Pore-network modelling, or digital petrophysics, is an emerging technology which allows computing physically consistent two- and three-phase flow functions such as relative permeability and capillary pressure curves at arbitrary wettability. Considering the difficulty in measuring these functions reliably in the laboratory, pore-network modelling is increasingly used to guide and complement costly and time-consuming SCAL programmes. Although pore-network modelling is now well-established for clastic reservoirs, applying it to carbonate rocks is significantly more challenging due to their complex and multi-scale pore structure, comprising micro- and macro-pores as well as cracks and fractures. We have hence developed a novel method to integrate pore-networks, which have been extracted at multiple scales directly from CT images at different resolutions, into a single pore-network model that can be used in subsequent calculations of two- and three-phase flow functions. This method has been validated by comparing computed two-phase relative permeability and capillary pressure curves for a multiscale network to the corresponding laboratory measurements. However, in this approach it is important to accurately consider the impact of the spatial distribution of fine network elements, which are extracted from high-resolution images. We therefore show the impact of the spatial correlation of high-resolution porosity on single- and two-phase fluid flow and propose a model that allows us to simulate the spatial correlation between coarse-scale pores and fine-scale porosity in the absence of a suitable CT image that segments the rock into three phases (pores, sub-resolution matrix porosity, and solid). We demonstrate the impact of the spatial correlation of microporosity on absolute and relative permeabilities by applying this model to various datasets, including CT images of an off-shore carbonate reservoir. This demonstrates that the spatial correlation of microporosity is one of the key factors controlling recovery from carbonate reservoirs and that our new method allows us to quantify it.@en