A systematic design and synthesis framework for multi-step, multi-mode and periodic sorption-enhanced reaction processes (SERP) is presented. The formulated nonlinear algebraic and partial differential equation (NAPDE)-based model simultaneously identifies optimal SERP cycle configurations, design specifications and operating conditions. Key modeling contributions include a generalized boundary-condition formulation and a representation that enables the selection of discrete operation modes and flow directions using continuous pressure variables. A simulation-based constrained grey-box optimization strategy is employed to obtain optimal cycles and design parameters. The framework has been used for designing two SERP systems, namely sorption-enhanced steam methane reforming (SE-SMR) and sorption-enhanced water gas shift reaction (SE-WGSR), for maximizing hydrogen productivity and minimizing hydrogenproduction cost. Specifically, a cyclic SE-SMR process is designed that obtains 95% pure hydrogen from natural gas with 35% higher productivity and 10.86% lower cost compared to existing small-scale, distributed systems. The developed synthesis framework can also be applied for other applications. (c) 2018 Elsevier Ltd. All rights reserved.