Computational identification of adsorption and desorption parameters for pore scale transport in periodic porous media

Abstract

Computational identification of unknown adsorption and desorption rates is discussed in conjunction with reactive flow considered at pore scale. The reactive transport is governed by incompressible Stokes equations, coupled with convection-diffusion equation for species transport. The surface reactions, namely adsorption and desorption, are accounted via Robin boundary conditions. Henry and Langmuir isotherms are considered. Measured concentration of the specie at the outlet of the domain has to be provided to carry out the identification procedure. Deterministic and stochastic parameter identification approaches are considered. The influence of the noise in the measurements on the accuracy of the identified parameters is discussed. Multistage identification procedure is suggested for the considered class of problems. The proposed identification approach is applicable for different geometries (random and periodic) and for a range of process parameters. In this paper the potential of the approach is demonstrated in identifying parameters of Langmuir isotherm for low Peclet and low Damkoler numbers reactive flow in a 2D periodic porous media with circular inclusions. Simulation results for random porous media and other regime parameters are subject of follow up papers. Finite element approximation in space and implicit time discretization are exploited.

Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport

“…In these figures, it can also be seen how credible intervals are reduced with the addition of observations. The obtained results even for noise variance 0.05 are comparable with work we have done in [22,23] using deterministic and stochastic approaches. The symbol in these figures shows the exact parameters and the • symbol shows the mean values.…”

“…This problem that has already been investigated by us in our previous works [22,23] in conjunction with deterministic methods for parameter identification, but for the completeness of the presentation we describe here it again.…”

“…The computational domain Ω is triangulated using the mesh generator software Gmsh [30]. In order to control the accuracy of results, computations on consecutively refined grids were performed on our previous work [23].…”

“…The breakthrough curve for these parameters is shown in Figure 2a. Detailed results of solving the direct problem can be found in our previous work [23].…”

“…In our previous works on reactive flows [22,23] a deterministic approach was considered, where the parameter space was divided into a uniform grid, where for each point the direct problem was solved to construct the residual functional. This approach was one of the simplest, but depending on the functionality, a denser mesh partition may be required, which could lead to a large amount of computation.…”