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The hyporheic zone is the ecotone between stream and river channel flow and groundwater that can process nutrients and improve water quality. Transient hyporheic zones occur in the riparian zone (bank storage or “lung model” exchange) during channel stage fluctuations. Recent studies show that soil pipes are widespread in stream banks and beneath floodplains, creating highly preferential flow between channel and riparian groundwater such that the traditional Darcy model of flow does not apply. We used MODFLOW with the conduit flow package to model a series of stream bank soil pipes and examined soil pipe density (number per m), length, diameter, height above baseflow water surface, connectivity, and matrix hydraulic conductivity on transient particle flow paths and total hyporheic exchange volume (i.e., bank storage) over the course of a peak flow (e.g., storm) event. We found that adding five soil pipes per meter more than doubled hyporheic volume. Soil pipe length was the most important control; adding one 1.5‐m‐long soil pipe caused a 73.4% increase in hyporheic volume. The effect of increasing soil pipe diameter on hyporheic volume leveled off at ~1 cm, as flow limitation switched from pipe flow to pipe‐matrix exchange. To validate our approach, we used the model to successfully reproduce trends from field studies. Our results highlight the need to consider soil pipes when modeling, monitoring, or managing bank storage, floodplain connectivity, or hyporheic exchange.