Chemical looping combustion (CLC) has emerged as an effective carbon capture and storage (CCS) technique. Yet, the intricate interaction of flow, temperature, and species fields presents challenges in comprehending the underlying mechanism from multi-scale aspects. In this work, a computational fluid dynamics-discrete element method (CFD-DEM) reactive model is developed, featuring a coarse-grained method to provide efficient calculation and a modified drag model to consider the polydispersity effect. After comprehensive validations, the integrated model is applied to simulate the CH4-fueled CLC process in a fuel reactor (FR), with a discussion of the effects of particle size distribution and reactor inner diameter on the system performance. The results demonstrate that the particle-scale polydispersity, bubble-scale dynamics, and reactor-scale structure can significantly influence the interactions between gaseous fuel and oxygen carriers in the CLC system. These factors play a crucial role in determining the thermochemical characteristics of the system. Particularly, bubbles in the FR with a smaller diameter display a characteristic of "fewer but larger", whereas bubbles in the newly devised FR with a larger diameter exhibit a feature of "more but smaller". Consequently, enhanced uniformity in gas-solid physicochemical properties, heightened CO2 concentration, and improved combustion efficiency can be achieved in our newly designed CLC reactor. Overall, this study imparts valuable multi-scale insights into the physical -thermal-chemical characteristics of the CLC process.