How Does Heat Transfer Affect Compressed Air Energy Storage in Salt Caverns?

[bkcaes]

Hi all,

I am trying to model temperature variation with time of compressed air energy storage in a salt cavern. For now I have considered a spherical (hollow) cavern in which air is injected. I have to solve {T}+[M]{T_dot}={Q} (here, Q is the first term and all other entries are zero).

My question:

I am trying to get an expression for Q as a function of time. It will constitute (heat from injection + heat from convection + heat from conduction through the rock mass), right?
Only heat from conduction through the rock mass is time dependent in my expression.
Q_inj = m_dot*Cp*(Tinj-Tair)
Q_conv = A*h*(T_cav.wall-Tair)
Q_cond = V*rho*c*(Tinit-Tamb)*exp(-t/k); k = rho*c/k

{T}, the temp vector, and time span would be given. I just want to know if my expressions above are right. If you could help me with this, it would be really great.

Thank you in advance.

 

[eljose79]

Thank you for your question. It seems like you are on the right track with your expressions for Q. To answer your question, yes, Q will indeed include terms for heat from injection, convection, and conduction through the rock mass. However, it is important to note that all of these terms can also be time-dependent, depending on the specific conditions and parameters of your model.

For example, the heat from injection (Q_inj) will depend on the mass flow rate (m_dot) and the difference in temperature between the injected air (Tinj) and the current air temperature (Tair). This temperature difference can change with time as the air cools down or heats up in the cavern.

Similarly, the heat from convection (Q_conv) will depend on the area of the cavern wall (A), the convective heat transfer coefficient (h), and the temperature difference between the cavern wall and the air. This temperature difference can also change with time as the air temperature changes.

Finally, the heat from conduction (Q_cond) will depend on the volume of the cavern (V), the density of the rock mass (rho), the specific heat capacity of the rock mass (c), the initial temperature of the rock mass (Tinit), the ambient temperature (Tamb), and the thermal conductivity of the rock mass (k). As you mentioned, the thermal conductivity can also vary with time, depending on the temperature and other factors.

Therefore, I would recommend considering all of these factors and their potential time-dependence when solving for Q in your model. It may also be helpful to gather more data or conduct experiments to better understand the specific conditions and parameters of your salt cavern and the compressed air energy storage process.

I hope this helps and wish you the best of luck with your research.