Heat and Mass Transfer Coefficients in Computer Simulation of Paper Drying

The development of a mathematical model and a computer program to facilitate the study of thc multi-cylinder paper drying process is presented. Experimentally determined values for different heat and mass transfer coefficients are used to ensure the physical validity of the model. A unique feature of the model is its inclusion of a mass transfer coefficient for the dryer fabric. Thus far. the mass transfer mechanisms in the web have not been included. Two heat transfer coefficients are used to tune the model to actual mill data. They areassigned values that are consistent with experimental data. The agreement between predicted and experimental data, obtained hom nine industrial paper dryers, is generally very good. The investigated basis weights range from 48 to 240 g/m2.

Calculations indicate that the condensate and contact heat transfer coefficients have a major influence on the drying process. The thermal conductivity of the paper and cylinder shell, respectively, are relatively important. whereas the influence of the fabric mass transfer coefficient and the cylinder-fabric-paper heat transfer coefficient are less pronounced. Some guidelines on how to obtain corect values are discussed.     

Heat and Mass Transfer Coefficients in Computer Simulation of Paper Drying

ABSTRACT

The development of a mathematical model and a computer program to facilitate the study of thc multi-cylinder paper drying process is presented. Experimentally determined values for different heat and mass transfer coefficients are used to ensure the physical validity of the model. A unique feature of the model is its inclusion of a mass transfer coefficient for the dryer fabric. Thus far. the mass transfer mechanisms in the web have not been included. Two heat transfer coefficients are used to tune the model to actual mill data. They areassigned values that are consistent with experimental data. The agreement between predicted and experimental data, obtained hom nine industrial paper dryers, is generally very good. The investigated basis weights range from 48 to 240 g/m2.

Calculations indicate that the condensate and contact heat transfer coefficients have a major influence on the drying process. The thermal conductivity of the paper and cylinder shell, respectively, are relatively important. whereas the influence of the fabric mass transfer coefficient and the cylinder-fabric-paper heat transfer coefficient are less pronounced. Some guidelines on how to obtain corect values are discussed.     

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.     

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.     

A Quasi‐Steady State Shell and Shrinking Core Approach to the Drying of Porous Particles and an Example of Parameter Identification

A quasi‐steady state shell and shrinking core approach which recognizes heat and mass transfer resistances in both the gas and particle phases for drying of a porous particle is proposed. A mean field model (constant properties) using this approach was embedded in a spreadsheet combined with a genetic algorithm for parameter identification to provide an easy means of characterizing the drying process from drying data. In drying, assuming a mean field, four major parameters are typically unknown: two related to the process (heat and mass transfer coefficients) and two which incorporate porous particle properties (shell thermal conductivity and vapour diffusivity). It is shown how these four parameters may be determined from experimental drying data. The model was applied to data for spouted bed drying of rice. For the particular case studied, external heat transfer was found to be the controlling mode, although resistance to moisture diffusion within the particle is important. The approach presented admits of future refinements to improve its scope and utility.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

Modeling and simulation of heat and mass transfer during drying of solids with hemispherical shell geometry

A heat and mass transfer model was proposed to describe the moisture and temperature evolution during drying of solid products with hemispherical shell geometry (HSG). The dimensionless form of the model was numerically solved for both several drying conditions and values of a geometrical factor related with the inner radius of the HSG to obtain their moisture and temperature profiles. In addition, average drying kinetics were calculated from the volume integration of local moisture values. A theoretical and numerical approach was used to develop a mass transfer analogy between the proposed HSG and a simpler flat slab-shaped product. These analogies provide simple mathematical expressions for drying process simulation and estimation of diffusion coefficients in solids with the proposed geometry, and may be applicable to other mass and heat transfer operations. Furthermore, the presented procedure may be used to develop similar expressions in other non-traditional or dissection geometries.     

ANALYSIS OF HEAT AND MASS TRANSFER DURING DRYING OF PAPER/BOARD

ABSTRACT

A mathematical model has been successfully developed to study the heat and mass transfer process during paper drying. This model takes into account the consective transfer of vapor and liquid apart from the known transport mechanisms of capillary flow of liquid, diffusion, vaporization-condensation, and heat conduction. The partial differential equations describing temperature, saturation and pressure change within the web during drying with associated boimdary conditions and initial conditions were solved using finite difference method. The model predictions show that during the drying process the web can be conveniently divided into three different zones, namely dry zone, wet zone and an intermediate zone. The movement of liquid and vapor in opposite directions in the intermediate zone is similar to the action of a heat pipe. Also, as drying proceeds the location of the intermediate zone and hence the heat pipe advances progressively through the thickness of the web.     

A Simulation Model for Heat Pump Dryer Plants for Fruits and Roots.

Dryer design requires food properties, drying rate and mass-heat transfer coefficients. These values change continuously during drying due to changes in food fractions, particularly the water fraction. The high energy demand and costs allied to inefficient devices, creates a great need for new processing equipment. Along these guide-lines, several heat pump drying research projects were established at the Norwegian University of Science and Technology. The heat pump dryer provides high quality final product as its drying conditions can be controlled. Its efficiency and non-polluting operation come from closed air-refrigerant circuits and from its ability to fully recover the latent heat of moist air as it exits the drying chamber. Most of the above features are quite the opposite of the conventional dryer characteristics. Several experiments were made on heat pump drying of fruits and roots at temperatures from -22.5 to 40°C to obtain data and correlations on thermophysical properties, specific enthalpy and rehydration. Also, tests were done on drying rate, moisture content, drying constant, effective mass diffusivity and heat and mass transfer equations. The next important phase is the development of a simulation model to predict the performance and characteristics of the heat pump dryer plant. The objectives of the present work are to develop and lo test a heat pump dryer simulation model. The simulation provides results on the characteristics of both plant and components which are integrated by heat and mass transfer equations. The program has menus with click-on icons, input and output pop-up dialogue boxes. The usual commands such as, file-open, file-save, edit-delete are available in this program simply called Hpdryer. The model contains moist air psychrometric. natural and conventional refrigerant property libraries. Ammonia is a time-tested, self-alarming and natural refrigerant. It has been used extensively in the past, and it has better thermodynamic and transport properties than halocarbons. Safety is easily attained by design and its restrictive standards have helped increase its use in several countries. There are 36 ammonia installations in Norway and in the United Kingdom, including a drying plant. Ammonia has zero Odp, zero Gwp and the recent R&D has led to viable small-sale heat pump plants. Ammonia and dichlarodifluoromethane refrigerants were used in the test cases simulated by Hpdryer madel.     

A Simulation Model for Heat Pump Dryer Plants for Fruits and Roots.

ABSTRACT

Dryer design requires food properties, drying rate and mass-heat transfer coefficients. These values change continuously during drying due to changes in food fractions, particularly the water fraction. The high energy demand and costs allied to inefficient devices, creates a great need for new processing equipment. Along these guide-lines, several heat pump drying research projects were established at the Norwegian University of Science and Technology. The heat pump dryer provides high quality final product as its drying conditions can be controlled. Its efficiency and non-polluting operation come from closed air-refrigerant circuits and from its ability to fully recover the latent heat of moist air as it exits the drying chamber. Most of the above features are quite the opposite of the conventional dryer characteristics. Several experiments were made on heat pump drying of fruits and roots at temperatures from -22.5 to 40°C to obtain data and correlations on thermophysical properties, specific enthalpy and rehydration. Also, tests were done on drying rate, moisture content, drying constant, effective mass diffusivity and heat and mass transfer equations. The next important phase is the development of a simulation model to predict the performance and characteristics of the heat pump dryer plant. The objectives of the present work are to develop and lo test a heat pump dryer simulation model. The simulation provides results on the characteristics of both plant and components which are integrated by heat and mass transfer equations. The program has menus with click-on icons, input and output pop-up dialogue boxes. The usual commands such as, file-open, file-save, edit-delete are available in this program simply called Hpdryer. The model contains moist air psychrometric. natural and conventional refrigerant property libraries. Ammonia is a time-tested, self-alarming and natural refrigerant. It has been used extensively in the past, and it has better thermodynamic and transport properties than halocarbons. Safety is easily attained by design and its restrictive standards have helped increase its use in several countries. There are 36 ammonia installations in Norway and in the United Kingdom, including a drying plant. Ammonia has zero Odp, zero Gwp and the recent R&D has led to viable small-sale heat pump plants. Ammonia and dichlarodifluoromethane refrigerants were used in the test cases simulated by Hpdryer madel.     

盘式连续干燥器的传质传热模型

建立了盘式连续干燥器内加热盘面物料的传质模型,给出了干燥器内料环高度、盘面积料量及干燥时间的计算方法.应用颗粒传热理论和扩散理论,导出了每道料环的传热计算公式,由该迭代公式可逐步计算出每道料环的出料温度、出料湿含量及干燥速率.扩散理论中的惟一经验参数——搅拌参数N_mix,在本模型中可由不同进料工况下的多组实验数据加以确定.最后给出了应用该模型进行计算的实例,结果表明,理论计算值与实测值吻合较好,误差一般在20%以内.     

用颗粒热传递模型计算旋转列管干燥机的传热系数

采用基于移动加热板的颗粒热传递模型计算大型旋转列管干燥机的传热系数。在料床完全混合的简化假设下 ,按物料在干燥机内的实际干燥过程分段计算各段的传热系数及整机总传热系数 ,其结果与干燥机的实际运行情况基本相符。     

Modeling Superheated Steam Vacuum Drying of Wood

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^-1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

OPTIMIZATION OF SINGLE-ZONE DRYING OF POLYMER SOLUTION COATINGS TO AVOID BLISTER DEFECTS

The optimal conditions for drying polymer-solvent coatings result from a trade-off between minimizing the residual solvent level and creating defects. Blistering defects can be caused by boiling the solvent within the coating. In this paper, we use a detailed drying model with automated constrained optimization to find optimal drying conditions for prototypical coatings that minimize the residual solvent without blistering the coating. The drying oven is assumed to have a single zone with fixed residence time. The optimal drying conditions include the oven air temperature and substrate-side and coating-side heat transfer coefficients The latter are constrained to physically reasonable values. According to our results, the optimal coating-side heat transfer coefficient is always equal to or greater than the optimal substrate-side heat transfer coefficient.     

Mathematical Model for Batch Drying in an Inert Medium Fluidized Bed

A modified three-phase model is proposed for batch drying of fine powders in an inert medium fluidized bed. The overall heat and mass transfer coefficients between the interstitial gas and solid phases have been determined by the proposed surface-stripping model in which the Biot number is a governing parameter. The effects of gas velocity, inlet gas temperature and mass ratio of starch to inert particles on the drying characteristics of starch in a 0.083 m ID × 0.80 m high medium fluidized bed have been determined. Based on the proposed model, the internal resistance of mass transfer at the powder is equal to the external resistance. The model predicts well the bed temperature, humidity of outlet gas, moisture content of solid particles, heat and mass transfer in an inert medium fluidized bed.     

Designing a sensor for local heat transfer in impingement driers

Drying homogeneity within technical web driers is an important issue in the coating industry, especially for drying sensitive functional films. In this paper we detail the construction of a simple sensor for point measurements of local heat transfer coefficients. A procedure for calibration is presented as well as a validation of the results by comparison to literature. The sensor is applied to characterize a fraction of a technical dryer indicating the position of hot spots.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

内置换热管振动流化床传热特性实验研究

在内置换热管的振动流化床中以玻璃珠为惰性粒子实验物料,测定惰性粒子振动流化床与加热管之间的传热系数,研究了惰性粒子处于流化状态时的传热特性,分析了操作气速、振动频率、惰性粒子直径等因素对传热过程的影响,建立了传热系数与各影响因素之间的关联式。研究结果可为干燥膏状物料时确定适宜的操作参数提供参考。     

HIGH INTENSITY DRYING

A mathematical model simulating the heat and mass transfer process during high intensity drying of paper and board has been developed. The model is successful in predicting the vapor pressure developments, pressure driven bulk flow of liquid and vapor, and increased drying rates during high-intensity drying, closely matching the experimental determination.

The model predicts substantial amounts of water removal in the liquid form during high-intensity drying being pushed out of the web by pressurized vapor zone. Water removal by pressure flow of liquid could account for as much as one-third of the total water removed.

Similar to drying under conventional conditions, the existence of a dry zone, wet zone and an intermediate zone with accompanying advancing heat pipe has also been shown for drying under high intensity conditions.