Global sensitivity analysis and Bayesian parameter inference for solute transport in porous media colonized by biofilms

Bayesian inversion of laboratory experiments of transport through limestone fractures

In this study, a novel experimental setup is proposed for which a column filled with glass beads and parallelepiped-shaped limestone beams is used to reconstruct a multiple fracture limestone media. The proposed setup produces asymmetric breakthrough curves (BTCs) that are consistent with the shape expected from the past field and lab-scale studies. Three transport experiments have been conducted under fast, medium, and slow flow velocity conditions. The research focuses on parameter and state estimation using Bayesian inference via Markov Chain Monte Carlo (MCMC) sampler, investigating the degree to which three models of transport through fractured media can reproduce the experimental results under the three flow conditions. The first transport model, named ADE, is based on the equivalent porous medium (EPM) approach and corresponds to the linear advection dispersion equation (ADE). The second model, named FOMIM (first-order mobile immobile), is based on the mobile/immobile approach and uses the dual porosity model with a linear first-order transfer between mobile and immobile regions. The third model, named NLMIM (non-linear mobile-immobile), uses a nonlinear transfer function between these two regions. The results of the three models show that almost all the unknown model input parameters can be well-estimated with narrow confidence intervals using the MCMC method. With respect to state estimation, the ADE model fails to reproduce correctly the tail of the BTCs observed under slow and medium flow conditions. The FOMIM model improves the tailing of the BTCs, but significant discrepancies remain between simulated and measured concentrations. The NLMIM model with velocity-dependent parameters is the only model that captures BTCs under all three conditions of slow, medium, and fast flow velocities.

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

Accurate simulation of flow and contaminant transport processes through unsaturated soils requires adequate knowledge of the soil parameters. This study deals with the hydraulic characterization of soils using laboratory experiments. A new strategy is developed by combining global sensitivity analysis (GSA) and Bayesian data-worth analysis (DWA) to obtain efficient data that ensure a good estimation of the soil properties. The strategy is applied for the estimation of soil properties from a laboratory infiltration experiment. Results of this study show that GSA allows identification of regions and periods of high sensitivity of each parameter and thereby, the observations prone to contain information for a successful calibration. Further, the sensitivity depicts a nonlinear behavior with regions of high influence and regions of weak influence inside the parameter space. Bayesian DWA, performed a priori, allows to quantify the improvement of the posterior uncertainty of the estimated parameters when adding a type of measurement. The results reveal that an accurate estimation of the soil properties can be obtained if the target parameter values are located in the regions of high influence in the parameter space.

Bayesian inversion for a biofilm model including quorum sensing

We propose a mathematical model based on a system of partial differential equations (PDEs) for biofilms. This model describes the time evolution of growth and degradation of biofilms which depend on environmental factors. The proposed model also includes quorum sensing (QS) and describes the cooperation among bacteria when they need to resist against external factors such as antibiotics. The applications include biofilms on teeth and medical implants, in drinking water, cooling water towers, food processing, oil recovery, paper manufacturing, and on ship hulls. We state existence and uniqueness of solutions of the proposed model and implement the mathematical model to discuss numerical simulations of biofilm growth and cooperation. We also determine the unknown parameters of the presented biofilm model by solving the corresponding inverse problem. To this end, we propose Bayesian inversion techniques and the delayed-rejection adaptive-Metropolis (DRAM) algorithm for the simultaneous extraction of multiple parameters from the measurements. These quantities cannot be determined directly from the experiments or from the computational model. Furthermore, we evaluate the presented model by comparing the simulations using the estimated parameter values with the measurement data. The results illustrate a very good agreement between the simulations and the measurements.

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations.