This paper introduces a general computational model for determining the velocity field in either reacting or non-reacting duct flows. The model is then applied to a catalytic cracking unit (FCC) of an oil refinery, to determine the velocity field inside the riser, where reactions take place to convert heavy petroleum fractions in lighter products, like middle distillates and light olefins, with high rates of conversion and productivity. The correct approach to simulate this process is to avoid the plug flow assumption and to solve the full fluid flow problem, based on the mass and momentum conservation equations in a complete formulation, which are shown in the literature to be computationally very expensive and time consuming, mainly in a three-dimensional (3-D) simulation. Since, the main objective of the simulation is the accurate determination of the concentration of the noble products, a very accurate velocity field is not mandatory. Therefore, bidimensional flow is assumed, and a modified set of unsteady mass and momentum conservation equations is proposed and the resulting 2-D differential equations are discretized in space using an upwind cell centered finite differences method, and the equations integrated in time with an implicit backward Euler scheme. The coarsest possible mesh is determined such that the solution relative error is within 5 % when compared to a steady state accurate finite element solution, which was obtained with a 2-D isoparametric, four-noded, linear element that was implemented to solve the complete Navier-Stokes equations for the finite element analysis program, FEAP . The objective of this work is to propose an alternative technique that gives a simplified treatment to the velocity field, to make possible the numerical calculation of the products concentrations in the riser and future application in optimization and real time control. Each cell, in this specific situation, can be understood as a perfect mixing reactor.