This paper presents an overview of two‐stage decoupling preconditioning techniques employed in the implicit parallel accurate reservoir simulator (IPARS) computational framework for modelling multi‐component multi‐phase flow in porous media. The underlying discretization method is implicit Euler in time and mixed finite elements or cell‐centred finite differences in space. IPARS permits rigorous, physically representative coupling of different physical and numerical flow models in different parts of the domain and accounts for structural discontinuities; the framework currently includes eight physical models. For simplicity of exposition, we have restricted our discussion to a two‐phase oil–water model and a three‐phase black oil model. Our decoupling approach involves extracting a pressure equation from the fully coupled linearized system thus allowing for a more accurate preconditioning of a discrete elliptic problem of lower dimension. Copyright © 2001 John Wiley & Sons, Ltd.