# Ocean Thermal Energy Conversion Using Double-Stage Rankine Cycle

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## Abstract

**:**

## 1. Introduction

## 2. Analysis Method

#### 2.1. Rankine Cycle

- (1)
- The working fluid is saturated vapor at the evaporator outlet.
- (2)
- The working fluid is saturated liquid at the condenser outlet.
- (3)
- The heat transfer part is negligible without the evaporator and in the condenser.
- (4)
- The pressure loss of the working fluid is negligible in the laying pipes, the evaporator, and the condenser.
- (5)
- The potential energy of the working fluid is negligible.

_{E}(4 => 1) is calculated using the following equations:

_{P}is the specific heat at constant pressure, U is the overall heat transfer coefficient, A is the heat transfer area and ΔT

_{m}is the mean temperature difference between the heat source and the working fluid. Subscript E means the evaporator, I and O are the heat exchanger inlet and outlet, Rankine is Rankine cycle, WF is the working fluid, WS is the warm seawater, and the numbers shown in the equations correspond to those shown in the schematic Figure 1.

_{C}(2 => 3) is calculated using the following equations:

_{th}are calculated using the following equation:

#### 2.2. Double-Stage Rankine Cycle

_{T}, the working fluid pumping power W

_{P}and the heat flow rate in the heat exchanger of the double-stage Rankine cycle are the sum of each stage of the Rankine cycle.

#### 2.3. Kalina Cycle

- (1)
- The working fluid is saturated liquid at condenser outlet and diffuser outlet.
- (2)
- The working fluid is separated into a saturated vapor and a saturated liquid in isothermal and isobaric process by the separator.
- (3)
- The heat transfer part is negligible without the evaporator and in the condenser.
- (4)
- The process in the diffuser is isenthalpic.
- (5)
- The pressure loss of the working fluid is negligible in the laying pipes, the evaporator, and the condenser.
- (6)
- The potential energy of the working fluid is negligible.

_{E}(4 => 5) and Q

_{C}(1→2), are respectively calculated using the following equations:

_{RG}(3 ≥ 4, 7 ≥ 8) is calculated by the following equations:

_{th}are calculated using Equation 8.

#### 2.4. Evaluation of Heat Transfer Process

_{S}) method for the purpose of a simplified calculation method. The conceptual diagram of the GMTD

_{S}method in the evaporation process is shown in Figure 8. The GMTD

_{S}method clearly shows the relations with the temperature change of the heat source and sufficient variations of the thermophysical properties of the working fluid required to evaluate the actual pinch pint temperature difference.

_{S}in the evaporator, (ΔT

_{m,GMTDs})

_{E}, is defined using the following equations:

_{WS,B}is the warm seawater temperature at T

_{4,B}. Subscript GMTDs means the GMTDs method, LMTD is the logarithmic mean temperature difference (LMTD) method and SC is the super-cooled liquid area of the working fluid, and WV is the wet vapor area.

_{m})

_{C}, is defined using following equation:

_{S}method as is the case in the evaporator.

#### 2.5. Maximum Power Evaluation

_{m,utilizable}, [3] from the heat source is defined as the maximum power efficiency, η

_{m}.

_{m,utilizable}, [3] is calculated for warm and cold seawater inlet temperatures, T

_{WSI}and T

_{CSI}, and heat capacity rates, C

_{WS}and C

_{CS}, by the following equations:

_{p}) is heat capacity rate, and N is the number of stages in the multistage cycle. The subscript N means the number of stages in the multistage cycle, opt is the conditions at the maximum utilizable power and utilizable is the utilizable power.

#### 2.6. Calculation Condition

^{3}kg/s), the number of heat transfer unit of the evaporator and the condenser is 2.0, and the number of heat transfer unit of the regenerator in the Kalina cycle is 1.5. The number of heat transfer unit, NTU, is defined as conventional evaluation of heat exchanger. Assuming that the number of heat transfer units NTU

_{E}and NTU

_{C}for the evaporator and the condenser can be expressed as:

_{E}and (UA)

_{C}, is assumed to be equal to those in the low-temperature cycle. The working fluid was three different kinds media: ammonia, HFC134a and ammonia/water mixture. Ammonia and HFC134a is applied to the single Rankine and double-stage Rankine cycles. Ammonia/water mixture is applied to the Kalina cycle, and the ammonia concentration at the evaporator inlet is 0.95 kg/kg. The physical properties of pure working fluids and non-azeotropic mixture are calculated using the REFPROP-database [20] and PROPATH-database [21], respectively.

## 3. Results and Discussion

#### 3.1. Comparison of Single Rankine, Double-Stage Rankine and Kalina Cycles

_{WS}, for single Rankine, double-stage Rankine and Kalina cycles. The chain line refers to the double-stage Rankine cycle using ammonia, the two-dot chain line to HFC134a, the dashed line to the single Rankine cycle using ammonia, the dotted line to HFC134a, the solid line to the Kalina cycle, and the circle mark to the maximum value of the power output. The warm seawater temperature change, ΔT

_{WS}, is the difference between warm seawater temperatures at evaporator inlet and outlet. The power output increased with an increase of the warm seawater temperature change. After reaching a maximum power output, the power output decreases because the effective temperature difference, the working fluid temperature difference between evaporation and condensation temperature, decreases with an increase of the warm seawater temperature change. The Kalina cycle shows lower power output than the single Rankine cycle for less than 3.6 °C, larger power output than the double-stage Rankine cycle for more than 5.0 °C, and lower power output than the double-stage Rankine cycle for more than 6.9 °C. The maximum power output of the Kalina cycle is largest in three cycles. In the single Rankine and the double-stage Rankine cycles, ammonia shows larger maximum power output than HFC134a, and has slightly lower warm seawater temperature change at the maximum power output, ΔT

_{WS,m}. In the double-stage Rankine cycle, the maximum power output, W

_{m}, is 6.35 MW and the change in warm seawater temperature, ΔT

_{WS,m}, is 5.72 °C when ammonia is the working fluid, whereas W

_{m}is 6.26 MW and ΔT

_{WS,m}is 5.79 °C when HFC134a is the working fluid. In the single Rankine cycle, W

_{m}is 5.76 MW and ΔT

_{WS,m}is 5.17 °C with ammonia, and W

_{m}is 5.70 MW and ΔT

_{WS,m}is 5.24 °C with HFC134a. The maximum power output of the Kalina cycle using ammonia/water mixture as working fluid is 6.42 MW and the change in warm seawater temperature is 5.80 °C. However, in previous studies [11,12,13], the effective temperature difference and heat transfer coefficient decrease when using non-azeotropic mixture. For that reason, the double-stage Rankine cycle allows for the improvement of OTEC system. The double-stage Rankine cycle can improve the maximum power output compared to the single Rankine cycle because of an increase of the warm seawater temperature change and a decrease of the irreversible losses in the heat exchange process. The results of the parametric performance analysis show that the double-stage Rankine cycle can reduce the irreversible losses in the heat exchange process as with the Kalina cycle using an ammonia/water mixture.

_{th}. In the single Rankine and the double-stage Rankine cycles, ammonia shows slightly higher thermal efficiency of the cycle at the maximum power output than HFC134a. However, the thermal efficiencies of the cycle at the maximum power are almost the same and approximately 3.2% when comparing three cycles. The thermal efficiency of the Kalina cycle has lower power output than the single Rankine cycle for more than 4.16%.

_{th}, with respect to the warm seawater temperature change, ΔT

_{WS}. The thermal efficiency of the cycle decreased with an increase in the warm seawater temperature change. The warm and the cold seawater’s source temperature changes between heat exchangers inlets and outlets increase, and the effective temperature difference of the working fluid decreases. The thermal efficiency of the cycle decreases with an increase of the warm seawater temperature change, owing to the decrease of the effective temperature difference. In the double-stage Rankine cycle, less irreversible loss occurs in the heat exchange process as the warm seawater temperature change increases. In particular, the warm seawater temperature change of the Kalina cycle has lower thermal efficiency than the single Rankine cycle for less than 3.6 °C.

_{E}and P

_{C}, with respect to the warm seawater temperature change, ΔT

_{WS}. Double-stage Rankine cycle can divide the temperature range of working fluid into two cycles. The evaporation and condensation pressures are different at each stage in the double-stage Rankine cycle. These pressures of the high-temperature cycle in double-stage Rankine cycle are higher than the single Rankine cycle. In the low-temperature cycle, the evaporation and condensation pressures are lower than the single Rankine cycle. The pressures of the Kalina cycle using ammonia/water mixture as working fluid are comparatively low compared to the single Rankine cycle using ammonia.

_{ETD}, with respect to the warm seawater temperature change, ΔT

_{WS}. The effective temperature difference of the double-stage Rankine cycle is higher than the single Rankine cycle because double-stage Rankine cycle can divide the temperature range of working fluid into two cycles. The difference of the effective temperature between double-stage Rankine and single Rankine cycles increases with an increase of the warm seawater temperature change. The effective temperature differences at the maximum power output are almost the same.

_{m}, with respect to the warm seawater temperature change, ΔT

_{WS}. The maximum power efficiency is the ratio of the power output on the maximum utilizable power, W

_{m,utilizable}[3]. The maximum power efficiency of the single Rankine cycle is highest in three cycles. The maximum utilizable power increases with an increase of the number of stages. In the case of the Kalina cycle, the number of stages for the maximum utilizable power is 100 stages, because the cycle also starts to resemble the cycle using non-azeotropic mixtures as the number of stages increases and the application of a relationship is possible. The maximum utilizable power of the single Rankine cycle is 7.95 MW, the double-stage Rankine cycle is 10.6 MW, and the Kalina cycle is 15.7 MW. On the other hand, the maximum power efficiency of the single Rankine cycle is approximately 72%, the double-stage Rankine cycle is 60–59%, and the Kalina cycle is 40.8%. Considering the maximum power efficiency obtained in the study, the double-stage Rankine and the Kalina cycles can improve the power output by reducing the irreversible losses in the cycle. The parameters at the maximum power output is shown in Table 1.

#### 3.2. The System Characteristics of the Double-Stage Rankine Cycle

_{WS,H}/ΔT

_{WS}, for the double-stage Rankine cycle. The warm seawater temperature change distribution ratio is the ratio of the temperature change of the high-temperature cycle in the double-stage Rankine cycle to total temperature change, ΔT

_{WS}. The warm seawater temperature change is fixed at the maximum power output with varying distribution ratio in the double-stage Rankine cycle. When the warm seawater temperature change of the high-temperature cycle in the double-stage Rankine cycle is small, the effective temperature difference of the working fluid increases, but the heat flow rate decreases. The power output of the high-temperature cycle is comparatively small at low warm seawater temperature change distribution ratio due to small heat flow rate. On the other hand, the power output of the low-temperature cycle is larger than the high-temperature cycle because of high heat flow rate of the low-temperature cycle. In the case of equal warm seawater temperature change of the high-temperature and the low-temperature cycles in the double-stage Rankine cycle, the power output of each cycle are almost the same. The power output of the double-stage Rankine cycle has a maximum value at equal warm seawater temperature change of each cycle.

_{WS,H}/ΔT

_{WS}, for single Rankine, double-stage Rankine and Kalina cycles. Figure 17a,b respectively show the results of ammonia and HFC134a as working fluid in single Rankine and double-stage Rankine cycles. The horizontal lines refer to the maximum power output of single Rankine and Kalina cycles. The power output of double-stage Rankine cycle is larger than the single Rankine cycle when the warm seawater temperature change distribution ratio ranges from 0.3 to 0.7.

_{th}, with respect to the warm seawater temperature change distribution ratio, ΔT

_{WS,H}/ΔT

_{WS}, for single Rankine, double-stage Rankine and Kalina cycles. The thermal efficiency of double-stage Rankine cycle is larger than the single Rankine cycle when the warm seawater temperature change distribution ratio ranges from 0.4 to 0.6.

_{th}, and the effective temperature difference of the high-temperature and the low-temperature cycles with respect to the warm seawater temperature change distribution ratio, ΔT

_{WS,H}/ΔT

_{WS}, for the double-stage Rankine cycle. The effective temperature differences using ammonia and HFC134a as working fluid are almost the same.

## 4. Conclusions

_{m}, is 6.35 MW and the change in warm seawater temperature, ΔT

_{WS,m}, is 5.72 °C when ammonia is the working fluid, whereas W

_{m}is 6.26 MW and ΔT

_{WS,m}is 5.79 °C when HFC134a is the working fluid.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**Fluid temperature in a counter-flow heat exchanger. This evaluation method proposed by Utamura et al. [19] and can evaluates relations with the temperature change of the heat source and variations of the thermophysical properties of the working fluid.

**Figure 11.**Relationship between the warm seawater temperature change and the thermal efficiency of the cycle.

**Figure 15.**Relationship between the maximum power efficiency and the warm seawater temperature change.

**Figure 16.**Relationship between the power output and the warm seawater temperature change distribution ratio.

**Figure 17.**(

**a**) Relationship between the power output and the warm seawater temperature change distribution ratio. The working fluid in the single Rankine and double-stage Rankine cycles is (

**a**) ammonia and (

**b**) HFC134a, respectively.

**Figure 19.**Relationship between the effective temperature difference and the warm seawater temperature change.

Parameter | Unit | S-R Ammonia | S-R HFC134a | D-R Ammonia | D-R HFC134a | Kalina |
---|---|---|---|---|---|---|

W_{m} | MW | 5.75 | 5.70 | 6.35 | 6.26 | 6.42 |

ΔT_{WS,m} | °C | 5.17 | 5.24 | 5.72 | 5.79 | 5.78 |

η_{th,m} | % | 3.20 | 3.13 | 3.25 | 3.22 | 3.20 |

W_{m,utilizable} | MW | 7.95 | 7.95 | 10.6 | 10.6 | 15.7 |

η_{m} | % | 72.4 | 71.7 | 59.9 | 59.0 | 40.8 |

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## Share and Cite

**MDPI and ACS Style**

Ikegami, Y.; Yasunaga, T.; Morisaki, T. Ocean Thermal Energy Conversion Using Double-Stage Rankine Cycle. *J. Mar. Sci. Eng.* **2018**, *6*, 21.
https://doi.org/10.3390/jmse6010021

**AMA Style**

Ikegami Y, Yasunaga T, Morisaki T. Ocean Thermal Energy Conversion Using Double-Stage Rankine Cycle. *Journal of Marine Science and Engineering*. 2018; 6(1):21.
https://doi.org/10.3390/jmse6010021

**Chicago/Turabian Style**

Ikegami, Yasuyuki, Takeshi Yasunaga, and Takafumi Morisaki. 2018. "Ocean Thermal Energy Conversion Using Double-Stage Rankine Cycle" *Journal of Marine Science and Engineering* 6, no. 1: 21.
https://doi.org/10.3390/jmse6010021