Hydrogen is a colorless, odorless, and flammable gas characterized by the smallest molecular weight among elemental gases. It possesses low density, low viscosity, and unique biochemical reactivity. Under identical temperature and pressure conditions, the density of hydrogen gas is only one-eighth that of methane, and its viscosity is merely 0.0101 mPa s at a pressure of 101.325 kPa and temperature of 0°C.

Current research indicates four primary pathways for natural hydrogen generation: (1) Natural radiolytic decomposition of deep groundwater induced by radioactive elements within highly radioactive rocks; (2) Reaction between subsurface hydrothermal fluids and peridotite during serpentinization, releasing hydrogen gas; (3) Deep-origin hydrogen emanating from the Earth’s core or mantle; and (4) Fault movements during rock fracturing processes, along with the associated formation of radicals.

Figure 1 presents macroscopic inelastic scatter cross-sections for quartz, calcite, dolomite, clay minerals, chlorite, water, oil, and hydrogen. It is evident from the figure that the macroscopic inelastic scatter cross-sections of hydrogen gas are significantly smaller compared to mineral constituents such as quartz, and also notably different from fluid phases like water and oil. This distinct difference serves as the fundamental principle for hydrogen evaluation using pulsed neutron logging techniques.

Figure 2 presents the distribution of capture gamma rays at the detector positions under conditions of either water- or hydrogen-filled formation pores. As observed from the figure, the spatial distribution of capture gamma rays in the hydrogen-bearing formation is significantly narrower compared to that in the water-bearing formation. When formation pores are filled with hydrogen gas instead of fresh water, the capture gamma counts recorded near the detector are substantially reduced—by nearly an order of magnitude of 20 times—highlighting the distinct neutron interaction characteristics of natural hydrogen. This phenomenon is primarily attributed to differences in neutron moderation capability between the borehole and the formation materials. A stronger neutron moderation effect results in an increased number of thermal neutrons generated after interactions between fast neutrons and the formation. Consequently, under identical conditions, a higher capture gamma-ray count rate is produced.

According to the two-group neutron diffusion theory (Huang, 1985), the thermal neutron flux resulting from inelastic scattering, elastic scattering, and radiative capture interactions between fast neutrons emitted by a pulsed neutron source and the formation medium can be expressed as: ϕ r = S Σ s 1 → 2 4 π D 1 D 2 κ 2 2 − κ 1 2 e − κ 1 r − e − κ 2 r r (1)

In Equation 1, S represents the neutron source strength, Σ s 1 → 2 denotes the scattering cross-section for fast neutrons moderating to the thermal energy group, D 1 and D 2 are diffusion coefficients for fast and thermal neutrons, respectively, κ 1 and κ 2 are the reciprocal of represent the slowing-down length and diffusion length, respectively, where κ = 1 / L = Σ / D .

By taking the gamma rays generated from the capture of thermal neutrons S γ r as the source term and substituting it into the gamma-ray diffusion equation, we obtain: D γ ∇ 2 ϕ γ r − Σ a γ ϕ γ r + S γ r = 0 (2)

In Equation 2, D γ is the gamma-ray diffusion coefficient, Σ a γ represents the gamma-ray absorption cross-section, S γ r = Σ c a p Y ϕ r , Σ c a p is the thermal neutron capture cross-section, Y is the number of gamma rays produced per captured neutron, and ϕ r is the thermal neutron flux. By solving the above equation using Green’s function integration, the capture gamma-ray counts at the detector position can be expressed as: ϕ γ r = Σ c a p Y S Σ s 1 → 2 16 π 2 D 1 D 2 D γ κ 2 2 − κ 1 2 e − κ 1 r − e − κ 2 r κ γ 2 − κ 1 2 r + e − κ 1 r − e − κ 2 r κ γ 2 − κ 2 2 r (3)

Thus, the ratio of capture gamma-ray counts at two different source-detector spacings r 1 and r 2 can be expressed as: R c a p = ϕ γ r 1 ϕ γ r 2 = r 2 r 1 · e − κ 1 r 1 − e − κ γ r 1 κ γ 2 − κ 1 2 − e − κ 2 r 1 − e − κ γ r 1 κ γ 2 − κ 2 2 e − κ 1 r 2 − e − κ γ r 2 κ γ 2 − κ 1 2 − e − κ 2 r 2 − e − κ γ r 2 κ γ 2 − κ 2 2 (4)

As indicated by Equation 4, when the source-detector spacings are fixed, the capture gamma-ray ratio is primarily influenced by the slowing-down length, diffusion length, and gamma-ray attenuation characteristics of the formation media. Considering that in compensated neutron logging the slowing-down length for fast neutrons is significantly greater than the diffusion length of thermal neutrons, the capture gamma-ray ratio predominantly reflects the neutron moderation capability of the formation.

A numerical calculation model, as shown in Figure 3, was established with porosities ranging from 0 to 20 p. u. at intervals of 5 p. u. The formation pores were separately filled with freshwater, natural gas (methane), and hydrogen, having densities of 1.0 g/cm³, 0.2 g/cm³, and 0.025 g/cm³, respectively. Capture gamma-ray data from the near and far detectors were recorded, and the ratio of capture gamma-ray counts was calculated, as illustrated in Figure 4.

From Figure 4, it can be observed that, for limestone formations, the capture gamma-ray ratio exhibits a significant positive correlation with porosity. As the porosity increases, the capture gamma-ray ratio also rises; however, the magnitude of this increase varies depending on the fluid filling the pores. Among the three fluids, freshwater has the strongest neutron moderation capability, followed by methane, with hydrogen being the weakest. Thus, for a given porosity, a stronger neutron moderation capability of the pore fluid results in a higher capture gamma-ray ratio. Therefore, the capture gamma-ray ratio is predominantly influenced by the neutron moderation properties of the pore-filling medium.

To further analyze the variations in capture gamma rays when pores are filled with natural gas or hydrogen, a dynamic variation parameter is defined as the ratio of the difference between capture gamma-ray counts in water-filled and gas-filled pores to the counts in water-filled pores, expressed mathematically as follows: w = R w − R g R w × 100 % (5) where, w is the dynamic variation, R w is the capture gamma-ray ratio under water-filled pore conditions, R g is the capture gamma-ray ratio under natural gas- or hydrogen-filled pore conditions. Figure 5 shows the dynamic variation ranges for formations with pores filled with natural gas and hydrogen, respectively. As illustrated, the capture gamma-ray dynamic range increases exponentially with increasing porosity. Specifically, when porosity ranges from 5 p. u. to 20 p. u., the dynamic variation range for hydrogen-filled pores is approximately 10% greater than that for natural gas-filled pores.

A numerical model, as illustrated in Figure 3, was established with a limestone formation matrix and a porosity of 10 p. u. The pores were filled with mixtures of hydrogen gas and freshwater. The pore-space gas saturation was systematically varied (100, 80, 60, 40, and 20%), and the corresponding capture-gamma ratios are presented in Figure 6.

As demonstrated in Figure 6, for a fixed hydrogen gas saturation, the capture gamma-ray ratio increases with increasing porosity. Conversely, for a constant porosity, the capture gamma-ray ratio decreases with increasing hydrogen gas saturation. In compensated neutron porosity logging, a negative hydrogen index often appears when pores contain low-density gases, because the neutron moderation capability of gas is lower than that of the rock matrix, resulting in underestimated porosity measurements. However, the capture gamma-ray ratio does not exhibit a similar “excavation effect” phenomenon. Instead, the capture gamma-ray counts consistently increase as the neutron moderation capability of the pore-filling fluid or gas increases.

A numerical model (Figure 3) was developed for three representative lithologies—serpentinite, granite, and shale—whose mineralogical compositions are listed in Table 1. For each case, porosity was fixed at 10 p. u. and the pore space was completely saturated with hydrogen gas. The resulting capture γ-ray ratios are presented in Figure 7. Granite and shale are dominated by quartz (SiO₂) and contain no structural water, although minor oxides such as FeO, Al₂O₃, K₂O, and CaO are present. In contrast, serpentinite is composed mainly of quartz and MgO and, in addition to the aforementioned trace oxides, includes approximately 10 wt% structural water.

Figure 8 shows the response of the capture gamma-ray ratio with varying porosity for hydrogen-filled pores under three different lithological matrices. When the formation matrix is granite or shale, the capture gamma-ray ratio increases with increasing porosity. However, for serpentinite, the ratio decreases as porosity increases. This response is attributed primarily to serpentinite’s greater structural-water content; because water provides markedly stronger neutron moderation than hydrogen gas, increasing porosity diminishes the bulk moderating capacity of serpentinite and consequently lowers the capture-gamma ratio. Figure 9 illustrates the dynamic variation ranges for different lithological matrices. The dynamic variation ranges for granite and shale are nearly identical and consistently larger than those of serpentinite, with the maximum difference in dynamic range reaching approximately 25%.

A numerical calculation model, as shown in Figure 3, was established with a granite formation matrix and a fixed porosity of 10 p. u. Hydrogen gas was used to fill the pores, with gas densities set at 0.0025 g/cm³, 0.05 g/cm³, and 0.1 g/cm³, respectively. Under subsurface high-temperature and high-pressure conditions, changes in temperature and pressure can alter the density of hydrogen gas. By examining the capture gamma-ray response at varying hydrogen densities, the variations in capture gamma-ray measurements under different pressure conditions were assessed.

Figure 10 presents the capture gamma-ray responses for the three hydrogen densities. When other conditions remain constant, higher pressures correspond to greater gas densities, leading to an increase in the capture gamma-ray ratio as hydrogen density increases within the pores. An increase in hydrogen gas density enhances the number of hydrogen atoms per unit volume, thereby strengthening neutron moderation capability and consequently increasing the capture gamma-ray ratio. Figure 11 illustrates the dynamic variation ranges under different hydrogen gas density conditions. As hydrogen density increases, the dynamic variation range decreases. This phenomenon arises because higher hydrogen densities result in an increased hydrogen index within the formation, enhancing neutron moderation capability. Consequently, the difference in neutron moderation between hydrogen-filled and water-filled pores diminishes, thereby reducing the dynamic variation range.

Based on the configuration shown in Figure 3, a numerical model was built for two borehole conditions—hydrogen-filled and freshwater-filled. Formation porosity was varied from 0 to 30 p. u. in 5 p. u. increments, with the pore space in each case filled by hydrogen or freshwater, respectively. The resulting capture-gamma count ratios as a function of porosity are presented in Figure 12. Based on the simulated data, Equation 5 was applied to calculate the dynamic response range for each borehole-fluid type across the porosity and the resulting trends are depicted in Figure 13.

Figure 12 presents the capture-gamma response characteristics under a range of formation conditions for boreholes filled with hydrogen and, for comparison, with freshwater. At any given porosity, the capture-gamma ratio is systematically lower in a hydrogen-filled borehole, owing to hydrogen’s low density and correspondingly smaller hydrogen index per unit volume, which reduce the neutron-capture probability relative to water. As a result, the absolute difference between the hydrogen- and freshwater-saturated cases is modest when the borehole fluid itself is hydrogen. Figure 13 plots the dynamic response range for boreholes filled with hydrogen and freshwater, respectively. The two curves are virtually coincident, indicating that the influence of borehole-fluid composition on the capture-gamma ratio is largely cancelled during the dynamic-range calculation. Hence, the overall dynamic response is essentially insensitive to whether the borehole is filled with hydrogen or freshwater.