Seven different liquefaction mechanisms that consist of reversible and irreversible steps are suggested for a Turkish lignite (Tunçbilek) in tetralin with the use of microwave heating. Compliance of the proposed mechanisms are determined by forming first order linear Discrete-time models with the experimental data and reaction rate constants are determined with the program written in MATLAB with the use of the Kalman filter. The most appropriate suggested model is determined by looking at the sum of the experimental data and squared differences of the values calculated with the model. The magnitude of the reaction rate constants is examined for the models that best fit. The obtained results show that majority of the oil is formed directly from coal. Furthermore, whereas coal:oil reaction step has maximum reaction rate constant, coal:asphaltene and coal:preasphaltene reaction steps have minimum rate constant. Models containing parallel and reversible steps are seen to provide a better fit to the experimental data. The best fit was obtained with model that has both reversible (between asphaltene:coal, asphaltene:oil, and asphaltene:preasphaltene) and irreversible (coal:oil, coal:preasphaltene and preasphaltene:oil) reaction steps. The model also evidenced that the reversible reactions are critical on the liquefaction of Tunçbilek coal.
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