A Vapour Preservative Treatment of Softwood Boards

0263±8762/97/$10.00+0.00 q Institution of Chemical Engineers

A VAPOUR PRESERVATIVE TREATMENT OF SOFTWOOD BOARDS J. M. EVANS*, R. B. KEEY (FELLOW)** and R. J. BURTON (MEMBER)² *Kingston Morrison Ltd, Wellington, New Zealand **Department of Chemical and Process Engineering, University of Canterbury, New Zealand ² NZFRI, Rotorua, New Zealand

V

apour Boron Treatment is a new and innovative method for timber preservation developed by the New Zealand Forest Research Institute. The process involves preservation with a vapour-phase chemical which signi® cantly decreases the treatment time compared with traditional aqueous-phase techniques. The boric acid retention pro® le in a piece of timber which has been treated by the new process can be accurately predicted by a model which includes both convective and diffusive ¯ uxes, if the initial moisture content of the timber is known. The reaction rate between the adsorbed water and trimethyl borate is a strong function of the differential heat of adsorption. Therefore, the lower the moisture content (the higher the differential heat of adsorption) the slower the reaction rate and the better the penetration of boric acid. It was found that a binary diffusion representation was adequate and consequently more elaborate diffusion models were not necessary. Keywords: vapour boron, timber treatment, diffusion, permeation, modelling

INTRODUCTION

Before a softwood such as Pinus radiata D. Don can be treated by the vapour boron treatment process, the timber is dried to a moisture content of between 3 and 9% (wt/wt dry basis). The wood is then placed in a treatment vessel which is evacuated to a pressure of between 5 and 15 kPa absolute. Finally, the preservative (usually trimethyl borate/methanol azeotrope) is injected onto a hot surface within the vessel. As the preservative evaporates, the pressure in the vessel increases and causes a `pressure-wave’ of trimethyl borate and methanol to travel through the wood. As this wave permeates the timber, the trimethyl borate reacts with both water vapour and adsorbed water to produce methanol and boric acid (equation (1):

In 1994, approximately 1.4 million cubic metres of timber (including roundwood) were treated with preservatives in New Zealand. Of this, just less than 400,000 m3 were treated with boron-based preservatives1 . The boron-preservative process involved either momentary immersion or spraying green timber with concentrated boric acid (18 to 25 % H3 BO3 equivalent) followed by stacking the timber under cover for about one month for each 25 mm of timber thickness. Boron-based preservatives are limited to the local (Australasian) market and to low decay hazard situations. The aqueous-phase process was extremely successful because of:

(CH3 O)3 B(g) + 3H2 O(g & l) !

3CH3 OH(g) + H3 BO3 #

(1) After a holding period of approximately ten minutes, a second vacuum is pulled to remove the methanol produced by the reaction (three moles of methanol are produced for every mole of trimethyl borate consumed). An alternative view of vapour-boron treatment is to consider the timber as a catalyst bed for producing methanol. One of the reactants, water, is adsorbed in notable quantities on the catalyst itself and so has a signi® cant vapour pressure within the free volume of the catalyst. The other reactant (trimethyl borate) enters the catalyst bed and strips the water from the catalyst. One of the products of the reaction (boric acid) is deposited on the catalyst, while the other product (methanol) can be removed from the catalyst bed by pulling a second vacuum. The New Zealand Forest Research Institute has carried out an extensive experimental programme studying the vapour-boron process2 . The results of this programme have

· low capital (plant costs); · simplicity of application process; · low preservative toxicity. However, in the mid 1970s some dramatic changes in the domestic market place resulted in an increase in interest in alternative treatment processes. The most signi® cant of theses changes was the increase in timber cost coupled with a dramatic increase in interest rates. The storage period for the aqueous-phase process requires that a company holds at least one-sixth of its total annual production in stock. This was proving costly, especially as it became dif® cult to predict how much timber would be required in the turbulent economic conditions of the time. Therefore, alternatives to the aqueous-phase process were sought. One alternative developed by the New Zealand Forest Research Institute was the vapour boron treatment process. 24

VAPOUR PRESERVATIVE TREATMENT OF SOFTWOOD BOARDS shown that the effectiveness of treatment (amount of boric acid retained in the core of the timber) is a strong function of the moisture content of the timber. The wetter the timber was, the less boric acid is retained in the core. The purpose of this study was twofold: ® rstly to discover the physical reason for this phenomenon; and secondly to investigate possible methods of getting greater core retentions at higher moisture contents. An accurate model had to be developed to assist in the optimization of the process and the development of the process as a viable alternative to aqueous-phase treatment methods.

Wood-Water Relationship

j

( ) E

= A exp - RT

(2)

The activation energy for any reaction with tightly bound water will be larger than the activation energy for that more loosely bound. Consequently, the reaction rate constant will be proportionately smaller. A slower hydrolysis reaction rate for trimethyl borate with the adsorbed water will result in more boric acid being formed in the central regions of the timber and a more even boric acid distribution.

MODEL DEVELOPMENT Booker and Evans5 have shown that ¯ uid movement in dry Pinus radiata D. Don can be described essentially by a one-dimensional model. Therefore, the model of the vapourboron treatment process needs only be one-dimensional as well. The continuity equation describes mass conservation in a control volume.The continuityequationfor a multicomponent Trans IChemE, Vol 75, Part A, January 1997

system with ¯ ow by both diffusive and permeative mechanisms can be written6,7 :

¶q i = - = ( (q i u + ji ))+ ri ¶t

(3)

In equation (3), the ® rst term on the right hand side ( q i u + ji ) describes the movement of the individual gas species. This term can be broken into two parts: the bulk movement of the gas (the q i u term), and the movement of the individual species relative to the bulk movement of the gas (or the diffusive term). The mass average velocity can be given by: u

The dominant parameter in the vapour-boron timber treatment process is the moisture content of the timber (see Nasheri and Laytner3 , for example). At 9% moisture content, it has been found to be virtually impossible to get any more than a super® cial penetration of boric acid in the timber, with virtually no boric acid being deposited in the core of the treated wood. Nasheri and Laytner3 suggest that above about 6% moisture content it is virtually impossible to get good penetration of boric acid, whereas below this moisture content the boric acid penetration is much more signi® cant. This phenomenon may be a direct result of changes in the way in which the water is adsorbed in the timber. There have been a number of studies and theories presented4 to explain the nature of adsorption on accessible carbohydrate substance. They all start from the same postulate: that at low moisture contents the adsorbed water is tightly bound as a monolayer to the carbohydrates. At higher moisture contents, this tightly bound water still exists; however, it is augmented by less tightly bound water. Essentially this sequence of adsorption may be described by the BET multilayer adsorption theory where the ® rst layer is considered tightly bound and subsequent layers are less tightly bound. From the Arrhenius equation (equation (2)) it may be seen that the reaction rate constant (j ) is dependent on the activation energy:

25

=S

n i=1

x i ui

(4)

Therefore, the bulk ¯ ow term is the average of the mass ¯ uxes of the individual gas species. The diffusive term represents the deviation from the average ¯ owrate of an individual species given by equation (4): ji

=q

i

(ui

- u)

(5)

The driving forces for diffusive ¯ ows are the differences in the individual partial pressures. In the vapour boron treatment process, the bulk ¯ ow of the gas mixture will be due to the total pressure drop (or the sum of the individual partial pressure drops). This type of ¯ ow is referred to as permeation. From the work of Evans et al.8 the pressure in the centre of a quarter-sawn 100 ´ 50 mm piece of high-temperature Pinus radiata D. Don will be very similar to the external pressure under typical treatment conditions (initial vacuum, total pressure increase form evaporation of preservative etc.) within 1 to 10 seconds. In contrast, the diffusion (of gases) is a much slower process in Pinus radiata D. Don than pressure-driven permeation. Booker and Evans5 and Allen et al.9 have adopted the approach of many earlier workers in applying Darcy’ s law to model the steady and unsteady-state ¯ ow of a gas through wood (in one dimension), where the pressure gradient is signi® cant: u

K ¶p

= - l ¶x

(6)

Comstock10 has shown that the speci® c permeability K (m2 ) of many timbers is only a function of the size and number of ¯ ow paths, and is independent of the viscosity of the ¯ uid used. The permeability k (m3 s1 kg- 1 ) is related to the speci® c permeability K (m2 ) by the expression11 permeability(k) =

specific permeability (K) dynamic viscosity (l )

(7)

Viscosity is a measure of the resistance of two layers in a ¯ uid to sliding across each other. As molecules in the gas mixture move and collide, they transfer momentum or energy. Because of this, viscosity is a property of the bulk ¯ uid rather than the individual components in that ¯ uid12 Consequently, when modelling the ¯ ow of a multicomponent ¯ uid, the viscosity of the mixture, and not the individual viscosities should be used.

26

EVANS et al.

The mass average velocity of a multicomponent mixture in timber can be described by the expression: n

u

å ¶p

i 1 = - km =

i

(8)

¶x

If the diffusive ¯ ux is signi® cant compared to the permeative ¯ ux, a continuity equation including diffusion ¯ ux has to be used (equation (3)). There are four gas-phase components of interest in the vapour boron process: trimethyl borate, methanol, air, and water vapour; and therefore, four permeative and diffusive ¯ uxes and four mass-balance equations:

¶r1 ¶t ¶q 2 ¶t ¶q 3 ¶t ¶q 4 ¶t

¶ k q ¶ptot j m 1 - 1 - j gas q 1 q 4 - j ad q 1 ¶x ¶ k q ¶ptot j m 2 - 2 + 3j gas q 1 q 4 + 3j ad q ¶x ¶x ¶ k q ¶ptot j m 3 - 3 ¶x ¶x ¶ k q ¶ptot j m 4 - 4 - 3j gas q 1 q 4 ¶x ¶x

= ¶x = = =

(9)

1

(10) (11) (12)

To calculate the diffusive ¯ ux for each species in a quaternary mixture is an overly dif® cult problem, as the diffusivities in a quaternary mixture are complex functions of mass fractions.7 Therefore, it is convenient that the diffusive ¯ ux be solved for a pseudo-binary system with the two species being A (trimethyl borate) and B (methanol, air and water). This grouping was chosen as the molecular masses of methanol, air, and water are signi® cantly lower than the molecular mass of trimethyl borate (diffusion coef® cients are strongly related to molecular mass). This pseudo-binary approach is similar to the use of `key’ binary groupings to model multicomponent distillation. The diffusion ¯ ux of A in a binary A-B mixture can be written: jA

= -q

d

T AB

¶x A ¶x

(13)

Equations (9)±(12) can therefore be rewritten to describe pseudo-binary diffusion (rather than quarternary diffusion), and converted to partial pressure instead of partial density (assuming a perfect gas relation between partial pressure and mass fraction):

¶p1 ¶t

¶ k p ¶ptot RT j m 1 A ¶x M1

= ¶x

- rgas p1 p4 - rad p1 ¶p2 ¶ k p ¶ptot RT m j m 2 2 B = t ¶ ¶x ¶x M2 + 3rgas p1 p4 + 3rad p1 RT ¶p3 ¶ k p ¶ptot m 3 = ¶t ¶x ¶x M3 m3 jB ¶p4 ¶ k p ¶ptot RT m j m 4 4 B - 3rgas p1 p4 = t ¶ ¶x ¶x M4

NUMERICAL METHODS Equations (14)±(17) form a family of coupled parabolic partial differential equations (PDE). As there is no obvious analytical solution to these equations, a numerical solution is required. These equations appear to be parabolic. However, on closer examination it becomes apparent that if the partial pressure of a particular species ( pi ) were zero, the second-order terms in the equation describing the mass balance for that species would tend to zero also. The equation would then become a ® rst-order partial differential equation which may behave very similarly to a hyperbolic equation. Carver13 has reported that the probability of getting `good solutions’ of hyperbolic equations using symmetrical difference formulae is low. The same author presented a number of plots which show the solution of a simple hyperbolic equation using a variety of central-difference methods. These oscillations were due to a wave propagating in the backwards, as well as in the forwards direction, which are a result of the differencing scheme used. Carver found that a backwards-difference formula completely removed the oscillations in the solution. Vichnevertsky and Tomalesky14 have shown that the ® rstorder, central-difference approximation to the ® rst-order hyperbolic equation (equation (18)) to be consistent with the solution of the wave equation (equation (19)). du du c = 0 (18) + dx dx d2 u d2 u c2 2 = 0 (19) 2 dx dx Vreugdenhil and Koren15 report that many numerical methods produce a small oscillation in the pressure pro® le when used to solve permeation (sometimes called advection) and diffusion problems. They also state that these oscillations are inconsistent with the physical situation. Many attempts have been made to construct numerical schemes which do not produce these oscillations, the most successful have usually employed some type of backwards (or upwind) differencing. It was, therefore, decided to discretize the family of partial differential eqautions above with a central-difference approximation solution to the second-order term, and a forwards-difference approximation to the ® rst-order term to solve the equations above . Both approximations were ® rstorder. The family of ordinary differential equation can then be solved using an ordinary differential equation solver such as DVODE. EXPERIMENTAL

(14)

(15) (16) (17)

Initial simulations of the vapour-boron treatment process and examination of the work carried out by the New Zealand Forest Research Institute (especially Nasheri and Laytner3 ) indicated that the experimental work should be concerned with three distinct variables. They were:

· moisture content; the moisture content of the wood has

always been found to determine the effectiveness of the treatment process. · vessel occupancy; this in¯ uences the total pressure rise in the treatment vessel and consequently the velocity of the permeating gas. Trans IChemE, Vol 75, Part A, January 1997

VAPOUR PRESERVATIVE TREATMENT OF SOFTWOOD BOARDS Table 1. Experimental design. moisture content (wt/wt oven dry basis)

0.03

trial trial trial trial trial trial trial trial trial trial

fast vaporization, low vessel occupancy repeat of 1 repeat of 1 repeat of 1 high occupancy, fast evaporation repeat of 5 repeat of 5 repeat of 5 low occupancy, slow vaporization repeat of 9

1 2 3 4 5 6 7 8 9 10

0.06

0.09

· rate of vaporization of the treatment chemical; this also in¯ uences the total pressure rise in the vessel.

Table 1 lists the trials that were undertaken. Treatment Rig The rig used for the treatments was made from 150 B mm glass sections. A stainless steel ¯ ange was placed between two of the sections which supported a 30 W hotplate which was used to evaporate the treatment chemicals. The pressure in the treatment vessel and the temperature within the vessel were measured and logged. Experimental Procedure The experimental procedure was as follows: 1. Lower treatment vessel into water bath and heat bath to about 50 8 C. 2. Weigh specimen. 3. Raise vessel and place test specimen inside, lower vessel back into water bath. 4. Start datalogging program and evacuate vessel. 5. Once the vessel has been completely evacuated, inject 20 mls of trimethyl borate / methanol azeotrope. 6. After the required period of time re-evacuate the vessel and stop datalogging. 7. Remove specimen, reweigh, and slice as illustrated in Figure 1. 8. Complete boron extraction and determination procedure as described in Section 3.3. Immediately after the an individual piece of timber had been treated it was cut into slices as shown in Figure 1. The

Figure 1. Diagram of sample slicing procedure.

Trans IChemE, Vol 75, Part A, January 1997

27

slices were approximately 2 mm thick, while the saw cuts were approximately 4 mm thick. For example, the boric acid retention in the ® rst slice taken from the sample was used to determine the boric acid retention in the ® rst 4 mm of the sample (the ® rst slice thickness plus half the thickness of the saw cut). The second slice was used to calculate the retention 4 to 10 mm into the sample and so on. A 1 g of a wood chip (approximately 2 ´ 2 ´ 5 mm) from each slice was soaked in 1 mol l- 1 sodium hydroxide at 60 8 C for 1Ý hours to leach all of the boric acid from the chip. The boric acid content of the solution was then measured using the method outlined in Evans16 . The uncertainty in this method is dif® cult to ascertain; however, it is not expected to be greater than 6 15%. RESULTS AND DISCUSSION OF EXPERIMENTAL RESULTS The boric retention pro® les for the three different moisture contents have distinctly different pro® les (Figure 2). In the high moisture content (9% wt/wt) sample, most of the boric acid has been deposited within 10 mm of the surface; whereas with the medium moisture content (6% wt/wt) sample, the pro® le is ¯ atter, with the boric acid penetrating very much further. The low moisture content (3% wt/wt) pro® le shows complete penetration of the boric acid with a very ¯ at pro® le. These results are typical of the results in all trials. It is dif® cult to compare the boric acid penetration pro® les between samples as the total retentions of boric acid in the samples varied greatly (from 1.4 g for the 9% moisture content specimen from sample 9 to 7.7 g for the 9% moisture content specimen from sample 8). Therefore, the retentions were normalized by dividing the retention for each slice by the total amount of boric acid in the sample. Figure 2 shows the mean retention curves at the three different moisture contents for the low-occupancy, fastevacuation trials. These curves were produced by taking the mean of the replicates for each test within each moisturecontent level. The assumption that the moisture content affects the shape of the retention curve was tested by comparing the mean normalized retentions of the individual slices for a particular moisture content with the retentions for another moisture content. If the means are signi® cantly different, then the shape of the curve is different. Comparison of the 3% and 6% curves for the fast evaporation and low occupancy trial (trials 1, 2, 3, and 4) shows that the retentions pro® les are signi® cantly different for the outermost three slices at the 0.05 level, whereas the mean retentions in both the inner slices (4 and 5) were not signi® cantly different. Comparisons between the 6% and 9% mean retention curves shows that slices 1, 3, and 4 have signi® cantly different means, whereas slices 2 and 5 do not. The shape of the boric acid retention curve, therefore, is a strong function of moisture content. At high moisture content the boric acid is deposited at the outer edges of the timber, whereas at lower moisture content the boric acid is more evenly distributed. Figures 3, 4, and 5 show the normalized boric acid retentions for the three moisture content levels tested (3%, 6%, and 9% wt/wt). These plots also show the mean normalized boric acid retention for each of the different

28

EVANS et al.

Figure 2. Typical experimental boric acid retention pro® les.

Figure 3. Mean retention curves for samples with a moisture content of 3 % (wt/wt oven dry basis).

Figure 4. Mean retention curves for samples with a moisture content of 6 % (wt/wt oven dry basis).

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29

Figure 5. Mean retention curves for samples with a moisture content of 9 % (wt/wt oven dry basis).

treatment conditions tested (fast/slow evaporation, and high/low occupancy). Signi® cant changes in treatment parameters (evaporation rate or occupancy etc.) do not change the shape characteristic curve markedly, indicating that, within the ranges of the variables tested, the rate of evaporation of preservative and the occupancy of the treatment vessel do not signi® cantly affect the shape of the boric acid deposition curve. However, the moisture content of the sample did have a very marked effect on the shape of the retention curves. This indicates that the most signi® cant variable in the effectiveness of the vapour-boron treatment process is the moisture content of the timber. SIMULATION OF EXPERIMENTAL RESULTS Input Data The parameters that need to be speci® ed for the proposed model of the vapour boron treatment process are:

· unsteady-state conductivity of the specimen and gas

mixture viscosity; · the gas diffusivity (usually trimethyl borate in methanol); · the moisture content of the wood; · radial dimension of the specimen; · radial surface area of sample; · volume of the wood sample; · volume of the treatment vessel; · the amount of water vapour in the vessel; · amount of preservative (trimethyl borate / methanol azeotrope) introduced into treatment vessel; · rate of evaporation of that preservative; · time until the vessel was evacuated (effectively ending treatment). The unsteady-state conductivity was estimated as 3.5 ´ 10- 13 m2 based on the previous experimental work8 on unsteady-state ¯ ow through Pinus radiata D. Don. The diffusivity of trimethyl borate in methanol has been estimated as 1.19 ´ 10- 5 m2 s- 1 using the method of Wilke and Lee described by Reid et al.12 . All the specimens to be treated were 100 mm x 50 mm x 600 mm ¯ at-sawn, Trans IChemE, Vol 75, Part A, January 1997

high-temperature dried Pinus radiata D. Don and, therefore, had a radial dimension of 50 mm and a radial surface area (the surface area of the sample aligned in the radial dimension) of 0.12 m2 . A quartersawn sample would have a radial dimension of 100 mm and a radial surface area of 0.06 m2 . The viscosity of the mixture of trimethyl borate, methanol, and water vapours has been estimated by the method of Lucas as outlined in Reid et al.12 . The viscosity (at 508 C) of trimethyl borate was calculated to be 1.49 ´ 10-5 Pa s, methanol as 1.32 ´ 10-5 Pa s, and water vapour 1.95 ´ 10-5 Pa s. The uncertainty in these predictions is reported to be approximately 6 5%. The viscosity of a number of different gas phase compositions of the trimethyl borate/methanol/air/water vapour systems was calculated using the method of Wilke.12 ). The results of these calculations showed that the viscosity of the mixture is not a strong function of the mole fractions of the gas species (in this particular case). For the purposes of the simulations a viscosity of 1.5 ´ 10-5 Pa s was assumed which was believed to be accurate to 6 10%. The partial pressure of water in the treatment vessel was estimated at 2 Pa, when the total pressure in the vessel was 10 Pa (the usual initial pressure before treatment). The rate of evaporation of preservative was calculated from the total pressure rise possible for the evaporation of 20 millilitres of trimethyl borate/methanol preservative in the treatment vessel divided by the time during which the pressure in the vessel rose. This assumes that the rate of evaporation is constant, which is true if the amount of heat input to the ¯ uid is constant and the heat used to heat the ¯ uid is insigni® cant compared to the heat used to evaporate the ¯ uid. For the fast evaporation trials, this condition would be reasonable as the hotplate did not cool signi® cantly and the pressure rose linearly with time. However, in the slow evaporation trials, there was no heat input into the hotplate, therefore, it cooled signi® cantly (from around 80 8 C to as low as 20 8 C) over the period it took to evaporate the preservative. This would mean that the rate of evaporation would decrease with time under these conditions. The

30

EVANS et al. Table 2. Reaction rate constants for adsorbed phase reaction.

moisture content (wt/wt oven dry basis) %

3%

6%

9

reaction rate constant (s- 1 )

0.17

0.27

1.4

length of treatment was taken directly from the measured pressure pro® le during the treatment process. RESULTS AND DISCUSSION OF NUMERICAL SIMULATIONS The pressure gradients within the timber ¯ atten soon after the evaporation of preservative has been completed, leaving a signi® cant amount of trimethyl borate unreacted in the treatment vessel. If no ¯ ow by diffusion processes was to occur, this trimethyl borate would remain unreacted. The PeÂclet number (equation (20)) indicates whether ¯ ow by diffusion or by permeation (sometimes called advection) is the dominant ¯ ow mechanism 15 . ul Pe = (20) D where Pe = PÂ eclet number, dimensionless

= velocity, m sl = dimension over which gradient 1

u

are significant, m D

= diffusivity, m

2

s- 1

Initially, the PeÂclet number would be large (approximately 100) due to the large pressure gradients (inducing a high gas velocity), indicating that permeation is the dominant ¯ ow mechanism. As the pressure gradients within the timber ¯ atten, the amount of ¯ ow by permeation will diminish. Then the PeÂclet number will decrease (to approximately 1) indicating the increasing signi® cance of

diffusion. Diffusion becomes the dominant mechanism soon after the evaporation of preservative is complete when there are no signi® cant pressure gradients within the timber. A problem associated with the vapour boron timber treatment process is that at high moisture contents (above 7% wt/wt oven dry basis) it is very dif® cult to get full penetration of boric acid to the centre of the timber. The hypothesis presented in this work is that the rate of the reaction between the adsorbed water and trimethyl borate has a signi® cant effect on the spatial deposition of boric acid during the treatment process. At moisture contents lower than 7% (wt/wt oven dry basis) the adsorbed water is much more tightly bound to wood substrate than at higher moisture contents17 . The more tightly the water is bound to the wood substrate the slower any reaction between the water and trimethyl borate is likely to be. To model the boric acid deposition for the three different moisture content tested, it is necessary to use three distinct reaction rate constants (in conjunction with the other variables used by the program). Table 2 shows the reaction rate constants used in the modelling of the experimental results. These reaction rates constants provided the best overall ® t to all the experimental results with each particular moisture content, and were estimated by trial and error. Figures 6, 7, and 8 show typical examples of plots comparing the simulations to experimental results. As can be seen from these ® gures, agreement between the simulation and experimental results is excellent for the high moisture content (9% wt/wt oven dry basis) samples. The simulation results use a single (estimated) reaction rate constant for the reaction between the adsorbed water and trimethyl borate for the range of moisture contents represented by these specimens (8.7% to 10.5% wt/wt oven dry basis). This assumes that the trimethyl borate is reacting with adsorbed water having very similar heats of adsorption throughout this moisture content range. One reason for this agreement may be that the vast majority of the boric acid is deposited in the outer 10 mm of the sample. Any discrepancies between the experimental and simulated results will most likely be restricted to this region. Therefore, if the model is able to predict the correct total

Figure 6. Typical experimental and simulation results for samples with a moisture content of 3 % (wt/wt oven dry basis).

Trans IChemE, Vol 75, Part A, January 1997

VAPOUR PRESERVATIVE TREATMENT OF SOFTWOOD BOARDS

31

Figure 7. Typical experimental and simulation results for samples with a moisture content of 6 % (wt/wt oven dry basis).

Figure 8. Typical experimental and simulation results for samples with a moisture content of 9 % (wt/wt oven dry basis).

amount of boric acid deposited, the deviation of the predicted deposition pro® le to the actual deposition pro® le will be minimal. The agreement between the medium (6% wt/wt oven dry basis) and the low moisture content (3% wt/wt oven dry basis) experiments and simulations is not as good as for the 9% (wt/wt oven dry basis) (Figures 6, 7, 8). This may be because the treated specimens had a wide range of moisture contents. Over this range of moisture-contents the heat of adsorption will have varied, resulting in variations in the reaction rate constants for the reaction between trimethyl borate and adsorbed water.

of the differential heat of adsorption. Therefore, the lower the moisture content (the higher the differential heat of adsorption) the slower the reaction rate and the better the penetration of boric acid. It was found that a binary diffusion representation was adequate and consequently more elaborate diffusion models were not necessary.

NOMENCLA TURE A DAB E ji

CONCLUSIO N The boric acid retention pro® le in a piece of timber which has been treated by the vapour boron process can be accurately predicted by a model which includes both convective and diffusive ¯ uxes if the initial moisture content of the timber is known. The reaction rate between the adsorbed water and trimethyl borate is a strong function Trans IChemE, Vol 75, Part A, January 1997

km K mi p pi Pe ri

pre-exponential factor diffusivity of trimethyl borate in a methanol, air and water mixture, m 2 s- 1 activation energy, J mol- 1 mass ¯ uxes of the ith species relative to mass average velocity, kg s- 1 m- 2 permeability of wood to a multicomponent mixture, m3 s kg- 1 speci® c permeability, m2 mass of species i divided by mass of methanol, air, and water, kg kg- 1 pressure, Pa partial pressure of component i, Pa PeÂclet number mass rate of production of the ith species, kg s- 1 m- 3

32 R t T u ui

EVANS et al. gas constant, J mole- 1 K- 1 time, s temperature, K mass average velocity, m s- 1 velocity of ith species, m s- 1

Greek letters j reaction rate constant l viscosity, Pa s q i mass concentration of ith species, kg m- 3 x A mass fraction of trimethyl borate, kg kg- 1 x i mass fraction of ith species, kg kg- 1

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ACKNOWLEDGEMENT One of us (JME) gratefully acknowledges the ® nancial and academic support of the New Zealand Forest Research Institute, to carry out the work described in this paper.

ADDRESS Correspondence concerning this paper should be addressed to Professor R. B. Keey, Department of Chemical and Process Engineering, University of Canterbury, Private Bag 4800, New Zealand. The manuscript was received 8 July 1996 and accepted for publication after revision 24 October 1996.

Trans IChemE, Vol 75, Part A, January 1997