T2Well semi-analytical solution in reservoir
I notice in the T2Well manual that you can turn on a semi-analytical solution of the reservoir by setting thermal conductivity in well cells to a negative value. I just wanted to ask what the governing equations are for this semi-analytical solution, and does the 1D momentum equation still hold in the wellbore using the drift flux model with this semi-analytical solution turned on?
In T2well, the heat contribution to the energy balance equation from the rock surrounding wellbore can be calculate using a semi-analytical solution. The part of energy is treated something like a source/sink term, which is added to energy balance equation after solving 1D momentum equation for mass flow and heat flow in the well. I would expect the impact of heat from surrounding rock is minor on the momentum equation if the temperature gradient (in the direction of well) is not significant and the drift flux model is still ok.
The equations for the semi-analytical heat exchange can be found at: https://www.sciencedirect.com/science/article/pii/S0375650511000484. They only affect energy equations, i.e. they are only for heat exchange with surrounding formations, where it is assumed there is no fluid flow in the formation but there is thermal conduction between the formation and the wellbore.