Engineering & Science
Soave-Redlich-Kwong (SRK) Equation of State: Alpha Cohesion & Pressure
Calculate Giorgio Soave’s acentric cohesion function α(T_r, ω) = [1 + (0.480 + 1.574ω - 0.176ω^2)(1 - SQRT(T / T_c))]^2 and real-gas SRK pressure P (bar) for hydrocarbon and natural-gas processing.
How Giorgio Soave (1972) turned cubic equations into refinery simulation workhorses!
Original Redlich-Kwong (1949) used a universal 1 / SQRT(T_r) attraction decay that predicted noble-gas pressures well—but missed hydrocarbon vapor pressures badly because non-spherical alkane chains depend on Pitzer’s acentric factor ω! Giorgio Soave (Chemical Engineering Science, 1972) replaced 1 / SQRT(T_r) with α(T_r, ω) = [1 + m(ω) * (1 - SQRT(T / T_c))]^2, where m(ω) = 0.480 + 1.574 * ω - 0.176 * ω^2, forcing the cubic equation of state to reproduce experimental vapor-liquid saturation curves!
Using R = 83.1446 bar·cm^3/(mol·K), critical attraction a_c = 0.42748 * R^2 * T_c^2 / P_c, and covolume b = 0.08664 * R * T_c / P_c, SRK pressure is P = R*T / (V_m - b) - a_c*α / (V_m*(V_m + b))! For dense propane vapor at T = 320 K and molar volume V_m = 450 cm^3/mol (T_c = 369.8 K, P_c = 42.48 bar, ω = 0.152, b = 62.71 cm^3/mol): ideal-gas law grossly overpredicts 59.13 bar, whereas SRK (α = 1.1023) nails real-gas intermolecular attraction at P = 23.25 bar!
| Propane State at Vm = 450 cm^3/mol (ω = 0.152) | Soave Cohesion α(Tr, ω) | Ideal Gas RT / Vm | SRK Real Pressure P (bar) |
|---|---|---|---|
| Subcritical Dense Gas (T = 320.0 K) | 1.1023 (> 1 Below Tc) | 59.13 bar | 23.25 bar (-60.7% Attraction!) |
| Critical Isotherm (T = Tc = 369.8 K) | 1.0000 (Exact Pivot) | 68.33 bar | 38.16 bar |
| Unphysical Compression (Vm <= b = 62.71) | Hard-Core Covolume Wall | "Invalid SRK State" | Requires Vm > b |
Soave-Redlich-Kwong Real-Gas Pressure P (bar)
Evaluates P = R*T/(V_m - b) - a_c*α/(V_m*(V_m + b)) with R = 83.1446 bar·cm^3/(mol·K) and guards V_m <= b.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B6 <= 0.08664 * 83.1446 * B3 / B4), "Invalid SRK State", ROUND((83.1446 * B2) / (B6 - 0.08664 * 83.1446 * B3 / B4) - (0.42748 * (83.1446 ^ 2) * (B3 ^ 2) / B4) * ((1 + (0.48 + 1.574 * B5 - 0.176 * (B5 ^ 2)) * (1 - SQRT(B2 / B3))) ^ 2) / (B6 * (B6 + 0.08664 * 83.1446 * B3 / B4)), 2))Soave Temperature-Dependent Cohesion Factor α(T_r, ω)
Returns dimensionless α(T_r, ω), which equals 1.0000 at T = T_c, exceeds 1 below T_c, and decays below 1 above T_c.
=IF(OR(B2 <= 0, B3 <= 0), "Invalid SRK State", ROUND((1 + (0.48 + 1.574 * B5 - 0.176 * (B5 ^ 2)) * (1 - SQRT(B2 / B3))) ^ 2, 4))Try the example
Use the original values or change them to test your understanding.