935 resultados para Nonlinear mathematical model


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In environmental studies it is necessary to know the adsorption behavior of metals by soils, since the unfavorable effects of heavy metals and even the micronutrients at high concentrations in the environment are related to these adsorbents' ability to immobilize them. A sample of a humic yellow red oxisol from Araponga region in the State of Minas Gerais, Brazil, was used to verify the adsorption behavior of Cu2+ ions in this substrate. The mathematical model described by Langmuir's adsorption equation in its linearized form was applied and the values of the maximum capacity b and those of the constant related to the bonding energy a were obtained. Aliquots of copper nitrate solutions containing several concentrations of this metal were added to soil samples, the pH being predetermined for developing the adsorption experiments. The chemical and physical characterization of soil sample were performed by determining the organic carbon, nitrogen and phosphorus concentrations, cation exchange capacity (CEC), pH, concentration of metals (Al, Fe, K, Mg, Ca, Zn, Cu, Ni, Cr, Co, Pb, and Cd), granulometric analysis and X-ray diffraction. Langmuir isotherms presented two distinct adsorption regions at both pH 4 and pH 5, showing that the adsorptive phenomenon occurs in two distinct stages. The adsorption sites for the lower part presented greater bonding energy and low adsorption capacity compared with the adsorption sites of the part of the curve corresponding to higher Cu concentrations in the equilibrating solution.

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Needle trap devices (NTDs) are a relatively new and promising tool for headspace (HS) analysis. In this study, a dynamic HS sampling procedure is evaluated for the determination of volatile organic compounds (VOCs) in whole blood samples. A full factorial design was used to evaluate the influence of the number of cycles and incubation time and it is demonstrated that the controlling factor in the process is the number of cycles. A mathematical model can be used to determine the most appropriate number of cycles required to adsorb a prefixed amount of VOCs present in the HS phase whenever quantitative adsorption is reached in each cycle. Matrix effect is of great importance when complex biological samples, such as blood, are analyzed. The evaluation of the salting out effect showed a significant improvement in the volatilization of VOCs to the HS in this type of matrices. Moreover, a 1:4 (blood:water) dilution is required to obtain quantitative recoveries of the target analytes when external calibration is used. The method developed gives detection limits in the 0.020–0.080 μg L−1 range (0.1–0.4 μg L−1 range for undiluted blood samples) with appropriate repeatability values (RSD < 15% at high level and <23% at LOQ level). Figure of merits of the method can be improved by using a smaller phase ratio (i.e., an increase in the blood volume and a decrease in the HS volume), which lead to lower detection limits, better repeatability values and greater sensibility. Twenty-eight blood samples have been evaluated with the proposed method and the results agree with those indicated in other studies. Benzene was the only target compound that gave significant differences between blood levels detected in volunteer non-smokers and smokers

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The data analyzed in this work were generated following the methodology developed by Molina et al.(J. Electroanal. Chem., 1979) for the calibration of a potentiometric system of measurement of hydrogen-ion concentrations resulting from neutralizations, at 25 ºC, of acidic or alkaline solutions at constant ionic strength (0.1 mol.l-1) held with NaClO4. The observed data present a serious deviation in relation to the mathematical model derived from the Nernst equation, for pH values ranging from 3 to 11, where pH=-log[H+]. We show that the minimization of the sum of the absolute values of the residuals gives estimates that are not influenced by outlying values.

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A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

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Natriumhypokloriittia voidaan valmistaa kloorista ja lipeästä jatkuvatoimisessa absorberissa. Tässä työssä tutkittiin kokeellisesti, miten kaasun ja nesteen virtausnopeudet vaikuttavat täytekappalekolonnin tulvimiseen ja painehäviöön, kuinka nopeasti kloori absorboituu lipeään ja kuinka suuri hypokloriittiliuoksen kierrätys tarvitaan, ettei hypokloriitti ala hajota. Lisäksi luotiin matemaattinen malli, jolla voidaan mitoittaa jatkuvatoiminen vastavirtaperiaatteella toimiva natriumhypokloriittireaktori. Kloori–lipeäsysteemin havaittiin tulvivan suuremmilla virtausnopeuksilla kuin ilma–vesisysteemin. Tosin osa kloorista absorboituu jo ennen täytekappalekerrosta, minkä vuoksi kaasun todellinen virtausnopeus täytekappalekerroksen alaosassa on pienempi kuin mitattu arvo. Kolonnin painehäviö nousee erittäin jyrkästi tulvimispisteen läheisyydessä. Koska kloori absorboituu lähes täydellisesti ja vain kolonnin alaosa tulvii, voidaan kolonnia painehäviön kannalta operoida lähellä tulvimispistettä. Sekä mallinnuksen että koetulosten perusteella yli 99,99 % kloorista absorboituu koeolosuhteissa kahden metrin täytekappalekerroksessa. Nopea absorptio johtuu erittäin nopeasta, irreversiibelistä kloorin reaktiosta ja prosessille tyypillisestä natriumhydroksidikonversion rajoittamisesta alle 94 %:iin. Jotta varmistetaan, ettei hypokloriitti ala hajota, valmista hypokloriittiliuosta täytyy kierrättää kolonniin vähintään noin 4-kertainen määrä tuoreen lipeän syöttömäärän nähden.

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In this paper, the mathematical model of the elliptical photoreactor , an special type of reactor that uses ultraviolet radiation, is presented. In the elliptical photoreactor the cylindrical reactor is irradiated from the outside by placing the lamp and the reactor at the foci of an elliptical reflector. The two main models of radiation -radial and difusse- are studied, an finally the general method of resolution of the mathematical model and its resolution in certain simple cases is shown.

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The effects of pre-incubation with mercury (Hg2+) and cadmium (Cd2+) on the activities of individual glycolytic enzymes, on the flux and on internal metabolite concentrations of the upper part of glycolysis were investigated in mouse muscle extracts. In the range of metal concentrations analysed we found that only hexokinase and phosphofructokinase, the enzymes that shared the control of the flux, were inhibited by Hg2+ and Cd2+. The concentrations of the internal metabolites glucose-6-phosphate and fructose-6-phosphate did not change significantly when Hg2+ and Cd2+ were added. A mathematical model was constructed to explore the mechanisms of inhibition of Hg2+ and Cd2+ on hexokinase and phosphofructokinase. Equations derived from detailed mechanistic models for each inhibition were fitted to the experimental data. In a concentration-dependent manner these equations describe the observed inhibition of enzyme activity. Under the conditions analysed, the integral model showed that the simultaneous inhibition of hexokinase and phosphofructokinase explains the observation that the concentrations of glucose-6-phosphate and fructose-6-phosphate did not change as the heavy metals decreased the glycolytic flux.

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COD is an important parameter to estimate the concentration of organic contaminants. The closed system technique with the use of K2Cr2O7 is the most important one, however, it has the inconvenience to suffer positive chemical interferences from inorganic compounds such as Fe2+ and H2O2 (not enough reported in the literature). This paper considers a statistical-experimental set capable to validate a empirical mathematical model generated from a 23 experimental design, in the presence of Fe2+ and H2O2. The t test shows that mathematical model has 99,99999% confidence degree and the experimental validation test indicates absolute mean error of 4,70%.

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Glycerol, a co-product of biodiesel production, was used as a carbon source for the kinetics studies and production of biosurfactants by P. aeruginosa MSIC02. The highest fermentative parameters (Y PX = 3.04 g g-1; Y PS = 0.189 g g-1, P B = 31.94 mg L-1 h-1 and P X = 10.5 mg L-1 h-1) were obtained at concentrations of 0.4% (w/v) NaNO3 and 2% (w/v) glycerol. The rhamnolipid exhibited 80% of emulsification on kerosene, surface tension of 32.5 mN m-1, CMC = 28.2 mg L-1, C20 (concentration of surfactant in the bulk phase that produces a reduction of 20 dyn/cm in the surface tension of the solvent) = 0.99 mg L-1, Γm (surface concentration excess) = 2.4 x 10-26 mol Å-2 and S (surface area) = 70.4 Ų molecule-1 with solutions containing 10% NaCl. A mathematical model based on logistic equation was considered to representing the process. Model parameters were estimated by non-linear regression method. This approach was able to give a good description of the process.

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In this study, a novel hybrid composite based on biodegradable hydrogel and Portland cement with promising technological properties was reported. In the first step, a full 23 with central point factorial design was utilized to obtain the enhanced polyacrylamide-carboxymethylcellulose hydrogel compositions. A mathematical model was devised, indicating that the 3 main variables were significant and the AAm and MBAAm variables positively contributed to the mode and showing that the CMC variable had the opposite contribution. In the second step, these compositions were mixed with Portland cement to obtain the hybrid composites. The presence of cement improved the mechanical properties of polymeric matrices, and electronic microscopic micrographics revealed that the hydrogels were well adhered to the cement phase and no phase separation between hydrogel and cement was detected. Finally, using the energy dispersive X-ray technique, the elements Na, Mg, Al, Si, S, K, Ca and Fe were detected in the polymeric matrix, consistent with the hybrid composite formation.

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The dissertation is based on four articles dealing with recalcitrant lignin water purification. Lignin, a complicated substance and recalcitrant to most treatment technologies, inhibits seriously pulp and paper industry waste management. Therefore, lignin is studied, using WO as a process method for its degradation. A special attention is paid to the improvement in biodegradability and the reduction of lignin content, since they have special importance for any following biological treatment. In most cases wet oxidation is not used as a complete ' mineralization method but as a pre treatment in order to eliminate toxic components and to reduce the high level of organics produced. The combination of wet oxidation with a biological treatment can be a good option due to its effectiveness and its relatively low technology cost. The literature part gives an overview of Advanced Oxidation Processes (AOPs). A hot oxidation process, wet oxidation (WO), is investigated in detail and is the AOP process used in the research. The background and main principles of wet oxidation, its industrial applications, the combination of wet oxidation with other water treatment technologies, principal reactions in WO, and key aspects of modelling and reaction kinetics are presented. There is also given a wood composition and lignin characterization (chemical composition, structure and origin), lignin containing waters, lignin degradation and reuse possibilities, and purification practices for lignin containing waters. The aim of the research was to investigate the effect of the operating conditions of WO, such as temperature, partial pressure of oxygen, pH and initial concentration of wastewater, on the efficiency, and to enhance the process and estimate optimal conditions for WO of recalcitrant lignin waters. Two different waters are studied (a lignin water model solution and debarking water from paper industry) to give as appropriate conditions as possible. Due to the great importance of re using and minimizing the residues of industries, further research is carried out using residual ash of an Estonian power plant as a catalyst in wet oxidation of lignin-containing water. Developing a kinetic model that includes in the prediction such parameters as TOC gives the opportunity to estimate the amount of emerging inorganic substances (degradation rate of waste) and not only the decrease of COD and BOD. The degradation target compound, lignin is included into the model through its COD value (CODligning). Such a kinetic model can be valuable in developing WO treatment processes for lignin containing waters, or other wastewaters containing one or more target compounds. In the first article, wet oxidation of "pure" lignin water was investigated as a model case with the aim of degrading lignin and enhancing water biodegradability. The experiments were performed at various temperatures (110 -190°C), partial oxygen pressures (0.5 -1.5 MPa) and pH (5, 9 and 12). The experiments showed that increasing the temperature notably improved the processes efficiency. 75% lignin reduction was detected at the lowest temperature tested and lignin removal improved to 100% at 190°C. The effect of temperature on the COD removal rate was lower, but clearly detectable. 53% of organics were oxidized at 190°C. The effect of pH occurred mostly on lignin removal. Increasing the pH enhanced the lignin removal efficiency from 60% to nearly 100%. A good biodegradability ratio (over 0.5) was generally achieved. The aim of the second article was to develop a mathematical model for "pure" lignin wet oxidation using lumped characteristics of water (COD, BOD, TOC) and lignin concentration. The model agreed well with the experimental data (R2 = 0.93 at pH 5 and 12) and concentration changes during wet oxidation followed adequately the experimental results. The model also showed correctly the trend of biodegradability (BOD/COD) changes. In the third article, the purpose of the research was to estimate optimal conditions for wet oxidation (WO) of debarking water from the paper industry. The WO experiments were' performed at various temperatures, partial oxygen pressures and pH. The experiments showed that lignin degradation and organics removal are affected remarkably by temperature and pH. 78-97% lignin reduction was detected at different WO conditions. Initial pH 12 caused faster removal of tannins/lignin content; but initial pH 5 was more effective for removal of total organics, represented by COD and TOC. Most of the decrease in organic substances concentrations occurred in the first 60 minutes. The aim of the fourth article was to compare the behaviour of two reaction kinetic models, based on experiments of wet oxidation of industrial debarking water under different conditions. The simpler model took into account only the changes in COD, BOD and TOC; the advanced model was similar to the model used in the second article. Comparing the results of the models, the second model was found to be more suitable for describing the kinetics of wet oxidation of debarking water. The significance of the reactions involved was compared on the basis of the model: for instance, lignin degraded first to other chemically oxidizable compounds rather than directly to biodegradable products. Catalytic wet oxidation of lignin containing waters is briefly presented at the end of the dissertation. Two completely different catalysts were used: a commercial Pt catalyst and waste power plant ash. CWO showed good performance using 1 g/L of residual ash gave lignin removal of 86% and COD removal of 39% at 150°C (a lower temperature and pressure than with WO). It was noted that the ash catalyst caused a remarkable removal rate for lignin degradation already during the pre heating for `zero' time, 58% of lignin was degraded. In general, wet oxidation is not recommended for use as a complete mineralization method, but as a pre treatment phase to eliminate toxic or difficultly biodegradable components and to reduce the high level of organics. Biological treatment is an appropriate post treatment method since easily biodegradable organic matter remains after the WO process. The combination of wet oxidation with subsequent biological treatment can be an effective option for the treatment of lignin containing waters.

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This research was motivated by the need to examine the potential application areas of process intensification technologies in Neste Oil Oyj. According to the company’s interest membrane reactor technology was chosen and applicability of this technology in refining industry was investigated. Moreover, Neste Oil suggested a project which is related to the CO2 capture from FCC unit flue gas stream. The flowrate of the flue gas is 180t/h and consist of approximately 14% by volume CO2. Membrane based absorption process (membrane contactor) was chosen as a potential technique to model CO2 capture from fluid catalytic cracking (FCC) unit effluent. In the design of membrane contactor, a mathematical model was developed to describe CO2 absorption from a gas mixture using monoethanole amine (MEA) aqueous solution. According to the results of literature survey, in the hollow fiber contactor for laminar flow conditions approximately 99 % percent of CO2 can be removed by using a 20 cm in length polyvinylidene fluoride (PDVF) membrane. Furthermore, the design of whole process was performed by using PRO/II simulation software and the CO2 removal efficiency of the whole process obtained as 97 %. The technical and economical comparisons among existing MEA absorption processes were performed to determine the advantages and disadvantages of membrane contactor technology.

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Direct leaching is an alternative to conventional roast-leach-electrowin (RLE) zinc production method. The basic reaction of direct leach method is the oxidation of sphalerite concentrate in acidic liquid by ferric iron. The reaction mechanism and kinetics, mass transfer and current modifications of zinc concentrate direct leaching process are considered. Particular attention is paid to the oxidation-reduction cycle of iron and its role in direct leaching of zinc concentrate, since it can be one of the limiting factors of the leaching process under certain conditions. The oxidation-reduction cycle of iron was experimentally studied with goal of gaining new knowledge for developing the direct leaching of zinc concentrate. In order to obtain this aim, ferrous iron oxidation experiments were carried out. Affect of such parameters as temperature, pressure, sulfuric acid concentration, ferrous iron and copper concentrations was studied. Based on the experimental results, mathematical model of the ferrous iron oxidation rate was developed. According to results obtained during the study, the reaction rate orders for ferrous iron concentration, oxygen concentration and copper concentration are 0.777, 0.652 and 0.0951 respectively. Values predicted by model were in good concordance with the experimental results. The reliability of estimated parameters was evaluated by MCMC analysis which showed good parameters reliability.

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Chemical looping combustion (CLC) provides a promising technology to help cut carbon dioxide emissions. CLC is based on separated oxidation and reduction processes. Oxygen carrier, which is made from metal and supporting material, is in continuous recirculation between the air and fuel reactors. The CLC process does not require separation unit for carbon dioxide. The fuel reactor can produce an almost pure carbon dioxide feed which decrease costs of carbon capture and storage (CCS). The CLC method is one of the most promising ones for energy efficient carbon capture. A large amount of literature was examined for this study and from it the most promising methods and designs were chosen. These methods and designs were combined as reactor system design which was then sized during the making of this thesis. Sizing was done with a mathematical model that was further improved during the study.

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The control of coating layer properties is becoming increasingly important as a result of an emerging demand for novel coated paper-based products and an increasing popularity of new coating application methods. The governing mechanisms of microstructure formation dynamics during consolidation and drying are nevertheless, still poorly understood. Some of the difficulties encountered by experimental methods can be overcome by the utilisation of numerical modelling and simulation-based studies of the consolidation process. The objective of this study was to improve the fundamental understanding of pigment coating consolidation and structure formation mechanisms taking place on the microscopic level. Furthermore, it is aimed to relate the impact of process and suspension properties to the microstructure of the coating layer. A mathematical model based on a modified Stokesian dynamics particle simulation technique was developed and applied in several studies of consolidation-related phenomena. The model includes particle-particle and particle-boundary hydrodynamics, colloidal interactions, Born repulsion, and a steric repulsion model. The Brownian motion and a free surface model were incorporated to enable the specific investigation of consolidation and drying. Filter cake stability was simulated in various particle systems, and subjected to a range of base substrate absorption rates and system temperatures. The stability of the filter cake was primarily affected by the absorption rate and size of particles. Temperature was also shown to have an influence. The consolidation of polydisperse systems, with varying wet coating thicknesses, was studied using imposed pilot trial and model-based drying conditions. The results show that drying methods have a clear influence on the microstructure development, on small particle distributions in the coating layer and also on the mobility of particles during consolidation. It is concluded that colloidal properties can significantly impact coating layer shrinkage as well as the internal solids concentration profile. Visualisations of particle system development in time and comparison of systems at different conditions are useful in illustrating coating layer structure formation mechanisms. The results aid in understanding the underlying mechanisms of pigment coating layer consolidation. Guidance is given regarding the relationship between coating process conditions and internal coating slurry properties and their effects on the microstructure of the coating.