We attempt the optimum design of the ultra-deep hydrodesulfurization required in the future or for the hydrogenation of aromatics in diesel oil, as the conventional reaction model based on n-th order of desulfurization is no more accurate enough. A further buildup of reaction simulator for reactor design was attempted. Distribution Function Model is developed in the present study. In this model, the distribution of rate constants is expressed with a Gamma function. It is clear that the predictions agreed well with the observed data, down to the ultra-deep desulfurization range. This model could also be applied for various kinds of oil fractions and wide desulfurization reaction conditions. The reactor sizes were estimated, compared with both the distribution function and n-th order reaction models, in order to obtain diesel oil of sulfur level required by European Auto-Oil II Program. The reactor size calculated by the Distribution Function Reaction Model is estimated as bring smaller than that estimated by the conventional 1.7th order. It means that a more competitive design of the process will be provided by the new model and will allow more practical feasibility study and the plant design for ultra-deep desulfurization process. (C) 2000 Elsevier Science Ltd. All rights reserved.