CFD and bubble column reactors:simulation and experiment

The simulation of two-phase flow in bubble columns using commercially available software fromFluent Incorporated is presented here. Data from a bubble column with a ratio of height to thecolumn diameter of 5 : 1 are compared with simulations and experimental results for time-averaged velocity and Reynolds stress proles are used to validate transient, two-dimensional simulations.The models are based on multiphase biological reactors with applications in the food industry. An example case of the mass transfer of oxygen through the liquid phase is also presented.

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction. To cite this article: A. Ern et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Peer reviewed

Multiphase flow in the vascular system of wood: From microscopic exploration to 3-D Lattice Boltzmann experiments

This paper provides insights into liquid free water dynamics in wood vessels based on Lattice Boltzmann experiments. The anatomy of real wood samples was reconstructed from systematic 3-D analyses of the vessel contours derived from successive microscopic images. This virtual vascular system was then used to supply fluid-solid boundary conditions to a two-phase Lattice Boltzmann scheme and investigate capillary invasion of this hydrophilic porous medium. Behavior of the liquid phase was strongly dependent on anatomical features, especially vessel bifurcations and reconnections. Various parameters were examined in numerical experiments with ideal vessel bifurcations, to clarify our interpretation of these features. (c) 2010 Elsevier Ltd. All rights reserved.

Enantioselective analysis of mirtazapine and its two major metabolites in human plasma by liquid chromatography-mass spectrometry after three-phase liquid-phase microextraction

A three-phase liquid-phase microextraction (LPME) method using porous polypropylene hollow fibre membrane with a sealed end was developed for the extraction of mirtazapine (MRT) and its two major metabolites, 8-hydroxymirtazapine (8-OHM) and demethylmirtazapine (DMR), from human plasma. The analytes were extracted from 1.0 mL of plasma, previously diluted and alkalinized with 3.0 mL 0.5 mol L-1 pH 8 phosphate buffer solution and supplemented with 15% sodium chloride (NaCl), using n-hexyl ether as organic solvent and 0.01 moL L-1 acetic acid solution as the acceptor phase. Haloperidol was used as internal standard. The chromatographic analyses were carried out on a chiral column, using acetonitrile-methanol-ethanol (98:1:1, v/v/v) plus 0.2% diethylamine as mobile phase, at a flow rate of 1.0 mL min(-1). Multi-reaction monitoring (MRM) detection was performed by mass spectrometry (MS-MS) using a triple-stage quadrupole and electrospray ionization interface operating in the positive ion mode. The mean recoveries were in 18.3-45.5% range with linear responses over the 1.25-125 ng mL(-1) concentration range for all enantiomers evaluated. The quantification limit (LOQ) was 1.25 ng mL(-1). Within-day and between-day assay precision and accuracy (2.5, 50 and 100 ng mL(-1)) showed relative standard deviation and the relative error lower than 11.9% for all enantiomers evaluated. Finally, the method was successfully used for the determination of mirtazapine and its metabolite enantiomers in plasma samples obtained after single drug administration of mirtazapine to a healthy volunteer. (c) 2007 Elsevier B.V. All rights reserved.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.