Here we investigate the impact of mudstone drape distribution on the effective permeability 26 of heterolithic, cross-bedded tidal sandstones using three-dimensional (3D) surface-based 27 "mini-models" that capture the geometry of cross-beds at an appropriate scale. The impact 28 of seven geometric parameters has been determined: (1) mudstone fraction, (2) sandstone 29 laminae thickness, (3) mudstone drape continuity, (4) toeset dip, (5) climb angle of foreset-30 toeset surfaces, (6) proportion of foresets to toesets, and (7) trough or tabular geometry of 31 the cross-beds. 32We begin by identifying a representative elementary volume (REV) of 1 m 3 , confirming 33 that the model volume of 9 m 3 yields representative permeability values. Effective 34 permeability decreases as the mudstone fraction increases, and is highly anisotropic: vertical 35 permeability falls to c. 0.5% of the sandstone permeability at a mudstone fraction of 25%, 36 while the horizontal permeability falls to c. 5% and c. 50% of the sandstone value in the dip 37 (across mudstone drapes) and strike (parallel to mudstone drapes) directions, respectively. 38There is considerable spread around these values, because each parameter investigated can 39 significantly impact effective permeability, with the impact depending upon the flow 40 direction and mudstone fraction. The results yield improved estimates of effective 41 permeability in heterolithic, cross-bedded sandstones, which can be used to populate 42 reservoir-scale model grid blocks using estimates of mudstone fraction and geometrical 43 parameters obtained from core and outcrop-analog data. 44 45