| Summary: | School of Chemical and Metallurgical Engineering, Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, South Africa, 2018 === Oil and Natural Gas are amongst the depletable resources of fossil energies. These characteristics have major implications in the supply demand equilibrium. For example, in a schematic way, the shortage (or the fear of shortage like during the oil crisis of 1973) automatically triggers a sudden price increase which decreases the demand according to the political economy of energy. The fear of shortage in the Sub-Saharan context is also an old issue in the African oil industry that always seeks to know what alternative solutions Africa has and how can the continent benefit from them. It is in this context that this work constitutes an extensive research that focused on biodiesel produced from ricinus communis oil. The goal of this research was the development of an advanced mathematical model of a ricinus communis oil based biodiesel production process, taking into account all phases, from planting ricinus communis trees, extracting oil, to biodiesel production. All these phases were thoroughly studied and models were developed based on mathematical principles. Firstly, a mathematical model based on the Pareto-Levy law was constructed in order to observe the sizes of plantations and the quantities of ricinus communis oil extracted. Secondly, another mathematical model was developed for the biodiesel production phase.
With regards to the first phase, the growth of ricinus communis plants was investigated: 65 ricinus communis trees were planted in the Limpopo province of South Africa. Plants grew and ricinus communis beans were manually harvested within a constant interval of 24 months. Observations of the growth of ricinus communis trees suggested that there was neither branch mortality nor amortisation. Results of the mathematical model developed for the first phase indicated that ricinus communis plants growth was not stochastic because its probability of ramification was as high as 0.95. Also, the probability of the ricinus communis branching process remained constant, at a value of 0.95. For each tree trunk, findings indicated that the probability of its process was reduced to 0.87 and its resulting probability ratio was equal to 0.84.
During the second phase, ricinus communis oil extraction through mechanical and chemical operations was performed. The extracted oil was a mixture of fatty ester acids where the main acid was ricinoleic. This acid imparted specific proprieties to ricinus communis oil, including the solubility into alcohol. It was also accompanied by oleic, linoleic and stearic acids.
vi
In addition, the problem of ricinus communis oil reserves was covered in a qualitative point of view and it justified the use of the Pareto-Levy distribution in order to model the quantities of ricinus communis oils stored for biofuels production. And the development of the mathematical model for oil extraction process and reserve storages was performed using the Doehlert experimental plan and response surface methodology (RSM). Thus, the reformulated Derrida’s Random Energy Model (REM) of ricinus communis oil reserve storages indicated that it was natural to represent those quantities by using the jumps of stable subordinators.
Furthermore, modelling of oil extraction based on ricinus communis plantations that had different sizes was designed. For this purpose, one important part of this study consisted on developing the best mathematical model that took into account the size inequality of the plantations. The main constraint for the development of this model was the low quantity of available data because they were whether inexistent, or expensive to obtain. Therefore, a model in which the estimation of parameters required a minimum input data was constructed. The model was constructed around mathematical observations and it was based on the description of ricinus communis plantations and oil. Also, in order to address the problem of inequalities observed on the size of plantations and on the quantities of ricinus communis oil, it was constructed based on the Pareto-Levy law. And, it also represented the ricinus communis oil production process, covered the indication of the ricinus communis plantations structures and indicated the types of biodiesel production performed.
In addition, while the stoichiometry of the reaction required 6 methanol moles for 1 ricinus communis oil mole (6:1 ratio) in order to obtain 6 esters moles of fatty acid and 1 glycerol mole, the performance was less compared to the performance obtained with the 24:1 ratio that was used and which corresponded to 66% of excess of methanol. Thus, under the model constructed, by increasing the methanol/ricinus communis oil molar ratio from 6:1 to 24:1, ester content was increased from 60.5% to 95.2%. This indicated that our model provided a fairly better performance than results observed in the literature. At the beginning of the experiment, both 3:1 and 4:1 molar ratios (33% of excess in methanol) were used. Further experiments were performed with 5:1 molar ratio (66% of excess in methanol) and so on until 24:1 and 25:1 molar ratios. From the excess of alcohol, a 90-95.2% conversion was achieved, which was good. It was also evident that a 3:1 ratio gave a lower performance and made intermediaries lower products such as diglycerides and triglycerides.
vii
During the third phase, biodiesel was produced from an alkaline transesterification reaction of ricinus communis seed oil. The transesterification reaction was performed on two different tests without changing the operational conditions (molar ratio and temperature of reaction) and experimental planning was operated to evaluate the impact of temperature in product yield and quality; 13 experiments were performed. During the first test, the duration of the reaction was set to 1 hour and during the second test, the duration of the reaction was set to 4 hours. The calculation of reaction performance of each test indicated that the 1-hour duration was not enough to convert the triglycerides into esters. Meanwhile, the 4-hour duration produced a conversion performance of 95.2%, which was aligned with the optimal performance found in the literature.The optimum performance, with a value of 84%, was obtained for the ethanol/vegetable oil molar ratio of 15:1, a KOH mass concentration of 0.5% and a temperature of 35℃. === XL2019
|
|---|
