This study presents several PSA with complex particle models: dusty gas model (PSA/DG), linear driving force (LDF) approximation to the DG (PSA/LDF-DG) and LDF approximation extensions when surface (PSA/LDF-DGSD) or micropore diffusion (PSA/LDF-DGMD) are important. A comparison between the PSA/DG and PSA/LDF-DG models is shown and discussed in two situations: short and long cycles. Also some results in the literature are discussed in the light of these LDF approximations. It was concluded that the PSA/LDF-DG is a good approximation to the PSA/DG for long cycles. For short cycles a special algorithm was developed, where two time scales have to be considered. It was also concluded that the time delay presented by the LDF-DG has to be considered in order to reproduce the PSA/DG results. This can explain the reason why some authors found difficulties using the LDF model in PSA simulations. Some simulation results are shown when the PSA/LDF-DGSD or PSA/LDF-DGMD models are used and compared with equivalent results of the PSA/LDF-DG model.