Engineering & Science
Pitzer / Lee-Kesler Second-Virial Compressibility Factor Z = Z0 + ω·Z1
Calculate real-gas compressibility factor Z = 1 + (B^0 + ω * B^1) * (P_r / T_r) using Abbott’s Pitzer-virial correlations B^0 = 0.083 - 0.422 / T_r^1.6 and B^1 = 0.139 - 0.172 / T_r^4.2.
Fast non-iterative compressibility Z without solving a cubic equation!
Cubic equations of state require Cardano root-finding or Goal Seek to get Z(T, P)—overkill for moderate-pressure gas pipelines and compressor suction drums! Three-parameter Pitzer / Lee-Kesler corresponding states expands compressibility linearly in acentric factor Z = Z^0 + ω * Z^1, and Michael M. Abbott’s (Smith, Van Ness & Abbott) analytical second-virial equations evaluate Z directly in a single cell: B^0 = 0.083 - 0.422 / T_r^1.6, B^1 = 0.139 - 0.172 / T_r^4.2, and Z = 1 + (B^0 + ω * B^1) * (P_r / T_r)!
Test compressed ethylene gas at T = 323.15 K (50 °C) and P = 15.0 bar (T_c = 282.3 K -> T_r = 1.1447; P_c = 50.4 bar -> P_r = 0.2976; ω = 0.087): B^0 = -0.2569 and B^1 = +0.0415 yield Z = 0.9341 (meaning real ethylene packs 1 / 0.9341 = 7.05% MORE mass into a pipeline than ideal gas P*V = R*T predicts!), relaxing to Z = 0.9956 at 1.0 bar!
| Ethylene Gas Pipeline State (T = 323.15 K, Tr = 1.1447) | Reduced Pressure Pr | Virial B0 & B1 | Compressibility Factor Z |
|---|---|---|---|
| Atmospheric Header (P = 1.0 bar) | 0.0198 | B0 = -0.2569, B1 = 0.0415 | 0.9956 (Nearly Ideal) |
| Medium-Pressure Feed (P = 15.0 bar) | 0.2976 | B0 = -0.2569, B1 = 0.0415 | 0.9341 (-6.59% Volume!) |
| Invalid Temperature (T <= 0 or Tc <= 0) | Domain Guard | "Invalid Virial Inputs" | Requires Positive T, Tc, Pc |
Generalized Pitzer Second-Virial Compressibility Factor Z
Evaluates 1 + ((0.083 - 0.422 / (T/T_c)^1.6) + ω * (0.139 - 0.172 / (T/T_c)^4.2)) * ((P/P_c) / (T/T_c)).
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 <= 0), "Invalid Virial Inputs", ROUND(1 + ((0.083 - 0.422 / ((B2 / B3) ^ 1.6)) + B6 * (0.139 - 0.172 / ((B2 / B3) ^ 4.2))) * ((B4 / B5) / (B2 / B3)), 4))Simple-Fluid Reduced Second Virial Coefficient B^0 = 0.083 - 0.422 / T_r^1.6
Returns dimensionless B^0 = B * P_c / (R * T_c) for spherical simple fluids (negative below the Boyle temperature T_r ≈ 2.77).
=IF(OR(B2 <= 0, B3 <= 0), "Invalid Virial Inputs", ROUND(0.083 - 0.422 / ((B2 / B3) ^ 1.6), 4))Try the example
Use the original values or change them to test your understanding.