Bayesian model averaging for estimating the spatial temperature distribution in a steam methane reforming furnace

In this work, we introduce a statistical-based model identification scheme that generates a high-fidelity model for the outer reforming tube wall temperature (OTWT) distribution as a function of the furnace-side feed (FSF) distribution, total FSF flow rate and interactions among neighboring reforming tubes from reformer data. The proposed scheme is structured to have two major components, namely, a prediction step and a correction step, which are designed to be parallelized so that the prediction and correction models of all reforming tubes are derived simultaneously from the reformer data and independently from one another. Initially, a computational fluid dynamics (CFD) model of an industrial-scale reformer created in our previous work is utilized to facilitate the generation of the training and testing data. Then, we propose the development of an algorithm for the prediction step based on Bayesian variable selection, Bayesian model averaging, sparse nonlinear regression, reformer geometry and theories of thermal radiation so that for each reforming tube, the prediction step can systematically identify predictors for the OTWT and simultaneously create a corresponding library of sub-prediction models. A collection of prediction models for all reforming tubes is defined as a prediction model for the OTWT distribution, which is expected to capture the dependence of the OTWT distribution on the FSF distribution and total FSF flow rate. Next, we propose an algorithm for the correction step designed based on ordinary Kriging so that for each reforming tube, the correction step creates a spatial model allowing the OTWT to be estimated from the predicted OTWT of the neighboring reforming tubes. A collection of correction models for all reforming tubes is defined as a correction model for the OTWT distribution, which is expected to adjust the predicted OTWT distribution to account for interactions among neighboring reforming tubes. Subsequently, the combined data-driven model for the OTWT distribution is created using the prediction and correction models for the OTWT distribution, which allows the combined model to account for the effect of interactions among neighboring reforming tubes while estimating the OTWT distribution based on the FSF distribution and total FSF flow rate. The proposed integrated model identification scheme is executed on the Hoffman2 cluster at UCLA to construct the data-driven model for the OTWT distribution from the training data, and the results from the goodness-of-fit and out-of-sample prediction tests of the data-driven model are used to demonstrate the effectiveness of the scheme proposed in this work.