# Analysis and Optimization of Atmospheric Drain Tank of Lng Carrier Steam Power Plant

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feed Water and Steam Condensate System

## 3. Data Collection

## 4. Thermodynamic Analysis

## 5. Energy and Exergy Analysis Results

^{−1}and reaching a ship speed of about 13 knots, the main sea water circulating pumps are stopped and cooling of the main condenser is taken over by the scoop system, which collects sea water according to the ship’s speed.

^{−1}, after which energy losses become lower and are distributed more equally through the upper range of the load range. Exergy flow losses of the atmospheric drain tank have an opposite trend to energy losses and increase even with the increased main propulsion turbine load (Figure 4). Exergy destruction amplitude is about 10 kW at the highest load, which is almost double compared to energy losses. The increment of exergy destruction with increased load is typical for disturbances in the system that may be connected to some equipment, under capacitance or similar construction design failure. The observed shortcoming may be improved by optimizing the respective component flow streams. The moment of decreasing exergy destruction trend at higher loads is at 1.5 min

^{−1}, where extraction of steam from the high-pressure turbine begins. The extracted steam is used for ship services. This moment obviously acts positively on the exergy destruction of the atmospheric drain tank.

## 6. Mathematical Formulation of Atmospheric Drain Tank Optimization Problem

_{i}of polynomial P(x

_{i}), i = 1, …, n is:

**X**and the vector with the coefficients a

_{i}, i = 0, …, k be denoted by a. The solution to (21) and (22) can be found by multiplying system (23) by the inverse of

**X**:

- Contaminated condensate cooler temperature outlet t
_{4}; - Clean condensate cooler temperature outlet t
_{5}; - Distillate temperature t
_{6}.

- Exergy of stream inlet to atmospheric drain tank from fresh water generator ex
_{1}; - Contaminated condensate cooler temperature outlet t
_{4}; - Exergy of stream inlet to atmospheric drain tank from gland steam condenser ex
_{2}; - Exergy of stream inlet to atmospheric drain tank from first-stage feed water heater ex
_{3}; - Mass flow inlet to atmospheric drain tank from m
_{1}to m_{6}are fixed; - Pressure from p
_{1}to p_{6}is fixed.

- Conservation of mass flow:$${\dot{m}}_{1}+{\dot{m}}_{2}+{\dot{m}}_{3}+{\dot{m}}_{4}+{\dot{m}}_{5}+{\dot{m}}_{6}={\dot{m}}_{7}.$$
_{7}is determined by partial temperature ratios of all mass flow participants:$${\dot{m}}_{1}\xb7{t}_{1}+{\dot{m}}_{2}\xb7{t}_{2}+{\dot{m}}_{3}\xb7{t}_{3}+{\dot{m}}_{4}\xb7{t}_{4}+{\dot{m}}_{5}\xb7{t}_{5}+{\dot{m}}_{6}\xb7{t}_{6}={\dot{m}}_{7}\xb7{t}_{7}.$$

- Contaminated condensate cooler temperature outlet:$$30\le {t}_{4}\le 140.$$
- Clean condensate cooler temperature outlet:$$30\le {t}_{5}\le 140.$$
- Distillate water temperature from the tank:$$20\le {t}_{6}\le 40.$$
- Energy efficiency of joining streams to atmospheric drain tank:$$0\le {\eta}_{I}\le 1\text{}\mathrm{or}\text{}0\le \frac{{\dot{m}}_{7}\xb7{h}_{7}}{{\dot{m}}_{1}\xb7{h}_{1}+{\dot{m}}_{2}\xb7{h}_{2}+{\dot{m}}_{3}\xb7{h}_{3}+{\dot{m}}_{4}\xb7{h}_{4}+{\dot{m}}_{5}\xb7{h}_{5}+{\dot{m}}_{6}\xb7{h}_{6}}\le 1.$$

- Constraint precision: 0.000001;
- Convergence: 0.0001;
- Derivatives: forward;
- Bounds on the variables: require;

## 7. Optimization Results

^{−1}at the main propulsion shaft, exergy efficiency increased by 3% to 4%.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$\dot{E}$ | energy flow, kW |

${\dot{E}}_{L}$ | energy loss, kW |

$\dot{S}$ | entropy flow rate, kW/K |

${e}_{x}$ | specific exergy, kJ/kg |

$\dot{E}x$ | exergy flow, kW |

$\dot{E}{x}_{d}$ | exergy destruction, kW |

h | enthalpy, kJ/k |

$\dot{m}$ | mass flow rate, kg/s |

$p$ | pressure, Pa |

$\dot{Q}$ | heat flow rate, kW |

$t$ | temperature, °C |

$T$ | temperature, K |

$\dot{W}$ | power, kW |

## Subscript

i | inlet |

k | boundary temperature |

o | outlet |

0 | referent temperature |

## Greek Letter

${\eta}_{I}$ | energy efficiency |

${\eta}_{II}$ | exergy efficiency |

## Abbreviations

BOG | boil-off gas |

HC | hydrocarbon |

HFO | heavy fuel oil |

## Appendix A

**Table A1.**Fresh water generator condensate, gland steam condenser and first-stage heater pressure condensate, temperature and mass data.

Main Turbine Propulsion Shaft Speed | Fresh Water Generator | Gland Steam Condenser | 1st Stage Feed Water Heater | ||||||
---|---|---|---|---|---|---|---|---|---|

n (min^{−1}) | t (°C) | p (MPa) | ṁ [kg/h] | t (°C) | p (MPa) | ṁ (kg/h) | t (°C) | p (MPa) | ṁ (kg/h) |

0.0 | 36.8 | 0.75 | 720 | 98.83 | 0.0973 | 196 | 86.0 | 0.550 | 1578 |

25.6 | 34.3 | 0.75 | 720 | 98.83 | 0.0973 | 417 | 90.0 | 0.549 | 3351 |

34.3 | 33.3 | 0.75 | 720 | 98.83 | 0.0973 | 468 | 92.0 | 0.452 | 3291 |

41.8 | 32.5 | 0.75 | 720 | 98.83 | 0.0973 | 476 | 89.0 | 0.550 | 3391 |

53.5 | 33.3 | 0.75 | 720 | 98.83 | 0.0973 | 410 | 83.0 | 0.549 | 3522 |

56.7 | 78.7 | 0.2 | 2845 | 98.83 | 0.0973 | 410 | 88.0 | 0.549 | 3688 |

61.5 | 78.7 | 0.2 | 3099 | 98.83 | 0.0973 | 410 | 90.0 | 0.548 | 4083 |

62.5 | 78.7 | 0.2 | 3060 | 98.83 | 0.0973 | 410 | 90.0 | 0.551 | 4013 |

63.6 | 78.7 | 0.2 | 3026 | 98.83 | 0.0973 | 410 | 88.0 | 0.548 | 4142 |

65.1 | 78.7 | 0.2 | 3309 | 98.83 | 0.0973 | 410 | 85.0 | 0.547 | 4197 |

66.1 | 78.7 | 0.2 | 3342 | 98.83 | 0.0973 | 410 | 84.0 | 0.546 | 4296 |

67.7 | 78.7 | 0.2 | 3328 | 98.83 | 0.0973 | 410 | 92.0 | 0.546 | 4260 |

68.7 | 78.7 | 0.2 | 3440 | 98.83 | 0.0973 | 410 | 94.0 | 0.082 | 4699 |

69.5 | 78.7 | 0.2 | 3500 | 98.83 | 0.0973 | 410 | 95.0 | 0.085 | 4652 |

70.4 | 78.7 | 0.2 | 3550 | 98.83 | 0.0973 | 410 | 95.5 | 0.087 | 4692 |

71.0 | 78.7 | 0.2 | 3454 | 98.83 | 0.0973 | 410 | 96.0 | 0.088 | 4699 |

73.1 | 78.7 | 0.2 | 3570 | 98.83 | 0.0973 | 410 | 97.8 | 0.094 | 4893 |

74.6 | 78.7 | 0.2 | 3756 | 98.83 | 0.0973 | 410 | 98.7 | 0.097 | 5161 |

76.6 | 78.7 | 0.2 | 3726 | 98.83 | 0.0973 | 410 | 99.6 | 0.100 | 5712 |

78.4 | 78.7 | 0.2 | 3906 | 98.83 | 0.0973 | 410 | 99.8 | 0.101 | 5952 |

79.5 | 78.7 | 0.2 | 3857 | 98.83 | 0.0973 | 410 | 102.0 | 0.110 | 5984 |

80.4 | 78.7 | 0.2 | 3639 | 98.83 | 0.0973 | 410 | 103.0 | 0.114 | 6083 |

81.5 | 78.7 | 0.2 | 3813 | 98.83 | 0.0973 | 410 | 103.0 | 0.114 | 5887 |

82.9 | 78.7 | 0.2 | 3753 | 98.83 | 0.0973 | 410 | 104.7 | 0.120 | 6362 |

83.0 | 78.7 | 0.2 | 3847 | 98.83 | 0.0973 | 410 | 105.0 | 0.121 | 6336 |

**Table A2.**Contaminated condensate cooler, condensate cooler and distillate water, temperature and mass data.

Main Turbine Propulsion Shaft Speed | Contaminated Condensate Cooler Flow | Condensate Cooler Flow | Distillate Water | ||||||
---|---|---|---|---|---|---|---|---|---|

n (min^{−1}) | t (°C) | p (MPa) | ṁ (kg/h) | t (°C) | p (MPa) | ṁ (kg/h) | t (°C) | p (MPa) | ṁ (kg/h) |

0.0 | 70 | 0.55 | 840 | 70 | 0.55 | 1327 | 29 | 0.11 | 561 |

25.6 | 70 | 0.65 | 1610 | 70 | 0.65 | 1607 | 29 | 0.11 | 663 |

34.3 | 70 | 0.65 | 1540 | 70 | 0.65 | 1418 | 29 | 0.11 | 695 |

41.8 | 70 | 0.65 | 1610 | 70 | 0.65 | 1211 | 29 | 0.11 | 653 |

53.5 | 70 | 0.65 | 1610 | 70 | 0.65 | 1294 | 29 | 0.11 | 745 |

56.7 | 70 | 0.65 | 1610 | 70 | 0.65 | 1303 | 29 | 0.11 | 764 |

61.5 | 70 | 0.65 | 1680 | 70 | 0.65 | 1118 | 29 | 0.11 | 793 |

62.5 | 70 | 0.65 | 1610 | 70 | 0.65 | 1425 | 29 | 0.11 | 789 |

63.6 | 70 | 0.65 | 1680 | 70 | 0.65 | 1122 | 29 | 0.11 | 815 |

65.1 | 70 | 0.65 | 1680 | 70 | 0.65 | 1012 | 29 | 0.11 | 822 |

66.1 | 70 | 0.65 | 1680 | 70 | 0.65 | 1128 | 29 | 0.11 | 852 |

67.7 | 70 | 0.65 | 1680 | 70 | 0.65 | 1243 | 29 | 0.11 | 876 |

68.7 | 70 | 0.65 | 1680 | 70 | 0.65 | 1133 | 29 | 0.11 | 865 |

69.5 | 70 | 0.65 | 1680 | 70 | 0.65 | 1249 | 29 | 0.11 | 868 |

70.4 | 70 | 0.65 | 1680 | 70 | 0.65 | 1134 | 29 | 0.11 | 867 |

71.0 | 70 | 0.65 | 1680 | 70 | 0.65 | 1135 | 29 | 0.11 | 861 |

73.1 | 70 | 0.65 | 1680 | 70 | 0.65 | 1021 | 29 | 0.11 | 922 |

74.6 | 70 | 0.65 | 1680 | 70 | 0.65 | 1120 | 29 | 0.11 | 933 |

76.6 | 70 | 0.65 | 1680 | 70 | 0.65 | 1231 | 29 | 0.11 | 939 |

78.4 | 70 | 0.65 | 1680 | 70 | 0.65 | 1122 | 29 | 0.11 | 977 |

79.5 | 70 | 0.65 | 1680 | 70 | 0.65 | 1237 | 29 | 0.11 | 978 |

80.4 | 70 | 0.65 | 1680 | 70 | 0.65 | 1346 | 29 | 0.11 | 1000 |

81.5 | 70 | 0.65 | 1680 | 70 | 0.65 | 358 | 29 | 0.11 | 1002 |

82.9 | 70 | 0.65 | 1610 | 70 | 0.65 | 2350 | 29 | 0.11 | 1022 |

83.0 | 70 | 0.65 | 1610 | 70 | 0.65 | 2244 | 29 | 0.11 | 1032 |

Main Turbine Propulsion Shaft Speed | Atmospheric Drain Tank Joined Streams | ||
---|---|---|---|

n (min^{−1}) | t (°C) | p (MPa) | ṁ (kg/h) |

0.0 | 67 | 0.11 | 5223 |

25.6 | 73 | 0.11 | 8349 |

34.3 | 74 | 0.11 | 8108 |

41.8 | 73 | 0.11 | 8043 |

53.5 | 70 | 0.11 | 8302 |

56.7 | 77 | 0.11 | 9050 |

61.5 | 78 | 0.11 | 10,290 |

62.5 | 78 | 0.11 | 10,448 |

63.6 | 78 | 0.11 | 10,369 |

65.1 | 76 | 0.11 | 10,325 |

66.1 | 76 | 0.11 | 10,566 |

67.7 | 78 | 0.11 | 10,665 |

68.7 | 80 | 0.11 | 11,051 |

69.5 | 80 | 0.11 | 11,113 |

70.4 | 81 | 0.11 | 11,035 |

71.0 | 81 | 0.11 | 11,035 |

73.0 | 82 | 0.11 | 11,171 |

74.6 | 82 | 0.11 | 11,564 |

76.6 | 83 | 0.11 | 12,220 |

78.4 | 84 | 0.11 | 12,393 |

79.5 | 85 | 0.11 | 12,552 |

80.4 | 85 | 0.11 | 12,777 |

81.5 | 86 | 0.11 | 11,597 |

82.9 | 85 | 0.11 | 14,020 |

83.0 | 85 | 0.11 | 13,961 |

**Table A4.**Optimized temperature from contaminated condensate cooler outlet, clean condensate cooler outlet and distillate tank outlet to atmospheric drain tank.

Main Turbine Propulsion Shaft Speed | Contaminated Condensate Cooler Flow | Condensate Cooler Flow | Distillate Water | ||||||
---|---|---|---|---|---|---|---|---|---|

n (min^{−1}) | t (°C) | p (MPa) | ṁ (kg/h) | t (°C) | p (MPa) | ṁ (kg/h) | t (°C) | p (MPa) | ṁ (kg/h) |

0.0 | 84.64 | 0.55 | 840 | 84.64 | 0.55 | 1327 | 40 | 0.11 | 561 |

25.6 | 90.83 | 0.65 | 1610 | 90.83 | 0.65 | 1607 | 40 | 0.11 | 663 |

34.3 | 92.57 | 0.65 | 1540 | 92.57 | 0.65 | 1418 | 40 | 0.11 | 695 |

41.8 | 90.30 | 0.65 | 1610 | 90.30 | 0.65 | 1211 | 40 | 0.11 | 653 |

53.5 | 84.82 | 0.65 | 1610 | 84.82 | 0.65 | 1294 | 40 | 0.11 | 745 |

56.7 | 85.75 | 0.65 | 1610 | 85.75 | 0.65 | 1303 | 40 | 0.11 | 764 |

61.5 | 86.85 | 0.65 | 1680 | 86.85 | 0.65 | 1118 | 40 | 0.11 | 793 |

62.5 | 86.90 | 0.65 | 1610 | 86.90 | 0.65 | 1425 | 40 | 0.11 | 789 |

63.6 | 85.74 | 0.65 | 1680 | 85.74 | 0.65 | 1122 | 40 | 0.11 | 815 |

65.1 | 83.84 | 0.65 | 1680 | 83.84 | 0.65 | 1012 | 40 | 0.11 | 822 |

66.1 | 83.29 | 0.65 | 1680 | 83.29 | 0.65 | 1128 | 40 | 0.11 | 852 |

67.7 | 87.86 | 0.65 | 1680 | 87.86 | 0.65 | 1243 | 40 | 0.11 | 876 |

68.7 | 88.53 | 0.65 | 1680 | 88.53 | 0.65 | 1133 | 40 | 0.11 | 865 |

69.5 | 89.09 | 0.65 | 1680 | 89.09 | 0.65 | 1249 | 40 | 0.11 | 868 |

70.4 | 89.37 | 0.65 | 1680 | 89.37 | 0.65 | 1134 | 40 | 0.11 | 867 |

71.0 | 89.81 | 0.65 | 1680 | 89.81 | 0.65 | 1135 | 40 | 0.11 | 861 |

73.1 | 90.93 | 0.65 | 1680 | 90.93 | 0.65 | 1021 | 40 | 0.11 | 922 |

74.6 | 91.55 | 0.65 | 1680 | 91.55 | 0.65 | 1120 | 40 | 0.11 | 933 |

76.6 | 92.66 | 0.65 | 1680 | 92.66 | 0.65 | 1231 | 40 | 0.11 | 939 |

78.4 | 92.73 | 0.65 | 1680 | 92.73 | 0.65 | 1122 | 40 | 0.11 | 977 |

79.5 | 94.38 | 0.65 | 1680 | 94.38 | 0.65 | 1237 | 40 | 0.11 | 978 |

80.4 | 95.45 | 0.65 | 1680 | 95.45 | 0.65 | 1346 | 40 | 0.11 | 1000 |

81.5 | 94.91 | 0.65 | 1680 | 94.91 | 0.65 | 358 | 40 | 0.11 | 1002 |

82.9 | 96.91 | 0.65 | 1610 | 96.91 | 0.65 | 2350 | 40 | 0.11 | 1022 |

83.0 | 96.96 | 0.65 | 1610 | 96.96 | 0.65 | 2244 | 40 | 0.11 | 1032 |

## Appendix B

^{4}− 0.000017560712·t

^{3}+ 0.008183264951·t

^{2}− 0.377604877762·t + 5.038272554766

^{2}= 0.999999999544

^{4}− 0.000017724546·t

^{3}+ 0.008198483260·t

^{2}− 0.378158562476·t + 4.575836547896

^{2}= 0.999999999420

^{4}− 0.000017674814·t

^{3}+ 0.008194275370·t

^{2}− 0.378007050602·t + 4.577893162052

^{2}= 0.999999999452

^{4}− 0.000017659707·t

^{3}+ 0.008192987671·t

^{2}− 0.377960479895·t + 4.578292957558

^{2}= 0.999999999452

^{4}− 0.000017646885·t

^{3}+ 0.008191909080·t

^{2}− 0.377921808781·t + 4.578797824676

^{2}= 0.999999999455

^{4}− 0.000017612085·t

^{3}+ 0.008188960776·t

^{2}− 0.377816106864·t + 4.583459267439

^{2}= 0.999999999472

^{4}− 0.000017550696·t

^{3}+ 0.008183545317·t

^{2}− 0.377613475150·t + 4.583763019346

^{2}= 0.999999999433

^{4}− 0.000017526578·t

^{3}+ 0.008181456140·t

^{2}− 0.377536693237·t + 4.585760948106

^{2}= 0.999999999452

^{4}− 0.000017533970·t

^{3}+ 0.008182090496·t

^{2}− 0.377559797341·t + 4.587064973324

^{2}= 0.999999999442

^{4}− 0.000017549625·t

^{3}+ 0.008183378488·t

^{2}− 0.377604963571·t + 4.596660891228

^{2}= 0.999999999461

^{4}− 0.000017543499·t

^{3}+ 0.008182856108·t

^{2}− 0.377586423719·t + 4.600440241904

^{2}= 0.999999999449

^{4}− 0.000017547513·t

^{3}+ 0.008183249124·t

^{2}− 0.377603071989·t + 4.606707460725

^{2}= 0.999999999451

^{4}− 0.000017542259·t

^{3}+ 0.008182768307·t

^{2}− 0.377584755059·t + 4.607463940507

^{2}= 0.999999999461

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**Figure 6.**Atmospheric drain tank condensate ratio in mixing point with feed water with main turbine load variation.

Equipment | Size |
---|---|

Main turbine power | 29,420 kW |

Main condenser vacuum | 38 mm Hg, at 27 °C of seawater |

Turbo generator | 2 × 3850 kW |

Feed pump | 570 kW |

Main boiler, steam generation | 2 × 70,000 kg/h |

Component | Measuring Equipment |
---|---|

1. Desuperheating outlet steam pressure | 1. Pressure transmitter Yamatake STG940 [23] |

2. Steam mass flow | 2. Differential pressure transmitter Yamatake JTD960A [24] |

3. Desuperheating steam outlet temperature | 3. Greisinger GTF 601-Pt100-immersion probe [25] |

4. Main propulsion turbine shaft power and rpm | 4. Kyma shaft power meter, Model KPM-PFS [26] |

5. First-stage feed heater temperature | 5. SIKA thermometers for industry and marine sector [27] |

6. Gland seal condenser temperature | 6. SIKA thermometers for industry and marine sector [27] |

7. Gland seal condenser pressure | 7. Differential pressure transmitter Yamatake JTD960A [24] |

8. Distillate water temperature gauge | 8. SIKA thermometers for industry and marine sector [27] |

9. Fresh water generator temperature gauge | 9. SIKA thermometers for industry and marine sector [27] |

10. Contaminated and clean condensate temperature gauge | 10. SIKA thermometers for industry and marine sector [27] |

11. Atmospheric drain tank temperature | 11. SIKA thermometers for industry and marine sector [27] |

12. 1st stage feed water pressure gauge | 12. SIKA pressure gauges, type MRE-M and MRE-g [28] |

13. Fresh water generator distillate flow meter | 13. Zenner international GmbH [29] |

14. Fresh water generator pressure gauge | 14. Type 1259 Process Pressure Gauge—Ashcroft [30] |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Poljak, I.; Bielić, T.; Mrzljak, V.; Orović, J.
Analysis and Optimization of Atmospheric Drain Tank of Lng Carrier Steam Power Plant. *J. Mar. Sci. Eng.* **2020**, *8*, 568.
https://doi.org/10.3390/jmse8080568

**AMA Style**

Poljak I, Bielić T, Mrzljak V, Orović J.
Analysis and Optimization of Atmospheric Drain Tank of Lng Carrier Steam Power Plant. *Journal of Marine Science and Engineering*. 2020; 8(8):568.
https://doi.org/10.3390/jmse8080568

**Chicago/Turabian Style**

Poljak, Igor, Toni Bielić, Vedran Mrzljak, and Josip Orović.
2020. "Analysis and Optimization of Atmospheric Drain Tank of Lng Carrier Steam Power Plant" *Journal of Marine Science and Engineering* 8, no. 8: 568.
https://doi.org/10.3390/jmse8080568