  Geothermal energy is a sustainable baseload source recognized for its ability
to provide clean energy on a large scale. Advanced Geothermal Systems (AGS) --
offer promising prototypes -- employ a closed-loop vascular layout that runs
deep beneath the Earth's surface. A working fluid (e.g., water or supercritical
carbon dioxide (sCO2)) circulates through the vasculature, entering the
subsurface at the inlet and exiting at the outlet with an elevated temperature.
For designing and performing cost-benefit analysis before deploying large-scale
projects and maintaining efficiency while enabling real-time monitoring during
the operational phase, modeling offers cost-effective solutions; often, it is
the only available option for performance assessment. A knowledge gap exists
due to the lack of a fast predictive modeling framework that considers the
vascular intricacies, particularly the jumps in the solution fields across the
channel. Noting that the channel diameter is considerably smaller in scale
compared to the surrounding geological domain, we develop a reduced-order
modeling (ROM) framework for closed-loop geothermal systems. This ROM
incorporates the jump conditions and provides a quick and accurate prediction
of the temperature field, including the outlet temperature, which directly
correlates with the power production capacity and thermal draw-down. We
demonstrate the predictive capabilities of the framework by establishing the
uniqueness of the solutions and reporting representative numerical solutions.
The modeling framework and the predictions reported in this paper benefit the
closed-loop geothermal community, enabling them to determine the system's
performance and optimal capacity.
