Understanding the transport of hydraulic fracturing (HF) fluid that is injected into the deep subsurface for shale gas extraction is important to ensure that shallow drinking water aquifers are not contaminated. Pressure gradients, permeable pathways such as faults or improperly abandoned wellbores, and the density contrast of the HF fluid to the surrounding brine could encourage upward HF fluid migration. In contrast, very low shale permeability and well production may work to keep HF fluid at depth and remove it from the subsurface. Single-phase flow and transport simulations are performed to quantify how much HF fluid is removed via the wellbore and how much reaches overlying aquifers. If a permeable pathway connects the shale reservoir to the overlying drinking water aquifer, the pressure transient due to injection and the density contrast allows rapid upward plume migration at early times, but well production reverses the direction of flow and removes a large amount of HF fluid from the subsurface. We present estimates of HF fluid migration to shallow aquifers during the first 1,000 years and show that the pressure transient from well operations should be included in subsequent numerical models while buoyancy may be neglected depending on depth and permeability.