2
PANKAJAKSHAN, PUDI, AND BISWAS
MAG finds applications in the manufacture of dyes,
softening agents, and plasticizers. Moreover, DAG and
TAG are excellent fuel additives, which on addition
to fuel reduces the viscosity of fuel and increases en-
gine efficiency and also these components improve the
antiknocking properties of gasoline when blended [3].
In the past two decades, various catalysts have been
developed and their performances were evaluated for
esterification of glycerol with acetic acid. Mineral acids
such as H2SO4, HCl, or H3PO4 were tried as homo-
geneous catalysts for esterification of glycerol [4–9].
However, the primary drawbacks associated with these
homogeneous catalysts were catalyst separation, prod-
uct purity, necessity of neutralization, and reactor cor-
rosion [5]. Therefore, several studies focused on the
development of various heterogeneous catalysts such
as zeolites [3,10], heteropolyacids [5,7], SBA-15 [8],
sulfated carbon nanotubes [11], zirconia [12], activated
carbon [5], and sulfated metal oxides [11,13,14] for the
esterification of glycerol with acetic acid. Recently,
Amberlyst and ion exchange resins have been shown
as effective catalysts in the presence of excess of glyc-
erol [2–4,10,15–17].
Despite the significance of the reaction, minimal
research attention has been devoted to the reaction ki-
netic study of glycerol acetylation reaction with acetic
acid [4,18–20]. Reaction kinetic modeling and estima-
tion of kinetic parameters are essential toward robust
catalyst design, scale-up, and optimization of chemical
process. Previous studies [4,20] reported acetylation of
glycerol with acetic acid as a combination of series–
parallel reaction pathways. Zhou et al. [4] studied the
reaction kinetics of acetylation of glycerol with acetic
acid by using Amberlyst-15 as catalysts. The first-order
consecutive series reaction scheme was proposed, and
the results obtained indicated that the apparent reac-
tion rate constants for all the reactions were influenced
by the initial mole ratio of acetic acid and glycerol.
Khayoon et al. [18] proposed that the reaction fol-
lowed consecutive series reaction pathway producing
MAG, DAG, and TAG with surface reaction as the
rate-limiting step. Patel and Singh [19] reported that
the esterification reaction followed first-order kinetics,
and the rates were not mass transfer limited in the pres-
ence of 1,2-tungstophosphoric acid anchored to differ-
ent supports. Most of the previous works [4,18,20]
reported the first-order rate equation for acetylation of
glycerol. Mufrodi et al. [20] suggested that, in the pres-
ence of sulfuric acid, triacetylglycerol synthesis was
an exothermic reaction, and hence higher temperatures
(>118°C) were not beneficial. In addition, they have
also found that the selectivity to triacetin decreased at
high temperature (>115°C) due to the evaporation of
acetic acid. The most popular mechanistic model re-
ported in the literature is the Langmuir–Hinshelwood–
Hougen–Watson (LHHW) model [4,18,19,21]. The
LHHW model is identified as the most reliable model,
which describe the catalytic reaction with high accu-
racy and produce the rate equations consistent with
the kinetic data within the experimental error. How-
ever, in all the previous studies, the LHHW model is
oversimplified by neglecting the resistance offered by
the adsorption and desorption steps during the reaction
and the simplified LHHW model reduced to the simple
Power law model. Therefore, the development of the
kinetic model by following the more realistic LHHW
approach is important for fundamental understanding
of the reaction kinetics of the glycerol acetylation re-
action.
Mathematical modeling of chemical reaction kinet-
ics and estimation of kinetic parameters often end up in
the problem of nonlinear parameter estimation. Appli-
cation of efficient optimization techniques is a key fac-
tor in obtaining physically significant kinetic param-
eters, which are estimated by minimizing the sum of
squared deviation between experimental and simulated
concentrations of reacting species. Improper choice of
initial guess for model parameters results in nonopti-
mal solutions in turn giving unrealistic values for the
model parameters. In this context, genetic algorithm
(GA) provides a lot of robustness and the applica-
tion of GA in problems of chemical kinetics is very
promising [22–28]. The traditional algorithms that are
based on the evaluation of derivatives fail in case of
discontinuous functions or if derivatives do not exist.
Other methods such as enumerative techniques—both
random search and grid search methods become com-
putationally expensive for problems involving a large
number of variables in the objective function. Unlike
most of the conventional optimization techniques, GA
does not require the evaluation of derivatives nor does
it need any other auxiliary information such as ini-
tial guess [22]. Therefore, GA is an ideal optimization
technique for parameter estimation in cases where large
uncertainty exists in model parameters and difficult to
make an initial guess. GA evaluates the objective func-
tion at different points in a population simultaneously
and selects the best solutions during each iteration.
The population with best solutions evolves to reach the
global optimum point.
In this study, a reaction pathway for the acetylation
of glycerol with a sulfated alumina catalyst is pro-
posed based on the experimental observations. The ki-
netic parameters were estimated based on the LHHW
model with proper validation for assumptions. Non-
linear parameter estimation was performed using the
GA optimization technique at the optimized reaction
conditions presented in our previous work [29].
International Journal of Chemical Kinetics DOI 10.1002/kin.21144