*2.3. Site Analysis*

### 2.3.1. The Minimum Criterion for [H2]Station-6 Modulation

Whether the pulsing *H*2 leakage criterion (9) is met depends on the parameter values. The last 3 lines in the Table 1 show the calculated cyclic gas inflow rates for temperature and pressure variations at the Sao Fancisco site. The maximum temperature-driven gas influx is an order of magnitude less than the pressure-driven influx, and too small to reverse even Prinzhofer's lowest venting estimate. The pressure-driven influx, on the other hand, could reverse the [*H*2] venting if the venting were at the low end of Prinzhofer's estimated range. For convenience we show the comparison in Table 2.

**Table 2.** Deep H2 flux estimated by Prinzhofer, assuming the concentration in the deep venting gas is 50% H2 compared to air flux in and out of vent that is driven by tidal atmospheric pressure changes. The air flux exceeds the venting flux for venting fluxes at the low end of the range estimated by Prinzhofer for a subsurface permeability of 1 Darcy.


The calculations assume a subsurface permeability of 1 Darcy, and porosities between 0.1 and 0.4. The two harmonic components of pressure-driven gas flow in Table 1 are summed to produce the values in the Table 2. The pressure-driven gas flux is not very sensitive to porosity (factor of 2 change for a factor of 4 change in porosity). This φ dependence arises because δ*p* depends on 1/ √ϕ (see Table 1). For a subsurface permeability of 10 darcies, δ1*dp* would be increased by √10 = 3.2, and the calculated pressure-driven air flux into the ground would range between 0.25 and 0.5 m<sup>3</sup> m<sup>−</sup><sup>2</sup> d−1.

Diurnal temperature changes penetrate so little into the subsurface that they cannot affect *H*2 a meter below the surface. From Table 1, the thermal skin depth for daily temperature variations is at most 10 cm. This means that at 20 cm depth the temperature variation will be 10% of that at the surface, and at 40 cm, 1%. Temperature variations thus do not appear to be a viable way to explain [*H*2] variations measured at 1 m depth in the Sao Francisco basin. We therefore do not consider them further in this paper.
