The multi-phase flow behavior of complex rocks with broad pore size distributions often digresses from classical relations. Pore-scale simulation methods can be a great tool to improve the understanding of this behavior. However, the broad range of pore sizes present makes it difficult to gather the experimental input data needed for these simulations and poses great computational challenges. We developed a novel micro-computed-tomography (micro-CT) based dual pore network model (DPNM), which takes microporosity into account in an upscaled fashion using symbolic network elements called micro-links, while treating the macroporosity as a traditional pore network model. The connectivity and conductivity of the microporosity is derived from local information measured on micro-CT scans. Microporous connectivity is allowed both in parallel and in series to the macropore network. We allow macropores to be drained as a consequence of their connection with microporosity, permitting simulations where the macropore network alone does not percolate. The validity of the method is shown by treating an artificial network and a network extracted from a micro-CT scan of Estaillades limestone.