EPSRC grant EP/L012227/1: Development of Unified Experimental and Theoretical Approach to Predict Reactive Transport in Subsurface Porous Media. The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. Also available at https://www.digitalrocksportal.org/projects/10, DOI:10.17612/P73W2C. Further details can be found in Muljadi et al., Advances in Water Resources (2015), URL:http://dx.doi.org/10.1016/j.advwatres.2015.05.019.