Comparison of Several Multi-Cylinder Paper Drying Simulation Models

ABSTRACT

Many models for simulation of paper drying in multi-cylinder dryer sections exist. In this work. three independently developed models are directly compared using the same reference data The models consired are the Texas A&M model, the Kuiosa model, and the VTT model. Predicted moisture contents plus cylinder and avenge web temperatures along the dryer section are presentcd for the different models. Predicted average evaporation rates during drying are also shown. Three major differences in the model details are highlighted. The effects of these differences on model accuracy evaluated by considering two different paper grades dried with two different machine geometries. This work is the first published direct comparison of different simulation models. The reference machine data provided can be used for comparison of these three models to other models.     

Steady-State Modeling of Multi-Cylinder Dryers in a Corrugating Paper Machine

In this study, a steady-state model was developed to describe the paper drying process and to analyze pocket dryer conditions for a multi-cylinder fluting paper machine in Iran's Mazandaran Wood and Paper Industries. The machine has 35 cylinders grouped in three drying groups and the cylinders are heated from the inside by steam. The model is based on the mass and energy balance relationships written for fiber, air, and water in the drying section. In this research, the heat of sorption and its variations with paper temperature and humidity changes have been taken into account. Temperature and moisture variation of the paper web and cylinder surface temperature in the machine direction were predicted by the proposed model. Also, temperature and humidity of air in the drying pockets and hood exhaust were estimated by the proposed model. Moreover, the model can predict the evaporation rate and specific drying rate with sufficient accuracy in comparison with the TAPPI standard. Finally, the main modeling parameters were compared with the available operating data and the effectiveness of the developed model was verified through validations.     

Modeling the Heat and Mass Transfer in Microwave Drying of White Oak

A 2D comprehensive heat and mass transfer model was developed to simulate the free liquid, vapor, and bound water movement in microwave drying of white oak specimens. The experimental and model results showed that, for white oak, moisture movement was easily impeded and high gradient of internal vapor pressure occurred. The internal vapor pressure was affected by sample dimension (length and thickness). At the same input power density, the internal pressure generated in the core increased with the sample length and thickness. However, as compared with sample length, sample thickness has less effect on the pressure gradient because of the high ratio of permeability between longitudinal and transverse directions.     

Experimental and Numerical Investigation of the Heat and Mass Transfer for Cut Tobacco During Two-Stage Convective Drying

In this article, a two-stage convective drying strategy was presented for dehydration of flue-cured tobacco. In order to develop the multistage drying method of tobacco, two-stage drying as well as traditional single-stage drying of cut tobacco was experimentally evaluated and accurately simulated by proposed heat and mass transfer models. The experiments were performed in a dual fixed bed dryer. Different air temperature combinations of 120°C/90°C, 110°C/80°C, and 100°C/70°C were employed during two-stage drying. The drying rate and temperature variations of cut tobacco were investigated. The results showed that the average drying rates during two-stage drying were nearly 50% higher than those obtained from lower-temperature single-stage drying. On the other hand, the two-stage drying method, which used high air temperature for the early period and low temperature for the late period, could reduce the exposure of tobacco to high temperature due to the low final temperature of the dried sample. The temperature and moisture evolution of cut tobacco at different air temperature combinations were consistent with simulation results by developed heat and mass transfer models. This indicated that the models had a good prediction precision for two-stage drying of cut tobacco. The model predictions can be useful for the design of a feasible two-stage drying process for flue-cured tobacco.     

Drying of Food Products Shaped as Longitudinal Sections of Solid and Annular Cylinders: Modeling and Simulation

A mass transfer model was proposed to describe the moisture evolution during drying of longitudinal sections of solid and annular cylinder-shaped food products. The dimensionless form of the model was numerically solved under the resulting combinations of two geometrical parameters (inner radius and angular cuts) to produce longitudinal sections of solid and annular cylinders. In addition, average drying curves were calculated from the volume integration of local moisture values. A mixed theoretical and numerical approach was used to develop the dimension similarity between the studied geometries and a simpler flat slab-shaped product in order to obtain an approximate analytical solution to the original, non-steady-state mass transfer problem, while an exact solution was also developed to highlight problem complexity. In order to validate actual results during water diffusivity estimation, potatoes were chosen as the food model, as this product can be easily shaped into either studied or traditional geometry with known solution. Different cuts (parallelepiped and longitudinal sections of both solid and annular cylinders) were obtained and air-dried (80°C, 2.5 m/s). In this regard, a simple method to estimate diffusion coefficients in 2D or 3D geometries is also presented. Under the described experimental conditions, water diffusivities for each geometry were estimated in the narrow range of 1.27–1.52 × 10^?9 m²/s, demonstrating the applicability of the proposed approach to solve mass transfer problems in products described by geometries lacking simple analytical solutions.     

Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.     

A Review of Drying Models Including Shrinkage Effects

ABSTRACT

This article presents a review of the different strategies used in the literature to model drying processes in which material shrinkage occurs. An analysis is provided of the different drying theories, the different approaches to deal with the shrinkage phenomenon, and the numerical methods used. It is common practice to directly apply the transfer models applicable for non-shrinking situations to the shrinking cases and to adopt a separate procedure to account for shrinkage. In addition, the use of effective transfer coefficients also abounds in the literature. Thus, coupling between the transfer processes and mechanical interactions is rarely considered.     

A Review of Drying Models Including Shrinkage Effects

This article presents a review of the different strategies used in the literature to model drying processes in which material shrinkage occurs. An analysis is provided of the different drying theories, the different approaches to deal with the shrinkage phenomenon, and the numerical methods used. It is common practice to directly apply the transfer models applicable for non-shrinking situations to the shrinking cases and to adopt a separate procedure to account for shrinkage. In addition, the use of effective transfer coefficients also abounds in the literature. Thus, coupling between the transfer processes and mechanical interactions is rarely considered.     

Energy Efficiency and Drying Kinetics of Recycled Paper Pulp

In this work, the influences of the air temperature and velocity on the drying kinetics of recycled paper pulp were analyzed. The increase of both variables positively influences the process, concerning the final moisture content and the drying time. However, optical microscopy and visual observation showed worse quality of the paper for drying conditions of high air temperature and velocity, presenting less uniformity and overdried surfaces. The dryer energy efficiency was evaluated by performance parameters and the results were compared with the ones obtained for other types of industrial paper dryers, presenting good agreement.     

Energy Efficiency and Drying Kinetics of Recycled Paper Pulp

In this work, the influences of the air temperature and velocity on the drying kinetics of recycled paper pulp were analyzed. The increase of both variables positively influences the process, concerning the final moisture content and the drying time. However, optical microscopy and visual observation showed worse quality of the paper for drying conditions of high air temperature and velocity, presenting less uniformity and overdried surfaces. The dryer energy efficiency was evaluated by performance parameters and the results were compared with the ones obtained for other types of industrial paper dryers, presenting good agreement.     

Application of Wood Drying Simulation Models in Commercial Lumber Manufacturing

Drying models are created both to develop a better understanding of the governing heat and mass transfer phenomena and to assist drying practitioners in achieving commercial goals. This article is a review of the application of wood drying and kiln simulation models to commercial lumber drying challenges. Examples from the literature are briefly reviewed and four selected applications in commercial lumber manufacturing are described. They include development of equalization schedules, assessment of green lumber sorting, development of alternative drying schedules, and assessment of fan reversal frequency and timing.     

Shrinkage of Recycled Paper Sheet During Drying

The properties of recycled paper are strongly affected by shrinking during drying, which depends on the drying conditions. An experimental study of the shrinkage phenomenon during drying of paper is presented. Drying experiments were conducted in a drying oven with controlled temperature. The temperature influence on shrinkage extent, porosity, and apparent density of the paper was evaluated. Structural changes on the paper surface after drying were analyzed by scanning electronic microscopy. Thickness contraction, surface, and volumetric shrinkage were correlated as a function of the moisture content. Lower apparent density values and more porous paper samples were obtained for higher temperatures.     

Simulation of Superheated Steam Drying from Coupling Models

Modeling of the transfer between a porous medium and its surroundings is commonly made using transfer coefficients that are theoretically well known only under boundary layer hypothesis. The resolution of Navier-Stokes equations in the surroundings of the product in order to get information about the boundary conditions avoids the classical use of these transfer coefficients. In this article, a modeling and a simulation of superheated steam drying of a rectangular piece of porous medium is proposed using a coupling method between a porous medium code and a CFD software. In some cases of superheated steam drying, even if a thermal boundary layer exists, a mass boundary layer cannot be defined. Moreover, boiling occurs during the process. An analysis of the interfacial transfer coupled with the analysis of the temperature, moisture content, and pressure profiles inside the porous medium is proposed.     

Simulation of Superheated Steam Drying from Coupling Models

Modeling of the transfer between a porous medium and its surroundings is commonly made using transfer coefficients that are theoretically well known only under boundary layer hypothesis. The resolution of Navier–Stokes equations in the surroundings of the product in order to get information about the boundary conditions avoids the classical use of these transfer coefficients. In this article, a modeling and a simulation of superheated steam drying of a rectangular piece of porous medium is proposed using a coupling method between a porous medium code and a CFD software. In some cases of superheated steam drying, even if a thermal boundary layer exists, a mass boundary layer cannot be defined. Moreover, boiling occurs during the process. An analysis of the interfacial transfer coupled with the analysis of the temperature, moisture content, and pressure profiles inside the porous medium is proposed.     

A Model for Through Drying of Tissue Paper at Constant Pressure Drop and High Drying Intensity

A mathematical model for through drying of paper at constant pressure drop was developed. The model is based on physical properties; hence, basis weight, pressure drop, drying air temperature, pore size distribution, initial gas fraction, and tortuosity are important input parameters to the model. The model was solved for different combinations of the variables basis weight, drying air temperature, and pressure drop corresponding to industrial conditions and the results were compared with data from bench-scale experiments. The simulations show that the drying rate curve is very sensitive to the air flow rate and that correctly modeling the correlation between pressure drop and air flow rate is the most important factor for a successful model for through drying. The model was tuned by adjusting the parameters initial gas fraction and tortuosity in order to give the best possible fit to experimental data. For a given basis weight and pressure drop, different drying air temperatures resulted in relatively constant values of the fitted parameters. This means that the model can well predict the effects of changes in drying air temperature based on a tuning of the model performed at the same basis weight and pressure drop. However, for a given basis weight, an increase in pressure drop yielded fitted parameters that were somewhat different; i.e., a lower initial gas fraction and a higher tortuosity, a change that increases the resistance to air flow. This implies that the correlation between pressure drop and air flow rate in the model does not quite capture the nonlinear relationship shown by the experiments.     

A Model for Through Drying of Tissue Paper at Constant Pressure Drop and High Drying Intensity

A mathematical model for through drying of paper at constant pressure drop was developed. The model is based on physical properties; hence, basis weight, pressure drop, drying air temperature, pore size distribution, initial gas fraction, and tortuosity are important input parameters to the model. The model was solved for different combinations of the variables basis weight, drying air temperature, and pressure drop corresponding to industrial conditions and the results were compared with data from bench-scale experiments. The simulations show that the drying rate curve is very sensitive to the air flow rate and that correctly modeling the correlation between pressure drop and air flow rate is the most important factor for a successful model for through drying. The model was tuned by adjusting the parameters initial gas fraction and tortuosity in order to give the best possible fit to experimental data. For a given basis weight and pressure drop, different drying air temperatures resulted in relatively constant values of the fitted parameters. This means that the model can well predict the effects of changes in drying air temperature based on a tuning of the model performed at the same basis weight and pressure drop. However, for a given basis weight, an increase in pressure drop yielded fitted parameters that were somewhat different; i.e., a lower initial gas fraction and a higher tortuosity, a change that increases the resistance to air flow. This implies that the correlation between pressure drop and air flow rate in the model does not quite capture the nonlinear relationship shown by the experiments.     

Heat Recovery of a Diammonium Phosphates Drying Unit

Solid product drying is a widely used unit operation in the chemical industry. It is highly energy intensive, requiring hot, dry air streams at high temperatures to dry a wide range of products. Exhaust air from a dryer is usually vented to the atmosphere with little or no heat recovery. In the present work, a study was performed to analyze the performance of an absorption heat transformer (AHT) applied to the evaluation of thermal rejections of drying unit of diammonium phosphates (DAP). First, a basic AHT system is described and the operating sequence is explained. Next, an application of the AHT system to an industrial company is analyzed. A numerical simulation of the system using Aspen Plus software was performed to determine the effect of different parameters on the AHT system performance and the results are presented in graphical form.     

Modeling and Numerical Analysis of an Atypical Convective Coal Drying Process

This work presents modeling and numerical simulation of batch convective coal drying in a deep packed bed after a high-pressure steam treatment (a part of the Fleissner coal drying process). The process is atypical, because ambient air is used to dry and cool hot particles, while usually, e.g., in the deep packed bed drying of biomaterials, hot air is contacting cold particles. Product-specific data (intraparticle mass transfer, gas-solids moisture equilibrium) for coal (here lignite) are taken over from literature. Available data on coal drying in packed beds of medium height are used for model validation. Then, the model is applied to the considered industrial process. The design point of the process is critically reviewed, and alternatives are developed by systematically simulating the influence of inlet air conditions (temperature, humidity, flow-rate) and coal particle size. This type of analysis is necessary for efficiently scheduling plant dryers, since coal particle size may change, and air inlet temperature and humidity are changing with the ambient conditions.