The hydraulic conductivity can control geotechnical design, resource recovery and waste disposal. We investigate the effect of pore-scale spatial variability on flow patterns and hydraulic conductivity using network models realized with various tube size distributions, coordination number, coefficient of variation, correlation and anisotropy. In addition, we analyse flow patterns to understand observed trends in hydraulic conductivity. In most cases, the hydraulic conductivity decreases as the variance in pore size increases because flow becomes gradually localized along fewer flow paths; as few as 10 per cent of pores may be responsible for 50 per cent of the total flow in media with high pore-size variability. Spatial correlation reduces the probability of small tubes being next to large ones and leads to higher hydraulic conductivity while focused fluid flow takes place along interconnected regions of high conductivity. A pronounced decrease in tortuosity is observed when pore size and spatial correlation in the flow direction are higher than in the transverse direction. These results highlight the relevance of grain size and formation history dependent pore size distribution and spatial variability on hydraulic conductivity, related geo-process and engineering applications.