Traditional analysis methods used to determine hydraulic properties from pumping tests work well in many porous media aquifers, but they often do not work in heterogeneous and fractured-rock aquifers, producing non-plausible and erroneous results. The generalized radial flow model developed by Barker (1988) can reveal information about heterogeneity characteristics and aquifer geometry from pumping test data by way of a flow dimension parameter. The physical meaning of non-integer flow dimensions has long been a subject of debate and research. We focus on understanding and interpreting non-radial flow through high permeability conduits within fractured aquifers. We develop and simulate flow within idealized non-radial flow conduits and expand on this concept by simulating pumping in non-fractal random fields with specific properties that mimic persistent sub-radial flow responses. Our results demonstrate that non-integer flow dimensions can arise from non-fractal geometries within aquifers. We expand on these geometric concepts and successfully simulate pumping in random fields that mimic well-test responses seen in the Culebra Dolomite above the Waste Isolation Pilot Plant.