Population Balance Concept Research Articles

Theoretical and conceptual framework for population ageing research

The ageing of the population is a contemporary phenomenon, but its foundations were laid decades ago. Changing age structures and the consequent demographic ageing has only recently become the subject of theoretical (re)consideration, since the theory of demographic transition only values fertility and mortality trajectories. The emergence of ?new? demography takes into account the momentum created by the previous trends in population dynamics and explains the future rejuvenation or ageing of the population. The importance of inherited age structure can be illustrated using an approach that represents distorted cohort flows, showing that baby booms and baby busts can play a crucial role in the future ageing of the population. While in the past it was fertility that predominantly affected age structure, recent research has revealed that changes in life expectancy are becoming a more prominent factor in shaping expected population ageing trends. The general theory of population ageing would have to consider the possible compression of morbidity, dynamic equilibrium, or the expansion of morbidity, since the future course of (healthy) life expectancy is determining the scope of the old and fragile population. The status of theory in demography has long been problematic, since the ?grandiose? theory of demographic transition had to be reevaluated. Modern approaches apply more flexible theoretical frameworks to explain contemporary demographic changes and provide a conceptual background. As such, the important paradigm for the demography of ageing should be the prospective paradigm, which uses information about the longevity of the population and transposes it to population ageing research. The theory of population metabolism seems to adequately define why population ageing is important for cohorts and generation change, especially in cases where distorted cohort flows create prominent cohort oscillation. The need to create adequate policies for changing age composition morphology is highlighted in the domain of institutional adaptation, where the concept of population balance can provide the appropriate framework. Also, as life events tend to take place more often at certain points in the life cycle - for example during adulthood and entering old age - the idea of population densities should be further explored.

Mathematical Modeling of Multiple Crystallization Elution Fractionation (m‐CEF) of Polyethylene and Ethylene/1‐Olefin Copolymer

SummaryMultiple crystallization elution fractionation (m‐CEF) is a new approach for operating CEF using multiple cooling/heating cycles to enhance physical separation of polymers with different chain crystallizabilities. In this work, an m‐CEF model was developed based on the concept of population balance with crystallization and dissolution kinetics. The model was found to describe the previously reported trend of experimental m‐CEF profiles well. Effect of m‐CEF operating cycles and column length was also examined.

Feasibility study of high-rate dissolved air flotation process for rapid wastewater treatment

One advantage of the flotation system is its high applicability as a compact facility. Recently, research for the introduction of additional high-rate dissolved air flotation (DAF) into conventional water treatment plants has been progressing in areas of remodeling water treatment plants, advanced treatment, and combined sewer overflow (CSO) treatment. For successful design and operation of high-rate DAF, laboratory experiments to verify model results and estimate standard values of major parameters by model simulation were performed in this study. With the model simulation having a population balance concept, an operational analysis of bubble-floc aggregates considering a hydraulic situation in the separation zone during high-rate DAF was conducted. Based on the model simulation results, a basic level for high-rate DAF design at a hydraulic loading rate of 30 m/h was determined. On the basis of population balance theory, it can describe the process of bubble-floc aggregate formation at a contact zone and calculate the rate of transfer into the separation zone.

A new theoretical method to calculate shale fracture conductivity based on the population balance equation

Abstract Shale fracture conductivity plays a critical role in determining the long term production of shale wells. High fracture conductivity is achieved by pumping more proppants and minimizing conductivity damage by fracturing fluid. Currently, fracture conductivity is either measured in laboratory following ISO 13503-5 or calculated using correlations derived from extensive laboratory tests by regression analysis. There is a need for a handy and practical tool to calculate shale fracture conductivity reflecting realistic fracturing designs. This paper presents a new correlation to calculate shale fracture conductivity that considers proppant properties, fracture design variables and formation mechanical properties. This correlation is based on the population balance equation for size reduction. It utilizes the population balance concept to predict the crushed proppant size distribution under increasing closure stress. Numerical solution of the integro-differential equation is validated by comparing the computed results with the measured data. The crushed grain size distribution determines the permeability of the sand pack. Fracture width is calculated separately by considering proppant embedment and proppant grain rearrangement. Fracture conductivity is then calculated and compared with laboratory measured conductivity. Finally, the effect of water damage to shale fracture conductivity is considered by bringing in a new modification term. Results show that the population balance equation can reasonably predict the crushed proppant size reduction by properly choosing the selection equation and breakage equation. The calculated shale fracture conductivity can match with the measured fracture conductivity using the Barnett Shale. An exponential expression can be used to account for the water damage effect in the Barnett Shale.

Mathematical Modeling of Crystallization Elution Fractionation of Ethylene/1‐Octene Copolymers

Crystallization elution fractionation (CEF) is a relatively new polyolefin characterization technique used to estimate the chemical composition distribution (CCD) of semicrystalline copolymers. CEF is developed to enhance the resolution and reduce the analysis time of temperature rising elution fractionation (TREF) by separating polymer samples in both the crystallization and elution steps. A model based on the concept of population balance, crystallization/dissolution kinetics, and dispersion model is developed to understand the CEF fractionation mechanisms. The proposed CEF model is found to describe well the experimental CEF profiles of a series of ethylene/1‐octene copolymers with different comonomer contents. image

Mathematical Model of Dynamic Crystallization of Ethylene/1‐Octene Copolymers

SummaryDynamic crystallization (DC) is a fractionation technique to enhance physical separation of polymers with different chain crystallizabilities by crystallizing polymer chains from solution in a column under a constant flow rate. In this work, a mathematical model for describing fractionation mechanism of dynamic crystallization based on the concept of population balance, crystallization kinetic, and dispersion models is proposed by the first time. The model was validated with experimental DC analysis of three ethylene/1‐octene copolymers. The simulated DC profiles were found to describe experimental results well.

Kinetics of magnesium hydroxide precipitation from sea bittern

Magnesium hydroxide is a valuable chemical produced almost in pure form from seawater and its bitterns through precipitation process. Product size distribution of magnesium hydroxide affects the ease of downstream processes of filtration and drying. Therefore, gaining insight into kinetic information in order to improve the size distribution of product particles is essential. In this work, a mechanistic model has been developed for precipitation of magnesium hydroxide from sea bittern. The parameters of model equations based on the population balance concept have been determined using the experimental data of precipitation from a pure synthetic solution containing 3% Mg 2+ and a sea bittern from salt production unit of a local petrochemical complex. The model suggests a higher nucleation rate coefficient and a lower growth rate coefficient for precipitation from the sea bittern compared to that from pure synthetic solution. The nucleation increase and growth decrease which were attributed to the effects of impurities in the bittern, would decrease the settling velocity of the product particles and therefore make the filtration process in industrial use more difficult. However, a larger coefficient of agglomeration rate was predicted by the model for precipitation from the bittern favor to product settling.

An experimental and theoretical study on the concept of dropwise condensation

Hydrophobic coatings have been created through self-assembled mono layers (SAMs) of n-octadecyl mercaptan (SAM-1) and stearic acid (SAM-2) on copper alloy (99.9% Cu, 0.1% P) surfaces to enhance steam condensation through dropwise condensation. When compared to complete filmwise condensation, n-octadecyl mercaptan (SAM-1) coated surface increased the condensation heat transfer rate by a factor of 3 for copper alloy surfaces, under vacuum condition (33.86 kPa) and to about eight times when operated under atmospheric condition (101 kPa). A model using the population balance concept is used to derive a theoretical formula to predict the drop-size distribution of small drops which grow mainly by direct condensation. All the important resistances to heat transfer such as the heat conduction through the drop, vapor–liquid interface are considered in developing this model. By knowing the contact angle of the drop made with the condensing surface and the maximum drop radius the sweeping effect of large falling drops could be calculated which is also incorporated into the model. The effect of interfacial heat transfer coefficient on heat transfer rate is also considered in developing the theoretical model. This is combined with the well known size distribution for large drops proposed by Le Fevre and Rose [E.J. Le Ferve, J.W. Rose, A theory of heat transfer by dropwise condensation, in: Proceedings of 3rd International Heat Transfer Conference, vol. 2, Chicago, 1966, pp. 362–375] which grow mainly by coalescence. There has been a satisfactory agreement between our experimental data and the present theoretical model.

Optimal control of a batch cooling seeded crystallizer

Temperature profile of a batch crystallization has a direct effect on the product qualities. This paper deals with finding a temperature profile such that an objective function pertinent to the final-time product qualities is minimized. By using the concept of population balance, a new method for solving the population balance equation (PBE) is introduced. The optimization algorithm finds the minimum of the objective function with respect to a parameter vector temperature input, subject to the mass balance dynamics as well as the PBE. The results for natural cooling, linear cooling and optimal cooling are compared. The sensitivity of the optimal solution with respect to the model parameters is computed. The proposed strategies are evaluated experimentally for an ammonium sulfate–water system.

Industrial Crystallization: Developments in Research and Technology

In this review paper developments in industrial crystallization are discussed with emphasis on recent highlights in the field. One of the most important past developments can be found in the introduction of the population balance concept. This will be discussed together with more recent developments and topics currently of great interest such as molecular modelling, polymorphism and polymorph prediction at the fundamental scientific level as well as melt crystallization equipment, eutectic freezing crystallization and crystallization control by means of on-line techniques at the applied, industrial level. Potential future directions for industrial crystallization are discussed with reference to past and present developments. The future of industrial crystallization is envisaged to lie in areas such as nano-particle production by means of crystallization and protein crystallization, in addition to some of those mentioned above.

Experimental study and modeling of fluidized bed coating and agglomeration

This work deals with the fluidized bed coating and agglomeration of solid particles. The effect of particle size on coating criteria was investigated using sand particles as the coating support and aqueous solutions containing NaCl as coating liquid. The results showed that both growth rate and efficiency increase with decreasing the particle size. The growth was mainly governed by layering for particles larger than 200 μm, whereas for finer particles it occurred by agglomeration. As the particle size became less than 90 μm, the coating operation led to uncontrolled growth and bed quenching. However, the coating of the same particles was successfully achieved by adding some coarser particles. In addition, a mathematical model based on the population balance concept, taking into account the simultaneous growth by layering and agglomeration, was established to predict the time evolution of the particle size distribution. The comparison between experimental and calculated data permitted the establishment of a law for the size dependency of the agglomeration kernel.

Modeling of heat transfer in dropwise condensation

A model using the population balance concept is developed to predict the drop size distribution for small drops that grow by direct condensation. The resistances to heat transfer due to the drop (conduction through the drop, vapor-liquid interfacial resistance, drop curvature) and due to the promoter layer and the sweeping effect of falling drops are incorporated into the model and are also included in calculating the heat transfer rate through a single drop. The total heat flux is calculated from the drop size distributions and the heat transfer rate through a single drop. Drop size distribution for large drops that grow by coalescence is obtained from the works of Rose and Glicksman. The work in this paper reveals that to adequately calculate the heat flux, all the resistances to heat transfer due to the drop and the promoter layer have to be included. Considering heat conduction through the drop as the only resistance to heat transfer overestimates the heat flux. The amount of overestimation increases as the temperature difference increases.

Kinetics of the cooling crystallization of sodium sesquisulfate from 4.5 mol/l sulfuric acid

AbstractSimulating effluent from chlorine dioxide generators, the crystallization kinetics of sodium sesquisulfate from 4.5 mol/L sulfuric acid were studied under cooling conditions. The crystal growth and nucleation rates were determined using the population balance concept and the crystal size distribution from a continuous mixed suspension mixed product removal (MSMPR) crystallizer. Crystallization temperatures studied were 45, 50, 55 and 60°C.The crystal growth and nucleation rate data were correlated to supersaturation and temperature. Nucleation rate was found to be a function of suspension density (secondary nucleation). The activation energies for nucleation and growth are reported.

Deposition of Inhaled Particles: Discussion of Present Modeling Techniques

A mathematical model of particle deposition in the mammalian respiratory system should include the following elements: morphology and geometry of the lung, gas flow structure in the inspiration–expiration cycle, and pattern of particle deposition as a result of particle mass and geometry coupled with the first two elements. The particle trajectory concept and particles population balance concept are discussed as the ways for calculating the efficiency of deposition. The influence of the particle shape, growth caused by water vapor deposition, coagulation, and deformation of the airways on the deposition is emphasized.

Mixed suspension - mixed product removal crystallization kinetics: Effect of the method of supersaturation generation

Three methods of continuous crystallization of potassium aluminium sulphate have been compared: crystallization by cooling, precipitation from solutions of component salts (potassium sulphate and aluminium sulphate) and salting-out with ethanol. Crystal size distribution of the products has been used to obtain crystallization kinetic data in two parallel ways, viz. using the concept of population balance and that of mass oversize distribution, both of which led to similar conclusions. The results of cooling and precipitation are comparable, but crystallization by salting-out with ethanol leads to smaller crystals and the results strongly depend on the alcohol concentration, which can be explained by the influence of micromixing.

Preparation of spherical wax matrices of sulfamethoxazole by wet spherical agglomeration technique using a CMSMPR agglomerator

Spherical wax matrices of sulfamethoxazole were prepared by a wet spherical agglomeration technique using a model continuous mixed suspension mixed product removal (CMSMPR) agglomerator to develop a practical continuous operation system. The average diameter of products increased at the initial stage of operation until reaching a maximum at 5 to 7 minutes elapsed after starting. This maximum point roughly corresponded to a half of average retention time. Thereafter the particle size decreased gradually and reached the equilibrium state. The average size of products obtained at steady state decreased on decreasing the feeding rate of bridging liquid, but increased on decreasing the agitation speed and the feeding rate of aqueous suspension. The rate of agglomeration was analysed using the concept of population balance proposed by Randolph and Sikdar. The agglomeration rate increased with increase of particle size for sizes above 200 – 300 μm. For sizes below 200 μm, the agglomeration rate was almost independent of particle size.