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Both hydrogen and natural gas are challenging to economically store onboard vehicles as fuels, due to their low volumetric energy density at ambient conditions. One strategy to densify these gases is to pack the fuel tank with a porous adsorbent material. The US Department of Energy (DOE) has set volumetric deliverable capacity targets which, if met, would help enable commercial adoption of hydrogen/natural gas as transportation fuels. Here, we present a theoretical upper bound on the deliverable capacity of a gas in a rigid porous material via an isothermal pressure swing. To provide an extremum, we consider a substrate that provides a spatially uniform potential energy field for the gas. Our bound relies directly on experimentally measured properties of the pure gas. We conclude that the deliverable capacity targets set by the DOE for room-temperature natural gas and hydrogen storage are just barely theoretically possible. The targets are likely to be impossible for any real, rigid porous material because of steric repulsion, which reduces the deliverable capacity below our upper bound. Limitations to the scope of applicability of our upper bound may guide fuel tank design and future material development. Firstly, one could avoid using an isothermal pressure swing by heating the adsorbent to drive off trapped, residual gas. Secondly, our upper bound assumes the material does not change its structure in response to adsorbed gas, suggesting that flexible materials could still satisfy the DOE targets.