Geothermal energy is a reliable and mature energy source, but it represents less than 1% of the total renewable energy mix. While the enhanced geothermal system (EGS) concept faces technical validation challenges and suffers from public acceptance issues, the development of unconventional deep-well designs can help to improve their efficiency and reliability. Modelling single-EGS-well designs is key to assessing their long-term thermal performances, particularly in unconventional geological settings. Numerical results obtained with the T2WELL/EOS1 code have been validated with available experimental data from a deep borehole heat exchanger (DBHE), where a temperature of 358 ${}^{\circ }$C has been measured at a depth of 1962 m. Based on a calibrated model, the thermal performances of two enhanced thermal conductive DBHEs with graphite were compared for high geothermal gradients. The analysis highlights the potential recovery of a variable fraction of vapour. Graphite used along the well appears to be the most suitable solution to enhance the thermal output by 5 to 8% when compared to conventional wells. The theoretical implementation of such well in the Newberry volcano field was investigated with a single and doublet DBHE. The findings provide a robust methodology to assess alternative engineering solutions to current geothermal practices.