kunz_2012

O. Kunz and W. Wagner, “The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004”, J. Chem. Eng. Data 57, 3032 (2012)

Source record · Catalogue · Review register

DOI: 10.1021/je300655b

Source kind: fit

Recorded technique: Fit: the GERG-2008 multi-fluid mixture model (the basis of ISO 20765-2/3) for 21 components: reduced Helmholtz energy = ideal-mixture part + sum of x_i times each component’s residual part + departure functions, with binary reducing functions for density and temperature (beta_v, gamma_v, beta_T, gamma_T), fitted to mixture p-rho-T, caloric and phase-equilibrium data.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Identity VALIDATED by the library. Printed page = pdf page + 3031 (checked on the rendered pages, 2026-09-30). The library’s text garbles Eqs. (42), (43) and (45) (‘E_ij’, ‘f_ij’, Delta alpha on both sides); the page prints F_ij alpha^r_ij(delta, tau). A small misprint in the original, ‘Delta alpha^r_ij = Delta alpha^r_gen’ (p. 3047), affects no parameter.

THE FORM (checked by a reader against the pages): the general multi-fluid model, Eqs. (1)-(7) (§2.2.1, p. 3035), Eq. (7) alpha^r = sum x_i alpha^r_oi + Delta alpha^r; the working form, Eqs. (8)-(11) (p. 3040), with the departure term sum x_i x_j F_ij alpha^r_ij; the reducing functions, Eqs. (16)-(17) (p. 3041), their general forms Eqs. (34)-(35) and the Lorentz-Berthelot limit Eqs. (37)-(38) (pp. 3045-3046). ‘The models default to the fundamental equation used for the respective substance’ (§2.2, p. 3034). GERG-2008’s own pure-fluid equations are 12-24-term technical equations (Table 1, p. 3033; O2 valid 54-303 K); CoolProp combines the binary parameters with the reference pure-fluid equations instead.

COMPONENTS (p. 3032; Table 1, p. 3033): methane, nitrogen, CO2, ethane, propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, CO, water, H2S, helium and argon.

BINARY PARAMETERS (Table A8, pp. 3077-3080, beta_v, gamma_v, beta_T, gamma_T; F_ij from Table A6, p. 3075): N2-O2 0.999521770, 0.997082328, 0.997190589, 0.995157044; N2-Ar 1.004166412, 1.002212182, 0.999069843, 0.990034831; O2-Ar 0.999746847, 0.993907223, 1.000023103, 0.990430423; N2-He 0.969501055, 0.932629867, 0.692868765, 1.471831580; CO2-Ar 1.008392428, 1.029205465, 0.996512863, 1.050971635 (fitted reducing functions, no departure function); N2-CO2 with a binary-specific departure function (F = 1). He-Ar, He-O2, He-H2, He-CO, Ar-H2, H2-O2 and O2-CO: all four parameters 1 and no departure function, the Lorentz-Berthelot pairs (grey in Fig. 1, p. 3039). For pairs with poor data ‘either the parameters of the reducing functions were set to unity or the linear combining rules’ were used (p. 3048); ‘for many mixtures containing oxygen, argon, and helium, no suitable data are available’ (p. 3039), and for combining-rule pairs ‘the uncertainty is basically considered to be unknown’ (p. 3044). CoolProp’s N2-O2 parameters are these (under the key Gernert-Thesis-2013, which kept them); its He-Ar, He-Ne and Ne-Ar are Tkaczuk et al.’s; its N2-Ar and O2-Ar are Gernert’s refits.

THE SECOND VIRIAL: no quadratic mixing rule for B is stated; B enters only through Table B1 (p. 3081), as the low-density limit of the residual part. The model’s B is not quadratic in composition in general (as Gernert, §5.2.4, shows).

STATED UNCERTAINTY (Table 6, p. 3045, gas-phase density of binaries at p <= 30 MPa): with a binary-specific departure function 0.1 % (1.2 <= T/T_r <= 1.4 and 1.4-2.0); generalized departure function 0.1-0.2 % and 0.1 %; fitted reducing functions only 0.5-1 % and 0.3-0.5 %, the similar pairs such as N2-O2, N2-Ar and O2-Ar ‘often near the lower value’ (p. 3044). Near ambient the N2-O2-Ar pairs have T/T_r of about 1.6-2.8, largely above the table. For air, 0.1-0.2 % to 900 K and 90 MPa (pp. 3044, 3080); the outlook proposes a departure function for the air pairs (p. 3080). Nothing transcribed.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

No formulas are recorded.

Corrections

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.