One of the benefits of pressurized chemical looping over other carbon capture technologies is the simplified purification of the flue gas to generate a CO2 product stream. However, polishing is required to remove residual impurities such as hydrocarbons and oxygen. These species are often restricted in pipeline specifications as they can be a source of corrosion or be problematic during compression, liquefaction, or pumping. Intensified heat exchange reactors are currently being developed at CanmetENERGY-Ottawa in collaboration with the University of Ottawa to eliminate these impurities. These compact reactor/heat exchanger units enable removal of impurities to very low levels (< 100 ppmv) while recovering valuable heat. The technology enables stoichiometric combustion in staged catalytic beds to remove either oxygen or hydrocarbons by injecting small amounts of additional fuel or oxidant, respectively. This compact system allows CO2 polishing in a small form factor, which is advantageous for deployment at small and medium scale industrial sites. In this work, a one-dimensional reduced-order reactor model is used to design an intensified heat exchange reactor for residual hydrocarbon removal in the flue gas from a 600 kWth PCL pilot plant. Parameters that are varied in the design include number of reaction stages, packed bed dimensions, and heat exchanger layout.