The Application of Mathematical Models to the Commercial High-Temperature Drying of Softwood Lumber

ABSTRACT

High temperature drying of softwood is used because it provides much faster drying rate than is possible at lower temperatures. However, the occurrence of some drying defects limits its use where the quality is critical. In order to understand the drying phenomena and to describe the drying processes, numcrous mathematical models have been developed in the past two decades. The diffusion model is the earliest attempt to describe wood drying processes and is relatively simple in form, so it is often used for stress analysis. However.further substantial work is still required before it is possible to apply the stress model to kiln control. Recently. transpon-based mathematical models have been receiving attention in modelling studies. This review discusses one of these models, a physiological-transport-based model, which has been further applied to the drying of mixed sap/heartwood boards and the drying of a kiln-wide stack. The mixed boards with a thin heanwood layer parallel to the flat surface are considered to have added difficulty in drying. In the analysis of the timber stack drying, a kiln-wide model is proposed in which the above physiological-transpon-based model is used to generate the characteristic drying curves. Airflow reversal is essential in kiln     

Mathematical Modeling of Kiln Drying of Softwood Timber: Model Development, Validation, and Practical Application

Mathematical modeling of wood drying is a powerful tool to better understand and quantify the effects of wood properties as well as the effects of drying and post-drying treatment conditions on drying and thus the wood drying models can be used to improve drying quality. The models that have been developed can be divided into three categories: models for drying a single board, models for drying a kiln-wide stack, and models for drying stress and deformation. The single-board drying model employs comprehensive heat and moisture mass transfer equations and can be used to investigate the influence of wood variability. The kiln-wide drying model, which is based on the transfer processes between wood and the drying medium, is able to examine the influence of drying schedules and wood properties. The stress model can predict stress development in drying and stress relief in final steam conditioning and post-kiln treatment. An integrated model can be used to optimize drying schedules and develop strategies for high-quality dried timber.     

EFFECTS OF SAWING PATTERN ON LUMBER DRYING: MODEL SIMULATION AND EXPERIMENTAL INVESTIGATION

The sawing pattern of lumber affects the drying rate due to transverse permeability differences. These permeability differences are considered in a single board drying model which is able to investigate the drying rates for boards with varying growth ring angles. For the drying of Pinus radiata lumber, the model predicts that the quartersawn boards need longer drying time than the flatsawn boards. The drying time difference was 10-15% of the total drying time for conventional temperature (CT) drying and accelerated conventional temperature (ACT) drying, but was less significant for high temperature (HT) drying. In the simulation of a kiln stack drying, a sawing pattern factor was introduced to the relative drying rate function, which reflected the effects of the growth ring angle and the drying temperatures. The modified kiln wide drying model was used to predict the drying rates for a kiln stack consisting of entirely flatsawn boards and a kiln stack consisting of entirely quartersawn boards. Drying tests were conducted using stacks of mixed flatsawn and quartersawn Pinus radiata sapwood boards. In the tests, three drying schedules were used which included CT, ACT and HT drying. The experimental results agree closely with the model predictions and thus, after further validation, the drying models can be used to predict commercial kiln drying of boards with different sawing patterns.     

EFFECTS OF SAWING PATTERN ON LUMBER DRYING: MODEL SIMULATION AND EXPERIMENTAL INVESTIGATION

ABSTRACT

The sawing pattern of lumber affects the drying rate due to transverse permeability differences. These permeability differences are considered in a single board drying model which is able to investigate the drying rates for boards with varying growth ring angles. For the drying of Pinus radiata lumber, the model predicts that the quartersawn boards need longer drying time than the flatsawn boards. The drying time difference was 10–15% of the total drying time for conventional temperature (CT) drying and accelerated conventional temperature (ACT) drying, but was less significant for high temperature (HT) drying. In the simulation of a kiln stack drying, a sawing pattern factor was introduced to the relative drying rate function, which reflected the effects of the growth ring angle and the drying temperatures. The modified kiln wide drying model was used to predict the drying rates for a kiln stack consisting of entirely flatsawn boards and a kiln stack consisting of entirely quartersawn boards. Drying tests were conducted using stacks of mixed flatsawn and quartersawn Pinus radiata sapwood boards. In the tests, three drying schedules were used which included CT, ACT and HT drying. The experimental results agree closely with the model predictions and thus, after further validation, the drying models can be used to predict commercial kiln drying of boards with different sawing patterns.     

AIRFLOW BEHAVIOUR IN TIMBER (LUMBER) KILNS

Even drying of stacked timber boards in a kiln depends, amongst other things, on having a uniform airflow through the pile. A study of possible airflow maldistribution in existing kilns has been carried out using a Perspex model of a kiln, with water as the fluid, which has been designed to be geometrically similar to an actual kiln and have dynamically similar flows. Measurements of local velocities were possible by tracing the flow of fine gas bubbles. The standard kiln arrangements result in significant recirculation zones before and after the stack, with a non-uniform incident velocity profile. Different design alternatives for the geometry of the plenum spaces on either side of the stack have been investigated.     

AIRFLOW BEHAVIOUR IN TIMBER (LUMBER) KILNS

ABSTRACT

Even drying of stacked timber boards in a kiln depends, amongst other things, on having a uniform airflow through the pile. A study of possible airflow maldistribution in existing kilns has been carried out using a Perspex model of a kiln, with water as the fluid, which has been designed to be geometrically similar to an actual kiln and have dynamically similar flows. Measurements of local velocities were possible by tracing the flow of fine gas bubbles. The standard kiln arrangements result in significant recirculation zones before and after the stack, with a non-uniform incident velocity profile. Different design alternatives for the geometry of the plenum spaces on either side of the stack have been investigated.     

STACK-WIDE EFFECTS IN THE MODELING OF SOLAR KILNS FOR DRYING TIMBER

This study examines the stack-wide effects due to the humidification and cooling of air as it passes through a 6 m wide stack of Australian ironbark timber for conditions that are representative of those for solar drying (dry and wet-bulb temperatures of 60 and 50°C, respectively). A solar kiln model for a greenhouse-type design has been modified to account for the drying of timber boards and the possibility of stack-wide effects, in terms of moisture-content differences in the streamwise direction of air flow through the stack. The maximum difference between the moisture contents of the leading and trailing boards is predicted to be 0.011 kg kg^-1 for these conditions, compared with timber moisture contents of 0.15-0.35 kg kg^-1. Hence, the stack-wide effect is insignificant for these conditions in this greenhouse kiln design and may be ignored, reducing the simulation time by over 50%. In addition, 14 elements within a finite-difference model for the drying of the timber boards (25 mm thick) gives predictions of the drying time that are acceptably accurate, while minimizing the computational time.     

Energy Saving in Industrial Wood Drying Addressed by a Multiscale Computational Model: Board, Stack, and Kiln

This article proposes a multiscale computational model able to calculate energy consumption in a batch lumber kiln. A dual-scale computational model of wood drying deals with the boards/stack interaction and serves as a basis for the present work. A new module was added here that calculates heat losses through kiln walls (convection, condensation) and the energy used by each kiln component (fans, heating elements, humidifier, vacuum pump, etc.). The corresponding mathematical formulation is presented and then theoretical results are compared to those collected in an industrial vacuum kiln. As application example, the effect of air reversal, air velocity, and kiln insulation are exhibited, which depicts the great potential and prospects of this new tool for energy savings in relation to the product quality.     

Energy Saving in Industrial Wood Drying Addressed by a Multiscale Computational Model: Board,Stack, and Kiln

This article proposes a multiscale computational model able to calculate energy consumption in a batch lumber kiln. A dual-scale computational model of wood drying deals with the boards/stack interaction and serves as a basis for the present work. A new module was added here that calculates heat losses through kiln walls (convection, condensation) and the energy used by each kiln component (fans, heating elements, humidifier, vacuum pump, etc.). The corresponding mathematical formulation is presented and then theoretical results are compared to those collected in an industrial vacuum kiln. As application example, the effect of air reversal, air velocity, and kiln insulation are exhibited, which depicts the great potential and prospects of this new tool for energy savings in relation to the product quality.     

Simulation of Drying Using a Kiln Model

A mathematical model was developed for simulating a convective batch lumber drying process. The model incorporates mass and heat transfer relationships within the lumber stack, as well as thermodynamic properties of the wood and drying air. It takes into account the change of air properties along the stack and its effect on the mass and heat transfer parameters. The model relies on a drying rate function that is an empirical correlation based on single-board tests. A drying rate function for western hemlock (Tsuga heterophylla) lumber was developed. The drying rate function was obtained based on experiment results from 500 small boards dried over a range of conditions used in commercial practice. The model was first validated against data available in the literature and then against large batches of hemlock dried in a laboratory kiln. In both cases, the model output was in good agreement with the average moisture content, the drying rates, and the temperatures measured in the larger batches.     

MOISTURE MOVEMENT ON DRYING SOFTWOOD BOARDS AND KILN DESIGN

This paper provides an overview of present understanding of how moisture can move through softwood boards, as a basis for determining kiln-seasoning strategies. Moisture in green wood is held essentially unbound, whereas below fibre saturation it is bound to a variable extent to the fibre walls. Sapwood, which is that part of the timber used for the transport of liquid nutrients, contains more moisture than physiologically inactive heartwood. Sawing the felled log creates a moisture-denuded layer at the damaged exposed surfaces. These features have a profound influence on the way that moisture can be removed on drying. Superimposed are differences arising from seasonal variations in the growth of wood between earlywood and latewood, which have different moisture permeabilities. When the width of the annual growth ring is relatively large compared with the board dimensions, moisture movement and the development of drying stresses depend markedly upon the sawing orientation relative to the grain direction. Quarter-sawn boards dry more uniformly (in the direction normal to the drying surfaces), but more slowly than flat-sawn boards. Most timber boards are stacked and then dried in box-shaped kilns. The uniformity of drying depends on the goodness of this stacking and on a uniform airflow being presented to the inlet face of the stack. Some non-uniformities can be mitigated by periodic reversals of the airflow direction through the stack and by overdrying the majority of boards to reduce wet spots, but there are limits, while overdrying reduces kiln capacity. Attention to aspects of the kiln geometry can reduce the fan-energy requirements and shorten the drying time, with a more uniform moisture content through out the kiln load.     

MOISTURE MOVEMENT ON DRYING SOFTWOOD BOARDS AND KILN DESIGN

ABSTRACT

This paper provides an overview of present understanding of how moisture can move through softwood boards, as a basis for determining kiln-seasoning strategies. Moisture in green wood is held essentially unbound, whereas below fibre saturation it is bound to a variable extent to the fibre walls. Sapwood, which is that part of the timber used for the transport of liquid nutrients, contains more moisture than physiologically inactive heartwood. Sawing the felled log creates a moisture-denuded layer at the damaged exposed surfaces. These features have a profound influence on the way that moisture can be removed on drying. Superimposed are differences arising from seasonal variations in the growth of wood between earlywood and latewood, which have different moisture permeabilities. When the width of the annual growth ring is relatively large compared with the board dimensions, moisture movement and the development of drying stresses depend markedly upon the sawing orientation relative to the grain direction. Quarter-sawn boards dry more uniformly (in the direction normal to the drying surfaces), but more slowly than flat-sawn boards. Most timber boards are stacked and then dried in box-shaped kilns. The uniformity of drying depends on the goodness of this stacking and on a uniform airflow being presented to the inlet face of the stack. Some non-uniformities can be mitigated by periodic reversals of the airflow direction through the stack and by overdrying the majority of boards to reduce wet spots, but there are limits, while overdrying reduces kiln capacity. Attention to aspects of the kiln geometry can reduce the fan-energy requirements and shorten the drying time, with a more uniform moisture content through out the kiln load.     

Model Predicted Effect of Process Variables on Kiln Drying of Pinus radiata Boards

The effects of kiln-drying process variables on drying time and final moisture content (MC) variability were assessed using a mathematical drying model (a kiln-wide model) developed earlier. Drying time was predicted to decrease by using higher air velocities and temperatures and, to a less extent, by increasing fan reversal frequencies. The drying time extended as board thickness or stack width increased. Increase in air velocity from 5 to 8 m/s tended to minimize the final MC variability. At least three reversals in the early stages of drying were required to reduce final moisture contents variation. The final MC variability increased with increasing stack width and with increasing temperature.     

Model Predicted Effect of Process Variables on Kiln Drying of Pinus radiata Boards

The effects of kiln-drying process variables on drying time and final moisture content (MC) variability were assessed using a mathematical drying model (a kiln-wide model) developed earlier. Drying time was predicted to decrease by using higher air velocities and temperatures and, to a less extent, by increasing fan reversal frequencies. The drying time extended as board thickness or stack width increased. Increase in air velocity from 5 to 8 m/s tended to minimize the final MC variability. At least three reversals in the early stages of drying were required to reduce final moisture contents variation. The final MC variability increased with increasing stack width and with increasing temperature.     

A Dual-Scale Computational Model of Kiln Wood Drying Including Single Board and Stack Level Simulation

This article proposes a dual-scale computational model of wood drying in a batch lumber kiln. The stack may consist of a large number of boards (typically 100) arranged in layers. Each single board of the stack is simulated using one module of TransPore, a comprehensive computational model for heat and mass transfer in porous media. Timber variability is taken into account by a Monte-Carlo method. Such a dual-scale model allows the drying simulation of a 100-board stack to be completed in less than 30 s on a PC with a 2.8-GHz Xeon processor. Sample simulations are presented to depict the great potential and prospects of this new tool.     

OPTIMIZATION OF A WOOD DRYER KILN USING THE MIXED INTEGER PROGRAMMING TECHNIQUE: A CASE STUDY

Abstract

When wood is to be utilized as a raw material for furniture, buildings etc., it must be dried from approximately 100% to 6% moisture content. This is achieved at least partly in a drying kiln. Heat for this purpose is provided by electrical means, or by steam from boilers fired with wood chips or oil. By making a close examination of monitored values from an actual drying kiln it has been possible to optimize the use of steam and electricity using the so called mixed integer programming technique Owing to the operating schedule for the drying kiln it has been necessary to divide the drying process in very short lime intervals i.e., a number of minutes. Since a drying cycle takes about two or three weeks, a considerable mathematical problem is presented and this has to be solved.     

OPTIMIZATION OF A WOOD DRYER KILN USING THE MIXED INTEGER PROGRAMMING TECHNIQUE: A CASE STUDY

When wood is to be utilized as a raw material for furniture, buildings etc., it must be dried from approximately 100% to 6% moisture content. This is achieved at least partly in a drying kiln. Heat for this purpose is provided by electrical means, or by steam from boilers fired with wood chips or oil. By making a close examination of monitored values from an actual drying kiln it has been possible to optimize the use of steam and electricity using the so called mixed integer programming technique Owing to the operating schedule for the drying kiln it has been necessary to divide the drying process in very short lime intervals i.e., a number of minutes. Since a drying cycle takes about two or three weeks, a considerable mathematical problem is presented and this has to be solved.     

A Dual-Scale Computational Model of Kiln Wood Drying Including Single Board and Stack Level Simulation

This article proposes a dual-scale computational model of wood drying in a batch lumber kiln. The stack may consist of a large number of boards (typically 100) arranged in layers. Each single board of the stack is simulated using one module of TransPore, a comprehensive computational model for heat and mass transfer in porous media. Timber variability is taken into account by a Monte-Carlo method. Such a dual-scale model allows the drying simulation of a 100-board stack to be completed in less than 30 s on a PC with a 2.8-GHz Xeon processor. Sample simulations are presented to depict the great potential and prospects of this new tool.     

SIMULATION OF DRYING IN A BATCH LUMBER KILN FROM SINGLE-BOARD TESTS

A deterministic model was developed to perform a board-by-board simulation of a forced convective batch lumber kiln. Individual board properties may be input and dryer operating parameters varied. The drying rates are empirical correlations based on single-board laboratory tests. The model incorporates the thermodynamic properties of the wood and gas, as well as mass and energy balances within the lumber stack. It also accounts for differences in heat and mass transfer resulting from position and changing gas properties throughout the dryer. The rate of drying predicted by the model and the final moisture content distribution were verified by weighing boards in a batch kiln before, during, and after drying. The application of the model is illustrated by simulating four common scenarios.     

SIMULATION OF DRYING IN A BATCH LUMBER KILN FROM SINGLE-BOARD TESTS

ABSTRACT

A deterministic model was developed to perform a board-by-board simulation of a forced convective batch lumber kiln. Individual board properties may be input and dryer operating parameters varied. The drying rates are empirical correlations based on single-board laboratory tests. The model incorporates the thermodynamic properties of the wood and gas, as well as mass and energy balances within the lumber stack. It also accounts for differences in heat and mass transfer resulting from position and changing gas properties throughout the dryer. The rate of drying predicted by the model and the final moisture content distribution were verified by weighing boards in a batch kiln before, during, and after drying. The application of the model is illustrated by simulating four common scenarios.