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We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damköhler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against published experimental data for the removal of Mercury(II) and CO2. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions, This publication is part of the research projects PID2020-115023RB-I00 (funding M. Aguareles, T.G. Myers, M. CalvoSchwarzwalder) financed by MCIN/AEI/ 10.13039/501100011033/. L.C. Auton and T.G. Myers acknowledge the CERCA Programme of the Generalitat de Catalunya for institutional support, their work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M). A. Valverde acknowledges support from the Margarita Salas UPC postdoctoral grants funded by the Spanish Ministry of Universities with European Union funds - NextGenerationEU. M. Aguareles acknowledges the support of the “consolidated research group” (Ref 2021 SGR01352) of the Catalan Ministry of Research and Universities. Open Access funding provided thanks to the CRUE-CSIC agreement with Elsevier, Postprint (published version)

Pinecone shells are assessed as a cost-effective biosorbent for the removal of metal ions Pb(II), Cu(II), Cd(II), Ni(II), and Cr(VI) in a fixed-bed column. Influent concentration, bed height, and flowrate are studied to improve efficiency. The breakthrough data is well fitted by the Sips adsorption model, suggesting a surface complexation mechanism, with maximum adsorption capacities of 11.1 mg/g for Cu(II) and 66 mg/g for Pb(II). In multimetal solutions, the uptake sequence at breakthrough and saturation is Pb(II) > Cu(II) > Cd(II). Characterization via FTIR and XRD reveals carboxyl and hydroxyl functional groups interacting with metal ions. Ca(II) does not compete with Pb(II), Cu(II), and Cd(II) adsorption, highlighting the ability of pinecone to adsorb heavy metals via surface complexation. Its application in the treatment of industrial effluents containing Cu(II), Ni(II), and Cr(VI) is explored. The study investigates bed media regeneration via eluting adsorbed metal ions with hydrochloric acid solutions. The potential of pinecone shells as an efficient biosorbent for removing toxic metal ions from industrial wastewater is emphasized. These findings enhance our understanding of the adsorption mechanism and underscore the fixed-bed column system's applicability in real-world scenarios, addressing environmental concerns related to heavy metal contamination of industrial effluents, This study was financed by the research project PID2019-107033GB- C22 (AEI/FEDER/UE) of the “Agencia Espa˜ nola de Investigaci´ on” MINECO. M.B. Amar and M. Mallek acknowledge the financial support of the Faculty of Science (University of Sfax, Tunisia) and of the Environmental and Analytical Chemistry Research Group of the Department of Chemistry (University of Girona, Spain). A. Cabrera-Codony and H. Monclús acknowledge Agencia Estatal de Investigaci´ on of the Spanish Ministry of Science, Innovation and Universities (MCIU) for partially funding this research through Juan de la Cierva (IJC2019-038874-I) and Ramon y Cajal (RYC2019-026434-I) Fellowships. LEQUIA has been recognized as a consolidated research group (Ref 2021 SGR1352) by the Catalan Ministry of Research and Universities. A. Valverde acknowledges support from the Margarita Salas UPC postdoctoral grants funded by the Spanish Ministry of Universities with European Union funds – NextGenerationEU (UNI/551/2021 UP2021- 034). This publication is part of the research projects PID2020- 115023RB-I00 (funding A. Cabrera-Codony and T. Myers) financed by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”. T. Myers acknowledges the CERCA Programme of the Generalitat de Catalunya and also the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M). Open Access funding provided thanks to the CRUE-CSIC agreement with Elsevier, Postprint (published version)

A mathematical model describing the erosion or leaching of a solid material by a flowing fluid in a column is developed. This involves an advection-diffusion equation coupled to a linear kinetic reaction describing the mass transfer between the solid and fluid. Two specific cases are analysed, the first where the extracted material has the same saturation solubility and rate of mass transfer throughout the process, the second where the solubility switches after a certain amount of erosion. In the first case there are only two model unknowns, the solubility and mass transfer coefficient, in the second there is a third unknown, the second solubility. Exploiting the fact that erosion is a slow process (relative to the flow rate) a perturbation solution based on the smallness of the amount removed is developed to describe the concentration and radius throughout the column. From this an analytical expression for the extracted fraction is obtained. The extracted fraction has a large linear section which results in a simple calculation to estimate the initial solubility from a very few or even a single data point. The remaining unknowns may also be easily calculated from the formula and later data points. A numerical solution, using finite differences, is developed to verify the perturbation solution. The analytical solution is also verified against experimental data for the removal of lanolin from wool fibres with a supercritical CO /ethanol solvent. Values for the mass transfer rate and two solubilities are obtained for different pressures and shown to provide excellent agreement with a series of experimental results for the extracted fraction., Peer Reviewed, Postprint (author's final draft)

In the present work, the results of a computational study aimed at assessing the conformational profile of bombesin are reported. The conformational space of the peptide was sampled by means of a 4 µs accelerated molecular dynamics simulation in water, using an explicit solvent model. The results were analyzed using Principal Component Analysis to get essential information on peptide fluctuations, along with cluster analysis to characterize different conformations in the sample. Analysis of the results suggests that the peptide adopts helical structures at the C-terminus that tend to unwind at the end of the peptide chain, since there are many structures exhibiting only two turns of a helix at the central segment of the peptide. In addition, the peptide also adopts hairpin turn structures at the N-terminus. Results of the simulation were confronted with available NMR results in a 2,2,2-trifluoroethanol/water (30% v/v) solution. Distances deduced form NOEs experiments only provide support to the presence of helical conformations that represent the most populated structures in the simulation. The absence of other conformations in the NMR experiments can be explained to be due to the a-helix enhancing nature of the solvent used in the experiments, Postprint (author's final draft)

Aplicat embargament des de la data de defensa fins al 9/10/2020, 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, 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 expr, Postprint (published version)

A new mathematical model is presented for the supercritical fluid extraction of lanoline from wool using near-critical ethanol-modified CO2, using our previous experimental data. The model is intended to account for the extraction of lanoline at conditions well above its melting point (60–80 °C) and pressures up to 150 bar. The model parameters are a Henry-type fluid-to-liquid partition coefficient for lanoline, K = Cg/CL, and a fluid-side mass-transfer coefficient, kG. For Re ~1, K is independent of velocity and wool packing density, but increases with pressure (K = 4 - 15 × 10-4). kG is found to be independent of temperature; it increases with velocity, decreases with pressure, and increases with wool packing density. The values found are kG = 5.66 × 10-6 m/s (70 bar) and kG = 1.51 × 10-6 m/s (150 bar), Postprint (published version)

Supercritical extraction of lanolin from raw wool with modified CO2 (5% ethanol) at temperatures above the melting point of lanolin (T = 36–42 ºC) is difficult to model because of the multicomponent diffusion in the liquid layer. In this work, a neural network model is proposed based on the experiments previously published by our research group. Experimentally, the extraction of a 100-cm3 packed bed of raw wool depends on five variables, i.e., temperature (60–80 ºC), pressure (120–200 bar), solvent mass flow rate (3–5 kg/h), wool packing density (127–318 kg/m3), and time (~ 1 h). A nonlinear autoregressive exogenous (5,3,1) neural network was designed and trained with the experimental data aug-mented using an empirical Weibull statistical function. This correctly predicts the lanolin breakthrough at the extractor exit with only ± 0.42% error. The simple arithmetics of neural network allows a fast optimization with Genetic Algorithm to find optimum operation conditions for the extraction process, Postprint (author's final draft)

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 reported, Postprint (published version)

A method is presented for the calculation of binary interaction parameters from reacting mixture data. The process studied is the supercritical methanol transesterification of triolein with CO2 as cosolvent. The reaction proceeds through 3 reversible reactions in series, on a solid catalyst (Nafion® SAC-13), for which the kinetics is known. To describe the reactor performance, the kinetic constants and the binary interaction parameters for the Peng-Robinson equation of state, are necessary, and were included in the reactor model. Previously published view-cell observations and thermodynamic calculations indicate that no condensation occurs in the reactor. Kinetic and thermodynamic parameters were determined by a global optimisation procedure. From the rate constants obtained, the process exhibits some reversibility, despite the excess of methanol used. Our methodology allows to obtain the binary interaction coefficients for the intermediate reaction species (dioleins and monooleins) that were unavailable so far. The method is sensitive to the errors in the measured concentrations, Postprint (author's final draft)

Due to the increase of municipal solid waste (MSW) as the population and their consume increase, new technologies of waste removal have to be developed, in order to find a MSW disposal method which do not fill lands and neither pollute the environment. Therefore, pyrolysis is raised as a way of MSW removal which at the same time can produce profitable products. This thesis is aimed at measuring the yields obtained from a pyrolysis process from different MSW mixtures, as well as the influence of temperature on the product yields is determined. For this purpose, a characterization of MSW components and the resulting products has been carried out by means of thermogravimetric, calorimetric and elemental analyses. After a quick introduction to the MSW production as well as the nowadays technologies of removal, the description of the equipment used during experimentation and discussion of results, the thesis arrives to final conclusions, where an overall view of the results is done., Outgoing