# Comparative Analysis of Isochoric and Isobaric Adiabatic Compressed Air Energy Storage

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## Abstract

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## 1. Introduction

_{2}at pressures below the critical pressure (Figure 1d). Changes from air in the gaseous state to the adsorbed state have also been proposed. Havel [8] proposes using zeolites for ‘Adsorption Enhanced CAES’, requiring heat to be added to the storage to de-adsorb the air during discharge.

## 2. ACAES Model

#### 2.1. Compressors

#### 2.2. Heat Exchangers

#### 2.3. Isochoric HPST

#### 2.4. Isobaric HPST

#### 2.5. Throttle Valve

#### 2.6. Thermal Energy Stores

#### 2.7. Air Expansion

#### 2.8. Idle and Recovery

#### 2.9. Model Parameters

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbols | |

A | Area, ${L}^{2}$, |

${c}_{p};{c}_{v}$ | Specific heat at constant pressure and volume, respectively, ${L}^{2}{T}^{-2}{\Theta}^{-1}$, |

${c}_{c}$ | Coolant specific heat, ${L}^{2}{T}^{-2}{\Theta}^{-1}$, |

C | Heat capacity, ${L}^{2}M{T}^{-3}{\Theta}^{-1}$, |

h | Specific enthalpy, ${L}^{2}{T}^{-2}$, |

H | Height, L, |

m | Mass, M, |

$\dot{m}$ | Mass flow rate, $M{T}^{-1}$, |

${N}_{c},{N}_{e}$ | Number of compressor and expander stages, |

P | Pressure, $M{L}^{-1}{T}^{-2}$, |

$\Delta {P}_{HEX}$ | Pressure drop in the heat exchanger $M{L}^{-1}{T}^{-2}$, |

Q | Heat transferred, ${L}^{2}M{T}^{-2}$, |

$\dot{Q}$ | Heat transfer rate, ${L}^{2}M{T}^{-3}$, |

r | Radius, L, |

T | Temperature, $\Theta $, |

t | time, T, |

u | Specific internal energy, ${L}^{2}M{T}^{-2}$, |

V | Volume, ${L}^{3}$, |

W | Work, ${L}^{2}M{T}^{-2}$, |

$\dot{W}$ | Power, ${L}^{2}M{T}^{-3}$, |

Greek characters | |

$\u03f5$ | Heat exchanger effectiveness, |

$\eta $ | Efficiency, |

$\kappa $ | Convective heat transfer coefficient, $M{T}^{-3}{\Theta}^{-1}$, |

$\chi $ | Instantaneous pressure ratio, |

$\Psi $ | Expansion ratio, |

Subscripts | |

1 | Condition on the beginning of the timestep, |

2 | Condition on the end of the timestep, |

a | Relative to ambient condition, |

c | Compressor or cold fluid, |

$cavern$ | Relative to HPST cavern, |

e | Expander, |

h | Hot fluid, |

$HPST$ | Relative to the High Pressure Storage, |

$in$ | Inlet condition, |

N | Condition at the ${n}^{th}$ compressor or heat exchanger outlet, |

$out$ | Outlet condition, |

s | Isentropic condition, |

$wall$ | HPST wall, |

Superscript | |

$bulk$ | Mixed conditions in TES, |

$HE{X}_{n}$ | Condition at the ${n}^{th}$ heat exchanger outlet, |

$MAX$ | Maximum condition, |

$MIN$ | Minimum condition, |

$REL$ | Relative condition, |

Dimensions | |

L | Length |

T | Time |

M | Mass |

$\Theta $ | Temperature |

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**Figure 1.**Four primary mechanisms for air storage in ACAES. (

**a**) Isochoric storage in a constant volume underground salt cavern. (

**b**) Isobaric storage with a shuttle pond. (

**c**) Isobaric storage with hydraulic compensation using a pump to regulate the fluid pressure. (

**d**) Isobaric storage using the liquid-vapour phase change in a volatile fluid.

**Figure 2.**Schematic diagram of the ACAES systems. (

**a**) Isochoric—the air leaving the HPST is throttled to the minimum storage pressure. (

**b**) Isobaric air storage is maintained so no throttle is included.

**Figure 3.**Illustrating the compressor off-design performance with three arbitrary differences between on-design and off-design isentropic efficiency. The inset illustrates a path on a real compressor map (adapted from [13]), whose increasing efficiency portion we model as a second degree polynomial.

**Figure 4.**The cavern is assumed to have cylindrical geometry, with constant wall temperature ${T}_{wall}$ and convective heat transfer coefficient $\kappa $. The cavern internal temperature (${T}_{HPST}=308$ K) indicates a mid-point depth around 550 m [17]. (

**a**) Cavern arrangement in the isochoric configuration, wherein volume and surface areas are constant, whilst pressure and temperature are variable. (

**b**) Cavern arrangement in the isobaric configuration where pressure is maintained by changing the available air storage volume.

**Figure 6.**Composite plot with main compressors operation figures during the charging process: (

**a**) Compressors 1 through 4 outlet pressure; (

**b**) isentropic efficiency (all machines operate with same efficiency in each case); (

**c**) each compressor outlet temperature; and (

**d**) total power (left axis, lines) and energy (right axis, shaded area) consumption, all for the isochoric and isobaric analysis. Note the isobaric scenario runs for longer than the isochoric. Data generated for $\Delta \eta =0.35$.

**Figure 7.**Composite plot depicting: (

**a**) storage temperature variation during the isochoric system charging and discharging periods (red and blue lines, respectively), as well the constant isobaric system temperature throughout charging and discharging. Additionally, the difference between final charging and initial discharging temperatures corresponds to the idle period temperature drop ($\Delta {T}_{idle}$), whilst the opposite corresponds to the recovery period temperature increase ($\Delta {T}_{recovery}$). (

**b**) power generation (left, lines) and cumulative energy generation (right, shaded areas) during the discharging period for both systems. Note the isobaric scenario runs for longer than the isochoric. Data generated for $\Delta \eta =0.35$.

**Figure 8.**Composite plot comparing key differences between the isobaric and isochoric system performance figures as a function of the compressor efficiency loss $\Delta \eta =\eta ({\chi}^{REL}=1)-\eta ({\chi}^{REL}=0)$. In (

**a**) Isochoric system Round-Trip Efficiency (RTE) compared to the isobaric system RTE (constant); and (

**b**) TES 1 and 2 final charging temperatures in isobaric and several isochoric conditions.

Parameter | Value | Parameter | Value |
---|---|---|---|

Cavern | |||

Volume | $3\times {10}^{5}\phantom{\rule{3.33333pt}{0ex}}$m${}^{3}$ | Wall area | $2.5\times {10}^{4}\phantom{\rule{3.33333pt}{0ex}}$m${}^{2}$ |

Maximum pressure | $7.5$ MPa | Minimum pressure cavern | 4 MPa |

Convective HTC (air to wall) | 30 Wm${}^{-2}$ K${}^{-1}$ | Wall temperature | 35 °C |

Initial temperature | 35 °C | Brine temperature | 35 °C |

Air | |||

$HE{X}_{5}$ outlet temperature | 35 °C | Mass flow rate | 100 kg s${}^{-1}$ |

${c}_{p}$ | 1004 J kg${}^{-1}$ K${}^{-1}$ | ${c}_{v}$ | 718 J kg${}^{-1}$ K${}^{-1}$ |

Components and ambient | |||

No. compression stages (${N}_{c}$) | 4 | No. expansion stages (${N}_{e}$) | 2 |

Compressor design isentropic efficiency | $0.85$ | Compressor off-design performance drop | $0.35$ |

Expander design isentropic efficiency | $0.9$ | air side HEX pressure drop $\Delta {p}_{HEX}$ | $0.01$ MPa |

Inter-cooling HEX effectiveness $\u03f5$ | $0.8$ | Heating HEX effectiveness | $0.9$ |

Coolant heat capacity (${c}_{c}$) | 1200 J kg${}^{-1}$ K${}^{-1}$ | Coolant initial temperature | 25 °C |

Variable | Unit | Isochoric | Isobaric |
---|---|---|---|

Total time (chg) | h | 31.2 | 70.7 |

Total time (dis) | h | 31.2 | 70.7 |

Stored air mass (min) | kg | 1.23 × 10${}^{7}$ | 0 |

Stored air mass (max) | kg | 2.53 × 10${}^{7}$ | 2.55 × 10${}^{7}$ |

Total compression power (min) | MW | 54.62 | 55.48 |

Total compression power (max) | MW | 76.7 | 55.48 |

Total expansion power (min) | MW | 30.87 | 34.13 |

Total expansion power (max) | MW | 30.91 | 34.13 |

HPST pressure loss (idle) | MPa | 0.03 | 0 |

HPST pressure gain (recovery) | MPa | 0.15 | 0 |

HPST temperature drop (idle) | K | 1.41 | 0 |

HPST temperature increase (recovery) | K | 10.93 | 0 |

Energy Consumption | GWh | 1.83 | 3.92 |

Energy Generation | GWh | 0.96 | 2.41 |

TES 1 max temperature | K | 422.08 | 415.29 |

TES 2 max temperature | K | 448.38 | 439.52 |

RTE | — | 0.525 | 0.615 |

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**MDPI and ACS Style**

Pottie, D.; Cardenas, B.; Garvey, S.; Rouse, J.; Hough, E.; Bagdanavicius, A.; Barbour, E.
Comparative Analysis of Isochoric and Isobaric Adiabatic Compressed Air Energy Storage. *Energies* **2023**, *16*, 2646.
https://doi.org/10.3390/en16062646

**AMA Style**

Pottie D, Cardenas B, Garvey S, Rouse J, Hough E, Bagdanavicius A, Barbour E.
Comparative Analysis of Isochoric and Isobaric Adiabatic Compressed Air Energy Storage. *Energies*. 2023; 16(6):2646.
https://doi.org/10.3390/en16062646

**Chicago/Turabian Style**

Pottie, Daniel, Bruno Cardenas, Seamus Garvey, James Rouse, Edward Hough, Audrius Bagdanavicius, and Edward Barbour.
2023. "Comparative Analysis of Isochoric and Isobaric Adiabatic Compressed Air Energy Storage" *Energies* 16, no. 6: 2646.
https://doi.org/10.3390/en16062646