Olefin polymerisation on heterogeneous catalysts is gaining importance due to widening of the polymer properties window. The supported active catalyst on the heterogeneous particle reacts with the monomer and produces polymer. Polymeric flow (PF) model is relatively simple and assume that particle morphology develops as the catalyst active sites move outwards along with the polymer formed thus leading to PF morphology. The multigrain (MG) model describes the particle morphology incorporating a more detailed picture of the underlying phenomena. The heterogeneous support fragments into tiny pieces by the polymer formed, while keeping the fragments together thus forming the MG morphology. The both state of the art models describes the monomer transport by Fick's diffusion (FD) alone and hence polymeric flow Fick's diffusion model (PF_FDM) and Multigrain Fick's diffusion model (MG_FDM). Both these models does not account for the monomer convection through interconnected pores. Single particle models that account for the convection through the pores, created by the pressure gradient due to the monomer consumption within the particle are discussed in the present work. The so-called advection-dispersion model (ADM) and the dusty gas model (DGM) is used to describe the convective flow. The PF morphology is retained in the advection-dispersion model (PF_ADM) and dusty gas model (PF_DGM) and similarly multigrain morphology is retained in the advection-dispersion (MG_ADM) and dusty gas model (MG_DGM). Comparison of convective flow models with state of the art models which use Fick's diffusion alone (PF_FDM, MG_FDM) has been made and published convective flow models are briefly discussed. (C) 2003 Elsevier Science Ltd. All rights reserved.