I am writing about the thermal modelling process. One thing I have to illustrate is the shape of my theoretical energy bulb. this is based on measuring the energy inputs and outputs. Well, it can't be the actual figure of eight twin borehole quite yet as the maths of that growing and shrinking, with varying surface area and volume is defeating. A simple single cylinder is what I have used, of a fixed height, so that expansion and contraction is wholly based on RADIUS. Thus the volume is relative to the square of the radius.
The bottle-shape is because you can ignore the performance of the bit nearest the ground, and the lower part is rounded off.