The SpinQuest experiment at Fermilab aims to measure the Sivers asymmetry for the $\bar{u}$ and $\bar{d}$ sea quarks in the range of 0.1 $< x_{B} <$ 0.5 using the Drell-Yan production of dimuon pairs. A nonzero Sivers asymmetry would provide an evidence for a nonzero orbital angular momentum of sea quarks. The proposed beam intensity is 1.5~$\times$~10$^{12}$ of 120 GeV unpolarized proton/sec. The experiment will utilizes a target system consisting of a 5T superconducting magnet, transversely polarized NH$_3$ and ND$_3$ targets, a $^4$He evaporation refrigerator, a 140 GHz microwave source and a large pumping system. The expected average of the target polarization is 80$\%$ for the proton and 32$\%$ for the deuteron. The polarization will be measured with three NMR coils per target cell. A quench analysis and simulation in the superconducting magnet are performed to determine the maximum intensity of the proton beam before the magnet become resistive. The simulation of quenches in the superconducting magnets is a multiphysics problem of highest complexity. The heat transfer from metal to helium goes through different transfer and boiling regimes as a function of temperature, heat flux, and transferred energy. All material properties are temperature dependent. A GEANT based simulation is used to calculate the heat deposited in the magnet and the subsequent cooling processes are modeled using the COMSOL Multiphysics.