Yes / Reverse osmosis process is used in many industrial applications ranging from solute-solvent to solvent-solvent and gaseous separation. A number of theoretical models have been developed to describe the separation and fluxes of solvent and solute in such processes. This paper looks into the scope and limitations of two main models (the irreversible thermodynamics and the solution diffusion models) used in the past by several researchers for solute-solvent feed separation. Despite the investigation of other complex models, the simple concepts of these models accelerate the feasibility of the implementation of reverse osmosis for different types of systems and variety of industries. Briefly, an extensive review of these mathematical models is conducted by collecting more than 70 examples from literature in this study. In addition, this review has covered the improvement of such models to make them compatible with multi-component systems with consideration of concentration polarization and solvent-solute-membrane interaction.

La synthèse de matériaux polymères stables en milieu organique a été réalisée sur la base d’une série de copolymères à blocs de type polyuréthane. La synthèse de membranes denses autosupportées a permis la caractérisation des différents polyuréthanes et la sélection des formulations les plus adaptées pour l’obtention de membranes composites à peau dense. Les propriétés des membranes ont été ajustées par modulation des réactifs de départ. Une bonne résistance aux solvants organiques a été notée et les flux de perméation les plus importants ont été obtenus avec les matériaux les plus souples. Une membrane rigide a été testée pour la récupération du catalyseur Grubbs-HoveydaII du toluène. Malgré un faible taux de gonflement, le taux de rejet était limité à 48%, permettant de rompre avec l’idée liant la rigidité du réseau à une bonne sélectivité. Une démarche compréhensive du mécanisme de transport en nanofiltration organique (NFO) a été menée sur des membranes en polydiméthylsiloxane (PDMS). L’effet de la pression sur le gonflement a été examiné à travers deux appareils mimant les conditions de pression en NFO. Il a été démontré que la pression n’affectait pas l’équilibre amont de sorption mais induisait une diminution du gonflement de l’interface aval de la membrane. Le gradient de gonflement a été proposé comme force motrice du transport des solvants. La perméation des solvants purs et des solutés a été ensuite étudiée. Le modèle de solution-diffusion a pu être proposé comme mécanisme de transport des solvants purs. La sélectivité des membranes s’est avérée être indépendante de l’affinité solvant-membrane mais dépendante de l’affinité soluté - solvant et soluté - membrane / The synthesis of polymeric solvent stable materials was carried out on the basis of block copolymers polyurethane. A series of self-supported dense membranes allowed characterizing the different polymers and the selection of the most suitable ones to prepare composite membranes with a dense top layer. The properties of the membranes were adjusted by tailoring the starting reagents. Good resistance of the membranes in organic solvents was observed and the most important permeation flows were obtained with the softer materials. A rigid membrane was tested for the recovery of the Grubbs-HoveydaII catalyst from toluene. Despite a low swelling rate, the selectivity of the membrane was limited to 48%. This result is in contradiction with the common idea stating that high selectivity is due to rigid polymer network. A comprehensive approach of the transport mechanism in organic solvent nanofiltration (OSN) was conducted using polydiméthylsiloxane membranes (PDMS). The effect of pressure on the swelling was examined using two devices mimicking the pressure conditions in OSN. It has been shown that the pressure does not affect the upstream equilibrium sorption but induced a decrease of the swelling of the downstream interface of the membrane. The swelling gradient between the two sides of the membrane was proposed as driving force of solvents transport. The nanofiltration of solvents and solutes were then studied. The results showed that the solution–diffusion model was fully valid for pure solvents transport. The selectivity of the membrane was found to be independent of the membrane-solvent interaction but affected by the solute-membrane affinity and solute-solvent interaction

Diffusion equations arise in areas such as fluid mechanics, cellular biology, weather forecasting, electronics, mechanical engineering, atomic physics, environmental science, medicine, etc. This dissertation considers equations of this type that arise in mathematical finance. For over 40 years traders in financial markets around the world have used Black-Scholes equations for valuing financial options. These equations need to be solved quickly and accurately so that the traders can make prompt and accurate investment decisions. One way to do this is to use parallel numerical algorithms. This dissertation develops and evaluates algorithms of this kind that are based on the Laplace transform, numerical inversion algorithms and finite difference methods. Laplace transform-based algorithms have faced a legitimate criticism that they are ill-posed i.e. prone to instability. We demonstrate with reference to the Black-Scholes equation, contrary to the received wisdom, that the use of the Laplace transform may be used to produce reasonably accurate solutions (i.e. to two decimal places), in a fast and reliable manner when used in conjunction with standard PDE techniques. To set the scene for the investigations that follow, the reader is introduced to financial options, option pricing and the one-dimensional and two-dimensional linear and nonlinear Black-Scholes equations. This is followed by a description of the Laplace transform method and in particular, four widely used numerical algorithms that can be used for finding inverse Laplace transform values. Chapter 4 describes methodology used in the investigations completed i.e. the programming environment used, the measures used to evaluate the performance of the numerical algorithms, the method of data collection used, issues in the design of parallel programs and the parameter values used. To demonstrate the potential of the Laplace transform based approach, Chapter 5 uses existing procedures of this kind to solve the one-dimensional, linear Black-Scholes equation. Chapters 6, 7, 8, and 9 then develop and evaluate new Laplace transform-finite difference algorithms for solving one-dimensional and two-dimensional, linear and nonlinear Black-Scholes equations. They also determine the optimal parameter values to use in each case i.e. the parameter values that produce the fastest and most accurate solutions. Chapters 7 and 9 also develop new, iterative Monte Carlo algorithms for calculating the reference solutions needed to determine the accuracy of the LTFD solutions. Chapter 10 identifies the general patterns of behaviour observed within the LTFD solutions and explains them. The dissertation then concludes by explaining how this programme of work can be extended. The investigations completed make significant contributions to knowledge. These are summarised at the end of the chapters in which they occur. Perhaps the most important of these is the development of fast and accurate numerical algorithms that can be used for solving diffusion equations in a variety of application areas.

Providing sustainable supplies of water and energy is a critical global challenge. Polymer membranes dominate desalination and could be crucial to power generation applications, which include reverse osmosis (RO), nanofiltration (NF), forward osmosis (FO), pressure-retarded osmosis (PRO), electrodialysis (ED), membrane capacitive deionization (CDI), and reverse electrodialysis (RED). Improved membranes with tailored water and salt transport properties are required to extend and optimize these technologies. Water and salt transport structure/property relationships provide the fundamental framework for optimizing polymer materials for membrane applications. The water and salt transport and free volume properties of a series of sulfonated styrenic pentablock copolymers were characterized. The polymers' water uptake and water permeability increase with degree of sulfonation, and the block molecular weights could be used to tune water uptake, permeability, and selectivity properties. The presence of fixed charge groups, i.e., sulfonate groups, on the polymer backbone influence the material's salt transport properties. Specifically, the salt permeability increases strongly with increasing salt concentration, and this increase is a result of increases in both salt sorption and diffusivity with salt concentration. The data for the sulfonated polymers, including a sulfonated polysulfone random copolymer, are compared to those for an uncharged polymer to determine the influence of polymer charge on salt transport properties. The sulfonated styrenic pentablock copolymer permeability data are compared to literature data using the water permeability and water/salt selectivity tradeoff relationship. Fundamental transport property comparisons can be made using this relationship. The effect of osmotic de-swelling on the polymers and the transport properties of composite membranes made from sulfonated styrenic pentablock copolymers are also discussed. The sulfonated styrenic pentablock copolymers were exposed to multi-valent ions to determine their effect on the polymer's salt transport properties. Magnesium chloride permeability depends less on upstream salt concentration than sodium chloride permeability, presumably due to stronger association between the sulfonate groups and magnesium compared to sodium ions. Triethylaluminum was used to neutralize the polymer's sulfonic acid functionality and presumably cross-link the polymer. The mechanical, transport, and free volume properties of these aluminum neutralized polymers were studied. / text

Yes / CO2 capture from natural gas was experimentally and theoretically studied using a dead-end polymeric permeation cell. A numerical model was proposed for the separation of CO2/CH4 using Polytetrafluoroethylene (PTFE) in a flat sheet membrane module and developed based upon the continuity, momentum and mass transfer equations. The slip velocity condition was considered to show the reflection of gas flow in contact with the membrane surface. The solution method was based on the well-known SIMPLE algorithm and implemented using MATLAB to determine the velocity and concentration profiles. Due to change in velocity direction in the membrane module, the hybrid differencing scheme was used to solve the diffusion-convection equation. The results of the model were compared with the experimental data obtained as part of this work and good agreement was observed. The distribution of CO2 concentration inside the feed and permeate chambers was shown and the velocity profile at the membrane surface was also determined using reflection factor for polymericmembrane. The modelling result revealed that increasing the amount of CO2 in gas feed resulted in an increase in the CO2 in the permeate stream while the gas feed pressure increased. By changing the permeability, the model developed by use of the solution-diffusion concept could be used for all polymeric membranes with flat sheet modules.

yes / Reverse osmosis (RO) has become a significant method for removing salts and organic compounds from seawater and wastewater in recent decades. Spiral-wound module has been widely used due to a number of special features such as high packing density, premium separation and low operating cost. In this paper, a two-dimensional mathematical model is developed for the transport of dilute aqueous solutions through a spiral-wound RO module and the operational characteristics of the process under steady state conditions are analysed. The model is based on the solution-diffusion model coupled with the concentration polarization mechanism. This model yields a set of Differential and Algebraic Equations (DAEs), which are solved using the gPROMS software. The model is validated using experimental data from the literature for the rejection of dimethylphenol as solute in aqueous solutions. The model is then used to simulate the process under steady state conditions to gain deeper insight of the process.

Orientador: Maria Regina Wolf Maciel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-08T23:42:41Z (GMT). No. of bitstreams: 1 Perioto_FabianoRomero_D.pdf: 1193759 bytes, checksum: 59c15d9b760f3098c6e92c822d878e78 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho de tese, foram realizadas a modelagem e a simulação dos processos de separação pervaporação e osmose inversa aplicados a sistemas binários. A premissa empregada foi o desenvolvimento de metodologias de predição das variáveis de processo da pervaporação e osmose inversa independentes de dados experimentais destes processos; os dados necessários para a predição destas variáveis foram propriedades fundamentais dos componentes puros da alimentação. A partir de uma revisão bibliográfica dos modelos existentes para o processo de pervaporação, foi definida uma metodologia de predição das variáveis de processo baseado no modelo solução-difusão. A etapa inicial da metodologia foi o desenvolvimento de um programa de cálculo das composições de sorção na membrana, baseado no modelo UNIQUAC e no método de contribuição de grupos UNIFAC, adaptados ao uso de polímeros. O programa foi validado pela aplicação a sistemas ideais e não-ideais sob o ponto de vista termodinâmico. Os resultados empregando o modelo UNIQUAC apresentaram boaconcordância com os dados experimentais; no caso dos resultados obtidos via UNIFAC para solventes orgânicos obteve-se um bom ajuste dos dados experimentais, mas, no caso da água, os resultados obtidos pelo modelo não foram adequados. Na segunda etapa da metodologia, foram realizados o estudo da predição do coeficiente de difusão na membrana, a partir do modelo do volume livre, seguindo a abordagem de Fick e Maxwell-Stefan; a determinação dos parâmetros necessários ao respectivo modelo; a aplicação a casos estudos e uma análise paramétrica. Os resultados obtidos concordaram bem com os dados experimentais. Com isto, a partir dos valores de sorção e coeficientes de difusão, foi elaborado um programa para a predição do processo de pervaporação; o programa foi aplicado a casos estudos citados na literatura. Foi também estudada a aplicação da pervaporação ao sistema fenol-água, considerando uma membrana de poli (dimetil siloxano) como agente de separação. Os resultados concordaram bem com os dados experimentais disponíveis e mostraram que uma melhor seletividade e performance de separação foram obtidos em concentrações de fenol na alimentação inferiores a 0,2 % molar. A etapa final do trabalho foi a elaboração de um programa para simulação do processo de osmose inversa tendo como base um modelo derivado da mecânica-estatística. A partir dos parâmetros do modelo, foram preditos a rejeição e fluxo do permeado da mistura etanol-água em uma membrana de poliamida. O coeficiente de difusão de Maxwell-Stefan em alta pressão foi predito e empregado na simulação da osmose inversa / Abstract: In this work, the modelling and simulation of pervaporation and reverse osmosis processes for binary mixtures were carried out. The development of prediction methodologies for process variables of pervaporation and reverse osmosis without the necessity of experimental data was the general guideline followed; the experimental data used in these methodologies were the fundamental properties of pure components of feed. Based on the literature review for available models for pervaporation process, a prediction methodology according to the solution-difusion model was choosen and developed. The inicial step for the methodology elaboration was the development of a software for sorption composition determination in the membrane, based on the UNIQUAC model and UNIFAC group contribution method, both suitable for polymer applications. The software was validated applying it forideal and non-ideal systems on thermodynamic viewpoint. The results obtained according to the UNIQUAC model agreed well with experimental data; in the case of the results obtained by the UNIFAC method when applied for organic solvents, it was obtained a good agreement with experimental data, but, on the other hand, for the water, the results showed that the model must be improved. In the second step of methodology development, the study of the prediction of the diffusion coefficient in the membrane according Fick and Maxwell-Stefan approaches, the determination of models parameters, the validation of the prediction method with experimental data and a parametric sensitivity analysis were carried out. The results agreed well with experimental data. So, using the sorption compositions and diffusion coeficients calculated, it was developed a software for pervaporation prediction; the software was applied for some cases of literature. It was also studied the application of pervaporation to phenol-water system using poly(dimethylsiloxane) as selective barrier. The results agreed well with available experimental data and showed that a best selectivity and separation performance were achieved for phenol concentration lesser than 0.2% molar in the feed side. The final step of this work was the development of a software for simulation of reverse osmosis process based on a mecanical-statistical model. By using the model parameters, the rejection and permeate flux of ethanol-water mixture were predicted in a poliamide membrane. The diffusion coefficient of Maxwell-Stefan in high pressure was predicted and used in the reverse osmosis simulation / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

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