# A Novel Ocean Thermal Energy Driven System for Sustainable Power and Fresh Water Supply

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## Abstract

**:**

## 1. Introduction

- 1.
- In this paper, we proposed a novel ocean thermal energy driven system for sustainable power and fresh water supply. The integrated system consisting of organic Rankine cycle and DCMD desalination will be introduced in Section 2.
- 2.
- A detailed mathematical model of the proposed cycle is to be established from the perspectives of thermodynamics and transmembrane transmit in Section 3.
- 3.
- Thermodynamic analyses on the proposed system will be carried out and the output performance of the system will be discussed in Section 4.
- 4.
- The conclusions of this work will be given in Section 5.

## 2. Description of the Integrated OTEC-DCMD System

#### 2.1. Power Generation Sub-Cycle (PGS)

#### 2.2. Water Production Sub-Cycle (WPC)

## 3. Mathematical Modelling of Mass, Energy and Exergy Balance

- 1.
- Ignore the heat loss in the system.
- 2.
- The system is in the steady-state operation.
- 3.
- All liquids are non-compressible and have uniform speed.
- 4.
- The membrane has good hydrophobic and air permeability, regardless of membrane wetting.
- 5.
- Ignore the kinetic and potential energy variation of fluid flowing between equipment.

#### 3.1. Balance Equation of the Integrated System

_{Q}, Ex

_{W}and Ex

_{dest}denote the exergy rates of heat transfer and work, and exergy destruction. “ex” characterizes the specific exergy, composed of the physical, chemical, potential and kinetic exergy and can be approximately expressed as:

#### 3.2. Balance Equation of Power Generation Sub-Cycle

_{t}≈ W

_{s}, where W

_{s}is shaft work.

_{t}can be obtained by the Equation (25).

_{WF}can be obtained from Equation (26).

_{WF}is volume flow rate of the working fluid (m

^{3}/s), p

_{5}and p

_{6}the pressure at working fluid pump inlet and outlet (kPa), and θ

_{WF}the working fluid pump efficiency.

#### 3.3. DCMD Water Production Sub-Cycle

#### 3.3.1. Mass and Heat Transfer Model

_{M}(kg·m

^{−2}·s

^{−1}·Pa

^{−1}) is the mass transfer coefficient and depends on the transmembrane mass transfer mode. p

_{F,W}(Pa) and p

_{p,w}(Pa) are the partial pressures of water vapor on the feed channel and the permeate channel, respectively. The subscripts “F” and “P” represent the feed channel and the permeate channel, respectively, and the subscripts “W” and “M” represent the parameters of main flow and on the membrane surface. p

_{F,W}can be calculated by Equation (29), where γ

_{W}is the activity coefficient of water, which is calculated by Equation (30) [24]; X

_{NaCl}is the molar fraction of NaCl in feed seawater and is calculated by Equation (31).The saturated vapor pressure p

_{v}

^{s}(T) (Pa) of pure water at different temperatures T (K) can be obtained from the Antoine Equation (32).

_{n}defined by Equation (33) [24]:

_{B}is Boltzmann’s constant (1.381 × 10

^{−23}J·mol

^{−1}·K

^{−1}), T

_{M}is the average temperature of the two membrane sides; δ

_{A}(2.641 × 10

^{−10}m) and δ

_{W}(3.711 × 10

^{−10}m) are the collision diameters of air and water molecules respectively; p is absolute pressure (Pa); Mwt

_{W}and Mwt

_{A}are the molecular weights of water and air, respectively. Generally, only the Molecular diffusion and Knudsen diffusion are considered to calculate the mass transfer coefficient K

_{M}when the total pressure of both sides are equal. Thus, K

_{M}can be calculated by Equation (35), which includes the molecular diffusion and Knudsen diffusion.

_{Wa}can be obtained by the following empirical formula:

_{M}(w·m

^{−2}) can be calculated by Equation (39):

_{H}(w·m

^{−2}) is the latent heat of vaporization through the membrane while q

_{C}(w·m

^{−2}) is the conducted heat which is considered as heat loss. δ (m) is the thickness of the membrane, and the enthalpy of evaporation of water ΔH

_{V}(kJ·kg

^{−1}) can be calculated by Equation (40).

#### 3.3.2. Balance Equations of DCMD Module

^{2}) and v (m·s

^{−1}) are the cross-section area and fluid speed of the feed channel. Thus, the number of the DCMD modules and the freshwater production rate can be derived as (46) and (47), respectively.

#### 3.4. Thermodynamic Performance Evaluation

## 4. Results and Discussions

#### 4.1. Power Generation Sub-Cycle and Exergy Analysis

#### 4.2. Water Production Sub-Cycle and Fresh Water Production

#### 4.2.1. Model Verification

^{-1}, and the pressure is the standard atmospheric pressure. Figure 5 shows a comparison of simulated permeate flux with experimental data in literature. The simulated values match with the experimental values very well, and the permeate flux increases with the feed temperature, due to the increase of the saturated vapor pressure in the feed channel. Figure 5 also shows that the constructed model is better fitted with the experiment under the lower temperature conditions, indicating its potential to predict the DCMD permeate flux under the OTEC temperature condition.

_{F}= v

_{P}= 0.145 m·s

^{−1}, p

_{F}= p

_{P}= p

_{0}, T

_{P}= 292.7 K,W

_{NaCl}= 0

#### 4.2.2. CFD Prediction of Water Production Performance

^{−1}and that of the permeate channel is 0.0029 m·s

^{−1}in this study. In practice, if there is space or membrane area limitation, the feed speed could increase to a proper extent to decrease the number of modules and the membrane area, and meanwhile, some loss of water production rate will be unavoidable.

_{M}also has an effect on the permeate flux, indirectly affecting the water conversion rate (α) and daily water production (DWP). In this study, the investigated channel length ranges from 0.125 m to 2.5 m. Figure 9 shows the influence of channel length L

_{M}on the α and DWP. The water production gradually increases with the channel length L

_{M}, in the beginning, with the maximum obtained when L

_{M}=0.75 m, then rapidly decreases. Although the membrane area increases with the channel length, the heat loss also increases simultaneously which cause the decrease of the permeate flux. Thus, an optimal channel length exists inevitably under the combined action of the membrane area increase and the permeate flux decrease. In our study, this optimal value is 0.75 m, at which the rate of water conversion reaches the maximum of 0.1% (Wet steam), and the daily water production can reach 58.874 t/d (Wet steam) while the power output of PGC is 100 kW.

#### 4.3. Analysis of the Integrated System

#### 4.3.1. Energy and Exergy Efficiency

#### 4.3.2. Economic Benefits

^{3}, and in Hawaii, the water is the most expensive, with the price of USD 2.23/m

^{3}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Q | Heat transfer rate (kW) |

W | Work rate (kW) |

S | Entropy (kW) |

Ex | Exergy (kW) |

m | Mass flow rate (kg·s^{−1}) |

h | Specific enthalpy (kJ·kg^{−1}) |

s | Specific entropy (kJ·kg^{−1}·K^{−1}) |

J | Permeate flux (kg·m^{−2}·h^{−1}) |

T | Temperature (℃,K) |

V | Flow rate (m^{3}·s^{−1}) |

A | Cross-section area (m^{2}) |

v | Velocity (m·s^{−1}) |

N | Number of modules |

ΔE | The change of exergy (kW) |

h_{r}c | The latent heat of vaporization (kJ·kg^{−1})Specific heat capacity (kJ·kg ^{−1}·K^{−1}) |

Greek letters | |

η | Thermal Efficiency (%) |

φ | Exergy Efficiency (%) |

α | Conversion rate (%) |

τ | Efficiency of turbine (%) |

θ | Efficiency of pump (%) |

Subscripts | |

Con | Condenser |

Eva | Evaporator |

WF | Work fluid |

WCR | Daily water production |

des | Destruction |

gen | Generation |

t | Turbine |

in | Inlet |

out | Output |

ph | Physics |

w | Work |

F | Feed channel |

P | Permeate channel |

h | Hot |

c | Cold |

d | Desalination |

b | Breadth of modules |

## Appendix A

Cycle | Energy Efficiency | Exergy Efficiency |
---|---|---|

Integrated OTEC System | ${\eta}_{\mathrm{System}}=\frac{{W}_{\mathrm{out}}+\alpha {m}_{19}{h}_{\mathrm{r}}}{c{m}_{19}\mathsf{\Delta}t}$ | ${\phi}_{\mathrm{System}}=\frac{{W}_{\mathrm{out}}+\alpha {m}_{19}e{x}_{19}}{E{x}_{\mathrm{System}}}$ |

WPC | ${\eta}_{\mathrm{WPC}}=\frac{\alpha {m}_{19}{h}_{\mathrm{r}}}{{Q}_{\mathrm{WPC}}}$ | ${\phi}_{\mathrm{WPC}}=\frac{\alpha {m}_{19}e{x}_{19}}{E{x}_{\mathrm{WPC}}}$ |

PGC | ${\eta}_{\mathrm{PGC}}=\frac{{W}_{\mathrm{out}}}{{Q}_{{}_{\mathrm{PGC}}}}$ | ${\phi}_{\mathrm{PGC}}=\frac{{W}_{\mathrm{out}}}{E{x}_{\mathrm{PGC}}}$ |

_{r}is the latent heat of vaporization, kJ/kg.

System Components | Exergy Efficiency Equations |
---|---|

Evaporator Condenser | ${\phi}_{\mathrm{E}}=\frac{\mathsf{\Delta}{E}_{\mathrm{c}}}{-\mathsf{\Delta}{E}_{\mathrm{h}}}$ ${\phi}_{\mathrm{C}}=\frac{\mathsf{\Delta}{E}_{\mathrm{c}}}{-\mathsf{\Delta}{E}_{\mathrm{h}}}$ |

Turbine | ${\phi}_{\mathrm{T}}={W}_{\mathrm{t}}/{m}_{3}(e{x}_{4}-e{x}_{3})$ |

WF pump | ${\phi}_{\mathrm{P}}={P}_{\mathrm{WF}}/{m}_{5}(e{x}_{6}-e{x}_{5})$ |

_{c}is the change in exergy of the cold fluid, and ΔE

_{h}is the change in exergy of the hot fluid.

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**Figure 1.**Schematic illustration of the proposed integrated the ocean thermal energy conversion (OTEC) system.

**Figure 7.**The influence of the feed channel velocity v

_{F}on the permeate channel velocity v

_{p}permeate flux J.

**Figure 8.**Influence of the feed channel velocity v

_{F}on the water conversion rate α and daily water production (DWP).

**Figure 9.**Influence of channel lengths L

_{M}on the water conversion rate α and daily water production DWP.

Working Fluid | Parameters | Dry Steam | Wet Steam |
---|---|---|---|

Ammonia | Evaporating temperature, °C | 22 | 24 |

Evaporating pressure, bar | 7.3 | 8 | |

Temperature of evaporator outlet, °C | 24 | 24 | |

Condensing temperature, °C | 9.5 | 9.5 | |

Condensing pressure, bar | 5.99 | 5.99 | |

Temperature of condenser outlet, °C | 9.5 | 9.5 | |

Mass flow rate of working fluid, kg/s | 5.131 | 3.544 | |

Seawater | Temperature of warm seawater inlet, °C | 28 | 28 |

Temperature of cold seawater inlet, °C | 5 | 5 | |

Mass flow rate of warm seawater, kg/s | 658.263 | 658.263 | |

Temperature drop of warm seawater, °C | 2.22 | 1.53 | |

Mass flow rate of cold seawater, kg/s | 523.413 | 523.413 | |

Temperature rise of cold seawater, °C | 2.75 | 1.88 | |

Power generation of turbine, kW | 100 | 100 | |

Working fluid pump power, kW | 1.361 | 1.344 |

Parameters | Dry Steam | Wet Steam |
---|---|---|

The inlet temperature of permeate channel, °C | 9.7 | 8.8 |

The outlet temperature of permeate channel, °C | 16.14 | 14.98 |

The inlet temperature of feed channel, °C | 25.8 | 26.47 |

The outlet temperature of feed channel, °C | 24.99 | 25.58 |

Components | Exergy Destruction Rate (kW) | Exergy Destruction Ratio (%) | ||
---|---|---|---|---|

Dry Steam | Wet Steam | Dry Steam | Wet Steam | |

Evaporator | 249.583 | 139.773 | 50.11 | 41.24 |

Condenser | 81.357 | 65.201 | 16.34 | 19.24 |

Turbine | 33.073 | 33.131 | 6.64 | 9.77 |

WF pump | 2.656 | 2.682 | 0.53 | 0.79 |

DCMD | 70.805 | 40.831 | 14.22 | 12.05 |

Heat exchanger | 60.571 | 57.333 | 12.16 | 16.91 |

Total | 498.045 | 338.952 | 100 | 100 |

Regions | Electricity Price (USD/kWh) | Water Price (USD/m^{3}) |
---|---|---|

Lamu (Kenya) | 0.224 | 0.78 |

Hawaii (USA) | 0.275 | 2.23 |

Tecoanapa (Mexico) | 0.192 | 0.7 |

FernandodeNoronha (Brazil) | 0.179 | 1.2 |

Manay (Philippine) | 0.199 | 0.365 |

Chennai (India) | 0.084 | 0.14 |

Kumejima (Japan) | 0.274 | 1.48 |

Montego (Jamaica) | 0.295 | 0.36 |

Subic (Fiji) | 0.135 | 0.253 |

Kuta (Indonesia) | 0.108 | 0.157 |

Rainbowbeach (Australia) | 0.246 | 1.98 |

Semporna (Malasysia) | 0.06 | 0.29 |

Ofu (Samoa) | 0.277 | 1.44 |

Port-Gentil (Gabon) | 0.207 | 0.54 |

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## Share and Cite

**MDPI and ACS Style**

Ma, Q.; Zheng, Y.; Lu, H.; Li, J.; Wang, S.; Wang, C.; Wu, Z.; Shen, Y.; Liu, X. A Novel Ocean Thermal Energy Driven System for Sustainable Power and Fresh Water Supply. *Membranes* **2022**, *12*, 160.
https://doi.org/10.3390/membranes12020160

**AMA Style**

Ma Q, Zheng Y, Lu H, Li J, Wang S, Wang C, Wu Z, Shen Y, Liu X. A Novel Ocean Thermal Energy Driven System for Sustainable Power and Fresh Water Supply. *Membranes*. 2022; 12(2):160.
https://doi.org/10.3390/membranes12020160

**Chicago/Turabian Style**

Ma, Qingfen, Yun Zheng, Hui Lu, Jingru Li, Shenghui Wang, Chengpeng Wang, Zhongye Wu, Yijun Shen, and Xuejin Liu. 2022. "A Novel Ocean Thermal Energy Driven System for Sustainable Power and Fresh Water Supply" *Membranes* 12, no. 2: 160.
https://doi.org/10.3390/membranes12020160