Pulsing seepages of native hydrogen (H2) have been observed at the surface on several emitting structures. It is still unclear whether this H2 pulsed flux is controlled by deep migration processes, atmosphere/near-surface interactions or by bacterial fermentation. Here, we investigate mechanisms that may trigger pulsating fluid migration at depth and the resulting periodicity. We set up a numerical model to simulate the migration of a deep constant fluid flow. To verify the model’s formulation to solve complex fluid flows, we first simulate the morphology and amplitude of 2D thermal anomalies induced by buoyancy-driven water flow within a fault zone. Then, we simulate the H2 gas flow along a 1-km draining fault, crosscut by a lower permeable rock layer to investigate the conditions for which a pulsing system is generated from a deep control. For a constant incoming flow of H2 at depth, persistent bursts at the surface only appear in the model if: (I) a permeability with an effective-stress dependency is used, (II) a strong contrast of permeability exists between the different zones, (III) a sufficiently high value of the initial effective stress state at the base of the low permeable layer exists, and (IV) the incoming and continuous fluid flow of H2 at depth remains low enough so that the overpressure does not “open” instantly the low permeability layer. The typical periodicity expected for this type of valve-fault control of H2 pulses at the surface is at a time scale of the order of 100 to 300 days.