Parameter Estimation in Mass Balance Model Applied in Fixed Bed Adsorption using the Markov Chain Monte Carlo Method

In this work, a mathematical model is adopted to predict the breakthrough curve in a fixed bed adsorption process, neglecting radial dispersion effects in the bed, with properties such as interstitial velocity and porosity being constant, linear adsorption kinetics and equilibrium relationship represented by the Langmuir isotherm. The resulting partial differential equation is numerically solved by the Method of Lines (MOL), while the Markov Chain Monte Carlo method is employed to estimate the model parameters, using simulated measures and a priori Gaussian probability distribution for the parameters, varying the mean and standard deviation. A convergence analysis was performed to look for numerical convergence between the number of nodes (N) used and the computational cost (CPU time) and it was observed that N = ۱۰۰ obtained the lowest computational cost (less than ۰.۲ s). The estimated values of Peclet's number (Pe) and Langmuir's constant (KL) showed deviations of ۷% and ۰.۰۱%, respectively, compared to their exact value which shows that the estimates were accurate, i.e., the parameters are close to the exact value. Also, the estimated values were within the credibility interval of ۹۹ % established, which shows precise estimates. The information taken from these estimates has become of fundamental importance in predicting the behavior of the breakthrough curve at different points in the bed, showing that the MOL in combination with the MCMC are efficient tools in the direct and inverse analysis of models of breakthrough curves.

کلیدواژه ها:

Adsorption ، Breakthrough Curve ، MCMC ، Parameter estimation ، Convergence analysis