Upconversion processes effectively convert two or more low energy photons into one higher energy photon, and have diverse applications in photovoltaics and biomedicine. Upconversion is generally spin-selective, and its magnetic field response can be used to examine the interplay between two different mechanisms for photochemical upconversion in solution: triplet-triplet annihilation, and singlet-oxygen mediated energy transfer. A kinetic model is developed and applied to explain the different photoluminescence profiles of oxygenated versus deoxygenated systems. From the magnetic field response, the triplet-triplet annihilation rate constant is estimated. The conditions required to maximize upconversion photoluminescence intensity in oxygenated solution are determined.