Over the past three decades, pressure swing adsorption (PSA) processes have been widely used as energy-efficient gas separation techniques, especially for high purity hydrogen purification from refinery gases. Models for PSA processes are multiple instances of partial differential equations (PDEs) in time and space with periodic boundary conditions that link the processing steps together. The solution of this coupled stiff PDE system is governed by steep fronts moving with time. As a result, the optimization of such systems represents a significant computational challenge to current differential algebraic equation (DAE) optimization techniques and nonlinear programming algorithms. Model reduction is one approach to generate cost-efficient low-order models which can be used as surrogate models in the optimization problems. This study develops a reduced-order model (ROM) based on proper orthogonal decomposition (POD), which is a low-dimensional approximation to a dynamic PDE-based model. The proposed method leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization and making the optimization problem computationally efficient. The method has been applied to the dynamic coupled PDE-based model of a two-bed four-step PSA process for separation of hydrogen from methane. Separate ROMs have been developed for each operating step with different POD modes for each of them. A significant reduction in the order of the number of states has been achieved. The reduced-order model has been successfully used to maximize hydrogen recovery by manipulating operating pressures, step times and feed and regeneration velocities, while meeting product purity and tight bounds on these parameters. Current results indicate the proposed ROM methodology as a promising surrogate modeling technique for cost-effective optimization purposes.