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.