Process Heat Transfer, Distillation Reboilers & Phase-Change Design
Mostinski Reduced-Pressure Kettle Reboiler Boiling h & CHF Formula
Calculate Reduced Pressure P_r = P / P_c, Mostinski Pressure Factor F_p, Nucleate Pool-Boiling Coefficient h_nb (W/m²·K), and Mostinski Maximum Critical Heat Flux q_crit (kW/m²).
Estimate kettle reboiler h_nb from Critical Pressure P_c (in kPa!) alone—no surface tension or liquid viscosity tables needed!
Detailed Rohsenow or Forster-Zuber boiling correlations require liquid-vapor density, surface tension, latent heat, and viscosity at operating pressure—properties often uncertain for hydrocarbon fractionation bottoms. Mostinski’s corresponding-states correlation predicts shell-side nucleate boiling heat transfer h_nb (W/(m²·K)) and maximum bundle Critical Heat Flux q_crit (kW/m²) from Critical Pressure P_c (MUST be in kPa, NOT bar!), Operating Pressure P (kPa, giving Reduced Pressure P_r = P / P_c), and Heat Flux q (W/m²): h_nb = 0.00417 * (P_c^0.69) * (q^0.70) * F_p where F_p = 1.8 * P_r^0.17 + 4 * P_r^1.2 + 10 * P_r^10, and single-tube q_crit = 0.367 * P_c * (P_r^0.35) * ((1 - P_r)^0.90) kW/m²! Entering P_c = 42.5 bar instead of 4,250 kPa underpredicts h_nb by 23.8x!
Verify on a Propane Depropanizer Kettle Reboiler—Critical_Pressure P_c = 4,250.0 kPa (42.5 bar, B2), Operating_Pressure P = 850.0 kPa (B3 -> Reduced Pressure P_r = 0.200 in E2 and Pressure Enhancement Factor F_p = 1.949 in E3), and Design_Tube_Heat_Flux q = 40,000 W/m² (40 kW/m², B4): Nucleate Boiling Coefficient hits h_nb = 4,314.89 W/(m²·K) (E4), safely far below Mostinski Single-Tube Critical Flux q_crit = 726.43 kW/m² (E5)!
| Mostinski Reboiler KPI (Propane Pc = 4,250 kPa, P = 850 kPa, q = 40,000 W/m²) | Formula | Verified Output |
|---|---|---|
| Reduced Pressure P_r | Operating_P_kPa / Critical_Pc_kPa | 0.200 (0.400 @ P = 1,700 kPa) |
| Mostinski Pressure Factor F_p | 1.8*Pr^0.17 + 4*Pr^1.2 + 10*Pr^10 | 1.949 (2.873 @ P = 1,700 kPa) |
| Nucleate Boiling h_nb (W/m²·K) | 0.00417 * (Pc^0.69) * (q^0.70) * F_p | 4,314.89 W/m²·K (6,361.75 @ 1,700 kPa) |
| Mostinski Critical Flux (kW/m²) | 0.367 * Pc * (Pr^0.35) * ((1 - Pr)^0.90) | 726.43 kW/m² (714.68 @ 1,700 kPa) |
Mostinski Corresponding-States Boiling Coefficient Formula
Validate Critical_Pc_kPa >= 500 (catches accidental bar entry!), 0.005 * P_c <= Operating_P_kPa <= 0.90 * P_c, and Heat_Flux_W_m2 > 0!
=LET(pc_k, B2, op_k, B3, qf_w, B4, IF(OR(pc_k < 500, op_k < 0.005 * pc_k, op_k > 0.9 * pc_k, qf_w <= 0), "Invalid Mostinski Input", LET(pr_f, op_k / pc_k, fp_m, 1.8 * (pr_f ^ 0.17) + 4 * (pr_f ^ 1.2) + 10 * (pr_f ^ 10), ROUND(0.00417 * (pc_k ^ 0.69) * (qf_w ^ 0.7) * fp_m, 2))))Higher-Pressure Column Operation Boiling Boost Check (Set Operating P = 1,700 kPa)
Double Operating_Pressure B3 from 850 kPa to 1,700 kPa (P_r = 0.400): Pressure Factor F_p E3 jumps from 1.949 to 2.873, boosting Nucleate Boiling h_nb E4 by 47.4% to 6,361.75 W/(m²·K) while Critical Flux E5 edges slightly past its P_r = 0.28 peak to 714.68 kW/m²!
=IF(ISTEXT(E4), E4, LET(pr_f, B3 / B2, ROUND(0.367 * B2 * (pr_f ^ 0.35) * ((1 - pr_f) ^ 0.9), 2)))Try the example
Use the original values or change them to test your understanding.