Having a bit of trouble developing a mathematical model for the heat transfer during the leaching process of a salt cavern.
The well/bore hole is approximately 0.15 meters in diameter and the cavity is 100 cubic meters and is spherical.
The surrounding salt rock is 60 degrees Celcius and the fresh water injected into the cavity is 7.5 degrees Celcius.
Fresh water is injected at 100 cubic metres per hour.
I assumed that there are no impurities at the bottom of the cavity the contents consists only of brine. Also, it takes between 10 and 20 hours to form the 100 cubic meter cavity.
In the end I'm trying to determine the brine temperature at the end of leaching and time it will take for the brine in the cavity to reach the temperature of the surrounding salt rock when leaching is stopped.
Assumptions:
when time=0, we can assume that the cavern brine is in thermal equilibrium with the salt formation.
the heat energy balance inside the cavern is made up of the heat exchanged with the entering water, the latent heat of solution and the heat entering the cavern volume across its bounding surface.
Any help would be very much appreciated.