# Performance Analysis of a 10 MW Ocean Thermal Energy Conversion Plant Using Rankine Cycle in Malaysia

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## Abstract

**:**

_{T}) divided by the net power (P

_{N}). γ decreases when the inlet temperature difference (inlet temperature of warm seawater (T

_{WSWI})—inlet temperature of cold seawater (T

_{CSWI})) increases. P

_{N}is clarified to be approximately 70–80% of the P

_{G}(gross power) using Malaysian ocean conditions.

## 1. Introduction

_{3}) was used commonly as the working fluid to drive a Rankine cycle heat engine to reduce the cost of electricity. However, the potential to apply the LNG cold energy is limited compared to the deep seawater. The small MW scale onshore plants can combine power generation, seawater desalination, and deep ocean water applications, including auriculate, air-conditioning, and agriculture. This is due to the characteristics of deep ocean water, which is clean, cold, virus and bacteria-free, and mineral-rich [8,9]. Seungtaek et al. (2020), revealed the possibility of OTEC and seawater desalination considering the local tariff of electricity as well as water [9]. By focusing on the large capacity OTEC plants, the upscaling scenario in Indonesia is proposed because of the higher contribution to carbon reduction, easier business, and strategy for the installation [10]. Moreover, Langer, et al. (2021) proposed a GIS-based method for the site selection and discussed a band of a cost analysis of large-scale OTEC systems showing the sensitivity of the design capacity, and seawater temperature at selected locations in Indonesia [10,11]. Adiputra et al. (2020), designed the retrofit of a 100 MW OTEC using a second-hand large ship as a lower cost option [12].

_{3}as the working fluid are reported.

## 2. Analysis Method

#### 2.1. OTEC Potential and Profile of Temperature

#### 2.2. Rankine Cycle

_{E}, and T

_{C}using NH

_{3}as the working fluid. The efficiency of NH

_{3}as the working fluid for the OTEC system was studied by Ganic and Wu (1980), and they found NH

_{3}to be the best fluid owing to its highest thermal efficiency [21]. These were supported by several other studies in which, the latent heat of NH

_{3}was found to be higher than halogenated hydrocarbons [22]. NH

_{3}also outranked other types of working fluids in performance under a subcritical OTEC system [23].

#### 2.3. Objective Function

_{T}with the net output P

_{N}(Net power) and is often used as the objective function for optimization [24,25]. It is clearly derived and identified in previous studies that the objective function γ, that is, the relationship between the total heat transfer area of the heat exchanger per (unit) 1 kW of output power and the inlet temperatures of warm and cold seawater, is important [26]. Therefore, the total heat transfer area of the heat exchanger in the objective function becomes small, and the net power output becomes large. As a result, the objective function becomes small (known as the minimum objective function) and the OTEC plant will be economically viable.

#### 2.3.1. Net Power

_{N}is defined as in Equation (2) [27,28],

_{N}= P

_{G}− (P

_{WSW}+ P

_{CSW}+ P

_{WF})

_{G}in Equation (2) is the generated power, also known as gross power, P

_{WSW}is warm seawater pumping power, P

_{CSW}is cold seawater pumping power, and P

_{WF}is working fluid pumping power, shown in Equations (3)–(6).

_{G}= m

_{WF}η

_{T}η

_{G}(h

_{1}− h

_{2})

_{WSW}is the total pressure difference between the warm seawater pipe and the cold seawater pipe, and ∆P

_{CSW}is the total pressure difference between the working fluid piping ∆P

_{WF}.

_{WSW}is the total pressure variance of the warm seawater pipe, shown in Equation (7),

_{WSW}= ΔP

_{WSWE}+ ΔP

_{WSWEA}

_{WSWE}, and ΔP

_{WSWEA}is the pressure difference around the evaporator.

_{WSWE}is the pressure difference in the evaporator and is calculated as in Equation (8).

_{E}is the friction factor in the evaporator.

_{WSWEA}is assumed as 1.0 [m].

_{CSW}is the total pressure difference of the cold seawater pipe, shown in Equation (9),

_{CSW}= ΔP

_{CSWC}+ ΔP

_{CSWCA}+ΔP

_{CSWP}

_{CSWC}is the pressure difference in the condenser, ΔP

_{CSWCA}is the pressure difference around the condenser, and ΔP

_{CSWP}is the pressure difference of the cold seawater piping.

_{CSWC}is calculated as the pressure difference in the condenser as shown in Equation (10),

_{C}is the friction factor in the condenser.

_{CSWCA}assumed it with 1.0 (m).

_{CSWP}has calculated pressure is the pressure difference of the cold seawater piping as shown in Equation (11),

_{CSWP}= ΔP

_{CSWPf}+ ΔP

_{CSWPD}

_{CSWPf}is the friction loss and ΔP

_{CSWPD}is the density difference of the cold seawater in the cold seawater piping, respectively.

_{CSWPf}is calculated using Equation (12) [29],

_{CSWPD}is calculated using Equation (13).

_{WF}is the total pressure difference of the working fluid piping, and is calculated using Equation (14),

_{WF}= [v

_{3}(P

_{1}− P

_{3})] + P

_{0}

_{1}= v

_{3}is the specific volume in the condensing temperature T

_{C}, P

_{1}the is evaporation pressure, P

_{3}is the condensing pressure, and P

_{0}is the pressure lost in working fluid piping (9.8 × 10

^{4}).

#### 2.3.2. Heat Transfer Area

_{T}, is given as in Equation (15) [30],

_{T}= A

_{E}+ A

_{C}

_{E}and A

_{C}are the heat transfer area of the evaporator and condenser and are calculated using Equations (16)–(19).

_{E}and Q

_{C}are the evaporator and condenser heat transfer rates. The logarithmic mean temperature differences of the evaporator and condenser are (ΔT

_{m})

_{E}and (ΔT

_{m})

_{C}.

_{E}and U

_{C}represent the evaporator and condenser’s overall heat transfer coefficients, respectively. The heat transfer coefficient on warm sea water α

_{WSW}, the boiling heat transfer coefficient B, and the thermal conductivity of the heat transfer surface k

_{WSW}can be used to calculate U

_{C}. The heat transfer coefficient on cold seawater CSW, the condensation heat transfer coefficient C, and the thermal conductivity of the heat transfer surface α

_{CSW}can be used to calculate U

_{C}. In an OTEC system, the heat transfer area of the heat exchanger must be estimated.

_{3}as the working fluid and plate-type evaporator to determine the boiling heat transfer coefficient. On the other hand, an empirical equation of a fluted plate was used for the heat transfer coefficient for condensation.

- (a)
- Boiling Heat Transfer Coefficient

_{B}is calculated from the Equations (20) and (21) [31],

^{−1})

- (b)
- Condensation Heat Transfer Coefficient

_{C}and steam vapor in the desalination condenser α

_{DC}is calculated from the Equation (27) [32].

- (c)
- Heat Transfer Coefficient of the Seawater side (Evaporator and Condenser)

_{WSW}, α

_{CSW}and are calculated from Equation (34) [33].

#### 2.4. Objective Function and Its Variables

_{E}, T

_{C}, V

_{WSW}, V

_{CSW})

_{WSW}, and inlet temperature of the cold seawater T

_{CSWI}are given, γ is a function of the evaporation temperature T

_{E}, condensation temperature T

_{C}, warm seawater velocity in the evaporator V

_{WSW}and cold seawater velocity in the condenser V

_{CSW}. A minimum value of the objective function γ

_{min}can be calculated by the steepest descent or Powell’s method using Equations (2)–(36).

#### Condition and Calculation Method

_{1}when one variable (for example T

_{E}) is slightly changed. Subsequently, the partial derivative for T

_{E}is obtained as (γ

_{1}− γ)/ΔT

_{E}. Then, as a new initial value for T

_{E}, the step is multiplied by an arbitrary constant δ

_{1}to proceed to the next step. Using the same method, T

_{C}, V

_{WSW}, and V

_{CSW}are obtained. As clearly shown in the Figure 1, γ is calculated using the new combination of variables to derive the minimum value of γ which is γ

_{min.}

_{3}and the seawater are taken from [34,35], respectively. In this paper, optimization is carried out using the REFPROP as the thermophysical properties of NH

_{3}. In previous studies, PROPATH and other approximate values were used for NH

_{3}which has resulted in a different optimization design.

## 3. Results and Discussion

#### 3.1. Minimum Objective Function

_{WSWI}− T

_{CSWI}). The value of the minimum objective function is decreased when the inlet temperature difference (T

_{WSWI}− T

_{CSWI}) is increased as can be seen in the Figure 5. In other words, the objective function γ is smaller when the warm seawater inlet temperature, T

_{WSWI}is higher and the cold seawater inlet temperature, T

_{CSWI}is lower.

_{WSWI}= 28.98 °C and T

_{CSWI}= 4.6 °C, γ = 7.44 m

^{2}/kW, whereas when T

_{WSWI}= 28.98 °C and T

_{CSWI}= 7.5 °C, γ = 9.14 m

^{2}/kW. Although the inlet temperature difference (T

_{WSWI}− T

_{CSWI}) under these two conditions is only 2.9 °C, the ratio of γ is 1:1.2 and significant. This indicates that the effect of cold seawater inlet temperature is large and impactful.

_{WSWI}− T

_{CSWI}) is shown in Figure 5 and is given by Equation (38) in solid line:

_{min}= 4.5 × 10

^{3}(T

_{WSWI}− T

_{CSWI})

^{−2.0}

_{min}= 1.3 × 10

^{5}(T

_{WSWI}− T

_{CSWI})

^{−3.2}

_{WSWI}= 28.98 °C and T

_{CSWI}= 4.6 °C, γ = 7.44 m

^{2}/kW from Equation (38), whereas γ = 4.73 m

^{2}/kW from Equation (39), respectively. γ is about 1.57 times larger. The reason for this increase is probably due to the smaller power generation output of 10 MW. This is because when the power output decreases, the performance of the heat exchanger deteriorates and the total heat transfer area increases. Nevertheless, it could also be due to the efficiency of each component in the OTEC system (turbine, heat exchanger, pumps, and others) having improved and it caused an improvement in the total OTEC system, attributing an increase in the net power output.

_{WSWI}and T

_{CSWI}change, considering within the range of (T

_{WSWI}− T

_{CSWI}), the objective function γ is determined only by the temperature difference between warm and cold seawater inlets. Performance analysis for the OTEC system must be done considering the minimum objective function for cost viability.

#### 3.2. Pumping Power and Net Power

_{N}, the warm seawater pumping power P

_{WSW}, the cold seawater pumping power P

_{CSW}and the working fluid pumping power P

_{WF}versus the inlet temperature difference (T

_{WSWI}− T

_{CSWI}). In the Figure 6a–c, cold seawater pipe length is 1000 m, 800 m, and 600 m, respectively.

_{WSWI}− T

_{CSWI}) is increased as can be seen in the Figure 6a–c. The working fluid pumping power is constant when an inlet temperature difference is increased. The working fluid pumping power is estimated to be 200 kW.

_{WSWI}− T

_{CSWI}) is increased, the value of the net power is increased when the inlet temperature difference (T

_{WSWI}− T

_{CSWI}) is increased as can be seen in the Figure 6a–c.

#### 3.3. Warm and Cold Seawater Flow Rate

_{WSWI}− T

_{CSWI}) is increased, the warm and cold sea water flow rate are decreased when the inlet temperature difference (T

_{WSWI}− T

_{CSWI}) is increased as can be seen in Figure 7a–c.

_{WSWI}= 28.98 °C and T

_{CSWI}= 4.6 °C, warm seawater flow rate m

_{WSW}= 4.321 × 10

^{7}kg/h, cold seawater flow rate m

_{CSW}= 4.151 × 10

^{7}kg/h, respectively. On the other hand, in the case of 600 m, T

_{WSWI}= 28.98 °C and T

_{CSWI}= 7.5 °C, warm seawater flow rate m

_{WSW}= 5.216 × 10

^{7}kg/h and cold seawater flow rate m

_{CSW}= 5.364 × 10

^{7}kg/h, respectively. An observation was made that the warm seawater flow rate m

_{WSW}ratio of 1000 m is smaller than 600 m at 1:1.2 and the cold seawater flow rate m

_{CSW}ratio of 1000 m is also smaller than 600 m at 1:1.3, respectively.

#### 3.4. Heat Transfer Area

_{T}, the heat transfer area of the evaporator A

_{E}, and the heat transfer area of the condenser A

_{C}versus the inlet temperature difference. In the Figure 8a–c, cold seawater pipe length is 1000 m, 800 m, and 600 m, respectively.

_{WSWI}− T

_{CSWI}) is increased as can be confirmed in Figure 8a–c.

_{WSWI}− T

_{CSWI}) is increased, and the heat transfer area of the evaporator and condenser is decreased when the inlet temperature difference (T

_{WSWI}− T

_{CSWI}) is increased as can be seen in the Figure 8a–c.

_{T}by considering cold seawater pipe lengths as 1000 m and 600 m is performed. In the case of 1000 m, T

_{WSWI}= 28.98 °C and T

_{CSWI}= 4.6 °C, the total heat transfer area A

_{T}= 6.446 × 10

^{5}m

^{2}. On the other end, in the case of 600 m, T

_{WSWI}= 28.98 °C and T

_{CSWI}= 7.5 °C, the total heat transfer area A

_{T}= 7.812 × 105 m

^{2}. It was observed that the total heat transfer area A

_{T}ratio of 1000 m is smaller than 600 m at 1:1.2.

## 4. Feasible OTEC Plant Specification

_{WSWI}− T

_{CSWI}). As a result, it is possible to estimate the total OTEC system output if the warm seawater inlet temperature T

_{WSWI}and the cold seawater inlet temperature T

_{CSWI}are known from surveys of other sea areas.

## 5. Conclusions

- The value of the minimum objective function is decreased when the inlet temperature difference (T
_{WSWI}− T_{CSWI}) is increased as can be seen in the Figure 5 (comparison between Equations (38) and (39)). Pertaining to this value, the minimum objective function versus the inlet temperature difference was derived and shown in Equation (38). Comparing 10 MW and 100 MW, the objective function of 10 MW is larger, resulting in a higher CAPEX. - The value of the warm seawater pumping power and cold seawater pumping power is decreased when the inlet temperature difference (T
_{WSWI}− T_{CSWI}) is increased. - Even if the inlet temperature difference is increased, the working fluid pumping power is constant. The working fluid pumping power is as small as 200 kW.
- Because the pumping power of the warm seawater and cold seawater decreases when the inlet temperature difference (T
_{WSWI}− T_{CSWI}) is increased, the value of the net power is increased when the inlet temperature difference (T_{WSWI}− T_{CSWI}) is increased. - The warm and cold sea water flow rate decreases as the inlet temperature difference increases.
- The value of the total heat transfer area, the heat transfer area of the evaporator, and the heat transfer area of the condenser decreased when the inlet temperature difference (T
_{WSWI}− T_{CSWI}) is increased.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | heat transfer area | (m^{2}) |

B_{o} | Bond number | (-) |

B_{o}* | modified Bond number | (-) |

c_{p} | specific heat at constant pressure | (kJ/kgK) |

d | diameter | (m) |

D_{eq} | equivalent diameter | (m) |

f_{p} | pressure factor | (-) |

g | gravitational acceleration | (m/s^{2}) |

Gr | Grashof number | (-) |

h | enthalpy | (kJ/kg) |

depth of flute | (m) | |

H | ratio of sensible to latent heat | (-) |

k | thermal conductivity | (W/mK) |

l | length | (m) |

L | latent heat | (kJ/kg) |

∆L | width of plate | (m) |

m | mass flow rate | (kg/s) |

Nu | Nusselt number | (-) |

P | Power | (W) |

Pressure | (Pa) | |

Pr | Prandtl number | (-) |

Prop | property | (-) |

ΔP | pressure difference | (Pa) |

q | heat flux | (W/m^{2}) |

Q | heat flow rate | (kJ) |

Re | Reynolds number | (-) |

t | thickness of plate | (mm) |

T | temperature | (°C) |

∆T | temperature difference | (°C) |

∆T_{m} | logarithmic temperature difference | (°C) |

U | overall heat transfer coefficient | (W/m^{2}K) |

v | specific volume | (m^{3}/kg) |

V | velocity | (m/s) |

X | non-dimensional number | (-) |

∆X | length of plate | (m) |

Y | non-dimensional number | (-) |

∆Y | clearance of plate | (m) |

α | heat transfer coefficient | (W/m^{2}K) |

γ | objective function | (m^{2}/kW) |

ζ | friction factor | (-) |

η | efficiency | (-) |

υ | dynamic viscosity | (Pa s) |

ν | kinematic viscosity | (m^{2}/s) |

ρ | density | (kg/m^{3}) |

σ | surface tension | (N/m) |

Subscripts | ||

a | atmosphere | |

B | boiling | |

C | condenser | |

CSW | cold seawater | |

D | density | |

E | evaporator | |

f | friction loss | |

G | generator | |

I | inlet | |

L | length | |

L | liquid | |

m | mean | |

min | minimum | |

N | net | |

O | outlet | |

T | turbine | |

V | vapor | |

W | wall | |

WF | working fluid | |

WSW | warm seawater |

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**Figure 1.**Steepest descent also known as Powell’s method—flow diagram of Rankine cycle method used in this study.

**Figure 2.**Depth and deep seawater temperature profile of several potential sites in Sabah at 1000 m, 800 m, and 600 m, respectively. For simulation purpose, the applied data for Kalumpang was retrieved from Japan Oceanographic Data Center (JODC) (2020) 1000 m (4.6 °C), 800 m (5.79 °C), and 600 m (7.5 °C), respectively.

**Figure 3.**The schematic diagram of OTEC cycle, where warm seawater is represented in red line, cold seawater in blue line and NH3, the working fluid in orange line.

**Figure 5.**Comparison of minimum objective function from Equation (38) (simulation from this study) and Equation (39) (comparing with empirical data from Uehara & Nakaoka, 1984)) [30].

**Figure 9.**A conceptual idea of the floating-type OTEC [38].

- Gross power P
_{G}
| [MW] | 10 |

- Warm seawater inlet temperature T
_{WSWI}
| [°C] | 25.0, 28.98, 31.0 |

- Cold seawater inlet temperature T
_{CSWI}
| [°C] | 4.6, 5.79, 7.5 |

- Cold seawater pipe length l
_{CSW}
| [m] | 1000, 800, 600 |

- Cold seawater pipe diameter d
_{CSW}
| [m] | 5 |

Dimensions of Evaporator and Condenser | ||

- Plate length ΔX
| [m] | 4 |

- Plate width ΔL
| [m] | 1.5 |

- Plate thickness t
| [mm] | 1 |

- Plate clearance in seawater side ΔY
_{WSW}, ΔY_{CSW}
| [mm] | 5 |

- Plate clearance in working fluid side ΔY
_{WF}
| [mm] | 5 |

- Thermal conductivity of plate (titanium) k
_{W}
| [W/m K] | 14.76 |

- Efficiency of turbine η
_{T}
| [%] | 85 |

- Efficiency of seawater pumps η
_{WSWP}, η_{CSWP}
| [%] | 80 |

- Efficiency of working fluid pump η
_{WFP}
| [%] | 75 |

- Efficiency of generator η
_{G}
| [%] | 96 |

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## Share and Cite

**MDPI and ACS Style**

Thirugnana, S.T.; Jaafar, A.B.; Rajoo, S.; Azmi, A.A.; Karthikeyan, H.J.; Yasunaga, T.; Nakaoka, T.; Kamyab, H.; Chelliapan, S.; Ikegami, Y.
Performance Analysis of a 10 MW Ocean Thermal Energy Conversion Plant Using Rankine Cycle in Malaysia. *Sustainability* **2023**, *15*, 3777.
https://doi.org/10.3390/su15043777

**AMA Style**

Thirugnana ST, Jaafar AB, Rajoo S, Azmi AA, Karthikeyan HJ, Yasunaga T, Nakaoka T, Kamyab H, Chelliapan S, Ikegami Y.
Performance Analysis of a 10 MW Ocean Thermal Energy Conversion Plant Using Rankine Cycle in Malaysia. *Sustainability*. 2023; 15(4):3777.
https://doi.org/10.3390/su15043777

**Chicago/Turabian Style**

Thirugnana, Sathiabama T., Abu Bakar Jaafar, Srithar Rajoo, Ahmad Aiman Azmi, Hariharan Jai Karthikeyan, Takeshi Yasunaga, Tsutomu Nakaoka, Hesam Kamyab, Shreeshivadasan Chelliapan, and Yasuyuki Ikegami.
2023. "Performance Analysis of a 10 MW Ocean Thermal Energy Conversion Plant Using Rankine Cycle in Malaysia" *Sustainability* 15, no. 4: 3777.
https://doi.org/10.3390/su15043777