http://inis.jinr.ru/sl/m_mathematics/mn_numerical methods/mnd_numerical calculus/allgower e.l., georg k. introduction to numerical continuation methods (colorado, 1990)(397s).pdf

Numerical Continuation Methods

Nature’s photosynthesis uses the sun’s energy with chlorophyll in plants as a catalyst to recycle carbon dioxide and water into new plant life. Only given sufficient geological time, millions of years, can new fossil fuels be formed naturally. The burning of our diminishing fossil fuel reserves is accompanied by large anthropogenic CO2 release, which is outpacing nature’s CO2 recycling capability, causing significant environmental harm. To supplement the natural carbon cycle, we have proposed and developed a feasible anthropogenic chemical recycling of carbon dioxide. Carbon dioxide is captured by absorption technologies from any natural or industrial source, from human activities, or even from the air itself. It can then be converted by feasible chemical transformations into fuels such as methanol, dimethyl ether, and varied products including synthetic hydrocarbons and even proteins for animal feed, thus supplementing our food chain. This concept of broad scope and framework is the basis of what we call...

Anthropogenic Chemical Carbon Cycle for a Sustainable Future

Lower olefins are key building blocks for the manufacture of plastics, cosmetics, and drugs. Traditionally, olefins with two to four carbons are produced by steam cracking of crude oil-derived naphtha, but there is a pressing need for alternative feedstocks and processes in view of supply limitations and of environmental issues. Although the Fischer-Tropsch synthesis has long offered a means to convert coal, biomass, and natural gas into hydrocarbon derivatives through the intermediacy of synthesis gas (a mixture of molecular hydrogen and carbon monoxide), selectivity toward lower olefins tends to be low. We report on the conversion of synthesis gas to C(2) through C(4) olefins with selectivity up to 60 weight percent, using catalysts that constitute iron nanoparticles (promoted by sulfur plus sodium) homogeneously dispersed on weakly interactive α-alumina or carbon nanofiber supports.

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Supported Iron Nanoparticles as Catalysts for Sustainable Production of Lower Olefins

Replacement of part of the fossil fuel consumption by renewable energy, in particular in the chemical industry, is a central strategy for resource and energy efficiency. This perspective will show that CO2 is the key molecule to proceed effectively in this direction. The routes, opportunities and barriers in increasing the share of renewable energy by using CO2 reaction and their impact on the chemical and energy value chains are discussed after introducing the general aspects of this topic evidencing the tight integration between the CO2 use and renewable energy insertion in the value chain of the process industry. The focus of this perspective article is on the catalytic aspects of the chemistries involved, with an analysis of the state-of-the-art, perspectives and targets to be developed. The reactions discussed are the production of short-chain olefins (ethylene, propylene) from CO2, and the conversion of carbon dioxide to syngas, formic acid, methanol and dimethyl ether, hydrocarbons via Fischer–Tropsch synthesis and methane. The relevance of availability, cost and environmental footprints of H2 production routes using renewable energies is addressed. The final part discusses the possible scenario for CO2 as an intermediary for the incorporation of renewable energy in the process industry, with a concise roadmap for catalysis needs and barriers to reach this goal.

Catalysis for CO2 conversion: a key technology for rapid introduction of renewable energy in the value chain of chemical industries

Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties so that can be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimization problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and tt can be expected this complete set of functions can be used for validation of new optimization in the future.

A Literature Survey of Benchmark Functions For Global Optimization Problems

Probleme du choix optimal du systeme de reacteurs en ecoulement permanent pour une serie de reactions ayant chacune une cinetique donnee. On s'interesse aux systemes isothermes sans changement de volume sur la reaction et le melange. On ne peut pas combiner ensemble les reacteurs parfaitement agites, les reacteurs piston ou les reacteurs a recyclage pour etendre la region accessible. On examine plusieurs exemples a deux dimensions

A geometric approach to steady flow reactors: the attainable region and optimization in concentration space

Carbon nanotubes (CNTs) were synthesized in a catalytic reaction over an iron catalyst using CaCO3 as a support. The purification of the carbon nanotubes (CNTs) and the oxidation of the CNTs surfaces were performed with HNO3. Iron-based catalysts supported on carbon nanotubes for use in the Fischer–Tropsch (FT) reaction were prepared either by incipient wetness or a deposition precipitation method using urea and then promoted with potassium and/or copper. The FT synthesis was carried out in a fixed-bed micro reactor (275 °C, 8 bar, CO/H2 = 2). The effect of Cu and promoters on CO conversion, product selectivity and FT synthesis activity were investigated and compared with data reported on other carbon-based supports. The potassium promoted catalysts gave higher yields of CO2 and C2 olefins and the lowest methane selectivity when compared to the unpromoted catalysts. Copper, while enhancing catalyst activity, did not have an effect on the FT product selectivity.

Fischer–Tropsch synthesis over iron catalysts supported on carbon nanotubes

The attainable region and optimal reactor structures

Given a system of reactions with known reaction kinetics and a known feed, it is of interest to find all the possible outlet conditions (the attainable region) for an arbitrary system of steady-flow reactors with any total volume. A geometric approach was used to derive a set of necessary conditions as well as a limited, but powerful, sufficiency condition for the attainable region. These results extend those previously obtained for isothermal, constant-density systems in concentration space to include adiabatic and variable-density systems in composition-volume space. It is also shown how the method can be used to find the attainable region for systems with constraints. In a previous paper (Glasser et al., 1987) (called GCH), the problem of finding the best steady-flow (one that will not support sustained oscillations) system of chemical reactors, given a set of reactions with its associated kinetics, was investigated. The system was constrained to be isothermal with no density changes on reaction or mixing, and the region examined was confined to the concentration space. The problem was solved by the use of geometric techniques to find the attainable region, that is, the region in the stoichiometric subspace that can be reached by any possible reactor system. Horn (1964) showed that if one could find the attainable region for a system then, provided the objective function was a simple function of only the basis variables, the problem of the optimization was relatively straightforward. There has been much previous work in the field of optimization of such systems. The method to minimize the total residence time for a single reaction occurring in a reactor system comprised of CSTR’s and plug flow and recycle reactors in series is, for instance, well-known. The minimum residence time is found by minimizing the area, representing the residence time of the reactors, on a reciprocal of the rate versus conversion graph. This usually involves a graphical search in order to determine the best

David Glasser

Papers

A geometric approach to steady flow reactors: the attainable region and optimization in concentration space

Fischer–Tropsch synthesis over iron catalysts supported on carbon nanotubes

The attainable region and optimal reactor structures

Geometry of the Attainable Region Generated by Reaction and Mixing: With and without Constraints

A study of the low temperature oxidation of coal