| name | organic-rankine-cycle |
| description | Organic Rankine Cycle (ORC) — thermodynamic analysis (T-s diagram, expander/pump work), working fluid selection (R245fa, R134a, n-pentane, toluene, siloxanes), heat source matching (pinch point, UA), isentropic efficiency, expander types (scroll, radial, axial), waste heat recovery (WHR), geothermal, solar thermal, design point optimization, and economic analysis (LCOE, payback period). |
| metadata | {"priority":7,"promptSignals":{"phrases":["organic Rankine cycle","ORC","waste heat recovery ORC","ORC working fluid","ORC expander","low-temperature power generation"],"minScore":3}} |
Organic Rankine Cycle (ORC) — Complete Skill
Thermodynamic Fundamentals
Cycle Description
ORC vs. Steam Rankine Cycle:
ORC uses organic working fluid (lower boiling point) instead of water
Suitable for heat sources: 80–350°C (water steam requires > 300°C economically)
Applications: waste heat recovery, geothermal, solar thermal, biomass
Ideal Rankine cycle states:
State 1: saturated (or subcooled) liquid → pump inlet
State 2: compressed liquid → pump exit; boiler inlet
State 3: superheated (or saturated) vapor → expander inlet
State 4: wet vapor or superheated vapor → expander exit (condenser inlet)
Condensation at constant pressure → back to State 1
Net work output:
W_net = W_expander - W_pump [kJ/kg or kW]
W_expander = h₃ - h₄s (isentropic) × η_expander [h₃ = inlet enthalpy; h₄s = isentropic exit]
W_pump = v₁ × (P₂ - P₁) / η_pump ≈ (h₂ - h₁) [v₁ = specific volume at pump inlet; small for liquids]
Thermal efficiency:
η_th = W_net / Q_in [Q_in = h₃ - h₂ = heat added in boiler + superheater]
η_Carnot = 1 - T_L / T_H [upper bound; T in Kelvin]
Typical ORC η_th: 5–20% (depending on source/sink temperatures)
Heat input:
Q_in = ṁ × (h₃ - h₂) [kW; ṁ = working fluid mass flow rate [kg/s]]
Back work ratio (BWR):
BWR = W_pump / W_expander [typically 1–5% for ORC; very small vs. gas turbine 40–60%]
T-s Diagram and Fluid Shape
Working fluid shapes (from saturation curve shape):
Wet fluid (isentropic expansion enters two-phase region): water, ammonia, R32
Isentropic fluid (nearly vertical right saturation curve): R11, R113, R245ca
Dry fluid (expansion stays in superheated region): R245fa, n-pentane, toluene, R134a, siloxanes
ORC preference: dry or isentropic fluids — avoid wet fluids (two-phase droplets damage expander)
Degree of superheat:
Wet fluids: need significant superheat → efficiency penalty
Dry fluids: can use saturated vapor at expander inlet → simpler; no superheater needed
Some ORC designs use internal heat exchanger (IHE/recuperator): preheat pump exit liquid using expander exit vapor → improve η
Recuperated ORC
With Internal Heat Exchanger (IHE):
State 4 (hot expander exit) preheats state 2 (cold pump exit) before boiler
Reduces Q_in required (less external heat needed for same T₃)
η_th_recuperated > η_th_basic by 2–5% (fluid-dependent)
Optimal when: large T difference between expander exit and saturation temperature
Working Fluid Selection
Selection Criteria
| Property | Requirement | Reason |
|---|
| Boiling point T_b | Match heat source T | Good thermal matching |
| Critical temperature T_c | T_c > T_source preferred | Avoid supercritical complexity |
| Molecular weight MW | High → lower speed of sound → lower expander Mach | Radial expander design |
| GWP | Low → < 150 for refrigerants post-F-Gas | Environmental regulation |
| ODP | Zero | No ozone depletion |
| Flammability | Non-flammable preferred for safety | Avoid ignition risk |
| Toxicity | Low toxicity | Worker safety |
| Thermal stability | Stable at source temperature | No decomposition |
Common Working Fluids
| Fluid | T_b (°C) | T_c (°C) | P_c (MPa) | MW | GWP | Notes |
|---|
| R245fa | 15.1 | 154.1 | 3.65 | 134 | 1,030 | Common ORC fluid; being phased out (GWP) |
| R1234ze(E) | -19.0 | 109.4 | 3.63 | 114 | 6 | Low GWP replacement; HFO |
| R1233zd(E) | 18.3 | 166.5 | 3.57 | 130 | < 1 | Near-zero GWP; hydrofluoroolefin |
| n-Pentane | 36.1 | 196.6 | 3.37 | 72 | ~20 | Natural fluid; flammable; high T applications |
| n-Hexane | 68.7 | 234.7 | 3.03 | 86 | ~3 | Flammable; WHR for > 200°C source |
| Toluene | 110.6 | 318.6 | 4.11 | 92 | ~3 | High-T ORC (300°C source); dry fluid |
| Cyclopentane | 49.3 | 238.5 | 4.51 | 70 | ~11 | Low GWP; high T |
| R134a | -26.4 | 101.1 | 4.06 | 102 | 1,430 | Low-T (80–100°C source) |
| MDM (siloxane) | 152.5 | 290.9 | 1.41 | 310 | — | Very high MW; 200–300°C source; no flammability |
| MM (siloxane) | 101.0 | 245.6 | 1.93 | 162 | — | High T; no flammability |
| Ammonia (NH₃) | -33.3 | 132.3 | 11.3 | 17 | 0 | Wet fluid; high P; toxic; excellent thermodynamics |
For waste heat 150–250°C: R245fa, R1233zd, cyclopentane, n-hexane
For geothermal (100–150°C): R134a, R245fa, R1234ze
For high-T (> 250°C): toluene, siloxanes, n-pentane
Thermodynamic Analysis
State Point Calculation
Step-by-step (using REFPROP or CoolProp):
-
Define: T_source [°C], T_sink [°C], P_evap, P_cond, η_exp, η_pump, fluid
-
Condensation pressure P_cond:
T_cond = T_sink + ΔT_pinch_condenser [ΔT_pinch ≈ 5–10°C]
P_cond = P_sat(T_cond) [from fluid property table or REFPROP]
-
Evaporation pressure P_evap:
T_evap = T_source - ΔT_pinch_evaporator [ΔT_pinch ≈ 10–15°C approach]
P_evap = P_sat(T_evap) [saturated vapor entry; or add superheat if wet fluid]
-
State 1: x₁ = 0 (saturated liquid at P_cond); h₁ = h_f(P_cond)
-
State 2: h₂ = h₁ + v₁ × (P_evap - P_cond) / η_pump [pump work]
-
State 3: saturated vapor at P_evap (or superheated if specified)
h₃ = h_g(P_evap) [for saturated; else h at T₃, P_evap from superheated table]
-
State 4s (isentropic): s₄s = s₃; h₄s = h(P_cond, s = s₃)
State 4 (actual): h₄ = h₃ - η_exp × (h₃ - h₄s)
-
Performance:
W_exp = h₃ - h₄ [kJ/kg]; W_pump = h₂ - h₁ [kJ/kg]
W_net = W_exp - W_pump; Q_in = h₃ - h₂
η_th = W_net / Q_in
Example (R245fa, T_source = 150°C, T_sink = 30°C):
T_cond = 35°C → P_cond = 1.04 bar
T_evap = 130°C → P_evap = 14.0 bar
η_exp = 0.80; η_pump = 0.75
h₁ = 246 kJ/kg; h₂ ≈ 248 kJ/kg (pump work small)
h₃ = 492 kJ/kg (sat. vapor at 130°C)
s₃ = 1.72 kJ/(kg·K); h₄s ≈ 448 kJ/kg (isentropic to 35°C)
h₄ = 492 - 0.80 × (492-448) = 457 kJ/kg
W_net = (492-457) - (248-246) = 35 - 2 = 33 kJ/kg
η_th = 33 / (492-248) = 13.5%
Heat Exchanger Design (Pinch Analysis)
Pinch point analysis:
Source fluid: T_source_in → T_source_out (cools as it transfers heat)
Working fluid: T₂ → T₃ (heats, boils, superheats)
Minimum temperature difference (ΔT_min = pinch):
ΔT_min = 5–15°C (higher → less HX cost but more exergy lost)
Pinch occurs at bubble point of working fluid (onset of boiling) for subcritical ORC
UA calculation:
Q = U × A × LMTD
LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂) [ΔT at each end of HX]
U (overall heat transfer coefficient): 200–400 W/(m²·K) for liquid-liquid; 50–200 for phase-change
Expander sizing:
Specific volume ratio: VR = v₄/v₃ [expansion ratio in volume]
VR = P_evap/P_cond × (ρ₃/ρ₄) = 5–20 for typical ORC
Isentropic enthalpy drop: Δh_is = h₃ - h₄s [kJ/kg]
Expander Technology
Expander Types
Scroll expander:
Capacity: 1–25 kWe; most compact; hermetic sealing possible
Efficiency η_is: 0.65–0.80; built-in volume ratio limited (VR ≈ 3–5)
Suitable for: small distributed ORC (< 25 kW); R245fa, R134a
Screw expander:
Capacity: 20–2,000 kWe; robust; handles wet steam
η_is: 0.70–0.85; VR ≈ 5–12 adjustable
Suitable for: geothermal, industrial WHR; moderate scale
Radial inflow turbine:
Capacity: 10 kW–5 MW; high efficiency
η_is: 0.80–0.90 (isentropic); high RPM (10,000–100,000 rpm)
Suitable for: higher power ORC; R245fa, siloxanes; need high-speed generator
Axial turbine:
Capacity: > 500 kW; multi-stage possible for large VR
η_is: 0.85–0.92 (multi-stage); standard turbomachinery design tools
Suitable for: large industrial ORC (> 500 kWe); geothermal power plants
Size parameter and specific speed:
S_p = V̇₄^0.5 / Δh_is^0.25 [m; relates to optimal expander size; S_p = 0.01–0.1 m for radial; 0.1–0.5 m for axial]
N_s = ω × V̇^0.5 / Δh_is^0.75 [dimensionless specific speed; N_s = 0.1–0.6 radial; 0.6–2.0 axial]
Applications
Waste Heat Recovery (WHR)
Industrial exhaust gas recovery:
Source: diesel engine exhaust (400–600°C at exhaust manifold; 200–350°C at stack after HRSG)
Net power output: 5–12% of engine rated power recovered as ORC electricity
Typical: 1 MWe engine → 50–120 kWe ORC with n-hexane or cyclopentane
Marine WHR:
Large two-stroke engines: 15–80 MW; ORC from exhaust + jacket water (combined heat sources)
ORC power output: 2–6% of main engine power = 300 kWe–4 MWe
Fluid: R245fa or custom; flat-plate or shell-and-tube HX for marine stability
Cement/glass/aluminum plant:
Kiln exhaust 200–350°C; recovery 1–5 MW typical
Toluene or siloxane ORC for high T
Geothermal
Flash cycle: high-T geothermal > 150°C → flash steam → standard steam turbine (not ORC)
Binary cycle ORC: geothermal brine 80–150°C → ORC with R134a or R245fa
Pros: no scaling (brine never flashes); total reinjection; closed loop
η_th: 7–12%; major commercial installations (Ormat Technologies, Turboden)
Solar Thermal
Linear concentrating collectors (parabolic trough):
Oil temperature 150–400°C → ORC with n-pentane or toluene
Solar-to-electric: η_solar × η_ORC = 0.50 × 0.15 = 7.5% (gross)
Intermittent operation → thermal storage (molten salt or thermocline) for dispatch
Economic Analysis
Specific Investment Cost (SIC)
ORC cost benchmarks:
Small ORC (10–100 kWe): $3,000–10,000 /kWe installed
Medium ORC (100–500 kWe): $2,000–5,000 /kWe
Large ORC (> 1 MWe): $1,000–3,000 /kWe
Geothermal binary: $2,500–4,000 /kWe (drilling cost dominant)
Simple payback period:
Payback [years] = SIC × P_net / (E_annual × C_electricity)
E_annual [kWh] = P_net × Capacity_Factor × 8,760 h/year
Capacity factor: 0.85–0.95 (continuous industrial WHR); 0.20–0.30 (solar, peak load)
LCOE (Levelized Cost of Energy):
LCOE = [SIC × P_net × CRF + O&M_annual] / E_annual
CRF = i(1+i)^n / ((1+i)^n - 1) [capital recovery factor; i = discount rate; n = project life]
ORC LCOE: $60–200 /MWh depending on scale and heat source quality
Standards and References
| Source | Scope |
|---|
| Quoilin et al. (2013) Renewable Sustainable Energy Rev. | ORC review and component modeling |
| Tchanche et al. (2011) Applied Thermal Eng. | Working fluid selection |
| IEC 61400 | Power conversion (adapted for ORC) |
| ASME PTC 6 | Steam turbine performance (applicable to ORC expanders) |
| NREL ORC Technical Report TP-5500-63552 | Low-temperature ORC design |
| ISO 13709 (API 610) | Pump standard (ORC feed pump) |
Output
Provide: heat source (T_source [°C], Q_available [kW] or ṁ_source [kg/s]), heat sink (T_sink [°C], cooling medium), working fluid selected with justification (T_b [°C], GWP, flammability), ORC architecture (basic/recuperated/dual-pressure), state points (T₁ [°C], P₁ [bar]; T₃ [°C], P₃ [bar]; h₁, h₂, h₃, h₄ [kJ/kg] from REFPROP/CoolProp), performance (W_net [kJ/kg]; W_net_total [kW]; η_th [%]), expander type and power (scroll/screw/radial/axial; P_exp [kWe]; η_is [%]; VR), heat exchanger sizing (Q_evap [kW]; ΔT_pinch [°C]; UA [kW/K]), working fluid mass flow rate ṁ [kg/s], economic estimate (SIC [$/kWe]; E_annual [MWh/year]; payback [years]), and applicable reference (Quoilin 2013, NREL TP-5500-63552).
