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.

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.

Recent advances in the preparation and utilization of carbon nanotubes for hydrogen storage

Recent progress in the production, purification, and experimental and theoretical investigations of carbon nanotubes for hydrogen storage are reviewed. From the industrial point of view, the chemical vapor deposition process has shown advantages over laser ablation and electric-arc-discharge methods. The ultimate goal in nanotube synthesis should be to gain control over geometrical aspects of nanotubes, such as location and orientation, and the atomic structure of nanotubes, including helicity and diameter. There is currently no effective and simple purification procedure that fulfills all requirements for processing carbon nanotubes. Purification is still the bottleneck for technical applications, especially where large amounts of material are required. Although the alkali-metal-doped carbon nanotubes showed high H-2 Weight uptake, further investigations indicated that some of this uptake was due to water rather than hydrogen. This discovery indicates a potential source of error in evaluation of the storage capacity of doped carbon nanotubes. Nevertheless, currently available single-wall nanotubes yield a hydrogen uptake value near 4 wt% under moderate pressure and room temperature. A further 50% increase is needed to meet U.S. Department of Energy targets for commercial exploitation. Meeting this target will require combining experimental and theoretical efforts to achieve a full understanding of the adsorption process, so that the uptake can be rationally optimized to commercially attractive levels. Large-scale production and purification of carbon nanotubes and remarkable improvement of H-2 storage capacity in carbon nanotubes represent significant technological and theoretical challenges in the years to come.

Tracks of Change - the changing value commitments of non-profit organisations

If nonprofit organisations are moving towards more market oriented ways of operating, is this changing the traditional meanings and value of commitments associated with their activities? This article discusses the findings of a research project conducted by the University of Queensland into the impact that changes in government policies are having on the community services sector, in particular disability services. The values and belief systems traditionally associated with the sector were found to be fundamentally unaltered.

Relationships between crude protein and mineral concentrations in alfalfa and value of alfalfa silage as a mineral source for periparturient cows

One hundred and eight samples from three cultivars of alfalfa were obtained from three cuttings in 1996-1998 to evaluate the relationship between crude protein (CP) and mineral concentrations of alfalfa with cutting and maturation. The CP content drastically decreased from 27.9 to 11.4% on DM with maturity. Highly positive correlations were observed between CP and K in the first and the second cutting of alfalfa. The Ca content remained almost constant throughout the growth period. Four multiparous Holstein cows were assigned an alfalfa silage diet or an orchardgrass silage diet from 3 weeks prepartum to 1 week postpartum to examine the effect on the mineral balance. In the prepartum and postpartum diet, the roughage to concentrate ratio was 70:30 and 50:50, with alfalfa being 50 and 100% of the roughage, respectively. The alfalfa contained 1.93% of K. No metabolic disorders occurred, but the body weight decreased drastically from 1 to 6 days postpartum with each diet because of the high milk production immediately after the parturition. Positive retention of N, Ca, P, Mg, and K was observed prepartum, whereas the cows had negative N and mineral retention from 2 to 4 days postpartum. The Ca and P absorption, and Mg retention of cows with the alfalfa diet were higher than with the grass diet. The plasma Ca and inorganic P were not affected by diet, but the plasma PTH at parturition and plasma hydroxyproline from 1 week prepartum to 1 week postpartum were higher with the alfalfa diet. These results suggest that the low K alfalfa is suitable not only to prevent the incidence of milk fever but also to increase Ca, P and Mg utilization of periparturient cows, but the mineral supplementation is needed for the postpartum cows immediately after the parturition. (C) 2001 Elsevier Science B.V. All rights reserved.

Valuing ecological functions of biodiversity in changbaishan mountain biosphere reserve in northeast china

Conservation of biodiversity can generate considerable indirect economic value and this is being increasingly recognized in China. For a forest ecosystem type of a nature reserve, the most important of its values are its ecological functions which provide human beings and other living things with beneficial environmental services. These services include water conservancy, soil protection, CO2 fixation and O-2 release, nutrient cycling, pollutant decomposition, and disease and pest control. Based on a case study in Changbaishan Mountain Biosphere Reserve in Northeast China, this paper provides a monetary valuation of these services by using opportunity cost and alternative cost methods. Using such an approach, this reserve is valued at 510.11 million yuan (USD 61.68 mill.) per year, 10 times higher than the opportunity cost (51.78 mill. yuan/ha.a) for regular timber production. While China has heeded United Nations Environmental Program (UNEP)'s call for economic evaluation of ecological functions, the assessment techniques used need to be improved in China and in the West for reasons mentioned.

The nutritive value of Rhodes grass (Chloris gayana) when treated with CaO, NaOH or a microbial inoculant and offered to dairy heifers as big-bale silage

A series of laboratory and animal studies examined the use of chemical and biological agents to enhance the digestibility of Rhodes grass (grass) cut at 60 (young) and 100 (mature) days of regrowth and ensiled as big round bales. The treatments included an untreated control (C), a microbial inoculant (I), NaOH, CaO and NaOH plus inoculant (NaOH + I). Inoculant was grown anaerobically, using a starter culture of rumen fluid from cattle given Rhodes grass. Treatments C, 1, NaOH, NaOH + I, were offered separately to twelve dairy heifers, in a 3 X 4 randomized complete block design, repeated twice for each grass silage. C and I had substantial mould growth, compared with no visible mould in NaOH or NaOH + 1. CaO treatment was effective in preventing mould growth, but had little effect on the chemical composition and in sacco digestibility of mature grass silage. NaOH reduced NDF content and increased in sacco digestibility (P < 0.05) but not the in vivo digestibility (P > 0.05) of both mature- and young-grass silage. The effects of other treatments on nutritive value were non-significant at both stages of maturity. NaOH increased the intake of mature-grass silage by 24-26% (P < 0.05), but had little effect on the intake of young-grass silage (P > 0.05). Treatment I consistently reduced grass silage intake (P < 005) for young-grass silage. The findings of these studies show that treating mature Rhodes grass with NaOH will improve its nutritive value and reduce mould growth in conserved herbage. However none of the treatments in this study had any consistently positive effects on the in vivo nutritive value or storage quality of young-grass silage.

Reconciling value estimates from the discounted cash flow model and the residual income model

This paper examines why practitioners and researchers get different estimates of equity value when they use a discounted cash flow (CF) model versus a residual income (RI) model. Both models are derived from the same underlying assumption -- that price is the present value of expected future net dividends discounted at the cost of equity capital -- but in practice and in research they frequently yield different estimates. We argue that the research literature devoted to comparing the accuracy of these two models is misguided; properly implemented, both models yield identical valuations for all firms in all years. We identify how prior research has applied inconsistent assumptions to the two models and show how these seemingly small errors cause surprisingly large differences in the value estimates. [ABSTRACT FROM AUTHOR]

Capacity utilisation and profitability: A decomposition of short-run profit efficiency

The principal aim of this paper is to measure the amount by which the profit of a multi-input, multi-output firm deviates from maximum short-run profit, and then to decompose this profit gap into components that are of practical use to managers. In particular, our interest is in the measurement of the contribution of unused capacity, along with measures of technical inefficiency, and allocative inefficiency, in this profit gap. We survey existing definitions of capacity and, after discussing their shortcomings, we propose a new ray economic capacity measure that involves short-run profit maximisation, with the output mix held constant. We go on to describe how the gap between observed profit and maximum profit can be calculated and decomposed using linear programming methods. The paper concludes with an empirical illustration, involving data on 28 international airline companies. The empirical results indicate that these airline companies achieve profit levels which are on average US$815m below potential levels, and that 70% of the gap may be attributed to unused capacity. (C) 2002 Elsevier Science B.V. All rights reserved.