On the predictivity of pore-scale simulations : estimating uncertainties with multilevel Monte Carlo

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics

A second order scheme for a Robin boundary condition in random walk algorithms

Random Walk (RW) is a common numerical tool for modeling the Advection-Diffusion equation. In this work, we develop a second order scheme for incorporating a heterogeneous reaction (i.e., a Robin boundary condition) in the RW model. In addition, we apply the approach in two test cases. We compare the second order scheme with the first order one as well as with analytical and other numerical solution. We show that the new scheme can reduce the computational error significantly, relative to the first order scheme. This reduction comes at no additional computational cost

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

© 2020, The Author(s). Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials

Application of dissipative particle dynamics to interfacial systems: Parameterization and scaling

Dissipative Particle Dynamics (DPD) is a stochastic particle model that is able to simulate larger systems over longer time scales than atomistic modeling approaches by including the concept of coarse-graining. Whether standard DPD can cover the whole mesoscale by changing the level of coarse-graining is still an open issue. A scaling scheme originally developed by Füchslin et al. (2009) was here applied to interfacial systems as one of the most successful uses of the classical DPD method. In particular, equilibrium properties such as the interfacial tension were analyzed at different levels of coarse-graining for planar oil–water interfaces with and without surfactant. A scaling factor for the interfacial tension was found due to the combined effect of the scaling scheme and the coarse-graining parameterization. Although the level of molecular description was largely decreased, promising results showed that it is possible to conserve the interfacial tension trend at increasing surfactant concentrations, remarkably reducing modeling complexity. The same approach was also employed to simulate a droplet configuration. Both planar and droplet conformations were maintained, showing that typical domain formations of multi-component systems can be performed in DPD by means of the scaling procedure. Therefore, we explored the possibility of describing oil–water and oil–water–surfactant systems in standard DPD using a scaling scheme with the aim of highlighting its advantages and limitations

The role of recirculation zones on non-Fickian transport phenomena in 3D porous media

In groundwater engineering, remediation techniques based on the injection of nano/particles have enjoined a particular success. Pore-scale numerical simulations are a powerful tool to study transport of solutes and colloidal suspensions in porous media, and are used to derive constitutive laws tune macro-scale models. In the Eulerian framework, the influence of the pore space geometry on transport phenomena was investigated thanks to computational fluid dynamics pore-scale simulations. Three different 3D periodic arrangements of spherical grains were used, namely face-centered-cubic (FCC), body-centered-cubic (BCC), and sphere-in-cube (SIC) packings, [1]. In Stokes regime, the transport of a conservative tracer and of particles undergoing instantaneous heterogeneous reaction were both investigated and the resulting outflow concentration (breakthrough curves) were analyzed: even if the porous media have the very same grains shape and size and the same porosity, the breakthrough curves present noteworthy differences, such as an enhanced tailing and early arrival times. The anomalous (non-Fickian) transport observed was indeed correlated with the peculiarities of the pore-space and to the presence of recirculation zones above all. The recirculation zones were detected at low Reynolds numbers and various methods, first of all a streaklines visualization, were adopted to describe qualitatively and quantitatively such zones. The analysis of the angle formed by velocity and vorticity vectors proved to be particularly effective in the detection of recirculation zones. At last, simulating the transport of particles undergoing instantaneous heterogeneous reactions, the role played by the medium structure is evident also evaluating the deposition efficiency coefficient, as its behavior clearly depends on the grains packing adopted. After more than fifty years, the study of anomalous transport in porous media still offers a breeding ground for researches in many different fields. Since in the groundwater framework the determination of this macro-scale parameter is a key factor to design effective remediation techniques, this work tries to exploit the potentiality of computational fluid dynamics to tackle the problem from the pore-scale, exploiting a practical approach

Analysis of the shear stresses in a filling line of parenteral products

Drug manufacturing consists of a series of operations, generally referred to as formulation, filling, and finishing. Filling represents the most critical step, in which the drug product undergoes different processes, including mixing, pumping, filtration, and final filling into vials. As filling lines operate under faster and faster conditions, there is concern over stability of protein-based products, which may be sensitive to temperature changes, oxidation, light, ionic strength and shear stress. Among these, shear stress has gained interest over the past decades because of its frequent occurrence in filling lines. Exposure of protein-based parenteral drugs to such stresses is believed to promote unfolding and subsequent aggregation, which might alter the biological activity of the drug and raise the potential for side effects. Several studies conducted in recent years have tried to shed light on the actual impact of shear stress on drug products, but the presence of additional stresses (such as interfacial stress) has complicated the interpretation of the results. In this controversial landscape, it is therefore necessary to quantify shear stress in the operating units of the filling process as a first step for broader experimental investigations. Therefore, starting from some typical operating units, we developed a model for calculating the shear stress distribution using a shear history-based approach. In detail, we considered a representative number of particles within the domain and followed their trajectories, which allowed us to determine the average shear stress. Several operating units were analyzed and the resulting shear stress exposures were determined. The field of scale-down approaches, used to scale the commercial process down to the laboratory level, was also explored. They allow to perform product characterization experiments using smaller volumes of the drug products. A new approach for scaling down the commercial process was proposed, which was compared with traditional approaches and shown to provide greater representativeness between the two scales

Molecular modeling of the interface of an egg yolk protein-based emulsion

Many food emulsions are stabilized by functional egg yolk biomolecules, which act as surfactants at the oil/water interface. Detailed experimental studies on egg yolk emulsifying properties have been largely hindered due to the difficulty in isolating individual chemical species. Therefore, this work presents a molecular model of an oil/water interfacial system where the emulsifier is one of the most surface-active proteins from the egg yolk low-density lipoproteins (LDL), the so-called Apovitellenin I. Dissipative particle dynamics (DPD) was here adopted in order to simulate large systems over long time scales, when compared with full-atom molecular dynamics (MD). Instead of a manual assignment of the DPD simulation parameters, a fully automated coarse-graining procedure was employed. The molecular interactions used in the DPD system were determined by means of a parameter calibration based on matching structural data from atomistic MD simulations. Despite the little availability of experimental data, the model was designed to test the most relevant physical properties of the protein investigated. Protein structural and dynamics properties obtained via MD and DPD were compared highlighting advantages and limits of each molecular technique. Promising results were achieved from DPD simulations of the oil/water interface. The proposed model was able to properly describe the protein surfactant behavior in terms of interfacial tension decrease at increasing protein surface concentration. Moreover, the adsorption time of a free protein molecule was estimated and, finally, an LDL-like particle adsorption mechanism was qualitatively reproduced