Compactable Porous and Fibrous Beds Formed from Dilute Pulp

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Ind. Eng. Chem. Res. 2002, 41, 572-578

SEPARATIONS Compactable Porous and Fibrous Beds Formed from Dilute Pulp Suspensions Jinsong Wang, Andrew Hrymak,* and Robert Pelton McMaster Centre for Pulp and Paper Research, Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7

A systematic experimental investigation of the formation of compactable fibrous mats from dilute pulp suspensions (8.00 kg/m3 fiber concentration or 0.533 vol % of solid) has been performed over a range of vacuum levels (10.0-66.7 kPa). An instrumental apparatus with a computerized data-acquisition system measured the operating vacuum and filtrate flow rate. The dynamic behavior of the mat formation process, in a transparent plastic filtration cell, was observed and videotaped. Dynamic fiber concentration profiles along the mat formation direction were inferred from the standard images using a gray-scale analysis calibrated against a set of known concentrations. A modified filtration model for compactable fibrous mat formation was proposed on the basis of Tiller’s filtration theory. The model captures the filtrate flux and mat thickness as functions of time and operating vacuum for a compactable mat, which have not been reported previously in the literature. Introduction Brownstock washing, an important unit operation in the production of kraft pulp, is used to separate pulp fibers from pulping liquor. In this operation, a large (∼10 m long, ∼4 m in diameter) screened drum is partially immersed into a vat containing 1 wt % of wood pulp fibers in aqueous pulping liquor. A vacuum is applied to the inside of the drum, causing the flow of the liquor through the screen and the subsequent buildup of a fiber pad on the drum surface. The drum rotates at about 4 rpm, causing an approximately 4-cmthick fiber pad on the drum screen surface to emerge from the vat. Water is sprayed onto the fiber pad after withdrawal from the vat to displace the liquor from the fiber pad. The pad is scraped from the drum surface just before the screen re-enters the vat. In previous work, we have extensively investigated the displacement washing zone. We have shown that the introduction of cationic polymers into the wash water improves displacement washing by the selective formation of lignin-polymer precipitates in the most open channels of the pad.1 For an overview of this work, see Pelton.2 Our current activities are focused on the pad formation process that occurs on the surface of the drum submerged in the vat. In preliminary work, we have shown that the presence of dispersed air causes channels to form in the pad, which lowers the liquor flux by as much as a factor of 10 compared with that for airfree pulp.3 Most of the negative effects due to the presence of dispersed air can be eliminated by defoamer * Author to whom correspondence should be addressed. Department of Chemical Engineering, McMaster University, Hamilton, Ontario Canada L8S 4L7. Tel.: 905.525.9140 x23136. Fax: 905.521.1350. E-mail: [email protected].

addition. Defoamer does not remove air from the pulp; instead, it appears to destabilize the bubbles, allowing them to pass through the pad and therefore not interfere with liquor flow and thus production. One of the objectives of our current work is to develop mechanistic models for the pulp pad formation process, which is essentially a filtration. In the case of wood pulp, the analysis of filtration is complicated by the fact that the fibers are not uniformly dispersed but are present as flocs.4 A further complication is that pulp pads can be compacted, causing the volume fraction of solids in the pad to increase in the flow direction and to be a function of the applied pressure. Empirical models of the overall brownstock drum washer operation have been developed;5-8 however, they do not account for the pad formation process. Similarly, the literature contains many experimental and theoretical descriptions of water flow through pulp pads.8-11 Although relatively little has been published on pulp pad formation, the general filtration literature contains a number of relevant contributions. One of the first filtration models is Ruth’s cake filtration model.12 Meyer13 proposed a differential equation for the pulp fiber filtration process but provided only a very simplified tentative solution to it. Other cake filtration models include those of Smiles,14 Atsumi and Akiyama,15 Wakeman,16 and Stamatakis and Tien.17,18 Each offers improvements in numerical methodology with respect to the moving interface, but they are all restricted in application to compactable pulp fiber systems. Jonsson and Jonsson19,20 proposed a dynamic model for filtration and wet pressing of a compactable porous media with a fixed mass of fiber and fixed relative thickness of each isotropic layer. The relative thickness of each layer is defined as the thickness of

10.1021/ie0105728 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/10/2002

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Figure 1. Schematic drawing of filtration cell and supporting equipment.

each layer divided by the total cake thickness, so the dimensionless relative thickness value lies between 0 and 1. The model due to Tiller et al.21,22 is the most commonly accepted in filtration theory, because of its reliability and relatively wide range of application. The parameters pertinent to wood fibers in Tiller’s model are not available. Empirical filtration formulas developed for other materials are doubtful when applied to a wood pulp fiber mat, because of the characteristics of water-swollen, compactable wood fibers. Some empirical relationships between volume reduction and applied pressure are available in the literature.23-25 These correlations are limited to a narrow pressure range, and no general wood pulp fiber bed compressibility correlation is available in the literature. This work proposes constitutive equations for compactibility and permeability by considering three pulp fiber characteristics (swelling due to water absorption, compactibility, and specific surface area) to be used with Tiller’s model in comparison with experimental measurements of pulp fiber-water filtration processes. Experimental Section (1) Apparatus. Figure 1 shows a schematic diagram of the experimental apparatus. The heart of the apparatus is the transparent acrylic visualization filtration cell with inside dimensions 200 × 155 × 20 mm (H × W × T). A metal washer screen with a measured resistance of R ) ∆P/(µq) ≈ 1.0 × 108 m-1 formed the top of the filtration cell. The screen resistance will increase when cake is deposited and fibers partially clog the screen medium. The resistance of the pipe connecting the filtration cell and vacuum accumulator was determined to be R ) ∆P/(µq) ≈ 1.2 × 109 m-1. Although the resistance of the filtration screen will increase when cake is deposited, it is still small in comparison to the resistance of the connecting piping. (1.1) Data Acquisition System. The operating vacuum was measured by pressure sensor (Celesco DP30-0001-111) that was connected via a DAS-802 A/D board (Keithley Metrabyte Co.) to a PC. A digital balance (Mettler PM16) that was directly connected to the PC was used to measure the collected mass of filtrate (water). TESTPOINT (Capital Equipment Corporation, version 2.0a, 1995) software was employed to collect data on the vacuum and mass of filtrate at a frequency of 1.0 Hz.

(1.2) Pulp Slurry Recirculation and Vacuum System. A Moyno progressing cavity pump (A1B SS03 AAA) was used to pump the pulp slurry from the pulp slurry tank into the vat. It overflowed through the other end of the vat and flowed back to the pulp slurry tank. A Welch duo-seal vacuum pump (Sargent-Welch Scientific Co., model 1400) was used to generate the vacuum. An air accumulator was employed to stabilize the vacuum. Vacuum was applied to the top of the filtration cell through a tube and control valve. With applied vacuum, the pulp slurry moved toward the screen, and the mat began to grow. The applied vacuum was adjusted manually to the desired vacuum level by a vacuum adjustment valve that was on top of the air accumulator. In this experiment, vacuum levels of 10.0, 20.0, 40.0, and 66.7 kPa (or 75, 150, 300, and 500 mmHg, respectively) were set. (1.3) Optical System. A light table (Visual Plus, model VP-4050v with a viewing size of 310 mm × 216 mm) was used as the background light of the filtration cell because of its homogeneous lighting effect, which was important for image analysis. A digital camcorder (Canon ZR,27 with 30 frames per second and 720 × 480 pixels per frame) was employed to record videos of the filtration cell. (2) Materials and Procedure. The wood pulp fibers used were fully bleached Northern Canadian unbeaten softwood kraft pulp. The mean fiber length of the pulp was measured to be 2.01 mm, and the coarseness was 0.206 mg/m. These results were based on an average of seven test runs on a Kajaani FS-200 fiber analyzer (courtesy of Ken Wong, Pulp and Paper Center, University of British Columbia). In a typical experiment, the pulp slurry in the vat and tank consisted of 40.0 L of water and 434.1 g of air-dried pulp fiber (about 7 wt % water content) mixed to a pulp slurry. After the slurry pump, the mixer in the tank, and the mixer in the vat were activated, the pulp slurry was circulated for about 10 min. The vacuum pump was started, and the vacuum level was set to the desired value by manually adjusting the valve on the top of the vacuum accumulator. Water was added to the top of the filtration cell, which was located between the filtration screen and the connecting pipe (from the filtration cell to the filtrate tank). The purpose of this operation was to eliminate the dead time in the filtrate flux measurements. The valve on the top of the filtration cell was slowly opened, the pulp slurry was allowed to touch the filtration screen, and then the valve was closed. The background lighting and digital camcorder were set up for image capture, with the white balance and exposure level set manually. Filtration measurements were started when the control valve on the top of filtration cell was opened in a quick motion. To test repeatability, 3 runs were made at each vacuum level for a total of 12 runs. After each experiment, the pulp slurry pump and mixers were kept running, and the fiber slurry in the vat was sampled (the total mass measured was 1050.33 g). The oven-dry fiber mass in this sample measured 8.38 g, and the oven-dry fiber density was 1500 kg/m3, so that the fiber (oven-dry) concentration was 8.00 kg/m3 (or 0.798% mass consistency). (3) Calibration of Gray-Scale Level and Fiber Concentration. A dilute pulp slurry of 0.1% mass concentration was introduced into a small tank with about 10 g of air-dried pulp (about 7% water content).

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Figure 3. Average gray-scale level of horizontal lines of pixels vs distance in mat formation direction for Figure 2.

Figure 2. Sample video frame (at a vacuum level of 20 kPa after 60 s).

The filtration cell was placed upside down, with the camcorder and background light the same as that used in the mat formation process studies. The water was allowed to drain out very slowly to achieve a relatively homogeneous mat. At higher fiber concentrations, we manually compressed the fiber mat. Images were recorded at mat thicknesses from 15.0 to 1.0 cm at 1.0cm intervals. The cross-sectional area of the filtration cell was 15.5 cm × 2.0 cm. From each calibration image, we found the mat thickness by checking the ruler at the left side of the image, so the volume of mat for each image was determined. The oven-dry fiber weight was measured after the calibration image-taking process was completed. The fiber concentration for each image was the total oven-dry mass of fiber divided by the total mat volume. The average gray-scale level of the mat image was determined by a simple Fortran code with a Postscript image file as the input gray-scale data file. A total of 85 image files corresponding to 85 experimental data points, with gray-scale levels corresponding to fiber concentrations from 10.77 to 198.92 kg/m3, were regressed using fourth-order polynomials. The grayscale levels were nearly constant at high fiber concentrations (over 160 kg/m3). This means that the error in the fiber concentration can be much larger than the error in the low fiber concentration area. Inferred fiber concentrations in this higher fiber concentration area either were not used (if it was not reasonable) or were used only as a reference. Experimental Results Single-frame images were recorded after 5, 10, 15, 20, 25, 30, 60, and 120 s for each run. Data in the image files were converted to dynamic gray-scale distribution plots and, with the correlation of the fiber concentration and gray-scale levels, were converted to local mat fiber concentration plots. Estimated local fiber concentrations greater than 160 kg/m3 were not very accurate, because the gray-scale levels were nearly constant at high fiber concentration. Figure 2 presents a sample image of the mat formation process, at an operating vacuum of 20 kPa, 60 s after the beginning of filtration process. The left side of

Figure 4. Fiber concentration in mat formation direction at a vacuum level of 10.0 kPa.

the image is a ruler. This image was cropped from the top of the filtration cell (0.00-0.13 m) to keep the fiber mat in the image (without ruler) and saved as a Postscript file (350 × 437 pixels, height × width). The Postscript format is composed of ASCII characters and is easily converted to a data file for postprocessing. The average gray-scale value of each line of pixels (total of 437) in the image was calculated. Along the mat formation direction of 0.130 m, there was a total of 350 pixels, so each pixel corresponds to 3.714 ×10-4 m. The average gray-scale level along the mat formation direction is shown in Figure 3, which corresponds to the image in Figure 2. There is no clear boundary between the fiber mat and pulp suspension flow at this fiber suspension concentration (8.0 kg/m3), as seen in Figures 2 and 3. The mat boundary or thickness is required to determine the pulp mass balance. The experimental images are analyzed through the gray-scale data to determine the mat boundary. The mat thickness was defined as the distance from the top of the filtration cell to the line, x, where the gray-scale level reached the average grayscale level of the remaining part of filtration cell (from x to 0.130 m). For example, in Figure 3, at x ) 0.086 m, the average gray-scale of the rest of cell (from 0.086 to 0.013 m) is 146, so this is taken as the boundary between mat and fiber suspension. The suspension area has a constant concentration with little variation because of its heterogeneity. The focus of this study was the fiber mat and its dynamic formation process, so only the mat portion of the image analysis is shown in Figure 4. Mat-suspension boundaries were located using the fiber concentration plots. The mat thicknesses for experiments at operating vacuum levels of 10, 20, 40, and 66.7 kPa are shown in Figure 5.

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Figure 5. Mat thickness at varied vacuum levels with definition 1.

Figure 8. Experimental and calculated filtrate fluxes as a function of the vacuum level.

Figure 6. Fiber concentration profile at different operating vacuum levels (after 10 s). Figure 9. Fiber compressibility experimental correlation.

in this fiber-water system through observations with dye tracer injection into the pulp-water suspension. Similar results have been reported previously.28 Model for Pulp Fiber Mat Formation Tiller’s model requires permeability and compressibility correlations for the pulp fiber. Compressibility data were measured with a piston compression apparatus29 and were fitted with a simple correlation, as shown in eq 1 and Figure 9. Figure 7. Experimental and calculated filtrate volumes as a function of the vacuum level.

In Figure 5, the operating vacuum had little influence on the growth in the mat thickness, because increasing the vacuum level provided more fiber on the screen and, at the same time, made the fiber mat more compacted. However, the operating vacuum strongly influenced the mat concentration profile in the low-vacuum range (1020 kPa). Figure 6 shows a plot of the fiber concentration profile after 10 s; similar results were also found in plots after 5, 15, 20, and 25 s. The influence of operating vacuum levels greater than 20 kPa on the fiber concentration profile diminished with increasing operating vacuum. The fiber concentration profile at a vacuum level of 66.7 kPa was within experimental error of the 40-kPa data. The total volume of the filtrate was measured as a function of time and the results are shown in Figure 7. The filtrate flux trend (Figure 8) appears similar to those obtained in conventional filtration experiments. From our observations, the compactable porous and fibrous mat was composed of layers with little heterogeneity. No flow channels in the fiber mat were found

C ) ap4 + bp3 + cp2 + dp + e

(1)

where

a ) -3.517 × 10-18 b ) 1.160 × 10-12 c ) 1.425 × 10-7 d ) 8.903 × 10-3 e ) 71.91 p (Pa) is the applied pressure and C (kg/m3) is the fiber concentration (average value for the mat). The most widely used of the expressions relating the permeability in Darcy’s law to some of the fiber properties is the Kozeny-Carman equation

K)

3 kS02(1 - )2

(2)

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Figure 10. Experimental average fiber concentration in the mat after 60 s.

where k is an empirically determined value (taken as 5.55 for pulp fiber;30 the Kozeny-Carman constant, k, is not constant). We found that allowing for variations in k or using a constant value of k ) 5.55 made little difference in the water flux calculation results. We simplified the calculation by assuming an estimated value of 5.55 for k. S0 is the surface area per unit volume of solids (m2/m3), and  is the porosity of the bed. An empirical expression for  was proposed in dimensionless form

 ) (1 - θ1)γC

(3)

where γ ) 1.0 m3/kg (constant) and θ1 is the solid fraction of swollen fiber bed at a fiber concentration of 1.0 kg/m3. The parameter θ1 was used to fit the permeability data and represents a characteristic of the water-swollen fiber. The estimated value24 of S0 is 2.71 × 105 m2/m3, and that of θ1 is 4.34 × 10-3. S0 and θ1 were regressed from eqs 2 and 3 with experimentally measured permeability (K) data with changing fiber concentration (C). Modeling Results A number of sample calculations at various vacuum levels were done with Tiller’s filtration equations (see the Appendix) and the fiber constitutive equations (eqs 1-3). The filtrate volume and flux are shown in Figures 7 and 8. From the system total mass balance, one obtains

L + V ) LCavg/C0

(4)

where L is the fiber mat thickness, V is the filtrate volume (per unit area), Cavg is the average fiber concentration in the mat, and C0 is the fiber concentration in the slurry (8.0 kg/m3 in this case). Although Cavg varies with the pressure drop through a mat, in a constant-pressure filtration process, Cavg can reach a steady-state constant value in seconds. It is usually assumed to be constant and equal to the experimental value obtained at the end of a run.22 In this case, C60, the average mat fiber concentration at 60 s, was taken to be Cavg for the cake thickness calculation. The experimentally measured values of C60 at various vacuum levels are shown in Figure 10, and the estimated mat thicknesses are shown in Figure 11. The flux calculation according to Tiller’s model agrees with the experimental data very well at each tested vacuum level. The mat thickness can only be estimated with the calculated filtrate volume (V) and the average

Figure 11. Experimental and calculated mat thicknesses as a function of the vacuum level.

fiber concentration in the mat (Cavg) in eq 4. The assumption that Cavg can be approximated by C60 increases the error in the mat thickness calculation during the initial few seconds of filtration (see Figure 11), but the calculated mat thicknesses agree with the experimental data to within the error in the fiber mat thickness measurements. As seen in Figure 11, the vacuum level has very little influence on the mat thickness. Conclusions Dynamic fiber concentration profiles of compactable porous fibrous beds formed from dilute pulp slurry were measured with gray-scale analysis. A clear boundary between the fibrous mat and slurry did not exist. Increasing operating vacuum did not increase the thickness of the fiber mat but did increase the fiber concentration in the mat with diminishing changes at vacuum levels above 20 kPa. The filtrate flux increased with increasing vacuum level for short times (less than 20 s). Tiller’s cake filtration model was modified with experimental fiber compressibility and permeability correlations. The calculated filtrate flux agreed with experimental measurements very well over the investigated vacuum range. The dynamic mat thickness can also be estimated with the calculated filtrate volume and the observed fiber concentration in the mat. Appendix: Tiller’s Filtration Model Tiller’s21,22 cake filtration model is composed of a mass balance, force balance, the Darcy-Shirato equation, an empirical constitutive compressibility model, and an empirical constitutive permeability model. From an overall system point of view, the mass balance can be written on a unit-area basis in the form

mass of slurry ) mass of cake + mass of filtrate or

w/s ) w/sc + Fv

(A1)

where w is the mass of dry solids per unit area, v is the filtrate volume per unit area, s is the mass fraction of solids in the slurry, sc is the average mass fraction of solids in the cake, and F is the density of the filtrate. Solving for v in equation A1 yields

v)

1 - s/sc w Fs

(A2)

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From the definition of sc, one obtains

sc )

Fs(1 - av)

(A3)

Fs(1 - av) + Fav

where the average porosity of the cake is

av ) 1 -

∫0pdps/R ∫0

(A4)

dps

p

Acknowledgment

R(1 - )

and R is the specific resistance given by

R)

1 Fs(1 - )k

(A5)

∫

∫0p-p

1

dps R(1 - ) (A6)

where σ () Fs/F) is the specific gravity of the dry solids. The pressure ps is the mechanical pressure on the solids, and pl is the pressure drop on the filtration screen. Tiller’s original empirical compressibility and permeability models for cake particle filtration (we used our eqs 1-3 to substitute them) were of the form

( ) ( )

s ) 0s 1 + k ) k0 1 +

Ps Pa

Ps Pa

Financial support from NSERC and the Dorset Chemical Company is gratefully acknowledged. The equipment was designed by Joe Maiolo, and experiments were performed with Yongmoon Kwon. Literature Cited

Tiller’s key filtration equation was

σ - s(σ - 1) p-p1 dps 1 vq1 ) 0 µFss R µFs

the situation is that the wood fibers are often beaten, which increases the surface area. Thus, for the same wood fiber, we have to develop a series of parameters to represent the degree of beaten fiber, i.e., the surface area, which makes Tiller’s eqs A7 and A8 more difficult to apply in pulp applications. S0 and θ1 were regressed from eqs 2 and 3 with experimentally measured permeability (K) data with changing fiber concentration (C).

β

(A7)

-δ

(A8)

where s is the cake solidity (volume fraction of cake occupied by solid) and k is the permeability. β, δ, 0s , and k0 are empirical constants for materials. Values of these constants in the two constitutive equations for various types of cakes can be found in the literature. Equation 1 is an experimental compressibility model for our wood fiber, and eq 3 is our proposed correlation between fiber porosity and fiber concentration. A combination of eqs 1 and 3 was used to substitute Tiller’s compressibility model, which is equation A7. The reason for this modification is that wood fiber swells in water and the trapped water within the fiber is no longer liquid. Thus, porosity cannot be calculated directly from the fiber concentration. The solid fraction will include the volumes of both fiber and absorbed water. Equation 3 is a new model to represent this behavior; for more detail, see Wang et al.26 The modified Kozeny-Carman equation (eq 2, used to substitute eq A8) was extensively employed in correlating the permeability of the pulp fiber. It contains two parameters, one representing the fiber surface area and the other representing the fiber water swelling. These two parameters have physical meanings and are easy to generalize to different kinds of wood fibers. Tiller’s constitutive equations (eqs A7 and A8) are very successful in conventional filtration, but they are difficult to apply to wood fibers because each of the three parameters in these equations is empirical. This means that we have to measure the three parameters for each wood fiber before we can use it. Further complicating

(1) Lappan, R. E.; Hrymak, A. N.; Pelton, R. H. PolymerEnhanced Brownstock Washing: Mill Trial. TAPPI J. 1996, 79 (11), 170. (2) Pelton, R. H. Polymer-Colloid Interactions in Pulp and Paper Manufacture. In Colloid-Polymer Interactions: From Fundamentals to Practice; Farinato, R. S., Dubin, P. L. Eds.; John Wiley & Sons: New York, 1999. (3) Wang, J.; Pelton, R. H.; Hrymak, A. N.; Kwon, Y. New Insights into Dispersed Air Effects in Brownstock Washing. TAPPI J. 2001, 84 (1), 1. (4) Kerekes, R. J. Pulp Floc Behavior in Entry Flow to Constrictions. TAPPI J. 1983, 66 (1), 88. (5) Han, Y.-S. Modeling and Simulation of Wood Pulp Washers. Ph.D. Dissertation, University of Idaho, Moscow, ID, 1989. (6) Wang, X. Dynamic Simulation of Brown Stock Washers and Bleach Plants. M.S. Dissertation, The University of British Columbia, Vancouver, BC, Canada, 1993. (7) Kempe, M. J. Dynamic Modeling of a Vacuum Drum Washing System. M. Eng. Dissertation, McMaster University, Hamilton, ON, Canada, 1995. (8) Zahrai, S.; Bark, F. H.; Martinez, D. M. A Numerical Study of Cake Formation in 2-D Cross-Flow Filtration. J. Pulp Pap. Sci. 1998, 24 (9), 281. (9) Wildfong, V. J.; Genco, J. M.; Shands, J. A.; Bousfield, D. W. Filtration Mechanics of Sheet Forming. Part I: Apparatus for Determination of Constant-Pressure Filtration Resistance. J. Pulp Pap. Sci. 2000, 26 (7), 250. (10) Chang, M. Y.; Robertson, A. A. Zeta Potential of Fibres. DC Streaming Potential Methodology. Can. J. Chem. Eng. 1967, 45 (4), 66. (11) Han, S. T. Compressibility and Permeability of Pulp Pads. Pulp Pap. Mag. Can. 1969, 70 (4), 65. (12) Ruth, B. F.; Montillon, G. H.; Montanna, R. F. Studies in Filtration I. Critical Analysis of Filtration Theory. Ind. Eng. Chem. 1933, 25 (76), 153. (13) Meyer, H. A Filtration Theory for Compressible Fibrous Beds Formed from Dilute Suspensions. TAPPI J. 1962, 45, 4. (14) Smile, D. E. A Theory of Constant-Pressure Filtration. Chem. Eng. Sci. 1970, 25, 985. (15) Atsumi, K.; Akiyama, T. A Study of Cake Filtration. J. Chem. Eng. Jpn. 1975, 8, 6. (16) Wakeman, R. J. A Numerical Integration of the Differential Equations Describing the Formation of and Flow in Compressible Filter Cakes. Trans. Inst. Chem. Eng. 1978, 56, 258. (17) Stamatakis, K. Analysis of Cake Formation and Growth in Liquid-Solid Separation. Ph.D. Dissertation, Syracuse University, Syracuse, NY, 1990. (18) Stamatakis, K.; Tien, C. Cake Formation and Growth in Cake Filtration. Chem. Eng. Sci. 1991, 46 (8), 1917. (19) Jonsson K. A.; Jonsson, B. T. L. Fluid Flow in Compressible Porous Media. I. Steady-State Conditions. AIChE J. 1992, 38 (9), 1340. (20) Jonsson K. A.; Jonsson, B. T. L. Fluid Flow in Compressible Porous Media. II. Dynamic Behavior. AIChE J. 1992, 38 (9), 1349. (21) Tiller, F. M. Compressible Cake Filtration. In The Scientific Basis of Filtration; Ives, K. J., Ed.; Noordhoff International Publishing Co.: Leyden, The Netherlands, 1975.

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(22) Tiller, F. M.; Cleveland, T.; Lu, R. Pumping Slurries Forming Highly Compactable Cakes. Ind. Eng. Chem. Res. 1999, 38, 590. (23) Campbell, W. B. The Physics of Water Removal. Pulp Pap. Mag. Can. 1947, 48, 3. (24) Ingmanson, W. L. An Investigation of the Mechanism of Water Removal from Pulp Slurries. TAPPI J. 1952, 35 (10), 439. (25) Ingmanson, W. L.; Whitney, P. P. The Filtration Resistance of Pulp Slurries. TAPPI J. 1954, 37 (11), 523. (26) Canon ZR Digital Video Camcorder Instruction Manual; Canon Inc.: Mississauga, Ontario, Canada, 1998. (27) Wang, J.; Hrymak, A. N.; Pelton, R. H. Specific Surface

and Effective Volume of Water Swollen Pulp Fibers by a Permeability Methodology. Pulp Pap. Sci., in press. (28) Wang, J. Experiments and Modelling of Pulp Mat Formation. Ph.D. Dissertation, McMaster University, Hamilton, ON, Canada, 2002. (29) Fowler, J. L.; Hertel, K. L. Flow of Gas through Porous Media. J. Appl. Phys. 1940, 11, 496.

Received for review July 3, 2001 Revised manuscript received November 2, 2001 Accepted November 9, 2001 IE0105728