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Devido à crescente implementação do Controle Preditivo baseado em Modelo (MPC) em outros processos além de refino e plantas petroquímicas, que geralmente possuem múltiplas entradas e saídas, tem-se um aumento na demanda de modelos gerados por identificação de sistemas. Identificar modelos que representem fielmente a dinâmica do processo depende em grande medida das características dos sinais de excitação dos processos. Assim, o foco deste trabalho é realizar um estudo dos sinais típicos usados em identificação de sistemas, PRBS e GBN, em uma abordagem multivariável. O estudo feito neste trabalho parte das características da geração dos sinais individualmente, depois é feita uma análise de correlação cruzada dos sinais de entrada, observando a influência desta sobre os resultados de identificação. Evitar uma alta correlação entre os sinais de entrada permite determinar o efeito de cada entrada sobre a saída no processo de identificação. Um ponto importante no projeto de sinais de identificação de sistemas multivariáveis é a frequência dos mesmos para conseguir excitar os processos nas regiões de frequência de operação normal e assim extrair a maior informação dinâmica possível do processo. As características estudadas são avaliadas por meio de testes em três plantas simuladas diferentes, categorizadas como mal, medianamente e bem condicionadas. Estas implementações foram feitas usando sinais GBN e PRBS de diferentes frequências. Expressões para a caracterização dos sinais de excitação foram avaliadas identificando os processos em malha aberta e malha fechada. Para as plantas mal condicionadas foram implementados sinais compostos por uma parte completamente correlacionada e uma parte não-correlacionada, conhecido como método de dois passos. Finalmente são realizados experimentos de identificação em uma aplicação em tempo real de uma planta piloto de neutralização de pH. Os testes realizados na planta foram feitos visando avaliar os estudos de frequência e correlação em uma aplicaficção real. Os resultados mostram que a condição de sinais completamente descorrelacionados n~ao deve ser cumprida para ter bons resultados nos modelos identificados. Isto permite ter mais exibilidade na geração do conjunto de sinais de excitação. / Due to the Predictive Control based on Model (MPC) rising in other process beyond refining and petrochemical plants, which in general have multiple inputs and outputs, there have been an increase in demand of models generated by system identification. Identify models that accurately represent the dynamics of the process depends largely on the characteristics of the processes excitation signals. Thus, the focus of this work is to perform a study of the typical signals used in identification systems, PRBS and GBN, in a multivariable approach. The study carried out in this work begins on the individual generation characteristics of the signals, and then an analysis is made of input signals cross-correlation, by observing the in uence of this on the identification results. Avoid a high correlation among the input signals allows to determine the effect of each input on the output of the identification process. An important point in the signals design for multivariable system identification is its frequency to get excite the processes in the normal operation frequency regions and thus extract the maximum dynamic information possible of the process. The studied characteristics are evaluated by testing three different simulated plants, categorized as well, medium and ill conditioned. These implementations were made using GBN and PRBS signals of dierent frequencies. Expressions to characterize the excitation signals were evaluated identifying the processes in open and closed-loop. For ill-conditioned plants were implemented signals composed by a fully correlated part and a non-correlated part, known as two-step method. Finally, identification experiments are performed on a real time application in a pilot pH neutralization plant. The tests were made in the plant in order to evaluate the frequency and correlation studies in a real application. The results show that the completely uncorrelated signals condition must not be satisfied to have good results on the identified models, which besides allows greater exibility in the generation of the excitation signals set.

Este trabalho consiste no estudo da estrutura sedimentar da Bacia do Paraná da região de Bebedouro utilizando função do receptor, ondas de superfície e sísmica de refração. Funções do Receptor (FR) mostram a resposta da estrutura geológica abaixo de uma estação sismográfica. Para diminuir a não unicidade na inversão do traço de uma FR, foram usadas curvas de dispersão de ondas de superfície como vínculos adicionais. Ondas de superfície foram também obtidas com a correlação cruzada de ruído sísmico ambiental. Esse método passivo permite a obtenção de dispersão em períodos intermediários entre os dados de telessismos e os dados de sísmica rasa auxiliando na determinação estruturas sedimentares. Foi utilizada a inversão conjunta de FR de alta e baixa frequência, dispersão de fase e grupo de períodos menores que 2 s e dispersão de ondas Love e Rayleigh continentais (períodos entre 10 e 100 s). Na inversão conjunta, foram usados vários modelos iniciais diferentes para garantir melhor cobertura do espaço de soluções possíveis. Os resultados mostram uma camada de basalto com uma espessura entre 200 e 400 m, sob uma camada superficial de arenito de 50 a 100m. O embasamento da bacia está torno de 2.5 3.0 km. A espessura e razão Vp/Vs crustal da região foi estimada em 40.0 (1.0) km e 1.78 (0.02). Foi possível identificar zonas de baixa velocidade dentro do pacote de basalto, possivelmente relacionadas a zonas de fraturas ou camadas de basalto alterado. Estas camadas de baixa velocidade estão na parte sul, próximas à área de maior sismicidade induzida e também relativamente mais perto dos poços profundos de maior vazão. Isto corrobora com a hipótese de que a sismicidade local está associada à exploração de poços e estrutura de falhas pré -existentes. / A study of the seismic structure of the Paraná Basin in Bebedouro, SP, was carried out with Receiver Functions (RF). Both low frequency (with ~0.5 Hz low pass filter) and high-frequency (~10Hz) RFs were jointly inverted with surface wave dispersion curves. Surface-wave data included: long-period group velocities of Rayleigh and Love waves from continental-scale tomography in the period range 10-100 s (useful to control crustal scale structure and Moho depth), intermediate period group velocities near 1s period obtained from cross-correlation of ambient noise (useful to control sedimentary structure), phase velocities near 0.2-1.0 s obtained from local earthquakes, and phase velocities of Rayleigh waves from shallow seismic refraction data near ~0.1 s period (useful to control shallow layers). Joint inversion was obtained with several different initial models to better cover all possible solutions. The results indicate that the basalt layer is 200 to 400m thick, beneath sandstones of about 50 100m thick. The Basin basement was detected between 2.5 3.0 km depth, consistent with expected values from regional bore-hole data in the Paraná Basin. Beneath several stations a low-velocity zone was detected in the middle of the basalt pack which is interpreted as a zone of fractured or altered basalt. This anomalous low-velocity layer was detected near the most seismically active zone in the Andes district. It is also relatively close to the deep wells with larger outflow. The existence of this low-velocity zone in the middle of the basalt layer is consistent with the model proposed for the water-well induced seismicity.

Com mais de metade de sua produção exportada e participação de aproximadamente um terço do mercado mundial, atualmente o Brasil é o maior exportador de açúcar e, portanto, espera-se que os preços do mercado físico do açúcar no Brasil apresentem algum grau de relacionamento os preços internacionais desta commodity, que são representados pelas cotações dos contratos futuros das bolsas de Nova Iorque (NYBOT) e de Londres (LIFFE) - primeiros vencimentos. No presente estudo são analisadas as relações entre os logaritmos das médias semanais dos preços domésticos de açúcar, representados pelo preço do Estado de São Paulo, principal produtor nacional, e preços internacionais convertidos em moeda brasileira. Utilizando os critérios de Akaike e Schwarz, foi determinado o número de defasagens auto-regressivas necessárias para ajustar modelos com a finalidade de testar a existência de raiz unitária, cujos resultados apontam para a estacionariedade das séries em torno de uma tendência determinista. A partir dos resíduos obtidos na estimação de modelos univariados auto-regressivos para cada variável, foram obtidas as funções de correlação cruzada (FCC) para cada par de variáveis usado no teste de causalidade. Os resultados das FCCs apontam tanto a existência de relação contemporânea significativa, como causalidade dos preços das bolsas internacionais para os preços domésticos do açúcar, sendo mais expressiva a relação causal das cotações dos contratos futuros da bolsa de Nova Iorque para os preços do mercado físico do açúcar no Brasil. Com base nesses resultados, foram especificados modelos que tinham como finalidade analisar o processo de transmissão de preços entre os mercados doméstico e internacional. Para evitar multicolinearidade, optou-se pela não inclusão de defasagens da variável dependente como explicativas nestes modelos e, para contornar problemas associados à correlação de resíduos nas equações ajustadas, as variáveis foram filtradas conforme a metodologia de Cochrane-Orcutt, fundamentando-se nos resultados da função de autocorrelação dos resíduos dos modelos ajustados de forma iterativa. As elasticidades obtidas nas funções de transmissão de preços indicam que os valores passados das cotações da NYBOT são referência para a formação de preço do mercado doméstico de açúcar, e que a influência contemporânea entre os preços das bolsas internacionais e o preço doméstico é pequena. Como a participação do Brasil no mercado internacional de açúcar é elevada, espera-se que de alguma maneira aspectos relativos ao mercado doméstico brasileiro dessa commodity afetem os preços internacionais. Dessa forma, buscou-se analisar o impacto que a produção brasileira de açúcar, a qual define o potencial de exportação dessa commodity pelo Brasil, tem sobre a formação do preço no mercado internacional. Para isso foi ajustada uma função utilizando como representativo do preço de açúcar no mercado internacional a média das cotações do contrato futuro de açúcar na bolsa de Nova Iorque no ano-safra internacional, isto é, entre setembro de um ano a agosto do subseqüente. Como variáveis explicativas foram considerados: o estoque inicial de cada ano-safra, a produção de açúcar do Brasil e a produção de açúcar dos demais países do mundo, também por ano-safra. Os resultados apontam que o direcionamento de mais matéria-prima para a produção de açúcar, considerando as baixas taxas de crescimento do consumo desse produto no mercado interno, tem efeito negativo e significativo no nível de preço a vigorar no mercado internacional. Isto poderia comprometer a rentabilidade do setor, não só porque os preços do açúcar exportado cairiam, mas também porque os menores preços do mercado internacional estariam afetando os recebidos pelo açúcar comercializado no mercado interno. / With more than a half of its production exported and about 30% of market share in the world sugar market, nowadays Brazil is the world’s leading exporter of sugar. So, it’s expected that the sugar physical prices in the State of São Paulo (CEPEA), Brazil´s leading production region, have any sort of relation with the international prices of this commodity. These international prices are represented by the nearby quotes of the sugar contracts at New York Board of Trade (NYBOT) and at London International Financial Futures and Options Exchange (LIFFE), both multiplied by the Brazilian currency exchange rate. The present study analyses the relations between the logarithms of the domestic and international weekly means of sugar prices. The number of auto-regressive lags necessaries to ajust models was determined by Akaike and Scharwz criterions, which objective was to test the existence of unit root. The results pointed to stationary series around deterministic trends. Through the residual data of auto-regressive univariated models that were estimated to each of the variables, it was obtained the cross correlation function (CCF) to each pair of variables to which the causality was tested. The CCF results indicated a significative contemporany relation between the variables and also causality from the international quotes to State of São Paulo domestic prices, mainly from NYBOT. Based on these results, it was obtained the number of lags of the explicative variable to specify the transmission price models between domestic and international sugar prices. To prevent multicolinearity, it was opted to not include lags of dependent variable as explicative variables, and, to skirt problems related to the correlation in the residual data in the adjusted equations, the variables were filtered by the Cochrane-Orcutt methodology, following the indicatives of the autocorrelation function (ACF) of the residual data from adjusted models in an interactive form. The elasticities obtained in the price transmission functions indicated that the past values of NYBOT quotes are reference to CEPEA prices, and that the contemporany influence between domestic and international prices is small. Considering that Brazilian share in the sugar international market is expressive, it’s expected that aspects related to Brazilian domestic market should cause any affect in the international prices level. So, to analyze the impact that Brazilian production of sugar, which defines the potential of exportation of this commodity for Brazil, has on the formation of the price in the international market, it was adjusted a function that uses as representative of the sugar price in the international market the mean of NYBOT nearby quotes between September to August (of the subsequent year). The variables international beginning stocks, Brazilian sugar production and rest of the world sugar production, all of them measured in the international sugar-marketing year, were considered as explicative ones. The results pointed that an increase in the Brazilian sugar cane production (in order to produce sugar), considering the low rates of the consumption evolution in the Brazilian domestic market, would have a negative and significant effect in the international sugar prices level. This event would affect the yield of sugar sector, not only because the sugar international price would decrease, but also because the lower prices in the international market would reduce the Brazilian domestic prices.

Este trabalho consiste no estudo da estrutura sedimentar da Bacia do Paraná da região de Bebedouro utilizando função do receptor, ondas de superfície e sísmica de refração. Funções do Receptor (FR) mostram a resposta da estrutura geológica abaixo de uma estação sismográfica. Para diminuir a não unicidade na inversão do traço de uma FR, foram usadas curvas de dispersão de ondas de superfície como vínculos adicionais. Ondas de superfície foram também obtidas com a correlação cruzada de ruído sísmico ambiental. Esse método passivo permite a obtenção de dispersão em períodos intermediários entre os dados de telessismos e os dados de sísmica rasa auxiliando na determinação estruturas sedimentares. Foi utilizada a inversão conjunta de FR de alta e baixa frequência, dispersão de fase e grupo de períodos menores que 2 s e dispersão de ondas Love e Rayleigh continentais (períodos entre 10 e 100 s). Na inversão conjunta, foram usados vários modelos iniciais diferentes para garantir melhor cobertura do espaço de soluções possíveis. Os resultados mostram uma camada de basalto com uma espessura entre 200 e 400 m, sob uma camada superficial de arenito de 50 a 100m. O embasamento da bacia está torno de 2.5 3.0 km. A espessura e razão Vp/Vs crustal da região foi estimada em 40.0 (1.0) km e 1.78 (0.02). Foi possível identificar zonas de baixa velocidade dentro do pacote de basalto, possivelmente relacionadas a zonas de fraturas ou camadas de basalto alterado. Estas camadas de baixa velocidade estão na parte sul, próximas à área de maior sismicidade induzida e também relativamente mais perto dos poços profundos de maior vazão. Isto corrobora com a hipótese de que a sismicidade local está associada à exploração de poços e estrutura de falhas pré -existentes. / A study of the seismic structure of the Paraná Basin in Bebedouro, SP, was carried out with Receiver Functions (RF). Both low frequency (with ~0.5 Hz low pass filter) and high-frequency (~10Hz) RFs were jointly inverted with surface wave dispersion curves. Surface-wave data included: long-period group velocities of Rayleigh and Love waves from continental-scale tomography in the period range 10-100 s (useful to control crustal scale structure and Moho depth), intermediate period group velocities near 1s period obtained from cross-correlation of ambient noise (useful to control sedimentary structure), phase velocities near 0.2-1.0 s obtained from local earthquakes, and phase velocities of Rayleigh waves from shallow seismic refraction data near ~0.1 s period (useful to control shallow layers). Joint inversion was obtained with several different initial models to better cover all possible solutions. The results indicate that the basalt layer is 200 to 400m thick, beneath sandstones of about 50 100m thick. The Basin basement was detected between 2.5 3.0 km depth, consistent with expected values from regional bore-hole data in the Paraná Basin. Beneath several stations a low-velocity zone was detected in the middle of the basalt pack which is interpreted as a zone of fractured or altered basalt. This anomalous low-velocity layer was detected near the most seismically active zone in the Andes district. It is also relatively close to the deep wells with larger outflow. The existence of this low-velocity zone in the middle of the basalt layer is consistent with the model proposed for the water-well induced seismicity.

The engineered barrier system is a basic element in the design of repository to isolate high level radioactive waste (HLW). In this system, the clay barrier plays a prominent role in dispersing the heat generated from the waste, reduce the flow of pore water from the host rock, and maintaining the structural stability of the waste canister. The compacted expansive clay (generally bentonite blocks) is initially in unsaturated state. During the life time of the repository, the barrier will undergo different coupled thermal, hydrological and mechanical (THM) phenomena due to heating (from the heat-emitting nuclear waste) and hydration (from the saturated host rock). The design of nuclear waste disposal requires the prediction of the long term barrier behavior (i.e. hundred or thousand years), so numerical modeling is a basic component of the repository design. The numerical analyses are performed using mathematical THM formulation and the associated numerical code. Constitutive models are an essential part of the numerical simulations. Those constitutive models represent the intrinsic behavior of the material for the individual physical phenomenon (i.e. thermal, hydraulic and mechanical). Deterministic analyses have shown the potential of such mathematical formulations to describe the physical behavior of the engineered barrier system. However, the effect of the inherent uncertainties associated with the different constitutive models on the global behavior of the isolation system has not been explored yet. The first part of this thesis is related to application of recent probabilistic methods to understand and assess the impact of uncertainties on the global THM model response. Experimental data associated with the FEBEX project has been adopted for the case study presented in this thesis. CODE_BRIGHT, a fully coupled THM finite element program, is used to perform the numerical THM analysis. The second part of this thesis focuses on the complex mechanical behavior observed in a barrier material subjected (during 5 years) to heating and hydration under actual repository conditions The studied experiment is the (ongoing) full scale in-situ FEBEX test at Grimsel test site, Switzerland. A partial dismantling of this experiment has allowed the inspection of the barrier material subjected to varying stresses due to hydration and heating. The clay underwent both elastic and plastic volumetric deformations at different suction and temperature levels with changes in the pre-consolidation pressure and voids ratio that are difficult to explain with conventional models. In this thesis a double structure elasto plastic model is proposed to study the mechanical behavior of this barrier material. The numerical modeling was performed with CODE_BRIGHT. The study shows that the double structure model explains satisfactorily the observed changes in the mechanical behavior of the clay material.

The progress of miniaturisation towards the nanoscopic scale in science and technology has also influenced the biosciences. This is particularly important, since proteins, as the smallest functional units of life, exhibit a spectacular wealth of functionalities, enabling them to fulfil complex tasks in cells and organisms. For this reason, they are often termed molecular or cellular “machines”. To be able to investigate and better understand these fascinating molecules in their native environment, new analytical methods must be developed, with appropriately high sensitivity and spatial and temporal resolution. We describe one very promising technique based on fluorescence spectroscopy, which allows a quantitative analysis of protein- protein interactions in the live cell. / Die zunehmende Miniaturisierung bis hin zum nanoskopischen Maßstab in vielen technischen Disziplinen hat auch die Lebenswissenschaften ergriffen. Dies ist insofern von großer Bedeutung, als die Proteine als kleinste funktionale Einheiten des Lebens trotz ihrer winzigen Abmessungen eine faszinierende Komplexität aufweisen, die es ihnen erlauben, hoch differenzierte und spezialisierte Aufgaben in der Zelle und im Organismus zu übernehmen. Aus diesem Grund werden sie in der modernen Biologie auch als molekulare oder zelluläre „Maschinen“ bezeichnet. Um diese kleinen Wunderwerke zu studieren und ihre Funktionsweise in ihrer natürlichen Umgebung zu analysieren, bedarf es innovativer Technologien, die es erlauben, mit maximaler räumlicher und zeitlicher Auflösung auch einzelne Moleküle in der lebenden Zelle sichtbar zu machen und zu verfolgen. Im Folgenden wird eine von uns entwickelte fluoreszenzspektroskopische Methode vorgestellt, mit deren Hilfe die komplizierten Interaktionen zwischen Proteinen in der lebenden Zelle aufgeklärt werden können.

This thesis studies the design and implementation of an ultra-sonic water depth sounder. The depth sounder is implemented in a hand-held smart console used by divers. Since the idea of echo sounding is to measure the flight time between transmitting the signal and receiving the echo, the main challenge of this task is to find a time-of-flight (ToF) estimation for a signal in noise. It should be suitable for this specific application and robust when implemented in the device. The thesis contains an investigation of suitable ToF methods. More detailed evaluations of the matched filter, also known as the correlation method, and the linear phase approach are done. Aspects like pulse frequency and duration, speed of sound in water and underwater noise are taken into account. The ToF-methods are evaluated through simulation and experiments. The matched filter approach is found suitable based on these simulations and tests with signals recorded by the console. This verification leads to the implementation of the algorithm on the device. The algorithm is tested in real time, the results are evaluated and improvements suggested. / Denna rapport behandlar skattning av vattendjup med hjälp av ultraljudspulser och implementation av detta. Djupmätaren implementeras i en handhållen dykarkonsoll. Eftersom grundidén i ekolodning är att mäta tiden mellan att pulsen skickas iväg och att ekot tas emot är en stor del av utmaningen att hitta en lämplig metod för att skatta flykttiden för en signal i brus. Metoden ska passa för detta användingsområde och vara robust. Rapporten tar upp tidigare forskning gjord inom flykttidsestimering. De metoder som utvärderas för implementation är det matchade filtret, också kallad korrelationsmetoden, och linjär fas-metoden. Andra aspekter som avvägs och utreds är pulsfrekvens och pulsvaraktighet, ljudets hastighet och brus under vattnet. Metoderna för att skatta flykttid utvärderas genom simuleringar. Det matchade filtret bedöms vara lämpligt baserat på dessa simuleringar och experiment med data inspelad med konsollen. Denna verifikation leder till att algoritmen implementeras på konsollen. Den implementerade algoritmen testas i realtid, resultaten utvärderas och förbättringar föreslås.

Les colonnes à bulles sont largement utilisées dans les domaines du génie chimique et biologique, grâce à leur configuration simple, exempte de toute partie mobile. Néanmoins, leur extrapolation aux échelles industrielles engendre des modifications de l’hydrodynamique globale (vitesse du liquide, taille des bulles) qui sont encore difficile à prédire avec les outils numériques disponibles.La thèse a pour objectif d’établir une base de données sur l’évolution radiale et axiale de l’hydrodynamique locale (taux de vide, taille de bulles, vitesse liquide), dans différentes tailles de colonnes allant de 0.15 à 3 m de diamètre, pour des vitesses superficielles gaz comprises entre 3 et 35 cm/s, générant des taux de vide atteignant les 35%. Les mesures de taux de vide local, de vitesse de bulles et de la taille verticale des bulles sont réalisées à l’aide d’une sonde optique 1C. De plus, une nouvelle méthode pour mesurer la taille horizontale des bulles à fort taux de vide et en écoulement fortement multidirectionnel est proposée dans cette thèse. Cette méthode est basée sur la corrélation croisée spatiale de signaux provenant de deux sondes optiques placées parallèlement à la même élévation, et à une distance l’une de l’autre devant nécessairement être plus faibles que les bulles les plus petites présentes dans l’écoulement. Les mesures de taille de bulles sont validées en les comparant à un traitement d’images par endoscopie. Pour des vitesses superficielles de gaz supérieures à 9 cm/s, un bon accord est trouvé entre les trois méthodes (sonde optique 1C, corrélation croisée et endoscopie). La taille des bulles augmente légèrement lorsque la vitesse superficielle gaz augmente, par contre elle n’est pas impactée de manière significative par le diamètre des colonnes. Une plus grande ségrégation radiale est tout de même visible dans les plus grandes colonnes testées.Un modèle 1D radial développé pour un écoulement invariant le long de l’axe de la colonne est utilisé pour tester différents formalismes de forces de trainée, utilisant les données expérimentales de taille moyenne de bulles. Les simulations montrent que pour prédire correctement le flux gazeux expérimental, il est nécessaire d’introduire un « swarm factor » (Simonnet et al, 2008) diminuant le coefficient de trainée à fort taux de vide. De plus, des simulations 3D URANS avec Fluent® sont réalisées avec la loi de trainée validée par le modèle 1D précédemment cité. Un bon accord est observé entre les valeurs expérimentales et simulées des profils radiaux de taux de vide et de vitesse liquide, pour des diamètres de colonne allant de 0.4 m à 3 m, et pour des vitesses superficielle gaz de 3 à 35 cm/s. / Bubble columns reactors are widely used in chemical and biological engineering due to its simple configuration without mobile parts. However, the scale-up prediction of a bubble columns reactors is still a challenging process, due to the lack reliable experimental data and models.The present work aims to construct detailed database of the radial and axial evolution of local hydrodynamics properties (gas hold-up, bubble size and velocity, liquid velocity) acquired in several bubble columns in a scale factor of 20 (from 0.15 to 3 m in diameter), for a superficial gas velocity from 3 to 35 cm/s, yielding gas hold-ups up to 35 %. Measurements of local gas hold-up, bubble velocity and bubble vertical size are performed by a 1C mono-fiber optical probe. Moreover, a novel method to measure mean horizontal diameter of bubbles at high void fraction and in a multi-directional flow is proposed. This method is based in the spatial-cross correlation of signal of two optical probes placed parallel side by side, at a given distance from each other, at the same elevation in the column. The validation of the bubble size measurements are performed through a comparison of the results with an endoscopic imaging method. For superficial gas velocities higher than 9 cm/s, a good agreement is found between the three methods (1C mono-fiber optical probe, cross-correlation and endoscopic imaging). A slight increase is registered with the increase of the superficial gas velocity, however there is no significant variation with the column diameter.A 1-D radial model of a bubbly flow (Ueyama and Miyauchi, 1979) developed for a invariant flow along the column axis, is used to benchmark several classic formalisms of the drag force, using experimental average bubble size. Results show that to correctly predict the experimental gas flowrate, it is necessary to use a Swarm factor (Simonnet et al, 2008) that reduces the drag coefficient for high gas hold-up values. Moreover, Fluent® 3D URANS simulations are performed using the previously validated drag force formalism. A good agreement is found between experimental and simulated radial profiles of gas holdup and liquid velocity for column diameters ranging from 0.4 m up to 3 m in diameter in a range of superficial gas velocities from 3 cm/s to 35 cm/s.