Pulsing emanations of native hydrogen (H2) have been observed at the surface of emitting structures, specifically “Fairy circles” in Minas Gerais State, Brazil. However, the underlying cause of these H2 pulses remains unclear. Possible controlling factors include deep migration processes, interactions with the atmosphere and near-surface conditions. In this study, we examine the mechanisms that may trigger pulsating fluid migration and the resulting periodicity, with particular attention to the influence of deep geological processes. We employed a numerical model to simulate the migration of a constant deep fluid flow. To ensure the accuracy of the model in solving complex fluid flows, we conducted initial simulations to compare the morphology and amplitude of 2D thermal anomalies induced by buoyancy-driven water flow within a fault zone with another numerical model. Following the validation of our model in capturing complex fluid flows, we proceeded to model the H2 gas flow along a 1-km draining fault, intersected by a low permeable rock layer acting as a “pressure relief valve” system. Our objective is to investigate the conditions that give rise to a pulsing regime. Our results indicate that sustained surface bursts in the model only occur if: (I) a permeability with an effective-stress dependency is considered, (II) a significant contrast in permeability exists between different zones, (III) an adequately high initial effective stress state is present at the base of the low-permeability layer, and (IV) the incoming and continuous fluid flow of H2 at depth is sufficiently low to prevent instant “opening" of the low-permeability layer due to overpressure. The predicted periodicity for surface H2 pulses regulated by the fault-valve mechanisms is expected to range from 100 to 300 days, representing a considerably longer duration compared to the measurements observed up to now in Brazilian Fairy circles.