In the new hydrodesulfurization (HDS) process by integrating the reaction and separation units in a single reactive column, the fixed cost and operational costs can be reduced, as well as more flexible operating conditions will be achievable. For investigating both the design and the operating aspects of reactive columns, computer simulation is needed. This study was performed using the RIPI (Research Institute of Petroleum Industry) method in different conditions such as various operating temperatures and pressures. For verifying the presented solving method, the results of simulating a typical n-butane absorber column by RIPI method were compared to the achieved results from the well-known inside-out method. The results show the capability of the RIPI method in converging the computations. Moreover, by substituting the power law model by the Langmuir-Hinshelwood kinetic model in computations, the effect of pressure variations on the HDS reactive column was investigated.