Heat Pipe Stability in Geothermal Reservoirs

Abstract

The heat pipe mechanism with steam rising and liquid falling to transfer heat to shallow levels with minimal mass transfer, is fundamental to conceptual and numerical models of geothermal reservoirs. When modeling the heat pipe mechanism numerically, an interesting stability question arises. For example, why is it easy to simulate a steady vapor dominated heat pipe when pressure and saturation are fixed at the bottom? Why is it easy to obtain a liquid dominated steady heat pipe when pressure and saturation are fixed at the top in the simulation? This is explained here to be a feature that is expected of a wave like solution for saturation, and it is shown that the numerical technique called upstream differencing mimics this feature in the steady state case. The results are general to relative permeability curves that sum to a constant value, provided they are monotonic.