A master equation model for bimolecular reaction via multi-well isomerization intermediates

A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

On the validity of the shrinking core model in noncatalytic gas solid reaction

By using a matched asymptotic expansion technique, the shrinking core model (SCM) used in non-catalytic gas solid reactions with general kinetic expression is rigorously justified in this paper as a special case of the homogeneous model when the reaction rate is much faster than that of diffusion. The time-pendent velocity of the moving reacted-unreacted interface is found to be proportional to the gas flux at that interface for all geometries of solid particles, and the thickness order of the reaction zone and also the degree of chemical reaction at the interface is discussed in this paper.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

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 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.

Health technology diffusion in developing countries: a case study of CT scanners in Brazil

Background The development of products and services for health care systems is one of the most important phenomena to have occurred in the field of health care over the last 50 years. It generates significant commercial, medical and social results. Although much has been done to understand how health technologies are adopted and regulated in developed countries, little attention has been paid to the situation in low- and middle-income countries (LMICs). Here we examine the institutional environment in which decisions are made regarding the adoption of expensive medical devices into the Brazilian health care system. Methods We used a case study strategy to address our research question. The empirical work relied on in-depth interviews (N = 16) with representatives of a wide range of actors and stakeholders that participate in the process of diffusion of CT (computerized tomography) scanners in Brazil, including manufacturers, health care organizations, medical specialty societies, health insurance companies, regulatory agencies and the Ministry of Health. Results The adoption of CT scanners is not determined by health policy makers or third-party payers of public and private sectors. Instead, decisions are primarily made by administrators of individual hospitals and clinics, strongly influenced by both physicians and sales representatives of the medical industry who act as change agents. Because this process is not properly regulated by public authorities, health care organizations are free to decide whether, when and how they will adopt a particular technology. Conclusions Our study identifies problems in how health care systems in LMICs adopt new, expensive medical technologies, and suggests that a set of innovative approaches and policy instruments are needed in order to balance the institutional and professional desire to practise a modern and expensive medicine in a context of health inequalities and basic health needs.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Detection of dengue viral RNA in Aedes aegypti (Diptera : Culicidae) exposed to sticky lures using reverse-transcriptase polymerase chain reaction

Active surveillance for dengue (DEN) virus infected mosquitoes can be an effective way to predict the risk of dengue infection in a given area. However, doing so may pose logistical problems if mosquitoes must be kept alive or frozen fresh to detect DEN virus. In an attempt to simplify mosquito processing, we evaluated the usefulness of a sticky lure and a seminested reverse-transcriptase polymerase chain reaction assay (RT-PCR) for detecting DEN virus RNA under laboratory conditions using experimentally infected Aedes aegypti (L.) mosquitoes. In the first experiment, 40 male mosquitoes were inoculated with 0.13 mul of a 10(4) pfu/ml DEN-2 stock solution. After a 7-d incubation period, the mosquitoes were applied to the sticky lure and kept at room temperatures of 23-30 degreesC. Following 7,10,14, and 28 d application, 10 mosquitoes each were removed from the lure pooled and assayed for virus. DEN virus nucleic acid was clearly detectable in all pools up to 28 d after death. A second study evaluated sensitivity and specificity using one, two, and five DEN-infected mosquitoes removed after 7, 10, 14, 21 and 30 d application and tested by RT-PCR. All four DEN serotypes were individually inoculated in mosquitoes and evaluated using the same procedures as experiment 1. The four serotypes were detectable in as few as one mosquito 30 d after application to the lure with no evidence of cross-reactivity. The combination of sticky lures and RT-PCR show promise for mosquito and dengue virus surveillance and warrant further evaluation.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Joining copper to stainless steel by friction stir diffusion process

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do Grau de Mestre em Engenharia Mecânica

The thermal effects on the methanol-to-olefins reaction: A modelling and experimental approach

With the projection of an increasing world population, hand-in-hand with a journey towards a bigger number of developed countries, further demand on basic chemical building blocks, as ethylene and propylene, has to be properly addressed in the next decades. The methanol-to-olefins (MTO) is an interesting reaction to produce those alkenes using coal, gas or alternative sources, like biomass, through syngas as a source for the production of methanol. This technology has been widely applied since 1985 and most of the processes are making use of zeolites as catalysts, particularly ZSM-5. Although its selectivity is not especially biased over light olefins, it resists to a quick deactivation by coke deposition, making it quite attractive when it comes to industrial environments; nevertheless, this is a highly exothermic reaction, which is hard to control and to anticipate problems, such as temperature runaways or hot-spots, inside the catalytic bed. The main focus of this project is to study those temperature effects, by addressing both experimental, where the catalytic performance and the temperature profiles are studied, and modelling fronts, which consists in a five step strategy to predict the weight fractions and activity. The mind-set of catalytic testing is present in all the developed assays. It was verified that the selectivity towards light olefins increases with temperature, although this also leads to a much faster catalyst deactivation. To oppose this effect, experiments were carried using a diluted bed, having been able to increase the catalyst lifetime between 32% and 47%. Additionally, experiments with three thermocouples placed inside the catalytic bed were performed, analysing the deactivation wave and the peaks of temperature throughout the bed. Regeneration was done between consecutive runs and it was concluded that this action can be a powerful means to increase the catalyst lifetime, maintaining a constant selectivity towards light olefins, by losing acid strength in a steam stabilised zeolitic structure. On the other hand, developments on the other approach lead to the construction of a raw basic model, able to predict weight fractions, that should be tuned to be a tool for deactivation and temperature profiles prediction.

Recent brazilian experience on farmer reaction and crop response to fertilizer use

(1) In the period 1965/77 fertilizer consumption in Brazil increased nearly fifteen foild from circa 200,000 tons of N + P2O5 + K2O to 3 million tons. During the fifteen years extending from 1950 to 1964 usage of the primary macronutrients was raised by a factor of 2 only. (2) Several explanations are given for the remarkable increase, namely: an experimental background which supplied data for recommendations of rates, time and type of application; a convenient governmental policy for minimum prices and rural credit; capacity of the industry to meet the demand of the fertilizer market; an adequate mechanism for the diffusion of the practice of fertilizer use to the farmer. (3) The extension work, which has caused a permanent change in the aptitude towards fertilization, was carried out in the traditional way by salesmen supported by a technical staff, as well as by agronomists of the official services. (4) Two new programs were started and conducted in a rather short time, both putting emphasis on the relatively new technology of fertilizer use. (5) The first program, conducted in the Southern part of the country, extended lab and green house work supplemented by a few field trials to small land owners - the so called "operação tatú" (operation armadillo). (6) The seconde program, covering a larger problem area in the Northeast and in Central Brazil, began directly in field as thousands of demonstrations and simple experiments with the participation of local people whose involvement was essential for the success of the initiative; in this case the official extension services, both foreign and national sources of funds, and universities did participate under the leadership of the Brazilian Association for the Diffusion of Fertilizers (ANDA). (7) It is felt that the Brazilian experience gained thereof could be useful to other countries under similar conditions.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.