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ARX and ARMAX Modelling of olefin metathesis reactive distillation process

Abdulwahab Giwa and Saidat Olanipekun Giwa

This work has been carried out to develop AutoRegressive with eXogenous Inputs (ARX) and AutoRegressive Moving Average with eXogenous Inputs (ARMAX) models for olefin metathesis process accomplished using a reactive distillation column. To achieve the work, Aspen HYSYS model of the process was first developed and simulated to obtain the data used to formulate the transfer function model of the process. The transfer function model was tested for stability, which was ascertained from the attainment of steady state by the output of the process, through simulation and, later, run using random number to generate the data required for the development of ARX and ARMAX models of the process that were also simulated and their performances compared. The results obtained revealed that the developed ARX and ARMAX models had moderate orders. Also, good agreements were found to exist between the measured mole fraction of bottom cis-2-hexene and the simulated ones, implying that the developed models were good representatives of the process. Moreover, the lower mean of squared error value and the higher fit value of the developed ARMAX model revealed that it was able to represent the process better than the developed ARX model. It is, therefore, recommended that ARMAX model should preferably be used to represent the olefin metathesis reactive distillation process for further studies