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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
511

Drowning-out crystallisation of benzoic acid : Influence of processing conditions and solvent composition on crystal size and shape

Holmbäck, Xiomara January 2002 (has links)
<p>The aim of the present investigation is to increase theunderstanding of the role played by the solvent in inhibitingor enhancing crystal growth. Drowning-out crystallizationexperiments has been performed by the controlled addition ofwater or ethanol water mixtures to a saturated solution ofbenzoic acid in ethanol-water mixtures. Crystal habitcontrolling factors have been identified.Seededcrystallization experiments have been carried out to evaluatethe effect of solvent composition on crystal habit at constantsupersaturation. The solubility of benzoic acid inethanol-water mixtures at the working temperatures has beendetermined.</p><p>Electro-zone sensing determinations and microscopicmeasurements are used to characterize the final crystallineproduct. It has been found that the shape of the benzoic acidcrystals grown from ethanol-water solutions ranges from needlesto platelets. Platy particles possess a predominant basal plane(001), bound by (010) and (100) faces, while needles aredeveloped along the b-axis. Long needle-shaped particles havebeen produced at low initial bulk concentration and highethanol concentration in the feed. Small platelets are obtainedat high initial bulk concentrations and high waterconcentration in the feed.</p><p>The effect of solvent composition on the growth rate hasbeen evaluated at constant supersaturation. Seed crystals arecharacterized by image analysis measurement both before andafter each experiment. Length and width dimensions have beenmeasured on the particle silhouette. The growth rate, thesolid-liquid interfacial energy and the surface entropy factorfor the (010) faces (length dimension) and (100) faces (widthdimension) have been estimated. The interfacial energy andsurface entropy factor decreases in the direction of increasingethanol concentration due to increasing solubility.</p><p>The results suggest that at low ethanol concentration(xEtOH<60%) growth proceeds by screw dislocation mechanism,and adsorption of ethanol molecules may reduce the growth rate.As the ethanol concentration increases above a critical value(xEtOH ≥60%), the growth mechanism shifts to surfacenucleation and the growth rate increases with increasingethanol concentration. It has been suggested that the observedeffect of the solvent composition on crystal habit is theresult of two conflicting effects here referred as the kineticand interfacial energy effects. High interactions of the pairethanol-benzoic acid seem to be responsible of the growthretardation (kinetic effect) exerted by the solvent. On theother hand, increased ethanol concentration leads to reduceinterfacial energy and increasing surface nucleation whichmight contribute to enhance growth kinetics.</p><p><b>Keywords:</b>drowning-out crystallisation, solventcomposition, benzoic acid, solubility, crystal growth,interfacial energy, surface entropy factor, growth mechanism,crystal shape distribution.</p>
512

Influence of Admixtures on Crystal Nucleation of Vanillin

Pino-García, Osvaldo January 2004 (has links)
<p>Admixtures like reactants and byproducts are solublenon-crystallizing compounds that can be present in industrialsolutions and affect crystallization of the main substance.This thesis provides experimental and molecular modellingresults on the influence of admixtures on crystal nucleation ofvanillin (VAN). Seven admixtures: acetovanillone (AVA),ethylvanillin (EVA), guaiacol (GUA), guaethol (GUE), 4-hydroxy-acetophenone (HAP), 4-hydroxy-benzaldehyde (HBA), andvanillic acid (VAC) have been used in this study. Classicalnucleation theory is used as the basis to establish arelationship between experimental induction time andsupersaturation, nucleation temperature, and interfacialenergy. A novel multicell device is designed, constructed, andused to increase the experimental efficiency in thedetermination of induction times by using 15 nucleation cellsof small volumes simultaneously. In spite of the largevariation observed in the experiments, the solid-liquidinterfacial energy for each VAN-admixture system can beestimated with an acceptable statistical confidence. At 1 mole% admixture concentration, the interfacial energy is increasedin the presence of GUA, GUE, and HBA, while it becomes lower inthe presence of the other admixtures. As the admixtureconcentration increases from 1 to 10 mole %, the interfacialenergy also increases. The interfacial energies obtained are inthe range 7-10 mJ m<sup>-2</sup>. Influence of admixtures on metastable zone widthand crystal aspect ratio of VAN is also presented. Theexperimental results show that the admixtures studied arepotential modifiers of the nucleation of VAN. Molecularmodelling by the program Cerius2 is used to identify the likelycrystal growth faces. Two approaches, the surface adsorptionand the lattice integration method, are applied to estimatequantitatively the admixture-crystal interaction energy on thedominating crystal faces of VAN,<i>i.e</i>., {0 0 1} and {1 0 0}. However, a simple and clearcorrelation between the experimental values of interfacialenergy and the calculated interaction energies cannot beidentified. A qualitative structural analysis reveals a certainrelationship between the molecular structure of admixtures andtheir effect on nucleation. The determination of the influenceof admixtures on nucleation is still a challenge. However, themolecular and crystal structural approach used in this thesiscan lead to an improved fundamental understanding ofcrystallization processes. Keywords: Crystallization,nucleation, vanillin, admixtures, additives, impurities,induction time, interfacial energy, molecular modelling,interaction energy.</p>
513

Gas transport properties of poly(n-alkyl acrylate) blends and modeling of modified atmosphere storage using selective and non-selective membranes

Kirkland, Bertha Shontae, 1976- 29 August 2008 (has links)
The gas transport properties of side-chain crystalline poly(n-alkyl acrylate) and poly(m-alkyl acrylate) blends are determined as a function of temperature for varying side-chain lengths, n and m, and blend compositions. The side chains of poly(n-alkyl acrylate)s crystallize independently of the main chain for n [is greater than or equal to] 10 which leads to an extraordinary increase in the permeability at the melting temperature of the crystallites. The compatibility of these polymers are examined and macroscopic homogeneity is observed for a small range of n and m when the difference /n - m/ is between 2 - 4 methylene units. Thermal analysis shows that the blend components crystallize independently of one another; at the same time, the crystallization of each component is hindered by the presence the other component. The permeation responses of these blends show two distinct permeation jumps as the crystallites from each component melt at their respective melting temperatures. Blends with continuous permeation responses are found to have higher effective activation energies than observed for common polymers. Thermal analysis proved to be a useful tool to help predict the permeation response for poly(alkyl acrylates); thus the thermal behavior of poly(n-alkyl acrylate) blended with n-aliphatic materials and random copolymers of poly(n-alkyl acrylates) are briefly examined. A bulk modified atmospheric storage design is proposed where produce is stored in a rigid chamber that is equipped with both selective and non-selective membrane modules that help regulate the oxygen entering and the carbon dioxide leaving the produce compartment. The design enables control of the atmosphere inside the chamber by modulating gas flow, i.e. the gas flow rate and composition, through the non-selective membrane by delivering fresh air upstream of the non-selective membrane. The model shows that the choice of materials for the selective and non-selective membranes dictate the range of concentrations achievable; however, the air flow rate allows the control between these ranges. The method to design a practical chamber from this model is also described.
514

Soft Colloids from p(NIPAm-co-AAc): Packing Dynamics and Structure

Muluneh, Melaku 03 August 2012 (has links)
Traditionally, the experimental model of choice for studying the structure and dynamics of glasses or crystals are hard-sphere colloids. An analogy with molecular or atomic materials is often drawn, in which each colloidal particle represents an atom or a molecule. Making the individual particles deformable allows an even wider range of phenomena to be observed. In this thesis, I report the three-dimensional confocal microscopic study of the structure and dynamics of aqueous suspensions of fluorescently labeled poly(N-Isopropylacrylamide)-co-(Acrylic Acid), or p(NIPAm-co-AAc), microgel particles of hydrodynamic diameter 1.0 - 1.5 μm. Image analysis techniques and particle tracking algorithms are used to quantify the particle dynamics and the suspension structure. The phase behavior of the suspensions is dependent on a number of factors including pH, temperature, and concentration. By adjusting the pH, the interactions between the microgel particles can be tuned from purely repulsive near neutral pH, to weakly attractive at low pH. At low pH and low concentration, dynamic arrest results mainly from crystallization driven by the attraction between particles; crystal nucleation occurs homogeneously throughout the sample. The dynamics is nucleation limited where fast crystallization follows a delay time. At low pH and high concentration, relaxation of the suspension is constrained and it evolves only slightly to form disordered solid. At neutral pH, the dynamics are a function of the particle number concentration only; a high concentration leads to the formation of a disordered soft glassy solid. Additionally, the three-dimensional image stacks are studied to determine crystal structure by calculating pair correlation functions, g(r), bond order parameters, and structure factors, s(q). The results show that crystal structure is independent of concentration, charge, size, and stiffness of particles remaining FCC under all conditions. At low concentrations and low pH, the structures formed are polycrystalline solids. Moreover, the ability of the particles to compress enables the suspensions to maintain their crystal structure when subjected to external stress. The results help us better understand the relationship between dynamics and structure in soft colloidal suspensions, enhance our ability to use the colloids to model materials, and improve applications of the colloids in industrial products. / Physics
515

Basaltic volcanism : deep mantle recycling, Plinian eruptions, and cooling-induced crystallization

Szramek, Lindsay Ann 04 March 2011 (has links)
Mafic magma is the most common magma erupted at the surface of the earth. It is generated from partial melting of the mantle, which has been subdivided into end-members based on unique geochemical signatures. One reason these end members, or heterogeneities, exist is subduction of lithospheric plates back into the mantle. The amount of elements, such as Cl and K, removed during subduction and recycled into the deep mantle, is poorly constrained. Additionally, the amount of volatiles, such as Cl, that are recycled into the deep mantle will strongly affect the behavior of the system. I have looked at Cl and K in HIMU source melts to see how it varies. Cl/Nb and K/Nb suggest that elevated Cl/K ratios are the result of depletion of K rather than increased Cl recycled into the deep mantle. After the mantle has partially melted and mafic melt has migrated to the surface, it usually erupts effusively or with low explosivity because of its low viscosity, but it is possible for larger eruptions to occur. These larger, Plinian eruptions, are not well understood in mafic systems. It is generally thought that basalt has a viscosity that is too low to allow for such an eruption to occur. Plinian eruptions require fragmentation to occur, which means the melt must undergo brittle failure. This may occur if the melt ascends rapidly enough to allow pressure to build in bubbles without the bubbles expanding. To test this, I have done decompression experiments to try to bracket the ascent rate for two Plinian eruptions. One eruption has a fast ascent, faster than those seen in more silicic melts, whereas the other eruption is unable to be reproduced in the lab, however it began with a increased viscosity in the partly crystallized magma. After fragmentation and eruption, it is generally thought that tephra do not continue to crystallize. We have found that crystallinity increases from rim to core in two basaltic pumice. Textural data along with a cooling model has allowed us to estimate growth rates in a natural system, which are similar to experimental data. / text
516

Dissolving the Rocks : Solubility Enhancement of Active Pharmaceutical Ingredients using Mesoporous Silica

Xia, Xin January 2014 (has links)
Poor aqueous solubility is one of the greatest barriers for new drug candidates to enter toxicology studies, let alone clinical trials. This thesis focuses on contributing to solving this problem, evaluating the oral toxicity of mesoporous silica particles, and enhancing the apparent solubility and bioavailability of active pharmaceutical ingredients in vitro and in vivo using mesoporous silica particles. Toxicological studies in rats showed that two types of mesoporous silica particles given by oral administration were well tolerated without showing clinical signs of toxicity. Solubility enhancement, including in vivo bioavailability and in vitro intracellular activity, has been evaluated for selected drug compounds. Mesoporous silica was shown to effectively increase drug solubility by stabilizing the amorphous state of APIs, such as itraconazole (anti-fungal), dasatinib (anti-cancer), atazanavir (anti-HIV) and PA-824 (anti-tuberculosis). Itraconazole was successfully loaded into a variety of porous silica materials showing a distinct improvement in the dissolution properties in comparison to non-porous silica materials (and the free drug). Microporosity in SBA-15 particles has advantages in stabilizing the supersaturation state of dasatinib. Small pore sizes show better confinement of atazanavir, contributing to a higher dissolution of the drug compound. In the in vivo animal studies, NFM-1 loaded with atazanavir shows a four-fold increase in bioavailability compared to free crystalline atazanavir. PA-824 has a higher dissolution rate and solubility after loading into AMS-6 mesoporous particles. The loaded particles show similar antibacterial activity as the free PA-824. This thesis aims at highlighting some of the important factors enabling the selection of adequate mesoporous structures to enhance the pharmacokinetic profile of poorly water-soluble compounds, and preparing the scientific framework for uncovering the effects of drug confinement within mesopores of varying structural properties. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: Submitted. Paper 5: Submitted.</p>
517

Διαχωρισμός και ανάκτηση φαινολικών ενώσεων από απόβλητα ελαιοτριβείου με τη μέθοδο της ψυχόμενης κρυστάλλωσης / Removal and recovery of phenolic compounds from olive mill wastewaters by cooling crystallization

Κοντός, Σπυρίδων 27 April 2015 (has links)
Μεταξύ των χρήσιμων συστατικών των παραπροϊόντων των υγρών εκροών ενός ελαιοτριβείου είναι οι φαινολικές ουσίες οι οποίες χαρακτηρίζονται από την υψηλή αντιοξειδωτική τους δράση. Οι φαινολικές ενώσεις, εφόσον ανακτηθούν, είναι δυνατόν να αξιοποιηθούν εμπορικά, αφού μπορούν να χρησιμοποιηθούν σε πολύ σημαντικούς τομείς όπως στην προστασία της υγείας του ανθρώπου (προστασία από τον διαβήτη, τον καρκίνο), στην βιομηχανία τροφίμων, στην κοσμετολογία κλπ.. Στην παρούσα εργασία, εξετάστηκε ο διαχωρισμός και η ανάκτηση των φαινολικών ενώσεων με τη μέθοδο της κρυστάλλωσης με ψύξη, από υδατικά διαλύματα. Οι φαινολικές ενώσεις που επιλέχθηκαν για μελέτη ήταν η φαινόλη κινναμικό οξύ [trans-cinnamic acid (TCA)] και η φαινόλη φερουλικό οξύ [ferulic acid (FA)]. Η επιλογή τους έγινε γιατί η χαμηλή διαλυτότητα τους, σε σύγκριση με τις αντίστοιχες της τυροσόλης και της υδροξυτυροσόλης, καθιστά πιο εύκολη τη διερεύνηση της επιλεκτικής τους κρυστάλλωσης στην ψυχόμενη επιφάνεια. Η πειραματική διαδικασία πραγματοποιούταν σε αντιδραστήρα διαλείποντος έργου όγκου, με διπλότοιχα τοιχώματα σε σταθερή θερμοκρασία η οποία ρυθμιζόταν με την βοήθεια θερμοστάτη ανακυκλοφορίας. Το προς κρυστάλλωση διάλυμα εισαγόταν στον αντιδραστήρα και θερμαινόταν σε σταθερή θερμοκρασία. Η κρυστάλλωση λάμβανε χώρα πάνω σε μια ψυχόμενη κυλινδρική επιφάνεια ανοξείδωτου χάλυβα που εμβαπτιζόταν στο διάλυμα. Η θερμοκρασία στην κυλινδρική επιφάνεια διατηρούνταν σταθερή. Ακολούθως, μετά το πέρας του κύκλου κρυστάλλωσης, οι κρύσταλλοι συλλέγονταν για την περαιτέρω ανάλυσή τους. Τα ποσοστά ανάκτησης των πολυφαινολών που επιτεύχθηκαν στην παρούσα εργασία, ήταν ιδιαίτερα υψηλά και ειδικότερα στα πειράματα που περιλάμβαναν διαλύματα υψηλού υπερκορεσμού και χαμηλής θερμοκρασίας ψυχόμενης επιφάνειας. Η παρακολούθηση της μεταβολής της θερμοκρασίας από την ψυχρή επιφάνεια προς τα τοιχώματα του αντιδραστήρα (στην ακτινική διεύθυνση) ως συνάρτηση του χρόνου, δίνει πληροφορίες για το σημείο έναρξης και για την ολοκλήρωση της διεργασίας της κρυσταλλικής ανάπτυξης. Σκοπός της παρούσας εργασίας είναι η κατάστρωση και επίλυση των ισοζυγίων μάζας και ενέργειας καθώς και ο προσδιορισμός (θεωρητικός και πειραματικός) του πάχους του αποτιθέμενου στερεού στην ψυχόμενη επιφάνεια. Η επίλυση των μερικών διαφορικών εξισώσεων δίνει αναλυτικές λύσεις για την κατανομή του προφίλ της υπέρψυξης και της συγκέντρωσης ως προς τα φαινολικά κλάσματα κατά μήκος του αντιδραστήρα. Δεδομένου ότι η υπέρψυξη αποτελεί και την κινούσα δύναμη για την κρυσταλλική ανάπτυξη, παρατηρήθηκε ότι ήταν δυνατή η αριστοποίηση της ανάκτησης των φαινολικών ενώσεων από υπέρθερμα διαλύματα με τη μέθοδο της κρυστάλλωσης με ψύξη. Το ποσοστό ανάκτησης που επιτεύχθηκε ήταν περίπου . Παράλληλα εξετάστηκε επίδραση της συναγωγής στην κρυσταλλική ανάπτυξη. Αυξανομένης της γωνιακής ταχύτητας, ευνοείται η κρυστάλλωση στο κυρίως διάλυμα και παρουσιάζεται μια μείωση στο τελικό ανακτώμενο στερεό μιας και τα moles της προς κρυστάλλωση ουσίας δεν έχουν τον απαραίτητο χρόνο να διαχυθούν και να κρυσταλλωθούν επιλεκτικά στην περιοχή όπου παρουσιάζεται διαφορά συγκέντρωσης. Η τελική σειρά πειραμάτων αφορούσε πειράματα κρυστάλλωσης με ψύξη μίγματος πολυφαινολών καθώς και προκαταρκτικών πειραμάτων αποβλήτου ελαιοτριβείου με σκοπό τη διερεύνηση της δυνατότητας ανάκτησης των πολυφαινολών από διάφορα διαλύματα και άπο το απόβλητο αντίστοιχα. Σε όλα τα παραπάνω, ο προσδιορισμός της υγρασίας στο στερεό κρυσταλλικό στρώμα ήταν υψίστης σημασίας για τον έλεγχο της καθαρότητας των ανακτώμενων κρυστάλλων. Το ποσοστό υγρασίας που προσδιορίστηκε ήταν πολύ μικρό και περίπου ίδιο με το αντίστοιχο ποσοστό των συνθετικών φαινολών / Phenolic compounds are among, the most complex and the most difficult to remove compounds from the by-products of olive mill wastewaters (OMW). Due to significant properties, including stability and anti-oxidative activity, the recovery of poly-phenols (PP) from OMW is of paramount importance. In the present work, trans-cinnamic acid and ferulic acid, model compounds for the PP present in OMW were removed by cooling crystallization from aqueous solutions. Cooling crystallization experiments were done in a batch reactor kept at constant temperature. Solutions of the two tested PP were prepared in the reactor and were allowed to equilibrate. Crystallization took place on the surface of a cylindrical stainless steel (SS) metal tube immersed into the supercooled solution. The SS surface was cooled at a lower temperature with respect to the respective melting point. With respect to each of the PP studied, the respective solubilities as a function of temperature were measured. The formation of PP crystal layers on the SS tube surface took place without any appreciable induction time. In the series of experiments done, the temperature and concentration profile in the batch reactor in the presence of the cooled SS surface were calculated on the basis of mass and heat transport equations for unstirred systems. The imposed super-cooling from the cold surface to the bulk solution, which is the driving force for the crystallization of the phenolic compounds on the SS surface, was thus estimated.
518

Process measurements and kinetics of unseeded batch cooling crystallization

Li, Huayu 08 June 2015 (has links)
This thesis describes the development of an empirical model of focus beam reflectance measurements (FBRM) and the application of the model to monitoring batch cooling crystallization and extracting information on crystallization kinetics. Batch crystallization is widely used in the fine chemical and pharmaceutical industries to purify and separate solid products. The crystal size distribution (CSD) of the final product greatly influences the product characteristics, such as purity, stability, and bioavailability. It also has a great effect on downstream processing. To achieve a desired CSD of the final product, batch crystallization processes need to be monitored, understood, and controlled. FBRM is a promising technique for in situ determination of the CSD. It is based on scattering of laser light and provides a chord-length distribution (CLD), which is a complex function of crystal geometry. In this thesis, an empirical correlation between CSDs and CLDs is established and applied in place of existing first-principles FBRM models. Built from experimental data, the empirical mapping of CSD and CLD is advantageous in representing some effects that are difficult to quantify by mathematical and physical expressions. The developed model enables computation of the CSD from measured CLDs, which can be followed during the evolution of the crystal population during batch cooling crystallization processes. Paracetamol, a common drug product also known as acetaminophen, is selected as the model compound in this thesis study. The empirical model was first established and verified in a paracetamol-nonsolvent (toluene) slurry, and later applied to the paracetamol-ethanol crystallization system. Complementary to the FBRM measurements, solute concentrations in the liquid phase were determined by in situ infrared spectra, and they were jointly implemented to monitor the crystallization process. The framework of measuring the CSD and the solute concentration allows the estimation of crystallization kinetics, including those for primary nucleation, secondary nucleation, and crystal growth. These parameters were determined simultaneously by fitting the full population balance model to process measurements obtained from multiple unseeded paracetamol-ethanol crystallization runs. The major contributions of this thesis study are (1) providing a novel methodology for using FBRM measurements to estimate CSD; (2) development of an experimental protocol that provided data sets rich in information on crystal growth and primary and secondary nucleation; (3) interpretation of kinetics so that appropriate model parameters could be extracted from fitting population balances to experimental data; (4) identification of the potential importance of secondary nucleation relative to primary nucleation. The protocol and methods developed in this study can be applied to other systems for evaluating and improving batch crystallization processes.
519

Κρυστάλλωση και αναστολή σχηματισμού αλάτων θειικού νατρίου / Crystallization and inhibition of crystal growth of sodium sulfate salts

Παπαδημητρίου, Ελένη 28 June 2007 (has links)
Στην παρούσα εργασία πραγματοποιήθηκε μελέτη της κινητικής της κρυστάλλωσης του Μιραμπιλίτη (δεκαένυδρο θειικό άλας), που είναι και το θερμοδυναμικά σταθερότερο άλας του θειικού νατρίου που κρυσταλλώνεται στις συνήθεις περιβαλλοντικές συνθήκες. Η μελέτη έγινε σε ασταθή υπέρκορα διαλύματα τα οποία παρασκευάζονται με διάλυση του θειικού νατρίου. Στην συνέχεια επιλέχθηκαν τρεις οργανοφωσφορικές ενώσεις προκειμένου να διερευνηθεί η επίδρασή τους στην κινητική της κρυστάλλωσης του Μιραμπιλίτη. Το κοινό χαρακτηριστικό αυτών των οργανοφωσφορικών ενώσεων είναι ότι έχουν ιονιζόμενες ομάδες στο μόριο τους και γι’ αυτό θεωρείται ότι μπορούν να δεσμεύουν είτε μέσω προσρόφησης ή με τον σχηματισμό επιφανειακών συμπλόκων, τα ενεργά κέντρα κρυστάλλωσης. / Our work is concerned with the investigation and inhibition of crystal growth for mirabilite. Mirabilite is a hydrated sodium sulfate salt and considers extremely hazardous for building materials as marble and concrete when it crystallizes heterogeneously in pores. The compounds tested with respect to their effect on the crystal growth of mirabilite were three organophosphorus compounds: HEDP, ATMP, HMDTMPA. Those organophosphorus compounds possesses ionizable groups and therefore are consider to be able to block by absorption the active growth sites forming possibly surface complexes.
520

MODELING THE METHANE HYDRATE FORMATION IN AN AQUEOUS FILM SUBMITED TO STEADY COOLING

Avendaño-Gómez, Juan Ramón, García-Sánchez, Fernando, Vázquez Gurrola, Dynora 07 1900 (has links)
The aim of this work is to model the thermal evolution inside a hydrate forming system which is submitted to an imposed steady cooling. The study system is a cylindrical thin film of aqueous solution at 19 Mpa, the methane is the hydrate forming molecule and it is assumed that methane is homogeneously dissolved in the aqueous phase. The model in this work takes into account two factors involved in the hydrate crystallization: 1) the stochastic nature of crystallization that causes sub-cooling and 2) the heat source term due to the exothermic enthalpy of hydrate formation. The model equation is based on the resolution of the continuity equation in terms of a heat balance. The crystallization of the methane hydrate occurs at supercooling conditions (Tcryst < TF), besides, the heat released during crystallization interferes with the imposed condition of steady decrease of temperature around the system. Thus, the inclusion of the heat source term has to be considered in order to take into account the influence of crystallization. The rate of heat released during the crystallization is governed by the probability of nucleation J(T ). The results provided by the model equation subjected to boundary conditions allow depict the evolution of temperature in the dispersed phase. The most singular point in the temperature–time curve is the onset time of hydrate crystallization. Three time intervals characterize the temperature evolution during the steady cooling: (1) linear cooling, (2) hydrate formation with a release of heat, (3) a last interval of steady cooling.

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