Fluvial deposits contain a high percentage of large-scale cross-bedding. The contrasting grain size of adjacent foreset laminae combined with poorly-sorted bottomsets cause a considerable permeability heterogeneity. Permeability measurements of studied outcrop sandstones range from 0.5 to 17 Darcy. Values of reservoir cores from various Dutch gas fields range from 10 mD up to several hundreds of mD. Average permeability values of the poorly-sorted bottomsets are significantly lower than average values of the well-sorted foresets. Adjacent foreset laminae show remarkably sharp contacts in distinctive grain size and sorting. Consequently, capillary characteristics differ per foreset lamina and between foreset laminae and bottomset. Detailed computer simulations show that oil is being trapped in low capillary pressure laminae as soon as surrounding higher capillary pressure laminae and bottomsets are flushed to immovable oil saturation. It is conceivable that considerable amounts of oil, considered movable, could be trapped by capillary forces on a cross-bed set scale.