SFB1313, Task Force: Software and Data

Abstract

Alterations in the pore morphology of porous materials cause changes to the characteristic hydraulic properties, which are mostly non-linear and inherently difficult to predetermine. Assuming the alterations are known with sufficient accuracy, the relation between the altered pore structure, measured in terms of porosity, and intrinsic permeability may be determined by simulations with enormous computational effort. We focus on microfluidic experiments during the course of which the pore space becomes increasingly occupied with solid precipitate over elapsed process time. To analyze these domains, we present a novel geometry-informed drag formulation which allows for solving pseudo-3D Stokes equations for image-based input data of clogging porous media with accuracy and efficiency. In a pre-processing step, local pore space properties are analyzed and employed to spatially vary the magnitude of the drag term, which reflects the influence of neglected 3D effects. Calibration and validation is achieved through fully 3D Finite Difference Stokes simulations of different benchmark cases. With the proposed formulation we achieve the high accuracy of the pseudo-3D methods as far as permeability is concerned (<30% deviation), but also with respect to local velocities, for a microfluidic domain throughout the clogging process. Noteworthy, the computational cost is being reduced to less than 1%. Combining the efficiency of a Stokes 2D simulation and accuracy of a 3D model the presented approach is rendered an interesting option to investigate remaining open questions, for example on anisotropy of effective hydraulic parameters during the clogging process.

Abstract

Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets in order to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid-fluid and solid-fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier-Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared to a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

Abstract

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid–porous interface. These models include a porous-medium model using Darcy’s law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems’ behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model’s predictive capabilities, and make a probabilistic model comparison.