In this research, Fischer Tropsch synthesis (FTS) has been modeled in the fixed bed chromatographic reactor for the first time by applying a rather complex dispersed plug flow model for fluid phase and linear driving force (LDF) model for adsorbent. Model equations are dynamic, multi-component, non-linear and heterogeneous including reaction and adsorption simultaneously Complex kinetics for FTS and water-gas shift (WGS) reaction and the multicomponent Langmuir adsorption isotherm is used in the model. A set of partial differential and ordinary differential equations with algebraic equations have been converted into a set of ordinary differential equations by using the orthogonal collocation technique. Then this set of equations has been solved by multi-step methods of Numerical Differentiation Formulae (NDF) or Backward Dif-ferentiation Formulae (BDF) Known as the Gear’s method. Consequently, results for dynamic model and effects of modeling parameters have been analyzed. Through this fixed bed chromatographic reactor model, one may develop a suitable configuration of simulated moving bed chromatographic reactors.