We examine permeable flow through porous materials using volcanic pyroclasts with simple pore geometries. Laminar lattice-Boltzmann (LB) fluid flow simulations through 3-D synchrotron x-ray microtomographic images allow us to model fluid flow through anisotropic pumiceous volcanic samples (tube pumice). We find a good correspondence between calculated permeability (using both simple approximations and LB simulations) and maximum laboratory permeability measured parallel to the direction of vesicle elongation in most tube pumice samples. Moreover, this comparison demonstrates that small vesicles control fluid flow through the pore structure of tube pumice, even when large, but isolated, vesicles are present. However, neither simple approximations nor LB models for flow through small tomographic volumes can adequately model permeable flow perpendicular to vesicle elongation or in material with complex geometries. This mismatch illustrates current limitations in both resolution of x-ray tomography for delicate pumice structures and shows the importance of scale in LB calculations.