# Optimization Design of the Organic Rankine Cycle for an Ocean Thermal Energy Conversion System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model and Method

#### 2.1. System Description

#### 2.2. Mathematical Model

#### 2.2.1. Power Calculation

- (1)
- The turbine output electric power

- (2)
- The electric power consumption of the working fluid pump

^{3}; ${\eta}_{p}$ is the efficiency of the pump; and ${h}_{3}$ and ${h}_{4}$ are the specific enthalpies at Point 3 and Point 4, respectively, kJ/kg.

- (3)
- The electric power consumption of the seawater pump

^{3}; ${\eta}_{w}$ is the efficiency of the seawater pump; ${\lambda}_{w}\text{}$ is the friction coefficient of the seawater pipe; ${l}_{w}$ is the length of the surface seawater pipe, m; ${d}_{w}$ is the diameter of the seawater pipe, m; and ${v}_{w}$ is the flow velocity of surface seawater, m/s.

- (4)
- The net output power of the OTEC plant

#### 2.2.2. Heat Transfer Area Calculation

- (1)
- Heat transfer area of the evaporator

^{2}. Coefficient $\text{}a$ = 2970.28 and $b$ = 0.549 when ${q}_{e}$ is less than 10 kW/m

^{2}, otherwise $a$ = 16354 and $b$ = 0.035 [26].

^{2}s;

^{2}K; ${k}_{c}$ is the thermal conductivity of the heat transfer tube, 100.4 W/m K (HAL77-2); ${d}_{i}$ is the inside diameter of the heat transfer tube, 0.01605 m; and ${h}_{i}$ is the heat transfer coefficient of seawater in the heat transfer tubes, W/m

^{2}K, and is calculated using Formula (28).

^{2}, otherwise $F$ is ${F}_{2}$.

^{2}K; ${\mathsf{\Delta}\mathrm{T}}_{m}$ is the logarithmic mean temperature difference, °C; $Q$ is the heat duty, kW; and $A$ is the heat transfer area, m

^{2}.

- (2)
- Heat transfer area of the condenser

^{−4}m; and ${h}_{oc}$ is the heat transfer coefficient at the outside of the condensate tube, W/m

^{2}K.

#### 2.2.3. Method

- (1)
- the objective functions

- (2)
- The constraints on the decision variable range

- (3)
- the evaluation indexes

^{2}, and the shaft power of the turbine and pump, kW; and $P$ is the operating pressure, barg. The $CEPCI2001$ and all coefficients, including ${K}_{1}$, ${K}_{2}$, ${K}_{3}$, ${C}_{1}$, ${C}_{2}$, ${C}_{3}$, ${F}_{bm}$ (or ${B}_{1}$, ${B}_{2}$, ${F}_{m}$) of evaporator(fixed tube sheet), condenser(fixed tube sheet), pump(carbon steel, centrifugal) and steam turbine, refer to Ref. [32]. The $CEPCI2017$ is 628.2 [33].

## 3. Results

#### 3.1. The Optimization Design Results

#### 3.2. The Effects of Decision Parameters on the Performance of the OTEC

- The effects of evaporating temperature and condensing temperature

- The effect of the pinch-point temperature difference

- The effect of the four decision parameters on the investment cost

## 4. Conclusions

- (1)
- The exergy efficiency, the net output power per unit area, the net thermal efficiency, and the net output power increase first and then decrease with the increase in evaporating temperature or condensing temperature.
- (2)
- The back work ratio (BWR) is seriously affected by the condensing temperature. Increasing the condensing temperature can decrease the BWR value; however, the net output power is not necessarily large when the BWR is small.
- (3)
- The parameters directly related to the pinch-point temperature difference are, mainly, the flow rate of the seawater, the area of the heat exchanger, and the seawater pump power consumption. A small pinch-point temperature difference is beneficial for the performance parameters (the exergy efficiency, the thermal efficiency of the OTEC, the net output power, the net output power per unit seawater flow rate, and the back work ratio).
- (4)
- The investment cost is not very sensitive to the pinch-point temperature difference and evaporating temperature and condensing temperature over wide ranges. The effects of evaporating temperature and condensing temperature on the investment cost per unit net output power are roughly similar to those on the net output power per unit heat exchange area. However, the change in the investment cost per unit net output power with the pinch-point temperature difference is mainly determined by the change trend of the net output power.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Pareto Point | ${\mathit{m}}_{\mathit{r}}$ | ${\mathit{T}}_{\mathit{e}}$ | ${\mathit{T}}_{\mathit{c}}$ | $\Delta {\mathit{T}}_{\mathit{w}}$ | $\Delta {\mathit{T}}_{\mathit{c}}$ | $\mathit{\gamma}$ | ${\mathit{\eta}}_{\mathit{e}\mathit{x}}$ | ${\mathit{\eta}}_{\mathit{O}\mathit{T}\mathit{E}\mathit{C}}$ | ${\mathit{\eta}}_{\mathit{O}\mathit{R}\mathit{C}}$ | BWR | WPSF | ${\mathit{W}}_{\mathit{n}\mathit{e}\mathit{t}}$ | ${\mathit{m}}_{\mathit{c}}$ | Cost |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

kg/s | °C | °C | °C | °C | kW/m^{2} | % | % | % | % | kJ/kg | kW | kg/s | × 10^{5} USD | |

1 | 5.993 | 23.46 | 12.50 | 0.53 | 0.51 | 0.075 | 27.47 | 2.420 | 2.476 | 7.529 | 0.288 | 28.17 | 33.74 | 4.909 |

2 | 6.585 | 23.43 | 12.34 | 0.69 | 0.56 | 0.092 | 26.84 | 2.432 | 2.504 | 8.093 | 0.281 | 31.14 | 38.09 | 4.926 |

3 | 6.748 | 23.37 | 12.27 | 0.80 | 0.57 | 0.097 | 26.54 | 2.429 | 2.507 | 8.287 | 0.278 | 31.89 | 39.43 | 4.927 |

4 | 6.950 | 23.23 | 12.03 | 1.09 | 0.59 | 0.106 | 25.70 | 2.438 | 2.529 | 8.716 | 0.268 | 33.01 | 42.01 | 4.928 |

5 | 7.112 | 23.21 | 11.96 | 1.21 | 0.75 | 0.117 | 24.95 | 2.438 | 2.541 | 9.151 | 0.261 | 33.79 | 44.42 | 4.877 |

6 | 7.027 | 23.20 | 11.98 | 1.06 | 1.42 | 0.131 | 23.53 | 2.415 | 2.534 | 9.780 | 0.257 | 33.06 | 48.17 | 4.681 |

7 | 7.134 | 23.03 | 11.69 | 1.36 | 1.25 | 0.139 | 23.12 | 2.431 | 2.563 | 10.132 | 0.251 | 33.85 | 49.96 | 4.708 |

8 | 7.586 | 23.02 | 11.86 | 1.50 | 1.28 | 0.147 | 22.69 | 2.378 | 2.522 | 10.671 | 0.242 | 35.17 | 51.91 | 4.766 |

9 | 6.651 | 22.88 | 11.61 | 2.09 | 1.24 | 0.148 | 21.50 | 2.414 | 2.548 | 10.250 | 0.222 | 31.34 | 47.10 | 4.495 |

10 | 7.117 | 23.24 | 11.50 | 1.48 | 1.78 | 0.163 | 21.04 | 2.467 | 2.647 | 11.713 | 0.230 | 34.33 | 56.13 | 4.614 |

11 | 7.157 | 23.38 | 11.77 | 1.86 | 1.66 | 0.170 | 20.44 | 2.436 | 2.617 | 11.868 | 0.207 | 34.04 | 52.80 | 4.579 |

12 | 7.497 | 23.13 | 11.67 | 1.71 | 2.35 | 0.185 | 18.82 | 2.349 | 2.588 | 14.002 | 0.208 | 34.39 | 63.49 | 4.560 |

13 | 7.562 | 23.09 | 11.60 | 2.69 | 2.51 | 0.218 | 15.51 | 2.247 | 2.596 | 18.016 | 0.156 | 33.19 | 67.02 | 4.473 |

14 | 7.510 | 22.93 | 11.43 | 2.56 | 3.09 | 0.226 | 14.03 | 2.166 | 2.600 | 21.053 | 0.154 | 31.80 | 78.06 | 4.411 |

15 | 6.791 | 22.86 | 11.14 | 3.27 | 2.71 | 0.230 | 13.11 | 2.207 | 2.649 | 21.001 | 0.130 | 29.36 | 69.26 | 4.247 |

16 | 7.432 | 23.23 | 11.58 | 2.98 | 3.00 | 0.234 | 12.56 | 2.108 | 2.627 | 23.979 | 0.122 | 30.62 | 73.12 | 4.394 |

17 | 7.503 | 22.84 | 11.11 | 3.32 | 3.08 | 0.241 | 11.18 | 2.009 | 2.650 | 28.117 | 0.114 | 29.53 | 84.02 | 4.408 |

18 | 7.503 | 22.84 | 11.09 | 3.30 | 3.14 | 0.242 | 11.01 | 1.996 | 2.656 | 28.741 | 0.113 | 29.34 | 85.94 | 4.408 |

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**Figure 7.**The seawater flow rate and the net output power per unit seawater flow rate at the Pareto frontier point.

**Figure 9.**The effect of evaporating temperature and condensing temperature on (

**a**) the net output power per unit area, (

**b**) the exergy efficiency, (

**c**) the thermal efficiency of OTEC, (

**d**) the net output power, (

**e**) the deep seawater flow rate, (

**f**) the surface seawater flow rate, (

**g**) the net output power per unit seawater flow rate, and (

**h**) the back work ratio.

**Figure 10.**The effect of the pinch-point temperature difference on (

**a**) the flow rate of seawater, (

**b**) the heat transfer area of the heat exchanger, (

**c**) the net output power per unit area, (

**d**) the exergy efficiency, (

**e**) the thermal efficiency of the OTEC, (

**f**) the net output power, (

**g**) the net output power per unit seawater flow rate, and (

**h**) the back work ratio.

**Figure 11.**The effect of (

**a**) evaporating and condensing temperature and (

**b**) pinch-point temperature differences on the investment cost.

**Figure 12.**The effect of (

**a**) the evaporating and condensing temperature and (

**b**) pinch-point temperature differences on the investment cost per unit net output power.

Parameters | Symbol | Value |
---|---|---|

Deep seawater temperature | ${T}_{ci}$ | 4 °C |

Surface seawater temperature | ${T}_{wi}$ | 28 °C |

Diameter of seawater pipe | ${d}_{w}$ | 0.35 m |

Length of deep seawater pipe | ${l}_{c}$ | 3000 m |

Length of surface seawater pipe | ${l}_{w}$ | 200 m |

Design isentropic efficiency of turbine | ${\eta}_{t}$ | 0.8 |

Design efficiency of generator | ${\eta}_{g}$ | 0.9 |

Design efficiency of working fluid pump | ${\eta}_{p}$ | 0.6 |

Design efficiency of seawater pump | ${\eta}_{w}$ | 0.8 |

Type of heat transfer pipe in evaporator | Turbo BII | |

Number of heat transfer pipes in evaporator | 478 | |

Type of heat transfer pipe in condenser | Turbo CII | |

Number of heat transfer pipes in condenser | 478 | |

Working fluid | R134a |

Point | Pressure (kPa) | Temperature (°C) | Enthalpy (kJ/kg) | Entropy (kJ/kg K) | Phase |
---|---|---|---|---|---|

1 | 631.09 | 23.24 | 411.43 | 1.7169 | Saturated vapor |

2 | 435.78 | 11.73 | 405.37 | 1.7222 | Superheated, 0.23 °C |

3 | 435.78 | 11.50 | 215.64 | 1.0557 | Saturated liquid |

4 | 631.09 | 11.67 | 215.91 | 1.0561 | Subcooled, 11.57 °C |

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**MDPI and ACS Style**

Yang, X.; Liu, Y.; Chen, Y.; Zhang, L.
Optimization Design of the Organic Rankine Cycle for an Ocean Thermal Energy Conversion System. *Energies* **2022**, *15*, 6683.
https://doi.org/10.3390/en15186683

**AMA Style**

Yang X, Liu Y, Chen Y, Zhang L.
Optimization Design of the Organic Rankine Cycle for an Ocean Thermal Energy Conversion System. *Energies*. 2022; 15(18):6683.
https://doi.org/10.3390/en15186683

**Chicago/Turabian Style**

Yang, Xiaowei, Yanjun Liu, Yun Chen, and Li Zhang.
2022. "Optimization Design of the Organic Rankine Cycle for an Ocean Thermal Energy Conversion System" *Energies* 15, no. 18: 6683.
https://doi.org/10.3390/en15186683