A consistent dimensional analysis of gas–liquid mass transfer in an aerated stirred tank containing purely viscous fluids with shear-thinning properties

This paper deals with gas–liquid mass transfer in an aerated stirred tank containing Newtonian or shearthinning fluids. The aim is to demonstrate that, for a given mixing system, an unique dimensionless correlation gathering all the mass transfer rates (150 kla measurements) can be obtained if and only if the variability of the rheological material parameters is correctly considered when implementing the theory of similarity. More particularly, it is clearly illustrated that a too gross simplification in the relevant list of the parameters characterizing the dependence of apparent viscosity with shear rates leads to pitfalls when building the PI-space set. This is then a striking example showing that a robust predictive correlation can be established when the non-constancy of fluid physical properties ceases to be neglected

Experimental and simulation studies on performance of a compact gas/liquid separation system

The need of exploiting the offshore oil reserves and reducing the equipment costs becomes the motivation for developing new compact separation techniques. In the past years, the development of compact separators has almost solely focused on the cyclonic type separators made of pipes, because of their simple construction, relatively low cost of manufacturing and being able to withstand high pressures. Considerable effort has been put into the separator test program and qualification, and consequently notable advances in the compact separation technique have been made. However the application has been held back due to lacking of reliable predicting and design tools. The objectives of this study were threefold. Firstly, an experimental study was carried out aiming at understanding the separation process and flow behaviours in a compact separator, named Pipe-SEP, operating at high inlet gas volume fraction (GVF). Secondly it is to gain insight of the gas and liquid droplet flow in the compact separator by means of Computational Fluid Dynamics (CFD) simulations. Last but not least, the understanding and insight gained above were used to develop a comprehensive performance predictive model, based on which, a reliable optimizing design procedure is suggested. An experimental study was carried out to test a 150-mm Pipe-SEP prototype with a water-air mixture. Three distinct flow regimes inside the Pipe-SEP were identified, namely swirled, agitated, and gas blow-by. The transition of the flow regimes was found to be affected by inlet flow characteristics, mixture properties, geometry of the separator, and downstream conditions. A predictive model capable of predicting the transition of flow regimes and the separation efficiency was developed. A comparison between the predicted result and experiment data demonstrated that the model could serve as a design tool to support decision-making in early design stages ... [cont.]

Bubble size, coalescence and particle motion in flowing foams

In minerals processing, froth flotation is used to separate valuable metal minerals from ore. The efficiency of a froth to recover these valuable minerals is closely related to the bubble size distribution through the depth of the froth. Measurement of the bubble size entering the froth and at the froth surface has been achieved previously; however measurement of the bubble size within the froth is extremely difficult as the mineral laden bubble surfaces are opaque and fragile. This work developed a flowing foam column to enable new measurement techniques, in particular visual measurement of the bubble size distribution and velocity profile throughout the depth of the foam. Two phase foam systems share their structure with three phase froth flotation systems, but are transparent in a thin layer. A foam column was constructed to contain a monolayer of overflowing and coalescing foam. This enabled direct measurement of the dynamic bubble size and coalescence through image analysis. The results showed a strong link between column geometry and the foam behaviour. In addition, the measured bubble streamlines closely matched simulated results from a foam velocity model. Positron Emission Particle Tracking (PEPT) is the only existing technique to measure particle behaviour inside froths. In this work, tracer particles with different size and hydrophobicity were tracked in a foam flowing column with PEPT. The particle trajectories were verified with image analysis, thereby increasing confidence in PEPT measurements of opaque flotation systems. The results showed that as hydrophilic tracer particles passed through the foam, their trajectory was determined by the local structure and changes of the foam, such as coalescence events. A hydrophobic tracer particle was involved in drop–off and reattachment events, however in the majority of cases still overflowed with the foam. The tracer particle did not always follow the bubble streamlines of the flowing foam, taking instead the shortest path to overflow which cut across streamlines. This work has developed an experimental methodology to validate flowing foam and coalescence models and has developed the necessary techniques to interpret PEPT trajectories in froth flotation

Multiphase contacting in PGM hydrometallurgy

This thesis describes hydrodynamic studies of the leach and solvent extraction stages of a Platinum Group Metal (PGM) hydrometallurgical flowsheet. The studies were motivated by the need to increase PGM throughput in Johnson Matthey’s PGM refining business. In the leach stage, key components in the feed are selectively dissolved using acids in a stirred tank before they are recovered by liquid-liquid (L-L) solvent extraction and finally purified. The work described in this thesis tackles four main areas: hydrodynamic studies of L-L PGM solvent extraction in both mixer and settler stages, whilst for the leach stage, studies of particle behaviour in gas evolving solid-liquid (S-L) reactions and gas-liquid-solid (GLS) characterisation by a novel Electrical Resistance Tomography (ERT) technique are performed. In the mixer-settler, the effects of impeller diameter, D, to vessel diameter, T, ratio (D/T), the phase flow ratio, cφ/dφ; (where cφis the continuous phase flow fraction and dφ is the dispersed phase flow fraction) and the specific power input,Tε, upon the droplet size distribution in a L-L system and their phase separation were investigated. Changing a smaller D/T impeller for a larger D/T impeller at constant P/V and cφ/dφincreased droplet size because the maximum shear rate decreased as a result of increasing ratio of impeller pumping capacity (Q) with tip speed (Utip). Changing a larger cφ/dφfor smaller cφ/dφat a fixed P/V and D/T impeller increased droplet size because turbulent dampening increased since the average density, ρ ∝ dφ. Meanwhile, Kolmogoroff-Hinze’s theory was shown to apply for the measured relationship between Tε and droplet size. A settler design criterion, which relates the dispersed phase concentration (Ca) in the dispersion band to the dispersed phase throughput (Qd/A) agreed with the model by Ryon et al. (1959). Ca was significantly dependent on P/V and Qd/A, whilst the effects of Qc/Qd (where Qc is the continuous phase flowrate and Qd is the dispersed phase flowrate) and D/T were minimal. Droplet size analysis of the sedimenting region of the dispersion band and dense packed layer revealed a transitional distribution of droplet sizes due to the counteracting effects of droplet sedimentation, hindered settling and droplet-droplet coalescence. Particle behaviour in gas evolving S-L systems were quantified using the Zwietering ‘just-suspended’ impeller speed (Njs) condition in a sponge nickel® and sodium hypochlorite system. The presence of gas caused Njs to increase, however a coherent relationship between Njs in an ungassed and gassed system 3 could not be easily ascertained. Further work with Positron Emission Particle Tracking (PEPT) was advised to quantify the relationship. A well-known electrical concept called skin effect, which describes how the effective resistance of an electrical conductor varies as the frequency of an alternating current (AC) increases and decreases, was used to investigate GLS behaviour via a novel ERT spectroscopic technique. The process relies on the change in effective resistance of conducting objects with changing AC frequency to selectively detect different phases. The concept was initially validated with static phantoms of a stainless steel and plume of gas before being applied to dispersible stainless steel particles and gas. ERT spectroscopy showed that two AC frequencies (0.3 kHz and 9.6 kHz) could successfully isolate and simultaneously detect the gas and solid phases at a fixed current. By subtracting solids and gas conductivity, the change in solids and gas holdup were obtained

Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods

The study and modelling of two-phase flow, even the simplest ones such as the bubbly flow, remains a challenge that requires exploring the physical phenomena from different spatial and temporal resolution levels. CFD (Computational Fluid Dynamics) is a widespread and promising tool for modelling, but nowadays, there is no single approach or method to predict the dynamics of these systems at the different resolution levels providing enough precision of the results. The inherent difficulties of the events occurring in this flow, mainly those related with the interface between phases, makes that low or intermediate resolution level approaches as system codes (RELAP, TRACE, ...) or 3D TFM (Two-Fluid Model) have significant issues to reproduce acceptable results, unless well-known scenarios and global values are considered. Instead, methods based on high resolution level such as Interfacial Tracking Method (ITM) or Volume Of Fluid (VOF) require a high computational effort that makes unfeasible its use in complex systems. In this thesis, an open-source simulation framework has been designed and developed using the OpenFOAM library to analyze the cases from microescale to macroscale levels. The different approaches and the information that is required in each one of them have been studied for bubbly flow. In the first part, the dynamics of single bubbles at a high resolution level have been examined through VOF. This technique has allowed to obtain accurate results related to the bubble formation, terminal velocity, path, wake and instabilities produced by the wake. However, this approach has been impractical for real scenarios with more than dozens of bubbles. Alternatively, this thesis proposes a CFD Discrete Element Method (CFD-DEM) technique, where each bubble is represented discretely. A novel solver for bubbly flow has been developed in this thesis. This includes a large number of improvements necessary to reproduce the bubble-bubble and bubble-wall interactions, turbulence, velocity seen by the bubbles, momentum and mass exchange term over the cells or bubble expansion, among others. But also new implementations as an algorithm to seed the bubbles in the system have been incorporated. As a result, this new solver gives more accurate results as the provided up to date. Following the decrease on resolution level, and therefore the required computational resources, a 3D TFM have been developed with a population balance equation solved with an implementation of the Quadrature Method Of Moments (QMOM). The solver is implemented with the same closure models as the CFD-DEM to analyze the effects involved with the lost of information due to the averaging of the instantaneous Navier-Stokes equation. The analysis of the results with CFD-DEM reveals the discrepancies found by considering averaged values and homogeneous flow in the models of the classical TFM formulation. Finally, for the lowest resolution level approach, the system code RELAP5/MOD3 is used for modelling the bubbly flow regime. The code has been modified to reproduce properly the two-phase flow characteristics in vertical pipes, comparing the performance of the calculation of the drag term based on drift-velocity and drag coefficient approaches.El estudio y modelado de flujos bifásicos, incluso los más simples como el bubbly flow, sigue siendo un reto que conlleva aproximarse a los fenómenos físicos que lo rigen desde diferentes niveles de resolución espacial y temporal. El uso de códigos CFD (Computational Fluid Dynamics) como herramienta de modelado está muy extendida y resulta prometedora, pero hoy por hoy, no existe una única aproximación o técnica de resolución que permita predecir la dinámica de estos sistemas en los diferentes niveles de resolución, y que ofrezca suficiente precisión en sus resultados. La dificultad intrínseca de los fenómenos que allí ocurren, sobre todo los ligados a la interfase entre ambas fases, hace que los códigos de bajo o medio nivel de resolución, como pueden ser los códigos de sistema (RELAP, TRACE, etc.) o los basados en aproximaciones 3D TFM (Two-Fluid Model) tengan serios problemas para ofrecer resultados aceptables, a no ser que se trate de escenarios muy conocidos y se busquen resultados globales. En cambio, códigos basados en alto nivel de resolución, como los que utilizan VOF (Volume Of Fluid), requirieren de un esfuerzo computacional tan elevado que no pueden ser aplicados a sistemas complejos. En esta tesis, mediante el uso de la librería OpenFOAM se ha creado un marco de simulación de código abierto para analizar los escenarios desde niveles de resolución de microescala a macroescala, analizando las diferentes aproximaciones, así como la información que es necesaria aportar en cada una de ellas, para el estudio del régimen de bubbly flow. En la primera parte se estudia la dinámica de burbujas individuales a un alto nivel de resolución mediante el uso del método VOF (Volume Of Fluid). Esta técnica ha permitido obtener resultados precisos como la formación de la burbuja, velocidad terminal, camino recorrido, estela producida por la burbuja e inestabilidades que produce en su camino. Pero esta aproximación resulta inviable para entornos reales con la participación de más de unas pocas decenas de burbujas. Como alternativa, se propone el uso de técnicas CFD-DEM (Discrete Element Methods) en la que se representa a las burbujas como partículas discretas. En esta tesis se ha desarrollado un nuevo solver para bubbly flow en el que se han añadido un gran número de nuevos modelos, como los necesarios para contemplar los choques entre burbujas o con las paredes, la turbulencia, la velocidad vista por las burbujas, la distribución del intercambio de momento y masas con el fluido en las diferentes celdas por cada una de las burbujas o la expansión de la fase gaseosa entre otros. Pero también se han tenido que incluir nuevos algoritmos como el necesario para inyectar de forma adecuada la fase gaseosa en el sistema. Este nuevo solver ofrece resultados con un nivel de resolución superior a los desarrollados hasta la fecha. Siguiendo con la reducción del nivel de resolución, y por tanto los recursos computacionales necesarios, se efectúa el desarrollo de un solver tridimensional de TFM en el que se ha implementado el método QMOM (Quadrature Method Of Moments) para resolver la ecuación de balance poblacional. El solver se desarrolla con los mismos modelos de cierre que el CFD-DEM para analizar los efectos relacionados con la pérdida de información debido al promediado de las ecuaciones instantáneas de Navier-Stokes. El análisis de resultados de CFD-DEM permite determinar las discrepancias encontradas por considerar los valores promediados y el flujo homogéneo de los modelos clásicos de TFM. Por último, como aproximación de nivel de resolución más bajo, se investiga el uso uso de códigos de sistema, utilizando el código RELAP5/MOD3 para analizar el modelado del flujo en condiciones de bubbly flow. El código es modificado para reproducir correctamente el flujo bifásico en tuberías verticales, comparando el comportamiento de aproximaciones para el cálculo del término dL'estudi i modelatge de fluxos bifàsics, fins i tot els més simples com bubbly flow, segueix sent un repte que comporta aproximar-se als fenòmens físics que ho regeixen des de diferents nivells de resolució espacial i temporal. L'ús de codis CFD (Computational Fluid Dynamics) com a eina de modelatge està molt estesa i resulta prometedora, però ara per ara, no existeix una única aproximació o tècnica de resolució que permeta predir la dinàmica d'aquests sistemes en els diferents nivells de resolució, i que oferisca suficient precisió en els seus resultats. Les dificultat intrínseques dels fenòmens que allí ocorren, sobre tots els lligats a la interfase entre les dues fases, fa que els codis de baix o mig nivell de resolució, com poden ser els codis de sistema (RELAP,TRACE, etc.) o els basats en aproximacions 3D TFM (Two-Fluid Model) tinguen seriosos problemes per a oferir resultats acceptables , llevat que es tracte d'escenaris molt coneguts i se persegueixen resultats globals. En canvi, codis basats en alt nivell de resolució, com els que utilitzen VOF (Volume Of Fluid), requereixen d'un esforç computacional tan elevat que no poden ser aplicats a sistemes complexos. En aquesta tesi, mitjançant l'ús de la llibreria OpenFOAM s'ha creat un marc de simulació de codi obert per a analitzar els escenaris des de nivells de resolució de microescala a macroescala, analitzant les diferents aproximacions, així com la informació que és necessària aportar en cadascuna d'elles, per a l'estudi del règim de bubbly flow. En la primera part s'estudia la dinàmica de bambolles individuals a un alt nivell de resolució mitjançant l'ús del mètode VOF. Aquesta tècnica ha permès obtenir resultats precisos com la formació de la bambolla, velocitat terminal, camí recorregut, estela produida per la bambolla i inestabilitats que produeix en el seu camí. Però aquesta aproximació resulta inviable per a entorns reals amb la participació de més d'unes poques desenes de bambolles. Com a alternativa en aqueix cas es proposa l'ús de tècniques CFD-DEM (Discrete Element Methods) en la qual es representa a les bambolles com a partícules discretes. En aquesta tesi s'ha desenvolupat un nou solver per a bubbly flow en el qual s'han afegit un gran nombre de nous models, com els necessaris per a contemplar els xocs entre bambolles o amb les parets, la turbulència, la velocitat vista per les bambolles, la distribució de l'intercanvi de moment i masses amb el fluid en les diferents cel·les per cadascuna de les bambolles o els models d'expansió de la fase gasosa entre uns altres. Però també s'ha hagut d'incloure nous algoritmes com el necessari per a injectar de forma adequada la fase gasosa en el sistema. Aquest nou solver ofereix resultats amb un nivell de resolució superior als desenvolupat fins la data. Seguint amb la reducció del nivell de resolució, i per tant els recursos computacionals necessaris, s'efectua el desenvolupament d'un solver tridimensional de TFM en el qual s'ha implementat el mètode QMOM (Quadrature Method Of Moments) per a resoldre l'equació de balanç poblacional. El solver es desenvolupa amb els mateixos models de tancament que el CFD-DEM per a analitzar els efectes relacionats amb la pèrdua d'informació a causa del promitjat de les equacions instantànies de Navier-Stokes. L'anàlisi de resultats de CFD-DEM permet determinar les discrepàncies ocasionades per considerar els valors promitjats i el flux homogeni dels models clàssics de TFM. Finalment, com a aproximació de nivell de resolució més baix, s'analitza l'ús de codis de sistema, utilitzant el codi RELAP5/MOD3 per a analitzar el modelatge del fluxos en règim de bubbly flow. El codi és modificat per a reproduir correctament les característiques del flux bifàsic en canonades verticals, comparant el comportament d'aproximacions per al càlcul del terme de drag basades en velocitat de drift flux model i de les basades en coePeña Monferrer, C. (2017). Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90493TESI

Mass Transfer in Multiphase Systems and its Applications

This book covers a number of developing topics in mass transfer processes in multiphase systems for a variety of applications. The book effectively blends theoretical, numerical, modeling and experimental aspects of mass transfer in multiphase systems that are usually encountered in many research areas such as chemical, reactor, environmental and petroleum engineering. From biological and chemical reactors to paper and wood industry and all the way to thin film, the 31 chapters of this book serve as an important reference for any researcher or engineer working in the field of mass transfer and related topics

Numerical modelling of polydispersed flows using an adaptive-mesh finite element method with application to froth flotation

An efficient numerical framework for the macroscale simulation of three-phase polydispersed flows is presented in this thesis. The primary focus of this research is on modelling the polydispersity in multiphase flows ensuring the tractability of the solution framework. Fluidity, an open-source adaptive-mesh finite element code, has been used for solving the coupled equations efficiently. Froth flotation is one of the most widely used mineral processing operations. The multiphase, turbulent and polydispersed nature of flow in the pulp phase in froth flotation makes it all the more challenging to model this process. Considering that two of the three phases in froth flotation are polydispersed, modelling this polydispersity is particularly important for an accurate prediction of the overall process. The direct quadrature method of moments (DQMOM) is implemented in the Fluidity code to solve the population balance equation (PBE) for modelling the polydispersity of the gas bubbles. The PBE is coupled to the Eulerian--Eulerian flow equations for the liquid and gas phases. Polydispersed solids are modelled using separate transport equations for the free and attached mineral particles for each size class. The PBE has been solved using DQMOM in a finite element framework for the first time in this work. The behaviour of various finite element and control volume discretisation schemes in the solution of the PBE is analysed. Rigorous verification and benchmarking is presented along with model validation on turbulent gravity-driven flow in a bubble column. This research also establishes the importance of modelling the polydispersity of solids in flotation columns, which is undertaken for the first time, for an accurate prediction of the flotation rate. The application of fully-unstructured anisotropic mesh adaptivity to the polydispersed framework is also analysed for the first time. Significant improvement in the solution efficiency is reported through its use.Open Acces

Modelling of the hydrodynamics of bubble columns using a two-fluid model coupled with a population balance approach

La simulazione di colonne a bolle in condizioni industriali è un problema di grande rilevanza. L’obiettivo principale di questo lavoro è prevedere con modelli computazionali la dimensione delle bolle, legata alla fluidodinamica dei reattori, considerando i fenomeni di rottura e di coalescenza. La validazione del modello è effettuata tramite il confronto con dati sperimentali appositamente raccolti, tra cui la dimensione delle bolle, ottenuta con un’innovativa tecnica di cross-correlazione. Gli esperimenti effettuati con acqua parzialmente contaminata e con acqua demineralizzata con l’eventuale aggiunta di etanolo, mostrano che gli additivi riducono la coalescenza e diminuiscono la dimensione media delle bolle. Sono stati inoltre utilizzati negli esperimenti con due sparger diversi, per disaccoppiare lo studio di rottura e coalescenza. I dati sperimentali sono stati utilizzati per convalidare simulazioni CFD 3D transitorie Euleriane-Euleriane. Il modello per la forza di trascinamento è corretto da un fattore di swarm per considerare l’effetto delle interazioni tra le bolle. Sono stati testati diversi modelli di turbolenza, nonché il contributo delle bolle sulla miscelazione degli scalari. Per prevedere la dimensione delle bolle, è stato utilizzato un bilancio di popolazione risolto con il metodo di quadratura dei momenti. Nella presente tesi viene proposto un set di kernel di rottura e coalescenza per prevedere le dimensioni delle bolle in diverse condizioni operative, considerando anche gli effetti dello scale-up.The simulation of bubble column reactors under industrial operating conditions is an exciting challenge. The main objective of this work is to predict the bubble size, in turn interconnected to the reactor hydrodynamic conditions, with computational models, by modelling bubble breakage and coalescence. Experimental data is collected for model validation, including bubble size measurements with an innovative cross-correlation technique. Experiments are carried out with tap water and demineralized water, with or without the addition of ethanol, and gathered results show that additives reduce coalescence and lower the mean bubble size. Two different spargers are used, in order to decouple the investigation of breakage and coalescence. The experimental data set is used to validate out unsteady three-dimensional Eulerian-Eulerian CFD simulations. A drag law for oblate bubbles is considered, together with a swarm factor, that accounts for the swarm effect. Several turbulence models are tested. The contribution of bubble induced turbulence (BIT) to scalar mixing is assessed. To predict bubble size, a population balance model is coupled to the hydrodynamic model and is solved with the quadrature method of moments. A set of breakage and coalescence kernels is proposed, capable of predicting the bubble size for different operating conditions. Scale-up effects are also investigated.La simulation de réacteurs à bulles en régime industriel est un grand défi. L'objectif principal de ce travail est la prédiction de la taille des bulles à l’aide d’un modèle numérique de bilan de population, basé sur la modélisation des phénomènes de brisure et de coalescence, et pouvant être couplé aux conditions hydrodynamiques présentes dans les réacteurs. Différentes données expérimentales sont obtenues pour valider le modèle. La taille des bulles est mesurée à l'aide d'une technique innovante de corrélation croisée. Les essais, réalisés en eau du réseau (partiellement contaminée) et en eau déminéralisée avec ajout éventuel d'éthanol, montrent que les additifs réduisent la coalescence et diminuent la taille moyenne des bulles. Deux distributeurs du gaz différents sont utilisés pour découpler l'étude de la brisure et de la coalescence. Les données expérimentales sont utilisées initialement pour valider des simulations CFD 3D transitoires Eulériennes-Eulériennes. La loi de traînée est corrigée par un facteur de swarm pour intégrer l’effet d’une fraction de gaz élevée. Différents modèles de turbulence sont testés. La contribution de la turbulence induite par les sillages de bulles au mélange de scalaires est évaluée. Enfin, pour prédire la taille des bulles, un bilan de population est couplé au modèle hydrodynamique préalablement validé et est résolu par la méthode de quadrature des moments (QMOM). Un set original de kernels de brisure et coalescence est proposé, capable de prédire la taille des bulles pour différentes conditions opératoires. Le comportement du modèle lors de l’extrapolation des réacteurs est également examiné