**1. Introduction**

Hydrogen gas may become an important part of the zero-carbon energy economy because its combustion produces only water vapor and no CO2. Hydrogen is generally considered a vector of energy because it is an agen<sup>t</sup> of energy transfer that needs to be manufactured from some other material, such as hydrocarbons or water, and thus carries energy from other sources. Several studies have shown, however, that there are natural sources of hydrogen that could be an important resource (Ward, 1933 [1]; Goebel et al., 1984 [2]; Newell et al., 2007 [3]; Sherwood-Lollar et al., 2014 [4]; Prinzhofer and Deville, 2015 [5]; Guélard et al., 2017 [6]; Prinzhofer et al., 2018 [7]). The Earth is naturally expelling native hydrogen through still-poorly determined physico-chemical processes.

As at the start of the petroleum era, we currently know only that hydrogen is seeping out of rocks and soils in many locations. Studies so far have focused on the chemistry of the seeps that have been discovered worldwide (Larin et al., 2014 [8]; Zgonnik et al., 2015 [9]; Deville and Prinzhofer, 2016 [10]; Prinzhofer et al., 2019 [11]) and the origin of the hydrogen (Larin, 1993 [12]; Gilevska, T., 2007 [13]; Milesi et al., 2015 [14]; Vacquand et al., 2018 [15]; Truche et al., 2018 [16]). The many seeps that have been found indicate the operation of an active hydrogen system, and transient accumulations of hydrogen at relatively shallow depth are known (Mali, Prinzhofer et al., 2018 [7], USA, Goebel et al.,

1984 [2]; Newell et al., 2007 [3]; Guélard et al., 2017 [5]). But we know little about the scale and economic potential of the hydrogen systems that are involved.

The most important parameter for gauging the magnitude of the hydrogen resource is the magnitude of the hydrogen ( *H*2) emission because it immediately suggests the probability of hydrogen accumulation under subsurface structures, and also indicates the sustainability of this source of energy. To better constrain the magnitude of the hydrogen emission, a permanent monitoring station has been installed at 16 ◦S in the dry, hot Sao Francisco Basin of Brazil. Venting is being monitored there with sensors that measure *H*2 concentrations at ~1 m depth around the perimeter of a 550 m diameter vent (Prinzhofer et al., 2019) [11]. The data indicate daily pulses of hydrogen emission. The maximum concentration of *H*2 in the venting gases usually occurs in the middle of the day, although some sensors have hydrogen concentration peaks at the beginning of the day, or even during the night. It appears that these variations are linked to complex external parameters such as biologic activity in the soils, temperature, atmospheric pressure, Earth tides, etc.

Importantly, the correlation between *H*2 concentrations and atmospheric pressure is not linear, but presents a kind of hysteresis in which there is a delay between the pressure variation in free air, the hydrogen concentration measured by the sensors at 1 m depth, and the gas movements induced in the porous soil. The soil generally has very low water saturation above the water table several meters below the surface. This paper investigates whether the variation of hydrogen concentrations in soils could be caused by diurnal/nocturnal variations in temperature or atmospheric pressure.

*H*2 gas is venting in the Sao Francisco Basin from slight topographic depressions that are circular, barren of vegetation, and aligned along a major fault. The water table is at 3 to 5 meters depth. The hydrogen venting from the 600 × 500 m study area is not continuous, but pulses on a daily cycle wherein *H*2 is detected by shallow (1 m depth) sensors for only about half the day, usually centered on high noon. Prinzhofer et al. (2019) [11] have estimated the emission rate is between 7000 and 178,000 m<sup>3</sup> *H*2 per day, based on the venting at Sensor 9 (Figure 1) where the volume of *H*2 venting is greatest and the concentration of *H*2 in the venting gas is sometimes above 1000 ppm. Hydrogen is thought to be generated in basins from the reduction of water attending ferrous to ferric iron oxidation (Welhan and Craig, 1979 [17]; Neal and Stranger, 1983 [18]; Abrajano et al., 1990 [19]; Sano et al., 1993 [20]; Charlou et al., 2002 [21]) and/or NH4 + decomposition at depths where the temperature exceeds 200 to 250 ◦C (Guélard et al., 2018) [22]. The H2 concentration was found to be 50% to 80% (with the rest *N2* and several percent C *H4*) in a deep drill hole in the Sao Francisco basin, and measurements at other sites in the basin found a source *H*2 concentration ranging from 50% to ~100%. This suggests that the undiluted hydrogen source at the vent we analyze has a hydrogen concentration of at least 50%.

We investigate whether, and under what circumstances, daily changes in either surface temperature or atmospheric pressure can cause gas flow to reverse (e.g., air to flow into the ground) for half the day and thus potentially explain why *H*2 is detected for only half a day. The initial method of analysis is to compute, for both temperature and pressure changes, the change in gas density as a function of depth, the variations in the rate of gas flow produced by these density changes, and the conditions under which the density-change-driven-flow could cause the flow of *H*2-free air into the vent subsurface for about half the day. It is found that variations in atmospheric pressure could account for the diurnal variations in *H*2 detection, but temperature variations cannot. The pressure-driven changes in hydrogen concentration at 1 m depth are then investigated quantitatively by comparing the timing and magnitude (phase relations between) of the calculated and observed modulation in hydrogen concentration. It is found that pressure variations must be blocked by a barrier of some kind when they have propagated about 25% of the distance they could potentially propagate into a gas-filled reservoir, and that the gas volume of the reservoir tapped needs to be at least 1000 times greater than the gas volume in the vent. These insights, obtained by simple 1D analytical and finite element analyses, sugges<sup>t</sup> how the Sao Francisco hydrogen system is operating, how the system could be tested by future drilling, and the kind of future 3D modeling that will be required to define the operation of this hydrogen system.

**Figure 1.** H2 is venting in a pulsating fashion from the periphery of a 600 × 500 m topographical depression barren of vegetation in the Sao Francisco sedimentary basin of Brazil at latitude ~16 ◦S. Sensor 6 is circled in red. Figure is from Prinzhofer et al. (2019).
