Compressed gas energy storage formula

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Discussion Overview

The discussion revolves around finding a formula to calculate the energy stored in compressed gas, specifically non-ideal gases like argon. The inquiry includes considerations of thermal energy resulting from compression and the efficiency of energy storage systems such as compressed air energy storage.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula for the energy stored in compressed non-ideal gases, emphasizing the need to account for thermal energy from compression.
  • Another participant suggests using conservation of energy principles, questioning the premise of the original inquiry.
  • Compressed air energy storage is identified as the main topic of discussion.
  • A participant proposes a general formula for energy storage but notes the inefficiencies in compressors and turbines, indicating that no simple formulas exist for these inefficiencies.
  • It is suggested that a reasonable estimate of net efficiency for compression and expansion could be around 60%, but this may drop to 20% if the gas is stored for extended periods, highlighting the importance of storage duration.
  • The original poster clarifies their request for a specific calculation of energy in joules for compressing argon to a specified pressure in a defined volume.

Areas of Agreement / Disagreement

Participants express varying views on the approach to calculating energy storage, with some focusing on theoretical formulas and others emphasizing practical considerations like efficiency and storage duration. The discussion remains unresolved regarding a specific formula for non-ideal gases.

Contextual Notes

Participants acknowledge limitations in existing formulas related to the inefficiencies of compressors and turbines, as well as the impact of thermal energy and storage duration on overall efficiency.

Petersenwill36
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TL;DR
Compressed gas energy storage formula
Hi,
I’m looking for formula to find the energy stored in a compressed gas for non ideal gases, for example, argon. The formula should also include the thermal energy caused by compression.

Thank you in advance.
 
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Can't you use conservation of energy? If we compress a gas, energy out equals energy in minus energy leaked to the environment. I'm sure you know that, so what is the premise of your question?
 
Compressed air energy storage is the topic.
 
Petersenwill36 said:
Compressed air energy storage is the topic.
OK. In that case you can use this formula $$Energy_{stored} = Energy_{in} - Energy_{lost}$$

But that's probably not much help. Compressors are not 100% efficient when compressing the gas. Turbines are not 100% efficient when re-expanding the gas. But there are no simple formulas for those inefficiencies.

So if there are no simple formulas, the next best thing is to just make a reasonable guess. 60% net efficiency for compression/expansion and conversion to/from electricity. However, if you let the gas sit overnight so that heat leaks to the environment, efficiency might shrink to 20%. Therefore, for how long it remains stored becomes an important parameter.

Are you assigned the task of designing compressed air energy storage?
 
Thank you for your help. I am looking for the amount of energy in joules stored in a pressurized gas. For example, the amount of energy required to compress argon to 1000 psi in a 2L vessel.
 

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