Hydrocracking of vacuum gas oil is an important chemical process involving complex reaction mixtures. The reaction is carried out in a trickle-bed reactor, considering reaction kinetics along with such hydrodynamic effects as mass transfer, intraparticle diffusion, and partial wetting. Since reaction kinetics is critical to modeling and simulation of a hydrocracking reactor, a modeling approach needs to capture the complex chemistry of the process, along with the elegance of the solution method. The complex chemistry of hydrocarbon is represented by an elegant continuous lumping approach to modeling. The true boiling point of the mixture is used as the characterization parameter. Since the rate constant of hydrocracking is assumed to be a monotonic function of the true boiling point, it is possible to reformulate mass-balance equations in terms of rate constant as a continuous variable. A novel distribution function p(k, K), which determines the fractional yield distribution of species, was formulated based on data from the cracking patterns of various model compounds. Resulting integrodifferential equations are solved numerically to obtain yields of various fractions as a function of reactor residence time. Model predictions are compared with limited published data to show the utility of the model.
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