De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Simulador computacional do comportamento em regime de poços de petróleo equipados com gas-lift contínuo

Amongst the results of the AutPoc Project - Automation of Wells, established between UFRN and Petrobras with the support of the CNPq, FINEP, CTPETRO, FUNPEC, was developed a simulator for equipped wells of oil with the method of rise for continuous gas-lift. The gas-lift is a method of rise sufficiently used in production offshore (sea production), and its basic concept is to inject gas in the deep one of the producing well of oil transform it less dense in order to facilitate its displacement since the reservoir until the surface. Based in the use of tables and equations that condense the biggest number of information on characteristics of the reservoir, the well and the valves of gas injection, it is allowed, through successive interpolations, to simulate representative curves of the physical behavior of the existing characteristic variable. With a simulator that approaches a computer of real the physical conditions of an oil well is possible to analyze peculiar behaviors with very bigger speeds, since the constants of time of the system in question well are raised e, moreover, to optimize costs with assays in field. The simulator presents great versatility, with prominance the analysis of the influence of parameters, as the static pressure, relation gas-liquid, pressure in the head of the well, BSW (Relation Basic Sediments and Water) in curves of request in deep of the well and the attainment of the curve of performance of the well where it can be simulated rules of control and otimization. In moving the rules of control, the simulator allows the use in two ways of simulation: the application of the control saw software simulated enclosed in the proper simulator, as well as the use of external controllers. This implies that the simulator can be used as tool of validation of control algorithms. Through the potentialities above cited, of course one another powerful application for the simulator appears: the didactic use of the tool. It will be possible to use it in formation courses and recycling of engineers

Conversão catalítica de clorometano em hidrocarbonetos

Amorphous silica-alumina and modified by incipient impregnation of iron, nickel, zinc and chromium were synthetized in oxide and metal state and evaluated as catalysts for the chloromethane conversion reaction. With known techniques their textural properties were determined and dynamics techniques in programmed temperature were used to find the acid properties of the materials. A thermodynamic model was used to determine the adsorption and desorption capacity of chloromethane. Two types of reactions were studied. Firstly the chloromethane was catalytically converted to hydrocarbons (T = 300 450 oC e m = 300 mg) in a fixed bed reactor with controlled pressure and flow. Secondly the deactivation of the unmodified support was studied (at 300 °C and m=250 g) in a micro-adsorver provided of gravimetric monitoring. The metal content (2,5%) and the chloromethane percent of the reagent mixture (10% chloromethane in nitrogen) were fixed for all the tests. From the results the chloromethane conversion and selectivity of the gaseous products (H2, CH4, C3 and C4) were determined as well as the energy of desorption (75,2 KJ/mol for Ni/Al2O3-SiO2 to 684 KJ/mol for the Zn/Al2O3-SiO2 catalyst) considering the desorption rate as a temperature function. The presence of a metal on the support showed to have an important significance in the chloromethane condensation. The oxide class catalyst presented a better performance toward the production of hydrocarbons. Especial mention to the ZnO/Al2O3-SiO2 that, in a gas phase basis, produced C3 83 % max. and C4 63% max., respectively, in the temperature of 450 oC and 20 hours on stream. Hydrogen was produced exclusively in the FeO/Al2O3-SiO2 catalysts (15 % max., T = 550 oC and 5,6 h on stream) and Ni/SiO2-Al2O3 (75 % max., T = 400 oC and 21,6 h on stream). All the catalysts produced methane (10 à 92 %), except for Ni/Al2O3-SiO2 and CrO/Al2O3-SiO2. In the deactivation study two models were proposed: The parallel model, where the product production competes with coke formation; and the sequential model, where the coke formation competes with the product desorption dessorption step. With the mass balance equations and the mechanism proposed six parameters were determined. Two kinetic parameters: the hydrocarbon formation constant, 8,46 10-4 min-1, the coke formation, 1,46 10-1 min-1; three thermodynamic constants (the global, 0,003, the chloromethane adsorption 0,417 bar-1, the hydrocarbon adsorption 2,266 bar-1), and the activity exponent of the coke formation (1,516). The model was reasonable well fitted and presented a satisfactory behavior in relation with the proposed mechanism