Macrokinetic Model Research Articles

Cell cycle model for recombinant Pichia pastoris during glycerol fed-batch cultivation

A cell cycle model is proposed for methylotrophic yeast Pichia pastoris grown on glycerol during fed-batch cultivation. Morphological differentiation of cells, such as unbudded daughter cell, unbudded parent cell and budding cell, is depicted by the model. During the cyclic growth, cells in different cycling period are assumed to undergo sequential shifting dominantly. The input of the cell cycle model is the specific growth rate, which is calculated from the macrokinetic model proposed previously. The cell cycle related variables, such as the fraction of budding cells and the cell density are then simulated. Model validation is carried out with the experimental data of off-line assays.

A macrokinetic model for myeloma cell culture based on stoichiometric balance

A macrokinetic model for a myeloma cell line is proposed. The model describes the dynamic balances of lactate, alanine, ATP and NADH during the metabolsim of glucose, glutamine and other amino acids. The metabolic pathways mainly include glycolysis, glutaminolysis, the trcicarboxylic acid cycle, the formation and utilization of amino acids, the respiratory chain, cell growth and cell death. The metabolic shift of glucose is especially considered because of a change in the rate of glycolysis. Thus the model functions in three modes to describe the behaviour of the myeloma cell line. On the basis of this model the macrokinetic bioreaction rates such as the specific substrate consumption rate, the specific growth rate, the specific acetyl-CoA formation rate, as well as the specific oxygen uptake rate, are estimated. The specific substrate consumption rate and the specific growth rate are then coupled into a bioreactor model such that the key variables, i.e., the cell density, the substrate and metabolite concentrations, are obtained. Experiments with batch and fed-batch cultures of a myeloma cell line (X63-Ag8.653) were used to validate the model. The prediction of the model was simulated by the rolling prediction approach.

Oxygen transfer model in recombinant Pichia pastoris and its application in biomass estimation

An oxygen transfer model was established for Pichia pastoris growing on glycerol and methanol in a stirred tank bioreactor and expressing a recombinant human serum albumin (rHSA). This was based on pseudo-steady state mass balance, where the volumetric O(2) transfer coefficient, k (L) a, was estimated as a function of power input per unit volume and aeration rate. Under pseudo-steady state, the O(2) transfer rate model matched the O(2) uptake rate obtained from a previous macrokinetic model. This procedure was also applied to estimate biomass concentration by using the on-line rolling identification approach.

A macrokinetic and regulator model for myeloma cell culture based on metabolic balance of pathways

A macrokinetic model is proposed to simulate the growth and metabolism of myeloma cell line in batch and fed-batch cultures. The model describes glycolysis, glutaminolysis, the TCA cycle, respiratory chain, formation of metabolites, as well as cell growth and death. In particular, metabolic shift in the glucose utilization is considered in response to the change of glycolysis rate during the cultivation. A closed loop regulator is introduced to approximate the induction of enzyme pool during lag phase after inoculation. Based on the model, the specific consumption rate of substrate, the specific growth rate, the specific acetyl CoA formation rate as well as the specific oxygen uptake rate are estimated. The specific substrate consumption rate and the specific growth rate are then coupled into a bioreactor model, which delivers the key variables, i.e., cell density, substrate and metabolite concentrations. Batch and fed-batch cultivations were used to validate the model.

Mathematical modeling of interfacial polycondensation

AbstractThe works on mathematical modeling of interfacial polycondensation are reviewed over the period since 1970s up to now. Attention is primarily paid to the techniques of local and macrokinetic modeling. Two approaches to the theoretical description of polycondensation have been formed up to date. The first one is based on analytical or semianalytical solution of differential balance equations using the stationary mass transfer approximation. The second one consists in numerical solution of the system of reaction–diffusion equations for the diffusion boundary layer of the reaction phase. The advantages and drawbacks of these approaches, specific features of their realization, basic results, as well as ways of combining these methods are discussed. A possibility of building a general model of interfacial polycondensation as a hierarchical combination of kinetic, local, and macrokinetic models is shown. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2698–2724, 2006

Non-isothermal melt- and cold-crystallization kinetics of poly(3-hydroxybutyrate)

Non-isothermal melt- and cold-crystallization and subsequent melting behavior of poly(3-hydroxybutyrate) (PHB) have been investigated by differential scanning calorimetry (DSC). The crystallization kinetics was studied by a direct fitting of the experimental data to various macrokinetic models, namely Avrami, Tobin and Ozawa models. All of the macrokinetic models were found to describe the experimental data for both the melt- and the cold-crystallization processes fairly well. For both the melt- and the cold-crystallization processes, the inversed half-time of crystallization and both the Avrami and the Tobin rate constants were all found to increase with increasing cooling or heating rate. For the melt-crystallization process, the Ozawa rate constant was found to decrease, while, for the cold-crystallization process, it was found to increase, with increasing temperature. Finally, the effective energy barrier for both the melt- and the cold-crystallization processes was found to decrease in its magnitude with increasing relative crystallinity.

A novel select-best and prepotency evolution algorithm and its application to develop industrial oxidation reaction macrokinetic model

A novel evolution algorithm with the select-best and prepotency operator (SPO), named select-best and prepotency evolution algorithm (SPEA), is proposed. The main genetic operators of SPEA are the proposed SPO and the uniform mutation operator. The SPO is defined as follows. Every individual in population has the same chance to select the best individual within its neighborhood range (the select-best range.) and produce new individuals through the crossover with the selected individual. Then the best one of two new individuals is selected as one individual of the next generation. With the SPO that preserves the diversity of individuals to avoid premature and can make excellent individuals be selected many a time, SPEA possesses advantages over conventional genetic algorithms. To compare the performances of SPEA with those of the real-coded genetic algorithm (GA), SPEA and the real-coded GA were applied to search the global optimal solution of a benchmark function. The comparison results demonstrated that SPEA spends less CPU time than the real-coded GA, the on-line, off-line, and local searching performances of SPEA are superior to those of the real-coded GA, and the probability of obtaining the global optimal solution for SPEA is larger than that for the real-coded GA. In addition, the relationship between the select-best neighborhood range and the CPU time consumed by SPEA was analyzed as well as the relationship between the select-best neighborhood range and the ratio of obtaining the global optimal solution. The results demonstrated that the proper ratio of the individual number in the select-best neighborhood to that in the population was 6%. Finally, SPEA was applied to develop a macrokinetic model of the industrial oxidation reaction of p-xylene to terephthalic acid (OXTA) in an Amoco reactor. The macrokinetic model based on the intrinsic kinetics model introduced the correction coefficients into the rate constants of the intrinsic kinetics model to indicate the mass transfer effects presented in the Amoco reactor. Then, with the data of the industrial OXTA, SPEA was employed to obtain the optimal correction coefficients, and the macrokinetic model with high precision for the industrial OXTA was developed.

Nonisothermal melt-crystallization kinetics of hydroxyapatite-filled poly(3-hydroxybutyrate) composites

The knowledge of biomedical implants ranging from drug delivery devices to tissue engineering and based on bioresorbable polymer composites is increasing, but the study of the crystallization kinetics of these kinds of composites is seldom a concern. The focus of our experimental research was the nonisothermal-crystallization behavior of poly(3-hydroxybutyrate) (PHB)/hydroxyapatite (HA) composites, which was monitored by means of differential scanning calorimetry at different cooling rates. Various macrokinetic models were applied to describe the process of nonisothermal crystallization. The results showed that the modified Avrami model and Mo's approach could describe the nonisothermal crystallization of the composites very well, but the Ozawa analysis alone was thought to be rather inapplicable. The values of the half-time and kinetic crystallizability showed that the crystallization rate increased with increasing cooling rates for both PHB and the composites. The HA particles served as additional nucleation sites, and low levels of HA resulted in dramatic increases in the crystallization rate with respect to pure PHB; however, high HA contents (> 20 wt %) clearly retarded the growth process. The activation energy for nonisothermal crystallization was evaluated with the Kissinger method and was found to vary with the incorporation of HA. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102:5388–5395, 2006

Macrokinetic mathematic model for inner oxidation of the alloys based on copper while annealing mechanically alloyed compositions of Cu-Al-CuO system

Macrokinetic mathematic model for inner oxidation of the alloys based on copper while annealing mechanically alloyed compositions of Cu-Al-CuO system

Model‐based specific growth rate control for Pichia pastoris to improve recombinant protein production

AbstractConstant specific growth rate control in the methanol growth phase was investigated for the fed‐batch cultivation of Pichia pastoris expressing recombinant human serum albumin (rHSA). The methanol feeding strategy was determined based on an earlier proposed macrokinetic model to maintain the specific growth rate at preset levels. The experimental results demonstrate that the control strategy of constant specific growth rate is more effective than that of constant feeding rate to maximize production. Furthermore, the most productive setpoint of the specific growth rate is found between 0.005 and 0.006 h−1, which yields protein concentrations higher than 5 g l−1 at 160 h. In addition, a setpoint of 0.008 h−1 is suggested as the upper limit for specific growth rate control for the given expression system. Copyright © 2005 Society of Chemical Industry

Steady State Isotopic Transient Kinetic Analysis of the acrolein oxidation on Mo–V–W-mixed oxide catalysts

Mixed oxide catalysts on the basis of molybdenum and vanadium are industrially important catalysts for the partial oxidation of acrolein to acrylic acid. For a better understanding of the oxygen pathways for an optimised model catalyst with the stoichiometric composition Mo 7.5V 2.5W 0.5O x , the so-called Steady State Isotopic Transient Kinetic Analysis (SSITKA) method was employed. After switching from 16O 2 to 18O 2 the formation of 18O-labelled acrolein was observed. Acrolein exchanges its carbonyl oxygen with oxygen from the solid catalyst. This exchange is also reflected in the isotopic distribution of the oxidation products (acrylic acid and combustion products). Subsequent desorption of acrolein, as well as further reaction to the oxidation products, can take place. Compared to the partial oxidation the incorporation of the isotopic tracer oxygen into the combustion by-products is much slower. This might be an indicator of an intermediate layer in the combustion pathway. To obtain activation parameters SSITKA experiments were performed over a temperature range between 322 and 391 °C. Based on the observations, a macro kinetic model was adapted upon. The activation energy for the exchange of the carbonyl oxygen of acrolein was found to be approximately 30 kJ mol −1.

A macrokinetic model for dimensioning of biofilters for VOC and odour treatment

Biofiltration is a cost-effective and environmentally sustainable technology for the treatment of exhaust gases from a variety of sources. Although the process setup is relative simple, many physical, chemical, and microbiological processes are involved. Microkinetic models attempting to cover all of these processes are often more complex than reliable; on the other hand, many macrokinetic approaches have a tendency to oversimplification. In order to develop a simple and accurate protocol to derive biofilter design criteria from experimental trials, a macrokinetic model based on chemical engineering fundamentals was developed. The model covers first-order kinetics as well as kinetics shifting from first-order at low substrate concentrations to zero-order at elevated concentrations and can be applied to single VOCs and odours as measured by olfactometry.

On the Modeling of the Kinetics of the Selective Deactivation of Catalysts. Application to the Fluidized Catalytic Cracking Process

The deactivation of a solid catalyst may affect in different ways each reaction taking place in a complex network. This creates a variation with time on stream of the product distribution at the reactor exit. To handle data from this common situation, a selective deactivation kinetic model fits the data much better than a nonselective one. Selective deactivation kinetic models are scarcely used because they are often complex and difficult to handle. They also introduce more deactivation kinetic parameters than the nonselective models. Nevertheless, selective deactivation kinetic models are a refinement and are a step forward in the modeling of deactivation kinetics. They might also improve the existing macrokinetic models for commercial reactors. In this paper, several new concepts and ideas are given relating to selective deactivation kinetic models. These concepts are applied to the kinetics of the deactivation of commercial fluidized catalytic cracking catalysts with commercial feedstocks. It is also proven how the kinetics of cracking of the feedstock (heavy oils) is much more affected by the catalyst deactivation than the cracking of the gasoline. A discussion of the results is included.

Influence of molecular characteristics on overall isothermal melt-crystallization behavior and equilibrium melting temperature of syndiotactic polypropylene

Overall isothermal melt-crystallization and subsequent melting behavior of metallocene-catalyzed syndiotactic polypropylene resins of various molecular weights were investigated using differential scanning calorimetry (DSC) technique. Two sets of molecular weight range were synthesized with two different metallocene catalyst systems. The kinetics of the overall isothermal melt-crystallization process was analyzed based on various macrokinetic models, i.e. the Avrami, Malkin and Urbanovici–Segal models. The effective activation energy describing the overall isothermal crystallization process over the crystallization temperature range studied was estimated based on an Arrhenius approximation of the obtained Avrami crystallization rate constants. The equilibrium melting temperature for each of these resins was estimated based on the linear and non-linear Hoffman–Weeks extrapolative methods.

Catalytic Hot Gas Cleaning with Monoliths in Biomass Gasification in Fluidized Beds. 1. Their Effectiveness for Tar Elimination

Full-size 15 × 15 × 30 cm nickel-based monoliths are tested for tar elimination in fuel gas produced by biomass gasification in a fluidized bed at a small pilot-plant scale. The feedstocks used were mixtures of pine wood chips and “orujillo”, the residue from olive oil production. Temperatures at the front or face of the monolith ranged from 820 to 956 °C, gas hourly space velocities in the monolith ranged from 1280 to 4550 h-1 (normal conditions, nc), area velocities ranged from 2.7 to 7.1 m/h, and superficial or face gas velocities at the inlet of the monolith ranged from 0.34 to 1.3 m/s. Samples of gas and tar were taken before and after the monolith reactor, and variations in gas composition and tar content were determined. Using a macrokinetic model presented elsewhere, some key kinetic constants for the tar-removal reaction are calculated for the monolith and used as indexes of its activity. The effects of some important operating conditions on the activity and sometimes on the deactivation of the monolith are presented here. The intrinsic activity of the monolith for tar abatement is finally compared with those of other competing catalysts such as dolomites and commercial steam-reforming catalysts. It is concluded that these monoliths are not very high in activity, but they can operate with a fuel gas containing particulates, thereby avoiding the use of hot filters, which are problematic when used in biomass gasification.

A Study on Optimal Feeding Strategy for Pichia pastoris

Abstract Pichia pastoris has been widely used as a host for the expression of heterologous proteins. This paper deals with the glycerol and methanol optimal feeding control in the cultivation of P. pastoris expressing recombinant human serum albumin. An earlier proposed macrokinetic model and a cell cycle model were used to determine the substrate feeding profiles. In the glycerol growth phase, the goal of substrate feeding control is to obtain high cell density as well as the desired level of the fraction of budding cells, while in the methanol growth phase, the goal of substrate feeding is to control the specific growth rate at various set-points. The effect of both glycerol and methanol feeding control strategies were evaluated experimentally. It was found that the productivity may be enhanced if the fraction of budding cells at the end of the glycerol growth phase is minimized and if the specific growth rate during the methanol phase controlled between 0.005 and 0.006 h-1.

Non-isothermal melt crystallization kinetics for ethylene–acrylic acid copolymers and ethylene–methyl acrylate–acrylic acid terpolymers

Non-isothermal melt crystallization kinetics and subsequent melting behavior for four different grades of ethylene–acrylic acid copolymer and three different grades of ethylene–methyl acrylate–acrylic acid terpolymer was investigated by differential scanning calorimetry technique. The non-isothermal melt crystallization data were analyzed based on the Ozawa and Ziabicki macrokinetic models. The effective energy barriers describing non-isothermal melt crystallization process for these resins were determined based on the differential iso-conversional method of Friedman. The amount of non-crystallizable, intra-molecular defects had substantial effects on the non-isothermal melt crystallization kinetics and subsequent melting behavior.

Selected Design Criteria for Ozone Production

AbstractOzone properties that cause a growing interest in its applications have been presented. A short analysis of ozone synthesis in electrical barrier discharges gives some suggestions concerning designs of ozonizers and power supply systems. The presented macrokinetic models make possible to calculate ozone concentration as well as ozone yield and productivity of an ozonizer. All the used formulas contain experimental constants depending on parameters that have not been taken a into account in any previously elaborated theory on ozone synthesis or operation of ozonizers. However, research into ozone synthesis and production continuously develops because of the growing demand for that oxidizer.

Macrokinetic model for methylotrophic Pichia pastoris based on stoichiometric balance

A macrokinetic model for Pichia pastoris expressing recombinant human serum albumin is proposed. The model describes the balances of some key metabolites, ATP and NADH, during glycerol and methanol metabolism. In the glycerol growth phase, the metabolic pathways mainly include phosphorylation, glycolysis, tricarboxylic acid cycle, and respiratory chain. In the methanol growth phase, methanol is oxidized to formaldehyde at first. Then, while a part of formaldehyde is oxidized to formate, the rest is condensed with xylulose-5-monophosphate to form glyceraldehyde-3-phosphate, and further assimilated to form cell constituents. The metabolic pathways following glyceraldehyde-3-phosphate were assumed to be similar to those in the glycerol growth phase. Based on the model, the macrokinetic bioreaction rates such as the specific substrate consumption rate, the specific growth rate, the specific acetyl–CoA formation rate as well as the specific oxygen uptake rate are obtained. The specific substrate consumption rate and the specific growth rate are then coupled into a bioreactor model such that the relationship between substrate feeding rates and the main state variables, i.e., the medium volume, the concentrations of the biomass, the substrate, and the product, is set up. Experimental results demonstrate that the model can describe the cell growth and the protein production with reasonable accuracy.

Non-isothermal melt crystallization kinetics for poly(trimethylene terephthalate)/poly(butylene terephthalate) blends

Various macrokinetic models, namely the Avrami, Ozawa, and Ziabicki models, were applied to describe the non-isothermal melt crystallization process of poly(trimethylene terephthalate) (PTT), poly(butylene terephthalate) (PBT), and their blends. Both the Avrami and the Ozawa models were found to describe the experimental data fairly well. Among the blend compositions studied, Ziabicki’s kinetic crystallizability parameter was found to decrease with increasing PTT content. The effective energy barrier for non-isothermal crystallization process of these blends, analyzed based on the differential iso-conversional method of Friedman, was found to be an increasing function of the relative degree of melt conversion. Within the relative degree of melt conversion range of less than ca. 0.5, the effective energy barrier was found to increase with increasing PTT content.