Mathematical modeling and simulating of an industrial top-fired steam methane reforming unit

Abstract

This work aims to develop phenomenological mathematical models in a steady and dynamic state of an industrial steam methane reforming unit (SMRU). For its complete description, four control volumes are considered: the catalytic tubular reactor, tube wall, furnace, and refractory. Effects often neglected in the literature, for example, radiation in the tube side, convection in the furnace, energy radiated by the reforming tubes and the refractory, as well as the energy absorbed by the gas in the furnace are investigated. The model also incorporates the kinetic expressions that define the reforming and combustion reactions. These reactions are described by rigorous mass and energy distributed balances, unlike the usual approach in the literature, where empirical correlations are used to describe the heat release profile of the furnace for the tubular reactors. A more precise prediction of these profiles is useful for understanding and monitoring the quality of the outlet gas for different inlet conditions without the need to know the length of the flame. The reformer's stationary model is validated using experimental data from the industrial partner and the literature. This model is used to investigate the influence of reforming kinetics on the reformer's performance. Different kinetic expressions commonly applied in the literature are compared with each other and the results, for different operating conditions, confirm that the reformer operates close to chemical equilibrium. Therefore, the kinetics have little effect on the reformer's performance, which is a function especially of the heat management sent to the reforming tubes. A statistical approach based on the design of experiments and the response surface methodology (RSM) is applied to identify the most important variables and interactions in the process. An optimization problem is formulated and solved in Excel, using the generalized reduced gradients method and the calculated optimal point is analyzed through contour surfaces. This statistical analysis shows that the steam to carbon ratio, feed flow to the tube, feed gas temperature, and combustion air temperature are the variables that most influence the performance of the reforming process. The study of the reformer evolves with the use of the dynamic model to predict the temporal and spatial behavior of these key variables. This study aims to extract more detailed information of the process, such as conditions that can result in temperature peaks that would not be provided with the use of a stationary model. Both models, stationary and dynamic, presented temperature and composition profiles consistent with the literature. Therefore, such models can serve as a valuable tool to assist operators in operational practice, as well as they can be used to develop and analyze control schemes in the investigated industrial unit.