Aquifer remediation with in situ soil washing techniques and enhanced oil removal typically involve the injection of liquid solutions into the geological formation to displace and mobilize non-aqueous phase liquids (NAPLs). The efficiency of these systems is oftentimes low because the displacing fluid bypasses large quantities of NAPL due to the inherent complexity of a heterogeneous natural system. Here, chaotic advection generated by a rotating periodic injection pulse is proposed as a method to enhance NAPL removal and mixing. To evaluate the method, we perform two-phase flow simulations in multiple realizations of random permeability fields with different correlation structures and connectivity between injection and extraction wells embedded in a five-spot pattern. Results show that chaotic advection can significantly improve removal efficiency and mixing depending on several controlling factors. Chaotic advection effects are more significant under unfavorable conditions, i.e., when injection and extraction wells are well-connected through preferential channels, permeabilities are highly heterogeneous, and/or the mobility ratio between the wetting and the non-wetting fluid is larger than one. Removal efficiency reaches its maximum value when the Kubo number is close to one, i.e., when the saturation front travels one range of the permeability field in an injection pulse. These effects can develop in just a few cycles. However, removal efficiency should undergo first an early stage with detrimental effects in order to maximize removal in the long term. Chaotic advection not only enhances NAPL removal and mixing, but also reduces the uncertainty, making the system more reliable and less dependent on heterogeneity.