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The Optimisation of Drying Schedules for Pinus radiata Sapwood Boards.

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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 (timl@chem.eng.usyd. 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. [2] 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 [3]. 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. [4] 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 [6] at 9OoC,from Keep [7] at 20°C over a range of moisture contents, and
data from Cousins [8] at ambient temperature for dry and green wood. Data from
239
T.A.G. Langrish, J.J.Nijdam and R.B. Keey
Carrington [6] and Keep [7] 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
[8] under similar conditions. All Cousins' strain values range between 1.0 and 1.5%
for greenwood at ambient conditions, while those of Keep [7] are 4.5% for the same
species (Pinus radiata). Cousins [8] 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 [6] and Keep [7] 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. [9] 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 [6] 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. [9] 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 [4]. 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. Keey
References
I.
2.
3
4.
5.
6.
7.
8.
9.
10
248
Salin, J-G.1988. Optimisation of the timber drying process using a combined drying simulation and
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Versailles, France, Roques, M. (ed.), pp. PB.13-17.
Doe, P.D., Booker, J.D., Innes, T.C., and Oliver, A.R. 1996. Optimal lumber seasoning using
acoustic emission sensing and real time strain modelling, In Proceedings of the Fifsh IUFRU
International Wood D v i n g Conference, Quebec, Canada, pp. 209-21 2.
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Langrish, T.A.G., Brooke, AS., Davis, C.L., Musch, H.E., and Barton, G.W.1997. An improved
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Technology - An Infernafional Journal, 15(1), 47-70.
Patwardhan, A.A., Rawlings, J.B., and Edgar, T.F. 1990. Non-linear model predictive control,
Chemical Engineering Communicafions,87,123- 14 1.
Carrington, M. 1996. High-temperature seasoning of softwood boards, M.E. Thesis, Department of
Chemical and Process Engineering, The University of Canterbury, Christchurch, New Zealand.
Keep, L.-B. 1998. The determination of time-dependent strains in Pinus radiata under kiln-drying
conditions, M.E. Thesis, Department of Chemical and Process Engineering, The University of
Canterbury, Christchurch, New Zealand.
Cousins, W.J.1974. Effect of strain-rate on the transverse strength of Pinus radiafa wood. Wood Sci.
Tech., 8, 307-321.
Nijdam, J.J., Langnsh, T.A.G., and Keey, R.B. 2000. A high-temperature drying model for softwood
timber, Chemical Engineering Science, 55( I 8), 3585-3598.
Nijdam, J.J., and Keey, R.B. 2000. Explorations with a new timber drying and stress model for Pinus
radinra. In Proceedings COST Wood & Wood Composite Conference, Aicher, S., (ed.), Stuttgart, pp.
241-252.
'
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