APPLICATION OF THE MARKOV CHAIN MONTE CARLO METHOD TO ESTIMATION OF PARAMETERS IN A MODEL OF ADSORPTION-ENHANCED REACTION PROCESS OF MERCURY REMOVAL FROM NATURAL GAS

APPLICATION OF THE MARKOV CHAIN MONTE CARLO METHOD TO ESTIMATION OF PARAMETERS IN A MODEL OF ADSORPTION-ENHANCED REACTION PROCESS OF MERCURY REMOVAL FROM NATURAL GAS

FERREIRA, J. L; ESTUMANO, D. C; MACÊDO, E. N

Oral:

A mathematical model proposed in the literature for the adsorption of mercury was solved numerically. This model involved the diffusion in the adsorbent particle, followed by a chemical reaction inside the solid matrix. The model was obtained based on the differential mass balance for the solute in a volume element bed with an equation involving diffusion and a first-order chemical reaction. For the direct solution of the problem, the Method of Lines (MOL) was applied to simplify the system of Partial Differential Equations (PDEs) into a system of time dependent Ordinary Differential Equations (ODEs). For the estimation of parameters, simulated measurements were generated with a normal distribution, with the direct solution as the mean and deviations of 10% regarding the maximum value of the exact solution. The sensor is located at the exit of the bed. Lastly, based on the sensitivity analysis, two parameters were chosen and estimated by the Markov Chain Monte Carlo (MCMC) method regarding the Gaussian distribution as a prior distribution to unknown parameters. In the estimation, the mean equal to the reference value with a standard deviation of 10% of the reference values. The results showed that the method was able to reproduce the reference values with relative errors of less than 3% for both the parameters.

A mathematical model proposed in the literature for the adsorption of mercury was solved numerically. This model involved the diffusion in the adsorbent particle, followed by a chemical reaction inside the solid matrix. The model was obtained based on the differential mass balance for the solute in a volume element bed with an equation involving diffusion and a first-order chemical reaction. For the direct solution of the problem, the Method of Lines (MOL) was applied to simplify the system of Partial Differential Equations (PDEs) into a system of time dependent Ordinary Differential Equations (ODEs). For the estimation of parameters, simulated measurements were generated with a normal distribution, with the direct solution as the mean and deviations of 10% regarding the maximum value of the exact solution. The sensor is located at the exit of the bed. Lastly, based on the sensitivity analysis, two parameters were chosen and estimated by the Markov Chain Monte Carlo (MCMC) method regarding the Gaussian distribution as a prior distribution to unknown parameters. In the estimation, the mean equal to the reference value with a standard deviation of 10% of the reference values. The results showed that the method was able to reproduce the reference values with relative errors of less than 3% for both the parameters.

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DOI: 10.5151/cobeq2018-CO.154

Referências bibliográficas

• [1] CAMARGO C. L. M, RESENDE N. S, OLIVEIRA A. G, SALIM V. M. M, TAVARES F. W,
• [2] Investigation of adsorption-enhanced reaction process of mercury removal from simulated natural gas
• [3] by mathematical modeling. Fuel, v. 129, p. 129-137, 2014.
• [4] GAMERMAN, D., Markov Chain Monte Carlo: Stochastic simulation for Bayesian Inference. 1ed.
• [5] London: Chapman & Hall, 1997.
• [6] ORLANDE, H., FUDYM, F., MAILLET, D., COTTA, R., Thermal Measurements and Inverse
• [7] Techniques, CRC Press, Boca Raton, 2011.
• [8] UNEP Chemicals Branch. The global atmospheric mercury assessment: sources, emissions and
• [9] transport. UNEP-Chemicals, Geneva, Switzerland, 2008.

Como citar:

FERREIRA, J. L; ESTUMANO, D. C; MACÊDO, E. N; "APPLICATION OF THE MARKOV CHAIN MONTE CARLO METHOD TO ESTIMATION OF PARAMETERS IN A MODEL OF ADSORPTION-ENHANCED REACTION PROCESS OF MERCURY REMOVAL FROM NATURAL GAS", p-4687-4690. In: . São Paulo: Blucher, 2018.
ISSN 23591757, DOI 10.5151/cobeq2018-CO.154