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Population Balance (population + balance)
Terms modified by Population Balance Selected AbstractsA Hybrid Galerkin,Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization KineticsMACROMOLECULAR REACTION ENGINEERING, Issue 9-10 2010Christof Schütte Abstract Population balance models describing not only the chain-length distribution of a polymer but also additional properties like branching or composition are still difficult to solve numerically. For simulation of such systems two essentially different approaches are discussed in the literature: deterministic solvers based on rate equations and stochastic Monte-Carlo (MC) strategies based on chemical master equations. The paper presents a novel hybrid approach to polymer reaction kinetics that combines the best of these two worlds. We discuss the theoretical conditions of the algorithm, describe its numerical realization, and show that, if applicable, it is more efficient than full-scale MC approaches and leads to more detailed information in additional property indices than deterministic solvers. [source] Offering Incentives for New Development: The Role of City Social Status, Politics, and Local Growth ExperiencesJOURNAL OF URBAN AFFAIRS, Issue 2 2002Paul G. Lewis The propensity of municipal governments to offer incentives for new development is empirically examined, drawing upon both the literature on local economic development policy and studies of local residential restrictions. The data are from a 1998 mail survey of city managers in California in which officials assessed the likelihood that their local governments would offer financial assistance or zoning changes to various types of new business and residential land uses in their communities. Multivariate analysis indicates that local conditions resulting from past growth patterns,commuting times, job/population balance, and housing affordability,play an important role in shaping respondents' assessments as to whether their cities are likely to grant incentives. Such factors deserve an important role in explaining local government growth orientations, alongside measures of community status, political institutions, and the strength of progrowth coalitions. [source] A multi-QMOM framework to describe multi-component agglomerates in liquid steelAICHE JOURNAL, Issue 9 2010L. Claudotte Abstract A variant of the quadrature method of moments (QMOM) for solving multiple population balance equations (PBE) is developed with the objective of application to steel industry processing. During the process of oxygen removal in a steel ladle, a large panel of oxide inclusions may be observed depending on the type of oxygen removal and addition elements. The final quality of the steel can be improved by accurate numerical simulation of the multi-component precipitation. The model proposed in this article takes into account the interactions between three major aspects of steelmaking modeling, namely fluid dynamics, thermo-kinetics and population balance. A commercial CFD code is used to predict the liquid steel hydrodynamics, whereas a home-made thermo-kinetic code adjusts chemical composition with nucleation and diffusion growth, and finally a set of PBE tracks the evolution of inclusion size with emphasis on particle aggregation. Each PBE is solved by QMOM, the first PBE/QMOM system describing the clusters and each remaining PBE/QMOM system being dedicated to the elementary particles of each inclusion species. It is shown how this coupled model can be used to investigate the cluster size and composition of a particular grade of steel (i.e., Fe-Al-Ti-O). © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Morphological population balance model in principal component spaceAICHE JOURNAL, Issue 9 2009Xue Z. Wang Abstract Multidimensional and morphological population balance (PB) models for crystallization processes have been proposed in literature, which can be used to simulate the dynamic evolution of particle shape as well as particle size distribution. These models, however, can become computationally expensive when the crystal has a large number of independent faces, and are not applicable to noncrystalline, irregularly shaped particles such as those encountered in granulation and milling. This article addresses these challenges by introducing principal component analysis (PCA) into morphological PB modeling. PCA transforms the shape description of a particle from a high-dimensional domain to a lower dimensional, principal component (PC) space. Morphological PB models can then be built in this latent variable space, greatly reducing the computational complexity. It also makes it possible to model noncrystalline irregularly shaped particles. The original particle shape at any time can be reconstructed from the PCs. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Crystal growth rate dispersion modeling using morphological population balanceAICHE JOURNAL, Issue 9 2008Cai Y. Ma Abstract Crystal growth in solution is a surface-controlled process. The variation of growth rates of different crystal faces is considered to be due to the molecular arrangement in the crystal unit cell as well as the crystal surface structures of different faces. As a result, for some crystals, the growth rate for a specific facet is not only a function of supersaturation, but also dependent on some other factors such as its size and the lattice spread angle. This phenomenon of growth rate dispersion (GRD) or fluctuation has been described in literature to have attributed to the formation of some interesting and sophisticated crystal structures observed in experimental studies. In this article, GRD is introduced to a recently proposed morphological population balance model to simulate the dynamic evolution of crystal size distribution in each face direction for the crystallization of potash alum, a chemical that has been reported to show GRD phenomenon and sophisticated crystal structures. The GRD is modeled as a function of the effective relative supersaturation, which is directly related to crystal size, lattice spread angle, relative supersaturation, and solution temperature. The predicted results clearly demonstrated the significant effect of GRD on the shape evolution of the crystals. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Generalization and numerical investigation of QMOMAICHE JOURNAL, Issue 1 2007R. Grosch Abstract A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate. © 2006 American Institute of Chemical Engineers AIChE J, 2007 [source] Modeling for simulation of fluidized-bed incineration processAICHE JOURNAL, Issue 6 2001F. Marias A mathematical model for the fluidized-bed incineration process was developed using the waste composed of wood, cardboard and polyvinyl chloride. It is based on heat and mass balances of the gas held within the five zones representing both the bubbling bed and freeboard and including heat transfer with sand and reacting particles of char (pyrolysis residue). The mixture fraction concept and assumption of chemical equilibrium are used to compute temperature and species concentration fields resulting from volatile combustion. These fields are affected by char combustion, which relies, in turn, on a model based on surface reaction and a full population balance. The formation of pollutants (NOx, SOx ) was also taken into account. The main steps involved by the numerical resolution of the model are discussed, and some results are shown for a 1 MW unit. [source] A Chemical Model for the Dispersion of Fillers in a Polymeric MatrixTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2002Tomas Lozano Abstract Particle size distribution affects strongly physical and mechanical properties of filled polymers. The proposed model uses agglomerate size population balance in its new mathematical formulation expressing agglomeration, break-up and erosion as an evolution of one particle subjected to mean-filed type interaction with others. The erosion parameters have been calculated with experiments in an internal mixer. Controlled breakup of agglomerates was carried out through capillary dies to evaluate breakup parameters. Calcium carbonate filled polypropylene system was used to validate the formulation. La distribution de taille des particules influe fortement sur les propriétés physiques et mécaniques des polymères composites. Un modèle basé sur les bilans de population de taille des agglomérats est proposé. La nouvelle formulation mathématique exprime l'agglomération, la rupture et l'érosion en fonction de l'évolution d'une particule soumise à une interaction représentative moyennée avec les autres. Les paramètres d'érosion ont été calculés lors d'expériences dans un mélangeur interne. La rupture contrôlée des agglomérats a été effectuée dans des filières capillaires afin d'évaluer les paramètres de rupture. La formulation est validée avec le système composite polypropylène-carbonate de calcium. [source] A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteriaBIOTECHNOLOGY & BIOENGINEERING, Issue 2 2009Konstantinos Spetsieris Abstract Cell population balance (CPB) models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions can be obtained through the Collins,Richmond inverse CPB modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation, and (c) the newborn cell subpopulation. This study presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these distributions. The method is generally applicable to rod-shaped cells dividing through the formation of a characteristic constriction. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. The method was applied to E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry. The new assay constitutes a powerful tool that can be used in conjunction with inverse CPB modeling to rigorously quantify single-cell behavior from data collected from highly heterogeneous cell populations. Biotechnol. Bioeng. 2009;102: 598,615. © 2008 Wiley Periodicals, Inc. [source] Simulation of Barium Sulfate Precipitation using CFD and FM-PDF Modeling in a Continuous Stirred TankCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 12 2007Z. Wang Abstract A mixing-precipitation model combining computational fluid dynamics (CFD), finite-mode PDF (probability density function) model, population balance and kinetic modeling has been proposed to simulate the barium sulfate precipitation process in a continuous stirred tank agitated by a Rushton turbine. The effect of various operating conditions such as impeller speed, feed concentration, feed position and mean residence time on the barium sulfate precipitation process is clearly demonstrated. It is shown that the mean crystal size increases by increasing the impeller speed and mean residence time. However, when the feed concentration is increased, the mean crystal size decreases. The predictions are in reasonable agreement with the experimental data in the literature. [source] Branching and Crosslinking in Coordination TerpolymerizationsMACROMOLECULAR REACTION ENGINEERING, Issue 4 2007Rolando C. S. Dias Abstract A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non-linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non-conjugated diene. A rather complex kinetic scheme involving crosslinking and long-chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z -average mean-square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi-batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs. [source] Kinetic Modeling of Non-Linear PolymerizationMACROMOLECULAR SYMPOSIA, Issue 1 2006Mário Rui P. F. N. Costa Abstract Recent developments of a method based upon population balances of generating functions of polymer chain length distributions (CLD) are presented. The calculation of the CLD and how to take into account chain length dependent reactivity are discussed. Prediction of polymer properties is also possible but only easily done for the average molecular radius of gyration; some results are presented for a radical polymerization including transfer to polymer and propagation with terminal double bonds. [source] Mathematical model of the rate-limiting steps for retrovirus-mediated gene transfer into mammalian cellsBIOTECHNOLOGY & BIOENGINEERING, Issue 1 2010Venkata S. Tayi Abstract A quantitative understanding of the process of retrovirus-mediated gene transfer into mammalian cells should assist the design and optimization of transduction protocols. We present a mathematical model of the process that incorporates the essential rate-limiting transduction steps including diffusion, convection and decay of viral vectors, their binding at the cell surface and entry into the cell cytoplasm, reverse transcription of uncoated RNA to form DNA intermediates, transport of the latter through the cytosol to the cell nucleus and, finally, nuclear import and integration of the delivered DNA into the target cell genome. Cell and virus population balances are used to account for the kinetics of multiple vector infections which influence the transduction efficiency and govern the integrated copy number. The mathematical model is validated using gibbon ape leukemia virus envelope pseudotyped retroviral vectors and K562 target cells. Viral intermediate complexes derived from the internalized retroviral vectors are found to remain stable inside the K562 cells and the cytoplasmic trafficking time is consistent with the time scale for retrovirus uncoating, reverse transcription and transport to the cell nucleus. The model predictions of transduction efficiency and integrated copy number agree well with experimental data for both static (i.e., standard gravity) and centrifugation-based gene transfer protocols. The formulation of the model can also be applied to transduction protocols involving lenti- or foamy-viruses and so should prove to be useful for the optimization of several types of gene transfer processes. Biotechnol. Bioeng. 2010;105: 195,209. © 2009 Wiley Periodicals, Inc. [source] Population balance modeling of the conidial aggregation of Aspergillus nigerBIOTECHNOLOGY & BIOENGINEERING, Issue 2 2008P.-J. Lin Abstract Numerous biotechnological production processes are based on the submerse cultivation of filamentous fungi. Process design, however, is often hampered by the complex growth pattern of these organisms. In the morphologic development of coagulating filamentous fungi, like Aspergillus niger, conidial aggregation is the first step of filamentous morphogenesis. For a proper description of this phenomenon it is necessary to characterize conidial populations. Kinetic studies performed with an in-line particle size analyzer suggested that two distinct aggregation steps have to be considered. The first step of conidial aggregation starts immediately after inoculation. Both the rate constants of formation and disintegration of aggregates have been determined by measuring the concentration of conidia at the beginning of the cultivation and the concentration of particles at steady state during the first hours of cultivation. In contrast to the first aggregation step, where the collision of conidia is presumed to be responsible for the process, the second aggregation step is thought to be initiated by germination of conidia. Growing hyphae provide additional surface for the attachment of non- germinated conidia, which leads to a strong decrease in particle concentration. The specific hyphal length growth rate and the ratio of particle concentration to the growing adhesion hyphal surface are decisive matters of the second aggregation step. Both aggregation steps can be described by population dynamics and simulated using the program package PARSIVAL (PARticle SIze eVALution) for the treatment of general particle population balances. Biotechnol. Bioeng. 2008;99: 341,350. © 2007 Wiley Periodicals, Inc. [source] | |||||||||||||