Engineering & Science
Stiel-Thodos High-Pressure & Supercritical Gas Residual Viscosity Formula
Calculate dense-fluid and supercritical CO₂ viscosity η = η_0 + Δη(ρ_r) (µPa·s) across pipelines and compressors using Leonard Stiel & George Thodos’s (1961) reduced-density correlation.
Why ideal kinetic-theory gas viscosity fails completely in supercritical CO₂ and high-pressure natural gas pipelines!
At low pressures, gas viscosity η_0 is independent of pressure—yet inside 100–250 bar supercritical CO_2 pipelines, hydrogen storage tanks, and ethylene compressors (reduced density ρ_r = ρ / ρ_c from 0.1 to 2.0), collisional momentum transfer across finite molecular diameters doubles or quadruples viscosity! Leonard I. Stiel and George Thodos (AIChE Journal, 1961) correlated residual viscosity departure (η - η_0) * ξ_cP = 1.08 × 10^-4 * (EXP(1.439 * ρ_r) - EXP(-1.11 * ρ_r^1.858)) for 0.1 <= ρ_r < 3.0, where ξ_cP = T_c^(1/6) / (M^0.5 * P_c_atm^(2/3)) (multiplied by 1,000 µPa·s/cP)!
Evaluate supercritical CO_2 (T_c = 304.1 K, P_c = 72.8 atm, M = 44.01 g/mol, dilute η_0 = 16.50 µPa·s): at ρ_r = 0.80, dense-fluid viscosity rises +78.3% to 29.42 µPa·s, and at liquid-like supercritical density ρ_r = 1.50 it reaches 57.75 µPa·s!
| Supercritical CO₂ Reduced Density ρ_r = ρ / ρ_c | Residual Departure Δη (µPa·s) | Total Dense Viscosity η (µPa·s) | Pipeline Regime |
|---|---|---|---|
| ρ_r = 0.80 (Near-Critical Compressor) | +12.92 µPa·s | 29.42 µPa·s | +78.3% over dilute η_0 = 16.5 |
| ρ_r = 1.50 (Dense Supercritical Trunkline) | +41.25 µPa·s | 57.75 µPa·s | 3.50× dilute viscosity |
| Invalid ρ_r <= 0 or ρ_r >= 3.0 | Out of Correlation Band | "Outside Stiel-Thodos Density Range" | Validity Guard |
Stiel-Thodos Dense / Supercritical Gas Viscosity η (µPa·s)
Adds residual viscosity departure Δη (µPa·s) to dilute gas viscosity η_0 (B2) from reduced density ρ_r (B3), T_c (B4, K), P_c (B5, atm), and molar mass M (B6, g/mol).
=IF(OR(B2 <= 0, B3 <= 0, B3 >= 3, B4 <= 0, B5 <= 0, B6 <= 0), "Outside Stiel-Thodos Density Range", ROUND(B2 + 1000 * (0.000108 * (EXP(1.439 * B3) - EXP(-1.11 * (B3 ^ 1.858)))) / ((B4 ^ (1 / 6)) / (SQRT(B6) * (B5 ^ (2 / 3)))), 2))Residual Dense-Fluid Viscosity Increment Δη = η - η_0 (µPa·s)
Isolates the high-pressure collisional viscosity departure above dilute kinetic theory.
=IF(OR(B3 <= 0, B3 >= 3, B4 <= 0, B5 <= 0, B6 <= 0), "Outside Stiel-Thodos Density Range", ROUND(1000 * (0.000108 * (EXP(1.439 * B3) - EXP(-1.11 * (B3 ^ 1.858)))) / ((B4 ^ (1 / 6)) / (SQRT(B6) * (B5 ^ (2 / 3)))), 2))Try the example
Use the original values or change them to test your understanding.