Dev. Chem. Eng. Mineral Process. 12(3/4), pp. 237-248, 2004. The Optimisation of Drying Schedules for Pinus radiata Sapwood Boards T.A.G. Langrish"', J.J. Nijdam' and R.B. Keey' ' Department of Chemical Engineering, University of Sydney, New South Wales 2006, Australia ' Wood Technology Research Centre, University of Canterbury, Private Bag 4800, Christchurch, New Zealand ~~ ~ ~ ~~~~ Optimal drying schedules have been predicted for the drying of Pinus radiata sapwood from an initial moisture content of 140% over a drying time of twenty-four hours for 5Omm-thick boards. Initially, a single pair of dry and wet-bulb temperatures (I 08°C. 6VC) over the full time period is estimated to keep the total tangential strain under 50% of the predicted limiting failure value. However, after twelve hours drying, more severe conditions may be used, with the final moisture content predicted to be reducedfrom 8.2%for a constant set of conditions throughout the schedule (lOS"C,60°C) to 2.4% when the dry-bulb temperature is raised from 108°C to 122°C after twelve hours. It is also possible to use a linearly increasing dry-bulb temperature after twelve hours, rising from 108°C to 155°C at the end of drying with a predicted final moisture content of 0.2%. However, to reduce the moisture content to only lo%, there is little difference between the ramped and twostep schedules, both yielding a total drying time of eighteen hours. The two-step schedule would be the easier to adopt in practice * Author for correspondence (firstname.lastname@example.org. edu.au). 23 7 T.A.G. Langrish, J.J. Nodam and R.B. Keey Introduction The overall context for this work is that optimisation of drying schedules for softwood timber has not been extensively reported. Salin [I] developed an optimised schedule for Scots pine (Pinus sylvestris) and spruce (Picea abies) for drylng in batch and progressive kilns. He developed a one-dimensional computer simulation model for softwood drying based on Fickian diffusion as the main transport process for moisture. A one-dimensional stress profile was estimated using an approach that included elastic and visco-elastic components of strain (without mechanosorptive effects). For the batch kiln, the wet-bulb temperature was kept constant at 44OC, but the dry-bulb temperature was adjusted to keep the maximum stress level below 80% of the tensile strength. The maximum dry-bulb temperature was 64”C, and the air velocity was 6.5 m s-’. A critical period was observed in the second day of drying (when the stress level reached its maximum), where a low wet-bulb depression of about 3OC was maintained (the drying was started with a wet-bulb depression of 6°C). After this critical period, a rapid increase in temperature was predicted to be possible. The maximum dry-bulb temperature was recommended to be below 80°C. The total drying time was six days for a moisture content change from 74% to 10%. Doe et al.  reported a PC-based kiln control system called the Clever Kiln Controller (CKC). The CKC contains the “Kilnsched” stress and moisture content model for eucalypt hardwoods developed by Oliver . In this system, acoustic emissions were also recorded using three sensors on sample boards in the kiln, and an “acoustic emission threshold” was specified. The CKC continually looked ahead to find a schedule that kept the dry-bulb temperatures as high as possible while keeping the surface strain under 50-75% of the estimated ultimate value (0.02 m m-’ for Tasmanian eucalypt hardwoods). When any of the acoustic emission sensors registered a level close to a specified maximum, the dry-bulb temperature was reduced. This control system has recently been commercialised on a limited scale, and a company has been formed, called “Clever Kiln Control Company Limited”, with the University of Tasmania as a major shareholder. 238 The Optimisation of Drying Schedulesfor Pinus radiata Sapwood Boards Optimised schedules for d y n g ironbark and other eucalypt timbers were developed by Langrish et al.  using a model predictive control (MPC) technique. Model predictive control (MPC) is a technique that allows process behaviour to be optimised, as described by Partwardhan et al. [SJ. The results obtained provide the “best” process conditions for each time step within a “prediction horizon”, the time period over which the future process behaviour is calculated. They used a one-stepahead prediction horizon, as a result of the slow moisture transport dynamics, with a four-hour time step. The aim in using MPC for timber drylng was to optimise the process conditions, namely the dry and wet-bulb temperatures as a fimction of moisture content, to obtain the best possible schedule (that is, one that combines acceptable checking with a reasonable drying time). The drying time was significantly reduced, from 137 hours to 122 hours for ironbark timber, and the timber quality was also improved significantly. The number of small and medium-sized cracks, both internally and at the surface, were reduced to less than a quarter of those observed with the original conventional schedule, suggesting that the original schedule was too aggressive in the early stages and that the sudden changes in the original schedule were seriously damaging the timber. The number of large cracks was also reduced in the optimised schedule. The improvement in timber value using the optimised schedule would be substantial, since over 90% of the timber from the optimised schedule was suitable for high-value products such as hrniture (A$2,000 per m3), while less than half of the timber dried using the conventional schedule was suitable for such use. The concept of drying at the maximum rate whle keeping within strain constraints, as used by the authors mentioned here, will now be applied to optimising drylng schedules for softwood timber with a more sophisticated mechanistic model for drying than has previously been applied for this purpose. Strain Criterion For Pinus radiata, there are three sets of data available for failure strains - data from Carrington  at 9OoC,from Keep  at 20°C over a range of moisture contents, and data from Cousins  at ambient temperature for dry and green wood. Data from 239 T.A.G. Langrish, J.J.Nijdam and R.B. Keey Carrington  and Keep  are plotted in Figure 1. A linear function Ef = (0.3(T-273.15)+8.9)X has been fitted to the slopes of each set of data to give a correlation for failure strain ( &f ) as a function of temperature (T, "C) and moisture content (X,kg kg-', oven-dry basis). The lines on either side of the square symbols show the predictions of the correlation at 60°C and 140°C. The deviation in slopes over this wide range of temperatures is close to the error of the estimated slope of a line passing through the square symbols. An uncertainty in the moisture trend is that the measured failure strain for green conditions given by Keep 171 is about three times greater than measured by Cousins  under similar conditions. All Cousins' strain values range between 1.0 and 1.5% for greenwood at ambient conditions, while those of Keep  are 4.5% for the same species (Pinus radiata). Cousins  measured his failure strains over a wide range of applied strain rates. 6 Fitted correlation (140 "C) - 5 ~- ' ,b Maxjmurn possible failure strain (4.3%) .- C + rn 20 "C(Keep 7) 90 "C(Carrington6) . ....... 140 "C Fitted correlation (60 "C) 0 5 10 15 20 25 30 Moisture Content (%) Figure 1. A comparison between the correlated failure strains in Pinus radiata and experimental failure strains. 240 The Optimisation of Dlying Schedulesfor Pinus radiata Sapwood Boards Data from both Carrington  and Keep  suggest an upper limit for the failure strain of about 4.3%. The reliability of these data sets has been assessed by running numerical drymg/stress-development simulations, whch are described briefly below and in more detail by Nijdam et al.  and Nijdam and Keey [lo], to see whether or not surface checking is predicted in different situations where surface checking is known to occur. Case 1. Accelerated Conventional Temperature (ACT) schedule (4 hours steaming, followed by 9O/6O0C) According to the literature, surface checking may develop with this schedule. The simulation predicts a surface strain during the constant rate period of 1.81%. The corresponding failure strain according to the linear correlation is 1.5% (corresponding to a simulated surface moisture content and temperature of 4.2% and 84.3"C), which indicates that surface checking may occur. Case 2. Known correction to ACT schedule to eliminate surface checking The problem of surface checks that develop when drylng at 9O/6O0C can be remedied by drylng the timber at 8O/6O0C for the first 24 hours, and then drylng at 9O/6O0C for the remainder of the schedule. The simulation predicts a surface strain during the constant rate period of 1.58%. The corresponding failure strain according to the correlation is 1.96% (corresponding to a simulated surface moisture content and temperature of 5.8% and 76.9"C), which indicates that surface checking does not occur. Given the agreement between the predictions and experimental observations for these cases, the correlation appears to work for temperatures close to 90"C, which indicates that the data of Carrington  is reasonable. Therefore, the failure strain criterion is: E~ = ( 0 . 3 ( T - 273 . 1 5 ) + 8.9)X (1) where T is in K and Xis in kg kg-' (oven-dry basis), with a maximum possible failure strain of 4.3%. 24 I T.A . G. Langrish, J.J.Nijdam and R.B. Keey Mathematical Model Drying and stress-strain models used for softwood timber have been reported by Nijdam et al.  and Nijdam and Keey [ 101, where a more detailed explanation of the process simulations employed in this work can be found. A grid of 10 nodes in the dry zone and 40 nodes in the wet zone has been used here for the simulations of the drymg of sapwood timber, and this grid has been found to give grid-independent solutions. The timber thickness has been taken as 50 mm. Numerical issues in ensuring robust simulation using the drymg and stress/strain models have been overcome. These issues include the need to specify minimum and maximum time steps of 0.0001 s and 0.1 s, respectively, and maximum absolute and relative tolerances in the numerical integration of 5 x and lo5, respectively, for all variables. A 24-hour drylng time has been chosen, with initial conditions of 140% for the moisture content and 20°C for the timber temperature. There are at least two possible approaches for implementing model predictive control in timber drymg [4, 51. One is to minimize the overall drying time 9 using time-varying controller inputs u(t) (which represent the dry and wet-bulb temperatures) that maintain the timber within all process constraints at all times. This may be expressed mathematically as follows: subject to 242 The Optimisation of Dving Schedulesfor Pinus radiata Sapwood Boards In the above equation, p represents the properties of the timber and X(t) and T(t) are the profiles of the moisture content and temperature within the timber. This approach is computationally very expensive, and a simpler approach is to minimize the average moisture content (within all appropriate constraints) over successive time intervals that are small relative to the overall drylng time, in the following way: subject to. I This approach has been implemented by initially using only one time horizon corresponding to the total drymg time, but subdivision of this prediction horizon is possible in the future. The maximum strain criterion (Equation 1) has been applied at each node throughout the timber, with the temperature and moisture content being provided by the drying model. This failure criterion has been compared with the total tangential strain. Results and Discussion When Equation (1) has been applied to quite aggressive drylng schedules, such as 155°C (dry-bulb temperature) and 55°C (wet-bulb temperature), it was predicted that the failure-strain was never exceeded. In fact, the failure strain was not exceeded even when the failure strain was set at 75% of the value given by Equation (1). However, simulations have shown that when the failure strain was set at 50% of the value given 243 T.A . G. Langrish, J.J. Ngdam and R.B. Keey by Equation (l), then the tangential strain exceeded this new upper limit, and therefore this limit (50% of the maximum value) has subsequently been used as the strain constraint. A single pair of dry and wet-bulb temperatures (108"C, 60°C) have been estimated to keep the total tangential strain under 50% of the limiting value, with this constraint (50% of the limit) being approached within 8 x m rn-'. The moisture content at the end of 24 hours is 8.2%. The CPU requirements for these optimisations, even using high-end workstations, are of the order of a week, so the optimisations are significantly time-consuming. 1 1.4 1.2 \ 0) Y -+2 hours c" 1.0 E +4 hours -m- 10 hours +16 hours Q, U 50 0.8 a! 5 .- C 0.6 u) 0.4 0.2 0.0 0.000 0.005 0.010 0.015 0.020 0.025 Distance from surface, rn Figure 2. Predicted profiles of moisture content as a function of distance from the surface of the boards at various times from the start of dvying, with a dry-bulb temperature of I08'C and a wet-bulb temperature of 60°C throughout dtying. 244 The Optimisation of DIying Schedulesfor Pinus radiata Sapwood Boards This suggested schedule has some similarities to the modified accelerated conventional schedule (Case 2 above), in that the wet-bulb temperature (60°C) is the same, and the wet-bulb depression is modest compared with a common hightemperature schedule. Over a 32-hour drylng period, the predicted similarity in the shape of the moisture-content profiles for moisture contents lower than fibre saturation (see Figure 2) suggests that until around 10 hours the drying conditions should be kept constant. The strain constraint is approached closely until almost 10 hours into drymg. This thirty-two hour drymg period is still relevant to the 24-hour period, because the same (constant) conditions were used for both drying periods, so the moisture-content profiles after 10 hours in a 24-hour drying cycle will be the same as those after 10 hours in a 32-hour drymg cycle. For the first 10 hours, the stresses and strains in the timber arise almost entirely due to steep moisture-content gradients near the surface of the timber. Small changes in temperature have a significant effect on this already large gradient in moisture content, through changes in the equilibrium moisture content near the surface. Hence the accurate prediction of the equilibrium moisture content may be more important than the transport properties in the timber during ths initial d y n g period. After the initial 10 to 12 hour period, more severe conditions may be used. For example, if the dry and wet-bulb temperatures of 108°C and 60"C, respectively, are maintained for the first 12 hours, it is predicted that dry and wet-bulb temperatures of 122°C and 60°C, respectively, can be applied for the remaining 12 hours (see Figure 3b). The final moisture content is predicted to be reduced from 8.2% (single set of conditions) to 2.4%. This behaviour (a possible increase in the severity of drying at low moisture contents) is also found in the optimisation of dqmg schedules for hardwood timber . It is also possible to use a linearly increasing (ramping) dry-bulb temperature after 12 hours, with the dry-bulb temperature increasing from 108OC to 155OC in the final 12-hour period (see Figure 3c). The resulting predicted final moisture content is 0.2%, which is less than both the single step (8.2%) and two-step (2.4%) schedules. However, in terms of reducing the average moisture content to lo%, there is little difference between the two-step and ramped schedules in t e r n of 245 T.A.G. Langrish, J.J.Ngdam and R.B. Keey predicted drying time (1 8 hours in both cases). The two-step schedule would be more straightforward to implement in practice than the ramped one. 140 170 : 120 160 a) Constant-condition u- schedule E f 8 es % 100 3P 80 8 40 1 60 pg 20 04 0 b) Two-step schedule -: c 100 6 12 Time, hours 18 24 140 170 120 160 0 100 150 80 140 '6 2 60 E 130 8 40 120 20 110 0 c Bc :s g i pE 0 ' 3 0 S! e 4 ?i 0 100 0 6 12 18 24 Time, hours c) Ramped schedule -: 140 170 120 160 0 100 150 80 140 0 E c c 8 es .Eo2 e" f -[ E 130 d 6o 40 P 120 $ i? 20 110 0 100 0 0 6 12 18 24 Time, hours Figure 3. Predicted moisture contents and suggested dry-bulb temperatures as a function of time for the drying of Pinus radiata sapwood with various drying schedules. 246 The Optimisation of Drying Schedulesfor Pinus radiata Sapwood Boards The drying schedules suggested here, which keep the total tangential strain of under 50% of the failure strain, may be compared with a conventional 12O0C/70"C schedule, where the total tangential strain is predicted by the procedure followed here, using these drying and stresdstrain models, to be over 50% of the failure strain. Hence the new schedules are predicted to give less damaging drying conditions throughout the seasoning period than the conventional schedule. Conclusions For the drylng of Pinus radiata sapwood from an initial moisture content of 140%, over a drying time of 24 hours, a single pair of dry and wet-bulb temperatures (108"C, 6OOC) for the full time period has been estimated in order to keep the total tangential strain under 50% of the predicted limiting value. This suggested schedule has some similarities to the modified accelerated conventional schedule, in that the wet-bulb temperature (60°C) is the same, and the wet-bulb depression is modest compared with a common high-temperature schedule. The similarity in the shape of the predicted moisture-content profiles (for lower moisture contents than fibre saturation) until around 10 hours into drylng means that the drying conditions should be kept constant until this time. However, after this time, more severe conditions may be used, with the final moisture content predicted to be reduced from 8.2% for a single set of conditions to 2.4% when the dry-bulb temperature is raised to 122°C. It is also possible to use a linearly increasing dry-bulb temperature after 12 hours, rising to 155°C at the end of drylng with a predicted final moisture content of 0.2%. However, to reduce the moisture content to only lo%, there is little difference between the ramped and twostep schedules, both yelding a total drying time of 18 hours. The two-step schedule would be the easier to adopt in practice. The new schedules are predicted to give less damaging drying conditions throughout the seasoning period than the conventional schedule. Acknowledgements Thanks are due to the New Zealand Foundation for Research Science and Technology (Public Good Science Fund) under sub-contract P2060 for financial support. 247 T.A. G. Langrish, J.J.Nudam and R.B. 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