# Performance Evaluation Concept for Ocean Thermal Energy Conversion toward Standardization and Intelligent Design

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{th}, is the ratio of the work of the heat engine, W, to the input heat transfer rate to the heat engine, Q

_{in}, as in the following expression:

_{th}is represented by the following expression:

_{m}of the work of the Carnot heat engine, which is the ideal heat engine, and the thermal efficiency η

_{th,CA}at that time are expressed by the following equations [15,16,17,18,19,20,21,22,23]:

## 2. Thermodynamics for OTEC

#### 2.1. Energy Conservation (First Law of Thermodynamics)

_{W}and the heat transfer rate to the deep seawater Q

_{C}:

_{p}(kJ/(kgK)) is the specific heat at constant pressure, U (kW/(kgK)) is the overall heat transfer coefficient of heat exchangers, A (m

^{2}) is the heat transfer area of heat exchangers, and ΔT

_{m}(K) is the logarithmic mean temperature difference. The subscripts of in, out, W, and C are inlet, outlet, warm surface seawater, and cold deep seawater, respectively.

_{th}, defined in Equation (1) as the ratio of available work from the heat engine, W, over the input heat transfer rate to the heat engine Q

_{in}. In general, we use Q

_{in}in the energy conversion process as a heat transfer rate from the heat source to the heat engine expressed by Equation (6). In the case of conventional power plants, the temperature difference between the combustion of fuel and the turbine inlet is large. However, in the OTEC system, the available temperature difference between seawater and the heat engine is small (i.e., the heat source temperature difference is only about 20 K, and even with a pinch temperature difference of 1 K in each, the available temperature of the heat engine will lose at least 10%). Therefore, the temperature difference of the inlet and outlet in the heat exchange process and the logarithmic temperature difference expressed in Equations (6) and (7) have a significant effect on the performance of heat engines. As a result, the relationship between the heat source and heat engines can be derived from Equations (3) and (4), which show the discrepancy of the maximum work condition and the maximum thermal efficiency condition.

_{0}(K) can be expressed as a transferable thermal energy Q

_{T}(kW) assuming the isobaric change during the heat exchange process [17]:

_{in}is Q

_{W}; however, the thermal energy Q

_{W}in Equation (6) is a part of Q

_{T}. The thermal energy collection efficiency η

_{T,in}should be considered as defined below:

_{net}is as follows:

_{P}is the total pumping power of seawater from intake to discharge.

#### 2.2. Exergy Efficiency (Second Law of Thermodynamics)

_{H}and T

_{L}are the highest and lowest temperatures in the heat engine, and they reach T

_{W,in}and T

_{C,in}, respectively.

_{gen,HE}is zero, the discharging seawater temperature is equal because of the equilibrium condition. Then, T

_{W,out}and T

_{C,out}are as follows [17]:

_{x,OTEC}: [17]:

_{ex,OTEC}is expressed as follows:

_{net}/m

_{C}.

## 3. Effectiveness of Performance Evaluation Method

_{gross}shows the power from heat engines because the pumping power of seawater is different in each location of the project, and it affects the results of ascertaining the effectiveness of the performance evaluation methods. Note that the assumption of the efficiency of the component is different in each study; however, this evaluation focuses on the trend of the relationship between thermal and exergic efficiencies.

_{gross}and the deep seawater flow rate m

_{C}using the data of Table 1. Moreover, Figure 7 shows the dependency of conventional and normalized thermal efficiencies η

_{th}, η

_{th,Nor}, and W

_{gross}/m

_{C}.

_{gross}seems to be proportional to m

_{C}because m

_{C}has the similar role as fuels in conventional power plants and an increase in m

_{C}results in increase in W

_{gross}. Therefore, the increase in W

_{gross}/m

_{C}will increase the efficiency of heat engines. However, according to Figure 7, η

_{th}has no clear correlation to W

_{gross}/m

_{C}. Additionally, η

_{th}is almost constant up to W

_{gross}/m

_{C}at 0.4, and there is considerable variation between η

_{th}and W

_{gross}/m

_{C}, whereas the normalized thermal efficiency is almost proportional to W

_{gross}/m

_{C}. Therefore, although the values of η

_{th,Nor}are smaller than η

_{th}, this indicates the energy conversion efficiency. According to Figure 7, the trend of η

_{th}clearly shows that the conventional thermal efficiency has the contradiction to indicate the performance of the system as efficient because Q

_{in}is obviously not the resource of energy in the OTEC, but most research only introduces η

_{th}as the thermal efficiency by following the traditional manner. Moreover, the crucial points in the thermal efficiency are relatively higher η

_{th}in Figure 7 such as the points at W

_{gross}/m

_{C}being 0.22 and 0.44; η

_{th,Nor}becomes lower compared to other points, which shows us the risk of the performance evaluation or design based on η

_{th}. Additionally, this is why we need normalization of the resource of energy in the thermal efficiency using Q

_{T}to consider the heat leak in the discharge process in Figure 2. Indeed, the values of η

_{th,Nor}are small because the resource of thermal energy Q

_{T}in Equation (12) includes the discharged thermal energy of heat engines to discharge process in Figure 2 to be equilibrium state.

_{ex,OTEC}defined in Equation (17) and the conventional and normalized thermal efficiencies η

_{th}and η

_{th,Nor}. According to Figure 8, the increase in η

_{ex,OTEC}provides only increase in η

_{th,Nor}and no clear relation between η

_{th}and η

_{ex,OTEC}. Additionally, η

_{ex,OTEC}are totally different in the staging of Rankine or Lorentz-like heat engines of η

_{th}, whereas η

_{th,Nor}is proportional to η

_{ex,OTEC}except the highest thermal efficiency condition due to the difference of design heat source temperature condition, while the purpose of the utilization of the staging Rankine and Lorentz-like cycle are to increase η

_{ex,OTEC}, and eventually most of their design condition achieves 35–40%. However, some of their η

_{ex,OTEC}are only about 20% and totally less than almost all of the simple Rankine cycle. Therefore, the exergy analysis using Equation (17) is very important to analyze the effectiveness of the design and the potential of improvement of design imbalance the in heat and mass balance.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{p} | Specific heat (kJ/(kg K)) |

E | Energy (kW) |

Ex | Exergy (kW) |

m | Mass flow rate (kg/s) |

Q | Heat transfer rate (kW) |

S | Entropy (kJ/K) |

T | Temperature (K) |

ΔT | Temperature difference (K) |

W | Work (kW) |

Greek Symbols | |

η | Efficiency (%) |

Subscripts | |

C | Cold deep seawater |

CA | Curzon–Ahlborn |

Car | Carnot cycle |

ex | Exergy |

ΔT | Temperature difference |

H | High-temperature working fluid temperature on heat engine |

HE | Heat engine |

L | Low-temperature working fluid temperature on heat engine |

in | Inlet |

net | Net |

Nor | Normalized |

m | Maximized |

out | Outlet |

OTEC | OTEC |

th | Thermal |

T | Transferable |

W | Warm surface seawater |

## References

- Martin, B.; Okamura, S.; Nakamura, Y.; Yasunaga, T.; Ikegami, Y. Status of the “Kumejima Model” for advanced deep seawater utilization. In Proceedings of the IEEE Conference Publications, Kobe, Japan, 6–8 October 2016; pp. 211–216. [Google Scholar]
- Uehara, H.; Ikegami, Y.; Nishida, T. OTEC system using a new cycle with Absorption and Extraction Process. Phys. Chem. Aqueous Syst.
**1995**, 862–869. [Google Scholar] [CrossRef] [Green Version] - Yasunaga, T.; Ikegami, Y.; Monde, M. Performance test of OTEC with ammonia/water as working fluid using shell and plate type heat exchangers (Effect of heat source temperature and flow rate). Trans. JSME B
**2008**, 74, 445–452. (In Japanese) [Google Scholar] [CrossRef] [Green Version] - Yasunaga, T.; Ikegami, Y. Fundamental characteristics in power generation by heat engines on ocean thermal energy conversion. Trans. JSME
**2020**, 86, 886. (In Japanese) [Google Scholar] [CrossRef] - Yasunaga, Y.; Ikegami, Y. Theoretical model construction for renewable low-grade thermal energy conversion: An insight from finite-time thermodynamics. IIR
**2020**, 1185. [Google Scholar] [CrossRef] - Uehara, H.; Ikegami, Y. Parametric performance analysis of OTEC using Kalina cycle. In Proceedings of the ASME/ASES Joint Solar Engineering Conference, Washington, DC, USA, 4–8 April 1993; pp. 203–207. [Google Scholar]
- Kalina, A.L. Combined cycle system with novel bottoming cycle. Trans. ASME J. Eng. Gas. Turbines Power
**1984**, 106, 737–742. [Google Scholar] [CrossRef] - Ikegami, Y.; Yasunaga, T.; Morisaki, T. Ocean Thermal Energy Conversion Using Double-Stage Rankine Cycle. J. Sci. Mar. Eng.
**2018**, 6, 32. [Google Scholar] - Bombarda, P.; Invernizzi, C.; Gaia, M. Performance Analysis of OTEC Plants with Multilevel Organic Rankine Cycle and Solar Hybridization. Trams. ASME J. Eng. Gas Turbine Power
**2013**, 135, 042302-1–042302-8. [Google Scholar] [CrossRef] - Bernardoni, C.; Binotti, M.; Giostri, A. Techno-economic analysis of closed OTEC cycles for power generation. Renew. Energy
**2019**, 132, 1018–1033. [Google Scholar] [CrossRef] - Lee, W.; Kim, S. The maximum power from a finite reservoir for a Lorentz cycle. Energy
**1992**, 17, 275–281. [Google Scholar] [CrossRef] - Bucher, M. New diagram for heat flows and work in a Carnot cycle. Am. J. Phys.
**1986**, 54, 850–851. [Google Scholar] [CrossRef] - Wallingford, J. Inefficiency and irreversibility in the Bucher diagram. Am. J. Phys.
**1989**, 57, 379–381. [Google Scholar] [CrossRef] - Bejan, A. Graphic Techniques for Teaching Engineering Thermodynamics. Mech. Eng. News
**1997**, 14, 26–28. [Google Scholar] - Ikegami, Y.; Bejan, A. On the thermodynamic optimization of power plants with heat transfer and fluid flow irreversibilities. Trans. ASME J. Sol. Energy Eng.
**1998**, 120, 139–144. [Google Scholar] [CrossRef] - Wu, C. Performance Bound for Real OTEC Heat Engines. Ocean Eng.
**1987**, 14, 349–354. [Google Scholar] [CrossRef] - Yasunaga, T.; Ikegami, Y. Finite-time thermodynamic model for evaluating heat engines in ocean thermal energy conversion. Entropy
**2020**, 22, 211. [Google Scholar] [CrossRef] [Green Version] - Johnson, D.H. The exergy of the ocean thermal resource and analysis of second-law efficiencies of idealized ocean thermal energy conversion power cycles. Energy
**1983**, 8, 927–946. [Google Scholar] [CrossRef] - Yasunaga, T.; Ikegami, Y. Application of finite-time thermodynamics for evaluation method of heat engines. Energy Procedia
**2017**, 129, 995–1001. [Google Scholar] [CrossRef] - Bejan, A. Advanced Engineering Thermodynamics, 3rd ed.; Wiley: New York, NY, USA, 1998; pp. 352–417. [Google Scholar]
- Novikov, I.I. The efficiency of atomic power stations. J. Nucl. Energy
**1958**, 7, 125–128. [Google Scholar] - Curzon, F.L.; Ahlborn, B. Efficiency of a Carnot engine at maximum power output. Am. J. Phys.
**1957**, 43, 22–24. [Google Scholar] [CrossRef] - Bejam, A. Models of power plants that generate minimum entropy while operating at maximum power. Am. J. Phys.
**1996**, 64, 1054–1059. [Google Scholar] [CrossRef] - Fontaine, K.; Yasunaga, T.; Ikegami, Y. OTEC maximum net power output using Carnot cycle and application to simplify heat exchanger selection. Entropy
**2019**, 21, 1143. [Google Scholar] [CrossRef] [Green Version] - Yasunaga, T.; Morisaki, T.; Ikegami, Y. Basic Heat Exchanger Performance Evaluation Method on OTEC. J. Sci. Mar. Eng.
**2018**, 6, 32. [Google Scholar] [CrossRef] [Green Version] - Morisaki, T.; Ikegami, Y. Evaluation of performance characteristics of multi-stage Rankine cycle based on maximum power. In Proceedings of the International Conference on Power Engineering-15 (ICOPE-15), Yokohama, Japan, 30 November–4 December 2015. [Google Scholar] [CrossRef]
- Chen, L.; Sun, F.; Wu, C. Optimal configuration of a two-heat-reservoir heat-engine with heat-leak and finite thermal-capacity. Appl. Energy
**2006**, 83, 71–81. [Google Scholar] [CrossRef] - Mitsui, T.; Ito, F.; Seya, Y.; Nakamoto, Y. Outline of the 100 kW OTEC plant in the Republic of Nauru. IEEE Trans. Power Appar. Syst.
**1983**, PAS-102, 3167–3171. [Google Scholar] [CrossRef] - Sinama, F.; Martins, M.; Journoud, A.; Marc, O.; Lucas, F. Thermodynamic analysis and optimization of a 10 MW OTEC Rankine cycle in Reunion Island with the equivalent Gibbs system method and generic optimization program GenOpt. Appl. Ocean Res.
**2015**, 53, 54–66. [Google Scholar] [CrossRef] - Yoon, J.; Son, C.; Baek, S.; Ye, B.H.; Kim, H. Performance characteristics of a high-efficiency R717 OTEC power cycle. Appl. Therm. Eng.
**2014**, 72, 304–308. [Google Scholar] [CrossRef] - NIthesh, K.G.; Chatterjee, D.; Oh, C.; Lee, Y. Design and performance analysis of radial-flow turbo expander for OTEC application. Renew. Energy
**2016**, 85, 834–843. [Google Scholar] [CrossRef] - Wu, Z.; Feng, H.; Chen, L.; Tang, W.; Shi, J.; Ge, Y. Constructal thermodynamics optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle. Energy Convers. Manag.
**2020**, 210, 15. [Google Scholar] [CrossRef]

**Figure 1.**Concept of a heat engine driven by heat and the relationship between temperature and energy in conventional thermal power plants; (

**a**) concept of a heat engine; (

**b**) conceptual T–E diagram. The heat source is the combustion of the fuel. The work of the heat engine is the difference between Q

_{in}and Q

_{out}.

**Figure 2.**Conceptual process flow in OTEC power generation. The process consists of four parts: heat in the sea, heat source supply, energy conversion, and discharge.

**Figure 3.**T–E diagram of seawater without energy conversion. Under the constant total mass flow rate of seawater as a design constraint, Q

_{T}is maximized when the balance of surface seawater and deep seawater heat capacities are equal, ${\left(m{c}_{p}\right)}_{W}={\left(m{c}_{p}\right)}_{C}$, in Equation (8) [17].

**Figure 4.**T–E diagram of the OTEC process using the Carnot heat engine. T

_{H}and T

_{L}are the highest and lowest temperatures in the heat engine, respectively.

**Figure 5.**Conceptual diagrams of an ideal heat engine for OTEC with infinite performance of heat exchangers. The heat engine temperature varies and completely follows the seawater temperature change during the heat transfer process. T

_{H}and T

_{L}are the highest and lowest temperatures in the heat engine, and they reach T

_{W,in}and T

_{C,in}, respectively; (

**a**) T–s diagram; (

**b**) T–E diagram.

**Figure 6.**Relation between deep seawater flow rate and gross power in design. The gross power is roughly proportional to the mass flow rate of deep seawater.

**Figure 7.**Dependency of conventional and normalized thermal efficiencies and gross power per deep seawater flow rate. The open circles show the thermal conventional efficiency, η

_{th}, and the close triangles show the normalized thermal efficiency, η

_{th,Nor}.

**Figure 8.**Relation between exergy efficiency and thermal efficiency. The open and close circles show the conventional thermal efficiency, η

_{th}, and the open and close triangles show the normalized thermal efficiency, η

_{th,Nor}.

Data Source [Reference] | T_{W}(K) | T_{C}(K) | m_{W} (kg/s) | m_{C}(kg/s) | W_{gross}(kW) | E_{x,OTEC}(kW) | η_{th}(%) | η_{th,Nor}(%) | η_{ex}(%) |
---|---|---|---|---|---|---|---|---|---|

Simple Rankine cycle | |||||||||

Mitsui et al. (1983) [28] | 303.15 | 281.15 | 403 | 392 | 85 | 641 | 2.5 | 0.49 | 13.2 |

Bernardoni et al. (2019) [10] | 301.15 | 277.15 | 8798 | 8500 | 3877 | 17,236 | 2.2 | 0.93 | 22.5 |

Ikeagmi et al. (2018) [8] | 302.15 | 279.15 | 8333 | 8333 | 5750 | 15,898 | 3.2 | 1.43 | 36.2 |

Sinama et al. (2015) [29] | 301.15 | 278.15 | 51,020 | 35,849 | 15,733 | 77,115 | 3.2 | 0.81 | 20.4 |

Yoo et al. (2014) [30] | 299.15 | 278.15 | 65 | 62 | 20 | 96 | 2.4 | 0.76 | 20.7 |

Bombarda et al. (2013) [9] | 301.15 | 279.15 | 8491 | 8242 | 5000 | 16,663 | 3.1 | 1.25 | 30.0 |

Nithesh et al. (2016) [31] | 302.15 | 280.15 | 260 | 260 | 1.9 | 7 | 2.1 | 1.07 | 28.2 |

Wu et al. (2020) [32] | 299.15 | 277.15 | 260 | 260 | 77.7 | 374 | 2.4 | 0.70 | 20.8 |

Double-Stage Rankine cycle | |||||||||

Ikeagmi et al. (2018) [8] | 302.15 | 279.15 | 8333 | 8333 | 6350 | 15,898 | 3.2 | 1.58 | 39.9 |

Bombarda et al. (2019) [9] | 301.15 | 279.15 | 8491 | 8242 | 6079 | 16,663 | 3.7 | 1.52 | 36.5 |

Wu et al. (2020) [32] | 299.15 | 277.15 | 260 | 260 | 78.8 | 374 | 2.5 | 0.71 | 21.1 |

Triple-Stage Rankine cycle | |||||||||

Bombarda et al. (2019) [9] | 301.15 | 279.15 | 8491 | 8242 | 6425 | 16,663 | 3.9 | 1.60 | 38.6 |

Lorentz-like heat engines such as Kalina and Uehara | |||||||||

Yoo et al. (2014) [30] | 299.15 | 278.15 | 65 | 62 | 20 | 96 | 2.4 | 0.76 | 20.7 |

Ikeagmi et al. (2018) [8] | 302.15 | 279.15 | 8333 | 8333 | 6420 | 15,898 | 3.2 | 1.60 | 40.4 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yasunaga, T.; Fontaine, K.; Ikegami, Y.
Performance Evaluation Concept for Ocean Thermal Energy Conversion toward Standardization and Intelligent Design. *Energies* **2021**, *14*, 2336.
https://doi.org/10.3390/en14082336

**AMA Style**

Yasunaga T, Fontaine K, Ikegami Y.
Performance Evaluation Concept for Ocean Thermal Energy Conversion toward Standardization and Intelligent Design. *Energies*. 2021; 14(8):2336.
https://doi.org/10.3390/en14082336

**Chicago/Turabian Style**

Yasunaga, Takeshi, Kevin Fontaine, and Yasuyuki Ikegami.
2021. "Performance Evaluation Concept for Ocean Thermal Energy Conversion toward Standardization and Intelligent Design" *Energies* 14, no. 8: 2336.
https://doi.org/10.3390/en14082336