Hydrogen is widely used as precursor across a variety of manufacturing industries, e.g., fertilizer (ammonia), petroleum refinery and methanol plants are responsible for 49%, 37% and 8% of world-wide hydrogen consumption, respectively . The current demand for hydrogen is large; for instance, the annual worldwide hydrogen production in 2008 was â¼500 billion Nm3
and corresponded to a global market of â¼$40 billion, and this demand is also expected to grow at an annual rate of 5% to 10%. Therefore, solving challenges encountered in commercial-scale production of hydrogen and optimizing these production lines has become an issue of great interest to both academia and industry. Among a variety of commercial hydrogen production processes, steam methane reforming (SMR) is by far the most common. For instance, SMR was responsible for 80% to 85% of the world-wide hydrogen production in 2007 . SMR is typically carried out in top-fired steam methane reforming furnaces which are the most expensive equipment in terms of the maintenance and operating costs compared to other major equipment such as the hydrotreating, prereforming, water-shift and purification units at centralized SMR-based facilities. For instance, the re-tubing cost of a furnace is â¼10% of the total capital investment, and the annual operating cost to procure fresh natural gas for a SMR-based hydrogen plant with a production rate of 2.7 million Nm3
per day is â¼$62 million . In practice, the energy efficiency of the reformer is subjected to various operational disturbances; for example, a failure in the flow control valve distribution prevents the optimized reformer fuel input determined off-line from being implemented. Hence, the need for a computationally efficient high-fidelity model for the reformer controlled variables (i.e., the outer tube wall temperature (OTWT) distribution) as a function of the reformer manipulated inputs (i.e., the flow control valve distribution and the total fuel flow rate) becomes apparent. First-principles models  and computational fluid dynamics (CFD) models  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 robust tool that allows the reformer fuel input 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.
Motivated by the above considerations, the present work introduces a statistical-based model identification scheme that generates a computationally efficient data-driven model for the OTWT distribution as a function of the total fuel flow rate, the fuel distribution and interactions among neighboring reforming tubes from reformer data. The proposed scheme is structured to have two fully-parallelized components, namely, a prediction step and a correction step. An algorithm for the prediction step is developed from Bayesian variable selection, Bayesian model averaging, sparse nonlinear regression, reformer geometry and theories of thermal radiation so that the OTWT of each reforming tube is computed based on the total fuel flow rate and its spatial distribution inside the reformer. An algorithm for the correction step is developed from the ordinary Kriging so that the OTWT of each reforming tube is computed based on the OTWTs of the neighboring reforming tubes. Finally, the data-driven model for the OTWT of each reforming tube is formulated as the weighted average of the respective prediction and correction models. Results from the goodness-of-fit and out-of-sample prediction tests of the data-driven model for the OTWT distribution are used to demonstrate the effectiveness of the scheme proposed in this work.
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