Chemical looping combustion is a transformative electricity generation process with the potential for high efficiency and a unique approach to carbon capture capable of achieving very low energy penalties. Chemical looping combustion systems based on moving bed and bubbling fluidized bed reactors have been proposed. This paper employs rigorous models utilizing the Institute for the Design of Advanced Energy Systems (IDAES) process systems engineering (PSE) framework, to optimize iron-based, methane-fueled chemical looping combustion processes based on both reactor concepts. The models account for reaction kinetics, mass and heat transfer, and hydrodynamics. Each system was optimized to minimize total annualized costs while combusting 99.9% of the methane feed of 125 mol/s. Within the assumptions of this study, the moving bed-based chemical looping combustion process has significant cost advantages compared to the bubbling fluidized bed-based chemical looping combustion process due to smaller reactor sizes and solids inventory, and lower electricity consumption. (C) 2019 Published by Elsevier B.V.