(645d) A Generalized Kinetic Model for Transesterification and Saponification

Owing to the depletion of fossil fuel resources and increasing environmental concerns, the search for alternative fuels such as biodiesel has gained enormous impetus in the past two decades. Plant and vegetable oils are so far the most prominent feedstocks for these alternative fuels. Rudolf Diesel was the first to test peanut oil as an alternative fuel for his engine about a century ago (Shay, 1993). During 1930s and 1940s, vegetable oils were used as alternative fuels in case of emergency (Singh and Singh, 2010). However, vegetable oils cannot directly substitute diesel due to their high viscosity, low volatility, and poor cold flow properties. Hence, they are processed to obtain biodiesels with properties similar to those of the petroleum-based diesel. This has attracted much attention in recent years (Verma and Sharma, 2016). Biodiesel is a non-toxic, renewable, and biodegradable fuel composed mainly of fatty acid esters. It is industrially produced via transesterification of vegetable oils with alcohol in the presence of a catalyst.

Though biodiesel holds promise as an alternative fuel, its production offers a significant challenge to researchers due to higher production costs compared to the production of petroleum based diesel. Hence, it becomes crucial to model and optimize the biodiesel production process with the aim to achieve lower costs along with meeting the standard property specifications. There are numerous research articles and literature review in modeling, simulation and optimization of biodiesel production process (Aransiola et al., 2014). However, in all of the studies, modeling the reaction kinetics is the foremost important step. The studies regarding kinetics of biodiesel production can be divided into two categories. In the first category (Vicente et al., 2006; Eze et al., 2014), the kinetic models are oversimplified and strongly dependent on the parent oil used for that study. Hence, there are a lot of inconsistencies in the reported values of the kinetic parameters. In the second category (Likozar and Levec, 2014a,b), the effect of the saponification reactions is not accounted for in the model which restricts their application to the case of water-free chemicals only. Therefore, in this article, we address these issues by proposing a kinetic parameter ranking and estimation framework that has the following key components,

1. A generalized kinetic model that considers both both transesterification and saponification reactions.
2. The model is suitable for any biodiesel feed containing the glycerides formed using the five most common fatty acids viz., Oleic (O), Linoleic (L), Linolenic (Ln), Palmitic (P) and Stearic (S).
3. A detailed sensitivity analysis of all model parameters.
4. Application of a Bayesian approach to estimate the most important six parameters.

The purpose of this work is to develop a generalized kinetic model for both transesterification and saponification reactions. It consists of a differential mass balance for the process of transesterification and saponification of each glyceride and ester formed by the major fatty acids present in oil. Eq. (1) shows the general form of differential equations in the model.

dC_x/dt = f_x(C,Θ) (1)

where x represents the different species such as glycerides, esters, methanol, glycerol, soaps, and free fatty acids; C_x represents the concentration of species x; and Θ represents the set of kinetic rate constants. Here, heterogeneity in the reaction system is neglected and the model is assumed to be in pseudo-homogeneous phase. This is a sound assumption for the industrial-scale process as they employ high mixing intensity. Our model consists of 71 species and 257 reactions. User-defined operational inputs for the model are temperature of the reactor, molar ratio of alcohol to oil, catalyst concentration (wt.% based on oil), and the composition of oil. The model response/output is the yield of fatty acid methyl ester (biodiesel) at different time points. The model parameters include the pre-exponential (Arrhenius) factors and the activation energies with respect to all the reactions. This sums up to 2 x 257 = 514 parameters. However, it is not practically feasible to estimate all the parameters of a reaction mechanism simultaneously. Thus, we employ finite difference approach based sensitivity analysis to identify the most significant parameters for estimation. Typically, the number of parameters estimated is limited by the available experimental observations. Here, we estimate the 6 most sensitive parameters using Bayesian approach of parameter estimation and 32 experimental observations. As the direct application of the Bayesian method is challenging over wide ranges in parameter space, it is prudent to employ a preliminary step of optimization to narrow down the ranges using sum of squared errors as an objective function. This is performed in 2 stages viz. a quasi-random global search as the first stage followed by an optimization using the Hooke-Jeeves algorithm. We then employ a Bayesian approach described in (Mosbach et al., 2012; Beers, 2006) over the optimized parameter ranges to study the effects of uncertainties in parameters on the model response. Due to the large number of evaluations of the model required for sampling from the distributions, we employed a surrogate model instead of directly evaluating the original model. The surrogate model was developed using the High Dimensional Model Representation (HDMR) technique.

Resulting distributions showed that we obtain a single optimal value obtained for each of the parameters respectively. We validate our model by conducting parametric studies over varied ranges of temperature, molar ratio of oil to alcohol and catalyst concentration. Our analysis indicates that the model could predict the cetane number and higher heating value of biodiesel formed using various parent oils with an average accuracy of around 3%. Finally, we performed mechanism reduction in order to find the minimum set of reactions that can represent the kinetics of 4 major oils viz., Cottonseed oil, Palm oil, Rapeseed oil and Soybean oil without significant loss of accuracy. We observe that the deviation in the dynamic concentration profiles increased from less than 1% to around 10% as we vary the size of the mechanism from 211 reactions to 175 reactions.

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