Modeling wellbore heat exchangers: Fully numerical to fully analytical solutions. (April 2019) - Tang, Hewei; Xu, Boyue; Hasan, A. Rashid; Sun, Zhuang; Killough, John
Abstract: The successful modeling of wellbore heat exchangers requires tight coupling between the formation heat conduction and the wellbore thermal dynamics. In this paper, we developed three representative solutions: a fully numerical solution that treats both formation and wellbore numerically, a semi-numerical solution that treats formation analytically and wellbore numerically and a fully analytical solution that treats both formation and wellbore analytically. The outlet temperature, pressure, and heat flow rate predicted by the three solutions are compared. The results of this comparison indicate that the fully numerical solution is the only accurate solution for the early transient time. After the system reaches quasi-steady state, temperature and heat flow estimated from all three solutions are in very good agreement. The analysis of transient fluid properties and mass flow rates revealed that constant fluid property model cannot accurately estimate the pressure loss for the system. The newly proposed fully analytical solution is applied in an economic analysis problem for calculating the optimal insulation thickness and mass flow rate to minimize the cost of generated power. Highlights: An analytical model considering both wellbore heat exchange and formation heat conduction is derived. A fully numerical model and a semi-numerical model are developed to compare with the analytical model. The analytical model is applied in a novel engineering optimization problem to minimize the cost of generated power. We used Matlab as the programming language.