Orientador: Osvaldir PecoraTaranto / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-10T20:17:23Z (GMT). No. of bitstreams: 1 Parise_MariaRegina_D.pdf: 3017112 bytes, checksum: f14db15e7314590127e2a9a2ff621c9c (MD5) Previous issue date: 2007 / Resumo: A defluidização parcial ou total de partículas sólidas é um fenômeno indesejável em aplicações industriais envolvendo operações com leito fluidizado. Se as mudanças na fluidodinâmica do leito forem detectadas a tempo, pode-se evitar-la com o aumento da velocidade do gás de fluidização e/ou, em alguns casos, mediante a alteração da vazão de sólidos alimentados no sistema. A utilização de uma técnica que permita rapidamente identificar a região onde o leito está tendendo à defluidização é de suma importância, pois dessa maneira pode-se atuar no processo impedindo que haja perda de eficiência ou até mesmo a necessidade de parar a produção. Este trabalho teve como objetivo o desenvolvimento de uma metodologia capaz de identificar essa região em leito fluidizado gás-sólido, através de medidas de flutuação de pressão analisadas utilizando a transformada de Fourier juntamente com a Distribuição Exponencial Gaussiana. Para a verificação da metodologia proposta foram realizados ensaios experimentais utilizando areia e celulose microcristalina, alterando-se a altura do leito e o diâmetro médio das partículas. Os resultados mostraram que o método identifica claramente a região onde o leito está tendendo à defluidização, e tem grande potencial em aplicações industriais para o controle on line de processos em leito fluidizado gás-sólido. Além disso, a metodologia pode ser importante para detectar mudança de regime para a relação altura do leito e diâmetro da coluna de fluidização (H/D) superiores à unidade. Adicionalmente, foram realizados ensaios de secagem utilizando celulose microcristalina visando à possibilidade da identificação do ponto crítico (teor de umidade existente no final do período de taxa constante) utilizando as seguintes técnicas: metodologia proposta neste trabalho, freqüência dominante e desvio padrão da flutuação de pressão. Observou-se que para o sólido utilizado não foi possível detectar o ponto crítico através desses três tipos de análise. No entanto, a metodologia proposta pode ser utilizada na identificação do momento que a secagem não se encontra na fluidização requerida e está tendendo à defluidização / Abstract: The partial or complete bed defluidization is an undesired phenomenon in industrial application involving fluidized bed operations. If the changes in the hydrodynamic of the fluidized bed are detected early enough, it may be prevented by increasing the gas velocity and/or, in some cases, changing the solid feed in the system. The use of a technique that can quickly identify the region where the bed is tending to the defluidization is very important, because one can act in the process avoiding loss of efficiency or even the necessity of shutting down the process. This work was as objective the development a methodology capable of identifying this region in gas-solid fluidized bed, by pressure fluctuation measurements analyzed using Fourier Transform and exponential Gaussian distribution. In order to verify the methodology proposed, experimental tests were carried out using microcrystalline cellulose and sand, where the fixed bed height and particle mean diameter were varied. Results showed that the method clearly identifies the region where the bed is tending to the defluidization, and it has great potential on industrial applications to on line process control in gas-solid fluidized bed. Also, the methodology can be important to detect regime changes at bed aspect ratios (H/D) higher than unit. Additionally, experimental drying test were carried out using microcrystalline cellulose particles to verify the possibility of identification of the critical drying point (the moisture content related to the end of the constant rate period) by the following techniques: the methodology proposed in the present work, the dominant frequency and standard deviation of pressure fluctuations. It was observed that for the solid material used it was not possible to detect the critical drying point. However, the methodology proposed can be used on identification the moment that the drying is not in the desired fluidization regime and it is tending to defluidization / Doutorado / Engenharia de Processos / Doutor em Engenharia Química

<p>Bio-inorganic structures have been found to exhibit impressive optical and mechanical properties, such as control of light and/or high fracture strength. Certain species of diatoms (single-celled algae) form siliceous microshells (frustules) with organized structures that affect the transmission of light or fracture strengths. It has been found that <i>Coscinodiscus wailesii</i> diatoms have frustules with a quasi-regular hexagonal pattern of pores, which act as micro-lenses. In terms of mechanical strength, <i>Fragilariopsis kerguelensis</i> diatom SiO₂ frustules have been observed to exhibit impressive compressive and tensile fracture stress values. In this study, shape-preserving chemical conversion (using gas/solid reactions) is used to transform biogenic structures (diatom frustules) into high IR refractive index or ultrahigh specific strength materials. High-fidelity MgO/Si, Mg₂Si, Ca₂Si, MgO/Ti, and Ti replicas are successfully synthesized and characterized by SEM, EDX, XRD, and TEM. Focal point imaging experiments are used to show that focusing behavior of MgO/Si and Mg₂Si replicas can be enhanced in the IR range upon conversion into higher index replicas. Mechanical properties of SiO₂ frustules, MgO/Ti replicas, and Ti replicas have been measured by using in-situ and ex-situ indentation, which revealed that the mechanical properties can be enhanced by the shape-preserved chemical conversion of Bio-inorganic structures.</p><p><br></p>

[pt] O nitreto de gálio (GaN) é um dos mais interessantes e promissores materiais para aplicação em dispositivos óptico- eletrônicos. GaN pode ser usado para a fabricação de diodos e lasers azuis. O desenvolvimento deste tipo de material está relacionado com três campos principais: 1) deposição de camadas de GaN cristalino; 2) produção de nano- filamentos a partir de reações confinadas no interior de nanotubos de carbono; 3) síntese de GaN em pó por diferentes métodos químicos. Recentemente, novas técnicas de deposição adotaram a sublimação de pós de GaN como fonte de gálio para a produção de nanofilamentos de GaN, filmes finos ou cristais. Estes métodos de sublimação mostram a necessidade do emprego de pós de GaN. No presente trabalho, é apresentada uma nova rota para a produção de pós de GaN a partir da reação gás-sólido entre Ga2O3 e NH3(g) utilizando o carbono como agente redutor no interior de um novo tipo de reator, disposto verticalmente. A partir desta rota obteve-se pós de GaN com conversões aproximadamente de 100% e com estrutura cristalina hexagonal. A quantidade de GaN obtida variou de acordo com os parâmetros experimentais adotados. Através de uma análise estatística foi possível determinar a influência da temperatura, razão molar de carbono/Ga2O3 e do tempo experimental sobre a taxa de produção de GaN. / [en] It is well known that gallium nitride (GaN) is one of the most interesting and promising materials for optoelectronic devices. GaN can be used for manufacturing blue light- emitting diodes and lasers. Development of this material is concerned with three main areas 1) deposition of GaN crystalline layers onto different substrates; 2) manufacturing of GaN nanorods from chemical reactions in the confined spaces provided by carbon nanotubes; 3) synthesis of GaN powders by different chemical methods. Recently, new deposition techniques have adopted sublimation of GaN powders as gallium source to produce GaN nanorods, thin films or bulk crystals. These sublimation methods rely on the supply of GaN powders. This thesis presents a new route to produce GaN powder from gas-solid chemical reaction between Ga2O3 and NH3 using carbon as reducing agent in a new reactor design. The GaN powder obtained from this route possesses a hexagonal crystal structure and was found to correspond to almost 100% conversion of Ga2O3. The amount of GaN present in the powders varied with experimental parameters. A statistical analysis showed the influence of temperature, carbon/Ga2O3 ratio and experimental time on the production of GaN powder.

No description available.

Room-temperature chemisorption of hexacyclic aromatic hydrocarbons on the 2x1, sputtered, oxidized and H-terminated Si(100) surfaces, as well as those upon post treatments of hydrogenation, oxidization and electron irradiation have been investigated by using thermal desorption spectrometry (TDS), Auger electron spectroscopy (AES) and low energy electron diffraction (LEED). This work focuses on the effects of the functional groups (phenyl, methyl, vinyl, heteroatom, and H atom) in the chemisorbed aromatic hydrocarbons (benzene, toluene, xylene isomers, styrene and pyridine) on organic functionalization of the Si(100) surface, particularly on such surface processes as cycloaddition, dative adsorption, hydrogen abstraction, desorption, dissociation, diffusion, and condensation polymerization. Unlike the earlier notion that hydrogen evolution in the hydrocarbon/Si(100) systems is the result of hydrocarbon dissociation (into smaller hydrocarbon fragments and H atoms) on the surface, condensation polymerization of the adsorbed aromatic hydrocarbons is proposed in the present work, in order to explain the higher-temperature hydrogen evolution feature in the toluene/Si(100) system. This hypothesis is supported by our TDS results for other hydrocarbon adsorbates, especially in the pyridine/Si(100) system where electron-induced condensation polymerization has been observed at room temperature. The improved techniques in the TDS experiments developed in the present work have enabled us to observe condensation polymerization and the effect of H on the surface processes (via surface reconstruction) on Si(100) for the first time. New analysis methods have also been developed to determine the adsorption coverage from the AES data, and this work has not only improved the accuracy of the elemental-coverage evaluation, but also provided a means to estimate the rate and the order of chemisorption. By using the density functional theory with the Gaussian 98 program, the adsorption geometries and the corresponding adsorption energies of various adsorption phases have been calculated. These computational results have provided useful insights into the chemisorption structures on the Si(100) surface. The present work also presents the development of three kinetics models for hydrogen evolution in the aforementioned aromatic-hydrocarbon systems on Si(100). Based on a modified collision theory with consideration of diffusion, these theoretical models have proven to be quite successful in simulating the observed TDS profiles and in estimating the kinetic parameters for the analysis of condensation polymerization in 2-dimensional diffusion systems. The present work illustrates that TDS experiments can be used effectively with quantum computation and theoretical kinetics modelling to elucidate the intricate nature of organosilicon surface chemistry.

Dans ce travail de thèse, réalisé à l'IMFT, nous nous sommes intéressés aux écoulements turbulents diphasiques gaz-solides et plus particulièrement au phénomène de couplage inverse qui correspond à la modulation de la turbulence par la phase dispersée. Ce mécanisme est crucial pour les écoulements à forts chargements massiques. Dans cette thèse, nous avons considéré une turbulence homogène isotrope stationnaire sans gravité dans laquelle des particules sont suivies individuellement d'une façon Lagrangienne. La turbulence du fluide porteur est obtenue par des simulations directes (DNS). Les particules sont sphériques, rigides et d'une taille inférieure aux plus petites échelles de la turbulence. Leur densité est bien plus grande que la densité du fluide. Dans ce cadre, la force la plus importante agissant sur les particules est celle de traînée. Les interactions inter-particules ainsi que la gravité ne sont pas prises en compte. Pour modéliser ce type d'écoulement, une approche stochastique est utilisée pour laquelle l'accélération du fluide est modélisée par une équation de Langevin. L'originalité de ce travail est la prise en compte de l'effet de la modulation de la turbulence par un terme additionnel. Nous avons proposé deux modèles : une force de couplage moyenne qui est définie à partir des vitesses moyennes des phases, et une force instantanée qui est définie à l'aide du formalisme mésoscopique Eulérien. La fermeture des modèles s’appuie sur la fonction d’autocorrélation Lagrangienne et l’équation de transport de l’énergie cinétique. Les modèles sont testés en terme de prédiction de la vitesse de dérive et des corrélations fluide-particule. Les résultats montrent que le modèle moyen, plus simple, prend en compte les effets principaux du couplage inverse. Cependant, le problème de fermeture pratique est reporté sur la modélisation de l’échelle intégrale Lagrangienne et l’énergie cinétique de la turbulence du fluide vue par les particules. / In this thesis, performed in IMFT, we are interested in the turbulent gas-solid flows and more specifically, in the phenomenon of turbulence modulation which is the modification of the structure of the turbulence due to the solid particles. This mechanism is crucial in flows with high particle mass-loadings. In this work, we considered a homogeneous isotropic turbulence without gravity kept stationary with stochastic type forcing. Discrete particles are tracked individually in Lagrangian manner. Turbulence of the carrier phase is obtained by using DNS. The particles are spherical, rigid and of a diameter smaller than the smallest scales of turbulence. Their density is very large in comparison to the density of the fluid. In this configuration the only force acting on the particles is the drag force. Volume fraction of particles is very small and inter-particle interactions are not considered. To model this type of flow, a stochastic approach is used where the fluid element accel- eration is modeled using stochastic Langevin equation. The originality in this work is an additional term in the stochastic equation which integrates the effect of the particles on the trajectory of fluid elements. To model this term, we proposed two types of modeling: a mean drag model which is defined using the mean velocities from the mean transport equations of the both phases and an instantaneous drag term which is written with the help of the Mesoscopic Eulerian Approach. The closure of the models is based on the Lagrangian auto- correlation function of the fluid velocity and on the transport equation of the fluid kinetic energies. The models are tested in terms of the fluid-particle correlations and fluid-particle turbulent drift velocity. The results show that the mean model, simple, takes into account the principal physical mechanism of turbulence modulation. However, practical closure problem is brought forward to the Lagrangian integral scale and the fluid kinetic energy of the fluid turbulence viewed by the particles.

Les émissions anthropiques de dioxyde de carbone, gaz à effet de serre, sont considérées comme les principales causes du réchauffement climatique. Le captage du dioxyde de carbone par l’oxyde de calcium, qui s’avère être une masse de captage appropriée, au cours de plusieurs cycles de carbonatation/décarbonatation est une solution à la diminution des émissions industrielles. Néanmoins, la capacité de captage du dioxyde de carbone par l’oxyde de calcium diminue au cours des cycles, soulevant ainsi des problèmes économiques majeurs. Actuellement, cette perte d’efficacité de captage est largement étudiée contrairement à la réaction même de carbonatation de CaO d’un point de vue fondamental.Dans l’optique de mieux comprendre la réaction de carbonatation de CaO, une étude cinétique a été menée par le biais d’expériences de thermogravimétrie sur poudre. L’approche cinétique a été basée sur des tests de cinétiques hétérogènes fondés sur les hypothèses de l’état pseudo-stationnaire et de l’étape limitante. Les courbes cinétiques expérimentales obtenues en conditions isothermes (450-650°C) et isobares (2-30 kPa) ont montré un temps de latence lié au processus de germination de la nouvelle phase, ainsi qu’un fort ralentissement de la réaction à partir d’un certain degré d’avancement. Ce temps de latence et le degré d’avancement correspondant au frein cinétique dépendent de la température et de la pression partielle de CO2. Afin d’en expliquer l’origine, des caractérisations texturales et morphologiques ont été effectuées à différents degrés d’avancement. Les modifications observées à l’échelle des agrégats ont suggéré une limitation de la vitesse de réaction par des phénomènes de transport de matière, susceptibles de bloquer l’accès du gaz au cœur des agrégats. Les décrochements en température réalisées en thermogravimétrie ont mis en évidence un comportement cinétique complexe. Trois domaines ont pu être distingués au cours de la réaction, quelles que soient la température et la pression partielle de CO2. L’interprétation de ces résultats a souligné le rôle de la porosité et de son évolution sur la cinétique, ainsi qu’un effet anti-Arrhenius dans le deuxième domaine.La modélisation cinétique a dû faire intervenir à la fois un modèle proche de la réalité physique à l’échelle des grains denses, mais également les processus de transport de matière et de chaleurs au sein de l’agrégat, afin de rendre compte des courbes expérimentales et de quantifier l’impact des différents paramètres expérimentaux sur la vitesse de réaction. Ce couplage échelle de la population des grains-échelle de l’agrégat a été réalisé à l’aide d’un logiciel de cinétique hétérogène, CIN4, développé au département PRESSIC, en collaboration avec la société ASTEK. Les simulations obtenues ont permis de décrire la réaction jusqu’au freinage cinétique. / Anthropogenic carbon dioxide (CO2) emissions, major contributors to the greenhouse effect, are considered as the main cause of global warming. So, decrease of CO2 emitted by large industrial combustion sources or power plants, is an important scientific goal. One of the approaches is based on CO2 separation and capture from flue gas, followed by sequestration in a wide range of geological formations. In this aim, CO2 is captured by sorbents like calcium oxide (CaO) in multi-cycle process of carbonation/decarbonation. However, it was shown that the most important limitations of such process are related to the reversibility of reaction. CaO rapidly loses activity towards CO2, so the maximum extent of carbonation decreases as long as the number of cycles increases. In order to well understand the processes and parameters influencing the capture capacity of CaO-based sorbents, it appears important to get details on the kinetic law governing the reaction, which have not been really studied up to now. To investigate this reaction, CaO carbonation kinetics was followed by means of thermogravimetric analysis (TGA) on divided materials. Special care was given to the validation of the usual kinetic assumptions such as steady state and rate-determining step assumptions. The aim was to obtain a model describing the reaction in order to explain the influence of intensive variables such as carbonation temperature and CO2 partial pressure. TGA curves obtained under isothermal and isobaric conditions showed an induction period linked to the nucleation process and a strong slowing down of the reaction rate once a given fractional conversion was reached. Both phenomena were observed to depend on carbonation temperature and CO2 partial pressure. To explain these results, the evolution of texture and microstructure of the solid during the reaction was regarded as essential. Reaction at the grain scale induces a volume increase from CaO to CaCO3 which causes a change in the porosity characteristics at the aggregates scale, which could block the access of the gas to the core of aggregates. Temperature jumps during TGA experiments have put in evidence a complex kinetic behavior since three distinct domains must be distinguished, over all the conversion range, whatever the temperature and CO2 pressure could be. The discussion of the results emphasizes the role of the porosity on the kinetic anti-Arrhenius behavior observed in the second domain. So carbonation reaction can be described by a two scales model: at a nonporous grain scale for the chemical reaction and at the aggregate scale, for the CO2 intergranular diffusion. The kinetic modeling, thanks to the software CIN4 (developed in collaboration with Astek), is able to couple both modeling scales in order to explain the kinetic slowing down and the influence of temperature and CO2 partial pressure on the reaction rate.

Orientador: Hélio Aparecido Navarro / Banca: Vicente Luiz Scalon / Banca: Luben Cabezas Gomez / Resumo: No presente trabalho desenvolve-se um estudo de modelagem matemática e simulação numérica do escoamento bifásico gás-sólido em leito fluidizado borbulhante. Utiliza-se o modelo Euleriano de duas fases separadas formulando o tensor das tensões da fase sólida através da teoria cinética dos escoamentos granulares. As simulações numéricas são realizadas através do código fonte MFIX (Multiphase Flow with Interphase eXchanges) desenvolvido no NETL (National Energy Technology Laboratory). Os resultados de simulação numérica são avaliados por meio da análise da influência dos seguintes parâmetros: malha computacional e esquemas de discretização dos termos convectivos das equações de conservação. Com base nos estudos teóricos e resultados obtidos durante o trabalho conclui-se que esquemas de primeira, tais como FOUP são altamente difusivos, já os resultados obtidos utilizando o esquema de alta ordem, Superbee, produziu resultados de melhor qualidade para as malhas testadas neste trabalho. Além disso, os resultados mostraram-se bastante dependentes do tamanho da malha computacional. / Abstract: In the present work is described a mathematical model and numerical simulation of gas-solid two-phase flow in a bubbling fluidized bed. It is used the Eulerian gas-solid two-fluid model and the solid phase stress tensor is modeled considering the kinetic theory of granular flows. The numerical simulations were developed using the MFIX (Multiphase Flow with Interphase eXchanges) code developed in NETL (National Energy Technology Laboratory). The numerical diffusion is analyzed considering a single bubbling detachment and its movement process in a two-dimensional bubbling fluidized bed using the bubble shape as a metric for results description. The influence of computacional grid it is also analyzed. It is concluded that SuperBee scheme produces the better results and analysis about estimating uncertainty in grid refinement should be studied. / Mestre

Reatores de leito fluidizado circulante são intensamente utilizados em aplicações de larga escala como craqueamento catalítico de petróleo e combustão de carvão. Projeto e desenvolvimento nestas áreas são fortemente baseados em plantas de demonstração, a custos elevadíssimos. Nesse contexto, tratamentos utilizando mecânica dos fluidos computacional assumem considerável relevância. Os complexos padrões de escoamento gás-sólido que se desenvolvem nos reatores de leito fluidizado circulante determinam taxas de reação e exigem, portanto, descrições hidrodinâmicas rigorosas. Os modelos Eulerianos do contínuo ou de dois fluidos são correntemente considerados a escolha mais prática na busca destas descrições. Estas formulações são baseadas na aplicação da hipótese de meio contínuo tanto para fases macroscopicamente contínuas quanto dispersas. Neste trabalho, desenvolve-se simulações numéricas para descrever processos hidrodinâmicos e reativos em reatores de leito fluidizado circulante aplicando modelagem de dois fluidos. Considera-se situações típicas de combustão em leito fluidizado circulante de carvão mineral. Como processo reativo considera-se a absorção de dióxido de enxofre por calcário. Realiza-se análises hidrodinâmicas, e de efeitos hidrodinâmicos sobre a reação de interesse. Realiza-se simulações de regime permanente e de regime transiente. Mostra-se que as simulações de regime permanente permitem análises qualitativas do processo, e provêem condições iniciais para simulações transientes diretamente no regime de escoamento estatisticamente permanente. Em relação à hidrodinâmica, conclui-se que os modelos de dois fluidos correntes são ainda bastante crus. São claramente necessárias melhores descrições reológicas e relações constitutivas sub-grade mais acuradas. Em relação à reação química, conclui-se que predições reativas acuradas somente poderão ser obtidas se descrições hidrodinâmicas rigorosas forem combinadas com descrições reativas igualmente rigorosas. / Circulating fluidized bed reactors are widely used in large scale applications such as catalytic cracking of petrol and coal combustion. Development and design in those areas are strongly based on demonstration plants, at extremely high costs. In this context, treatments applying computational fluid mechanics assume considerable relevance. The complex gas-solid flow patterns which develop inside the circulating fluidized bed reactors determine reaction rates, so that rigorous hydrodynamic descriptions are required. The continuum Eulerian or two-fluid models are currently considered the more practical choice for providing such descriptions. Those formulations are based on the application of the continuum hypothesis for both macroscopically continuous and dispersed phases. In this work numerical simulation is performed to describe both hydrodynamics and reactive processes in circulating fluidized beds applying two-fluid modeling. Typical situations of circulating fluidized bed coal combustion are considered. The reactive process considered is the absorption of sulfur dioxide by limestone. Analyses are performed of hydrodynamics, and regarding hydrodynamic effects over the concerning reaction. Both steady state and transient simulations are performed. It is shown that steady state simulations allow qualitative analyses, and do provide initial conditions for transient runs straightly inside the statistical steady state flow regime. Concerning hydrodynamics, it is concluded that the current two-fluid models are still very crude. Clearly, better rheological descriptions are required alongside with more accurate sub-grid constitutive relations. Regarding chemical reaction, it is concluded that accurate reactive predictions shall only be found if rigorous hydrodynamic descriptions are combined with equally rigorous reaction descriptions.

Fenômenos multifásicos são frequentemente observados na natureza, tais como nas gotas de chuva ou neve no ar, nos vulcões e tempestades de areia, e em diversas outras situações. Na solução desses problemas que envolvem escoamentos gás-sólidos e granulares são frequentemente utilizadas duas abordagens: a contínua (formulação Euleriana-Euleriana) e a discreta (formulação Euleriana-Lagrangiana). Na abordagem discreta pode-se utilizar dois modelos para descrever o contato entre as partículas: o modelo de esfera rígida e o modelo de esfera suave. Neste trabalho é realizado um estudo detalhado dos modelos de contato, com foco na modelagem de esfera suave, que é baseada em um sistema dinâmico mola-massa-amortecedor. Por meio desse estudo, com a finalidade de aprimorar o modelo de contato não-linear, são propostas duas relações para o mecanismo de contato de partículas. Essas relações são fundamentadas em um modelo dinâmico, com não-linearidades nas partes conservativas e dissipativas, não apresentando descontinuidades entre as acelerações do início e do fim do contato. A metodologia de desenvolvimento da presente pesquisa está dividida em três partes: pesquisa bibliográfica dos modelos de contato; estudo analítico e numérico desses modelos e testes de problemas com a realização de experimentos numéricos, utilizando o código computacional MFIX (Multiphase Flow with Interphase eXchange). As novas aproximações propostas neste trabalho são analisadas e aplicadas em três diferentes problemas: de dinâmica, escoamento gás-sólido e escoamento granular. Os resultados obtidos utilizando as relações são comparados com dados disponíveis na literatura, mostrando-se adequados para os casos investigados neste trabalho. / Multiphase flow are frequently observed in nature, such as rain drops in air or snowfalls, volcanoes and sandstorms, and several other situations. For solving these problems which involve gas-solid and granular flows are often used two models: the continuous model (Eulerian-Eulerian formulation) and the discrete model (Eulerian-Lagrangian formulation). There are two main contact models used in DEM, the hard-sphere model and the soft-sphere model. In this work is carried out a detailed study of contact models, focusing on soft-sphere model, based on a dynamic system modeled as nonlinear mass-spring-damper. In order to improve the nonlinear contact model, in this study it is proposed two new approximate relations for determining the damping coefficient and duration of contact for a specific nonlinear soft-sphere contact model where the contact force is continuous at the start and end of the contact. The methodology of the development of this work is divided into three parts: literature research of the contact models; analytical and numerical study of these models and test problems with numerical experiments, using the open source code MFIX (Multiphase Flow with Interphase eXchange). The proposed relations are analyzed and applied in three different problems: dynamic problem, gas-solid flow and granular flow. All results are compared with literature data showing good agreement for these cases studied in the present work.