similarly, combining the bond energy method with
the values obtained from Tables 1 and 2, enthalpy
change of the reaction is estimated:
Non-isothermal modeling of glycerol oxidation.
For approaching the solution of Eq. (42) of the
Experimental, there is assumed no variation of density,
(ρ1 = ρ2 = ρ). The solution is reached with Eq. (5) to
Eq. (17) for variation of reaction temperature over
oxidation time.
ΔHr, kJ/mol = {[(91.7 + 5197) + (51.6 + 1062)]
– [(88.11 + 4712) + 2(41 + 1840)]} = –319.81. (2)
It is evident that the values for ΔHr obtained using
thermodynamic tables and bond energy method are
related accordingly. Considering that specific heat
capacity values for glyceraldehyde and glycerol are
similar (0.219 kJ mol–1 K–1) [4] and that of H2O is
equal to 0.0752 kJ mol–1 K–1 [5], the value of Cp can be
deduced from the Eq. (37) of the Experimental:
.
aG(ΔH)0r G
V
dT
(5)
(T1 − T),
+
=
V
dt
ρCpV
.
0
aG(ΔH)r G + ρCpV(T1 − T)
dT
dt
,
(6)
(7)
(8)
Cp reacrion blend, kJ mol–1 K–1
=
ρCpV
= 1/3(0.219) + 2/3(0.0752) = 0.123.
(3)
Therefore, in order to calculate the adiabatic
temperature difference, the corresponding calculated
ρCpVdt
⌠
⌡
⌠
=
dt,
.
values of ΔHr and Cp reacrion blend, nr = 3 and (ΔH)vap
=
0
aG(ΔH)r G + ρCpV(T1 − T)
H2O
⌡
40.72 kJ/mol are substituted in Eq. (36) according to
Eq. (4):
dt
⌠
319.81 − 2(40.72)
t,
=
ρCpVdt
.
(4)
0
= 645.99.
ΔT, K =
aG(ΔH)r G + ρCpV(T1 − T)
3(0.123)
⌡
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 84 No. 11 2014

2230
BELTRÁN-PRIETO et al.
Table 2. Enthalpy change due to the vaporization stage for
glycerol, H2O2, glyceraldehyde, and H2O [12]
.
ρCpV(T1 − T)
V
0
−
.
ln | aG(ΔH)r G| + ln 1 +
V
0
Compound
Glycerol
H2O2
∆Hvap, kJ/mol
91.70
aG(ΔH)r G
V
0
+
.
(13)
(14)
ln | aG(ΔH)r G| = t,
51.60
V
.
Glyceraldehyde
H2O
88.11
ρCpV(T1 − T)
V
41.00
−
.
ln
1 +
= t,
V
0
aG(ΔH)r G
.
1
0
.
.
a (ΔH) G + ρC V(T − T)| + C = t,
ln |
(9)
G
r
p
1
−ρCpV
−V
ρCpV(T1 − T)
tV
ρCpV
−
=
ln
(15)
(16)
1 +
1 +
,
V
0
.
aG(ΔH)r G
1
0
(10)
a (ΔH) G + ρC V(T − T)| + C = t.
ln |
G
r
p
1
.
tV
.
V
ρCpV(T1 − T)
e−
=
,
For calculation of constant C, it is considered that
at zero time the input and output temperatures of
cooling water are equal (t = 0, T = T1).
V
0
aG(ΔH)r G
and solving for T:
.
.
tV
1
0
a (ΔH) G + ρC V(T − T)| + C = 0,
ln |
G
r
p
1
0
.
ρCpV
−V
−
e
aG(ΔH)r G
V
(17)
V
+ T1.
T =
1 −
V
0
ln | aG(ΔH)r G|.
.
C =
(11)
V
The profile of temperature as function of time in
Substituting the value of constant C in Eq. (10)
leads to:
glycerol oxidation to glyceraldehyde is represented by
the above Eq. (17) and Fig. 1. The influence of aG,
time, and G on temperature is presented accordingly in
Figs. 2 and 3. This system, as a real one, fulfils the
strong physical condition of the feasibility (the outputs
.
1
0
−V
.
a (ΔH) G + ρC V(T − T)|
G r p 1
ln |
+
V
V
0
are functions only of the state variables). Considering
.
ln | aG(ΔH)r G| = t,
(12)
.
V
the input variables as T1, G, V, and aG, and the output
variable as T, the system becomes:
·
ΔX·1x1 = A1x1 ΔX1x1 + B1x4 ΔU4x1,
ΔY = ΔX,
(18)
where A is the state matrix of dimension 1×1 and B is
the control matrix of dimension 1×4. The elements of
both matrices A and B correspond to the systems
presented in Eqs. (19) and (20) respectively and are
expressed in Eq. (21):
.
∂f 0
∂T
V0
V
(19)
= a11,
=
.
∂f 0
∂T1
∂f 0
∂G
V0
aG0(ΔH)0r G
=
= b12;
= b11;
=
V
ρCpV
Time, s
(ΔH)0r G0
T10− T0
∂f 0
Fig. 1. Profile of temperature as function of time for
glycerol oxidation to glyceraldehyde.
(20)
= b14,
. =
= b13;
∂V
ρCpV
V
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 84 No. 11 2014

NON-ISOTHERMAL MODELING OF GLYCEROL OXIDATION REACTION
Temperature, °C
2231
Temperature, °C
1 × 10–4
1 × 10–4
aG
aG
Fig. 3. Profile of reaction temperature as function of aG and
mass flow input of glycerol for glycerol oxidation to gly-
ceraldehyde.
Fig. 2. Determination of reaction temperature during the
oxidation reaction of glycerol to glyceraldehyde at different
values of mass flow input of dilute glycerol.
aG0(ΔH)0r
.
.
V0
(ΔG*G0)
*
−(ΔT*) + (ΔT1 ) +
ΔT* =
.
0
ΔΤ
−
ΔT =
T0V0ρCp
V
(ΔH)r0G0
.
.
ΔΤ1
(T10 − T0)
(ΔaG aG0).
(25)
*
+
T10− T0
(ΔH)0r G0
ρCpV
ΔV
+
.
aG0(ΔH)0r
ρCpV
T0
ΔG
V0
T0V0ρCp
.
(21)
.
ΔV
+
V
V
ΔaG
This can be also expressed in matrix form as in
Eq. (26).
The multiplication step leads to expression (22).
.
ΔT* = −[ΔT*]
.
.
aG0(ΔH)0r
ρCpV
V0
∗
V0
dΔT
aG0(ΔH)0r G0
T0V0ρCp
(ΔH)0r G0aG0
ΔΤ +
ΔΤ1 +
T01 − T0
T0
ΔΤ1
ΔG
−
=
ΔG∗
V
V
+ 1
.
dt
.
T0V0ρCp
.
.
ΔV∗
ΔaG
T10 − T0
(ΔH)0r G0
.
∗
(22)
(26)
+
ΔV +
ΔaG .
ρCpV
V
With elements A and B:
A* = [−1],
For control purpose it is necessary to introduce the
following dimensionless dependences, represented
with “*”:
aG0(ΔH)0r G0
T0V0ρCp
(ΔH)0r G0aG0
T0V0ρCp
T01 − T0
T0
B* =
ΔG
ΔT1
1
ΔT
T0
.
ΔT1
=
ΔG* =
*
.
(27)
ΔT* =
;
.
;
.
;
G0
T0
.
ΔaG
(23)
ΔV
*
ΔV* =
.
0
; ΔaG
=
.
V0
aG
In order to determine the transfer function to
represent the dynamic system, it is required to obtain
the Laplace Transform of expression (18) as presented
in Eq. (28) to Eq. (32):
Implementation of the above dimensionless
relations in Eq. (22), followed by the multiplication of
both sides of the equation by V/(T0V0) gives:
d(ΔT*T0)
V0
V0
sΔXL = AΔXL +BΔUL,
(s – A)ΔXL = BΔUL,
ΔXL = ΔYL,
(28)
(29)
(30)
(31)
(32)
(ΔT1 T0)
*
(ΔT*T0) +
−
=
dt
V
V
(T10 − T0)
aG0(ΔH)0r
.
.
(ΔG*G0) +
(ΔH)r0G0
ρCpV
0
ΔV
V
+
V
ρCpV
(s – A)ΔYL = BΔUL,
(ΔYL)/( ΔUL) = (s – A)–1B.
0
ΔaG*aG
,
(24)
+
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 84 No. 11 2014

2232
BELTRÁN-PRIETO et al.
The term (ΔYL)/(ΔUL), represents the relationship
EXPERIMENTAL
between the output and the input of the process. It is
also known as the Transfer function. The substitution
of Eq. (27) into Eq. (32) leads to expressions (33) and (34):
Estimation of thermodynamics parameters. In
order to analyze variation of adiabatic temperature in
the course of glycerol oxidation a reaction model using
H2O2 is presented and discussed.
ΔYL
= G(s) = [s + 1]−1
ΔUL
C3H8O2 + H2O2 → C3H6O3 + 2H2O.
(35)
aG0(ΔH)0r G0
T0V0ρCp
(ΔH)0r G0aG0
T0V0ρCp
Calculation of adiabatic temperature difference of
the reaction (35) is performed using Eq. (36):
T01 − T0
T0
1
×
,
(33)
.
.
−(ΔH)r −2(ΔH)vap
H2O
G(s)
.
ΔΤ =
nrCp reaction blend
(36)
aG0(ΔH)0r G0
(ΔH)0r G0aG0
T01 − T0
T0(s + 1)
1
.
=
.
.
T0V0ρCp(s + 1)
The term nr corresponds to the number of mols in
the reaction blend, Cp represents the specific heat of
the reaction blend and can be calculated using Eq. (37).
The numerator represents enthalpy of the reaction and
enthalpy of vaporization of water (40.74 kJ/mol).
(s + 1)
T0V0ρCp(s + 1)
(34)
Estimation of adiabatic temperature rise during the
highly exothermic reactions is the most common
method for determination of hazardous behavior.
According to the value obtained from Eq. (2), ΔHr =
–319.81 kJ/mol the partial oxidation of glycerol is
highly exothermic reaction. In exothermic reactions
the energy evolved may appear in many forms, but for
practical purposes it is usually obtained in the form of
heat. In view of several legal and economic
implications of disastrous explosion and catastrophic
effects it is essential to cool the reaction down to
eliminate runaway conditions. So, intensive research
has been performed for avoiding the danger of
explosion by reducing the heat caused by the reaction
[6]. If the heat released by the reaction is not removed
fast enough, a severe non-uniform temperature
distribution can occur within the reactor, which in turn
can lead to different rates of reaction. The effect of
heat and mass transfer becomes more important for
faster reaction rates, when these become rate
controlling in heterogeneous reactions. Temperature
distribution can be controlled by varying the tube
diameter, residence time and cooling rate.
Cp reaction blend = (1/3)Cp glyceraldehyde + (2/3)Cp(H2O). (37)
In order to evaluate the enthalpy change of the
reaction ∆Hr, two different methods are discussed. The
first one involves the use of values obtained from
thermodynamic tables and the second method applies
the bond energy. Based on thermodynamic tables [7],
values of the energy of formation ∆Hf of glycerol
(–668.43 kJ/mol), glyceraldehyde (598.312 kJ/mol),
H2O2 (–187.8 kJ/mol), and H2O (–285.83 kJ/mol) were
applied in Eq. (38) to calculate enthalpy of the
reaction. In this equation n and m stand for the number
of reactants and products respectively.
m
n
298 K
f products
298 K
.
f reactants
(ΔH)r =
Σ
(ΔH)
−
Σ
(ΔH)
i=1
i=1
(38)
(39)
The second procedure involved the Eq. (39).
m
n
(ΔH)r =
Σ
(ΔH)bonds broken
−
Σ
(ΔH)bonds formed.
i=1
i=1
The bond enthalpies are presented in Table 1.
Estimation of the transfer function is particularly
important in the control of a chemical reactor
calculated specifically for a non-isothermic reaction
system. Such system implies higher oxidation and rate
of conversion of glycerol. Another important indicator
of the technology is the adiabatic temperature
difference in the reaction mixture and it is necessary to
know also the standard enthalpy of the reaction. The
values are estimated from published thermodynamic
tables and the bond energy using bond enthalpies,
achieving very good agreement between the calculated
values of heat of the reaction for both procedures.
Table 2 exhibits the values of enthalpy change in
vaporization stage ∆Hvap (kJ/mol).
Non-isothermal modeling of glycerol oxidation.
A linear mathematical model including input, output
and inner-state variables for oxidation of glycerol is
proposed to describe the final stage in the process. In
this model the heat transfer between the coolant and
the reactor can be determined using the enthalpy
values of the oxidation reaction, the mass flow input of
glycerol, the volume flow rate, the mass fraction of
pure glycerol in the mass flow, and the input
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 84 No. 11 2014

NON-ISOTHERMAL MODELING OF GLYCEROL OXIDATION REACTION
CONCLUSIONS
2233
u1 = T1
.
.
.
In the present research the adiabatic temperature
change in the course of oxidation of glycerol is
studied. The reaction is exothermic which makes the
control of temperature to be essential to guarantee
safety of the process, particularly at the industrial
scale. For this purpose, a mathematical model is
proposed. The transfer function describes the system
and represents the relation between the input
parameters and the response (variation of temperature)
during the exothermic reaction.
u2 = G
.
X1 = T = f1}ΔX
ΔU
X1 = T = y1}ΔY
u3 = V
u4 = aG
Fig. 4. Scheme of the system presenting the input, state
variables and output.
Glycerol
Fluid for cooling
.
Cp, T1, V, ρ
ACKNOWLEDGMENTS
The project was financially supported by the
European Regional Development Fund under the
Project CEBIA-Tech no. CZ.1.05/2.1.00/03.0089 and
Tomas Bata University Internal Grant (IGA/
FAI/2014/011). J.C.B-P. author also thanks the
doctoral scholarship provided by the National Council
of Science and Technology (CONACYT) in Mexico.
Glyceraldehyde
Fluid for cooling
.
Cp, T1, V, ρ
Fig. 5. Scheme of the chemical reactor for oxidation of
glycerol considering glyceraldehyde as the main product.
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·
X = dX/dt.
(41)
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·
·
GΔHr0aG + ρ1VT1Cp = Vρ2CpT + ρ2CpV(dT/dt), (42)
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fraction of pure glycerol in the mass flow, ρ is density
·
(kg/m3), V the volume flow rate (m3/s), T1 and T the
input and output temperatures of the cooling water (°C)
respectively, Cp is the specific heat (J deg–1 kg–1), V is
the volume of reactor (m3), and t is time (s). Solution
of the above equation leads to estimation of the
temperature profile, which can be applied also to
evaluation of the influence that any input parameter
has on temperature response at different intervals of time.
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 84 No. 11 2014