Shape matters
To reduce the thermal losses of a storage the surface-to-volume ratio should be minimized. The perfect shape is a sphere, but this seems to have some serious disadvantages when using for BILS. Second best seems to be a cylindrical storage (…see what is down in your heating room). With a bit of calculus we find that for a given volume V, the optimum radius r and optimum height h are
or even simpler
fir the time being, BILS are therefore cylinders which have a r/h ratio in th erange of about 2.
Size matters
As for all storages, big storages have a better surface to volume ratio and therefore lower thermal losses: The bigger the better. To illustrate the effect, we have computed the temperature decay of a conventional Class B (European eneregy label) storage of 500 l, heatet up to 99°C in an environment of 4°C. Such a storage will have lost 50% of the energy after about 10.5 days. A similar storage with 50 Mio liters but with a similar "Class B" insulation, will need more than a year to lose 50% of its energy.
To be continued....