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Gas-phase vs. aqueous-phase H2 sensing

A hydrogen exploration program will eventually put two numbers side by side that look comparable and are not: “412 ppm H2 in the soil-gas probe” and “38 nM dissolved H2 in the monitoring well.” Both are honestly labeled “the hydrogen concentration,” both come from calibrated measurements, both are the same molecule. But one describes H2 as free gas mixed with soil air; the other describes H2 dissolved in liquid water. They use different kinds of units (ppm is a ratio of molecule counts, nanomolar is a concentration in solution) and cannot be charted or averaged together without a conversion. That conversion is one 200-year-old equation, Henry’s law.

The conversion alone does not make the two numbers mean the same thing geologically. Gas-phase H2 is controlled mostly by physics (diffusion, weather, wet-soil capping); dissolved H2 is controlled mostly by biology (microbes drawing it down to whatever floor their metabolism tolerates), so a dissolved number reads less as “how much gas is down there” and more as “which microbial community controls this patch of aquifer.” This page teaches both halves: the arithmetic bridge, and why a smart explorer wants both numbers even with the conversion done perfectly.

Gas-phase H2 occurs when H2 mixes with other gas molecules and moves freely: air-filled pores of unsaturated soil, gas bubbling from drilling mud, or the headspace above a liquid sample. The natural unit is a mole fraction (ppmv), interchangeable with mole fraction for an ideal gas; the underlying physical quantity is partial pressure pH2p_{H_2}. Gas-phase H2 is the fastest-moving form near the surface: it diffuses through soil roughly 3–4× faster than methane and 4–5× faster than CO2, equilibrates with the atmosphere in hours to days, tracks weather fronts within minutes, and is sensitive to any wet-soil cap (Environmental covariance, Soil-gas surveys).

Aqueous-phase (dissolved) H2 is the same molecule surrounded by water: groundwater, formation brine, porewater, spring water. The unit is a molar concentration CaqC_{aq} (mol/L), almost always reported in nanomolar (nM) or micromolar (µM) because H2 dissolves poorly. It moves on the clock of groundwater flow and microbial metabolism (days to years), and its steady-state value is set less by the arriving flux than by how fast the local microbial community consumes it.

Why a real play produces both at once. A deep H2 source (serpentinization, radiolysis, deep degassing; see Geologic context) exchanges with any water it touches as it migrates: dissolving into saturated intervals, exsolving back to free gas where pressure drops. A single play shows up as free gas under a caprock, a dissolved-H2 halo in crossed groundwater, and gas bubbling from springs. Treating one phase as “the” signal is a real blind spot: at the FF4 seep site in Western Australia, dry soil-gas monitoring recorded seasonal peaks of only 52–493 ppm while the same site’s shallow groundwater, agitated to strip its dissolved gas, degassed up to 1,684 ppm, more than three times the highest dry-soil reading, because a saturated near-surface zone trapped and carried H2 the dry-soil sensor never saw [10]. A program that only ever probes dry ground can miss most of the true near-surface signal at a wet site.

Table 1: the core contrast

Gas-phase (soil gas / mud gas / headspace)Aqueous-phase (dissolved H2)
What you’re really measuringPartial pressure pH2p_{H_2}Molar concentration CaqC_{aq}
Everyday unitppmv, vol %, %LELnM, µM (rarely mg/L, only near saturation)
Typical exploration range~1 ppm (soil-gas anomaly threshold) to tens of vol % (wellhead gas)~0.05 nM (biological floor) to low µM (near-source, high-flux)
Mainly controlled byPhysics: diffusion, weather-driven advection, soil-moisture cappingBiology: microbial redox appetite (mainly); deep-source equilibrium (secondarily)
Responds on a timescale ofHours–daysDays–years
A “high” reading meansStrong local flux and/or a weak barrier, right nowA weak or absent local microbial sink, or a flux overwhelming a normal sink
A “low” reading meansWeak flux, strong sink, or transport barrier (ambiguous which)An actively consuming, low-redox community; does not rule out a strong deep source
Common field artifactsBarometric swings, drilling-induced H2, rainfall capping, diurnal cycleDegassing during ascent, air contamination, steel-casing corrosion H2

At equilibrium, the amount of a gas dissolved in a liquid is proportional to that gas’s partial pressure in contact with the liquid (the sealed-soda-bottle relationship): double the gas pressure, double the dissolved concentration.

Caq=kH pH2C_{aq} = k_H\, p_{H_2}

where CaqC_{aq} is aqueous molar concentration (mol/L), pH2p_{H_2} is the H2 partial pressure (atm), and kHk_H is the Henry’s-law solubility constant, specific to H2 and to the water’s temperature and salinity. For H2 in fresh water at 25 °C, the NIST value is

kH≈7.8×10−4 mol kg−1 bar−1≈7.8×10−4 mol L−1 atm−1 (dilute solution) [1]k_H \approx 7.8\times10^{-4}\ \mathrm{mol\,kg^{-1}\,bar^{-1}} \approx 7.8\times10^{-4}\ \mathrm{mol\,L^{-1}\,atm^{-1}}\ \text{(dilute solution)}\ [1]

close to an independent value of 8.13×10−48.13\times10^{-4} M/atm, and sometimes given in reciprocal form as kH−1≈1,282 L atm mol−1k_H^{-1}\approx1{,}282\ \mathrm{L\,atm\,mol^{-1}} (1/(7.8×10−4)=1,282.11/(7.8\times10^{-4}) = 1{,}282.1) [1]. That reciprocal answers an intuitive question: it would take about 1,282 liters of water to hold one mole of dissolved H2 in equilibrium with 1 atm of H2 gas. Sander’s compilation of Henry’s-law constants for >4,600 species is the reference for this class of number [2].

The dimensionless partition ratio. kHk_H carries awkward units, so it is often re-expressed as a unitless concentration ratio HccH_{cc}. Two reciprocal conventions exist; be explicit about which:

Hcc(gas/aq)=CgasCaq=1kHRT,Hcc(aq/gas)=CaqCgas=kHRTH_{cc}^{(gas/aq)} = \frac{C_{gas}}{C_{aq}} = \frac{1}{k_H R T}, \qquad H_{cc}^{(aq/gas)} = \frac{C_{aq}}{C_{gas}} = k_H R T

Using R=0.082057 L atm mol−1 K−1R = 0.082057\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}} (the CODATA-exact 8.314462618 J mol−1 K−18.314462618\ \mathrm{J\,mol^{-1}\,K^{-1}} [11]) at T=298.15T = 298.15 K: kHRT=(7.8×10−4)(24.466)=0.01908k_H R T = (7.8\times10^{-4})(24.466) = 0.01908, so Hcc(gas/aq)≈52.4H_{cc}^{(gas/aq)} \approx 52.4 and Hcc(aq/gas)≈0.0191H_{cc}^{(aq/gas)} \approx 0.0191 (25 °C, dilute freshwater).

kHk_H is a variable, not a constant. The 7.8×10−47.8\times10^{-4} value is fresh water at 25 °C; two things move it in real field water. Temperature: H2 solubility is non-monotonic, passing through a minimum near 320 K (47 °C) at moderate pressure then rising, with one PWR-water study finding kHk_H change roughly 40% between 290 °C and 330 °C at 20 MPa. Salinity: dissolved salts drive H2 out of solution (salting-out), by the Setschenow relation

log⁡10 ⁣(S0S)=KS msalt\log_{10}\!\left(\frac{S_0}{S}\right) = K_S\, m_{salt}

where S0S_0 and SS are pure-water and brine solubilities. The foundational low-pressure H2-brine dataset is Crozier and Yamamoto (1974) [4]; recent high-pressure work (to 20 MPa, 298–373 K) finds ~15% solubility loss per additional 1 mol/kg NaCl, warning that skipping the correction can exceed 200% error in a brine mass balance [5]. Full treatment: Dissolved H2 in groundwater. Never apply the room-temperature freshwater kHk_H to hot, saline formation water without correcting; the error can be a factor of two or more.

Why the same molecule tells two different stories

Section titled “Why the same molecule tells two different stories”

Henry’s law describes equilibrium, saying nothing about kinetics or what is actively pulling the system away from equilibrium. That gap is why the two phases diagnose different things:

  • Gas-phase is dominated by physical transport. Diffusion (Fick’s law, J=−D ∂C/∂zJ = -D\,\partial C/\partial z), advection from barometric pumping, and a fast biological sink of aerobic H2-oxidizers at the top of the soil column (Environmental covariance). A soil-gas number behaves like a flux proxy, responding in hours to days.
  • Dissolved-phase is dominated by microbial redox kinetics. H2 is the shared fuel (interspecies hydrogen transfer) for essentially every anaerobic respiration strategy in groundwater: denitrifiers, iron- and manganese-reducers, sulfate-reducers, methanogens. Competing guilds draw the dissolved pool down to whatever floor the dominant guild can profit from. The standing concentration is a microbially imposed steady state, roughly [H2]ss≈Jgeo/(V kbio)[H_2]_{ss} \approx J_{geo}/(V\,k_{bio}) where JgeoJ_{geo} is the deep flux and kbiok_{bio} the microbial removal rate, not a passive readout of a deep source’s partial pressure (full derivation: Dissolved H2 in groundwater).

The redox-indicator ladder. Each successive electron acceptor in the thermodynamic order (oxygen, nitrate, manganese oxide, iron oxide, sulfate, then CO2/methanogenesis) yields less energy per mole of H2, so each guild profits only by tolerating higher standing H2. Lovley and Goodwin showed dissolved H2 in anoxic sediment sorts cleanly by the dominant process [6], later validated in aquifers [7][8]:

Dominant process consuming the H2Dissolved H2 threshold
Manganese(IV) or nitrate reductionbelow 0.05 nM
Iron(III) reductionaround 0.2 nM
Sulfate reduction1–1.5 nM
Methane production (methanogenesis)7–10 nM, broadening to ~15 nM at some field sites

A gas-phase reading has no analog of this ladder: a partial pressure alone says nothing about the redox chemistry of the ground it passed through. A dissolved-H2 number does, almost for free: a sample surviving at 8 nM rather than scavenged below 0.05 nM shows the aquifer’s most energetically generous electron acceptors (oxygen, nitrate, reactive iron/manganese) are exhausted or absent. Dissolved-H2 sensing is not a wetter, more sensitive soil-gas sensing; it reads microbial ecology as a proxy for geochemical history.

All calculations use kH=7.8×10−4 mol L−1 atm−1k_H = 7.8\times10^{-4}\ \mathrm{mol\,L^{-1}\,atm^{-1}} (NIST, 25 °C, dilute freshwater, 1 atm total) [1] unless a correction is stated.

Forward: gas concentration → equivalent dissolved concentration. Water in equilibrium with 100 ppmv H2 gas:

pH2=100×10−6 atm=1.00×10−4 atmp_{H_2} = 100\times10^{-6}\ \mathrm{atm} = 1.00\times10^{-4}\ \mathrm{atm} Caq=kH pH2=(7.8×10−4)×(1.00×10−4)=7.8×10−8 mol/L≈78 nM (≈0.16 μg/L)C_{aq} = k_H\, p_{H_2} = (7.8\times10^{-4}) \times (1.00\times10^{-4}) = 7.8\times10^{-8}\ \mathrm{mol/L} \approx 78\ \mathrm{nM}\ (\approx 0.16\ \mu\mathrm{g/L})

The alternate kH=8.13×10−4k_H = 8.13\times10^{-4} gives 81 nM, so “≈80 nM” is a fair anchor. That 78 nM sits above the entire TEAP range (top ~7–10 nM), so water in simple physical equilibrium with a 100 ppm gas anomaly, with zero microbial drawdown, would already read as an outlier for almost any biologically active aquifer. This is the arithmetic proof that a program measuring single-digit nM dissolved H2 at a confirmed 100+ ppm soil-gas site is not looking at a broken sensor; it is looking at a microbial community holding the aqueous pool far below its equilibrium ceiling.

Reverse: dissolved concentration → equivalent gas-phase partial pressure, pH2=Caq/kHp_{H_2} = C_{aq}/k_H:

CaqC_{aq} measuredWhat it means geochemicallyEquivalent equilibrium pH2p_{H_2}How that compares
0.05 nMTEAP floor: nitrate/Mn(IV) reduction6.4×10−86.4\times10^{-8} atm ≈ 0.064 ppmBelow the ~0.53 ppm atmospheric background
0.2 nMIron(III) reduction2.6×10−72.6\times10^{-7} atm ≈ 0.26 ppmAbout half of atmospheric background
1.5 nMSulfate reduction (upper bound)1.9×10−61.9\times10^{-6} atm ≈ 1.9 ppmJust above the ~1 ppm soil-gas anomaly threshold
10 nMMethanogenesis onset1.3×10−51.3\times10^{-5} atm ≈ 12.8 ppm~24× atmospheric background
15 nMMethanogenesis, upper end1.9×10−51.9\times10^{-5} atm ≈ 19.2 ppmFour orders below a percent-level free-gas anomaly
78 nMEquilibrium with a 100 ppm soil-gas anomaly (above)1.0×10−41.0\times10^{-4} atm = 100 ppm, by construction—
0.78 mMSaturation at 1 atm pure H2 gas, 25 °C1 atm = 1,000,000 ppmMatches the reported 1.6 mg/L “hydrogen water” ceiling [3]

The methanogenesis row sets the practical ceiling: even the top of the biologically plausible range (≈15 nM) corresponds to only ~19 ppm equilibrium gas pressure, a modest anomaly, not the tens-of-percent wellhead concentrations exploration cares about. This is why dissolved H2 should never be read as a resource-size or flux-magnitude proxy: a well at the top of the biologically achievable range is, by mass balance, indistinguishable from equilibrium with a trivial few-tens-of-ppm source. The diagnostic value is which TEAP rung it sits on, not its size.

Counter-example: past the microbial ceiling. At FF4, the agitated-groundwater headspace method (a fast field grab, not a careful equilibrium bubble-strip) measured up to 1,684 ppm H2 degassing from shallow (~1 m), highly saline (77,000 ppm TDS) groundwater [10]. Treating that as roughly an equilibrium partial pressure:

Caq≈(7.8×10−4)×(1.684×10−3 atm)≈1.3×10−6 mol/L=1.3 μM (1,300 nM)C_{aq} \approx (7.8\times10^{-4}) \times (1.684\times10^{-3}\ \mathrm{atm}) \approx 1.3\times10^{-6}\ \mathrm{mol/L} = 1.3\ \mu M\ (1{,}300\ nM)

roughly 130× the top of the methanogenesis threshold, an unambiguous sign this water traps and carries a large flux the dry-soil probe missed. Two caveats push toward caution: 77,000 ppm TDS is ~1.3–1.5 mol/kg NaCl-equivalent, so salting-out suppresses true solubility 20–25% and the back-calculation is if anything an underestimate; and rapid agitation is not a controlled bubble-strip, so the ppm is better read as strong qualitative confirmation than a precise partial pressure (Dissolved H2 in groundwater).

Why headspace stripping works. For a sealed vial with equal water and headspace volumes and Hcc(gas/aq)≈52.4H_{cc}^{(gas/aq)} \approx 52.4, the fraction of total H2 ending in the gas after shaking to equilibrium is

fgas=Hcc VgasHcc Vgas+Vwater=52.452.4+1≈0.981 (98.1%)f_{gas} = \frac{H_{cc}\,V_{gas}}{H_{cc}\,V_{gas} + V_{water}} = \frac{52.4}{52.4 + 1} \approx 0.981\ (98.1\%)

so shaking a water sample with an equal-volume headspace moves ~98% of its dissolved H2 into the gas phase, where a cheap gas sensor can read it. This is the basis of the EPA headspace-equilibration technique and the FF4 field method [10], and why “strip it into a headspace, then use a gas sensor” is the dominant practical answer for dissolved H2.

Unit-conversion anchors. At 25 °C and 1 atm, Vm=RT/P=24.47 L/molV_m = RT/P = 24.47\ \mathrm{L/mol}, so for H2 (M=2.016 g/molM = 2.016\ \mathrm{g/mol}): Cmg/m3=ppmv×2.016/24.47=ppmv×0.0824C_{mg/m^3} = \mathrm{ppmv}\times2.016/24.47 = \mathrm{ppmv}\times0.0824.

Gas-phase H2mg/m³ (25 °C, 1 atm)Equivalent dissolved CaqC_{aq} (freshwater, 25 °C)
0.53 ppm (atmospheric background)0.044 mg/m³0.41 nM
1 ppm (minimum soil-gas anomaly threshold)0.082 mg/m³0.78 nM
100 ppm8.24 mg/m³78 nM
40,000 ppm = 4 vol% (LEL)3,296 mg/m³31.2 µM
1,000,000 ppm = 100%82,400 mg/m³0.78 mM (saturation)

The LEL row is worth sitting with: water in equilibrium with an explosive 4 vol% headspace holds only ~31 µM dissolved H2, three to four orders below saturation yet still ~2,000–3,000× above the top of the TEAP ladder. That is the bridge between the safety world (4 vol% matters; see Standards & regulations) and the redox-indicator world (15 nM matters), ranges separated by ~six orders of magnitude, and why a combustible-gas safety sensor and a dissolved-H2 redox microsensor solve different problems. General conversion mechanics: Concentration units.

How this shapes sensor choice and field practice

Section titled “How this shapes sensor choice and field practice”

Default order of operations. A gas-phase soil-gas survey (percussion probe, handheld electrochemical analyzer, grid walking) is cheap, fast, and well validated for first-pass reconnaissance (Soil-gas surveys, decision framework in Sensor selection). Per FF4, a weak dry result at a shallow-water-table site is not evidence of absence; any such site should get a groundwater-headspace or dissolved-H2 follow-up before being written off.

Use dissolved H2 to ask “is this a live system, and what’s eating it?” Placing a result on the TEAP ladder converts presence/absence into a process diagnosis:

  • Sub-nanomolar (nitrate/iron reduction) despite a confirmed nearby gas source: a robust microbial sink is intercepting the flux, and soil gas elsewhere may under-read it.
  • Methanogenic levels (5–15+ nM) with elevated dissolved methane: a weak sink or co-generated biogenic methane; pair with isotope fingerprinting before calling the H2 geologic.
  • Far above the ladder (hundreds of nM to µM, as at FF4): H2 arriving faster than microbes consume it, a strong positive for an active flux.

Match the sensor to the phase, not the target concentration (Table 2 summarizes the per-family selection discussion):

Table 2: matching measurement to phase

PhaseWhat you measureTypical sensor/methodKey limitation
Free soil gasPartial pressure in pore airElectrochemical handhelds; pellistor/thermal-conductivity for %LEL range (Electrochemical cells, Catalytic pellistors, Thermal conductivity & acoustic sensors)Barometric, drilling, moisture-capping artifacts
Mud gas (drilling)Gas from drilling-fluid returnsH2-capable GC-TCD, wellsite MS, not legacy FID (reads zero H2) (Mud-gas logging)Drill-bit and corrosion H2 can dominate
Headspace / stripped gasH2 partitioned out of a water sampleSame gas sensors as soil gas, applied to the headspace; reduction-gas GC for sub-ppb-equivalent workRequires Henry’s-law + volume-ratio back-calculation for true CaqC_{aq}
Dissolved H2, direct in-situAqueous concentration, no extractionClark-type amperometric microsensor (LOD ~300 nM)LOD sits above the whole 0.05–15 nM TEAP ladder
Dissolved H2, bubble-strip/GCBubble equilibrated, then quantified by GCChapelle- or Microseeps-cell + reduction-gas GC (Dissolved H2 in groundwater)Slow (10 min–2 h to equilibrium); artifacts at the signal’s scale
Deep formation water, downholeWater kept above its bubble point at reservoir pressureWireline/formation-tester pressure-preserving samplers (Downhole deployment)Bespoke, single-well; no off-the-shelf downhole sensor

For a drilling program, run mud-gas logging (real-time, gas-phase, whole-wellbore) and a pressure-preserved formation-water sample (point-in-time, aqueous-phase) as complements: the water sample is the only way to learn whether a target interval sits near its bubble point, itself a prospectivity indicator. Budget QA/QC into every phase (Calibration & QA/QC, Reading the specs).

QuantityValueWhat it’s for
kHk_H (H2, fresh water, 25 °C)7.8×10−4 mol L−1 atm−17.8\times10^{-4}\ \mathrm{mol\,L^{-1}\,atm^{-1}}The Henry’s-law constant: Caq=kH pH2C_{aq}=k_H\,p_{H_2}
kH−1k_H^{-1}≈1,282 L·atm/molLiters of water to hold 1 mol dissolved H2 at 1 atm equilibrium
Hcc(gas/aq)H_{cc}^{(gas/aq)}≈52.4Gas-phase concentration is ~52× the aqueous concentration at equilibrium
Headspace stripping efficiency (1:1 vol)≈98.1% of dissolved H2 moves to gasBasis for headspace/bubble-strip sampling
Salting-out~15% solubility loss per mol/kg NaClNever skip a salinity correction for brine
Temperature effectNon-monotonic; up to ~40% swing near reservoir T/PNever skip a temperature correction for hot water
TEAP floor (Mn/NO3⁻ reduction)<0.05 nM ≈ 0.064 ppm-equivalentBottom rung of the redox ladder
TEAP: Fe(III) reduction≈0.2 nM ≈ 0.26 ppm-equivalentSecond rung
TEAP: sulfate reduction1–1.5 nM ≈ 1.9 ppm-equivalentThird rung
TEAP: methanogenesis7–15 nM ≈ 13–19 ppm-equivalentTop rung; ceiling of “biologically ordinary” dissolved H2
Atmospheric background0.53 ppm gas ≈ 0.41 nM dissolved-equivalentFloor below which sampling artifacts become suspect
LEL (4 vol%)40,000 ppm gas ≈ 31.2 µM dissolved-equivalentSafety threshold; ~2,000–3,000× the top of the TEAP ladder
Saturation (1 atm pure H2, 25 °C)0.78 mM ≈ 1.6 mg/LCeiling for freshwater dissolved-H2 at surface pressure
Full reference list (11 entries)

[1] NIST WebBook, “Hydrogen” — Henry’s-law constant data (k°H ≈ 0.00078 mol kg⁻¹ bar⁻¹; alternate literature value 8.13×10⁻⁴ M/atm; reciprocal 1,282 L·atm/mol). https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=10

[2] Sander, R., “Compilation of Henry’s law constants (version 4.0) for water as solvent,” Atmospheric Chemistry and Physics 15:4399–4981 (2015). DOI: 10.5194/acp-15-4399-2015. https://acp.copernicus.org/articles/15/4399/2015/

[3] Molecular Hydrogen Institute, “Concentration and Solubility of H2” (saturation ≈1.6 mg/L / 1.6 ppm / 0.8 mM at 1 atm/room temperature). https://molecularhydrogeninstitute.org/concentration-and-solubility-of-h2/

[4] Crozier, T.E., Yamamoto, S., “Solubility of hydrogen in water, sea water, and sodium chloride solutions,” Journal of Chemical & Engineering Data 19(3):242–244 (1974). https://pubs.acs.org/doi/10.1021/je60062a007

[5] Chabab, S., Théveneau, P., Coquelet, C., Corvisier, J., Paricaud, P., “Measurements and predictive models of high-pressure H2 solubility in brine (H2O+NaCl) for underground hydrogen storage application,” International Journal of Hydrogen Energy 45:32206–32220 (2020). https://www.sciencedirect.com/science/article/abs/pii/S0360319920332195

[6] Lovley, D.R., Goodwin, S., “Hydrogen concentrations as an indicator of the predominant terminal electron-accepting reactions in aquatic sediments,” Geochimica et Cosmochimica Acta 52(12):2993–3003 (1988). https://www.sciencedirect.com/science/article/abs/pii/0016703788901639

[7] Lovley, D.R., Chapelle, F.H., Woodward, J.C., “Use of Dissolved H2 Concentrations To Determine Distribution of Microbially Catalyzed Redox Reactions in Anoxic Groundwater,” Environmental Science & Technology 28(7):1205–1210 (1994). https://pubs.acs.org/doi/abs/10.1021/es00056a005

[8] Chapelle, F.H. et al., “Deducing the Distribution of Terminal Electron-Accepting Processes in Hydrologically Diverse Ground Water Systems,” Water Resources Research 31(2):359–371 (1995). https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/94WR02525

[9] Chapelle, F.H., Vroblesky, D.A., Woodward, J.C., Lovley, D.R., “Practical Considerations for Measuring Hydrogen Concentrations in Groundwater,” Environmental Science & Technology 31(10):2873–2877 (1997). https://www.usgs.gov/publications/practical-considerations-measuring-hydrogen-concentrations-groundwater

[10] “A natural hydrogen seep in Western Australia: Observed characteristics and controls,” Science and Technology for Energy Transition (STET), article stet20240139 (2024). https://www.stet-review.org/articles/stet/full_html/2024/01/stet20240139/stet20240139.html

[11] NIST/CODATA, “Molar gas constant” — R = 8.314462618 J mol⁻¹ K⁻¹ (exact, 2019 SI redefinition). https://physics.nist.gov/cgi-bin/cuu/Value?r