Oxy-fuel based pulse detonation system can be used for direct power extraction when combined with magnetohydrodynamics (MHD). A space-time conservation element solution element (CE/SE) method is used to investigate the operational envelope of oxy-coal detonations with gaseous methane as a surrogate fuel. The CE/SE method results in a consistent multidimensional formulation for structured/unstructured meshes by providing flux conservation in space and time without the need for complex Riemann solvers to capture solution discontinuities. A modified revised Jones-Lindstedt (JL-R) reaction mechanism accounting for radicals such as O, OH, and H was used as a reduced mechanism to simulate detonation waves from CH4−O2 combustion. The numerical scheme is first verified by comparing predictions with the ZND theory and other published data to show excellent agreement. For shock-induced detonation, the effect of driver shock temperature, pressure, stoichiometric ratio (ϕ) and initial driver shock length, on detonation initiation and propagation was investigated. The simulations accurately predicted detonation velocities, at various ϕ values, compared with available experimental data. The results show that higher gas temperatures and velocities are achieved through oxy-detonations compared to air. The chosen reduced chemical kinetic mechanism, that accounts for radical disassociation, is found to be critical in appropriately limiting heat release during oxy-combustion, thereby predicting detonation temperature and velocity accurately.