Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

CONCENTRATION FIELDS NEAR AIR-WATER INTERFACES DURING INTERFACIAL MASS TRANSPORT: OXYGEN TRANSPORT AND RANDOM SQUARE WAVE ANALYSIS

Mass transfer across a gas-liquid interface was studied theoretically and experimentally, using transfer of oxygen into water as the gas-liquid system. The experimental results support the conclusions of a theoretical description of the concentration field that uses random square waves approximations. The effect of diffusion over the concentration records was quantified. It is shown that the peak of the normalized rills concentration fluctuation profiles must be lower than 0.5, and that the position of the peak of the rms value is an adequate measure of the thickness of the diffusive layer. The position of the peak is the boundary between the regions more subject to molecular diffusion or to turbulent transport of dissolved mass.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Mass Transport In The Equatorial Indian Ocean

In the equatorial oceans, the meridional currents are far less energetic than their zonal counterparts. The response of the Equatorial Indian Ocean to the seasonal reversals in the zonal wind field. is quite interesting and unique. A modest attempt, considering the shortcomings in the hydrographic data availability and distribution, is made to evaluate the variability in the zonal transport of mass. in_ both space and time. The peculiarities in its hydrological regime imposed upon by the seasonally varying winds is best appreciated when compared with the quasi permanent circulation characteristics of the Pacific and Atlanti'c.The major features of the tequatorial mass transport is outlined in the introductory chapter of this thesis for the Pacific and Atlantic Mass transport studies in the Indian Ocean, as can be seen from the earlier studies, gis“ the least known and understood, though could have captured the attention of both the experimentalist and the theoretician alike. owing to its complexity. Since in the Indian Ocean, the studies on the zonal mass transport are limited and are confined to the equator only, an attempt has been made to compute the mass transport extending from 5 N to 20 S.

Mass transport effects in the borohydride oxidation reaction-Influence of the residence time on the reaction onset and faradaic efficiency

The borohydride oxidation reaction (BOR) was studied on Pt and Au electrodes by cyclic voltammetry in dilute alkaline borohydride solutions (0.1 M NaOH + 10(-3) mol L(-1) NaBH(4)). More specifically, the electrodes were considered as either Vulcan XC72-supported Pt or Au (noted as Pt/C and Au/C, respectively) active layers or smooth Pt or Au surfaces, the latter possibly being covered by a layer of (non-metalized) Vulcan XC72 carbon powder. The BOR onset potential and the number of electrons (n(e-)) exchanged per BH(4)(-) anion (faradaic efficiency) were investigated for these electrodes, to determine whether the residence time of reaction intermediates (at the electrode surface or inside the porous layer) does influence the overall reaction pathway/completion. For the carbon-supported platinum, n(e-) strongly depends on the thickness of the active layer. While thin (ca. 0.5 mu m-thick) Pt/C active layers yield n(e-) < 4, thick layers (approximately 3 mu m) yield n(e-)approximate to 8, which can be ascribed to the sufficient residence time of the molecules formed within the active layer (H(2), by heterogeneous hydrolysis, or BOR intermediates) enabling further (near-complete) oxidation. This puts into evidence that not only the nature of the electrocatalyst is important to reach high BOR efficiency, but also the structure/thickness of the active layer. The same trend applies for Au/C active layers and for smooth Pt or Au surfaces covered with a layer of (inactive) Vulcan XC72. In addition, the BOR onset usually shifts negative when the reaction intermediates are trapped, which suggests that some of the intermediates are more easily oxidized than BH(4)(-) itself; based on literature data, BH(3)OH(-) species is a likely candidate. (C) 2011 Elsevier B.V. All rights reserved.

A bounded upwinding scheme for computing convection-dominated transport problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sintering and mass transport features of (Sn,Ti)O2 polycrystalline ceramics

Different (Sn,Ti)O2 compositions were sintered at 1450 °C for 2 h with the purpose of investigating their sintering and mass transport properties. Highly dense ceramics were obtained and their structural properties studied by X-ray diffraction and scanning electron microscopy. The changes in lattice parameters were analyzed by the Rietveld method and two mass transport mechanisms were observed during sintering in different temperature ranges, evidenced by the linear shrinkage rate as a function of temperature. The effect of the concentration of TiO2 on mass transport and densiffication during sintering was analyzed by considering the intrinsic defects. System densiffication was attributed to a mass transport mechanism in the SnO2 matrix, caused by the presence of TiO2, which formed a solid solution phase. The change in the mass transport mechanism was attributed to chemical bonding between SnO2 and TiO2, which improves ionic difusion as the concentration of TiO2 increased in (Sn,Ti)O2 compositions. © 2002 Elsevier Science Ltd. All rights reserved.

Water masses, mass transport and variability of the Canary current in autumn

Máster en Oceanografía

Mass-transport deposits on Mediterranean continental margins

Extensive mass transport deposits and multiple slide scars testify widespread and recurrent submarine sediment failures occurring during the late Quaternary on the SW-Adriatic and SE-Sicilian margins. These mass movements and their consequences contributed to shape the continental slopes and fill the basins with characteristic signatures. Geomorphological, seismo-stratigraphic, sedimentological and biostratigraphic data provide clues to: 1) define distinct failure mechanisms investigating on factors that determine dissimilar organization of coeval displaced masses, 2) reconstruct successive phases of failure stressing on the same location where slide scars crosscut and mass-transport deposits overlap, 3) analyze regional setting and indicate the most suitable place where to calculate mass wasting frequency. Discussions on the role of fluid flow, currents activity and tectonic deformation determine a wider view on the construction of the studied continental margins.