Optimizing the pine wood drying process using a critical diffusion coefficient and a timed moistening impulse

The local diffusion coefficient can be experimentally determined according to Fick's first law (Fick, 1855; Crank, 1956; Salin, 1990; Tamme, 2016): (1) F=−D∂u∂x, F = - D{{\partial u} \over {\partial x}}, where F – mass flux, (kg/m²s); D – diffusion coefficient, (m²/s); u – mass concentration, (kg/m³); x – coordinate, (m).

During the convective drying of wood, heat is transferred from the surrounding air through the surface to the interior of the wood and, at the expense of the heat energy being transferred to it, the moisture evaporates from the wood, i.e., the wood is dried. The main equations for describing the heat flow of dry air which is transferred to wood and the heat flow of moist air which leaves the wood are as follows (Salin, 1990): (2) ∅1=αS(T0−T), {\emptyset _1} = \alpha S\left({{T_0} - T} \right), (3) ∅2=βcpS(T0−T), {\emptyset _2} = \beta {{\rm{c}}_p}S\left({{T_0} - T} \right), where Ø₁ and Ø₂ – heat flow (W); α – heat transfer coefficient (W/m² °C); ß – mass transfer coefficient (m²/s); c_p – the specific heat of humid air in equilibrium with the wood's surface (J/°C m³); S – the surface area of the specimen (m²); T₀ – surrounding air temperature (°C); T – wood surface temperature (°C).

As part of the laboratory drying experiment, three pine sapwood specimens were used which had been cut from the same board with a cross-section of 35 mm (thickness) x 150 mm (width) and a length of 100 mm along the wood fibres. Sensors were attached to specimen a) to monitor the drying process; and with specimen b) being the reference specimen for determining the drying curve by weighing; while specimen c) was used to determine the moisture content of the wood at different depths by the slicing method (Tremblay et al., 2000; Tamme et al., 2021).

For a wood drying optimization system, it is first necessary to develop reliable and accurate sensors to be able to record the average moisture, local moisture, and surface moisture levels in the wood, as well as including a sensor to record the deformation of the wood's surface. These sensors must simultaneously withstand temperatures of 50–80°C and high relative humidity levels of 95–100% RH which are characteristic of a convective kiln (Tamme et al., 2021). In addition to the laboratory drying experiment, it is necessary to carry out various simulations using the commercial program, TORKSIM v5.11 for the optimization process. As there are no specified sensors in the standard equipment of any industrial wood dryers as supplied which would allow any optimization, it makes sense under laboratory conditions to optimize a specific drying recipe (i.e., create a drying plan) which is to be used in an industrial dryer, and then to incorporate the laboratory-optimized method into standard industry practices once it has been proved to be the right choice.

The methodology for the experiment is described in more detail, together with photos, in the final report for the EIC contract No 16200 (Tamme et al., 2021). The basic scheme for the experiment is shown in Figure 1(a) and Figure 1(b) in the photograph.

Figure 1

Figure 1

For monitoring the drying process, the 9-channel data logger Almemo 2890-9 manufactured by Ahlborn (Ahlborn, 2021) as well as the 8-channel data loggers Thermofox and Gigamodule produced by Scanntronik (Scanntronik, 2021) were used. Drying simulation was done with the program TORKSIM v5.11. For entering the simulation results and experiment log files in the data processing aggregate table, the so-called robot laboratory assistant was used to reduce manual processes and avoid human error in data entry (Tamme, 2013; Romann et al., 2014). For data processing and figure formatting, the spreadsheet program Excel and freeware program MatPlotLib v. 3.4.3. were applied.

When calibrating electrical resistance sensors for wood MC monitoring sensors, a cross-section linear calibration function was used, an example of which is shown in Figure 2 at depth levels of 1 mm and 4 mm below the wood's surface. The points A, B, C, and D which are shown in Figure 2 are known as calibration points with corresponding coordinates (x = 10LogR; y = MC%). For sections AB, BC, and CD, the calibration function was presented in a generalised form (Tamme et al., 2021): (4) y−y1y2−y1=x−x1x2−x1. {{y - {y_1}} \over {{y_2} - {y_1}}} = {{x - {x_1}} \over {{x_2} - {x_1}}}.

Figure 2

From Formula (4), one calibration function was derived for each section at a particular depth level. Corresponding calibration functions are shown in Table 1. To calibrate the electrodes being used in the experiment at depths of 1 mm, 4 mm, 8 mm, 12 mm, and 18 mm into the wood's MC sensors, three calibration functions are required for each depth level, so that a total of fifteen calibration functions were derived in order to be able to monitor the wood's MC through five depth electrodes. Six of them are presented in Table 1. The feasibility of using the cross-section linear calibration function was proven by means of modelling for two papers (Tamme et al., 2014; Tamme, 2016).

In the laboratory drying experiment and the drying simulation, an industrial drying schedule was used for pine wood specifically, which is presented in Table 2.

The diffusion coefficient was determined from Fick's first law according to Formula (1) (Tamme et al., 2011). Fick's first law, in the form of a partial derivative differential equation Formula (1), is not directly suitable for processing experimental data or the simulation data. Firstly, in Formula (1) the partial derivatives must be adjusted for finite increments in order to process the experimental and simulation data. Secondly, the experiment and simulation data are dimensionless with relative units (MC %). In order for the diffusion coefficient (DC) which is found in finite increments to acquire the correct dimensions (m²/s), a constant which contains the dimensions of the units of measurement must be introduced into the formula for practical use. Thirdly, both the experimental data and the simulation data contain random errors, which must be carefully filtered out prior to calculating the DC. In principle, the diffusion coefficient DC can be given according to Formula (1) as the ratio of the mass flux to the gradient: (5) D=−MassfluxGradient, D = - {{Massflux} \over {Gradient}}, (6) Massflux=−Δ(MC%)mdryΔt*S, Massflux = - \Delta \left({MC\%} \right){{{m_{dry}}} \over {\Delta t*S}}, (7) Gradient=Δ(MC%)ρwood, dryΔx, Gradient = \Delta \left({MC\%} \right){{{\rho _{wood,\,dry}}} \over {\Delta x}}, where D – diffusion coefficient (DC) (m²/s); Δ(MC%) – the finite increment of the wood's MC% on the time axis for the mass flux and in the material thickness (x-axis) for the gradient (MC%); m_dry – the wood's dry mass (kg); S – the specimen's surface area (m²); Δt – the time increment (s); ρ_{wood, dry} – the wood's dry density (kg/m³); Δx – the x coordinate's increment (m).

After filtering out the random errors, the DC calculation is presented schematically using the four-point method shown in Figure 3. The coordinates of the points which have been marked with the ‘diamond’ marker in Figure 3 are presented in Table 3. The principle of the four-point method is that, initially, two mass flux values were obtained at depths of 1 mm and 4 mm, from which the arithmetic mean mass flux was obtained following averaging. Two gradients were also obtained at two different time points, which were then arithmetically averaged. Finally, the average DC at the average depth, i.e., (1 + 4) / 2 = 2.5 mm deep from the wood's surface, was calculated according to Formula (5).

Figure 3

After carrying out these calculations, the values of the experimental DC were following: DC1ph. = 27^* 10⁻⁴ mm²/s in the first drying phase and DC2ph. = 18^* 10⁻⁴ mm²/s in the second drying phase (Tamme et al., 2021). At the end of the first drying phase and at the beginning of the second drying phase, the simulated DC has an almost equal value (i.e., 11.8 ^* 10⁻⁴ mm² / s).

As the drying process passes from the first drying phase to the second drying phase, a sharp decrease in the numerical value of DC occurs at 94 hours. From Figure 3 it can be concluded that there is a sharp decrease in mass flux in the second drying phase when compared with the first drying phase. The gradient is approximately constant in the first drying phase, and there is a minimal decrease in the average gradient in the second drying phase. Consequently, the sharp decrease in DC is due to the sharp decrease in mass flux in the second drying phase. Consequently, in order to optimize the drying process, the first drying phase should remain within the region of the maximum mass flux for as long as possible. This fact should be taken into account when optimizing the drying schedule. The maximum value of the diffusion coefficient immediately before entering into the second drying phase was named the critical diffusion coefficient. Mass flux, gradient, and critical DC are values which are difficult to determine under industrial wood drying conditions. Therefore, based on the separating line of the first and second drying phase, it makes more sense to determine the critical relative humidity (RH) of the drying air on the basis of the laboratory test, below which the drying process enters the second drying phase. Monitoring the critical RH value is not a problem in industrial conditions, as wood dryers are usually standard-equipped with a corresponding sensor and a logging option. The determination of critical RH is shown schematically in Figure 4.

Figure 4

The ability to be able to determine the critical RH on the basis of sensor readings alone would be of great practical value under industrial conditions, as the somewhat complex procedure for calibrating the sensors and the equally complex procedure for determining the critical DC would both be eliminated.

The distinction between the first and second drying phase based on the log file of an electrical resistance sensor (i.e., before calibrating into a sensor for the wood's MC) is illustrated in Figure 5. Figure 5 shows that, at 1 mm and 4 mm, electrical resistance starts to increase systematically from 94 hours (i.e., at the transition point to the second drying phase), when compared to the linear trend line for the average electrical resistance in the first drying phase.

Figure 5

The distinction between the first and the second drying phases is illustrated in Figure 6, based on the log files of three sets of temperature sensors and the displacement sensor. It can be seen from Figure 6 that, at the beginning of the second drying phase, the thermocouple readings from the wood's surface and from the centre part begin to diverge. At the same time, the readings from the displacement sensor, which registers the shrinkage of the wood surface, begin to decrease. Both changes in the sensor readings start at 94 hours of drying. Therefore, the first and second drying phase can experimentally be distinguished in four independent ways: according to (a) uncalibrated and (b) calibrated electrical resistance sensors, (c) a displacement sensor, and (d) log files of three temperature sensors.

Figure 6

A short three-hour moistening impulse was generated during the experiment, in the second phase of drying, starting at 116 hours, in order to verify the response of, and delay inherent in the sensors. From the initial level of RH = 65.1% at 116 hours, the relative humidity RH of the climate chamber air was increased to 95% by opening the valve with a manually operated humidifier, and was maintained at this level for three hours. The humidifier valve was then closed, and the climate chamber's automation quickly restored the RH value of the air in the chamber as prescribed by the drying program. The effect of the moistening impulse on the electrical resistance sensors is shown in an enlarged format in Figure 7. The real effect of the moistening impulse on the displacement sensor is shown in Figure 6. Figure 6 shows that the moistening impulse essentially has no effect on the temperature sensors (thermo-couples).

Figure 7

The expansion of the wood's surface layer which was identified in Figure 6 counteracts the tensile stresses in the surface layer which are caused by drying. Consequently, a precisely timed moistening impulse based on a simulation could in practice be used to alleviate the maximum tensile stresses to a safe limit (0.33) in the surface layer, thereby reducing the risk of drying cracks appearing due to tensile stresses.

The industrial drying schedule (see Table 2) shows that the drying schedule satisfies the main optimization conditions which were set in the TORKSIM program, i.e., the maximum relative tensile stresses in the surface layer are less than the maximum allowable value of 0.33 (Salin 2007; Tamme et al., 2021). Whether the industrial drying schedule being used in the experiment is also the optimum one in terms of drying time is something which still needs to be confirmed. To this end a new drying schedule was drawn up, based on the definitions of critical DC and its associated critical RH. A corresponding optimized drying schedule (Tamme et al., 2021) is presented in Table 3, and the drying results which were simulated with the optimized drying schedule are shown in Figure 8.

Figure 8

Figure 9 shows that an optimized drying schedule can provide an MC in the wood which is up to 30.9 % lower with the same drying time when compared to an unoptimized drying schedule at virtually the same relative stress levels (0.25) (Tamme et al., 2021).

Figure 9

Another way to shorten the drying time is to force the drying process (Tamme et al., 2011). The drying time in the initial drying schedule was reduced by using as a basis the consideration that the relative humidity of the drying air would decrease by 16% RH per day (Tamme et al., 2011). Forced drying of this type would reduce the overall drying time by about 3.5 days when compared to the original industrial drying regime (see Table 5). In principle, the same thing was done using the StatEase Design Expert program, when the drying time was randomly varied within a predetermined range (Sova et al., 2016, Tamme et al., 2021). Usually, an arbitrary shortening of the drying time in the drying schedule, i.e., forcing the drying process, leads to an increase in the drying stresses above the dangerous level (0.33). According to the results which were obtained previously, dangerous stresses can be neutralised by means of a precisely timed moistening impulse in the second drying phase. The forced drying schedule is presented in Table 4. The corresponding simulation results for the forced drying schedule are presented in Figure 10.

Figure 10

Figure 10 and Table 4 indicate that, due to the forcing of the drying schedule, the total drying time decreased by 84 hours but, due to the moistening impulse which was added to the drying schedule, the drying time increased by ca 1 h, and the simulated stress decreased by 0.30. Therefore the savings in the drying time at safe stresses (0.30) in order to achieve the same final moisture content of 12% MC was set at 83 hours.

The statistical processing phase should at least broadly reflect the causal relationships between the physical processes which take place during the drying of the wood. From this general point of view, it would be interesting to be able to study the compatibility of the ‘electric fingerprint’ of wood drying, i.e., the log files regarding the wood's electrical resistance levels, and the relative stresses in simulated wood, in two cases shown in detail below: a) by examining on a non-statistical basis the coincidence of the maximum point of the electrical indicator on the drying time scale; and b) by compiling a linear model of the relationship between the electrical indicators of the behaviour of the wood's surface layer and its central part.

The electrical surface-core ratio (ESCR) was chosen as an electrical indicator of the behaviour of the wood's surface layer and inner layer, defined as follows: (8) (ESCR)=(10 LogR1mm+10 LogR4mm)/(10 LogR8mm+10 LogR12mm+10 LogR18mm). \matrix{{\left({{\rm{ESCR}}} \right) = \left({10\,{\rm{LogR}}1{\rm{mm}} +} \right.} \cr {\left. {10\,{\rm{LogR}}4{\rm{mm}}} \right)/\left({10\,{\rm{LogR}}8{\rm{mm}}} \right. +} \cr {\left. {10\,{\rm{LogR}}12{\rm{mm +}}10\,{\rm{LogR}}18{\rm{mm}}} \right).} \cr}

Using the Scanntronik Gigamodule measurement channel designations in the electrical resistance log file, the formula can be shortened: (9) ESCR=(U1+U2)/(U3+U4+U5). {\rm{ESCR}} = \left({{\rm{U}}1 + {\rm{U}}2} \right)/\left({{\rm{U}}3 + {\rm{U}}4 + {\rm{U}}5} \right).

In Figure 11, the drying time scale on the ESCR graph shows three clearly distinguishable elements of the laboratory drying experiment, with the correct turnout time: firstly, the transition from the first drying phase to the second drying phase at 92 hours. (Note: the transition of the drying phases begins at 94 hours, with a slow rise, and only becomes noticeable at 100 hours in Figure 11); secondly: the start of the moistening impulse at 116 hours; third: the full coincidence of the maximum ESCR and the maximum simulated relative stress at 143 hours.

Figure 11

In the linear model of electrical indicators for the wood's surface layer and inner layer in Figure 12, the determination coefficient is R² = 0.9838, which indicates the existence of a strong causal relationship between the wood's surface layer and inner layer in the drying test. Based on the model, it can be assumed that the moisture content of the wood's surface layer controls the moisture content of its inner layer.

Figure 12

The potential advantages of the wood tension indicator which is presented in Figure 11 over an indicator which is based on acoustic emission (AE) (Tiitta et al., 2010) include a simpler technical implementation, better reliability in the harsh climatic conditions of a wood dryer, and higher sensitivity levels. However, the advantages and disadvantages of both indicators would be identified by the use of a benchmark.

There is relatively good agreement between the drying experiment and the simulation results in the simulated and experimentally determined drying curves (see Figure 8), the wood's moisture profile before the end of the second phase of the drying experiment at 142 hours (see Figure 13 (b) ), the wood's surface simulated and measured in terms of temperature from the start of drying to 60 hours into the process (see Figure 6), and at simulated wood stresses at the maximum level of the ESCR graph as determined through the experiment (Figure 11).

Figure 13

The critical DC, which is something that is characteristic of the experiment (see Figure 3), is very weakly expressed based on the simulation results. At the end of the first drying phase and at the beginning of the second drying phase, the simulated DC (diffusion coefficient) has an almost equal value (i.e., 11.8 ^* 10⁻⁴ mm² / s).

The DC's numerical values as determined and simulated through the experiment also differ significantly both ten hours before and ten hours after the 94-hour mark, which is when the transition from the first drying phase to the second drying phase takes place (accordingly: DC1ph. = 27^*10⁻⁴ mm²/s, DC2ph. = 18^*10⁻⁴ mm²/s, and DCsim. = 11.8^*10⁻⁴ mm²/s) There is also no agreement between the wood MC profiles which have been simulated and determined from the experiment at 92 hours (Figure 13 (a)), at the measured and simulated wood surface temperatures after 60 hours until the end of the drying experiment (Figure 6). From the significant difference between the simulated and measured wood surface temperatures it can be concluded that the heat transfer coefficient and mass transfer coefficient in theoretical background Formulas (2) and (3) are no longer constant after 60 hours, but instead depend upon the wood moisture content.