Abstract — This thesis is about pore scale characterisation and the modelling of multiphase flow in complex natural sandstones. These sandstones typically have been exposed to multiple diagenetic processes, contain substantial cements, clays, secondary porosity and contain a wide range of pore sizes. These issues create challenges in imaging and modelling of these systems. Multiscale 2D scanning electron microscopy (SEM) and 3D X-ray micro computed tomography (μCT) have been used to image sandstone samples from two North Sea petroleum reservoirs. The pore space was characterised from the imaging data to quantify the pore size and pore coordination number distributions. Despite the combination of multiple complex diagenetic processes, the pore space characterisations show some regular character that can be represented by empirical mathematical models. The pore size distributions can be fitted to modified power law (Pareto) distributions with an exponential cut-off at large radii. The frequency distribution of coordination numbers follows an exponential model; additionally the mean and standard deviation of the coordination number are power law functions of the pore radius. An empirical relationship between 2D and 3D coordination number is proposed based on an analysis of random sections extracted from 3D volumes. This relationship makes it possible to estimate multiscale 3D connectivity from high resolution 2D imaging. A stochastic algorithm has been developed to generate 3D pore networks from 2D imaging data. The stochastic algorithm has a recursive process that naturally fits into multiscale pore structure hierarchies. The methodology has been validated by calculating single phase permeability, capillary pressure and relative permeability from quasi-static pore network modelling for comparison with measured data and results from μCT pore networks. Relative permeability and capillary pressure generated from stochastic pore networks have been applied in a field scale continuum model to examine the effect of changing wettability and wettability heterogeneity. The results show that a heterogeneous wettability distribution can yield a lower oil recovery than a homogeneous oil-wet or homogeneous water-wet assumption.