Modeling of a two-phase CO2-filled vertical borehole for geothermal heat pump applications

Abstract

A numerical model has been developed to study the complex thermal behavior of a CO2-filled vertical geothermal borehole consisting of a long copper U-tube embedded in a solid material (grout). The model accounts for combinations of single-phase and two-phase fluid flow which may occur along the U-tube length. An explicit solution for fully coupled steady-state conservation equations of mass, momentum and energy is applied. The borehole is divided into small volume elements due to relatively significant changes in the thermophysical properties of the fluid. Borehole wall temperature variations as well as thermal interaction between tube sections are taken into account and the model predicts the fluid temperature, pressure and two-phase quality profiles.A case in which the borehole is assumed to be an evaporator of a direct-expansion ground coupled heat pump is studied. The model is used to assess the thermal performance of the borehole as well as pressure, temperature, and quality variations of CO2 along the U-tube. According to the results, the pressure variation of the fluid in the two-phase region has unavoidable consequences on the temperature variation. Results indicate that the proposed borehole can extract relatively large amounts of energy due to the superior two-phase heat transfer characteristics of CO2. Furthermore, the heat exchange rate between the ground and the upward flow leg in the two-phase region is greater than that between the ground and the downward flow, which is the opposite of conventional boreholes with a performance drop from the downward flow to the upward flow.