Modeling Water Transport in Saturated Wood - ACS Symposium

Chapter 14 Modeling Water Transport in Saturated Wood

Downloaded by UNIV OF ARIZONA on August 6, 2012 | http://pubs.acs.org Publication Date: April 16, 2007 | doi: 10.1021/bk-2007-0954.ch014

Aaron J. Jacobson and Sujit Banerjee Institute of Paper Science and Technology and School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 500 Tenth Street N. W., Atlanta, G A 30332-0620

The diffusion rate of tritiated water into water-saturated pine and aspen particles was studied in order to establish a benchmark for the transport of solutes into wood. The diffusion follows a Fickian mechanism. The tortuosity for the diffusion of water into wood is quite low at about 1.6 and increases with decreasing particle size. The tortuosity for aspen is higher because the shorter fiber structure in aspen gives rise to a more extensive network of pores. Diffusion into free and bound water occurs at the same rate. Also, diffusion into and out of the particles is nearly identical, demonstrating the reversibility of the process. No hysteresis was evident, in contrast to behavior for water adsorption on unsaturated wood. The implications of these findings to pulping and wood drying are discussed.

© 2007 American Chemical Society

In Materials, Chemicals, and Energy from Forest Biomass; Argyropoulos, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 2007.

219


220 The main components of wood are hemicelluloses, cellulose, and lignin. Each constituent can be processed further into other products through chemical or biological processes. In native wood these components are integrated into structures that require energy to separate. In kraft pulping, the action of chemicals at high temperature and pressure separates most of the lignin from the cellulose, but removes most of the hemicelluloses as well. Even if the lignin were removed selectively, there would still be issues with the cellulose because of its crystallinity and high degree of polymerization \ which would restrict the ingress of chemical or biological reagents. Chemicals can transport into wood through penetration and diffusion. Penetration is the liquid transfer into the air-filled cavities of the chips and is driven by capillary forces and pressure. Once penetration is complete, the only way for chemicals to enter wood is through diffusion, which is governed by Fick's law, equation 1,

dm dC — = -D—dydz dt dx m

m

(1)

where dm/dt is the transfer rate of dissolved material, D represents the diffusion constant, dc/dx is the concentration gradient in the ^-direction, and dydz stands for the available cross section. For both diffusion and penetration, the dimensions of the wood are key components in describing the mass transport. For the production of chemicals from wood biomass the shape and size of the wood should not have an effect on the quality of the product. In fact, very small wood pieces such as sawdust could be preferred because of the shorter diffusion path lengths involved and the higher degree of cellulose exposure. In this paper the results are reported on the diffusion of water into saturated wood in order to establish a reference point against which the uptake of other compounds could be benchmarked.

Diffusion in Porous Media Diffusion in porous media such as saturated soils is very similar to diffusion in saturated wood particles. There is no flow of water, so any mass transfer through the soil must occur through diffusion. Solutes can only move through the liquid-filled areas of the solid . Thus, the effective diffusion coefficient will relate to the actual path taken by the solute . The shape and size of the solid is very important. In soils research, the material may be manipulated to give a particular shape. Rao et al. successfully modeled soil aggregates as spheres, and used chloride ions and tritiated water to 2

3

4


221 characterize the diffusion process. The equations governing diffusion into solids are complex and cannot be solved analytically for some geometries. In diffusion studies the particles are usually modeled as cylinders or spheres since the differential equations governing their shapes have been solved. In some instances creative modifications are needed. Novakowski and van der Kamp used a radial diffusion method for analyzing soil samples, where their soil samples were removed as large cylindrical samples, and the center was cored out to allow for a diffusion reservoir. One method that applies to both spherical and non-spherical particles is to reduce them to an equivalent sphere. This can be accomplished in several ways, Rao et a l . modeled cubic aggregates with spheres that had an equivalent volume. Thus an effective spherical radius could be determined and used in the equations. Because diffusion equations are dependent on the size of the solid, it is helpful to have a narrow size distribution. If the particles have a wider range of sizes, use of a weighted average is effective. The use of tritiated water (HTO) allows diffusion to be measured in saturated media, and has been applied to the study of sediments, soils, and membranes . Tritiated water is a conservative tracer; i.e. it moves with water and can be used to track water flow. It has been extensively used for this purpose in hydrogeology and other fields * . 5


6

7>

9

g

11

Diffusion of Tritiated Water into Wood Materials and Methods Freshly cut Southern pine {Pima taeda) particles were obtained from the Georgia-Pacific particleboard plant in Vienna, G A . Aspen (Populus tremuloides) chips from Alberta, Canada were obtained from Millar Western and then processed into small particles in a Wiley mill. They were fractionated with multiple Tyler sieves mounted to an automated shaker and stored airtight in a cold room. The screen openings ranged from 0.6 to 4.0 mm. The particles were stirred in deionized water for at least 24 hours, at which point no floating material was observed. They were then washed at least ten times to remove any particulate matter or extractives that may have diffused out of the wood, filtered, and stored in airtight vessels. Experiments were completed shortly thereafter to minimize moisture loss from the wood. A 40 ml aliquot of tritiated water (from Amersham Biosciences) was added to about 20 g. of the wet wood particles in a Pyrex bottle. Samples (100 μΐ) were removed at timed intervals, added to vials containing 10 ml of Scintiverse Ε scintillation cocktail (from Fisher Scientific), and the radioactivity determined with a liquid



222 scintillation counter. Measurements were continued until the tritium concentration in water leveled off, indicating that equilibrium had been reached. This point corresponded to within one percent of the equilibrium value expected from the amount of water added and the water content of the wood. In some experiments, the wood was removed after equilibrium was established, resuspended in water, and the diffusion of the tritiated water out of the particles measured by periodically sampling the bulk water. The geometry of particles of each size fraction was determined. Wet particles (not used in the experiment) were placed on a white background and painstakingly aligned into rows and columns. Images were then captured with a digital camera and analyzed with ImageJ software version 1.32 from the National Institute o f Health. The software converted the images to 8-bit thresholded images. The particle analysis yielded perimeter, area, longest and shortest dimensions, and the aspect ratio. The thickness dimension could not be imaged and was measured manually from at least 150 particles from each size fraction. This dimension was at least six times smaller than the longest dimension. An effective radius was used in the model. A similar approach was taken in analogous experiments using a mixture of particles of different shapes and sizes . 6

Data Analysis The aspect ratios of the particles suggested that they could be modeled as cylinders. Fick's second law describes mass transfer in cylindrical coordinates through E q 2, where C represents the concentration of species a, D is the a

e

ÔC

2

-=Ζλ

Ôt

0 b

C(r,t) = 0;0 0.5. For aspen particles in the 2.0 - 2.4 mm size range the r value 15

15

t

2


226 Figure 3 shows that the hardwood tortuosity increases to a greater extent than that of softwood with decreasing particle size. The reasons for this difference are not understood, but tortuosity would increase i f pore closure occurred while the particles were being cut. Hardwood fibers are shorter in length and smaller in diameter than their softwood counterparts , and the tortuosity of hardwood could, therefore, be more sensitive to pore closure. There was no apparent difference between diffusion into bound water and into free water, i.e. the diffusion coefficients remained constant throughout the process. This differs from the isothermal adsorption of the water vapor into dry wood , where Fick's law is not obeyed, since the diffusion coefficient changes as wood picks up more moisture. Also, in similar diffusion experiments in soil, all the water was accessible to diffusion . The lower tortuosity of pine as compared to aspen may have applications in pulping and wood drying. Uniform chips are required for consistent pulping; small chips tend to overcook. However, the tortuosity of aspen chips increases with decreasing chip size, which will tend to offset the size effect. Such a benefit will not apply to pine, which will overcook. Our preliminary studies confirm this behavior. Our results also apply to wood drying. Liquid flow is significant when sapwood boards are dried . The flow exiting the wood during early drying should follow the same pathways through which water diffuses into wood. Although wood drying is affected by other variables, the more tortuous path in aspen will make drying more difficult in the initial and constant rate regimes, as is the case for most hardwoods compared with softwoods . 19


2 0

2

2 1

22

Conclusions In conclusion, the diffusion of water into small water-saturated wood particles can be modeled by using the sorption kinetics equation for cylinders. The diffusion coefficients are temperature-dependent and remain unchanged for diffusion into and out of the particles. As expected, the tortuosity of water is temperature-independent. The tortuosity for hardwood particles is higher than that for softwood, most likely because of the smaller fibers in hardwood. A n increase in tortuosity with decreasing particle size was observed for both hardwood and softwood, with the effect being more pronounced for hardwood. Work on the tortuosity of components in pulping liquor is currently underway.

References 1.

Thomas, M.; Malcolm, G.; Malcolm, E . W., Alkaline Pulping, ed.; Tappi Press: 1989; 'Vol.' 5.


227 Table I. Diffusion parameters of water into particles.


Size fraction (mm)

Direction

Pine 2.0 - 2.4 1.7-2.0 1.7-2.0 1.4-1.7 Aspen 2.0-2.4 2.0 - 2.4 1.7-2.0 1.7-2.0 1.4-1.7 1.4-1.7

Temperature (°C)

D^x 10 ernes', (a)

Tortuosity

In In In In

25 25 4 25

11.1(0.5) 6.8 (0.8) 3.5 (0.5) 6.0 (0.9)

1.6 2.5 2.2 2.9

In Out In Out In Out

25 25 25 25 25 25

7.2(2.8) 8.3(1.4) 4.9(1.2) 4.9(1.2) 3.1(1.2) 2.9 (0.3)

3.0 2.4 4.1 4.1 6.8 6.6

10-1

8H

t

6-

Ο β

4

i

2H 0.48

I

j

ι

ι

ι

ι

0.42 0.36 0.30 Cylinder radius (cm)

0.24

Figure 3. Tortuosity of particles. The circles and triangles represent pine and aspen, respectively. (Reproduced with permission from Holzforshung: 2006, 60, 509-563. Copyright 2006 Walter de Gruyter.)


225 1η

0.8-

8

S

0.6-

0.4-

0.2

0-f— —ι— —τ—'—ι—•—ι—«—ι 1

1


0

40

80

120

Time (s)

160

200

Figure 2. Approach to equilibrium for pine particles in the size range of 1.7-2.0 mm at two temperatures. (Reproduced with permission from Holzforshung: 2006, 60, 509-563. Copyright 2006 Walter de Gruyter.)

for such a plot was 0.98. This degree of linearity was typical for all the experiments. For aspen, the diffusion into and out of the particles is nearly identical, demonstrating that diffusion of water into saturated wood particles is completely reversible. There was no hysteresis for the saturated wood as is common for water adsorption into unsaturated wood. Therefore, all the regions in fully saturated wood are equally accessible to the diffusing water molecules. Water that is bound to the wood structure readily exchanges with the loosely bound bulk water. The observation that tortuosity increases with decreasing particle size has been reported in other areas. Cadmium uptake into chitosan particles showed a similar relationship . The authors suggest that although they modeled the chitosan particles as spheres, the larger particles were actually flat discs, which would increase the uptake efficiency and would be reflected in the tortuosity factor. The sulfation reaction on different limestone sorbents also showed that tortuosity increased as the particle size decreased . This occurred only for limestone particles with a unimodal pore size distribution. Particles with a wider distribution showed no change in tortuosity with changing particle size. The authors speculate that the increase in tortuosity for smaller particles may be due to variations in porosity. It is possible that the movement of tritium into the system could occur through proton transfer rather through the movement of the tagged water molecule. If this were the case, then the diffusion coefficient would have been much larger than that typical for water. The self-diffusion coefficient of H D O , HTO, and H 0 at 25°C are all nearly identical . If proton transfer were significant, there would be appreciable differences among these coefficients. 17

18

1818

1 8

2

13


228 2. 3. 4. 5. 6.


7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Van Der Kamp, G.; Stempvoort, D . R.; Wassenaar, L . I., Water Resources Res. 1996, 32, (6), pp 1815-1822. Moldrup, P.; Olesen, T.; Komatsu, T.; Schjonning, P.; Rolston, D . E., Soil Sci. Soc. Am. J 2001, 65, pp 613-623. Rao, P. S. C.; Jessup, R. E.; Rolston, D. E.; Davidson, J. M.; Kilcrease, D. P., Soil Sci. Soc. Am. J 1980, 44, pp 684-688. Novakowski, K . S.; Van Der Kamp, G., Water Resources Res. 1996, 32, (6), pp 1823-1830. Rao, P. S. C.; Jessup, R. E.; Addiscott, T. M.,Soil Sci. 1982, 133, (8), pp 342349. Kohne, J. M.; Gerke, H . H . ; Kohne, S., Soil Sci. Soc. Am. J 2002, 66, (September-October), pp 1430-1438. Nitta, K . ; Natsuisaka, M.; Tanioka, Α., Desalination 1999, 123, pp 9-14. Hutchison, J. M.; Seaman, J. C.; Aburime, S. Α.; Radcliffe, D. E.,Vadose zone J.l 2003, 2, pp 702-714. Kendall, C.; McDonnell, J. J., Isotope Tracers in Catchment Hydrology, ed.; Elselvier: Amsterdam, 1998; p 839. Livingston, H . D.; Povinec, P. P., Health Phys. 2002, 82, pp 656-668. Crank, J., The Mathematics of Diffusion. 2nd ed.; Clarendon Press: Oxford, 1975; p 414. Pruppacher, H . R.,The J. of Chem. Phys. 1972, 56, (1), pp 101-107. Mahoney, M. W.; Jorgensen, W. L . , J. of Chem. Phys. 2001, 114, (1), pp 363-366. Isenberg, I. H., Pulpwoods of the United States and Canada - Conifers. Third ed.; The Institute of Paper Chemistry: Appleton, 1980; 'Vol.' 1, p 219. Price, W . S.; Ide, H . ; Arata, Y., J. of Phys. Chem. A 1999, 103, pp 448-450. Evans, J. R.; Davids, W. G.; MacRae, J. D.; Amirbahman, Α., Water Res. 2002, 36, pp 3219-3226. Adanez, J.; Gayan, P.; Garcia-Labiano, F., Ind. Eng. Chem. Res. 1996, 35, (7), pp 2190-2197. Isenberg, I. H . , Pulpwoods of the United States and Canada - Hardwoods. Third ed.; The Institute of Paper Chemistry: Appleton, 1981; 'Vol.' 2, p 168. Stamm, A . J., Forest Prod. J. 1959,9, pp 27-32. Pang, S.; Haslett, A . N., Drying Tech. 1995, 13, (8&9), pp 1635-1674. Martin, M.; Canteri, L., Drying Tech. 1997, 15, (5), pp 1293-1325.


Modeling Water Transport in Saturated Wood - ACS Symposium

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