Predicting long-term production from gas shale reservoirs has been a major challenge for the petroleum industry. To better understand how production profiles are likely to evolve with time, we have conducted laboratory experiments examining the effects of confining stress and pore pressure on permeability. Experiments were conducted on intact core samples from the Barnett, Eagle Ford, Marcellus, and Montney shale reservoirs. The methodology used to measure permeability allows us to separate the reduction of permeability with depletion (because of the resultant increase in effective confining stress) and the increase in permeability associated with Knudsen diffusion and molecular slippage (also known as Klinkenberg) effects at very low pore pressure. By separating these effects, we are able to estimate the relative contribution of both Darcy and diffusive fluxes to total flow in depleted reservoirs. Our data show that the effective permeability of the rock is significantly enhanced at very low pore pressures (<1000 psi [<6.9 MPa]) because of the slippage effects. We use the magnitude of the Klinkenberg effect to estimate the effective aperture of the flow paths within the samples and compare these estimates to scanning electron microscopy image observations. Our results suggest effective flow paths to be on the order from tens of nanometers in most samples to 100-200 nm, in a relatively high-permeability Eagle Ford sample. Finally, to gain insight on the scale dependence of permeability measurements, the same core plugs were crushed, and permeability was again measured at the particle scale using the so-called Gas Research Institute method. The results show much lower permeability than the intact core samples, with very little correlation to the measurements on the larger scale cores.