a single sphere along with appropriate boundary conditions on the sphere and also mass transfer equation inside the particle is simulated simultaneously with commercial software Fluent 6.3.26. A user defined function (UDF) is used to determine the particle wall boundary conditions on the catalyst. Hence the normal velocity component on the fluid-solid interface is computed using mass flux across the solid boundary.To validate the result, dimensionless Sherwood number around the spherical particles are compared .Also The variation of Sherwood umber versus angle from stagnation point is reviewed and breakthrough curve is showed qualitatively and also the effect of velocity and mesh size in diagrams is presented.The results show that this model can be used to simulate the adsorption for porous media. Path line velocities and concentration profiles show that commonly used models of porous media can not present an exact solution to the porous media problem due to their significant simplifications.Next step , the packed bed For 8, 14 layout and three types of 20 layout (DEM method) is analyzed and simulated.The contoure of Pressure and velocity is analyzed and the pressure drop result is compared with empirical correlation.On the other hand the effect of Reynolds number in pressure drop diagram for packed bed with 14 , 20 layout is showed.Also the results showed pressure drop in random packing is higher tha the ordered packing.The velocity vector and contoure of pressure in different wall segment and Renolds number is indicated.The result suggest that Velocity magnitude in near the wall is increased and the increase of Reynolds number leads to increase the possibility of eddy formation that caused reverse flow in outlet.Also the increase of Reynolds number leads to growth radial velocity near the wall , more than the center of packed bed. This eddy leads to increase velocity more than the inlet velocity.This condition influenced on mass and heat transfer coefficient strongly.Finally the momentum and mass transfer equation for fluid and solid phase and also physical adsorption for packed bed with 8 layout is solved.Since Lack of laboratory results for this type of geometry and also impossible conditions to test the experiment ,the result and breakthrough curve is analyzed qualitatively.The results is showed that the consentration profile in the particle is depended on radius and angular strongly. This profile is not symmetric.On the other hand this profile is showed that the assumption of LDF model is established when the velocity field around the sphere is fully development.At the end of this project, the result is showed that usage of arameters such as bed void and specific area can not predict correctly the mass transfer coefficient and flow field.