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REVIEW 5 major objections 7 minor 54 references

Modeling and Simulation of Coupled Biochemical and Two-Phase Compositional Flow in Underground Hydrogen Storage

T0 review · 5 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that bio-geochemical reactions must be coupled into underground hydrogen storage flow models, because methanogenic microbes can turn about 10% of stored hydrogen into methane at literature microbial densities and up to…

desk verdict A useful modeling integration with a sign error in the microbial source term that makes the reported H2 loss numbers untrustworthy as written. read the letter →

arxiv 2506.02582 v1 pith:KR3DLLEQ submitted 2025-06-03 physics.comp-ph math-phmath.MP

Elyes Ahmed , Brahim Amaziane , Salaheddine Chabab , Stéphanie Delage Santacreu , Guillaume Galliéro , Olav M{o}yner , Xavier Raynaud This is my paper
classification physics.comp-phmath-phmath.MP
keywords undergroundhydrogenstoragemethanogenicarchaeadoubleMonodkineticscompositionaltwo-phaseflowSøreide-Whitsonequationofstatesolubilityinbrinebio-cloggingreservoirsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish that bio-geochemical reactions, not just physical trapping and dissolution, control how much injected hydrogen can be recovered from porous underground storage. It builds a two-phase, multicomponent flow model in which the growth and decay of methanogenic archaea is coupled to the mass balance of every chemical species, so that hydrogen and carbon dioxide consumed by the microbes become methane and water. The model is thermodynamically calibrated with a brine-aware equation of state that reproduces measured H$_2$ and CO$_2$ solubility, which matters because microbes can only eat hydrogen that is dissolved in the water phase. In storage-cycle simulations the framework predicts roughly 10% hydrogen loss at microbial densities reported in the literature and up to roughly 47% at higher densities, along with methane contamination of the produced gas. If these numbers are right, any assessment of underground hydrogen storage that ignores microbial activity will overestimate recoverable hydrogen and underestimate purity risks.

What carries the argument

The load-bearing object is the double Monod growth law coupled through a source term to an overall-composition two-phase flow model. The growth rate is $\psi_{\mathrm{growth}} = \psi_{\mathrm{growth}}^{\max} \dfrac{X_{l,\mathrm{H}_2}}{l_{\mathrm{H}_2} + X_{l,\mathrm{H}_2}} \dfrac{X_{l,\mathrm{CO}_2}}{l_{\mathrm{CO}_2} + X_{l,\mathrm{CO}_2}}$, with the microbial population normalized by its initial density so the equations stay well conditioned, and the species source term proportional to $\psi_{\mathrm{growth}} N S_l / Y_{\mathrm{H}_2}$. The thermodynamic backbone is the Søreide-Whitson equation of state, a Peng-Robinson variant with salt-dependent $\alpha$ functions and phase-specific binary interaction parameters, implemented so that H$_2$ and CO$_2$ dissolve into brine at experimentally measured levels; without this, the microbial source term is starved. Bio-clogging closes the loop by reducing porosity and permeability as the population grows, using a critical-density porosity reduction law and a porosity-permeability relation.

What would settle it

A field or core-flood measurement of methanogenic hydrogen consumption in a candidate storage aquifer: if actual consumption at an initial density around $10^8$ cells per cubic meter does not approach the model's roughly 10% loss over the storage cycles, then the kinetic parameters or the assumed density are wrong.

Watch

Extended reading notes

Core claim

The central claim, on the authors' own terms, is that microbial methanogenesis is a first-order process for underground hydrogen storage: once the thermodynamics are fixed with an equation of state that correctly dissolves hydrogen into the aqueous phase, the coupled model predicts that methanogens convert 9.78% of stored hydrogen to methane at $n_0 = 10^8\,\mathrm{m}^{-3}$ in the 3D aquifer case (7.5% in the larger benchmark) and 47.63% at $n_0 = 10^9\,\mathrm{m}^{-3}$, while production efficiency falls from roughly 94.3% to 90.1% at the high density. The same simulations show produced gas becoming methane-contaminated, salinity lowering solubility and shrinking the microbial population only slightly, and bio-clogging altering flow paths and pressure rather than total hydrogen consumption in the well-free cases. The authors present this as evidence that compositionally resolved, bio-geochemically coupled simulation is necessary for screening UHS sites and injection strategies.

Load-bearing premise

The predicted hydrogen-loss percentages depend on the initial microbial density in the reservoir and on laboratory Monod growth parameters being valid at reservoir conditions, neither of which is established by measurements in this paper.

Editorial extensions

If this is right

  • At initial microbial densities reported in the literature, underground storage of hydrogen in porous aquifers loses about 10% of the injected hydrogen to methanogenesis over several cycles, rising to roughly 47% if the initial density is ten times higher.
  • Because much of the consumed hydrogen reappears as methane, produced gas purity, not just total recovered mass, is the main storage-quality risk from microbial activity.
  • Salinity reduces H$_2$ and CO$_2$ solubility by tens of percent and shrinks the microbial population, but in the simulated cases it changes hydrogen loss by less than one percentage point.
  • Bio-clogging reduces porosity and permeability near the growing colony; in the 2D dome case it slightly increases chemical conversion by lengthening residence time, while in the well-free 1D cases it changes pressure and saturation rather than total hydrogen consumption.
  • The choice of equation of state matters: with the standard Peng-Robinson EoS the model predicts slower microbial conversion than with the brine-corrected Søreide-Whitson EoS, because less hydrogen dissolves into the water where microbes live.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The sharp jump in loss between $n_0 = 10^8$ and $10^9\,\mathrm{m}^{-3}$ implies that field screening should treat initial microbial density as an uncertain parameter and report hydrogen loss as a range, not a single value.
  • Because the same stoichiometric source-term structure can be rewritten for sulfate-reducing or homoacetogenic reactions, the framework should generalize to other hydrogen-consuming metabolisms, a direction the authors note is straightforward.
  • If laboratory Monod parameters do not transfer to reservoir conditions, the ordering of losses between different sites could change even though the qualitative conclusion that microbial activity matters would not.
  • A direct thermodynamic test is already available in the paper: the Søreide-Whitson EoS matches experimental H$_2$ solubility within about 3% relative error, whereas Peng-Robinson is off by roughly 90%, so any UHS simulator using an uncorrected cubic EoS will systematically underfeed the microbial model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 7 minor

Summary. The manuscript develops and demonstrates a fully coupled two-phase compositional flow model with microbial methanogenesis in MRST. It implements a Søreide–Whitson EoS for H2/CO2 solubility, a double-Monod model for archaeal growth with linear decay, bio-clogging porosity/permeability reduction, and molecular diffusion. The SW EoS is validated against experimental solubility data (Table 5), and four simulation test cases (1D, 2D, 3D regular, and a large 3D benchmark) examine H2 loss, CH4 production, salinity effects, diffusion, and bio-clogging. The central quantitative claim is that microbial activity can cause roughly 10% H2 loss at literature microbial densities and up to about 47% at higher densities, with methane contamination of the produced gas.

Significance. If correct, the integrated module would be a valuable open quantitative tool for UHS site screening and injection-strategy evaluation. The SW EoS solubility validation is quantitative and convincing (mean errors below 3% for H2 and below 11% for CO2 in Table 5), the simulation setups are described in detail, the reported loss/production numbers are genuine forward outputs rather than fitted targets, and the solver performance metrics in Tables 11 and 13 are practically useful. However, the model equations contain a sign inconsistency in the microbial source term, and the headline loss range depends on inputs whose values are partly outside the cited literature ranges and on unmeasured initial microbial densities. These issues must be resolved before the central claim is fully supported.

major comments (5)
  1. [§2.2, Eq. (6)] Equation (6) has an internal sign inconsistency. With the stated stoichiometric coefficients [γ_H2, γ_CO2, γ_CH4, γ_H2O] = [−4, 1, 1, 2] and the definition γ_i^H2 = n0 γ_i M_i / γ_H2, the source term on the RHS is positive for H2 and negative for CH4, i.e., it produces H2 and consumes CH4, the exact opposite of reaction (1). This contradicts the H2 losses and CH4 production reported in Sections 4.1–4.4. The formula as written therefore cannot be the basis for the simulation results. The authors should correct the stoichiometric vector, the definition of γ_i^H2, or the sign of the source term so that reactants are consumed and products produced, and they should state explicitly which form is implemented in the MRST code.
  2. [§4.1, Table 6 and Table 1] The microbial parameters used in the simulations lie partly outside the literature ranges cited in Table 1. In Table 6, ψ_growth^max = 1.338×10−4 s−1 exceeds the tabulated maximum of 3.009×10−5 s−1 by a factor of about 4.4, b_decay = 1.35×10−6 s−1 exceeds the stated maximum of 1.019×10−6 s−1, and l_H2 = 3.6×10−7 exceeds the tabulated upper value of 3.24×10−7. Since the headline H2 loss in Table 10 changes from 9.78% at n0 = 10^8 to 47.63% at n0 = 10^9, the quantitative loss range is highly sensitive to inputs that are either unmeasured (n0) or outside the cited ranges. A sensitivity analysis over the Table 1 ranges is needed before the conclusion that losses reach 10–47% can be supported.
  3. [§2.3, Eqs. (11)–(12), and §4.1] The bio-clogging model in Section 2.3 depends on the hand-set parameters c_p and N_c. In Section 4.1 the text states 'we set cp = 1 and Nc = 2n0 = 180', but Table 6 gives n0 = 1.0×10^9 m−3, so 2n0 = 2×10^9, not 180; this numerical inconsistency needs correction. No sensitivity analysis or literature calibration is given for c_p or N_c, even though bio-clogging is reported to increase H2 loss (Table 8) and to change pressure and saturation significantly (Figure 3). Please provide a justification or a sensitivity study for these parameters.
  4. [§3.3] The compositional validation with the SW EoS is explicitly not shown: the text states that 'A similar validation using the SW-EoS (not shown) confirmed agreement' with MRST-PR and other commercial simulators, but no quantitative result is presented. Since implementing the SW EoS in the compositional MRST module is a central contribution of this work, this validation should be included as a figure or table with error measures, or replaced by a reference to a published benchmark.
  5. [§2.1 and §4.3.2] The coupled microbial model is not validated against experimental or field data, and the comparison with Khoshnevis et al. (2023) in Section 4.3.2 is qualitative only ('consistent'). Given that the central claim is a quantitative range of hydrogen loss (10–47%), the authors should either benchmark the reactive transport model against measured batch/core data or clearly reframe the results as scenario illustrations rather than predictions.
minor comments (7)
  1. [§4.3.2] Section 4.3.2 describes six simulation cases but then refers to 'the sixth case' for the molecular-diffusion run in pure water; this is actually a seventh case. Please renumber the cases.
  2. [Throughout] Use CH4 instead of C1 for methane throughout, or define C1 explicitly at first use; Table 10 and Section 4.3.2 mix both notations.
  3. [Table 10] In Table 10, the column header 'Molecular Diffusion (m s−2)' is not meaningful; it should be 'on/off' or 'diffusion coefficient (m^2 s^-1)'.
  4. [§2.1 and §4.1] Equation (2) includes a microbial diffusion term, but Section 2.1 states that transport of the microbial population is neglected and Section 4.1 neglects microbial diffusion; please reconcile this inconsistency.
  5. [Throughout] There are several typos, e.g., 'Sreide-Whitson' should be 'Søreide–Whitson' (abstract, Sections 3 and 4), 'we use compare SW and PR EoSs' in Section 4.1, and 'microbiel' in Section 4.4.
  6. [Figure 3] The Figure 3 caption says 'Evolution of molar fractions at three times (top)', but the top panels plot dissolved H2 in the liquid phase versus time; the caption should match the panels.
  7. [Tables 8 and 10] The definition of 'H2 loss' is not given; please state whether it is the consumed fraction of the total or injected H2 and over which time horizon the percentage is computed.

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity in the SW EoS benchmark: BIPs and validation data both come from Chabab et al.; central microbial-loss results remain independent forward simulations.

  1. fitted input called prediction [Section 3.1-3.2, Eq. (18), Table 3, Figures 1-2 and Table 5]
    "Then, the model has been improved by Chabab et al. for CO 2 and H 2 solubilities in water and NaCl brine.(Chabab et al. (2019, 2024)). ... Then, they are compared with the experimental data provided by Chabab et al . (2020, 2019)."

    The 'improved' SW EoS is the Chabab et al. version, and its phase-specific BIPs (Eq. 18, Table 3) are taken from Chabab et al. (2021, 2024). The paper then benchmarks the model against 'experimental data provided by Chabab et al. (2020, 2019)' and figure data 'collected from Chabab et al. (2024)'—the same authors who developed and fitted those BIPs. The quoted SW errors (H2 mean 1.4-3.0%, CO2 mean 2.4-5.7%) therefore check that the implementation reproduces its own calibration data; they are not independent predictions of gas solubility.

full rationale

The derivation chain for the headline results—double Monod growth and decay (Eqs. 2-4), the stoichiometric source term (Eq. 6), compositional transport (Eqs. 7-9), SW phase equilibrium, and bio-clogging (Eqs. 11-12)—is executed in MRST. The microbial kinetic parameters in Table 6 are literature ranges (Table 1), not parameters fitted to the 1D/2D/3D H2-loss outputs, so the 9.78%/47.63% and 7.5%/19.1% losses are genuine forward-simulation results. Benchmarks against Khoshnevis et al. (2023) and Hogeweg et al. (2022) are external, and validation against the CO2-flood benchmark of Voskov and Tchelepi/Møyner is a code-consistency test rather than a self-fulfilling premise. The only material circularity I can exhibit is the SW EoS support: the model version and BIPs come from Chabab et al., and the experimental data used to show agreement are from the same Chabab et al. papers, so the solubility match is a calibration-consistency check. This is partial and supporting, not a collapse of the central claim, so the score is 4. Separately, Eq. (6) as printed appears to have a stoichiometric sign error (with [gamma]=[-4,1,1,2] and gamma_i^{H2}=n0 gamma_i M_i/gamma_H2, the H2 source is positive and CH4 source negative, opposite to reaction (1)); that is a correctness issue rather than a circularity. The strong n0-sensitivity (9.78% vs 47.63%) is parameter uncertainty, not circularity.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

All assumptions and parameters come from cited literature or are hand-set; no new physical entities are introduced. The largest free-input sensitivity is the initial microbial density n0, which changes H2 loss by a factor of about five in Table 10.

free parameters (8)
  • ψ_growth_max (maximum growth rate) = 1.338e-4 s^-1 (Table 6)
    Controls microbial growth speed; taken from the literature range in Table 1, not measured for the simulated reservoirs.
  • b_decay (decay rate) = 1.35e-6 s^-1
    Determines net biomass together with growth; literature-sourced.
  • l_H2 (half-saturation for H2) = 3.6e-7
    Sets the H2 concentration at which growth rate is half-maximal; literature-sourced.
  • l_CO2 (half-saturation for CO2) = 1.98e-6
    Sets the CO2 concentration at which growth is half-maximal; literature-sourced.
  • Y_H2 (yield coefficient) = 3.9e11 mol^-1
    Converts microbial growth into H2 consumption; literature-sourced.
  • n0 (initial microbial density) = 1e9 m^-3 in 1D; 1e8 and 1e9 m^-3 in 3D
    Major sensitivity input: H2 loss changes from 9.78% to 47.63% in Table 10. Not measured in-situ.
  • c_p and N_c (bio-clogging parameters) = c_p = 1, N_c = 2 (text says 2n0 = 180)
    Chosen by hand; the text's 'Nc = 2n0 = 180' is inconsistent with n0 = 1e9 in the same section.
  • SW EoS binary interaction parameters k_ζ,ij = Coefficients in Table 3
    Fitted to solubility data in earlier Søreide-Whitson and Chabab et al. work; reused here as inputs.
assumptions (8)
  • domain assumption Methanogenesis follows stoichiometric reaction 4H2 + CO2 -> CH4 + 2H2O and is the only H2-consuming reaction.
    Eq. (1) and Section 2.1; no sulfate reduction or homoacetogenesis is included despite their potential presence in reservoirs.
  • domain assumption Microorganisms live only in the water phase; advective transport of microbes is neglected, with only liquid-phase diffusion considered.
    Eq. (2) and text on p.6; chemotaxis and microbial advection are omitted.
  • domain assumption Double Monod kinetics with no inhibition terms describe microbial growth and decay.
    Eqs. (3)-(4); parameters come from laboratory cultures, with no reservoir calibration.
  • domain assumption Søreide-Whitson EoS with phase-specific binary interaction parameters is accurate for H2 and CO2 solubility at UHS conditions.
    Section 3; validation is against data partly produced by the same group, and the BIPs were previously fitted to similar data.
  • domain assumption Salinity is constant and brine is treated as a pseudo-component H2O + NaCl, excluded from flash composition.
    Section 3.1 states salinity is a constant input parameter rather than a composition during flash calculations.
  • ad hoc to paper Bio-clogging reduces porosity and permeability according to the empirical formulas in Eqs. (11)-(12).
    Adopted from Eddaoui et al.; the strength parameters c_p and N_c are hand-set for the simulations.
  • standard math Fickian diffusion with Millington-Quirk tortuosity describes molecular transport of components.
    Eqs. (8c) and (9); a standard porous-media transport assumption.
  • standard math Local thermodynamic equilibrium and equality of fugacities hold at each cell.
    Eq. (10c); a standard compositional simulation assumption.

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Cite this review

Pith. "Pith review of Modeling and Simulation of Coupled Biochemical and Two-Phase Compositional Flow in Underground Hydrogen Storage." pith.science (2026). https://pith.science/paper/KR3DLLEQ

@misc{pith2026250602582,
  author       = {Pith},
  title        = {Pith review of: Modeling and Simulation of Coupled Biochemical and Two-Phase Compositional Flow in Underground Hydrogen Storage},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KR3DLLEQ}},
  note         = {Machine review of arXiv:2506.02582}
}
read the original abstract

Integrating microbial activity into underground hydrogen storage models is crucial for simulating long-term reservoir behavior. In this work, we present a coupled framework that incorporates bio-geochemical reactions and compositional flow models within the Matlab Reservoir Simulation Toolbox (MRST). Microbial growth and decay are modeled using a double Monod formulation, with populations influenced by hydrogen and carbon dioxide availability. First, a refined Equation of State (EoS) is employed to accurately capture hydrogen dissolution, thereby improving phase behavior and modeling of microbial activity. The model is then discretized using a cell-centered finite-volume method with implicit Euler time discretization. A fully coupled fully implicit strategy is considered. Our implementation builds upon MRST's compositional module by incorporating the S{\o}reide-Whitson EoS, microbial reaction kinetics, and specific effects such as bio-clogging and molecular diffusion. Through a series of 1D, 2D and 3D simulations, we analyze the effects of microbial-induced bio-geochemical transformations on underground hydrogen storage in porous media.These results highlight that accounting for bio-geochemical effects can substantially impact hydrogen loss, purity, and overall storage performance.

Figures

Figures reproduced from arXiv: 2506.02582 by the authors.

Figure 1
Figure 1. H2 solubility as a function of pressure at different temperatures. Solubility in pure water is modeled using PR and SW equations of state (left), while solubility in saline water is shown using the SW model (right). Data collected from Chabab et al. (2024). 40 60 80 100 120 140 pressure (bar) 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 CO2 molar fraction CO2 solubility in pure water CO2 , Exp CO2 , SW CO2 , … view at source ↗
Figure 2
Figure 2. CO2 solubility along with pressure for different temperatures.CO2 solubility in pure captured with the PR and SW EoS models (left). CO2 solubility in salt water captured with the SW model (right). Data collected from Chabab et al. (2020). 13 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. 1D case: Evolution of molar fractions at three times (top) and mean pressure and saturation (bottom). simulation is around 6.2%. In the water-rich one, all H2 was consumed after 3.5 years [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: 1D case: H2 and CO2 loss vs. CH4 production (%) (top) and dissolved H2 in the liquid phase (bottom), given by the ratio of liquid phase H2 mass to the total H2 mass. 0 1 2 3 4 5 6 Time (years) -100 -50 0 50 100 150 200 Component Change (%) Water-rich case SW PR CH4 CO2…
Figure 5
Figure 5. Figure 5: 1D case: Comparing PR and SW. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Reproduced from Ahmed et al. (2024): (left) 2D aquifer geometry and (right) capillary pressure curves used in the numerical experiments. r = 5, ensuring structural trapping. Symbol Description Caprock Storage zone Bedrock K (mD) Permeability 1.0 × 10−4 10 1.0 × 10−2 Φr…
Figure 7
Figure 7. Figure 7: 2D aquifer: Distribution of microbial (normalized) density and mole fractions after the build-up phase, as well as the first and last injection cycles. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: 2D aquifer: Impact of biochemical transformation on cyclic H2 injection. Porosity 0.1 0.15 0.2 0.25 Permeability 1 2 3 4 5 6 7 8 9 10-15 [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: 2D aquifer: bio-clogging due to biochemical transformation. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Test 3: microbial activity (left) and H2 solubility (right) in the vicinity of the well at the end of the first injection period. 0 100 200 300 400 500 600 700 time (days) 90 95 100 105 pressure (bar) Mean pressure in the pure water reservoir pressure, with archae, n0…
Figure 11
Figure 11. Figure 11: Test 3: evolution of the mean pressure in the reservoir(left). Evolution of total microbial population (right) in a pure water and salt water aquifer (right) during 6 cycles. 0 100 200 300 400 500 600 700 time (days) -5 -4 -3 -2 -1 0 1 H2 Production (kg/day) H2 well r…
Figure 12
Figure 12. Figure 12: Test 3: H2, CO2 and C1 production in the well of the pure water aquifer. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]
Figure 13
Figure 13. Figure 13: H2 loss, CO2 consumption and H2 efficiency production in the well of both pure and salt water aquifer during 6 cycles. 4.4 Test 4: 3D underground hydrogen storage with complex mix￾ture This test case is based on a large-scale 3D benchmark developed by the Institute of…
Figure 14
Figure 14. Figure 14: Test 4: Distribution of microbial population (left) and H2 mole fraction at the end of build-up phase. 1 2 3 4 5 Time (years) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 H2 totMass (kg) 105 no bacteria n0 = 1e8 n0 = 1e9 0 1 2 3 4 5 Time (years) -20 -15 -10 -5 0 5 CO2 totMass (kg) 10…
Figure 15
Figure 15. Figure 15: Test 4: Impact of biochemical transformation on cyclic H2 injection. Total H2 loss amounts for 7.5 % for n0 = 1.0e8 and 19.1% for n0 = 1.0e9. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png]

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    " write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1 'skip if FUNCTION new.block.check...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.