Thermodynamics, Geothermal Power & Industrial Waste-Heat Recovery
Organic Rankine Cycle (ORC) Back-Work & Net Power Formula
Calculate Organic Rankine Cycle (ORC) Working-Fluid Mass Flow (kg/s), Organic Feed-Pump Back-Work Ratio (%), Net Electrical Output (kWe), and Net Thermal Efficiency (%).
Never ignore feed-pump back-work in an Organic Rankine Cycle—it consumes 10%–18% of turbine output!
In a conventional high-temperature water-steam Rankine cycle, boiler feed-pump work is under 2% of turbine output because water has a huge latent heat of vaporization (~2,000 kJ/kg). In a low-grade geothermal or industrial waste-heat Organic Rankine Cycle (ORC) running R245fa, cyclopentane, or isobutane (90°C–160°C), evaporator enthalpy rise is 8x smaller (~250 kJ/kg) and expander enthalpy drop is ~40 kJ/kg—forcing high organic mass flow where high-pressure feed-pump work (W_pump) consumes 10%–18% of gross turbine power! Neglecting Back-Work Ratio (BWR = h_pump / h_turb) overstates net generator kWe by 14%+.
Verify on a 10,000 kWth Binary Geothermal ORC Skid—Evaporator_Heat_Input = 10,000 kWth (B2), Organic_Evap_Enthalpy_Rise = 250 kJ/kg (B3 -> Working-Fluid Mass Flow = 10,000 / 250 = 40.00 kg/s in E2), Turbine_Enthalpy_Drop = 40.0 kJ/kg (1,600 kW gross shaft, B4), FeedPump_Enthalpy_Work = 5.0 kJ/kg (200 kW parasitic pump, B5 -> Back-Work Ratio = 5 / 40 = 12.50% in E3), and Generator_Efficiency = 0.95 (95.0%, B6): Net Electrical Output equals 40 * (40 - 5) * 0.95 = 1,330.00 kWe (E4), yielding a 13.30% Net ORC Thermal Efficiency (E5)!
| ORC Plant Metric (10,000 kWth, 250 kJ/kg Evap, 40 kJ/kg Turb, 5 kJ/kg Pump) | Formula | Verified Output |
|---|---|---|
| Organic Mass Flow Rate (kg/s) | Evap_Heat_kW / Evap_Enthalpy_Rise | 40.00 kg/s |
| Feed-Pump Back-Work Ratio (%) | (Pump_Work_kJ_kg / Turbine_Drop_kJ_kg) * 100 | 12.50% (0.00% Idealized) |
| Net Electrical Power (kWe) | Mass_Flow * (Turbine_Drop - Pump_Work) * Gen_Eff | 1,330.00 kWe (1,520.00 Naive) |
| Net ORC Thermal Efficiency (%) | (Net_Electrical_kWe / Evap_Heat_kW) * 100 | 13.30% (15.20% Naive) |
ORC Net Electrical Power & Back-Work Deduction Formula
Validate Heat_Input > 0, Evap_Enthalpy_Rise > Turbine_Drop > Pump_Work >= 0, and Generator_Eff in (0, 1]!
=LET(q_in, B2, dh_e, B3, dh_t, B4, dh_p, B5, gn_e, B6, IF(OR(q_in <= 0, dh_e <= dh_t, dh_t <= dh_p, dh_p < 0, gn_e <= 0, gn_e > 1), "Invalid ORC Cycle Input", LET(m_wf, q_in / dh_e, ROUND(m_wf * (dh_t - dh_p) * gn_e, 2))))Zero-Pump-Work Overestimation Check (Set Feed-Pump Work = 0 kJ/kg)
Set FeedPump_Enthalpy_Work B5 to 0.0 kJ/kg (the naive steam-table shortcut): Net Power E4 jumps artificially from 1,330.00 kWe to 1,520.00 kWe (15.20% efficiency E5)—a 190 kWe phantom-power error!
=IF(ISTEXT(E4), E4, ROUND((E4 / B2) * 100, 2))Try the example
Use the original values or change them to test your understanding.