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.

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 analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (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.

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.

Finite element modelling of rock alteration and metamorphic process in hydrothermal systems

We use the finite element method to simulate the rock alteration and metamorphic process in hydrothermal systems. In particular, we consider the fluid-rock interaction problems in pore-fluid saturated porous rocks. Since the fluid rock interaction takes place at the contact interface between the pore-fluid and solid minerals, it is governed by the chemical reaction which usually takes place very slowly at this contact interface, from the geochemical point of view. Due to the relative slowness of the rate of the chemical reaction to the velocity of the pore-fluid flow in the hydrothermal system to be considered, there exists a retardation zone, in which the conventional static theory in geochemistry does not hold true. Since this issue is often overlooked by some purely numerical modellers, it is emphasized in this paper. The related results from a typical rock alteration and metamorphic problem in a hydrothermal system have shown not only the detailed rock alteration and metamorphic process, but also the size of the retardation zone in the hydrothermal system. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Finite element modelling of reactive fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins

We present the finite element simulations of reactive mineral carrying fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for Load, zinc and iron minerals in the regime of temperature-gradient-driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore-fluid velocity and the equilibrium concentration of this particular kind of mineral Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral-carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

Finite element analysis of mechanical properties in discontinuously reinforced metal matrix composites with ultrafine microstructure

This investigation focused on the finite element analyses of elastic and plastic properties of aluminium/alumina composite materials with ultrafine microstructure. The commonly used unit cell model was used to predict the elastic properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the plastic properties of the composites and the associated strengthening mechanism within the metal matrix material were investigated. The grain size of the matrix material was found to be an important factor influencing the mechanical properties of the composites studied. (C) 1997 Elsevier Science S.A.

Finite Element Modeling for Development and Optimization of a Bone Plate for Mandibular Fracture in Dogs

This study aimed to develop a plate to treat fractures of the mandibular body in dogs and to validate the project using finite elements and biomechanical essays. Mandible prototypes were produced with 10 oblique ventrorostral fractures (favorable) and 10 oblique ventrocaudal fractures (unfavorable). Three groups were established for each fracture type. Osteosynthesis with a pure titanium plate of double-arch geometry and blocked monocortical screws offree angulanon were used. The mechanical resistance of the prototype with unfavorable fracture was lower than that of the fcworable fracture. In both fractures, the deflection increased and the relative stiffness decreased proportionally to the diminishing screw number The finite element analysis validated this plate study, since the maximum tension concentration observed on the plate was lower than the resistance limit tension admitted by the titanium. In conclusion, the double-arch geometry plate fixed with blocked monocortical screws has sufficient resistance to stabilize oblique,fractures, without compromising mandibular dental or neurovascular structures. J Vet Dent 24 (7); 212 - 221, 2010

A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses

Objective. To evaluate the biaxial and short-beam uniaxial strength tests applied to resin composites based upon their Weibull parameters, fractographic features and stress distribution. Methods. Disk- (15 mm x 1 mm) and beam-shaped specimens (10 mm x 2 mm x 1 mm) of three commercial composites (Concept/Vigodent, CA; Heliomolar/Ivoclar-Vivadent, HE; Z250/3M ESPE, FZ) were prepared. After 48h dry storage at 37 degrees C, disks and beams were submitted to piston-on-three-balls (BI) and three-point bending (UNI) tests, respectively. Data were analyzed by Weibull statistics. Fractured surfaces were observed under stereomicroscope and scanning electron microscope. Maximum principal stress (sigma(1)) distribution was determined by finite element analysis (FEA). Maximum sigma(1-BI) and sigma(1-UNI) were compared to FZ strengths calculated by applying the average failure loads to the analytical equations (sigma(a-BI) and sigma(a-UNI)). Results. For BI, characteristic strengths were: 169.9a (FZ), 122.4b (CA) and 104.8c (HE), and for UNI were: 160.3a (FZ), 98.2b (CA) and 91.6b (HE). Weibull moduli ( m) were similar within the same test. CA and HE presented statistically higher m for BI. Surface pores ( BI) and edge flaws ( UNI) were the most frequent fracture origins. sigma(1-BI) was 14% lower than sigma(a-BI.) sigma(1-UNI) was 43% higher than sigma(a-UNI). Significance. Compared to the short-beam uniaxial test, the biaxial test detected more differences among composites and displayed less data scattering for two of the tested materials. Also, biaxial strength was closer to the material`s strength estimated by FEA. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Vertical Root Fracture in Upper Premolars with Endodontic Posts: Finite Element Analysis

Upper premolars restored with endodontic posts present a high incidence of vertical root fracture (VRF). Two hypotheses were tested: (1) the smaller mesiodistal diameter favors stress concentration in the root and (2) the lack of an effective bonding between root and post increases the risk of VRF. Using finite element analysis, maximum principal stress was analyzed in 3-dimensional intact upper second premolar models. From the intact models, new models were built including endodontic posts of different elastic modulus (E = 37 or E = 200 GPa) with circular or oval cross-section, either bonded or nonbonded to circular or oval cross-section root canals. The first hypothesis was partially confirmed because the conditions involving nonbonded, low-modulus posts showed lower tensile stress for oval canals compared to circular canals. Tensile stress peaks for the nonbonded models were approximately three times higher than for the bonded or intact models, therefore confirming the second hypothesis. (J Endod 2009;35:117-120)

Finite Element Analysis of Shear Versus Torsion Adhesive Strength Tests for Dental Resin Composites

Stress distributions in torsion and wire-loop shear tests were compared using three-dimensional (3-D) linear-elastic finite element method, in an attempt to predict the ideal conditions for testing adhesive strength of dental resin composites to dentin. The torsion test presented lower variability in stress concentration at the adhesive interface with changes in the proportion adhesive thickness/resin composite diameter, as well as lower variability with changes in the resin composite elastic modulus. Moreover, the torsion test eliminated variability from changes in loading distance, and reduced the cohesive fracture tendency in the dentin. The torsion test seems to be more appropriate than wire-loop shear test for testing the resin composite-tooth interface strength. (c) Koninklijke Brill NV, Leiden, 2009

Finite-Element Analysis of Stress on Dental Implant Prosthesis

Background: Understanding how clinical variables affect stress distribution facilitates optimal prosthesis design and fabrication and may lead to a decrease in mechanical failures as well as improve implant longevity. Purpose: In this study, the many clinical variations present in implant-supported prosthesis were analyzed by 3-D finite element method. Materials and Method: A geometrical model representing the anterior segment of a human mandible treated with 5 implants supporting a framework was created to perform the tests. The variables introduced in the computer model were cantilever length, elastic modulus of cancellous bone, abutment length, implant length, and framework alloy (AgPd or CoCr). The computer was programmed with physical properties of the materials as derived from the literature, and a 100N vertical load was used to simulate the occlusal force. Images with the fringes of stress were obtained and the maximum stress at each site was plotted in graphs for comparison. Results: Stresses clustered at the elements closest to the loading point. Stress increase was found to be proportional to the increase in cantilever length and inversely proportional to the increase in the elastic modulus of cancellous bone. Increasing the abutment length resulted in a decrease of stress on implants and framework. Stress decrease could not be demonstrated with implants longer than 13 mm. A stiffer framework may allow better stress distribution. Conclusion: The relative physical properties of the many materials involved in an implant-supported prosthesis system affect the way stresses are distributed.