We report on results from primary drainage experiments on quasi-two-dimensional porous models. The models are transparent, allowing the displacement process and structure to be monitored in space and time during primary drainage experiments carried out at various speeds. By combining detailed information on the displacement structure with global measurements of pressure, saturation and the capillary number Ca, we obtain a scaling relation relating pressure, saturation, system size and capillary number. This scaling relation allows pressure-saturation curves for a wide range of capillary numbers to be collapsed on the same master curve. We also show that in the case of primary drainage, the dynamic effect in the capillary pressure-saturation relationship observed on partially water saturated soil samples might be explained by the combined effect of capillary pressure along the invasion front of the gaseous phase, and pressure changes caused by viscous effects in the wetting fluid phase.