Spatially distributed first-principles process models provide an accurate physical description of chemical processes, but lead to large-scale models whose numerical solution can be challenging and computationally expensive. Therefore, fast reduced order models are requited for model-based real-the applications, such as advanced process control and dynamic real-time optimization. In this papery-we focus on the model reduction Of a bubbling fluidized bed (BFB) adsorber, which is a key component of a postcombustion carbon capture System. From a temporal aspect, dynamic reduced models are generated using the nullspace projection and eigenvalue analysis method, with the basic idea of quasi-steady state approximation for the states with fast dynamics. From a spatial aspect, dynamic reduced models are developed using orthogonal collocation and proper orthogonal decomposition to reduce the size of the rigorous model. Finally, a computationally efficient and accurate dynamic reduced model is developed for the BFB adsorber by combining temporal and spatial model reduction techniques, Which is,suitable for an online optimization-based control strategy.