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Impact of hydrogen addition, up to 20 % (mol/mol), on the thermodynamic ($p$, $\rho$, $T$) properties of a reference high-calorific natural gas mixture with significant ethane and propane content

T0 review · 0 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read High-precision density data on ethane-rich natural gas with 10% and 20% hydrogen show that all three reference equations of state predict densities less accurately than for methane-dominant gas, deviating up to 0.44% at low temperatures…

desk verdict Solid new density data for H2-enriched high-calorific natural gas; the central EoS-degradation claim holds, with a minor compressibility inconsistency to fix. read the letter →

arxiv 2506.01082 v1 pith:RX5HWBMZ submitted 2025-06-01 physics.chem-ph

Daniel Lozano-Martín , Heinrich Kipphardt , Peyman Khanipour , Dirk Tuma , Alfonso Horrillo , César R. Chamorro This is my paper
classification physics.chem-ph PACS 51.30.+i
keywords hydrogen-enrichednaturalgassingle-sinkerdensimeterdensityequationofstateGERG-2008AGA8-DC92gravimetricmixturepreparationisothermalcompressibility
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

This paper reports new high-precision density measurements for a synthetic high-calorific natural gas containing 85% methane, 9% ethane, and 3% propane, plus two hydrogen-enriched derivatives with 10% and 20% hydrogen. The measurements, made with a single-sinker densimeter at 260 to 350 K and pressures up to 20 MPa, are compared with three reference equations of state: AGA8-DC92, GERG-2008, and an improved GERG-2008. The central finding is that all three models predict densities less accurately for these ethane- and propane-rich mixtures than for the methane-dominant mixtures studied earlier, with deviations growing at low temperature and high pressure and reaching 0.44% for GERG-2008 on the 10% hydrogen mixture. This matters because custody transfer, pipeline operation, and hydrogen-grid blending rely on these equations to convert pressure and temperature into density and energy content; if the models overstate their accuracy on realistic heavier natural gas, billing and capacity calculations inherit the error.

What carries the argument

The load-bearing instrument is a single-sinker magnetic-suspension densimeter, whose density equation combines sinker buoyancy with corrections for a force-transmission error split into an apparatus-specific factor and a fluid-specific magnetic-susceptibility term. The mixtures themselves are the other carrier of the argument: they were prepared gravimetrically under ISO 6142-1 and validated by gas chromatography, so the composition is known to roughly 0.001 to 0.005 mol% and the density deviations cannot be blamed on preparation. The three equations of state — AGA8-DC92, GERG-2008, and an improved GERG-2008 built from updated pure-fluid and binary departure functions — supply the predictions against which the measured densities are compared. The statistical engine is a set of relative-deviation metrics (AARD, BiasRD, RMSRD, MaxRD) computed at every state point.

What would settle it

Measure the same three gravimetric mixtures in a two-sinker densimeter, which compensates adsorption effects, or after repeated evacuation and flushing at 260 K and pressures from 1 to 20 MPa; if the 0.2 to 0.44% deviations persist, they are true equation-of-state errors, while if they shrink, part of the reported deviation is a sorption artifact.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is a documented accuracy boundary: all three reference equations of state perform worse for a high-calorific natural gas with significant ethane (9%) and propane (3%) content than for the methane-rich (>97%) gas tested in the companion study, both with and without hydrogen addition. For the hydrogen-free mixture G 432, AGA8-DC92 stays within its claimed 0.1% uncertainty except near 260 K and 2 to 10 MPa, while GERG-2008 and the improved GERG-2008 deviate up to 0.21% and 0.28%. For the 10% hydrogen mixture G 455, GERG-2008 reaches -0.44% and the improved version -0.38%; for the 20% hydrogen mixture G 456, maximum deviations are 0.28% (AGA8-DC92), 0.34% (GERG-2008), and 0.30% (improved GERG-2008). The paper concludes that equation-of-state accuracy decreases for mixtures that deviate from simple methane-rich compositions, especially at lower temperatures and higher pressures.

Load-bearing premise

The argument assumes that gas adsorption and desorption on the densimeter cell walls do not measurably change the sample composition or the measured density, especially at low pressures where the largest relative uncertainties occur.

Editorial extensions

If this is right

  • For custody transfer and pipeline metering, using AGA8-DC92 or GERG-2008 on ethane-rich hydrogen-enriched gas at low temperature and high pressure can produce density errors several times larger than the models' claimed 0.1% uncertainty.
  • The improved GERG-2008 does not fix the problem: on the 10% hydrogen mixture it is among the worse performers, deviating by -0.38% at 260 K near 13 MPa.
  • The new data give reference-quality targets for refitting binary departure functions, particularly for methane-ethane, methane-propane, and hydrogen-heavy-hydrocarbon interactions.
  • AGA8-DC92 remains the most consistent of the three models on these mixtures, but its deviations still grow with hydrogen content, from 0.15% maximum on the hydrogen-free gas to 0.28% on the 20% hydrogen gas.

Reading between the lines

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

  • If the error scales with ethane and propane content, real grid gas (which often contains 5-15% ethane) may be systematically miscalculated; testing intermediate ethane levels would show whether the trend is monotonic.
  • The nonzero low-pressure deviations suggest sorption may contaminate low-density data points; a quantitative sorption correction could shrink the apparent equation-of-state errors.
  • The non-monotonic hydrogen effect (10% hydrogen worse than 20% for the GERG models) hints at cancellation between opposing binary-model errors, which could guide future parameterization of hydrogen and hydrocarbon interactions.
  • Re-analyzing the cell gas composition by gas chromatography after the density runs would reveal whether adsorption or desorption altered the effective mixture, separating experimental artifacts from genuine model deficiencies.
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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

0 major / 6 minor

Summary. The manuscript reports new (p, ρ, T) density measurements for a high-calorific natural gas mixture containing about 9 % ethane and 3 % propane, and for two hydrogen-enriched derivatives with nominal 10 % and 20 % hydrogen content, over the range (260–350) K and pressures up to 20 MPa, using a single-sinker magnetic suspension densimeter. The experimental densities are compared with three equations of state: AGA8-DC92, GERG-2008, and an improved GERG-2008 variant. The central finding is that all three models reproduce the densities of the methane-rich mixtures from the authors' prior work better than those of the ethane/propane-rich mixtures studied here, with maximum deviations reaching 0.44 % for GERG-2008 on the 10 % hydrogen blend. The data tables and uncertainty budgets are presented in detail, and the statistical comparison with earlier literature is systematic.

Significance. The paper provides valuable reference-quality density data for hydrogen-enriched natural gas with realistic heavier-hydrocarbon content, a topic of direct relevance to EoS validation for gas-grid decarbonization scenarios. The mixture preparation follows ISO 6142-1 with independent GC validation; the uncertainty budget (Eqs. 2–3) is detailed; complete data tables are given; and the comparison with the prior methane-rich study is quantitative. The main conclusion is robust: the largest deviations occur at high pressure and low temperature, where they exceed the stated experimental expanded uncertainty by a wide margin, so they cannot be dismissed as measurement noise or as the low-pressure sorption effect discussed in Section 4.1. The compressibility section contains an internal inconsistency (see minor comments) that does not affect the density-based central claim.

minor comments (6)
  1. [Section 4.1] The statement that sorption-induced deviations 'are well below the experimental uncertainty' is not backed by a quantitative estimate; the paper correctly states that the single-sinker densimeter cannot quantify this influence, so this sentence should be reworded as an explicit assumption or supported by an order-of-magnitude estimate based on the Richter and Kleinrahm analysis.
  2. [Section 4.2 and Table 7] The text reports MaxRD values of 1.9 %, 1.6 %, and 1.3 % for the derivative comparisons and then states that 'all deviations are located within the estimated expanded (k = 2) uncertainty of κT, Ur(κT) = 0.7 %'; since the MaxRD values exceed 0.7 %, this is internally inconsistent and needs to be corrected or rephrased.
  3. [Section 4.2] The sentence 'The κT values span from (0.0361 to 0.5427) MPa-1 at 250 K' appears to refer to Table 7, which starts at 260 K; the temperature should be 260 K or the table should include 250 K data.
  4. [Section 4.1 and Table 6] The text uses the abbreviation 'MarRD' where 'MaxRD' is meant, and in Table 6 the GERG-2008 BiasRD entry for G456 appears as '0.003 9' with an awkward line break; these should be fixed.
  5. [Section 3.2] The 'improved GERG-2008' is described as combining updates from references [53] and [54], but the manuscript does not state whether the calculations were performed with REFPROP 10 or a modified in-house code, nor which binary parameters were changed; a short implementation note or reference to the supplement would improve reproducibility.
  6. [Table 1] In the normalized composition block for G456, the rows for nitrogen, carbon dioxide, ethane, and propane appear in an order that does not match the original table; please verify that the values and uncertainties are aligned with the correct components.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central EoS-accuracy claim rests on independent gravimetric density data, not on fitted or self-referential inputs.

full rationale

The measured densities are obtained from a single-sinker densimeter using Eq. (1), where all calibration parameters (sinker volume, counterweights, phi_0, and epsilon_rho) are fixed by prior calibrations rather than fitted to the present (p, rho, T) data. The EoS predictions are computed from independently gravimetrically prepared compositions, so the comparison in Tables 3-6 is a direct residual analysis with no adjustable parameter. The only EoS use within the measurement chain appears in Eq. (3), where REFPROP supplies partial derivatives for uncertainty propagation; this does not alter the measured density values and cannot force the observed residuals. The central conclusion, that all three equations of state perform worse for mixtures with significant ethane and propane content, follows from the residual statistics rather than from any defining relationship between the EoS and the data. Self-citations such as [32] and [45] provide prior calibration data and a comparison dataset, but they are fixed external inputs, not outputs of this work, and the central claim does not reduce to them. The acknowledged sorption effect is a limitation for low-pressure points, whereas the main deviations (up to -0.44%) occur at higher pressures and lower temperatures where the experimental expanded uncertainty is small, so the conclusion is not an artifact of that effect. No circular step was identified.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted in this work. The measurement model (Eq. 1) uses apparatus constants determined in prior publications. The central claim relies on standard uncertainty propagation, cubic spline interpolation, and the validity of the reference EoS models as implemented in REFPROP 10.

assumptions (4)
  • domain assumption Validity of force transmission error correction
    Eq. 1 includes the apparatus-specific constant epsilon_rho determined in [45] for oxygen-containing mixtures; the paper assumes it applies to hydrogen-rich hydrocarbons and that the fluid-specific term is negligible for diamagnetic fluids (Section 2.2).
  • domain assumption Accuracy of gravimetric mixture preparation
    The compositions in Table 1 are accepted as accurate based on ISO 6142-1 and GC validation (Section 2.1).
  • standard math Cubic spline interpolation yields reliable derivatives
    Isothermal compressibility in Table 7 is derived by spline interpolation of density vs pressure (Section 4.2).
  • domain assumption EoS implementations in REFPROP are correct
    REFPROP 10 is used to compute density derivatives for uncertainty propagation and to calculate mixture properties (Section 3.1).

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Cite this review

Pith. "Pith review of Impact of hydrogen addition, up to 20 % (mol/mol), on the thermodynamic ($p$, $\rho$, $T$) properties of a reference high-calorific natural gas mixture with significant ethane and propane content." pith.science (2026). https://pith.science/paper/RX5HWBMZ

@misc{pith2026250601082,
  author       = {Pith},
  title        = {Pith review of: Impact of hydrogen addition, up to 20 % (mol/mol), on the thermodynamic ($p$, $\rho$, $T$) properties of a reference high-calorific natural gas mixture with significant ethane and propane content},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RX5HWBMZ}},
  note         = {Machine review of arXiv:2506.01082}
}
read the original abstract

Injecting hydrogen into the natural gas grid supports gradual decarbonization. To check the accuracy of equations of state for hydrogen-enriched natural gas mixtures, precise density data from well-characterized reference mixtures are essential. In a prior study, we provided experimental measurements for a natural gas constituted mainly of methane and for two derived hydrogen-enriched mixtures. In the present study, being the second and final part of our investigation, density measurements for a high-calorific natural gas with significant ethane and propane content, along with two hydrogen-enriched variants (10 and 20 mol-% hydrogen) are provided. The mixtures are gravimetrically prepared following ISO 6142-1. Density measurements, conducted with a single-sinker densimeter at temperatures from (260-350) K and pressures up to 20 MPa, are compared with three equations of state: AGA8-DC92, GERG-2008, and an improved GERG-2008. Results indicate that all models perform better for methane-dominant mixtures than for those containing heavier hydrocarbons.

Figures

Figures reproduced from arXiv: 2506.01082 by the authors.

Figure 1
Figure 1. p, T-phase diagram with experimental points () and the calculated phase envelope (solid line) using the improved GERG EoS [52–54] for: a) NG mixture G 432 (H2-free), b) H2NG mixture G 455 (10 % H2), and c) H2NG gas mixture G 456 (20 % H2). The marked temperature and pressure ranges indicate the validity of the AGA8-DC92 EoS [19] and GERG-2008 EoS [20,21], as well as the area of interest for the gas industry. 0 10 2… view at source ↗

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Pith tools

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