The steam methane reforming (SMR) process is a common method for commercial-scale hydrogen production [1]. At hydrogen manufacturing plants, the SMR process is typically carried out in a top-fired steam methane reformer that has two closed domains, i.e., the furnace side (in which fuel is burned in excess air to generate thermal energy that drives the SMR process) and the tube side (a collection of hundreds of nickel-based catalyst packed bed reactors, which are commonly referred to as reforming tubes). In top-fired reformers, a major factor that prevents reformers from being operated at the design capacity is the nonuniformity in outer tube wall temperature (OTWT) distributions (distributions of the outer reforming tube wall temperatures at a given distance from the reforming tube outlet) inside the reformer due to maximum temperature limitations of the material from which the reforming tubes are constructed. A number of references in the SMR literature have investigated furnace balancing methods (i.e., developing a fuel distribution for the burners that reduces the nonuniformity in the OTWT distribution at a given distance from the reforming tube outlet) in an attempt to improve the plant efficiency [2,3]. To determine an appropriate fuel distribution, the relationship between the mass flow rate of fuel through the burners and the outer tube wall temperatures at a specific distance from the reforming tube outlet must be modeled. First-principles models [4] and computational fluid dynamics (CFD) models [3] of the reformer may require significant computation time if solved repeatedly as part of an optimization problem that seeks to reduce nonuniformity in the OTWT distribution, and therefore would not be suitable for designing a real-time furnace balancing scheme that allows the fuel distribution to be adjusted to account for disturbances. Data-driven modeling is an appealing alternative as data-driven models are computationally inexpensive and can have reasonable accuracy. However, standard data-driven modeling procedures (i.e., subset selection) which could be used to derive a single best model relating the OTWT’s and the mass flow rates through the burners may not be sufficient because they do not account for the fact that the single model selected is not necessarily the actual model [5]. If the model uncertainty is not accounted for when the model is used for predicting appropriate fuel distributions within the furnace balancing algorithm, there is a potential that the algorithm may select an inappropriate high-risk action (e.g., increasing a mass flow rate through a burner when it should not be increased due to temperature limitations of the reforming tubes).
Motivated by this, the present work focuses on developing a two-step data-driven modeling procedure that utilizes the Bayesian model averaging framework with non-informative prior density distributions on models and model-specific parameters, conditional autoregressive (CAR) modeling, information on the reformer geometry and knowledge of thermal radiative heat transfer to derive a hybrid data-driven model (i.e., a model based both on the geometry/physics of the reformer and also on the reformer operating data). Then, the performance on out-of-sample predictions of the model is demonstrated to be superior compared to those of the other models derived from standard subset modeling approaches (i.e., Lasso and Nonnegative Garrote). The proposed data-driven model also has the potential to be used for monitoring purposes (e.g., when a unit of an infrared camera system used for monitoring the outer reforming tube wall temperatures goes offline temporarily, the data-driven model can estimate the missing data based on the fuel distribution).
[1] Ewan BCR, Allen RWK. A figure of merit assessment of the routes to hydrogen. International Journal of Hydrogen Energy. 2005;30:809–819.
[2] Kumar A, Baldea M, Edgar TF, Ezekoye OA. Smart manufacturing approach for efficient operation of industrial steam-methane reformers. Industrial & Engineering Chemistry Research. 2015; 54:4360–4370.
[3] Tran A, Aguirre A, Crose M, Durand H, Christofides PD. Temperature balancing in steam methane reforming furnace via an integrated CFD/data-based optimization approach. Computers & Chemical Engineering. in press.
[4] Latham D. Master’s Thesis: Mathematical Modeling of an Industrial Steam Methane Reformer. Queen’s University, 2008.
[5] Raftery AE, Madigan D, Hoeting JA. Bayesian model averaging for linear regression models. Journal of the American Statistical Association. 1997;92:179–191.
