A multi-scale network integration approach introduced by Jiang et al.  is used to generate a representative pore-network for a carbonate rock with a pore-size distribution across several orders of magnitude. We predict the macroscopic flow parameters of the rock utilising i) 3D images captured by X-ray computed micro-tomography and ii) pore-network flow simulations. To capture the multi-scale pore-size distribution of the rock we imaged four different rock samples at different resolutions and integrated the data to produce a pore-network model that combines information at several length-scales that cannot be recovered from a single tomographic image. A workflow for selection of the number and length-scale of the required input networks for the network integration process, as well as fine tuning the model parameters is presented. Mercury injection capillary-pressure data were used to evaluate independently the multi-scale networks. We explore single-scale, two-scale, and three-scale network models and discuss their representativeness by comparing simulated capillary-pressure versus saturation curves with laboratory measurements. We demonstrate that for carbonate rocks with wide pore-size distributions, it may be required to integrate networks extracted from two or three discrete tomographic data sets in order to simulate macroscopic flow parameters. This article is protected by copyright. All rights reserved.