Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport

Vasiliy V. Grigoriev and Petr N. Vabishchevich
Additional contact information
Vasiliy V. Grigoriev: Multiscale Model Reduction Laboratory, North-Eastern Federal University, 58 Belinskogo St., 677000 Yakutsk, Russia
Petr N. Vabishchevich: Multiscale Model Reduction Laboratory, North-Eastern Federal University, 58 Belinskogo St., 677000 Yakutsk, Russia

Mathematics, 2021, vol. 9, issue 16, 1-16

Abstract: Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.

Keywords: uncertainty quantification; parameter identification; Bayesian inference; Markov chain Monte Carlo; porous media; finite element method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1974/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1974/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1974-:d:616835

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().