Modeling Particle Formation at Spray Drying Using Population Balances

There have been several efforts to simulate the physical processes in a single droplet during spray drying in the last several years, but most of the models do not describe the solid formation in detail. In this work, the development of the microscopic solid structure in a droplet during spray drying is simulated. A radial-symmetric model of the droplet is used to simulate the mass and heat transport. The solid formation at every radial discretization point is obtained by the solution of population balances. This way, the distribution of the particle number density in the droplet depending on the macroscopic process parameters can be predicted. The model equations are solved in a normalized coordinate system to be able to describe the shrinkage of the droplet. The suitability of these population balances will also be discussed. For the validation, monodisperse single droplets consisting of a solution or suspension are dried with constant boundary conditions.     

SIMULATION OF DRYING SUSPENSIONS IN SPOUT-FLUID BEDS OF INERT PARTICLES

In spouted and spout fluid bed dryers, the suspension is spread into the bed of inert particles, covering these particles with a thin layer. As the inert particles circulate, this suspension layer is dried and must become brittle enough to break off by the particle attrition. The powder produced is then carried out by air. Problems with the spout stability, particle agglomeration and powder deposits inside the column should be overcome by controlling the drying operation. The present work is aimed at modeling and simulating the drying of suspensions, such as organic and biological pastes, in conical spout-fluid beds of inert particles. A computer program has been developed combining the air flow and particle circulation models with the mass and energy balances and the drying kinetic equations in order to describe this drying process. The effect of cohesive forces is also incorporated to the fluid flow model. Simulation results are analyzed and compared with experimental data reported in the literature. Implication of these results in drying suspensions is also discussed.     

Modeling Particle Formation at Spray Drying Using Population Balances

There have been several efforts to simulate the physical processes in a single droplet during spray drying in the last several years, but most of the models do not describe the solid formation in detail. In this work, the development of the microscopic solid structure in a droplet during spray drying is simulated. A radial-symmetric model of the droplet is used to simulate the mass and heat transport. The solid formation at every radial discretization point is obtained by the solution of population balances. This way, the distribution of the particle number density in the droplet depending on the macroscopic process parameters can be predicted. The model equations are solved in a normalized coordinate system to be able to describe the shrinkage of the droplet. The suitability of these population balances will also be discussed. For the validation, monodisperse single droplets consisting of a solution or suspension are dried with constant boundary conditions.     

Modeling of the drying process in paper plants

In this study a model for the drying process in paper production plants was developed based on the mass and heat balances around drying cycles. Relationships for the heat transfer coefficients between the web and the air as well as between the drying cylinder and the web were extracted from the closed-loop plant operation data. It was found that the heat transfer coefficients could be represented effectively in terms of moisture content, basis weight and reel velocity. The effectiveness of the proposed model was illustrated through numerical simulations. From the comparison with the operation data, the proposed model represents the paper plant being considered with sufficient accuracy.     

Dynamic modeling of paper drying processes

A dynamic model describing the behavior of a multi-cylinder drying section in paper production plants was developed based on the mass and heat balances around drying cylinders. The balance equations consist of sets of differential equations describing heat and mass transfer around the canvas, the web and the drying cylinders. Values of cylinder temperatures and moisture contents were estimated and compared with operation data. To obtain further information for energy consumption, the generation of entropy at each drying cylinder was investigated based on the model developed.     

The Comparison of Two Models of Convective Drying of Shrinking Materials Using Apple Tissue as an Example

Modeling of drying of capillary-porous materials is a mathematically complex problem. It takes into consideration simultaneous heat and mass transfer inside the material with physicochemical properties changing during the drying process. Modeling of the process mentioned above consists of describing the heat and mass transfer balances by means of differential equations. Moisture diffusion coefficient as a function of moisture content and temperature of the material is a crucial parameter that controls the process. An additional problem occurs when moving boundary of the shrinking material is taken into account. In the present work, the identification of diffusion coefficient as a function of moisture content and temperature on the basis of two different models is shown. The two models include the Pakowski model (defined in the stationary coordinates) and the Kechaou model (defined in moving coordinates). Experimental data necessary to verify the models were obtained on the basis of series of tests for different boundary conditions performed on an apple tissue. During the drying process, samples of apple undergo significant volumetric shrinkage. In this article, the comparison of the two models describing the convective drying process of shrinking material is presented together with the comparison of the identified moisture diffusion coefficient.     

The Comparison of Two Models of Convective Drying of Shrinking Materials Using Apple Tissue as an Example

Modeling of drying of capillary-porous materials is a mathematically complex problem. It takes into consideration simultaneous heat and mass transfer inside the material with physicochemical properties changing during the drying process. Modeling of the process mentioned above consists of describing the heat and mass transfer balances by means of differential equations. Moisture diffusion coefficient as a function of moisture content and temperature of the material is a crucial parameter that controls the process. An additional problem occurs when moving boundary of the shrinking material is taken into account. In the present work, the identification of diffusion coefficient as a function of moisture content and temperature on the basis of two different models is shown. The two models include the Pakowski model (defined in the stationary coordinates) and the Kechaou model (defined in moving coordinates). Experimental data necessary to verify the models were obtained on the basis of series of tests for different boundary conditions performed on an apple tissue. During the drying process, samples of apple undergo significant volumetric shrinkage. In this article, the comparison of the two models describing the convective drying process of shrinking material is presented together with the comparison of the identified moisture diffusion coefficient.     

Thermodynamic characterization of single-stage spray dryers: Mass and energy balances for milk drying

Spray drying is an efficient unit operation applied in food drying that demands a high amount of energy compared to vacuum evaporation and membrane filtration. The objective of this work was to present a mathematical model-like basis for the construction of mass and energy balances. For this purpose, two lab-scale single spray dryers in milk drying with different evaporative capacities have been used as example. The values of the absolute humidity, mass and energy losses, energetic specific consumption (ESC), and the efficiency of the process were obtained by calculations developed in this work. The mathematical model was valid for the evaluation of mass and energy losses, and it allowed us to compare the efficiencies of spray dryers with different designs. From this model, it is possible to compare different drying processes and dryers.     

Towards a Complete Population Balance Model for Fluidized-Bed Spray Agglomeration

This article concerns the simultaneous processes of agglomeration and drying. In order to predict temperatures and moisture content in gas and particle phase, heat and mass transfer mechanism and particle size enlargement has been considered in one model. The model takes heat and mass transfer phenomena between particle phase, suspension gas, and bypass gas into account. The disperse phase is modeled by a three-dimensional population balance (PBE), which can be reduced to a set of three one-dimensional PBEs. The latter are coupled with heat and mass transfer balances of the gas phase. Furthermore, some simulation and experimental results are presented.     

Fluidized Bed Air Drying: Experimental Study and Model Development

The presented study describes the processes and mechanisms of batch fluidized bed drying. The influencing factors of hot air drying are theoretically and experimentally examined, in order to present the relations between temperature and humidity profiles and all other drying parameters. A physical model is presented to facilitate the calculation of the drying processes under defined conditions. Three succeeding drying stages are therefore modeled. Mass and energy balances including all components taking part in the process are formulated. The model clarities the drying process under the assumption of pure heat transfer mechanisms. It does not contain adaptive parameters and takes into account an inactive bypass fraction of the fluidization and drying medium. The evaluation of the model was successful for two fluidized bed plants with nominal widths of 100 mm and 400 mm. The experiments showed sufficient accuracy and transferability of the model to equipment of application‐oriented dimensions.     

A one-dimensional plug-flow model of a counter-current spray drying tower

A one-dimensional numerical model for a detergent slurry drying process in a counter-current spray drying tower is developed for the prediction of the gas and droplet/particle temperature profiles within the tower. The model accommodates droplets/particles over a range of sizes. A semi-empirical slurry droplet drying model is integrated with a counter-current tower simulation based on mass, energy and particulate phase momentum balances in order to calculate the drying rate and the particle residence time within the tower. The coupled first order ordinary differential equations for the two phases are solved numerically using the iterative shooting method in an algorithm developed within MATLAB. The predictions of the numerical model are compared with industrial pilot plant data. The results are found to vary significantly with the specified size distribution of the droplets. Despite the simplicity of the model in ignoring the coalescence, agglomeration, wall deposition and re-entrainment, the model gives reasonable agreement with the experimental data.     

An Experimental Study and Mathematical Simulation of Wheat Drying

A fixed-bed dryer was designed and constructed and drying experiments with fixed beds of wheat were carried out under various conditions of drying air with wheat of several initial moisture contents. The air temperature and moisture content of wheat at various levels within the beds were measured periodically. A computer program based on energy and mass balances was developed to simulate the deep bed drying process. Experimental data from the dryer were compared with the results from this program. The results showed that there was good agreement between the simulated drying rates between the layers and those experimentally observed. In addition, there was a good agreement with respect to the shapes of the drying air temperature profiles.     

Dynamic modeling of the steam supply system for a paper drying cylinder

A dynamic model describing the principles of a steam supply system for a paper drying cylinder used in paper production plants was developed based on the mass and heat balances around the cylinder. The balance equations consist of sets of differential equations describing heat and mass transfer around the canvas, the web and the drying cylinder. The effects of the steam valve adjustment on steam pressure, temperature and moisture content were investigated based on the model developed. It was found that application of simple model predictive control to the operation of steam supply system is enough to achieve satisfactory drying performance in a single paper drying cylinder.     

Moisture Prediction During Paste Drying in a Spouted Bed

The objective of this work was to derive and experimentally verify a hybrid CST/neural network model to determine the moisture content of the powders produced during paste drying in a spouted bed and describe the highly coupled heat and the mass transfer. The model was derived from overall energy and mass balances with effective drying kinetics given by a neural network. Simulations were performed in MatLab and drying experiments for model verification were carried out for different pastes in a conical, semi-pilot-scale spouted bed.     

Air-Drying of Seeds: A Review

Beginning with harvesting, seeds are usually subjected to a series of processes which include drying for immediate or future use. Seed quality can be influenced by several factors during drying. This article presents a review of the seed air-drying process, including mathematical models based on differential equations derived from mass and energy balances for seeds and air in fixed and moving bed dryers. The article concludes with an overview of several potential drying technologies that can be applied to seeds.     

喷雾干燥过程工艺参数的模拟计算

对喷雾干燥的计算机模拟计算进行了初步探讨，用FORTRAN语言编制了程序，对喷雾干燥过程进行了总体衡算和微元衡算，使计算快速、准确，而且便于程序与数据管理。结果表明，计算机完全可以替代人工手算。     

An Experimental Study and Mathematical Simulation of Wheat Drying

Abstract

A fixed-bed dryer was designed and constructed and drying experiments with fixed beds of wheat were carried out under various conditions of drying air with wheat of several initial moisture contents. The air temperature and moisture content of wheat at various levels within the beds were measured periodically. A computer program based on energy and mass balances was developed to simulate the deep bed drying process. Experimental data from the dryer were compared with the results from this program. The results showed that there was good agreement between the simulated drying rates between the layers and those experimentally observed. In addition, there was a good agreement with respect to the shapes of the drying air temperature profiles.     

A model of the coagulation process with solid particles and flocs in a turbulent flow

A mathematical model was developed on the basis of population balances to predict the floc size distribution in a coagulating suspension. The coagulation process is performed in a stirred tank reactor with a turbulent flow field. In the population model the influence of the different local energy charges inside the reactor is taken into account. Moreover two sorts of particles are distinguished, i.e. the originally present and completely dispersed primary particles and the flocs. Contrary to the primary particles the flocs can be disrupted due to pressure and shear forces as they are mechanically not very stable. This different behaviour requires separate population balances for the two sorts of particles. The model parameters that are necessary are adapted to one single experiment.For the steady state the results represent different floc size distributions dependent on the solid concentration and the energy charge. Moreover it is shown that the assumption of an ideally mixed reactor that is often used cannot be maintained to be always true for the prediction of the resulting floc size distribution. The calculation results achieved are validated by image processing measurements of coagulating quartz particles in an aqueous suspension.     

Modelling spatial distributions of moisture and quality during drying of granular baker's yeast

A distributed parameter model was developed to predict the drying behaviour of granular baker's yeast by setting up material and heat balances at the particle level. Temperature and moisture gradients were calculated for cylindrical and spherical granules. The performance of the model with two granule sizes was compared with experimental measurements. The model was initially used for non‐shrinking granules but later modified to take shrinkage into account. The reduction in granule size during the course of drying was estimated and good correspondence with experimental measurements was obtained. In addition to temperature and moisture gradients, the product quality was predicted during drying and compared to experimental results. The accuracy of the model was better than the lumped parameter model.     

过程优化控制技术在SPVC干燥过程中的应用

阐述了采用"悬浮干燥过程优化控制技术"改造SPVC干燥装置的情况。运行数据表明,该技术提高了旋风干燥塔塔温控制精度、悬浮树脂成品的优级品率及挥发物指标。