Macrokinetic Model Research Articles

Impact of the reg1 mutation glycocen accumulation and glucose consumption rates in Saccharomyces cerevisiae cells based on a macrokinetic model

In S. cerevisiae, catabolite repression controls glycogen accumulation and glucose consumption. Glycogen is responsible for stress resistance, and its accumulation in derepression conditions results in a yeast with good quality. In yeast cells, catabolite repression also named glucose effect takes place at the transcriptional levels, decreasing enzyme respiration and causing the cells to enter a fermentative metabolism, low cell mass yield and yeast with poor quality. Since glucose is always present in molasses the glucose effect occurs in industrial media. A quantitative characterization of cell growth, substrate consumption and glycogen formation was undertaken based on an unstructured macrokinetic model for a reg1/hex2 mutant, capable of the respiration while growing on glucose, and its isogenic repressible strain (REG1/HEX2). The results show that the estimated value to maximum specific glycogen accumulation rate (muG,MAX) is eight times greater in the reg1/hex2 mutant than its isogenic strain, and the glucose affinity constant (K SS) is fifth times greater in reg1/hex2 mutant than in its isogenic strain with less glucose uptake by the former channeling glucose into cell mass growth and glycogen accumulation simultaneously. This approach may be one more tool to improve the glucose removal in yeast production. Thus, disruption of the REG1/HEX2 gene may constitute an important strategy for producing commercial yeast.

Isothermal melt-crystallization and melting behavior for three linear aromatic polyesters

Isothermal crystallization and subsequent melting behavior for three different types of linear aromatic polyester, namely poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT), were investigated (with an emphasis on PTT in comparison with PET and PBT). These polyesters were different in the number of methylene groups (i.e. 2, 3, and 4 for PET, PTT, and PBT, respectively). Isothermal crystallization studies were carried out in a differential scanning calorimeter (DSC) over the crystallization temperature range of 182–208 °C. The wide-angle X-ray diffraction (WAXD) technique was used to obtain information about crystal modification and apparent degree of crystallinity. The kinetics of the crystallization process was assessed by a direct fitting of the experimental data to the Avrami, Tobin, and Malkin macrokinetic models. It was found that the crystallization rates of these polyesters were in the following order: PBT>PTT>PET, and the melting of these polyesters exhibited multiple-melting phenomenon. Lastly, the equilibrium melting temperature for these polyesters was estimated based on the linear and non-linear Hoffman–Weeks (LHW and NLHW) extrapolative methods.

Application of different macrokinetic models to the isothermal crystallization of PP/talc blends

The crystallization kinetics of neat polypropylene (PP) and of PP composites containing 2, 5, 10 and 30 wt% of talc was studied. Various kinetic equations, namely the Avrami, Velisaris–Seferis, Dietz, Khanna, Malkin models, have been applied to describe the kinetics of crystallization from the melt state under isothermal conditions. The results suggested that experimental data of the Avrami’s exponent, “ n”, is approximately 2, meaning that the crystallization of PP alone and of its composites with talc is a two-dimensional growth process. Experimental data of PP alone can be best described by the Avrami, Velisaris–Seferis, Dietz and Malkin models; whereas the models that in the case of composites better correlate their behavior are those of Velisaris–Seferis, followed by Avrami’s.

Model-based optimization of temperature and feed control strategies for glycerol production by fed-batch culture of osmophilic yeast Candida krusei

In this study, the optimization of temperature and feed control strategies for glycerol production by fed-batch culture of osmophilic yeast Candida krusei was investigated to maximize the final yield whilst to control the residual glucose at a low concentration. For the purposes of convenient control performance and easy numerical solution, the entire fermentation process was proposed being divided into multi-subintervals. In each subinterval, temperature was controlled constantly; while glucose and corn steep liquor were fed in pulse form at each start. Both piecewise-constant temperature (PCT) and discrete-pulse feed (DPF) control strategies were optimized by the complex method of Box based on previous macro-kinetic model and verified experimentally in a 600 ml airlift loop reactor. It was found that, by model-based optimization of only DPF control strategies, the final glycerol yield were significantly improved compared with those by previous empirical strategies. The yield could be improved further by optimization of both PCT and DPF control strategies and by selecting the first half of the whole fermentation process as the control emphasis. The optimization approach proposed appeared promising to solve the multivariable control problem in many fermentation processes.

Optimization of Glycerol Fed-Batch Fermentation in Different Reactor States: A Variable Kinetic Parameter Approach

To optimize the fed-batch processes of glycerol fermentation in different reactor states, typical bioreactors including 500-mL shaking flask, 600-mL and 15-L airlift loop reactor, and 5-L stirred vessel were investigated. It was found that by reestimating the values of only two variable kinetic parameters associated with physical transport phenomena in a reactor, the macrokinetic model of glycerol fermentation proposed in previous work could describe well the batch processes in different reactor states. This variable kinetic parameter (VKP) approach was further applied to model-based optimization of discrete-pulse feed (DPF) strategies of both glucose and corn steep slurry for glycerol fed-batch fermentation. The experimental results showed that, compared with the feed strategies determined just by limited experimental optimization in previous work, the DPF strategies with VKPs adjusted could improve glycerol productivity at least by 27% in the scale-down and scale-up reactor states. The approach proposed appeared promising for further modeling and optimization of glycerol fermentation or the similar bioprocesses in larger scales.

A combinatorial approach to surface contacts in solid phase reactions

Macro-kinetic models for solid phase reactions require information about the contact area between reactants. A classical probability is presented to calculate the expectancy value for contact between two specified species when three different solid phases are present in the system. Consider the generic reaction aA(s)+ bB(s)→ cC(s,g) (if C is volatile the two-phase problem results). The expectancy value depends on the surface area densities σ i = N i v where N i denotes the particle density of species i and v i is the volume per particle—instead of using distributions, the analysis is based on average particle sizes. To include the important role of particle geometry, the reactants are modeled as rectangular rhombi. The differences in reaction rate are investigated for cubes (quasi-spheres), platelets and needles by adjusting the aspect ratios. As the reaction proceeds reactants are consumed and products form that change the probabilities for reactant contacts. The evolution of particle sizes must be tracked and mechanisms that affect particle sizes must be included in the model. The dimensions change with reaction, compression and fracture. Fracture is described by the Hiramatsu–Oko equation that relates bed pressure with an equilibrium dimension. The particle size of the (solid) product depends specifically on the reaction mechanism. To illustrate the combinatorial approach, it is applied to a mechanism where C desorbs from the A/B interface, but then it either nucleates to form C particles or adsorbs on existing C particles. Factors that influence the reaction rate are initial particle sizes, aspect ratios, fracture criteria and stoichiometry.

Application of the Avrami, Tobin, Malkin, and Urbanovici–Segal macrokinetic models to isothermal crystallization of syndiotactic polypropylene

Various kinetic equations, namely the Avrami, Tobin, Malkin, and Urbanovici–Segal models, have been applied to describe the kinetics of primary crystallization from the melt state of syndiotactic polypropylene (s-PP) under isothermal conditions. Analysis was carried out using a data-fitting procedure, in which the experimental data were fitted directly to each model using a non-linear multi-variable regression program. The results suggested that the experimental data of s-PP can be best described by the Urbanovici–Segal model, followed by the Avrami, Malkin, and Tobin models, respectively.

Multipulse feed strategy for glycerol fed-batch fermentation: a steady-state nonlinear optimization approach.

During glycerol fed-batch fermentation, the process could be divided into multiple equal subintervals, and the feed operation was performed in pulse form at the start of each subinterval. Based on the macrokinetic models, the multipulse feed strategy for both glucose and corn steep slurry was determined by a general nonlinear optimization approach to maximize the final glycerol productivity and still control the residual glucose at a low concentration. The experimental results in a 600-mL Airlift Loop Reactor showed that the tested data with this strategy agreed well with the corresponding model prediction, and that the feed mode with nonlinear optimization could improve the glycerol productivity significantly compared with those determined just by limited experimental optimization in previous studies.

Kinetics of Phase-Transfer Formation of Potassium Carbazolate, Catalyzed with 18-Crown-6

Kinetics of formation of potassium carbazolate in the system liquid-solid, catalyzed with 18-crown-6, was studied. Applicability of the previously proposed macrokinetic model to this process was demonstrated.

Isothermal melt- and cold-crystallization kinetics and subsequent melting behavior in syndiotactic polypropylene: a differential scanning calorimetry study

The isothermal melt- and cold-crystallization kinetics and subsequent melting behavior of syndiotactic polypropylene (s-PP) were investigated using differential scanning calorimetry (DSC). The overall crystallization kinetics was determined by directly fitting the experimental data to the Avrami and Malkin macrokinetic models using a non-linear multi-variable regression program. When plotted as a function of crystallization temperature, the overall crystallization rate parameters for melt-crystallization process exhibited an unmistakable double bell-shaped curve, while those for cold-crystallization process showed the typical bell-shaped curve. Comparison of the overall crystallization rate parameters obtained for both melt- and cold-crystallization processes indicated that crystallization from the glassy state proceeded at a much greater rate than that from the melt state. Melting of samples isothermally crystallized at low and moderate crystallization temperatures exhibited multiple-melting phenomenon. Determination of the equilibrium melting temperature according to the “linear” and “non-linear” Hoffman–Weeks extrapolative methods provided values of ca. 145 and 182°C, respectively.

Application of the Avrami, Tobin, Malkin, and Simultaneous Avrami Macrokinetic Models to Isothermal Crystallization of Syndiotactic Polypropylenes

Various macrokinetic models (the Avrami, Tobin, Malkin, and simultaneous Avrami models) were applied to describe the primary crystallization of syndiotactic polypropylene (sPP) under isothermal conditions. Analysis of the experimental data was carried out using a direct-fitting method such that the experimental data were fitted directly to each macrokinetic model using a nonlinear multivariable regression program. Comparison of the kinetics parameters obtained from the program to those obtained from the traditional analytical procedure suggested that applicability and reliability of the direct-fitting method are satisfactory. Prediction of the time-dependent relative evolution of crystallinity at other crystallization temperatures was demonstrated based on the bulk kinetics parameters obtained from the analysis.

Nonisothermal bulk crystallization and subsequent melting behavior of syndiotactic polypropylenes: Crystallization from the melt state

Various macrokinetic models, namely, the Avrami, the Tobin, and the Ozawa models, were applied to describe the crystallization process of syndiotactic polypropylene (s-PP) under nonisothermal conditions. Both Avrami and Tobin models were shown to provide a fair description of the experimental data. The Avrami exponent na was found to range from 2.4 to 5.3, while the Tobin exponent nt was found to range from 3.1 to 6.7. The Ozawa model was found to describe the nonisothermal crystallization kinetics of s-PP very well. The Ziabicki's kinetic crystallizability, suggesting the crystallization ability of polymers from the melt when cooled at a unit cooling rate, was also evaluated and was found to range from 0.93 to 1.40°C s−1. The energy barrier for nonisothermal crystallization, based on the Augis–Bennett method, was found to range from −78.6 to −108.1 kJ mol−1. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 338–354, 2000

INVITED REVIEW: Kinetic models for normal and impaired growth

Although microkinetic models are expected to play in the future the same role that macrokinetic models have played in the past, classic mechanistic growth functions are still worthy of study and may still provide insight into auxological problems. The rather rigid shape of macrokinetic models may ignore many interesting fluctuations of growth velocity, but a strong structure allows a robust estimate of growth kinetics even in the case of growth profiles which are largely incomplete, as those derived from current clinical records. In any case, the too simplified shape of these models may be adjusted, to some extent, by adding some unstructured smooth function of residuals which takes into account minor aspects of growth (such as slight spurts during childhood), which cannot be detected in an individual profile because of random errors and inadequate number of observations. This paper recalls the reasons why growth models are useful, analyses briefly the structure and the characteristics of the two fundamental human growth functions, i.e. triple-logistic and PB1, and shows how the use of PB1 model may be extended also to impaired growth, e.g. in girls with Turner syndrome. In this regard, the use of the same model for normal and pathological growth offers the important advantage that differences between growth patterns are not confounded with differences between models.Obwohl von mikrokinetischen Modellen erwartet wird, dass sie in der Zukunft dieselbe Rolle spielen werden, wie die makrokinetischen in der Vergangenheit, verdienen die klassischen mechanistischen Wachtumsfunktionen immer noch der Beachtung und sie konnen immer noch Einblicke in auxologische Probleme vermitteln. Die ziemlich rigide Form makrokinetischer Modelle ignoriert moglicherweise viele interessante Fluktuationen der Wachstumsgeschwindigkeit, eine feste Struktur ermoglicht jedoch eine robuste Schatzung der Wachstumskinetik. Dies gilt auch in Fallen, in denen die Wachstumsprofile sehr luckenhaft sind, wie zum Beispiel bei Daten, die klinischen Unterlagen entnommen wurden. Die zu stark vereinfachende Form dieser Modelle kann jedenfalls in gewissem Mass durch das Hinzufugen einer unstrukturierten glattenden Funktion der Residuen angepasst werden, die weniger bedeutende Aspekte des Wachstums (wie kleine Spurts im Kindesalter) berucksichtigt, welche in einem individuellen Profil aufgrund von Zufallsfehlern und einer ungenugenden Anzahl von Beobachtungen nicht entdeckt werden konnen. In dieser Arbeit wird erneut ins Gedachtnis gerufen, weshalb Wachstumsmodelle sinnvoll sind, es werden die Struktur und die Charakateristika der zwei grundlegenden Wachstumsfunktionen, das Triple-Logistic-Modell und das PB1-Modell, kurz analysiert und es wird gezeigt, wie das PB1-Modell zur Anwendung auf ein gestortes Wachstum, wie z.B. bei Madchen mit Turner Syndrom, erweitert werden kann. In dieser Hinsicht bietet die Verwendung desselben Modells fur das normale und das gestorte Wachstums den bedeutenden Vorteil, dass Unterschiede in den Modellen keinen Confounder der Unterschiede im Wachstumsmuster darstellen.Bien que les modeles microkinetiques soient appeles a jouer dans le futur le meme role que les modeles macrokinetiques ont joue dans le passe, les classiques fonctions mecanistes de croissance meritent toujours d'etre etudiees et sont toujours en mesure d'apporter des eclaircissements de problemes auxologiques. La forme relativement rigide des modeles macrokinetiques peut parfois ignorer de nombreuses fluctuations interessantes de la vitesse de croissance, mais une structure forte permet une estimation robuste de la kinetique de la croissance, meme dans le cas de profils de croissance largement incomplets, tels que ceux qui sont elabores a partir des dossiers cliniques habituels. Dans tous les cas, la forme trop simplifiee de ces modeles peut etre ajustee jusqu'a un certain point en ajoutant quelque fonction lisse des residus non structuree, qui prend en compte des aspects mineurs de la croissance (tels que les petites accelerations pendant l'enfance), qui ne peuvent pas etre detectees dans un profil individuel par suite des erreurs stochastiques et du petit nombre d'observations. Cet article rappelle les raisons pour lesquelles les modeles de croissance sont utiles, analyse brievement les structures et caracteristiques de deux fonctions fondamentales de la croissance humaine, soit. triple logistique et PB1 et montre comment l'usage du modele PB1 peut aussi etre etendu a la croissance perturbee comme par exemple chez les filles presentant le syndrome de Turner. Dans cette perspectives, l'utilisation du meme modele de croissance normale et pathologique offre l'avantage important que les differences entre modes de croissance ne sont pas confondus avec les differences entre modeles.

A study on the kinetic process of reaction synthesis of TiC: Part I. Experimental research and theoretical model

The micromechanism and the macrokinetic process of synthesis TiC in preparing Al/TiC by direct reaction synthesis (DRS) have been investigated in detail by observing the microstructure of the water-quenched preform by scanning electron microscopy (SEM) and energy* dispersive X-ray (EDX) analysis. The results have shown that the micromechanism of reaction is a solution-precipitation mechanism, in which carbon powders in the preform were surrounded by a Ti-rich Al-Ti-C melt layer and reacted with titanium in the layer to synthesize TiC particles, and TiC precipitated from the layer and scattered over the alloy melt. The macrokinetic model of reaction synthesis of TiC can be divided into four stages: heating and melting stage, initial reaction stage, complete reaction stage, and cooling stage. In the end, a macrokinetic model has been set up based on the experimental results.

The macrokinetic model of thermosetting polymers by phase-change theory

The general rate law frequently used to describe the cure process of thermosetting polymers (thermosets) can be deduced by analysing the Avrami theory. Every parameter in it can be given reasonably. From the macrokinetic model, it is also possible to describe the non-isothermal cure process of thermosets. A comparative example shows that the theoretical prediction is in good agreement with the experimental data.

Experimental design for the identification of macrokinetic models and model discrimination

An experimental design method for the identification of macrokinetic models was developed applying an extended D-optimal design criterion. The D-optimal design criterion was modified to consider variable measurement variances as well as multivariate macrokinetic models. The macrokinetics of formate dehydrogenase (FDH) production with Candida boidinii were thus identified within 10 steady state experiments in a labscale continuous stirred tank reactor (10 model parameters). Closed loop control (nutristat) was applied to set-up the operating states suggested by this experimental design method. After each set of steady state experiments the quality of macrokinetic parameters was characterized statistically. For model discrimination a parameter discrimination algorithm based on entropy formulations was adapted. Again a multivariate criterion considering variable measurement variances was developed. This discrimination algorithm was applied to discriminate the macrokinetic model of FDH production with Candida boidinii out of 10 different macrokinetic approaches. An unequivocal discrimination result could be obtained calculating model specific probabilities. These were compared with commonly used sum of squares values. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 564-576, 1997.

Experimental design for the identification of macrokinetic models and model discrimination

Experimental design for the identification of macrokinetic models and model discrimination

Biomass Gasification with Steam in Fluidized Bed: Effectiveness of CaO, MgO, and CaO−MgO for Hot Raw Gas Cleaning

The upgrading of the raw hot gas from a bubbling fluidized bed biomass gasifier is studied using cheap calcined minerals or rocks downstream from the gasifier. Biomass gasification is made with steam (not air) at 750−780 °C and about 0.5−1.0 kg of biomass/h. Calcined solids used are dolomite (MgO−CaO), pure calcite (CaO), and pure magnesite (MgO). Variables studied have been temperature of the secondary bed (780−910 °C), time of contact or space-time of the gas (0.08−0.32 kg·h/m3n), and particle diameter (1−4 mm) and type of mineral. Their effects on tar conversion, tar amount in the exit gas, product distribution, and gas composition are presented. Using a macrokinetic model for the tar disappearance network, the activities of the stones are expressed by their apparent kinetic constant. Apparent energies of activation for tar elimination (42−47 kJ/mol) and preexponential and effectiveness factors are given for all tested solids of which the most active is the calcined dolomite.

Surface recombination in breakdown time delay experiments: Effect of different cathode materials

The late afterglow in nitrogen with iron electrode is studied by the breakdown time delay method, i.e., by measuring the breakdown time delay td as a function of the afterglow time τ. It is proposed that the cause of the secondary electrons initiating the breakdown is the energy of the surface recombination of nitrogen atoms on the iron electrode. The gas-phase and macrokinetic diffusive models are used to describe the experimental breakdown time delay data. By fitting the theoretical curve to the experimental data: (1) it has been confirmed that the recombination on the molybdenum glass is of the second order and the value of the surface recombination coefficient is determined at 4 mbar; (2) it has been shown that the surface recombination on the iron electrode is of the second order, and the effective recombination coefficients are determined; (3) the analytical form of the recombination coefficient as a function of the adsorption characteristics of surfaces and the pressure of the parent gas has been derived. In addition, the orders of surface recombination on the molybdenum-, aluminum-, and gold-plated electrode were determined by the same method.

Bioelectrode response modulation caused by periodical carbon paste filling process

Carbon paste electrodes (CPEs) doped with glucose oxidase showed periodical variation of responses when new surfaces of the electrode were exposed to glucose solution. The periodicity of the responses was analyzed by discrete Fourier transformation. At an enzyme activity in carbon paste (CP) of 0.11–0.18 U mg −1 the main harmonic was 3.7–6.5 mm in length (12.4–21.6 slices of the electrode). The periodical change of response correlated with the periodicity of the CPE filling process. The modulation factor, expressed as modulation amplitude divided by the mean value of the parameter, depended on enzyme activity in the CP matrix. It was 15.1% and 2.8% at enzyme activities of 0.16 and 1.28 U mg −1, respectively. The ohmic resistance of the CPEs measured by mercury electrode also changed periodically. The modulation amplitude of resistance was almost independent of enzyme activity and it was 2.0 Ω when CP contained 0.16 and 1.28 U mg −1 enzyme activity, respectively. The periodicity of the resistance modulation also correlated with the periodicity of the electrode filling process. To explain the periodical changes of the responses of the CPEs and factors influencing the modulation factor, the bioelectrode response dependence on enzyme activity was determined and a macrokinetic model was build. The CPE responses exhibit a saturating dependence on enzyme activity, which was explained by external diffusion limitation of the process. The model of external diffusion predicts that: (i) periodical CPE response variation is determined by biocatalytical activity modulation of the CPE surface; (ii) the modulation factor is a function of enzyme activity in CP matrix. The surface activity variation is related to pinhole formation on the electrode surface and coverage of the electrode by the pasting liquid. The surface coverage depends on the variation of local CP composition caused by periodical CP pressing, during the filling process.