Chapter 4: RESULTS AND DISCUSSION 61 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Exploratory Cooks Exploratory cooks were done in order to determine the relationship between the H-factor and kappa number relationship before preparing the cooked chips for the pressure drop experiments. The H-factor is a reaction co-ordinate given by H = t E a / RT Ae 0 dt (4.1) where A (= 5.67 10 18 /hr) is the pre-exponential factor, E a (= 32 kcal/mole) is the Arrhenius activation energy, T is the temperature (Kelvin), R (= 1.987 10-3 kcal/mole K) is the gas constant, and t is the time (hr) (Vroom, 1957). The H-factor is related to yield and kappa number which is proportional to the lignin content in the pulp. For example, for two cooks targeting the same kappa number but having different H-factors, the one with the lower H-factor indicates that a shorter cooking time is required to achieve the same kappa number. This translates into a shorter cooking period and increased digester throughput if the cooking temperature is maintained constant. Additionally, lower H-factor always indicates a lower level of alkaline peeling reactions and higher pulp yield. Table 4.1 shows the correlation of H-factor and kappa number of white spruce chips used in this study. These results can be used to predict the H-factor and control the cook if the targeted kappa number is given. In Figure 4.1, it is shown that there is no significant difference between the four furnishes. This implies that, for these particular wood chips, chip size distribution is not a major factor that influence the H-factor vs. kappa number relationship.
Chapter 4: RESULTS AND DISCUSSION 62 H -factor 1600 1400 1200 1000 800 100% Accept 87.5% Accept + 12.5% Pins 75% Accept + 25% Pins 100% Pins 600 400 15 20 25 30 35 40 45 50 55 60 65 70 Kappa Number Figure 4.1: H-factor vs. kappa number for all exploratory cooks. Solid lines are fits correlation developed by using equations from Table 4.1. The error bar is the average repeatability for kappa number.
Chapter 4: RESULTS AND DISCUSSION 63 Table 4.1: Correlations of H-factor (HF) as a function of kappa number (k). Furnishes Correlation R 2 100% Accepts 0. 9007 ( ) HF = 22558 κ 0.996 HF 0. = 23738 κ 0.999 HF 0. = 25515 κ 0.996 HF 0. = 20699 κ 0.997 100% Pins ( ) 9032 87.5% Accepts + 12.5% Pins ( ) 9232 75% Accepts + 25% Pins ( ) 8693 Table 4.2 and Figure 4.2 show the results of yield vs. kappa number relationship for the white spruce used. Pulping pin chips resulted in a yield drop of approximately 3% compared with other furnishes. This result has significant industrial implications. The yield loss for pin chips is expected, because the surface area-to-volume ratio is quite large for pin chips. Pulping liquors are, therefore, able to penetrate much more rapidly then they can penetrate the larger sized accept chips. The net result is that the pin chips become easily cooked and a yield loss is experienced (Hatton, August 1973). Correlations between yield and kappa number in Table 4.2 are valid over the range 20 k 65. Table 4.2: Regression analysis of yield as a function of kappa number. Furnishes Correlation R 2 100% Accepts yield (%) = 0. 1407 κ + 44. 17 0.964 100% Pins yield (%) = 0. 1558 κ + 42. 31 0.999 87.5% Accepts + 12.5% Pins yield (%) = 0. 1499 κ + 43. 82 0.994 75% Accepts + 25% Pins yield (%) = 0. 1415 κ + 43. 98 0.999 Figure 4.2 also shows that having pin chips in the accept furnish does not seem so bad as far as pulp yield is concerned. The yield is not much different between 100% accepts and both mixed furnishes. For example, at kappa number 20, the predicted yield for 100% accepts is 46.9% while the predicted yield for both mixed furnishes are 46.8%.
Chapter 4: RESULTS AND DISCUSSION 64 54 53 52 51 100% Accept 100% Pins 87.5% Accepts + 12.5% Pins 75% Accepts + 25% Pins Yield % 50 49 48 47 46 45 15 20 25 30 35 40 45 50 55 60 65 70 Kappa Number Figure 4.2: Yield vs. kappa number for different chip size distribution of exploratory cooks. The error bar is the average repeatability for kappa number.
Chapter 4: RESULTS AND DISCUSSION 65 4.2 Compressibility of Cooked Chip Columns Figure 4.3: A series of pictures showing the degree of compaction on cooked chip columns (100% pins; kappa number = 47) at different compacting pressure applied ranging from 0 to 17 kpa.
Chapter 4: RESULTS AND DISCUSSION 66 Mechanical properties of chips change during cooking. The chips become more flexible as lignin and carbohydrates are dissolved from the cell walls. Cooked chips may easily break apart into fibers after the middle lamella has lost sufficient lignin. As a result, resistance of chips to stress may decrease with degree of delignification. Therefore, compressibility will increase with reduced lignin content (Gullichsen, 1999). The term compressibility will be used throughout the text to describe the bed height change as loading is applied. It is the ratio of changed height over original height and defined as H o H p Compressib ility(%) = 100 (4.2) H where H o is initial height (m) and H p is height after having loading (m). Figure 4.3 illustrates the degree of compressibility of a cooked pin chip column at kappa number of 47. It clearly shows that the bed becomes more packed with increased loading. For example, the bed can be compressed to about 50% of the original height under a load of 17.3 ± 0.3 kpa. The degree of compressibility is even higher at lower kappa numbers as shown in Figure 4.4. This is because as the lignin content decreases, kappa number decreased and chip flexibility is increased. As we know, cooked chips have similar dimensions as the original chips except that the cooked chips have less lignin content (depend on the cooking time). When a comparison is made between 100% pins and 100% accepts, as shown in Figures 4.4 and 4.5, it is shown that 100% accepts is more compressible. The reason is that 100% accepts generally pack more loosely than 100% pins. This loosely cooked chip packing tends to form a higher void fraction bed. For example, void fraction for 100% accepts is 0.57 while for 100% pins is 0.55, at kappa number of 24 and at initial packing (P c = 0 kpa). When the higher void fraction bed subjected to a compacting pressure, the chip bed will more easily be compressed. This leads to a reduction of void fraction. For example, at kappa number 24, 100% accepts can o
Chapter 4: RESULTS AND DISCUSSION 67 be compressed about 40% while 100% pins can be compressed about 35%, at 5.8 ± 0.3 kpa loading. Overall, a general trend shows that the degree of compressibility is higher at lower kappa numbers at any chip size distribution. 60% 50% kappa No. = 69 kappa No. = 47 kappa No. = 24 Comp ressib ility ( % ) 40% 30% 20% 10% 0% 5.8 8.6 11.5 14.4 17.3 Compacting Pressure (kpa) Figure 4.4: Degree of compressibility for 100% cooked pin chips at compacting pressure ranging from 5.8 kpa to 17.3 kpa. The error bars are the accuracy of the measured height.
Chapter 4: RESULTS AND DISCUSSION 68 60 50 kappa No. = 70 kappa No. = 48 kappa No. = 24 Comp ressib ility ( % ) 40 30 20 10 0 5.8 8.6 11.5 14.4 17.3 Compacting Pressure (kpa) Figure 4.5: Degree of compressibility for 100% cooked accept chips at compacting pressure ranging from 5.8 kpa to 17.3 kpa. The error bars are the accuracy of measured height.
Chapter 4: RESULTS AND DISCUSSION 69 60% 50% kappa No. = 66 kappa No. = 42 kappa No. = 22 Comp ressib ility ( % ) 40% 30% 20% 10% 0% 5.8 8.6 11.5 14.4 17.3 Compacting Pressure (kpa) Figure 4.6: Degree of compressibility for 87.5% accepts + 12.5% pins at compacting pressure ranging from 5.8 kpa to 17.3 kpa. The error bars are the accuracy of measured height.
Chapter 4: RESULTS AND DISCUSSION 70 60% 50% kappa No. = 65 kappa No. = 43 kappa No. = 23 Comp ressibility ( % ) 40% 30% 20% 10% 0% 5.8 8.6 11.5 14.4 17.3 Compacting Pressure (kpa) Figure 4.7: Degree of compressibility for 75% accepts + 25% pins at compacting pressure ranging from 5.8 kpa to 17.3 kpa. The error bars are the accuracy of measured height.
Chapter 4: RESULTS AND DISCUSSION 71 4.3 Void Fraction Results 4.3.1 Comparison between Two Methods In this study, all void fractions were determined based on the density method. The equation used for calculating void fraction is: H 0 o ρ b H p ε l = 1 (4.3) Yρ c where 0 ρ b is the measured bulk density of cooked chips, Y is the fractional yield after the cook, and ρ c is the uncooked chip density. In order to compare with density method, one of the furnishes (87.5 % accepts + 12.5% pins) was used to study the void fraction by the displacement method. The results are shown in Table 4.3 with error bars being generated based on standard deviation. From the table, we can see that the void fraction determined by the displacement method generally gave lower void fraction than the density method. The reason for this could be that in the displacement method some water was trapped in interstices which contributed to the low void fraction. Therefore, we concluded that the density method is more reliable than the displacement method. Note that throughout the text we used the density method to calculate the void fraction. Table 4.3: Comparison between two methods for determining the void fraction (87.5% accepts + 12.5% pins). The void fractions are average value. The errors were generated based on standard deviation. Kappa Number Void Fraction (Displacement Method) Void Fraction (Density Method) Difference Difference % 21.8 0.566 ± 0.031 0.560 ± 0.002 0.006 ± 0.031 1.6 ± 0.1 42.3 0.570 ± 0.030 0.589 ± 0.009 0.019 ± 0.031 3.2 ± 0.1 66.1 0.574 ± 0.034 0.606 ± 0.009 0.032 ± 0.035 5.3 ± 0.1 180.0 0.636 ± 0.011 0.670 ± 0.009 0.034 ± 0.014 5.1 ± 0.1
Chapter 4: RESULTS AND DISCUSSION 72 4.3.2 Effect of Height on Void Fraction To investigate the variation of local void fraction along the column height, we selected one chip furnish (87.5% accepts + 12.5% pins) for the study. The local void fraction was determined experimentally using the water displacement procedure under no flow and no loading conditions. The results are shown in Table 4.4. These results clearly show that local void fraction is a function of column height with the void fraction slightly decreasing from top to bottom. This confirms with Harkonen (1987) that the cooked chip column is elastic and compressible and the flexibility of the chip column affects the void fraction in it. Table 4.4: The effect of height and kappa number on void fraction for cooked chips of 87.5% accepts + 12.5% pins. The errors were generated based on standard deviation. Column Section Kappa no. 21.8 Kappa no. 42.6 Kappa no. 66.1 (Each is 10 cm in height) Mean void fraction Section 1 (Top) 0.584 ± 0.006 0.586 ± 0.012 0.587 ± 0.012 Section 2 0.599 ± 0.006 0.599 ± 0.004 0.612 ± 0.011 Section 3 0.573 ± 0.015 0.570 ± 0.004 0.570 ± 0.016 Section 4 (Bottom) 0.522 ± 0.003 0.525 ± 0.004 0.525 ± 0.006 Average 0.569 ± 0.004 0.570 ± 0.004 0.574 ± 0.006 4.3.3 Effect of Kappa Number on Void Fraction at P c = 0 kpa In Section 4.2, we discussed that the chips become more flexible as lignin and carbohydrates dissolve from the cell walls. This can be proved from Figure 4.8. As you can see from this figure, the uncooked wood chips (full lignin content) have a void fraction of 0.67. As the degree of delignification increases (kappa number decreases), the void fraction decreases. For example, the kappa number decreases from 70 to 20, the void fraction decreases from 0.62 to 0.55, respectively. Harkonen (1987) reports that there is no change in external void fraction regardless of degree of delignification (kappa number). Essentially, he shows that initial void fraction for
Chapter 4: RESULTS AND DISCUSSION 73 uncooked wood chips and chips cooked to different kappa numbers had identical void fractions. However, our experiments show that initial void fraction is dependent on the kappa number when no load is applied. Table 4.5 reports the values from the literature and our results. It is shown that the initial void fraction for chips bed is between 0.591 and 0.670. The reasons for this variation might be the differences in packing, chipping method, chip type, wood chip geometry, chip size distribution, and wood species. The transfer of chips to the test apparatus may also account for this change. Other researchers determined the pressure drop in-situ. Lindqvist s (1994) data contains a range of void fraction because he performed the experiments on different chip size distributions, as shown in Table 4.5. He found that having fines in the mixture decreased the void fraction. Two wood types, hardwood (Lammi, 1996) and softwood (Wang and Gullichsen, 1998; Lindqvist, 1994; Harkonen, 1987) have been studied in the literature. However, due to the limited literature data available, it is difficult to conclude that whether wood type affects the void fraction. 4.3.4 Effect of Compacting Pressure and Kappa Number The void fraction of a cooked chips bed is affected by the compacting pressure. Typical results are shown in Figures 4.9 and 4.10. These findings show that void fraction can be reduced from around 60% to less than 10% by increasing loading from 0 to 17.3 ± 0.3 kpa. We notice that the void fraction is decreased with increased compacting pressure, as shown in Figures 4.9 and 4.10. The void fraction for cooked chips is also strongly affected by kappa number at different loadings. The results are shown in Figure 4.11 and 4.12. These findings show that void fraction decreases with decreased kappa number at a fixed compacting pressure.
Chapter 4: RESULTS AND DISCUSSION 74 0.70 Averag e V o id F ra c tio n a t P c = 0kPa 0.68 0.66 0.64 0.62 0.60 0.58 0.56 0.54 100% accepts 87.5% accepts + 12.5% pins 75% accepts + 100% pins 100% pins 0 20 40 60 80 100 120 140 160 180 200 Kappa Number Figure 4.8: Initial void fraction, using density method, at different chip size distribution for white spruce without compaction. The range of kappa number is between 20 and 180. The dot line ( ) is the regression line for 100% accepts while the solid line ( ) is the regression line for 100% pins.
Chapter 4: RESULTS AND DISCUSSION 75 Table 4.5: Literature and this work values of initial void fraction. References Wood Chips Initial Void Fraction Wang and Gullichsen (1998) Scandinavian Pine 0.663 Fraction of accepts chips of sawmill chips. Chips passed through a 13 mm round hole but retained on a 7 mm round hole. Wang and Gullichsen (1998) Scandinavian Pine 0.840 Using new chipping method. The chip has dimension of 4 mm thick and 40 mm in length. Lammi (1996) Eucalyptus Camaldulensis 0.591 + 45 mm hole 1.1% + 8 mm bar 4.8% + 13 mm hole 78.8% + 7 mm hole 12.6% + 3 mm hole 2.2% + fines 0.5% Lammi (1996) Scandinavian Birch 0.630 + 45 mm hole 0.6% + 8 mm bar 9.2% + 13 mm hole 51.4% + 7 mm hole 31.2% + 3 mm hole 6.4% + fines 1.1% Lindqvist (1994) Scandinavian Pine (mix 1) 0.604 + 6 mm bar 22.1% + 4 mm bar 44.2% + 2 mm bar 29.1% + 3 mm hole 4.6% Lindqvist (1994) Scandinavian Pine (mix 2) 0.615 + 6 mm bar 23.2% + 4 mm bar 46.3% + 2 mm bar 30.5% Lindqvist (1994) Scandinavian Pine (mix 3) 0.647 + 4 mm bar 60.3% + 2 mm bar 39.7% Harkonen (1987) Scandinavian Pine (not Specified) 0.644 This work White spruce 100% accepts 87.5% accepts + 12.5% pins 75% accepts + 25% pins 100% pins 0.670
Chapter 4: RESULTS AND DISCUSSION 76 0.70 0.60 0.50 kappa number = 70 kappa number = 48 kappa number = 24 V o id F ra c tio n (-) 0.40 0.30 0.20 0.10 0.00 0 5 10 15 20 Compacting Pressure (kpa) Figure 4.9: Effect of compacting pressure on void fraction at different kappa numbers (100% accepts). Solid lines are given using Equation 4.4 (page 85) with variables found in Table 4.7.
Chapter 4: RESULTS AND DISCUSSION 77 0.70 0.60 0.50 kappa number = 69 kappa number = 47 kappa number = 24 Void Fraction (-) 0.40 0.30 0.20 0.10 0.00 0 5 10 15 20 Compacting Pressure (kpa) Figure 4.10: Effect of compacting pressure on void fraction at different kappa numbers (100% pins). Solid lines are given using Equation 4.4 (page 85) with variables found in Table 4.7.
Chapter 4: RESULTS AND DISCUSSION 78 0.70 V o id F ractio n (-) 0.60 0.50 0.40 0.30 0.20 0 kpa 5.8 kpa 8.6 kpa 11.5 kpa 14.4 kpa 17.3 kpa 0.10 0.00 0 10 20 30 40 50 60 70 80 Kappa Number Figure 4.11: Effect of compacting pressure and kappa number on void fraction for 100% accepts. Solid lines are given using Equation 4.4 with variables found in Table 4.7. The error bars are the error of estimation.
Chapter 4: RESULTS AND DISCUSSION 79 0.7 V oid Fraction (-) 0.6 0.5 0.4 0.3 0.2 0 kpa 5.8 kpa 8.5 kpa 11.5 kpa 14.4 kpa 17.3 kpa 0.1 0 0 10 20 30 40 50 60 70 80 Kappa Number Figure 4.12: Effect of compacting pressure and kappa number on void fraction for 100% pins. Solid lines are given using Equation 4.4 with variables found in Table 4.7. The error bars are the error of estimation.
Chapter 4: RESULTS AND DISCUSSION 80 4.3.5 Effect of Chip Size Distribution Chip size distribution may have an effect on the void fraction in the column. As shown in Table 4.6, the void fractions are slightly different in all four furnishes. However, there is no significant difference between them. The percent difference is about 2% in between the maximum and minimum void fraction. In Figure 4.13, it is shown that the mixed of 75 % accepts with 25% pins shows a lowest void fraction. This can be explained by the fact that when small particles, such as pins are added into accepts fraction that the pin particles tend to orient themselves to fill and occupy the void spaces in between the larger particles (accept chips). Table 4.6: Comparison of different furnishes for kappa number range 65-70 at no compaction. Standard deviations based on multiple measurements are given. Furnish Kappa number Void fraction 100% accepts 69.9 0.623±0.009 87.5% accepts + 12.5% pins 66.1 0.617±0.009 75% accepts + 25% pins 65.0 0.612±0.009 100% pins 69.0 0.618±0.009 4.3.6 Effect of Superficial Velocity on Void Fraction Superficial velocity could affect the void fraction of the bed. Figures 4.14, 4.15, and 4.16 illustrate this effect with data from 100% pins at kappa number of 24, 48, and 69, respectively. At kappa number 24, the void fraction is reduced significantly with increased superficial velocity at compacting pressure between 5.8 kpa and 8.6 kpa. However, the effect is not apparent at compacting pressure higher than 8.6 kpa. This is because above compacting pressure of 8.6 kpa, as shown in Figure 4.14, the chips change in void fraction is not as great as at lower compacting pressure, e.g. 5.8 kpa and 8.6 kpa. Therefore, flow velocity has no effect on void fraction under high compacting pressure.
Chapter 4: RESULTS AND DISCUSSION 81 From Figures 4.16, we can see that at kappa number 69, the flow velocity has little effect on void fraction compared to kappa number 24 (as shown in Figure 4.14). This is because the chip bed is more flexible and compressible at lower kappa number. Therefore, it is more compressible at lower kappa number and in turns decreases the void fraction of the bed. Void Fraction ( - ) 0.80 0.70 0.60 0.50 0.40 100% accepts 100% accepts (predicted) 87.5% accepts + 12.5% pins 87.5% accepts + 12.5% pins (predicted) 75% accepts + 25% pins 75% accepts + 25% pins (predicted) 100% pins 100% pins (predicted) 0.30 0.20 0 5 10 15 20 Compacting Pressure (kpa) Figure 4.13: Effect of chip size distribution on void fraction at kappa number of 65-70. Solid lines are given using Equation 4.4 with variables found in Table 4.7.
Chapter 4: RESULTS AND DISCUSSION 82 0.50 0.45 0.40 0.35 V o id F ra c tio n 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Pc = 5.8 kpa Pc = 8.6 kpa Pc = 11.5 kpa Pc = 14.4 kpa Pc = 17.3 kpa 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.14: The effect of superficial velocity on void fraction for 100% pins at kappa number of 24. Solid lines are given using linear regression fit in Excel.
Chapter 4: RESULTS AND DISCUSSION 83 0.50 0.45 0.40 0.35 V o id F ractio n 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Pc = 5.76 kpa Pc = 8.63 kpa Pc = 11.51 kpa Pc = 14.39 kpa Pc = 17.27 kpa 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.15: The effect of superficial velocity on void fraction for 100% pins at kappa number of 48. Solid lines are given using linear regression fit in Excel.
Chapter 4: RESULTS AND DISCUSSION 84 0.50 0.45 0.40 0.35 V o id F ra c tio n 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Pc = 5.76 kpa Pc = 8.63 kpa Pc = 11.51 kpa Pc = 14.39 kpa Pc = 17.27 kpa 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.16: The effect of superficial velocity on void fraction for 100% pins at kappa number of 69. Solid lines are given using linear regression fit in Excel.
Chapter 4: RESULTS AND DISCUSSION 85 4.3.7 Comparison between Experimental and Literature Results In this section, we present two methods used to correlate void fraction. They are: 1. average void fraction over different superficial velocities (at fixed compacting pressure and kappa number) as a function of compacting pressure and kappa number, 2. void fraction as a function of compacting pressure and kappa number at zero superficial velocity, The data were fitted to an equation of the form l x c y x c ε = a + bp + cκ + dp κ y (4.4) where a, b, c, d, x and y are the variables that can be solved in Matlab program. A program is written in Matlab to solve and to optimize the variables in order to get a best fit (see Appendix H). ε l is liquid void fraction (dimensionless), P c is compacting pressure (in kpa), and κ is kappa number. Equation 4.4 can be rearranged into a traditional form (Martinez et al., 2001): P y 1 / x ε l ( a + cκ ) n c = = m( ε y g ε l ) ( b + dκ ) (4.5) where, m y n = [ ( b + dκ )] in kpa, n 1 / x y =, and ε a + cκ. The term ε is the gel point, which g = g is a common term used to represent the void fraction for which the packed bed starts to have strength. The parameter m is the stiffness of network, with dimension of kpa, and can be thought of as a Young s modulus. The derivation from Equation 4.4 to Equation 4.5 can be found in Appendix L. In Appendix L, the calculation shows that the variation of void fraction along the height of the bed is insignificance and the use of an average void fraction as a means of characterizing the bed in our analysis is appropriate.
Chapter 4: RESULTS AND DISCUSSION 86 Equation 4.4 correlates the average void fraction with the effect of compacting pressure, kappa number, and interaction between compacting pressure and kappa number. Equation 4.4 was solved by using multiple linear regression technique (see Appendix H). This correlation is good for kappa numbers between 20 (3% lignin) to 180 (27% lignin) for the white spruce chips studied. Kappa number 20 is the about lowest kappa number used in this study and kappa number 180 is the initial lignin content (27%) of the wood chip. When a compaction load is applied to the chip column, the value for b is expected to be negative because an increase in compacting pressure reduces the void fraction as is found. The results of the correlation are obtained by using multiple regression analysis on the Matlab program (Appendix H). We varied x and y over a range from 0.1 to 3.0 with step change of 0.01 and obtained the variables (a, b, c, and d) with correlation coefficients (R 2 ) at about 0.99, as shown in Tables 4.7 and 4.8. We also ran the program with all the data and compared with all four correlations. As you can see in Tables 4.7 and 4.8, method 1 gives better correlations than method 2. Therefore, we used the correlations obtained from method 1 (as shown in Table 4.7) to predict the void fraction. Table 4.7: Correlation results for all chip size distributions using method 1 with Equation 4.4. Furnishes a b c d x y R 2 100% pins 0.529-0.0633 0.00389 0.00150 0.82 0.70 0.996 75% accepts + 0.537-0.0724 0.00353 0.00091 0.73 0.7 0.993 25% pins 87.5% accepts + 0.556-0.0636 0.00109 0.00037 0.78 0.90 0.991 12.5% pins 100% accepts 0.545-0.0788 0.00347 0.00145 0.71 0.70 0.998 Average of values 0.542-0.0695 0.00300 0.00106 0.76 0.75 --- All data correlated 0.541-0.0699 0.00301 0.00110 0.76 0.73 0.984
Chapter 4: RESULTS AND DISCUSSION 87 Table 4.8: Correlation results for all chip size distributions using method 2 with Equation 4.4. Furnishes a b c d x y R 2 100% pins 0.537-0.05163 0.00368 0.00129 0.90 0.70 0.994 75% accepts + 0.542-0.05370 0.00337 0.00072 0.84 0.70 0.986 25% pins 87.5% accepts + 0.559-0.04832 0.00106 0.00030 0.88 0.90 0.988 12.5% pins 100% accepts 0.537-0.05363 0.00293 0.00086 0.83 0.74 0.993 Average of values 0.544-0.05182 0.00276 0.00079 0.86 0.76 --- All data correlated 0.552-0.04994 0.00132 0.00040 0.87 0.87 0.978 The general equation we used to predict the void fraction is based on method 1 with all data correlated results: ( ) 0. 76 0. 73 76 0 73 0 00301 0 00110( ) 0.. P +. κ. P ε = 0. 541 0. 0699 + κ (4.6) l c and Equation 4.6 is valid for P c = 0 to18 kpa and κ = 20 to 180. Figure 4.17 shows graphically the predicted void fraction, using Equation 4.6, as a function of kappa number at various compacting pressures. Predicted void fractions from Equation 4.6 are also compared with calculated void fractions, as shown in Figure 4.18. c One should note that, all these equations are only valid for white spruce species. As shown in Figure 4.19, wood species may affect the liquid void volume. Our correlation shows a lower void fraction than literature. We conclude that the void fraction depends on both the wood species and small extent on chip size distribution (refer to Table 4.7). In contrast, the literature modeling equations (Wang and Gullichsen, 1998; Lammi, 1996; Lindqvist, 1994; Harkonen, 1987) did not adequately correlate our experimental data. The general equation (Harkonen, 1987) that literature provided is in the form of k 1 Pc = k0 + ( k2 + k ln( κ )) (4.7) 10 ε l 3
Chapter 4: RESULTS AND DISCUSSION 88 or can be written as k k 1 1 Pc Pc ε l = k0 + k2 + k3 ln( κ ) (4.8) 10 10 where k 0, k 1, k 2 and k 3 are constants determined empirically. P c is compacting pressure (in kpa) and κ is the kappa number. The existing literature equations do not consider the effect of kappa number on the void fraction when no compacting pressure is applied. 1.00 0.90 0.80 0.70 Void Fraction 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0 kpa 3 kpa 5 kpa 8 kpa 10 kpa 14 kpa 18 kpa 0 20 40 60 80 100 120 140 160 180 200 Kappa Number Figure 4.17: Predicted void fraction, by using Equation 4.6, as a function of kappa number at various compacting pressures (0 to 18 kpa).
Chapter 4: RESULTS AND DISCUSSION 89 0.80 0.70 Measured Void Fraction ( - ) 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Predicted Void Fraction (-) Figure 4.18: Comparison of measured and predicted void fraction. Predicted void fractions are determined by Equation 4.6.
Chapter 4: RESULTS AND DISCUSSION 90 0.70 0.60 0.50 Void Fraction ( - ) 0.40 0.30 0.20 0.10 0.00 Wang (1998) Linqvist, mix1 (1994) Harkonen (1987) Our Correlation 0 5 10 15 20 Compacting Pressure (kpa) Figure 4.19: Comparison between experimental correlation and selected literatures at fixed kappa number of 25 under various compacting pressures. Our correlation line is given using Equation 4.6.
Chapter 4: RESULTS AND DISCUSSION 91 4.4 Pressure Drop (Flow Resistance) 4.4.1 Effect of Superficial Velocity on Pressure Drop Pressure drop is used to characterize energy loss through packed columns. In this study, pressure drop measurement is the technique employed to study the flow resistance of white spruce chips having different chip size distributions at different kappa numbers and compacting pressures. Figure 4.20 illustrates a typical curve of pressure drop versus superficial velocity. Superficial velocity, for the range of flow rates tested, varied from 0 to 10 mm/s in the test column. An estimate of the error associated with pressure drop values was based on the standard deviation of the mean obtained by averaging the individual test points. This error is represented by error bar in Figure 4.20. The general trend indicates that the relationship between pressure drop and superficial velocity is non-linear. This shows that increases in pressure drop with increased superficial velocity. In this particular case, 100% accepts at kappa number 70 and P c = 5.7 kpa, the pressure drop can be increased from 0 to 12 kpa/m as superficial velocity increases from 0 to 10 mm/s. The pressure drop is increased by increasing the compacting pressure, decreasing the kappa number and is affected by the chip size distribution at a given superficial velocity. 4.4.2 Effect of Compacting Pressure on Pressure Drop Compacting pressure is one of the factors that affect the pressure drop under similar flow velocity. Figures 4.21, 4.22, 4.23 and 4.24 illustrate how the compacting pressure affects pressure drop for the different mixture furnishes.
Chapter 4: RESULTS AND DISCUSSION 92 12 10 p ( kpa/m ) Pressure D ro 8 6 4 2 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.20: Pressure drop as a function of superficial velocity for 100% white spruce accepts at kappa number of 70 and P c = 5.7 kpa. Average void fraction is 0.446. Solid line is given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 93 60 p ( kpa/m ) Pressure D ro 50 40 30 20 10 5.8 kpa 8.6 kpa 11.5 kpa 14.4 kpa 17.3 kpa 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.21: Effect of compacting pressure (kpa) on pressure drop for 100% accepts at kappa number of 48. Average void fraction for P c 5.8 kpa, 8.6 kpa, 11.5 kpa, 14.4 kpa, and 17.3 kpa are 0.403, 0.340, 0.267, 0.204, and 0.167, respectively. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 94 p ( kpa/m ) Pressure D ro 80 70 60 50 40 30 20 5.8 kpa 8.6 kpa 11.5 kpa 14.4 kpa 17.3 kpa 10 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.22: Effect of compacting pressure (kpa) on pressure drop for 100% pins at kappa number of 47. Average void fraction for P c 5.8 kpa, 8.6 kpa, 11.5 kpa, 14.4 kpa, and 17.3 kpa are 0.423, 0.355, 0.299, 0.228, and 0.176, respectively. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 95 60 p ( kpa/m ) Pressure D ro 50 40 30 20 10 5.8 kpa 8.6 kpa 11.5 kpa 14.4 kpa 17.3 kpa 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.23: Effect of compacting pressure (kpa) on pressure drop for 87.5% accepts + 12.5% pins at kappa number of 42. Average void fraction for P c 5.8 kpa, 8.6 kpa, 11.5 kpa, 14.4 kpa, and 17.3 kpa are 0.375, 0.280, 0.189, 0.134, and 0.096, respectively. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 96 p ( kpa/m ) Pressure D ro 60 50 40 30 20 10 5.8 kpa 8.6 kpa 11.5 kpa 14.4 kpa 17.3 kpa 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.24: Effect of compacting pressure (kpa) on pressure drop for 75% accepts + 25% pins at kappa number of 43. Average void fraction for P c 5.8 kpa, 8.6 kpa, 11.5 kpa, 14.4 kpa, and 17.3 kpa are 0.388, 0.319, 0.243, 0.169, and 0.131, respectively. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 97 Pressure drop increases with increased compacting pressure at a given superficial velocity. As discusses in Section 4.2, void fraction is reduced as the loading increases. 4.4.3 Effect of kappa Number on Pressure Drop Figure 4.25 shows a typical plot of how kappa number affects the pressure drop at constant compacting pressure. This figure illustrates that a decrease in kappa number increases the pressure drop under similar flow and loading conditions. For example, at a superficial velocity of 6 mm/s, the pressure drop increases from 7 kpa/m to 20 kpa/m when kappa number drops from 69 to 24. The reason for this increased pressure drop is that cooked chips at lower kappa number are easily compressed under loading. This leads to decrease in void fraction and causes a higher flow resistance in the bed. 4.4.4 Effect of Chip Size Distribution on Pressure Drop Figures 4.26, 4.27, and 4.28 illustrate the effect of chip size distribution on pressure drop at P c =11.5 kpa and different kappa numbers. We expected that the 100% accepts will have a lower pressure drop with respect to others as they form a bed with a higher void fraction than other fractions. However, with chip mixtures, two phenomena can occur. When smaller particles are mixed into a bed of larger particles, the smaller particles can increase the column void fraction by forcing the larger particles apart. On the other hand, the smaller particles can decrease the void fraction by occupying voids between the larger chips (Dullien, 1992). In our results, it can be seen that the latter factor has dominated, e.g. at conditions of P c = 11.5 kpa and kappa number range of 65 to 70, the average void fraction for each furnishes are: 100% accepts = 0.33; 87.5% accepts + 12.5% pins = 0.30; 75% accepts + 25% pins = 0.27; 100% pins = 0.35. Here, the
Chapter 4: RESULTS AND DISCUSSION 98 mixture of accepts and pins has a higher pressure drop and lower void fraction than for the 100% pins or 100% accepts fraction. Wall effects may contribute a systematic error to the pressure drop measurements made. The wall effect (fluid channeling along the wall due to the discontinuity between the particles and the wall) increases with increasing particle size (Eisfeld and Schnitclein, 2001). Thus, fluid is expected to channel more through a bed of large particles (the accept chips) than small ones (pin chips). If channeling occurred, a lower pressure drop would be measured. Unfortunately, the magnitude of this effect is not known for our system.
Chapter 4: RESULTS AND DISCUSSION 99 50 p ( kpa/m ) Pressure D ro 45 40 35 30 25 20 15 10 5 kappa number = 24 kappa number = 47 kappa number = 69 0 0 2 4 6 8 Superficial Velocity (mm/s) 10 Figure 4.25: Effect of different kappa numbers on pressure drop for 100% white spruces pins at P c = 8.6 kpa. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 100 60 Pressure Drop ( kpa/m ) 50 40 30 20 100% accepts (kappa no. = 70) 87.5% accepts + 12.5% pins (kappa no. = 66) 75% accepts + 25% pins (kappa no. = 65) 100% pins (kappa no. = 69) 10 0 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.26: Effect of chip size distribution on pressure drop. Conditions at: P c = 11.5 kpa and kappa number range of 65 to 70. The average void fraction for each furnishes are: 100% accepts = 0.33; 87.5% accepts + 12.5% pins = 0.30; 75% accepts + 25% pins = 0.27; 100% pins = 0.35. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 101 p ( kpa/m ) Pressure Dro 60 50 40 30 20 10 100% accepts (kappa no. = 48) 87.5% accepts + 12.5 % pins (kappa no.= 42) 75% accepts + 25% pins (kappa no. = 43) 100% pins (kappa no. = 48) 0 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.27: Effect of chip size distribution on pressure drop. Conditions at: P c = 11.5 kpa and kappa number range of 42 to 48. The average void fraction for each furnishes are: 100% accepts = 0.27; 87.5% accepts + 12.5% pins = 0.24; 75% accepts + 25% pins = 0.19; 100% pins = 0.30. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 102 60 50 Pressure Drop (kpa/m) 40 30 20 10 0 100% accepts (kappa no. = 24) 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) 87.5% accepts + 12.5 % pins (kappa no. = 22) 75% accepts + 25% pins (kappa no.= 23) 100% pins (kappa no. = 24) Figure 4.28: Effect of chip size distribution on pressure drop. Conditions at: P c = 11.5 kpa and kappa number range of 22 to 24. The average void fraction for each furnishes are: 100% accepts = 0.20; 87.5% accepts + 12.5% pins = 0.15; 75% accepts + 25% pins = 0.19; 100% pins = 0.18. Solid lines are given using second order polynomial regression in Excel.
Chapter 4: RESULTS AND DISCUSSION 103 4.4.5 Comparison between Experimental and Literature Results Experimental data (pressure drop, superficial velocity, and void fraction) were correlated based on the Ergun equation (1952) with the particle diameter and the fluid properties are grouped into the coefficients R 1 and R 2 following Harkonen s procedure (1987). Thus dp dl 2 ( 1 ε ) ( 1 ε ) 2 = R1 U + R2 U (4.9) ε ε l 3 l l 3 l where dp/dl is pressure drop in Pa/m, U is superficial velocity in m/s, ε l is the average void fraction, and R 1 and R 2 are empirical coefficients. However, one should note that R 1 and R 2 obtained from Equation 4.9 will be different from literature values. Since R 1 and R 2 are dependent on the particle geometry and particle size distribution and they are inversely proportional to d p 2 and d p, respectively. By using Equation 4.9 the experimental data are correlated with correlation coefficient (R 2 ) ranging from 0.74 to 0.91. The results are shown in Table 4.9 for the four furnishes studied. Table 4.9: R 1 and R 2 values found based on Equation 4.9 for different chip size fractions of cooked chips at kappa numbers 20 to 180. Size fraction R 1 R 2 R 2 100% pins 10650 13.78 10 6 0.763 75% accepts + 25% pins 66190 4.72 10 6 0.816 87.5% accepts + 12.5% pins 59550 4.57 10 6 0.740 100% accepts 40151 5.77 10 6 0.913 Figure 4.29 shows a plot of pressure drop as a function of superficial velocity and chip size distribution under the conditions at kappa number 60 and compacting pressure 8.6 kpa. The void fraction is determined by using Equation 4.6 under the conditions stated above and found to be 0.354. As you can see in Figure 4.29, having the same void fraction for each chip size distribution, we found that 100% pins gave a higher pressure drop. It is expected since R 2 value of 100% pins is much higher than others, as shown in Table 4.9. It means that 100% pins
Chapter 4: RESULTS AND DISCUSSION 104 experience more kinetic loss than other chip size distributions due to the small dimensions of the pin chips. Harkonen s (1987) pressure drop equation is widely used (example, Saltin, 1992 and He et al., 1999) to model digesters. Therefore, we selected this equation to compare to our results. Other correlation such as Lindqvist (1994), Lammi (1996) and Wang et al. (1998) are not used in the comparison because their equations contain negative values of R 2 which are inconsistent with our findings. Our findings show a number of distinct differences from those reported by Harkonen (1987), as shown in Figure 4.29. We found that our correlation predicts a higher pressure drop than Harkonen s prediction. The possible reason for the discrepancy could be the use of difference wood species, chip size distribution, and chip geometries. Moreover, Harkonen performed the experiments at a temperature of 170 0 C (µ = 0.068 10-3 kg/m s, ρ = 885 kg/m 3 ) using water. While our test were made at 23 0 C (µ = 0.925 10-3 kg/m s, ρ = 997.6 kg/m 3 ). This will impact the values of R 1 and R 2 found. Therefore, instead of using R 1 and R 2, we should use A and B constants which are not dependent on fluid properties and particle diameter. Section 4.4.6 discusses the use of A and B constants. Comparison between the experimental measured and predicted pressure drop of all four furnishes using Equation 4.9 are made in Figure 4.30 to Figure 4.33. R 1 and R 2 are found in Table 4.9.
Chapter 4: RESULTS AND DISCUSSION 105 25 (1) 100% pins p ( kpa/m) Pressure Dro 20 15 10 5 (2) 75% accepts + 25% pins (3) 87.5% accepts + 12.5% pins (4) 100% accepts (5) Harkonen (1987) (1) (2) (3) (4) (5) 0 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.29: Comparison between the pressure drop of experimental results and Harkonen (1987) with superficial velocities ranging from 0 to 10 mm/s. Void fraction is determined based on compacting pressure 8.6 kpa and kappa number 60 and calculated using Equation 4.6 and found to be 0.354.
Chapter 4: RESULTS AND DISCUSSION 106 80 70 p (kpa/m) Predicted Pressure Dro 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Measured Pressure Drop (kpa/m) Figure 4.30: Comparison of predicted and experimental measured pressure drop of 100% pins. Predicted pressure drop are obtained by using Equation 4.9 with R 1 and R 2 found in Table 4.9.
Chapter 4: RESULTS AND DISCUSSION 107 80 p, kpa/m 70 60 Predicted Pressure Dro 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Measured Pressure Drop, kpa/m Figure 4.31: Comparison of predicted and experimental measured pressure drop of 100% accepts. Predicted pressure drop are obtained by using Equation 4.9 with R 1 and R 2 found in Table 4.9.
Chapter 4: RESULTS AND DISCUSSION 108 80 p (kpa/m) Predicted Pressure Dro 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Measured Pressure Drop (kpa/m) Figure 4.32: Comparison of predicted and experimental measured pressure drop of 75% accepts + 25% pins. Predicted pressure drop are obtained by using Equation 4.9 with R 1 and R 2 found in Table 4.9.
Chapter 4: RESULTS AND DISCUSSION 109 80 p ( kpa/m ) Predicted Pressure D ro 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Measured Pressure Drop (kpa/m) Figure 4.33: Comparison of predicted and experimental measured pressure drop of 87.5% accepts + 12.5% pins. Predicted pressure drop are obtained by using Equation 4.9 with R 1 and R 2 found in Table 4.9.
Chapter 4: RESULTS AND DISCUSSION 110 4.4.6 Comparison with Ergun Equation (1952) Ergun (1952) equation can be fitted to a relationship like that of Equation 4.9, but include the particle diameter and fluid properties, as follows: dp dl 2 ( 1 ε ) ρ ( 1 ε ) 2 µ l l = A U + B U (4.10) 2 3 3 d d p ε p ε l l where d p is the particle diameter, ρ is the density of fluid, µ is the viscosity of fluid, and A and B are the empirical coefficients. In Ergun s work, spherical particles were used and yielded Equation 4.10 with A and B to be 150 and 1.75, respectively. In our work, the chips have a wide size distribution and have irregular geometries. Therefore, we used Sauter mean diameter to determine the equivalent diameter of the wood chips (see Appendix B). The empirical coefficients of A and B for experimental data of cooked chips are shown in Table 4.10. These findings show that A values for mixtures and 100% accepts are about 15 times more than Ergun s constant. Although the reason for this is not clear, there are still some contributing factors that lead to shortcomings of using the Ergun equation to predict the average chip size. Two questions should be considered and could be the answers for this shortcoming. First, should the effect of the column diameter be included in the analysis? Since it is known that in packed beds of low column diameter, non-uniform liquid distribution near the wall could be experienced (Yin et al., 2000; Winterberg and Tsotsas, 2000; Chu and Ng, 1989). Second, should a measure of the packing arrangement and particle size distribution be included in Ergun equation? Recent work (Schulze et al., 1999) on groundwater flow in natural soils also suggests the need for inclusion of a measure of the heterogeneity of the porous medium in Ergun equation. However, such properties are difficult to quantify, and to date, have not been successfully included in correlations of fluid flow in packed beds (Schulze et al., 1999).
Chapter 4: RESULTS AND DISCUSSION 111 For the parameter B, which corresponds to the loss of kinetic energy due to inertial forces, the scatter is great as well. It can be seen that 27 < B < 60 with an average of 39.5 for all the our experiments. The values of B are clearly greater than for spheres (B = 1.75) found by Ergun (1952) and parallelepipedal particles (2.73 < B < 12.2) found by Comiti and Renaud (1989). A possible explanation for this discrepancy is that for packed bed of cooked chips in a vertical cylindrical column, the mean orientation of the cooked chips (considered as parallelepipedal particles) is nearly perpendicular to the flow direction. It is assumed that a jettype flow occurs when the fluid meets the main face of the cooked chips. The thinner the cooked chips, the greater the number of particles layers and, consequently, the greater the jet frequency which causes large deviation of kinetic energy losses (Comiti and Renaud, 1989). Table 4.10: A and B values found based on Equation 4.10 for different chip size fractions of cooked chips. Size fraction (cooked chips) A B Measured d p (m) 100% pins 274 60 3.78 10-3 75% accepts + 25% pins 2120 27 5.66 10-3 87.5% accepts + 12.5% pins 2267 28 6.17 10-3 100% accepts 1846 39 6.78 10-3 4.4.7 Can Uncooked Chips Pressure Drop be Used to Predict Cooked Chips? Pressure drop of uncooked chips at different chip size distributions were also studied, as shown in Figure 4.34. The average void fraction of all four size distributions were determined to be 0.670. Experimental data were correlated by using Equation 4.9 to find R 1 and R 2. Equation 4.10 was used to find A and B constants. Table 4.11 shows the results of R 1, R 2, A, and B for uncooked chips. Comparing the data in Table 4.10 of cooked chips and Table 4.11 of uncooked chips, A and B values are different for a given chip size distribution. Therefore, we conclude that pressure drop from uncooked chips can not be used to predict the pressure drop of cooked chips.
Chapter 4: RESULTS AND DISCUSSION 112 There are couple of reasons which could be responsible for this. First, pressure drop data of uncooked chips are correlated only with a single void fraction, e.g. 0.670. However, in cooked chips, void fraction is changed by different kappa number, compacting pressure, and superficial velocity. In turns, this affects the pressure drop. Moreover, cooked chips data are correlated with wide range of void fraction, e.g. between 0.600 and 0.050. Second, there could be a difference in geometries and dimensions between the cooked and uncooked chips. Unfortunately we can not quantify how much the difference between them, however we observed the dimensions changed for low kappa number cooked chips, e.g. kappa number 20. Third, uncooked chips formed a stable and incompressible column, while cooked chips are more flexible and compressible. Table 4.11: R 1 and R 2 values found based on Equation 4.9 for different chip size fractions of uncooked chips. Size fraction R 1 R 2 A B R 2 (uncooked chips) 100% pins 28723 6.74 10 6 410 25 0.998 75% accepts + 25% pins 5524 5.19 10 6 177 29 0.997 87.5% accepts + 12.5% pins 4971 4.56 10 6 189 28 0.996 100% accepts 6905 4.01 10 6 317 27 0.998
Chapter 4: RESULTS AND DISCUSSION 113 Pressure Drop (kpa/m) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 100% pins 75% accepts + 25% pins 87.5% accepts + 12.5% pins 100% accepts 0 1 2 3 4 5 6 7 8 9 10 Superficial Velocity (mm/s) Figure 4.34: Pressure drop vs. superficial velocity of uncooked chips at different chip size distributions. All four size distributions have an average void fraction of 0.670. Solid lines are given using Equation 4.9 with variables found in Table 4.11.
Chapter 4: RESULTS AND DISCUSSION 114 4.4.8 Chip Bed Uniformity In order to investigate why the Ergun equation can not adequately correlate our data, one sample (100% accepts at kappa number 48) was used to measure the local void fraction along the column height. The technique we used is to divide the column into four sections. At the top of every section, we put a smart chip as a marker. We measured the local void fraction based on the density method. In this study, we compressed the bed with three compacting pressures: 5.8, 11.5, and 17.3 kpa. Once the bed was compressed, it took about 10 minutes to reach equilibrium compression. After stabilization, we set a flowrate through the bed and measured the local void fraction using the marker chips. As you can see in Table 4.12, the local void fraction differed with height. As more loading was applied, the local void fraction is decreased significantly, noticeably at the upper and lower section. The pressure drop will be higher when void fraction is lower. Pressure drop was calculated by using our correlation (Equation 4.9) we developed with two cases: local void fraction and average void fraction. Table 4.12 shows the results of these tests. As you can see, the calculated pressure drop using local void fraction and average void fraction can be significantly different, particular at higher compacting pressures and flowrate. This will affect the accuracy of the correlation we developed, since we correlated the data using the average void volume in the column. Consequently, the Ergun equation must be used cautiously when applied to chip beds as it does not take into account the compressibility effects. Thus, the Ergun equation should be integrated over the column height to properly account for the compressibility of the chips. As this appears to be non-uniform in our tests, a method to measure the local void fraction must be developed.
Chapter 4: RESULTS AND DISCUSSION 115 Table 4.12: Test results of chip bed uniformity. Pressure drop are calculated using local void fraction and average void fraction. Pc = 0 kpa; U = 0 mm/s Height (cm) Relative H (cm) Liquid local void fraction Calculated local pressure drop (Pa) 42.5 10.9 0.658 0 31.6 10.1 0.588 0 21.5 9.5 0.589 0 12.0 12.0 0.577 0 Total 0.603 Sum = 0 Pc = 5.76 kpa; U = 1.0 mm/s 29.7 6.8 0.453 10.9 22.9 6.3 0.339 33.8 16.6 7.1 0.451 11.6 9.5 9.5 0.466 13.4 Total 0.432 Sum = 69.6 Average void fraction = 0.603 Calculated pressure drop = 0 Pa Average void fraction = 0.432 Calculated pressure drop = 58.3 Pa % diff = 19.4% Pc = 5.76 kpa; U = 8.34 mm/s 28.2 6.6 0.436 265 21.6 6.3 0.339 663 15.3 6.4 0.391 396 8.9 8.9 0.430 378 Total 0.402 Sum = 1705 Pc = 11.5 kpa; U = 1.5 mm/s 24.0 4.6 0.191 333 19.4 5.9 0.294 91 13.5 5.6 0.304 77 7.9 7.9 0.358 58 Total 0.297 Sum = 560 Average void fraction = 0.402 Calculated pressure drop = 1561 Pa % diff = 9.2% Average void fraction = 0.297 Calculated pressure drop = 357 Pa % diff = 56.7% Pc = 11.5 kpa; U = 5.3 mm/s 20.9 4.4 0.154 3525 16.5 5.4 0.229 1146 11.1 5.1 0.235 982 6.0 6.0 0.154 4793 Total 0.193 Sum = 10446 Average void fraction = 0.193 Calculated pressure drop = 7894 Pa % diff = 32.3%