Ocean Thermal Energy Conversion: Formulas & Table

Q: Why is the thermodynamic efficiency of OTEC plants so low compared to fossil or nuclear plants?

Thermodynamic efficiency is bounded by the Carnot limit (η Carnot = 1 − T C / T H ). Because an OTEC plant operates across a narrow 20°C to 24°C range, theoretical Carnot efficiency cannot exceed 7% to 8%, resulting in practical net plant efficiencies of 2% to 3%. However, the fuel (solar-heated seawater) is free and continuously replenished.

Ocean thermal energy conversion (OTEC) is a marine renewable energy technology that exploits the temperature gradient between warm surface seawater and cold deep ocean water to drive a thermodynamic heat engine and generate baseload electricity. In tropical waters, surface layers reach 24°C to 30°C while deep waters at 800 to 1,000 meters remain near 4°C, providing continuous clean power alongside co-products like freshwater desalination and deep-water cooling.

What is ocean thermal energy conversion?

Ocean thermal energy conversion operates as a continuous solar thermal engine using the ocean as a natural storage reservoir. Warm surface water evaporates a working fluid to drive a turbine, while cold deep ocean water condenses the vapor back into liquid. Because OTEC relies on thermodynamic principles governing low-temperature heat engines, its energy extraction is bounded by narrow thermal gradients of 18°C to 26°C, requiring high-efficiency heat exchangers and strict parasitic pumping optimization.

Thermodynamic formulas and efficiency limits

Evaluating an ocean thermal energy conversion facility requires calculating theoretical thermodynamic ceilings, endoreversible efficiency limits, seawater thermal duty, and parasitic pumping power.

1. Carnot Maximum Theoretical Efficiency

The upper theoretical efficiency limit between warm surface water at absolute temperature T_H and cold deep water at T_C is governed by the Carnot cycle:

η_Carnot = 1 − (T_C / T_H) = ΔT / T_H

Where T_H and T_C are measured in Kelvin (K = °C + 273.15), and ΔT is the total temperature difference (T_H − T_C).

2. Curzon-Ahlborn Endoreversible Efficiency

Accounting for finite-rate heat transfer across heat exchangers, the Curzon-Ahlborn efficiency defines the theoretical efficiency at maximum power output:

η_CA = 1 − √(T_C / T_H)

At T_H = 26°C (299.15 K) and T_C = 4°C (277.15 K), the Carnot limit is 7.35%, while the Curzon-Ahlborn limit is 3.75%.

3. Seawater Thermal Duty and Flow Rate

Thermal power extracted from warm seawater across the evaporator is calculated as:

Q̇_H = ρ_sw · V̇_warm · c_p · ΔT_warm,drop

Where ρ_sw is seawater density (1,025 kg/m³), c_p is seawater specific heat (4.00 kJ/(kg·K)), V̇_warm is volumetric flow rate (m³/s), and ΔT_warm,drop is seawater temperature drop across the evaporator (typically 3.5°C to 4.5°C).

4. Net Power and Pumping Losses

Net electrical power exported to the grid subtracts internal auxiliary pumping loads from gross generator output:

P_net = P_gross − (P_pump,warm + P_pump,cold + P_aux)

Hydraulic pumping power for each intake is calculated as:

P_pump = (ρ_sw · g · V̇ · h_loss) / η_pump

Where g is 9.81 m/s², h_loss is total dynamic head loss in meters, and η_pump is pump efficiency (~75% to 85%). Parasitic pumping typically consumes 25% to 35% of gross generation.

Ocean thermal energy conversion lookup table

This lookup table lists thermodynamic efficiency limits, empirical cycle efficiencies, and required seawater volumetric flow rates across representative tropical temperatures. Values assume seawater density ρ = 1,025 kg/m³, specific heat c_p = 4.00 kJ/(kg·K), an evaporator seawater temperature drop of 4.0°C, a condenser seawater temperature rise of 4.5°C, an ammonia Rankine cycle, and parasitic pumping consuming 28% of gross output (net output = 72% of gross). Sourced from IRENA Technology Brief E23 and international marine energy benchmarks.

Rounding: Efficiencies are rounded to two decimal places (0.01%); volumetric flow rates are rounded to two decimal places (0.01 m³/s per MW net).

Surface Temp T_H (°C)	Deep Temp T_C (°C)	Temp Difference ΔT (°C)	Carnot Efficiency η_Carnot (%)	Curzon-Ahlborn η_CA (%)	Gross Efficiency η_gross (%)	Net Plant Efficiency η_net (%)	Warm Water Flow (m³/s per MW net)	Cold Water Flow (m³/s per MW net)
22.0	4.0	18.0	6.10	3.10	2.81	2.02	3.02	2.61
24.0	4.0	20.0	6.73	3.42	3.10	2.23	2.74	2.36
25.0	4.0	21.0	7.04	3.59	3.24	2.33	2.61	2.25
26.0	4.0	22.0	7.35	3.75	3.38	2.44	2.50	2.15
27.0	4.0	23.0	7.66	3.91	3.52	2.54	2.40	2.06
28.0	4.0	24.0	7.97	4.07	3.67	2.64	2.31	1.98
29.0	4.0	25.0	8.27	4.23	3.81	2.74	2.23	1.90
30.0	4.0	26.0	8.58	4.38	3.95	2.84	2.15	1.83
24.0	5.0	19.0	6.39	3.25	2.94	2.12	2.88	2.48
26.0	5.0	21.0	7.02	3.57	3.23	2.32	2.62	2.26
28.0	5.0	23.0	7.64	3.89	3.51	2.53	2.41	2.07
30.0	5.0	25.0	8.25	4.21	3.79	2.73	2.23	1.91

Worked engineering calculation examples

Example 1: Efficiency Bounds for a Tropical Site

An ocean site records surface seawater temperature T_H = 26.0°C and deep water temperature T_C = 4.0°C at 900 m depth. Determine the Carnot and Curzon-Ahlborn efficiency limits.

Absolute temperatures: T_H = 26.0 + 273.15 = 299.15 K; T_C = 4.0 + 273.15 = 277.15 K; ΔT = 22.0 K.
Carnot efficiency: η_Carnot = 1 − (277.15 / 299.15) = 1 − 0.9265 = 0.0735 (or 7.35%).
Curzon-Ahlborn efficiency: η_CA = 1 − √(277.15 / 299.15) = 1 − √0.9265 = 1 − 0.9625 = 0.0375 (or 3.75%).

The maximum power conversion limit under finite heat transfer kinetics is 3.75%.

Example 2: Sizing Flow Rates for a 10 MW Net Plant

Size seawater flow requirements for a 10 MW net closed-cycle ammonia facility at the Example 1 site (gross efficiency = 3.38%, parasitic pumping load = 28% of gross generation, evaporator cooling ΔT = 4.0°C, condenser warming ΔT = 4.5°C).

Gross capacity: P_gross = 10,000 kW / (1 − 0.28) = 10,000 / 0.72 = 13,889 kW (13.89 MW). Pumping load is 3,889 kW.
Thermal duty: Q̇_H = 13,889 kW / 0.0338 = 410,917 kW (~410.9 MW_th).
Warm seawater flow: V̇_warm = 410,917 / (1,025 · 4.00 · 4.0) = 410,917 / 16,400 = 25.06 m³/s (2.51 m³/s per MW net).
Cold seawater flow: Heat rejection Q̇_C = 410,917 − 13,889 = 397,028 kW. V̇_cold = 397,028 / (1,025 · 4.00 · 4.5) = 397,028 / 18,450 = 21.52 m³/s (2.15 m³/s per MW net).

High-precision marine flowmeters are installed on both pipelines to balance flow rates and monitor hydraulic friction head losses.

How to calculate OTEC parameters in Python, R, and Excel

1. Microsoft Excel Formulas

Cell B1: Warm surface temperature T_H (°C); Cell B2: Cold deep temperature T_C (°C); Cell B3: Net capacity P_net (MW).
Carnot Efficiency (%): =((B1-B2)/(B1+273.15))*100
Curzon-Ahlborn Efficiency (%): =(1-SQRT((B2+273.15)/(B1+273.15)))*100
Warm Seawater Flow (m³/s): =((B3*1000/0.72)/( (0.46*(((B1-B2)/(B1+273.15))*100))/100 ))/(1025*4.00*4.0)
Cold Seawater Flow (m³/s): =(((B3*1000/0.72)/( (0.46*(((B1-B2)/(B1+273.15))*100))/100 ))-(B3*1000/0.72))/(1025*4.00*4.5)

2. R Script

calc_otec <- function(t_warm_c, t_cold_c, p_net_mw = 1.0) {
  t_warm_k <- t_warm_c + 273.15
  t_cold_k <- t_cold_c + 273.15
  delta_t <- t_warm_c - t_cold_c
  
  eta_carnot <- (delta_t / t_warm_k) * 100
  eta_ca <- (1 - sqrt(t_cold_k / t_warm_k)) * 100
  eta_gross <- 0.46 * eta_carnot
  eta_net <- 0.72 * eta_gross
  
  p_gross_kw <- (p_net_mw * 1000) / 0.72
  q_h_kw <- p_gross_kw / (eta_gross / 100)
  q_c_kw <- q_h_kw - p_gross_kw
  
  v_warm <- q_h_kw / (1025 * 4.00 * 4.0)
  v_cold <- q_c_kw / (1025 * 4.00 * 4.5)
  
  data.frame(
    Delta_T_C = round(delta_t, 1),
    Eta_Carnot_Pct = round(eta_carnot, 2),
    Eta_CA_Pct = round(eta_ca, 2),
    Eta_Gross_Pct = round(eta_gross, 2),
    Eta_Net_Pct = round(eta_net, 2),
    Gross_MW = round(p_gross_kw / 1000, 2),
    Warm_Flow_m3s = round(v_warm, 2),
    Cold_Flow_m3s = round(v_cold, 2)
  )
}
calc_otec(26.0, 4.0, 10.0)

3. Python Script

import math

def calculate_otec(t_warm_c: float, t_cold_c: float, p_net_mw: float = 1.0) -> dict:
    """Calculates OTEC thermodynamic limits and seawater flow rates."""
    t_warm_k = t_warm_c + 273.15
    t_cold_k = t_cold_c + 273.15
    delta_t = t_warm_c - t_cold_c

    eta_carnot = (delta_t / t_warm_k) * 100.0
    eta_ca = (1.0 - math.sqrt(t_cold_k / t_warm_k)) * 100.0
    eta_gross = 0.46 * eta_carnot
    eta_net = 0.72 * eta_gross

    p_gross_kw = (p_net_mw * 1000.0) / 0.72
    q_h_kw = p_gross_kw / (eta_gross / 100.0)
    q_c_kw = q_h_kw - p_gross_kw

    v_warm_m3s = q_h_kw / (1025.0 * 4.00 * 4.0)
    v_cold_m3s = q_c_kw / (1025.0 * 4.00 * 4.5)

    return {
        "delta_t_c": round(delta_t, 1),
        "carnot_efficiency_pct": round(eta_carnot, 2),
        "curzon_ahlborn_efficiency_pct": round(eta_ca, 2),
        "gross_efficiency_pct": round(eta_gross, 2),
        "net_efficiency_pct": round(eta_net, 2),
        "gross_power_mw": round(p_gross_kw / 1000.0, 2),
        "warm_flow_m3s": round(v_warm_m3s, 2),
        "cold_flow_m3s": round(v_cold_m3s, 2),
    }

if __name__ == "__main__":
    plant = calculate_otec(26.0, 4.0, 10.0)
    for k, v in plant.items():
        print(f"{k}: {v}")

Plant architectures and working fluid selection

OTEC systems employ three primary thermodynamic configurations:

Closed-Cycle OTEC: Warm seawater vaporizes pure anhydrous ammonia (NH₃) in an evaporator. Expanding vapor powers a turbine-generator and is recondensed by cold deep seawater in a compact heat exchanger. Ammonia is the preferred working fluid due to its high latent heat of vaporization, high thermal conductivity, and favorable saturation pressure (5 to 10 bar) across operating temperatures.
Open-Cycle OTEC: Warm seawater flash-evaporates under a low-pressure vacuum (~0.03 bar / 3 kPa) at 25°C. Low-pressure steam drives an axial vapor turbine. Condensing the steam against cold seawater in a surface condenser yields desalted potable water as a secondary co-product (~2,000 m³ of freshwater per day per MW net power).
Hybrid-Cycle OTEC: Integrates vacuum flash evaporation with a secondary ammonia Rankine loop, simultaneously co-generating electricity and freshwater.

Plant structural integrity, marine risers, and turbine boundaries follow IEC TS 62600-20:2019 standards for onshore, shelf-mounted, and floating platforms.

Siting criteria and marine engineering considerations

Commercial deployment requires meeting strict environmental and hydrodynamic conditions:

Thermal Resource: Requires a sustained annual temperature gradient (ΔT) of at least 20°C (36°F) between surface and deep water, typical within equatorial regions (±20° latitude). In marine renewable planning, this baseline complements regional solar irradiance and high-temperature concentrating solar power systems.
Cold-Water Pipe (CWP): Sinking large-diameter (1 to 4 m) high-density polyethylene (HDPE) or composite conduits to 800–1,000 m depths requires managing hydroelastic vortex-induced vibrations (VIV) and ocean currents.
Cooling Integration: Effluent discharged from cold-water condensers (7°C to 10°C) can be coupled to seawater air conditioning (SWAC) district systems. Verified in building energy simulation studies, SWAC can displace up to 85% to 90% of electrical air-conditioning demand.
Regulatory Framework: In U.S. waters, commercial licensing, environmental reviews, and artificial upwelling compliance are administered under the Ocean Thermal Energy Conversion Act of 1980 (42 U.S.C. 9101 et seq.) by the National Oceanic and Atmospheric Administration (NOAA).

Frequently asked questions

What is the minimum temperature difference required for ocean thermal energy conversion?

A sustained temperature difference (ΔT) of at least 20°C (36°F) between warm surface seawater and cold deep seawater is required. At lower gradients, parasitic pumping loads consume an unsustainable share of turbine output, reducing net electricity generation to zero.

Why is the thermodynamic efficiency of OTEC plants so low compared to fossil or nuclear plants?

Thermodynamic efficiency is bounded by the Carnot limit (η_Carnot = 1 − T_C / T_H). Because an OTEC plant operates across a narrow 20°C to 24°C range, theoretical Carnot efficiency cannot exceed 7% to 8%, resulting in practical net plant efficiencies of 2% to 3%. However, the fuel (solar-heated seawater) is free and continuously replenished.

What working fluid is most commonly used in closed-cycle OTEC systems?

Pure anhydrous ammonia (NH₃) is the standard working fluid. It possesses high latent heat of vaporization, excellent heat transfer coefficients, and convenient saturation vapor pressures (5 to 10 bar) across the 4°C to 28°C ocean temperature regime.

Can an ocean thermal energy conversion plant produce fresh drinking water?

Yes. Open-cycle OTEC systems flash-evaporate warm seawater under vacuum. Condensing the resulting steam produces desalted freshwater at rates of approximately 2,000 cubic meters (2 million liters) per day per megawatt of net power.

What is the difference between Carnot efficiency and Curzon-Ahlborn efficiency in OTEC design?

Carnot efficiency defines the reversible theoretical maximum efficiency operating with zero temperature drop across heat exchangers. The Curzon-Ahlborn efficiency models an endoreversible system with finite heat transfer rates, establishing the maximum efficiency achievable at maximum power output.

Sources

International Electrotechnical Commission (IEC). IEC TS 62600-20:2019: Marine energy – Wave, tidal and other water current converters – Part 20: Design and analysis of an Ocean Thermal Energy Conversion (OTEC) plant – General guidance. International Electrotechnical Commission, Geneva, Switzerland. Accessed November 9, 2026. https://webstore.iec.ch/publication/61578
International Renewable Energy Agency (IRENA) and IEA-ETSAP. Ocean Thermal Energy Conversion: Technology Brief (IEA-ETSAP and IRENA Technology Brief E23). IRENA, Abu Dhabi, UAE (2014). Accessed November 9, 2026. https://www.irena.org/publications/2014/Jun/Ocean-Thermal-Energy-Conversion
National Renewable Energy Laboratory (NREL) / U.S. Department of Energy (DOE). Open-Cycle Ocean Thermal Energy Conversion (OTEC) Research: Progress Summary and a Design Study (NREL/TP-252-2331). Golden, CO. Accessed November 9, 2026. https://www.nrel.gov/docs/legosti/old/2331.pdf
U.S. National Oceanic and Atmospheric Administration (NOAA). Ocean Thermal Energy Conversion Act of 1980 (Public Law 96-320; 42 U.S.C. 9101 et seq.). U.S. Government Publishing Office. Accessed November 9, 2026. https://www.govinfo.gov/app/details/USCODE-2011-title42/USCODE-2011-title42-chap99