Selective artificial ground freezing (S-AGF) applications usually extend to very deep levels (more than 400 meters); numerical modeling of such large AGF applications encounters two main issues: (i) Predicting the variable heat extraction capacity along the freeze-pipe depth and (ii) the extremely long computational time. In this paper, we develop novel semi-conjugate reduced-order models that accurately predict heat extraction along the freeze-pipe while substantially reducing the computational time. In regards to the thermal modeling novelty, the freeze-pipe boundary condition of S-AGF is mathematically derived considering the development of the coolant flow temperature and boundary layer. As for the computational novelty, fast semi-conjugate reduced-order algorithms are developed for S-AGF, with the optional incorporation of analytical solutions and spatial correction. The models are validated against experimental data and verified with established fully-conjugate models. The thermal results demonstrate that the phase transition front profile of the frozen ground is primarily shaped by the thermal development of the flow. On the other hand, the computational results reveal that the computational time of the reduced-order algorithms is decreased by more than 99%, as compared with the established models. In short, our proposed reduced-order models are proven to be reliable and computationally efficient, which shows potential for practical field application.