Uranium carbide is a candidate fuel for Generation IV nuclear fission reactors due to its higher thermal conductivity and metal atom density than its oxide fuel counterpart. However, in order for carbide fuels to be implemented, a reprocessing method must be devised to increase fuel efficiency and limit the volume of nuclear waste produced. Currently, nuclear fuel is reprocessed by first dissolving it in nitric acid. However, when carbide fuel is dissolved in this way, organic compounds are formed in the resulting solution. These organics have been observed to complex the plutonium (IV) and uranium (VI) ions in the solution making their extraction from the solution for further processing significantly more difficult. Therefore, a method of removing the organic compounds, or preventing their formation, must be found. Mathematical models have been constructed that simulate both the dissolution of a UC/(U, Pu)C pellet in nitric acid, and a pre-oxidative process that implements a conversion into UO2 removing the possibility of organic formation. Models have been built by mathematically describing the physical processes, particularly heat and mass transfer, involved followed by a numerical solution generated using finite difference methods. Available literature was consulted for reaction coefficients and information on reaction products initially, with experimental data then used where possible to derive new coefficients and compare to the literature values. Further models were then produced through the modification of commercial code that uses the Lattice Boltzmann Method to calculate fluid flow around the pellet and consider batch processes. The completed models assist in characterising the proposed reprocessing method for carbide fuels by predicting reaction completion times under various initial conditions and therefore suggest the optimal oxidation and dissolution conditions. The result is a powerful tool for use by the nuclear industry in assessing the most feasible reprocessing method.