Particle modelling in biomass combustion using orthogonal collocation

Development of an accurate and computational efficient biomass particle model to predict particle pyrolysis and combustion is the focus of this paper. Partial differential equations (PDEs) for heat and mass balance are transformed into a system of coupled ordinary differential equations (ODEs) with the use of orthogonal collocation as the particle discretization method. The orthogonal collocation method is incorporated with comprehensive physicochemical mechanisms to predict the behavior of biomass components during particle pyrolysis and combustion. Heat adsorption by evaporated gas and water movement by diffusion inside the biomass matrix are included in the present work, in parallel with the effect of Stefan flow on the heat and mass transfer rates at the particle surface. Abandoning the classical interface-based modelling approach, the present approach allows decoupling between biomass components and spatial resolution, and the prediction of continuous intra-particle profiles. The new particle model is proven to be accurate and stable through its high degree of agreement with simulation results for particle pyrolysis and combustion experiments using different particle moisture contents and geometrical shapes. The intra-particle temperature gradient, as well as particle mass and size evolution, can be predicted accurately, as validated against experimental data. It is shown that six collocation points provide satisfying resolution. The computational efficiency is confirmed by the short simulation time that was found to be approximately three orders of magnitude faster than mesh-based simulations. This implies that the current model can be used for computational fluid dynamic (CFD) analysis through implementation as sub-grid-scale models to design, for example, biomass furnaces

Modelling and analysis of CVD processes for ceramic membrane preparation

A mathematical model is presented that describes the modified chemical vapour deposition (CVD) process (which takes place in advance of the electrochemical vapour deposition (EVD) process) to deposit ZrO2 inside porous media for the preparation and modification of ceramic membranes. The isobaric model takes into account intrapore Knudsen diffusion of ZrCl4 and H2O, which enter the membrane from opposite sides, and Langmuir-Hinshelwood reaction of the solid product ZrO2 on the internal pore wall. The processes occurring in one single pore are investigated, and the change in pore geometry during deposition is taken into account. Based upon this model, the deposition profile is studied. The model fits reasonably well with experimental results

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

The modeling and control of freeze dryers

Two models of the freeze drying process were constructed and used to study various operational policies in order to determine the policy that would provide the shortest drying times. The sublimation model which accounts only for the removal of frozen water, is found to predict shorter times for the free water removal phase than the sorption-sublimation model which properly accounts for the removal of frozen and bound water. This study shows that the policy which produces the shortest free water removal phase, also produces the shortest overall drying time. This policy, predicted by both models, holds the chamber pressure at its lowest value, heats the upper surface by radiation and the lower surface by conduction, the heating plates operate at different temperatures such that the melting and scorch constraints are both encountered and held during free water removal phase, and uses a low condenser temperature. During the free water removal phase, at least 80% of the total amount of heat supplied to the sample, is transferred through the frozen layer. The sorption-sublimation model provides sorbed water as well as temperature profiles in the dried layer during the free water removal phase and during the terminal drying phase. This study, by developing bound water profiles, incorporates an important factor for operational policies for quality retention in freeze drying. The temperature and sorbed water data predicted by the sorption-sublimation model during drying, can be combined with kinetic data on product deterioration to determine operational policies which may minimize not only the drying time but also the deteriorative changes. The economics of the freeze drying process were also studied, and it is shown that the policy that produces the shortest drying time, will operate the dryer most economically for a given sample thickness. The economic analysis suggests that large sample sizes would increase dryer capacity, and models which account for the removal of frozen water only, predict erroneous economic results --Abstract, pages iii-iv

Uncertainty Quantification and Apportionment in Air Quality Models using the Polynomial Chaos Method

Simulations of large-scale physical systems are often affected by the uncertainties in data, in model parameters, and by incomplete knowledge of the underlying physics. The traditional deterministic simulations do not account for such uncertainties. It is of interest to extend simulation results with ``error bars'' that quantify the degree of uncertainty. This added information provides a confidence level for the simulation result. For example, the air quality forecast with an associated uncertainty information is very useful for making policy decisions regarding environmental protection. Techniques such as Monte Carlo (MC) and response surface are popular for uncertainty quantification, but accurate results require a large number of runs. This incurs a high computational cost, which maybe prohibitive for large-scale models. The polynomial chaos (PC) method was proposed as a practical and efficient approach for uncertainty quantification, and has been successfully applied in many engineering fields. Polynomial chaos uses a spectral representation of uncertainty. It has the ability to handle both linear and nonlinear problems with either Gaussian or non-Gaussian uncertainties. This work extends the functionality of the polynomial chaos method to Source Uncertainty Apportionment (SUA), i.e., we use the polynomial chaos approach to attribute the uncertainty in model results to different sources of uncertainty. The uncertainty quantification and source apportionment are implemented in the Sulfur Transport Eulerian Model (STEM-III). It allows us to assess the combined effects of different sources of uncertainty to the ozone forecast. It also enables to quantify the contribution of each source to the total uncertainty in the predicted ozone levels

Extraction of solid lanoline from raw wool with near-critical ethanol-modified CO2 —A mass transfer model

This study deals with the modeling of the extraction of solid lanoline from raw wool under near-critical conditions using 5% ethanol in CO2, using our previous experimental data. A mass-transfer model is developed to explain the extraction results at T¿=¿30¿°C, below the melting point of lanoline (36–42¿°C). Two variables are studied, the extraction pressure and the solvent mass flowrate. Our model depends on three parameters: the solubilities of the two lanoline fractions and the lanoline mass transfer coefficient. The model is a set of first-order partial differential equations, that is solved by orthogonal collocation in combination of optimization of the parameters. The fluid-side mass-transfer coefficient decreases with extraction pressure and is about 5¿×¿10-6 m/s for Re < 1 (at 70–150¿bar) and depends on fluid velocity. The solubilities of lanoline fractions, independent of flowrate, agree very well with those previously reportedPostprint (published version