A MATHEMATICAL MODEL OF HIGH INTENSITY PAPER DRYING

High intensity drying occurs when one web surface is heated to the thermodynamic saturation temperature corresponding to the local hydraulic pressure. Rapid vapor generation causes the process to be driven by a total pressure gradient, so vapor leaves the web by a bulk flow mechanism rather than a slower diffusion mechanism. Vapor pressure build-up promotes rapid web heating and offers the opportunity for liquid removal by displacement. Lower energy usage can result if only a part of the moisture is evaporated.     

HIGH-INTENSITY DRYING OF PAPER

High-intensity contact drying denotes drying under suf- ficiently intensive heating conditions that, following a brief warmup period, the mist paper web operates at internal tem- peratures in excess of the ambient boiling point. A simplified, two-zone analytical model is first presented. The paper is depicted as having a dry layer, of ever-increasing thickness, adjacent to the hot surface. Heat conduction through this layer (the rate-limiting step) causes evaporation at the interface with the “wet zone.” The vapor is then considered to flow through the wet zone into the ambient. Results of bench-scale experiments are discussed. Drying rates as much as twenty times conventional rates are indicated. The drying rate increases with hot surface/boiling point tem- perature difference and applied mechanical pressure. The instsn- taneous drying rate decreases continuously after a brief warmup period. The vapor pressure at the hot surfacelpaper interface rises quickly to a peak value, followed by a continuously- diminishing level. The heat flux shows a rapid rise to boiling- like conditions, followed by a drop to a range compatible with measured drying rates. The temperature of the open side of the sheet is constant during drying, after its initial rise to the boiling point. The experimental results are compatible with pre- dictions of the model.     

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 MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

ABSTRACT

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

A MATHEMATICAL MODEL FOR DRYING OF SHRINKING MATERIALS

A mathematical model has been developed to describe heat and mass transfer within materials undergoing shrinkage during drying. Both heat and mass transfer equations are solved simultaneously using a numerical technique A beat pump dryer has been used to conduct experiments to validate the model. Several samples were placed in the drver and after the commencement of each drying test one sample was taken oat at rceular time interval: The bone-dry mass of each piece was also determined. This enables to determine moisture distribution within the materials. Temperatures at different locations of the material were measured with thermocouples. The predicted temperature and moisture distribution within the material agreed fairly well with the experimental results.     

CONVECTIVE DRYING OF PAPER CALCULATED WITH A NEW MODEL OF THE PAPER STRUCTURE

Paper drying models are based on the assumption of a rigid solid matrix. Because of the interaction of water molecules and paper fibre the dimensions of the sheet are changing, especially the thickness. These changes influence the moisture transport within the material. A model of the paper structure has been developed taking into account different kinds of pores in the paper.

By the assistance of this model the dependence between water content and thickness or transport parameters as permeability and thermal conductivity can be predicted. The only informations which are needed are sorption isotherms, apparent paper density and permeability of the single phase flow. Further informations as the pore size distribution are useful but not necessary.

The transport parameters are generated in the suggested way for wood pulp. It is shown that in the case of convective drying, the agreement between experimental results and model simulations is good.     

CONVECTIVE DRYING OF PAPER CALCULATED WITH A NEW MODEL OF THE PAPER STRUCTURE

Paper drying models are based on the assumption of a rigid solid matrix. Because of the interaction of water molecules and paper fibre the dimensions of the sheet are changing, especially the thickness. These changes influence the moisture transport within the material. A model of the paper structure has been developed taking into account different kinds of pores in the paper.

By the assistance of this model the dependence between water content and thickness or transport parameters as permeability and thermal conductivity can be predicted. The only informations which are needed are sorption isotherms, apparent paper density and permeability of the single phase flow. Further informations as the pore size distribution are useful but not necessary.

The transport parameters are generated in the suggested way for wood pulp. It is shown that in the case of convective drying, the agreement between experimental results and model simulations is good.     

CONSTRUCTION OF AN ANALYTICAL MODEL OF PAPER DRYING

ABSTRACT

A theoretical model developed is presented to simulate the paper drying process on a production paper machine. The paper sheet is represented as a matrix of pulpfibres which contains free and bound water, water vapour and air. The model is heavily dependent upon a wide range of physical data including pore size distribution, permeability sorptive characteristics, thermal conductivity, specific heat capacity, density, diffusion coefficients and shrinkage characteristics as well as heat and mass transfer behaviour at the interfaces. Theoretical relationships to describe these parameters in terms of the physical pore structure are developed and compared with published data. The model was compared against actual measurements on the Australian Newsprint Mills Boyer PM3 newsprint machine. The comparison with actual machine moisture content values showed the model prediction of moisture change during drying to cylinder No. 38 on PM3 to be 2% less than actual and 0.1% more than actual by the exit from the drying cylinder. In terms of predicting thermal energy consumption of the paper machine a 91% correlation was obtained.     

CONSTRUCTION OF AN ANALYTICAL MODEL OF PAPER DRYING

A theoretical model developed is presented to simulate the paper drying process on a production paper machine. The paper sheet is represented as a matrix of pulpfibres which contains free and bound water, water vapour and air. The model is heavily dependent upon a wide range of physical data including pore size distribution, permeability sorptive characteristics, thermal conductivity, specific heat capacity, density, diffusion coefficients and shrinkage characteristics as well as heat and mass transfer behaviour at the interfaces. Theoretical relationships to describe these parameters in terms of the physical pore structure are developed and compared with published data. The model was compared against actual measurements on the Australian Newsprint Mills Boyer PM3 newsprint machine. The comparison with actual machine moisture content values showed the model prediction of moisture change during drying to cylinder No. 38 on PM3 to be 2% less than actual and 0.1% more than actual by the exit from the drying cylinder. In terms of predicting thermal energy consumption of the paper machine a 91% correlation was obtained.     

IMPROVING MDF FIBRE DRYING OPERATION BY APPLICATION OF A MATHEMATICAL MODEL

Fibre drying is an important process in production of medium density fibreboard (MDF) which consumes a large amount of energy, affects product quality and, without appropriate control, causes environmental concerns. Based on fundamental knowledge of wood fibre-water relationships and heat/mass transfer, a mathematical model has been developed to simulate the MDF fibre drying processes. The model is able to predict fibre moisture content, air temperature and air humidity along the dryer length. After validation against the measured air temperature and humidity, the model has been extended to include both fibre drying and fibre conditioning, the latter occurring in the dry fibre conveyers. Due to potential benefits in reducing emissions of volatile organic compounds (VOCs) and in improving panel quality, lower drying temperatures are more desirable than higher temperatures. However, in order to achieve the target moisture content after drying, a higher air velocity is needed or a second-stage dryer is added. The model was employed to determine the air velocity required and to assist in designing a second dryer for further drying and recovery of moist vapour and heat. A further study was undertaken to investigate fibre drying or fibre conditioning in the fibre conveyers and, once again, the fibre drying model was used to determine the air conditions.     

A COMPREHENSIVE MATHEMATICAL MODEL FOR A MULTIZONE TUBULAR HIGH PRESSURE LDPE REACTOR

In this study a comprehensive mathematical model of high pressure tubular ethylene polymerization reactors is presented. A fairly general reaction mechanism is employed to describe the complex kinetics of ethylene polymerization. To determine the variation of molecular properties along the reactor length the method of moments is applied to the infinite set of species balance equations to transform it into a low order system of differential equations in terms of the leading moments of the number chain length distribution. Detailed algebraic equations are given describing the variation of kinetic rate constants, thermodynamic and transport properties of the reaction mixture with temperature, pressure and composition. A new correlation is derived to describe the change of reaction viscosity with reactor operating conditions. The model permits a realistic calculation of temperature and pressure profiles, monomer and initiator concentrations, molecular properties of LDPE (i.e. M_n, M_m, LCB and SCB) as well as the variation of inside film heat transfer coefficient with respect to the reactor length. Simulation results are presented illustrating the effects of initiator concentration, inlet pressure, chain transfer concentration and wall fouling on the polymer quality and reactor operation. The present model predictions are in good agreement with experimental observations in industrial high pressure tubular LDPE reactors.     

DRYING OF PULP AND PAPER SLUDGE IN A PULSED FLUID BED DRYER

ABSTRACT

Hydrodynamics and drying kinetics for the pulp and paper primary sludge dried in a pulsed fluid bed dryer with relocated air stream are presented. Batch experiments have indicated that drying of disintegrated sludge to the required 12% moisture content takes place during the first drying period at practically constant material temperature close to the wet bulb temperature with respect to the inlet air conditions. Equations were developed for pressure drop, minimum pulsed-fluidization velocity, dynamic bed height, and volumetric mass transfer coefficient. Continuous experiments under drying conditions determined from the average residence time concept have confirmed that transportation of disintegrated sludge along the dryer follows the plug flow model.

     

IMPROVING MDF FIBRE DRYING OPERATION BY APPLICATION OF A MATHEMATICAL MODEL

Fibre drying is an important process in production of medium density fibreboard (MDF) which consumes a large amount of energy, affects product quality and, without appropriate control, causes environmental concerns. Based on fundamental knowledge of wood fibre-water relationships and heat/mass transfer, a mathematical model has been developed to simulate the MDF fibre drying processes. The model is able to predict fibre moisture content, air temperature and air humidity along the dryer length. After validation against the measured air temperature and humidity, the model has been extended to include both fibre drying and fibre conditioning, the latter occurring in the dry fibre conveyers. Due to potential benefits in reducing emissions of volatile organic compounds (VOCs) and in improving panel quality, lower drying temperatures are more desirable than higher temperatures. However, in order to achieve the target moisture content after drying, a higher air velocity is needed or a second-stage dryer is added. The model was employed to determine the air velocity required and to assist in designing a second dryer for further drying and recovery of moist vapour and heat. A further study was undertaken to investigate fibre drying or fibre conditioning in the fibre conveyers and, once again, the fibre drying model was used to determine the air conditions.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

DRYING OF PULP AND PAPER SLUDGE IN A PULSED FLUID BED DRYER

Hydrodynamics and drying kinetics for the pulp and paper primary sludge dried in a pulsed fluid bed dryer with relocated air stream are presented. Batch experiments have indicated that drying of disintegrated sludge to the required 12% moisture content takes place during the first drying period at practically constant material temperature close to the wet bulb temperature with respect to the inlet air conditions. Equations were developed for pressure drop, minimum pulsed-fluidization velocity, dynamic bed height, and volumetric mass transfer coefficient. Continuous experiments under drying conditions determined from the average residence time concept have confirmed that transportation of disintegrated sludge along the dryer follows the plug flow model.     

PROTOTYPE HIGH TEMPERATURE/HIGH PRESSURE KILN FOR THE EVALUATION OF WOOD DRYING SCHEDULES

A new laboratory kiln was developed and built to perform over a very wide range of drying conditions. For example, the dry bulb temperature can vary from 30°C to 150°C and the dew point can be adjusted between 20°C and 130°C. Obviously, with such a high level of dew point, pressures over atmospheric pressure may be induced inside the chamber. For this reason, the kiln has been designed to withstand pressure of up to 3 bars. This kiln can also perform vacuum drying.

A programmable controller allows the temperature levels to be maintained within ± 0.2°C. Because the whole kiln can be heated only through the agitated water present at the bottom of the kiln, the load temperature can be increased up to 130°C in saturated conditions, without any change of moisture content.

The kiln has various sensors attached and is capable of withstanding severe conditions (high temperature, saturated vapour and elevated pressures). At present, air and water temperatures as well as temperature at different locations within the board can be collected during the drying process. A load cell and pressure gauges are also available. The first tests performed using this equipment are presented at the end of the paper.     

PROTOTYPE HIGH TEMPERATURE/HIGH PRESSURE KILN FOR THE EVALUATION OF WOOD DRYING SCHEDULES

ABSTRACT

A new laboratory kiln was developed and built to perform over a very wide range of drying conditions. For example, the dry bulb temperature can vary from 30°C to 150°C and the dew point can be adjusted between 20°C and 130°C. Obviously, with such a high level of dew point, pressures over atmospheric pressure may be induced inside the chamber. For this reason, the kiln has been designed to withstand pressure of up to 3 bars. This kiln can also perform vacuum drying.

A programmable controller allows the temperature levels to be maintained within ± 0.2°C. Because the whole kiln can be heated only through the agitated water present at the bottom of the kiln, the load temperature can be increased up to 130°C in saturated conditions, without any change of moisture content.

The kiln has various sensors attached and is capable of withstanding severe conditions (high temperature, saturated vapour and elevated pressures). At present, air and water temperatures as well as temperature at different locations within the board can be collected during the drying process. A load cell and pressure gauges are also available. The first tests performed using this equipment are presented at the end of the paper.     

A MATHEMATICAL MODEL FOR THE CONTINUOUS VACUUM DRYING OF HIGHLY VISCOUS FOODSTUFFS

An improved mathematical model for the continuous vacuum drying of highly viscous and heat-sensitive food-stuffs was proposed. The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment of time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh fish meat paste.