Use of mathematical methods in the resolution of chemical engineering problems

This thesis consists of a compendium of five works that illustrate the utilization of selected mathematical methods to solve specific chemical engineering problems. Hence, the thesis is intended to cover both, a review of fundamental mathematical procedures for the solution of models raised from chemical phenomena, and a demonstration of their effectiveness to obtain useful novel significant results. The opening paper explores diverse global optimization algorithms to adjust both kinetic constants and the binary interaction parameters (BIPs) for the Peng-Robinson equation of state to the experimental data. Those parameters are essential to determine the model raised from the supercritical transesterification of triolein with methanol to produce biodiesel, with CO2 as cosolvent, consisting of three reversible reaction in series. Here, a novel model merging the ordinary differential equations system raised from kinetic mechanism and the time-dependent thermodynamic state of the complex mixture is presented for diverse operating conditions. Among all results obtained, novel binary interaction coefficients for the intermediate reaction species (dioleins and monooleins) highlight. The second and fourth papers included in this thesis are aimed at the study of lanolin extraction from raw wool, using 5% ethanol in CO2. The former explores solid lanolin extraction under near-critical conditions by means of a mass-transfer model based on the shrinking-core concept, while the latter is addressed at the liquid lanolin supercritical extraction. Both models result in a partial differential equations (PDEs) system determined by the solubility of multiphasic lanolin, Henry-type partition coefficient and the lanolin mass transfer coefficient. Hence, in each paper the raised PDEs system is solved through a different method: in the second paper orthogonal collocation method is employed, while in the fourth paper finite differences method is used combined with the numerical integration of an expression previously obtained by means of the Laplace transform. Finally, an optimization procedure is used in order to fit the extraction parameters to the experimental data, achieving coherent results that agree well with those previously reported. Between the cases exposed, liquid lanolin extraction is significantly complex to model because of the diffusion phenomena that may occur inside the two lanolin fraction mixture added to the diffusion of solvent in the interphase. Therefore, in the third work a nonlinear autoregressive exogenous neural network model is designed to predict the outcoming extracted fraction of lanolin at diverse temperatures, pressures, solvent mass flow rates, wool packing densities and times. The problem with the scarce data available for training of the neural network is overcome by augmenting experimental data using an empirical Weibull function, which correctly predicts the lanolin breakthrough at the extractor exit. This hybrid Weibull - Neural Network algorithm results in a low prediction error and conform a powerful tool for optimizing operating conditions, proved by the fast convergence of genetic algorithm procedure. This thesis closes with Molecular Dynamics simulations for peptide-folding studies, followed by a Principal Component Analysis (PCA) and clustering analysis to understand the Free Energy Landscape of the peptide (FEL). Those methods are aimed at assessing the conformational profile of bombesin, a peptide with interest in drug design as a possible novel agonist and/or antagonist in the fight against cancer. Results suggest that the peptide adopts mainly helical structures at the C-terminus and, to a lesser extent, hairpin turn structures at the N-terminus. Those results agree with those available from NMR in a 2,2,2-trifluoroethanol/water (30% v/v), and point out a suitable a-helix conformation for binding where Trp8 and His12 interaction has a significant role.Aquesta tesi consta d'un compendi de cinc treballs que il·lustren la utilització de mètodes matemàtics per resoldre problemes específics d'enginyeria química. Per tant, la tesi està destinada a ser una revisió dels procediments matemàtics fonamentals per a la solució de models derivats de fenòmens químics i, a més, una demostració de la seva efectivitat per obtenir resultats útils i innovadors. L'article que obre la tesi explora diferents algoritmes d'optimització global per ajustar tant les constants cinètiques com el Paràmetres d'Interacció Binària (PIB) per a l'equació d'estat de Peng Robinsos a les dades experimentals. Aquests paràmetres són essencials per determinar el model derivat de la transesterificació supercrítica de la trioleïna amb metanol per produir biodièsel, amb CO2 com a cosolvent, que consisteix en tres reaccions reversibles en sèrie. Aquí, es presenta un nou model que fusiona el sistema d'EDOs derivat del mecanisme cinètic i l'estat termodinàmic de la barreja per a condicions de funcionament diverses. Entre tots els resultats obtinguts, destaquen els nous PIBs trobats per a les espècies de reacció intermèdies. El segon i quart treball inclosos en aquesta tesi estan destinats a l'estudi de l'extracció de lanolina de llana crua amb 5% d'etanol en CO2. El primer explora l'extracció de lanolina sòlida en condicions gairebé crítiques mitjançant un model de transferència de massa basat en el concepte del nucli minvant, mentre que el segon s'adreça al cas de l'extracció supercrítica de lanolina líquida. Ambdós models donen com a resultat un sistema d'EDPs determinat per la solubilitat de la lanolina multifàsica, el coeficient de partició de Henry i el coeficient de transferències de massa. Per tant, a cada article el sistema d'EDPs obtingut es resol mitjançant un mètode diferent: en el article s'utilitza un mètode de col·laboració ortogonal, mentre que en el quart s'utilitza el mètode de diferències finites combinat amb la integració numèrica d'una expressió obtinguda mitjançant la Transformada de Laplace. Finalment, es porta a terme una optimització per ajustar els paràmetres d'extracció a les dades experimentals, aconseguint resultats coherents que coincideixen amb els reportats anteriorment. Entre els casos expotsats, l'extracció de lanolina líquida és significativament complexa de modelar a causa dels fenòmens de difusió que es poden produir a l'interior de les dues fraccions de lanolina a més de la difusió del dissolvent en la interfase. Per tant, en el tercer treball es dissenya un model de xarxa neuronal exògena no lineal autoregressiva per predir la fracció extreta de lanlina a diverses temperatures, pressions, cabals de dissolvent, densitats d'empaquetament i temps. El problema derivat de l'escassetat de dades disponibles per a l'entrenament de la xarxa neuronal es supera amb l'augment d'aquestes mitjançant una funció de Weibull empírica, que prediu correctament l'avanç de la lanolina a la sortida de l'extractor. Aquest algoritme híbrid Weibull - xarxa neuronal resulta en un baix error de predicció i conforma una potent eina per optimitzar les condicions operatives, demostrada per la ràpida convergència de l'algoritme genètic utilitzat. Aquesta tesi tanca amb simulacions de Dinàmica Molecular per a l'estudi del plegament de pèptids seguint d'un Anàlisi de Components Principals (ACP) i del "clustering" per a l'anàlisi del Paisatge d'Energia Lliure (PEL). L'objectiu és avaluar el perfil conformacional de la bombesina, un pèptid amb interès en el disseny de fàrmacs com a possible nou agonista i/o antagonista en la lluita contra el càncer. Els resultats suggereixen que el pèptid adopta estructures helicoïdals principalment al extrem C, i també en menor mesura estructures de forquilla al extrem N. Aquests resultats coincideixen amb els disponibles de RMN en 2,2-trifluoroetanol/aigua (30% v/v) i indiquen una conformació d’hèlix a adequada per a la unió on la interacció Trp8 i His12 té un paper important

Summaries of FY 1996 engineering research

This report documents the Basic Energy Sciences (BES) Engineering Research Program for fiscal year 1996; it provides a summary for each of the program projects in addition to a brief program overview. The report is intended to provide staff of Congressional committees, other executive departments, and other DOE offices with substantive program information so as to facilitate governmental overview and coordination of Federal research programs. Of equal importance, its availability facilitates communication of program information to interested research engineers and scientists. Each BES Division administers basic, mission oriented research programs in the area indicated by its title. The BES Engineering Research Program is one such program; it is administered by the Engineering and Geosciences Division of BES. In preparing this report the principal investigators were asked to submit summaries for their projects that were specifically applicable to fiscal year 1996. The summaries received have been edited if necessary, but the press for timely publication made it impractical to have the investigators review and approve the revised summaries prior to publication. For more information about a given project, it is suggested that the investigators be contacted directly

Application of Microbubbles Generated by Fluidic Oscillation in the Upgrading of Bio Fuels

With increasing energy demand and environmental concerns associated with the use of fossil-based fuels, the use of renewable sources of energy, such as biomass, has attracted considerable attention. Biofuels, such as bioethanol and bio-oil which are derived from the pyrolysis of biomass, are potential candidates to replace conventional fuels. However, the utilization of these fuels poses some challenges. In the case of bioethanol, it must have a composition higher than 98% to be used as an additive to gasoline in automobile engines. Pyrolysis oils, on the other hand, suffer from thermal instability, low heating values due to high water content and high acidity due to high acid content. In both cases, conventional distillation is not a feasible method for separation due to the azeotropic barrier, the high operating temperatures and the long residence times associated with its operation. The current work is a serious attempt to address these concerns by using a novel distillation technique mediated by hot microbubbles. The study suggests injecting a hot carrier gas in the form of microbubbles to remove the volatile components from the liquid phase and thus minimizing the sensible heat transfer to the liquid. Preliminary experiments were carried out with a 50 vol/vol ethanol-water mixture to evaluate the separation ability of microbubble mediated distillation. The experiments were planned based on a central composite rotatable design method, from which an empirical model was developed, giving an inference about the optimum operating conditions of the process. The results from the binary distillation experiments showed that upon decreasing the height of the liquid mixture in the bubble tank and increasing the temperature of air microbubbles, the separation efficiency of ethanol was improved significantly. Furthermore, it was demonstrated that separation can be achieved with only a small rise in the temperature of the liquid mixture, making this system suitable for treating thermally sensitive mixtures. Microbubble mediated distillation was successful for breaking the equilibrium barrier in separating liquid mixtures by traditional distillation. The enrichment of ethanol in the vapor phase was found to be higher than that predicted from equilibrium conditions for all liquid ethanol mole fractions considered, including the azeotrope, and within a very short contact time for the microbubbles in the liquid phase (i.e. thin liquid levels). Ethanol with a purity of 98.2% vol. was obtained using a thin liquid level of 3 mm in conjunction with a microbubble air temperature of 90C. Microbubble distillation was used to isolate the major problematic components, water and carboxylic acids, from a model bio-oil mixture. The model mixture was chosen to contain water, acetic acid and hydroxy propanone with concentrations close to those in real bio-oil mixtures. It was found that 84% of the water content and 75% of the corrosive acid content were removed from the model mixture after 150 min. These reductions, in turn, will increase the calorific value, reduce the corrosivity and improve the stability of the bio-oil mixture. This upgrading was accomplished with only a slight increase in the liquid temperature of about 5C under conditions of 3 mm liquid depth and 100C microbubble air temperature making this technique convenient for separating bio-oil mixtures without affecting their quality. A computational model of a single gas microbubble was developed using a Galerkin finite element method to complement the binary distillation experiments of ethanol-water mixtures. This model incorporates a novel rate law that evolves on a timescale related to the internal mixing of the microbubbles of 10-3 s. The model predictions were shown to be in very good agreement with the experimental data, demonstrating that the ratios of ethanol to water in the microbubble regime are higher than those predicted from equilibrium theory for all initial bubble temperatures and all liquid ethanol mole fractions considered. Furthermore, these ratios were achieved within very short contact times in the liquid mixture. The modelling data demonstrate that at shorter residence times, microbubbles are more efficient than fine bubbles in the separation process, however, as time passes the effect of bubble size diminishes. The modelling also showed improvements in the stripping efficiency of ethanol upon increasing the temperature of the air microbubbles, and an increase in the gas temperature with decreasing the residence time of the microbubbles. All of these results are consistent with experimental findings

Advanced Topics in Mass Transfer

This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics

APPLICATION OF MACHINE LEARNING TO CHF MODELLING

Accurate prediction of CHF is still a challenging issue in the study of boiling heat transfer. Many factors contribute to the occurrence of CHF and the various trigger mechanisms are proposed to unravel physical phenomena behind CHF. However, those mechanisms cannot cover the multiple primary factors simultaneously and even some of them still remain controversially unresolved. In light of the complexity and difficulty of CHF modelling, hereby an ensemble-learning based framework is proposed to model and predict CHF based on the databank of CHF. Some prior trials have been done for three primary aspects of dominant factors, that is, surface morphology, geometrical dimension and operation condition. These three primary constituents are respectively analyzed though three different sub-models of the ensemble framework in Chapter 3, 4 and 5. In Chapter Three, relevant experiments about micro-pillar enhanced CHF are reviewed and the corresponding databank of microstructure enhanced CHF is compiled based on those CHF experiments from published papers. Although the impacts of micro-pillars on CHF are still not clear, through qualitative analyses, the parametrical trends of CHF with respect to geometrical parameters of pillar array can be roughly foreseen. Meanwhile, this study also evaluates performance of prediction accuracy among four current physical models of microstructure-enhanced CHF. Comparative results show that two capillary wicking models have higher prediction accuracy. Particularly, a special terminology, zero-infinity convergence, is introduced to discuss the parametrical trends of CHF and qualitatively assess veracity of two capillary wicking models. Given the drawbacks of current physical models, the DBN is proposed to more accurately predict CHF and study parametric trends of CHF based on the microstructure enhanced CHF databank. Different from the training process of other regression modelling problems, constrained CHF points, which are artificially derived from the training data datasets, are required to be coupled with the raw training datasets for achieving the zero-infinity convergence of the DBN based CHF model, exhibiting accurate parametric trends of CHF and improving the prediction accuracy. This new training technique provides a new reliable solution to the similar constrained machine learning problems. Numerical results demonstrate that DBN can achieve the best performance of CHF prediction in terms of prediction accuracy. Through studying parametrical trends of CHF reveals that micro pillar arrays with the same parameters on heat transfer substrates with different dimensional sizes presents different CHF enhancement profiles. The presented methodology provides new insights for CHF modelling in pool boiling enhanced by other surface modification techniques, including porous layer coating, nanoparticle deposition, textured roughen, and nanowire fabrication. The effects of dimensions and materials of boiling surfaces on CHF are correlated and studied through the GRNN modelling in Chapter Four. Instead of inputting all parameters that indicate the thermal properties of materials into the trained model, the aggregated parameters from the primitive parameters of thermal properties, thermal activity and thermal diffusivity, are utilized as the input parameters of the trained model. This technique not only could capture the effects of thermal properties of materials on CHF effectively but also helps reduce the computational loads. The trained model shows the similar parametric trends of CHF to that of the traditional empirical correlation with respect to the thermal activity. If the thermal activity of heat transfer substrate is beyond a certain value, the corresponding effect of thermal activity will be absent, which somehow implies that the thickness of heat transfer substrate will not impact CHF after the asymptomatic thickness is reached. On the other hand, thermal diffusivity still affects CHF occurrence even if the effect of thermal activity is negligible. When coming to the effect of dimension size on CHF, it was found that when the side length of square heat transfer substrate is 5 times greater than the capillary length of working fluid, the CHF will be independent on the side length. Otherwise, CHF will be affected by the side length, and the influence of side length on CHF reaches ultimate if the side length of square boiling surface is exactly equal to the Raleigh-Plateau instability wavelength. This instability wavelength is only dependent on the thermal properties of working fluids, meaning that the optimal side length for CHF optimization is only related to the thermal properties of working fluid, namely, the surface tension, and the liquid and vapor densities of working fluid. In Chapter Five of this study, n-support vector machine is adopted to explore and study experimental strategies for the data-driven approaches of CHF look-up table construction, on the basis of sparingly-distributed experimental CHF data points. In the virtue of the CHF look-up table of Groeneveld et al (2007), those CHF data was used as the reference data of this research. In this data collection, CHF data of the subcooled flow boiling (Xe \u3c 0) is chosen to concentrate on the PWR steady-state condition because the in the normal operation of PWR, the system is under the subcooled flow boiling. The numerical results have demonstrated that ν-SVM trained by well sparsely-distributed training data in the parameter region of interest (pressure and mass flux) can yield a fairly acceptable degree of CHF prediction accuracy. Procuring training data points that can imply the parametric behaviors of CHF with respect to pressure and mass flux for support vector machine is the essential key of machine learning to achieving a high level of CHF prediction accuracy. For capturing the pressure-variant CHF behavior, training data that are in the proximity of the CHF inflection point significantly contribute to the improvement of prediction accuracy. Hence, training data preparation physics-informed with knowledge of CHF inflection points definitely augments the prediction accuracy of CHF. How the parametrical trends of CHF with respect to pressure and mass flux are close to the linear trends determines the level of prediction accuracy when lacking of a good spread of training data points. Besides, it is found that CHF extrapolation to a higher pressure with many data points collected at different low pressures can be effectively achieved by SVM if a few CHF data points are available under the high pressure, especially for PWR pressure of 15.5 MPa. This announces a possibility of strategic integration experiments between high pressure and low pressure, reducing experimental costs associated with the high pressure testing in terms of efforts and money. The proposed methodologies provides engineers and experimentalists with useful strategies to construct the look-up table tabulation of advanced cladding materials of ATFs. It is found out that there are multiple sub-problems that could be divided for CHF prediction and each sub-problem has its individual suitable machine learning model. Those prior work done by this study proves that the data-driven CHF modelling by sub-models can provide accurate CHF prediction under various scenarios and correct parametrical trends with respect to separate variables. Last but not least, another contribution of this thesis to the field of boiling heat transfer is that two databanks of experimental CHF data are compiled for the CHF enhancement by microstructures. The compiled databanks provide useful information and guidelines to the future design of surface structures that will possibly be applied to heat exchanger and nuclear fuel rod

First International Conference on Laboratory Research for Planetary Atmospheres

Proceedings of the First International Conference on Laboratory Research for Planetary Atmospheres are presented. The covered areas of research include: photon spectroscopy, chemical kinetics, thermodynamics, and charged particle interactions. This report contains the 12 invited papers, 27 contributed poster papers, and 5 plenary review papers presented at the conference. A list of attendees and a reprint of the Report of the Subgroup on Strategies for Planetary Atmospheres Exploration (SPASE) are provided in two appendices

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Characterization, modeling, and simulation of multiscale directed-assembly systems

Nanoscience is a rapidly developing field at the nexus of all physical sciences which holds the potential for mankind to gain a new level of control of matter over matter and energy altogether. Directed-assembly is an emerging field within nanoscience in which non-equilibrium system dynamics are controlled to produce scalable, arbitrarily complex and interconnected multi-layered structures with custom chemical, biologically or environmentally-responsive, electronic, or optical properties. We construct mathematical models and interpret data from direct-assembly experiments via application and augmentation of classical and contemporary physics, biology, and chemistry methods. Crystal growth, protein pathway mapping, LASER tweezers optical trapping, and colloid processing are areas of directed-assembly with established experimental techniques. We apply a custom set of characterization, modeling, and simulation techniques to experiments to each of these four areas. Many of these techniques can be applied across several experimental areas within directed-assembly and to systems featuring multiscale system dynamics in general. We pay special attention to mathematical methods for bridging models of system dynamics across scale regimes, as they are particularly applicable and relevant to directed-assembly. We employ massively parallel simulations, enabled by custom software, to establish underlying system dynamics and develop new device production methods

Pulsed-Laser Induced Dewetting of Metallic Nanostructures

This dissertation explores the fluid dynamics of nano and microscale liquid metal filaments, with an emphasis on experimentally investigating the influences and causes of filament breakup and metallic nanostructure formation. Understanding and manipulating the liquid state properties of materials, especially metals, have the potential to advance the development of future technology, particularly nanoscale technology. The combination of top-down nanofabrication techniques with bottom-up, intrinsic self-assembly mechanisms are a powerful fusion, because it permits new and unusual nanostructures to be created, whilst revealing interesting nanoscale physics. In fluid dynamics, wetting and dewetting is the spontaneous natural process that occurs when a liquid supported on a substrate seeks to minimize its systems energy. Either by covering the substrate surface, in the case of wetting, or by rupturing and assembling into a collection of smaller liquid fragments; typically droplets, with minimal contact and surface area with the substrate and the surrounding gaseous environment. Due to metal’s unique liquid state properties, like low viscosity and high surface energy, the dewetting phase is the prescient realm to experimentally access and study the governing dynamics, instabilities, and mass transport behind metallic nanostructure formation. The work contained in this dissertation seeks to address some basic scientific questions, such as: How to develop reasonably simple but predictive models to describe the competition between instability mechanisms that result in filament coalescence or fragmentation, as a function of filament extent? How to manipulate the intrinsic material properties of liquid metals, like surface energy, to initiate instabilities, like those similar to the Rayleigh-Plateau instability, to encourage self-assembly at the nanoscale? A focused and collaborative approach is contained herein where experiments will be used to drive theoretical and computational simulations and vice versa

Research and technology, fiscal year 1986, Marshall Space Flight Center

The Marshall Space Flight Center is continuing its vigorous efforts in space-related research and technology. Extensive activities in advanced studies have led to the approval of the Orbital Maneuvering Vehicle as a new start. Significant progress was made in definition studies of liquid rocket engine systems for future space transportation needs and the conceptualization of advanced laucnch vehicles. The space systems definition studies have brought the Advanced X-ray Astrophysics Facility and Gravity Probe-B to a high degree of maturity. Both are ready for project implementation. Also discussed include significant advances in low gravity sciences, solar terrestrial physics, high energy astrophysics, atmospheric sciences, propulsion systems, and on the critical element of the Space Shuttle Main Engine in particular. The goals of improving the productivity of high-cost repetitive operations on reusable transportation systems, and extending the useful life of such systems are examined. The research and technology highlighted provides a foundation for progress on the Hubble Space Telescope, the Space Station, all elements of the Space Transportation System, and the many other projects assigned to this Center