A Systematic Simulation and Proposed Optimization of the Pressure Swing Adsorption Process for N 2 /CH 4 Separation under External Disturbances Weina Sun, † Yuanhui Shen, † Donghui Zhang,* ,† Huawei Yang, † and Hui Ma ‡ † Collaborative Innovation Center of Chemical Science and Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ‡ School of Architecture, Tianjin University, Tianjin 300072, China ABSTRACT: This work presents a detailed study of the systematic simulation, optimization, and control of a pressure swing adsorption (PSA) process that used activated carbon as adsorbent to recover CH 4 from a gas mixture (70% N 2 /30% CH 4 ). The state-of-the-art reduced space successive quadratic-programming (r-SQP) optimization algorithm is employed to find the optimal values of the decision variables with additional constraints. The best closed loop recovery obtained for the PSA system under consideration is around 98% with purity of 80%. The control strategy is based on the regulatory proportional-integral- derivative (PID) controller because of its practicability and stability. Additional constraints that guaranteed the flexibility and adaptability of the PID controller were imposed on the optimization-based PSA system. The ability of the control system to reject various disturbances was evaluated and compared with the open loop conditions. Results demonstrated that the well- designed control system showed a wonderful performance in the presence of multiple disturbances. 1. INTRODUCTION In coal bed methane (CBM), N 2 and CH 4 are the main components and the concentration of methane usually lies between 20% and 35%, which means the CBM is unable to be utilized directly. In China, most CBM is discharged into the atmosphere, which is a waste of a resource and increases the greenhouse effect. 1 The greenhouse warming potential of CH 4 is 25 times higher than that of the well-known greenhouse gas carbon dioxide. 2 From the standpoint of environmental protection, upgrading the low-concentration coal bed methane is extremely advantageous with the more stringent restriction on the emission amount of greenhouse gases such as carbon dioxide and methane. Meanwhile, methane has a lower cost than traditional fossil fuels such as gasoline or diesel, which can generate significant economic benefit 3,4 in the face of the severe global energy situation. To remove the existing nitrogen, many unit operations of chemical engineering such as cryogenic distillation, 5 membrane-based separation, 6 and pressure swing adsorption (PSA) 1,7-9 have been proven to be feasible. Among all the feasible unit operations, PSA proved itself to be the most desirable because of its low operating cost compared with cryogenic distillation and efficient automatic operation in contrast with membrane-based separation. The inventions of PSA occurred before the underlying theories behind it were fully understood. Since its practical application in the late 1950s, PSA technology has evidenced substantial growth in terms of scale, versatility, and complex- ity. 10 The PSA process consists of multiple interactive beds filled with adsorbents and operates in a cyclic manner, which is called periodic operation. To simulate and optimize the PSA system, rigorous mathematical models consisting of coupled partial differential and algebraic equations (PDAEs) distributed over time and space that describe material, energy, and the momentum balances together with transport phenomena and equilibrium equations have to be formulated to describe the highly nonlinear nature and dynamic behavior of the real PSA plants. 11,12 In the last three decades, many mathematical models of adsorption beds with different complexities have been established and simulated. Owing to the tedious and time- consuming solution procedure of the thousands of PDAEs of the whole PSA system, those not only accurate but also simplified models are desirable to decrease the essential computational time and accelerate optimization studies. 13 In addition to its highly nonlinear and dynamic nature, the PSA system poses extra challenges because of its highly interactive characteristics among process variables, especially design parameters such as step times, pressure, temperature, gas velocity, and bed dimensions. Consequently, it is difficult to find the optimum conditions through experiments of trial and error, which is a waste of time and an irrational utilization of resources. A great deal of research concerning simulation and optimization of simplified model-based PSA processes has been reported in the literature. Nilchan proposed a complete discretization approach. 14 In this approach, the space and the temporal domain are discretized simultaneously, which reduces the PDAEs-based model equations to a large set of nonlinear algebraic equations. The resulting optimization formulation is a rather small nonlinear programming (NLP) problem which is easy to solve using a standard NLP solver. Jiang et al. apply the direct determination approach proposed by Smith and Westerberg 16 and Croft and LeVan 17 and simultaneous tailored approach, a reduced space successive quadratic-programming Received: March 24, 2015 Revised: July 6, 2015 Accepted: July 9, 2015 Article pubs.acs.org/IECR © XXXX American Chemical Society A DOI: 10.1021/acs.iecr.5b01862 Ind. Eng. Chem. Res. XXXX, XXX, XXX-XXX