This paper presents a mathematical model developed for the operating simulation of a trickle-bed reactor. Furthermore, the model has been fixed to emulate the operation of the three reactors used at the gas oil hydrotreatment reactors available at Amuay refinery (PDVSA). The differential mass balances of the chemical species present in the process system are defined based on the mass conservation equation at the gas and the liquid phase. Moreover, mass transfer resistance on the inner catalyst particle is evaluated in terms of the catalyst effectiveness factor. Also, mass transfer coefficients, gas solubilities and transport properties of the chemical species available in the gas and liquid phase are evaluated with the help of mathematical correlations obtained from gas oil desulfurization experiments adjusted at the operating conditions available in the Amuay refinery gas oil hydrotreatment units. In addition, the model includes mathematical expressions for the rate of reaction (HDS and HDN) described with the help of kinetic equations of the Langmuir-Hinshelwood type. Furthermore, the kinetic parameters involved in the chemical reactions considered in the reactor model were estimated using a multidimensional simplex algorithm under the commercial reactor process conditions.