organic-rankine-cycle

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):

1. Define: T_source [°C], T_sink [°C], P_evap, P_cond, η_exp, η_pump, fluid

2. 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]

3. 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]

4. State 1: x₁ = 0 (saturated liquid at P_cond); h₁ = h_f(P_cond)

5. State 2: h₂ = h₁ + v₁ × (P_evap - P_cond) / η_pump [pump work]

6. 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]

7. State 4s (isentropic): s₄s = s₃; h₄s = h(P_cond, s = s₃) State 4 (actual): h₄ = h₃ - η_exp × (h₃ - h₄s)

8. 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).