Pore connectivity is limited in shale formations, unlike in conventional reservoirs, for which cyclic void models, such as the regular-lattice model, are often used to represent the connectivity. In the cyclic models, the random assignment of throat sizes to lattice elements leads to a plateau-like variation of a capillary pressure with wetting phase saturation during a drainage displacement. Here, we develop acyclic void models in which the spatial distribution of throat sizes is not random. For certain spatial distributions these models yield a non-plateau-like drainage displacement. Such models thus provide more realistic representations of the void space in samples for which drainage experiments reveal the non-plateau-like trend of the capillary pressure versus saturation. Gas shales commonly show such a trend, and using the developed models, we predict the no-slip permeability of shale samples whose mercury intrusion capillary pressures curves were measured under confined boundary conditions. The predicted permeabilities are in good agreement with the lab measurements reported for these samples. Other models either fail to account for the non-plateau-like trend of the drainage as they adopt a random pore size distribution or they overestimate the no-slip permeability for saturated flow. The models developed here could have applications in other porous media whose drainage data do not exhibit a plateau-like variation. (C) 2014 Elsevier Ltd. All rights reserved.