Engineering & Science
Herning-Zipperer Rule: Multicomponent Natural Gas Mixture Viscosity Formula
Calculate multicomponent hydrocarbon & flue-gas mixture viscosity μ_m = Σ(y_i * μ_i * SQRT(M_i)) / Σ(y_i * SQRT(M_i)) using square-root molecular weights.
Industry-standard pipeline viscosity rule when binary collision parameters aren’t tabulated!
Fritz Herning and Ludwig Zipperer (1936) simplified Wilke’s N^2 binary matrix into a single O(N) vector summation that natural-gas pipeline and flare-header engineers still rely on daily: weight each component’s pure gas viscosity μ_i by y_i * SQRT(M_i) (where M_i is molecular weight in g/mol), then divide by Σ(y_i * SQRT(M_i))!
Model a 3-component sales gas stream of 85% Methane (M = 16.04, μ = 11.0 μPa·s), 10% Ethane (M = 30.07, μ = 9.5 μPa·s), and 5% CO2 (M = 44.01, μ = 14.8 μPa·s): Σ(y_i * SQRT(M_i)) = 4.2843 and Herning-Zipperer mixture viscosity is μ_m = 11.102 μPa·s—climbing to 12.364 μPa·s in a sour/high-CO2 stream (60% CH4, 10% C2H6, 30% CO2)!
| Gas Stream Composition (CH4 / C2H6 / CO2) | Denominator Σ y_i√M_i | Herning-Zipperer μ_m (μPa·s) | Pipeline Application |
|---|---|---|---|
| 85% CH4, 10% C2H6, 5% CO2 | 4.2843 | 11.102 μPa·s | Pipeline sales gas Reynolds number |
| 60% CH4, 10% C2H6, 30% CO2 | 4.9457 | 12.364 μPa·s | High-CO2 acid gas gathering |
| Mole Fractions Σ y_i <> 1 | Error Guard | "Mole Fractions Must Sum to 1" | Mass-Balance Audit |
Herning-Zipperer Multicomponent Gas Mixture Viscosity μ_m (μPa·s)
Divides SUM(E2:E4) = Σ(y_i * μ_i * SQRT(M_i)) by SUM(F2:F4) = Σ(y_i * SQRT(M_i)), enforcing Σ y_i = 1.
=IF(ABS(SUM(B2:B4) - 1) > 0.0001, "Mole Fractions Must Sum to 1", ROUND(SUM(E2:E4) / SUM(F2:F4), 3))Square-Root Molecular-Weight Normalization Factor Σ(y_i * SQRT(M_i))
Reports the mixture’s √M-weighted denominator SUM(F2:F4).
=IF(ABS(SUM(B2:B4) - 1) > 0.0001, "Mole Fractions Must Sum to 1", ROUND(SUM(F2:F4), 4))Try the example
Use the original values or change them to test your understanding.