Apple osmotic dehydration described by three-dimensional numerical solution of the diffusion equation

ABSTRACT

In the present study, experimental data of osmotic dehydration kinetics of apple, cut into slices with parallelepiped shape, were simulated using two types of diffusion models. Model 1 considers the constant values of mass diffusivities and volume of the slices. Model 2, on the other hand, considers variable mass diffusivities and also the shrinkage of the product. The numerical solution of the three-dimensional diffusion equation in Cartesian coordinates was obtained through the finite volume method, with a fully implicit formulation and boundary condition of the first kind. Process parameters were determined by optimization using the experimental data sets, through the minimization of an objective function, called χ². The results of the osmotic dehydration kinetics were compatible with those of other studies found in the literature. Process temperature and osmotic solution concentration had influence on the phenomenon, but temperature was preponderant. A study was conducted on water and sucrose distribution during the osmotic dehydration. The results obtained through the mathematical model that considered the variable diffusivity and shrinkage showed greater adequacy to the experimental data.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

SCALE ANALYSIS AND PARAMETRIC STUDY OF TRANSIENT HEAT/MASS TRANSFER IN THE PRESENCE OF NONPOROUS SOLID ADSORPTION

A transient, two-dimensional theoretical analysis of combined heat and mass transfer in the presence of adsorption/desorption is developed to study the fundamentals of heat and mass transfer dynamics. A parallel-plate rectangular channel is used as a model system. Appropriate surface boundary conditions for heat and mass transfer and adsorption/desorption interactions are formulated. A scale analysis of the governing equations is performed in order to identify the dimensionless physical parameters governing the process and to obtain the order-of-magnitude estimates for characteristic time constants of the system dynamics. Predictions of the scale analysis are validated against the results of the parametric study obtained through the numerical solutions of the governing equations. The findings demonstrate that the scale analysis is a very powerful analytical tool which allows one to evaluate the effects of different process parameters on heat and mass transfer dynamics in the presence of adsorption without performing the exhaustive numerical calculations.     

Modeling of Diffusion in Capillary Porous Materials During the Drying Process

ABSTRACT

This paper presents a model of heterogenous diffusion in capillary porous materials during the process of drying. The governing heat and mass transfer equations have been established using the liquid as well as vapor flow. Two models have been presented. Model 1 does not consider the heat conduction while the model 2 has been established by considering the conduction. The developed models and the numerical solutions of the resulting differential equations can take into account the moisture and temperature dependent thermophysical properties of the product. All equations have been established in spherical coordinates but the programme written for the purpose of calculations can be used for other geometries also. Numerical calculations have been performed for gas concrete and tiles using model 1, while model 2 has been used for gas concrete only because of the lack of data for thermophysical properties of the tile. For gas concrete it was seen that conduction has only marginal effect on the drying process and the numerical predictions of the drying process were reasonably accurate.     

Numerical simulation of the mass loss process in pyrolizing char materials

We present here a decoupling technique to tackle the entanglement of the nonlinear boundary condition and the movement of the char/virgin front for a thermal pyrolysis model for charring materials. Standard numerical techniques to solve moving front problems — often referred to as Stefan problems — encounter difficulties when dealing with nonlinear boundaries. While special integral methods have been developed to solve this problem, they suffer from several limitations which the technique described here overcomes. The newly developed technique is compared with the exact analytical solutions for some simple ideal situations which demonstrate that the numerical method is capable of producing accurate numerical solutions. The pyrolysis model is also used to simulate the mass loss process from a white pine sample exposed to a constant radiative flux in a nitrogen atmosphere. Comparison with experimental results demonstrates that the predictions of mass loss rates and temperature profile within the solid material are in good agreement with the experiment. Copyright © 1999 John Wiley & Sons, Ltd.     

低温膜蒸馏及其过程模拟

采用聚丙烯中空纤维膜对纯水介质膜蒸馏、冷侧盐水循环有温差膜蒸馏及等温渗透膜蒸馏进行了实验研究,建立了描述膜蒸馏过程的传质及传热数学模型,以实验数据为基础对模型中的参数进行了回归并对数学模型进行了计算机数值求解,计算结果与实验数据吻合较好     

Modeling the mass transfers during the elaboration of chitosan‐activated carbon composites for medical applications

Hydrogels composites composed of chitosan and activated carbon were prepared for medical applications using the vapor‐induced phase separation process. Since the gelation process involves mass exchanges between the polymer solution and the air, the kinetics of mass transfer were investigated through experimental and modeling approaches. Among the formulation and process parameters, gravimetric measurements exhibited that mass transfers were mostly controlled by the initial ammonia partial pressure. A nonisotherm mass‐transfer model was developed to predict the nonsolvent and solvent exchange rates, therefore, the water and ammonia concentration profiles within the sample during the process. The numerical results were successively validated with gravimetrical kinetic curves obtained in a chamber where the process parameters were controlled. The model aimed also at predicting the pH moving front along the film thickness. The gelation time could also be predicted for different operating conditions (formulation and process parameters). © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Experimental and model-based study of biohydration of acrylonitrile to acrylamide in a microstructured chemical system

Experimental and model-based studies of acrylonitrile biohydration catalyzed by free cells were conducted in this work. The high ratios of the two phases of the reaction system and the effects of inhibition and inactivation on the enzyme make the process complicated; thus, its exact kinetics have never been reported. To fully understand and model the reaction, a microstructured chemical system was employed to investigate droplet dispersion, the mass transfer process, the intrinsic kinetics with inhibition and inactivation, and the preparation process of acrylamide. By adjusting the structure size and flow conditions of the microreactor, acrylonitrile droplets of 40 μm were obtained and enhanced mass transfer was achieved. Compared to previous studies, the microchemical system in our work provides more accurate kinetic parameters, with a much higher maximum reaction rate and much smaller Michaelis constant. The numerical predictions of the process model show good agreement with experimental results.     

Ultrasonic-Assisted Osmotic Dehydration of Carrot Followed by Convective Drying with Continuous and Intermittent Heating

The aim of the studies was to analyze the effect of ultrasound action on osmotic pretreatment and then on drying kinetics in continuous and intermittent drying conditions, and on the final product quality. This article presents the results of intermittent-convective drying of carrot preceded by ultrasonic assisted osmotic dehydration in fructose aqueous solutions. The theoretical drying kinetics developed from the numerical solution of mathematical model is validated using the experimental data. It has been shown that combination of ultrasonic assisted osmosis with intermittent-convective drying accelerates the drying process and improves the quality of dried biomaterial. A good adherence of the numerically determined kinetic curves confirms the usefulness of the presented model and its possible application to construction of controlled and optimized drying processes.     

Osmotic dehydration of lemon (Citrus limon L.) slices: Modeling mass transfer kinetics correlated with dry matter holding capacity and juice sac losses

Osmotic dehydration of lemon slices was performed using hypertonic NaCl solution. Due to low dry matter holding capacity (DHC) of lemon, the moisture loss, salt gain, and solid loss kinetics during osmotic dehydration were studied by considering the loss of juice sacs from lemon. The slices were immersed in the osmotic solutions maintained with four concentrations of NaCl (5–20%, w/v) and three temperatures (30, 40, and 50°C) for predetermined time intervals (10–180?min). The sample to solution ratio was maintained at 1:10. Azuara model based on Peleg model was used to determine the equilibrium moisture loss and salt gain. Apart from the moisture loss and salt gain, it was found that the loss of solid constituents and juice sacs from the fruit into the osmotic solution was significant. Therefore, the DHC was determined to correlate the rate of solid loss. The DHC was found to be greatly affected by temperature as lemon was less capable to withhold its cell integrity at higher temperature. A combined correlation model was used to determine the effect of osmosis time, solution concentration, and temperature on moisture loss, salt gain, and solid loss. High temperature is not preferable for osmotic dehydration of lemon as it increases losses. The optimal condition was found to be 20% salt concentration and 30°C osmotic solution for 180?min to attain high moisture loss, less solid loss, and required salt uptake within allowable limits.     

吸附型固载二氧化氯释放过程动力学

对两剂型固载二氧化氯产品自动释放二氧化氯气体的过程进行了实验研究。提出了吸附型固载二氧化氯活化反应的分段动力学方程和渗透传质速率方程，通过模型分析探讨了产品的释放规律及其影响因素，并获得可应用于实际释放过程的动力学模型。     

Incorporation of osmotic pressure in an integrated incremental model for predicting RO or NF permeate concentration

Consideration of concentration, recovery and osmotic pressure has been incorporated in a fully integrated diffusion based mass transfer model identified as integrated osmotic pressure model (IOPM). Osmotic pressure was incorporated into the model using correction coefficients that were calculated from boundary conditions, which were determined from the feed and concentrate streams osmotic pressures. Predicted permeate stream water quality using IOPM and the homogenous solution diffusion model (HSDM) were compared with and without consideration of osmotic pressure. IOPM was verified using independently developed data from full and pilot scale plants. The numerical simulation and statistical assessment show that osmotic pressure corrected models are superior to non-osmotic pressure corrected models, and that IOPM improved predictability of permeate stream water quality.     

An Eulerian modeling approach of wood gasification in a bubbling fluidized bed reactor using char as bed material

We present an Eulerian multiphase approach for modeling the gasification of wood in fluidized beds. The kinetic theory of granular material is used to evaluate constitutive properties of the dispersed solid phase. Comprehensive models for wood pyrolysis, char gasification and homogeneous gas phase reactions are taken into account. The dispersed solid phase within the reactor is modeled as three continuous phases, i.e., one phase representing wood and two char phases with different diameters. In contrast to most other studies we investigate a fluidized bed which consists of wood and char particles without additional inert particles such as limestone or olivine. 2D simulation results for a lab-scale bubbling fluidized bed reactor are presented and compared with experimental data for product gas and tar concentrations and temperature. We investigate the influence of two different classes of parameters on product gas concentrations and temperature: (i) operating conditions such as initial bed height, wood feeding rate, and reactor throughput and (ii) model parameters like thermal boundary conditions, primary pyrolysis kinetics, and secondary pyrolysis model. Two different pyrolysis models are implemented and are compared against each other. The numerical results indicate (i) a relatively low influence of the investigated operating conditions on the main product gas components, (ii) a high sensitivity of main product gas components CO and CO₂ on the thermal boundary condition, and (iii) a very strong influence of operating conditions and model parameters on the tar content in the product gas.     

Calculation of characteristics of heat and mass transfer during destruction of thermoprotective material

The process of nonstationary heat and mass transfer in a carbon-epoxy composite under the action of a high-enthalpy flow is analyzed numerically within the framework of the mathematical model of a reacting medium. Analytical solutions have been obtained for the value of mass entrainment from the material surface, depending on the entrainment velocity at the expense of pyrolysis of the carbon-epoxy composite. The solutions obtained are in agreement with the results of numerical integration for constant and variable parameters of retardation. The possibility of simplifying the boundary conditions is analyzed, and recommendations for performing serial calculations are offered.Research Institute of Applied Mathematics and Mechanics, Tomsk 634050. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 4, pp. 76–84, July–August, 1994.     

Convective drying of osmotically dehydrated apples described by three-dimensional numerical solution of the diffusion equation with analysis of water effective diffusivity spatial distribution

Abstract

This study presents two liquid diffusion models to represent the convective drying of apple, osmotically dehydrated in sucrose solution, cut into parallelepiped-shaped pieces. Model 1 considered water diffusivity and the volume of the slices with constant values. Model 2 considered water effective diffusivity and the dimensions of the slices as variable. The numerical solution of the three-dimensional diffusion equation in Cartesian coordinates was obtained through the finite volume method, with a fully implicit formulation and boundary condition of the third kind. Process parameters were estimated by an optimizer using experimental data. A spatial distribution analysis was carried out for water effective diffusivity and moisture content in the apple slices. The results showed that the concentration of the osmotic solution used in the pretreatment influenced the drying process and that the mathematical model that considered a variable diffusivity and shrinkage was more suitable to describe the experimental data.     

Dimensionless Formulation of Convective Heat Transfer in Fry‐Drying of Sewage Sludge

Fry‐drying is an alternative for heat and mass transfer intensification. The process reuses waste oil as a heating medium for drying by contact with the wet sludge. At the end of the process, a stable derived fuel is obtained, a granular solid composed of the dried indigenous sewage solid and the impregnated oil. The fry‐dried sludge is storable and transportable without any pathogen elements. Knowledge about heat and mass transfer rates during the frying process is essential in order to assess the quality of the final product such as calorific value, oil uptake, porosity changes, etc. The heat transfer properties including transfer by free convection between the solid and the frying oil are fundamental for the process design and manufacturing of the fry‐dried product. The convective heat coefficient by temperature measurement and overall energy balance calculation is determined. The heat flux is calculated from the fry‐drying kinetics including moisture loss and oil intake kinetics. Various hydrodynamic regimes for convective heat transfer during the frying process are discussed (non‐boiling, boiling, and low‐boiling regime). A dimensionless formulation for estimating the convective transfer is proposed.     

Modeling of heat recovery from a steam‐gas mixture in a high‐temperature sorption process

A high pressure condenser is considered to remove water vapor as well as recover heat from the desorbed steam—CO₂ gas mixture in a novel sorption enhanced reaction process. It is possible to have water condensation at the gas side as well as water evaporation at the coolant water side because of large temperature difference between the hot and cold side. A model of heat and mass transfer and phase change was developed to understand the complex phenomena associated with the simultaneous condensation and evaporation taking place in the unit. A finite difference method was used to solve the boundary value problem. Additional insight was obtained by describing the operating lines and equilibrium condition in an enthalpy diagram. The model was used to explore the performance in terms of the heat recovery. The heat recovery was best at the beginning of the process when the superheated steam was generated. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Numerical simulation of temperature and concentration distributions in fluidized beds with liquid injection

In this paper a numerical simulation study of dynamic behavior of a fluidized bed with liquid injection is presented. A continuum model has been developed taking into account the mass and energy balances of solid, gas as well as liquid to describe the temperature and concentration distributions in gas-solid-fluidized beds. The model considers the deposition efficiency of the liquid droplets as well as the influence of the spray nozzle region. For solving the non-linear partial differential equations with discrete boundary conditions a finite element method is used. Numerical computations have been done with two different schemes of time integration, a fully implicit and a semi implicit scheme. The complex correlations of mass and liquid flow rates, mass and heat transfer, drying, and transient two-dimensional air humidity, air temperature, particle wetting, liquid film temperature and particle temperature were simulated. The model was validated with transient measurements of the air temperature and air humidity at the outlet of a fluidized bed with water injection.     

Drying of clay slabs: Experimental determination and prediction by two-dimensional diffusion models

Experiments on convective drying of clay slabs with an initial moisture content of 0.11 (dry basis, db) were performed at 50 and 90 °C. A two-dimensional numerical solution of the diffusion equation with a boundary condition of the third kind was proposed to describe the process using a constant (model 1) and variable (model 2) effective mass diffusivity value. The solution was coupled with an optimizer to determine the process parameters at each temperature using experimental datasets. The analyses of the results indicated good agreement for model 2 between each experimental dataset and the corresponding simulation.