Markov Chain Monte Carlo Analysis of the Variable-Volume Exothermic Model for a Continuously Stirred Tank Reactor

  • J. P. Muhirwa Department of Applied Mathematics and Computational Science (AMCS), Nelson Mandela African Institution of Science and Technology Tanzania (NM-AIST), Tanzania | Department of Mathematics, University of Rwanda, College of Science and Technology (UR-CST), Rwanda
  • S. I. Mbalawata Research Department, African Institute for Mathematical Sciences, Rwanda
  • V. G. Masanja Department of Applied Mathematics and Computational Science (AMCS), Nelson Mandela African Institution of Science and Technology Tanzania (NM-AIST), Tanzania


In this paper, a variable-volume Continuously Stirred Tank Reactor (CSTR) deterministic exothermic model has been formulated based on the Reynold Transport Theorem. The numerical analysis of the formulated model and the identifiability of its physical parameters are done by using the least squares and the Delayed-Rejection Adaptive Metropolis (DRAM) method. The least square estimates provide the prior information for the DRAM method. The overall numerical results show that the model gives an insight in describing the dynamics of CSTR processes, and 14 parameters of the CSTR are well identified through DRAM convergence diagnostic tests, such as trace, scatter, autocorrelation, histograms, and marginal density plots. Global sensitivity analysis was further performed, by using the partial rank correlation coefficients obtained from the Latin hypercube sampling method, in order to study and quantify the impact of estimated parameters, uncertainties on the model outputs. The results showed that 7 among the 14 estimated model parameters are very sensitive to the model outcomes and so those parameters need to be handled and treated carefully.

Keywords: parameter identifiability, variable volume, exothermic, CSRT, RTT, MCMC, DRAM


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