Process Heat Integration, Pinch Technology & Energy Efficiency
Pinch Analysis Minimum Hot & Cold Utility (Delta Tmin) Formula
Calculate Hot-Stream Cooling Duty (kW), Maximum Process-to-Process Heat Recovery (kW), Minimum Cooling-Water Utility Q_C,min (kW), and Minimum Steam Hot Utility Q_H,min (kW).
Equal 3,000 kW hot and cold enthalpy duties DO NOT mean zero steam utility—Second-Law Delta_T_min blocks low-grade heat!
A classic First-Law process-engineering trap is seeing a Hot Stream cooling from T_h,in = 200°C to T_h,out = 50°C at heat-capacity flowrate CP_h = 20 kW/K (Q_hot = 3,000 kW) alongside a Cold Stream heating from T_c,in = 60°C to T_c,out = 180°C at CP_c = 25 kW/K (Q_cold = 3,000 kW) and assuming 100% heat recovery with 0 kW external steam! Under Linnhoff Pinch Analysis with minimum exchanger approach Delta_T_min = 20 K, the Cold Stream entering at 60°C can ONLY absorb heat from Hot Stream temperatures >= 60 + 20 = 80°C! Every kW of Hot-Stream enthalpy below 80°C (20 * (80 - 50) = 600 kW) MUST be rejected to Cooling Water (Q_C,min), capping Process Heat Recovery at 2,400 kW and requiring an identical 600 kW of External Steam (Q_H,min) above the pinch!
Verify this 2-Stream Pinch Benchmark—Hot_CP = 20.0 kW/K (B2), Hot_In_Temp = 200.0°C (B3), Hot_Out_Temp = 50.0°C (B4 -> Q_hot = 3,000.00 kW in E2), Cold_CP = 25.0 kW/K (B5), Cold_In_Temp = 60.0°C (B6), Cold_Out_Temp = 180.0°C (B7), and Approach_Delta_T_min = 20.0 K (B8): Feasible Hot-Above-Cold-Pinch Recovery is MIN(CP_h * MAX(0, T_h,in - (T_c,in + dT)), CP_c * MAX(0, (T_h,in - dT) - T_c,in), Q_hot, Q_cold) = 2,400.00 kW (E3), Minimum Cold Utility Q_C,min equals 3,000 - 2,400 = 600.00 kW (E4), and Minimum Hot Utility Q_H,min equals 600.00 kW (E5)! If your engineering team later inspects this cloud collaboration workbook via the Arte Sheets ChatGPT `0.1.0` connector (currently `In review` / `Not published`), remember `read_range` returns up to 200 raw inputs/formulas plus the workbook `revision` without recalculating—and ordinary MCP tool calls consume `0` Arte AI credits under the `120` calls/min per-account limiter.
| 2-Stream Pinch Target KPI (Hot 200->50°C @20, Cold 60->180°C @25, dTmin=20 K) | Formula | Verified Output |
|---|---|---|
| Total Hot Stream Enthalpy (kW) | CP_h * (T_h,in - T_h,out) | 3,000.00 kW |
| Max Feasible Heat Recovery (kW) | Second-Law Interval Pinch Envelope | 2,400.00 kW (2,600 @ dTmin = 10 K) |
| Minimum Cold Utility Q_C,min (kW) | Q_hot_total - Max_Heat_Recovery | 600.00 kW (400.00 @ dTmin = 10 K) |
| Minimum Hot Utility Q_H,min (kW) | Q_cold_total - Max_Heat_Recovery | 600.00 kW (400.00 @ dTmin = 10 K) |
Exact Two-Stream Pinch Maximum Heat Recovery Formula
Validate CP_h > 0, CP_c > 0, T_h,in > T_h,out, T_c,out > T_c,in, and Delta_T_min > 0!
=LET(cp_h, B2, th_i, B3, th_o, B4, cp_c, B5, tc_i, B6, tc_o, B7, dt_m, B8, IF(OR(cp_h <= 0, cp_c <= 0, th_i <= th_o, tc_o <= tc_i, dt_m <= 0), "Invalid Pinch Input", LET(qh_t, cp_h * (th_i - th_o), qc_t, cp_c * (tc_o - tc_i), q_hi, cp_h * MAX(0, th_i - (tc_i + dt_m)), q_co, cp_c * MAX(0, (th_i - dt_m) - tc_i), ROUND(MIN(qh_t, qc_t, q_hi, q_co), 2))))Plate-Exchanger Tighter Approach Savings Check (Set Delta_T_min = 10 K)
Tighten Approach_Delta_T_min B8 from 20.0 K (shell-and-tube) down to 10.0 K (welded plate exchanger): Maximum Process Heat Recovery E3 rises to 2,600.00 kW, cutting BOTH Cooling Water E4 and Steam Hot Utility E5 by 200 kW each down to 400.00 kW!
=IF(ISTEXT(E3), E3, ROUND(B5 * (B7 - B6) - E3, 2))Try the example
Use the original values or change them to test your understanding.