Steady-solution selection and existence in geothermal heat pipes—II. The conductive case

Abstract

The behavior of steady geothermal heat pipe solutions is considered, when permeability is reduced to values where conduction effects become important. This extends previous work, in which permeability was large enough for convective effects to dominate. The effect of reduced permeability is studied using computer visualization techniques and qualitative differential equation methods. It is found that as permeability is reduced, conduction effects first appear near a permeability of 10 −15 m 2, for typical geothermal reservoir parameter values. Solution behavior in the temperature-saturation phase plane is fundamentally affected: solutions starting from pure liquid at cooler temperatures, and having a portion that is gravity-driven and liquid-dominated, can no longer cross to pure vapor at hotter temperatures; and solutions starting from pure vapor at hotter temperatures, and having a portion that is gravity-driven and vapor-dominated, can no longer cross to pure liquid at cooler temperatures. The distinction between vapor-dominated and liquid-dominated solutions disappears, with all solutions having appreciable variations in saturation with depth.