Compressed Air Energy Storage

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.<br class="Apple-interchange-newline">