The effect of heat transferin the formation in vertical direction
If the effect of the heat loss from the well bore in vertical direction through the formation is to be included.

After such long times, repeated startup-shutdowns and heat transfer to/from other wells will be more significant than vertical heat loss.

Compared to gas or a solid insulation material in the space it will be best to have water in the space between the production pipes due to the following: Water (or another liquid) gives good heat transfer between the production pipes, such that one line can be kept warm during shutdown or production at a low rate from the other(s) lines that are producing.

However, to keep the weight down such that it can float during tow-out, it may be required to have low-density insulation material in all available empty spaces including the space between the production lines. This complicates thermal modeling significantly and rigorous finite element or finite difference models are required.

Therefore, this is the brief instruction of heat transfer.