# Exergy-Based and Economic Evaluation of Liquefaction Processes for Cryogenics Energy Storage

^{1}

^{2}

^{*}

## Abstract

**:**

_{char}) were achieved by the Kapitza process.

## 1. Introduction

#### State of the Art

## 2. Methods

#### 2.1. Design and Simulation

^{®}(Version 9, Aspen Technology Inc., Bedford, MA, USA) was chosen as a suitable software for process simulation. With the aid of the simulation software, all mass and energy balances are fulfilled and the specific enthalpy and entropy values of all streams and substances are calculated. The Peng-Robinson equation of state was employed and the simulation was performed under steady-state conditions. Fortran routines are integrated to calculate exergy values for the exergetic analysis. Six liquefaction processes were simulated: the simple Linde, the precooled Linde, the dual pressure Linde, the simple Claude, the Kapitza and the Heylandt process. At first, the liquefaction processes were manually optimized and later modified to accommodate the cold storage. The assumptions made in simulation are given in Table 2.

_{2}and 21% O

_{2}(a1). The compression block is the same for all systems. The air exits the last intercooler of the three-stage compression at a temperature of 25 °C and a pressure of p

_{max,CM}of 200 bar (a2). The largest part of the thermal energy increase during compression is recovered in a heat storage. The heat storage is realized with pressurized water tanks (5 bar, 205 °C). The design of the liquefaction block is different for each system. Two types of liquefaction processes can be distinguished: Linde-based (Figure 3) and Claude-based (Figure 4) liquefaction processes. The liquefied air exits the flasher and is stored at a temperature of −192 °C and slightly elevated pressure 1.3 bar. The liquid is stored in an insulated storage tank with boil-off losses of 0.2 %

_{Vol}.

#### 2.2. Energetic and Exergetic Analyses

#### 2.3. Economic Analysis

_{2017}= 567.5 [33]). The derived cost equations of the BMC for each type of component can be found in [34].

_{char}).

#### 2.4. Exergoeconomic Analysis

## 3. Results and Discussions

#### 3.1. Energetic and Exergetic Analyses

_{liquid air}) and the highest liquid yields (0.609, 0.629, 0.609).

#### 3.2. Economic Analysis

_{char}, 792 €/kW

_{char}and 691 €/kW

_{char}, respectively.

#### 3.3. Exergoeconomic Analysis

_{dis}, see Table 9. The specific investment costs of the total CES system is approximated from 500–3,000 €/kW [6,7,36] in literature. The levelized cost of discharged electricity (LCOE

_{dis}) of the CES systems based on the Claude, the Heylandt, and the Kapitza process are expected to reach 175.6 €/MWh

_{el}, 175.3 €/MWh

_{el}and 172.0 €/MWh

_{el}, respectively. For industrial application 120‒200 €/MWh are set as goal. A sensitivity analysis of the LCOE and comparison to other technologies was reported in [34]. The final RTE of 47–49% are also in line with the expected 40–60%, which confirms the presented results.

_{2}). Regarding the RTE of PHS and CAES, CES efficiency is still the greatest obstacle. The high exergy density of CES (120–200 kWh/m

^{3}[36])—the absence of geographical constraints—remains the technologies greatest advantage.

## 4. Conclusions

- The integration of the charging unit with cold exergy recovery was shown to substantially augment the liquid yield $\gamma $, significantly reduce the specific power requirement ${w}_{char}$ and significantly improve the exergetic efficiency $\epsilon $ of all liquefaction processes assessed.
- The simple Claude, the Heylandt and the Kapitza processes were found to reach the highest exergetic efficiencies and liquid yields, as well as the lowest specific power requirements for liquefaction.
- The sensitivity analysis showed that for liquefaction pressures of 125 bar and higher, the Heylandt process reaches the highest exergetic efficiencies, at lower pressures the Claude and the Kapitza process are superior.
- The economic analysis revealed that the Kapitza process-based system has the lowest specific investment cost and total revenue requirement.
- The exergoeconomic analysis demonstrated that the Kapitza process is the most cost-effective liquefaction process to be considered for CES with cold storage. The average cost of the exergy of the final product was the lowest in the Kapitza process.
- The results were compared to values from literature. The specific power consumption of the presented air liquefaction processes with cold storage (≤264 kWh/ton) was found to be approximately half the values reported in literature. The production cost of liquid air was found to be significantly reduced with the integrating cold storage (18–26 €/ton).
- The final results on system level were found to be in line with the values reported for CES specific investment cost and RTE. Finally, CES was evaluated cost-competitive with other bulk-energy storage technologies.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of cryogenic energy storage steps of operation (charge, storage, discharge), heat and cold recovery and storage.

**Figure 5.**Results of exergy analysis of the liquefaction processes with/without integrated cold storage.

**Figure 6.**Sensitivity analysis results of the Claude, the Kapitza and the Heylandt process: exergetic efficiency $\epsilon $ over splitting ratio $r$, for various values of the liquefaction pressure. The maximum efficiency line is indicated with a solid black line.

**Figure 7.**Maximum exergetic efficiency graphs as a function of the splitting ratio $r$ for the Claude, Kapitza and Heylandt processes.

**Figure 8.**Maximum liquid yield graphs of the three Claude-based processes for different pressures and splitting ratios.

**Figure 9.**Minimum specific power graphs of the three Claude-based processes for different pressures and splitting ratios.

**Figure 10.**Bare module costs of the evaluated Claude-based systems with indicated cost shares of the contributing component groups.

**Figure 11.**Sum of the cost rates associated with the initial investment of the component ${\dot{Z}}_{k}$ and the exergy destruction ${\dot{C}}_{D,k}$ and exergoeconomic factor $f$ of the respective component(s).

Source | Process | p_{char}, bar | $\mathit{\gamma}$, - | Cold Storage Configuration | p_{dis}, bar | η_{RTE}, % |
---|---|---|---|---|---|---|

[12] | Linde-Hampson | 120 | 0.83 | fluid tanks (CH_{4}O, C_{3}H_{8}) | 50 | 50–60 |

[15] | Integr. Linde-Hampson | 90 | 0.60 | fluid tanks (CH_{4}O, C_{3}H_{8}) | 120 | 60 |

[9] | Heylandt | 180 | 0.61 | fluid tanks (CH_{4}O, R218) | 150 | 41 |

[16] | Modified Claude | 180 | 0.86 | packed bed gravel (air) | 75 | 48.5 |

[17] | 2 Turbine Claude/Collins | 54 | NA | packed bed gravel (air) | 150 | 47 |

[6] | 4 Turbine Claude | 56.8 | 0.551 ^{1} | packed bed gravel (air) | 190 | >50 |

[18] | Linde-Hampson | 180 | 0.842 | fluid tanks (CH_{4}O, C_{3}H_{8}) | 65 | 50 |

[19] | Linde-Hampson | 140 | NA | NA | 70 | 47.2 |

[11] | Linde-Hampson | 20 | 0.70 | direct integration (ideal) | 100 | 20–50 |

[8] | Linde-Hampson ² | ~130 | 0.44–0.74 | fluid tanks (CH_{4}O, R218) | 112–120 | 28–37 |

[8] | Expander cycle | NA | NA | fluid tanks (CH_{4}O, R218) | NA | 40–46 |

[20] | Single expander | 135 | 0.84 | fluid tanks (CH_{4}O, C_{3}H_{8}) | 80 | 50–58 |

^{1}calculated from: 12 h charging, 3:1 (charge-to-discharge ratio), ${\dot{m}}_{char}$ = 34.1 kg/s.

^{2}with cold expander/throttling valve.

Parameter | Value, Unit |
---|---|

Isentropic efficiencies (compressors, expanders) | η_{is,CM} = 87% [8], η_{is,EX} = 80% [17] |

Intercooler exit temperature and pinch | T_{exit, IC} = 25 °C, ΔT_{pinch, IC} = 5 K [15] |

Main heat exchanger pinch temperature difference | ΔT_{pinch, MHE} = 1–3 K [8,17] |

Maximal pressure of compression | p_{max, CM} = 200 bar [22] |

Ambient conditions | T_{amb} = 15 °C, p_{amb} = 1.013 bar |

**Table 3.**Stream values for the states indicated in the flowsheets in Figure 3.

Stream | Variable, Unit | Simple Linde | Precooled Linde | Dual-Pressure Linde | ||||
---|---|---|---|---|---|---|---|---|

With Storage | With Storage | With Storage | ||||||

1 | $\dot{m}$ | kg/h | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |

$T$ | °C | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 33.4 | 33.4 | |

2 | $\dot{m}$ | kg/h | 100.0 | 100.0 | 100.0 | 100.0 | 547.3 | 137.3 |

$T$ | °C | −102.4 | −125.3 | −113.6 | −138.7 | 24.1 | 24.2 | |

$p$ | bar | 200.0 | 1.03 | 200.0 | 200.0 | 30.4 | 30.4 | |

3 | $\dot{m}$ | kg/h | 100.0 | 100 | 100 | 100 | 547.3 | 137.3 |

$T$ | °C | −191.8 | −191.7 | −192.3 | −193.1 | 25.0 | 25.0 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 200.0 | 200.0 | |

4 | $\dot{m}$ | kg/h | 9.0 | 31.2 | 19.8 | 44.1 | 547.3 | 137.3 |

$T$ | °C | −191.8 | −192.7 | −192.3 | −193.1 | −105.0 | −124.5 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 200.0 | 200.0 | |

5 | $\dot{m}$ | kg/h | 91.0 | 68.8 | 80.2 | 55.9 | 547.3 | 137.3 |

$T$ | °C | −191.8 | −192.7 | −192.3 | −193.1 | −146.2 | −146.2 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 30.4 | 30.4 | |

6 | $\dot{m}$ | kg/h | 91.0 | 68.8 | 80.2 | 55.9 | 100.0 | 100.0 |

$T$ | °C | 24.0 | 24.0 | 24.0 | −95.8 | −146.2 | −146.2 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 30.4 | 30.4 | |

7 | $\dot{m}$ | kg/h | - | - | - | - | 100.0 | 100.0 |

$T$ | °C | - | - | - | - | −192.9 | −192.9 | |

$p$ | bar | - | - | - | - | 1.03 | 1.03 | |

8 | $\dot{m}$ | kg/h | - | - | - | - | 40.0 | 40.0 |

$T$ | °C | - | - | - | - | −193.0 | −193.0 | |

$p$ | bar | - | - | - | - | 1.03 | 1.03 | |

9 | $\dot{m}$ | kg/h | - | - | - | - | 60.0 | 60.0 |

$T$ | °C | - | - | - | - | −193.0 | −193.0 | |

$p$ | bar | - | - | - | - | 1.03 | 1.03 | |

10 | $\dot{m}$ | kg/h | - | - | - | - | 60.0 | 60.0 |

$T$ | °C | - | - | - | - | 24.0 | 24.0 | |

$p$ | bar | - | - | - | - | 1.03 | 1.03 | |

11 | $\dot{m}$ | kg/h | - | - | - | - | 447.3 | 37.3 |

$T$ | °C | - | - | - | - | −146.2 | −146.2 | |

$p$ | bar | - | - | - | - | 30.4 | 30.4 | |

12 | $\dot{m}$ | kg/h | - | - | - | - | 447.3 | 37.3 |

$T$ | °C | - | - | - | - | 24.0 | 24.0 | |

$p$ | bar | - | - | - | - | 30.4 | 30.4 |

**Table 4.**Stream values for the states indicated in the flowsheets in Figure 4.

Stream | Variable, Unit | Claude | Kapitza | Heylandt | ||||
---|---|---|---|---|---|---|---|---|

With Storage | With Storage | With Storage | ||||||

1 | $\dot{m}$ | kg/h | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |

$T$ | °C | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | |

2 | $\dot{m}$ | kg/h | 100.0 | 100.0 | 100.0 | 100.0 | 36.0 | 76.1 |

$T$ | °C | −4.0 | −2.0 | −4.0 | −2.0 | 25.0 | 25.0 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | |

3 | $\dot{m}$ | kg/h | 34.3 | 73.2 | 34.3 | 73.3 | 36.0 | 76.1 |

$T$ | °C | −4.0 | −2.0 | −4.0 | −2.0 | −177.6 | −180.5 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | |

4 | $\dot{m}$ | kg/h | 34.3 | 73.2 | 34.3 | 73.3 | 36.0 | 76.1 |

$T$ | °C | −190.8 | −182.8 | −190.6 | −182.8 | −193.9 | −194.0 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 1.03 | 1.03 | |

5 | $\dot{m}$ | kg/h | 34.3 | 73.2 | 34.3 | 73.3 | 28.6 | 62.3 |

$T$ | °C | −194.1 | −194.0 | −194.1 | −194.0 | −193.9 | −194.0 | |

$p$ | bar | 1.03 | 200.0 | 1.03 | 1.03 | 1.03 | 1.03 | |

6 | $\dot{m}$ | kg/h | 31.2 | 61.5 | 31.1 | 61.5 | 7.4 | 13.7 |

$T$ | °C | −194.1 | −194.0 | −194.1 | −194.0 | −176.5 | −179.0 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | |

7 | $\dot{m}$ | kg/h | 3.1 | 11.8 | 3.2 | 11.8 | 71.4 | 37.7 |

$T$ | °C | −194.1 | −194.0 | −194.1 | −194.0 | −176.4 | −177.4 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | |

8 | $\dot{m}$ | kg/h | 3.1 | 11.8 | 68.9 | 38.5 | 71.4 | 37.7 |

$T$ | °C | −192.0 | −191.0 | −191.7 | −192.1 | −7.3 | 24.0 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | |

9 | $\dot{m}$ | kg/h | 65.7 | 26.8 | 65.7 | 26.7 | 64.0 | 24.0 |

$T$ | °C | −4.0 | −2.0 | −4.0 | −2.0 | 25.0 | 25.0 | |

$p$ | bar | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | 200.0 | |

10 | $\dot{m}$ | kg/h | 65.7 | 26.8 | 65.7 | 26.7 | 64.0 | 24.0 |

$T$ | °C | −191.6 | −191.2 | −191.6 | −191.2 | −176.4 | −176.4 | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | 1.03 | |

11 | $\dot{m}$ | kg/h | 68.8 | 73.0 | - | - | - | - |

$T$ | °C | −191.7 | −182.8 | - | - | - | - | |

$p$ | bar | 1.03 | 200.0 | - | - | - | - | |

12 | $\dot{m}$ | kg/h | 68.8 | 38.6 | 68.9 | 73.3 | - | - |

$T$ | °C | 24.0 | 23.4 | 24.0 | 24.0 | - | - | |

$p$ | bar | 1.03 | 1.03 | 1.03 | 1.03 | - | - |

Assumption | Value |
---|---|

Service facilities, architectural work | 30% of BMC |

Contingencies | 15% of BMC |

Effective interest rate | 8% |

Average inflation rate | 3% |

Plant economic life | 30 years |

Annual full load operation | 2882 h/a |

Annual OMC | 1.5% of FCI |

Mean cost of charged electricity | 17.2 €/MWh |

Parameter | Unit | Claude | Heylandt | Kapitza |
---|---|---|---|---|

Liquefaction pressure | bar | 95 | 130 | 95 |

Charging capacity | MW | 20 | 20 | 20 |

Liquefaction capacity | tons/day | 606 | 608 | 606 |

Storage capacity | MWh | 76.6 | 78.4 | 76.6 |

Liquid yield | - | 0.54 | 0.59 | 0.54 |

Parameter | Claude | Heylandt | Kapitza | Unit |
---|---|---|---|---|

Average cost of exergy of the fuel, ${\mathrm{c}}_{F,tot}$ | 44.3 | 61.2 | 44.0 | €/MWh |

Average cost of exergy of the losses, ${\mathrm{c}}_{L,tot}$ | 39.3 | 43.7 | 39.2 | €/MWh |

Average cost of exergy of the product, ${\mathrm{c}}_{P,tot}$ | 88.8 | 114.8 | 88.0 | €/MWh |

Average cost of exergy of the liquid air, ${\mathrm{c}}_{liquidair}$ | 95.4 | 133.4 | 94.6 | €/MWh |

Average cost of exergy of the heat, ${\mathrm{c}}_{q,hot}$ | 67.9 | 63.1 | 67.5 | €/MWh |

Parameter | Unit | Claude | Heylandt | Kapitza | Reference |
---|---|---|---|---|---|

Specific power consumption | kWh/ton | 264.0 | 263.3 | 264.0 | 520–760 [13], 439 [35] |

Production cost of liquid air | €/ton | 18.6 | 25.9 | 18.4 | 37–48 [35] |

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**MDPI and ACS Style**

Hamdy, S.; Moser, F.; Morosuk, T.; Tsatsaronis, G.
Exergy-Based and Economic Evaluation of Liquefaction Processes for Cryogenics Energy Storage. *Energies* **2019**, *12*, 493.
https://doi.org/10.3390/en12030493

**AMA Style**

Hamdy S, Moser F, Morosuk T, Tsatsaronis G.
Exergy-Based and Economic Evaluation of Liquefaction Processes for Cryogenics Energy Storage. *Energies*. 2019; 12(3):493.
https://doi.org/10.3390/en12030493

**Chicago/Turabian Style**

Hamdy, Sarah, Francisco Moser, Tatiana Morosuk, and George Tsatsaronis.
2019. "Exergy-Based and Economic Evaluation of Liquefaction Processes for Cryogenics Energy Storage" *Energies* 12, no. 3: 493.
https://doi.org/10.3390/en12030493