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A New Experimental Technique for Determining Local Dispersion Coefficient in Displacement Washing
A NEW EXPERIMENTAL TECHNIQUE FOR DETERMINING LOCAL DISPERSION COEFFICIENT IN DISPLACEMENT WASHING J. Lindau, P. Sedin and H. Theliander Chalmers University of Technology, Chemical Engineering and Biological Engineering, Gothenburg, Sweden.
Abstract: A new experimental technique has been developed in order to study the washing characteristics in a filter cake during displacement washing. The test material primarily used was paper pulp which forms highly heterogeneous filter cakes where the local values of, for example, porosity may be assumed to differ substantially from the average values. The experimental equipment used was a piston filter press equipped with a g-radiation source and a scintillation detector that was used to measure concentrations of different species inside the filter cake at different bed heights. In these experiments, Csþ ions were used as the tracer compound for studying displacement washing. The filtrate was also collected and, from the displacement curves based on the concentration in the filtrate, the dispersion coefficients and the Peclet number could be determined; these values were used to calculate local displacement curves. The calculated local displacement curves agreed well with the measured local displacement curves showing that local measurement of the dispersion coefficient is a very valuable tool for studying the washing of filter cakes. Keywords: cake washing; paper pulp; experimental technique; dispersion; local properties.
INTRODUCTION
Correspondence to: Professor H. Theliander, Chalmers University of Technology, Chemical Engineering and Biological Engineering, Kemiva¨gen 10, Gothenburg 412 96, Sweden. E-mail: [email protected]
DOI: 10.1205/cherd06059 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, March 2007 # 2007 Institution of Chemical Engineers
The washing of filter cakes is a commonlyused industrial operation in, for example, the paper pulp and mineral industries. A cake is washed in order to separate the filtrate from the cake, thus removing impurities or recovering valuable liquor. In some cases, both the cake and the filtrate are considered valuable: one example of this is washing of paper pulp. In an ideal washing operation, all of the original liquor is displaced by one void volume of wash water. This is, however, not the situation in reality. There are several different phenomena responsible for the deviation from the ideal case, e.g., adsorption and various phenomena related to the structure of the cake and the flow conditions, which are normally included with diffusion and called dispersion. Even though the ideal case cannot be achieved, it is nonetheless important to try to make the process as ideal as possible, and thereby minimize the amount of wash liquid used. In order to make the process as ideal as possible, it is important to have a solid understanding of the washing process and the factors influencing it. This is, however, far from a trivial task. Displacement washing is a complex process which is influenced by a number of factors as mentioned above; a complete model has not yet been presented. The
most commonly-used model is the dispersion model where the diffusion coefficient in the transport equation is replaced by a dispersion coefficient (Lapidus and Amundson, 1952; Sherman, 1964; Poirier et al., 1988). In the case of pulp washing, a more advanced model was proposed by Gra¨hs (1975). He assumed that the bed consists of three different zones: the fibre material, a zone with stagnant liquor and a zone with flowing liquor. He then devised a set of differential equations to describe the mass transfer between these zones. Even though several different models have been used to describe displacement washing, the experimental technique used is more or less the same: some specie of interest is washed out from the cake and the concentration of the specie in the wash water is measured. This technique has been used, with some modifications, by e.g., Sherman (1964); Gra¨hs (1976); Lee (1979); Gre´n and Stro¨m (1985); Wakeman and Attwood (1988) and Trinh et al. (1989). Even though many interesting conclusions have been drawn from the resulting washing curves, this measurement technique has several drawbacks. One is that the concentrations of the measured species in the filtrate are the averaged values of the local concentrations in the bed, and not the actual local 357
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concentrations. Another drawback is that this technique only provides implicit information about what happens inside the bed. If data could be attained from within the bed during the washing process, more detailed knowledge of the washing process could be gained. The aim of this work has therefore been to develop a new experimental method that makes it possible to measure concentrations inside the bed during the washing stage. The materials used to develop this new technique are paper pulp and calcium silicate. Pulp is an interesting material: not only is the material heterogeneous in itself, it also forms heterogeneous beds due to its tendency to form flocs. A softwood pulp fibre is approximately 2–4 mm long and 20–40 mm wide (Sjo¨stro¨m, 1993); such a heterogeneous material makes local measurements especially interesting. Calcium silicate is less heterogeneous and has therefore been used to perform a validation experiment.
EXPERIMENTAL Equipment The experimental equipment used is a test filter piston press as shown in Figure 1. The experimental equipment has earlier been described in more detail (Johansson and Theliander, 2003; Sedin et al., 2003). The filter chamber is made of Plexiglas and has an inner diameter of 6 cm. The bottom of the chamber consists of a perforated plate through which the filtrate can exit. Munktell filter paper number 5 was
Figure 1. Experimental set-up.
used as the filter media. The bed can be compacted to any desired height of up to 10 cm and the height of the bed is measured by a position sensor mounted on the piston’s rod. The piston press is equipped with a concentration measuring system consisting of a NaI(TI) scintillation detector with a g-radiation source. The attenuation of g-rays is proportional to the density of the medium and the atomic number. A suitable tracer substance is therefore one that has an atomic number as different from the atoms present in the system as possible. The Csþ ion was therefore chosen as the measured specie instead of Naþ, which is more commonly used in pulp washing experiments since it is one of the key species that is washed out in a pulp mill. It is, however, reasonable to assume that the dispersion effect is similar for Csþ and Naþ since they are both alkali metals and exhibit similar chemical behaviour. It has been difficult to circumvent the fact that, in washing experiments, the wash fluid mixes with the fluid at the inlet of the bed. This problem has been discussed e.g., Sherman (1964) and Wakeman (1990). In order to minimize this problem, a sintered metal plate has been used to separate the wash fluid from the pulp cake. The wash fluid does not penetrate the sintered plate until pressure has been applied. Using a sintered plate is also an efficient way of distributing the wash water evenly over the cake.
Methodology The paper pulp used is bleached sulphate softwood pulp taken from a Swedish pulp mill. The fibre length was on average 2.45 mm and the average width was 30.2 mm. The pulp was washed several times with an acidic solution (HCl) in order to remove metal ions. Twenty grams of CsCl was then added to 25 g of pulp. The pulp was suspended in 7 L of deionized water, which gave a pulp consistency of 3.6 g L21 and a pH of 4. The slurry was mixed thoroughly and pumped into the washing equipment. When 5 L of slurry had been pumped through the device, the inlet was closed and the pulp mat was compacted to the desired bed height. After measuring the attenuation of CsCl at different bed heights pressure was applied to the wash fluid and the washing process began. The wash water pressure was 0.4 bar for Experiments 1 to 5 (see Table 1), 0.15 bar for Experiments 6 to 9 and 0.2 bar for Experiments 10 to 14. Deionized water was used as the wash fluid. During the washing run,
Table 1. Experimental condition and results Group
Exp.
A
1 2 3 4 5 6 7 8 9 10 11 12 13 14
B
C
2
L 10 (m)
h L21
u 105 (m s21)
1
Pe
DL 108 (m2 s21)
Residual 104
3.11 3.18 3.12 3.08 3.10 4.02 4.07 3.81 4.10 4.95 5.00 5.00 5.00 5.04
0.52 0.69 0.84 0.35 0.19 0.25 0.88 0.60 0.39 0.09 0.90 0.30 0.50 0.70
5.54 4.19 4.77 4.62 3.70 6.00 4.83 4.86 5.12 3.20 3.80 3.87 3.65 4.41
0.838 0.837 0.833 0.837 0.833 0.872 0.872 0.883 0.876 0.898 0.899 0.898 0.896 0.896
47.6 36.2 39.5 43.2 34.7 58.5 28.4 107 48.7 94.6 135 107 64 53.3
3.63 3.69 3.77 3.29 3.30 4.12 6.92 1.74 4.31 1.65 1.41 1.81 2.85 4.16
3.27 4.31 1.64 4.20 3.91 5.86 3.60 2.97 3.35 5.97 6.19 5.75 3.14 3.77
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DETERMINING LOCAL DISPERSION COEFFICIENT IN DISPLACEMENT WASHING the filtrate was collected at one minute intervals; the attenuation of CsCl, at a predetermined height, was measured at two minute intervals. The ideal situation would be to measure the concentration of CsCl at several different heights in the same pulp cake. However, since a pulp washing experiment only takes 30 min, and the measuring time has to be at least 2 min in order to obtain an acceptable measurement error, this is not possible; several experiments with identical experimental conditions but different measurement heights were performed instead. The attenuation of CsCl was also measured after the washing stage. The measurement error was less than 0.1% for the measured intensity before and after the washing stage. The measured intensity during the washing stage has a larger error, the exact value of which is difficult to determine: the intensity fluctuates not only as a result of the measurement error but also from an actual change in CsCl concentration. However, the measurement error at the end of the experiment where the CsCl concentration does not change can be estimated to be about 1%. There are also additional errors due to the heterogeneous characteristics of the pulp fibre cakes formed. The washing run lasted between 25 and 40 min, corresponding to two to three void volumes of water. The concentration of Csþ in the filtrate was measured with an atomic absorption spectrometer. The measurement error was, on average, 1.5%. The cake was dried in an oven and weighed. It was thereafter wet-digested and the Csþ content was measured. A washing experiment with a more homogeneous material, calcium silicate (CaSiO3), was performed, in order to make an initial test of the measurement technique using a material forming relatively homogeneous filter cakes. In this experiment, 344 g calcium silicate was added to 3656 g of water. Forty grams of CsCl was subsequently added to the mixture. The filtrate was collected at ten minutes intervals. The CsCl concentration was measured at two different heights at five minute intervals.
EVALUATION OF EXPERIMENTS Washing Experiment The dispersion model, with a source term accounting for the sorption of solute on the fibres, was used to evaluate the experimental data. @c @c @2 c 1 @h þ u DL 2 ¼ @t @z @z m @t
(1)
where m ¼ 1=ð1 1Þ is the volumetric void to solid ratio. In order to solve the partial differential equation, a relationship between the concentration of the solute in the liquid phase and the sorbed solute is needed. Several different relationships have been used in earlier investigations (Sherman, 1964; Gra¨hs, 1975). Here, a linear relationship will be used:
h ¼ Kc þ K0
(2)
where K is a constant that can be determined from measurements. K0 does not have to be determined: it does not appear in the final equation since the derivative of a constant is zero.
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The following boundary and initial conditions have been used: c(0, t) ¼ c0 ¼ 0
(3)
c(1, t) ¼ ci (1) c(z, 0) ¼ ci (z) ¼ ci
(4) (5)
Equation (1) has together with boundary conditions (3) and (4) and an initial condition (5) been solved by Lapidus and Amundson (1952). The solution is: sffiffiffiffiffiffi! " c 1 1 lw uL ¼1 erfc pffiffiffiffiffiffiffi ci 2 2 lw DL sffiffiffiffiffiffi!# 1 þ lw uL ðuL=DL Þ þe erfc pffiffiffiffiffiffiffi 2 lw DL
(6)
where
l¼
1 1 K þ ðK=1Þ
Intensity Measurements The attenuation of g-rays in a medium can be expressed as I ¼ I0 emx
(7)
where I is the measured intensity, I0 the background intensity and m the attenuation coefficient of the medium of length x. For a multicomponent system, equation (7) can be rewritten as X N I mi xi ln ¼ I0 i¼1
(8)
In this experiment, there are three major species present: pulp, water and CsCl. Equation (8) can therefore be written as I (9) ln ¼ mw xw mp xp mCsCl xCsCl I0 The intensity was measured at a time t1 (I1) and after the pulp was washed (I2). The pulp is not removed during the washing phase and xp1 is therefore equal to xp2. If I2 is subtracted from I1 the pulp contribution is eliminated, resulting in equation (10): I1 I2 ln ln ¼ mCsCl (xCsCl,1 xCsCl,2 ) I0 I0 mw (xw,1 xw,2 )
(10)
The decrease in CsCl is equal to the increase in water, i.e., (xCsCl,1 xCsCl,2 ) ¼ (xw,1 xw,2 )
(11)
This leads to the following equation: I1 I2 ln ¼ mCsCl (xCsCl,1 xCsCl,2 ) ln I0 I0
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þ mw (xCsCl,1 xCsCl,2 )
(12)
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The length difference can then be expressed as DxCsCl ¼
lnðI2 =I0 Þ lnðI1 =I0 Þ mCsCl mw
(13)
The concentration difference is finally DcCsCl ¼
DxCsCl rCsCl d
(14)
where d ¼ 0.06 m is the diameter of the filtration chamber and rCsCl ¼ 3988 g L21. The values of mw and mCsCl have been measured and found to be 19 m21 and 2598 m21, respectively. The calculated values for mw and mCsCl based on Bertin (1975) are 18.18 m21 and 2803 m21, respectively at 59.94 keV. In order to compare the washing curves based on the filtrate with the local washing curves a relationship between c in equation (6) and Dc in equation (14) is needed. The relationship can be written in the following way: Dc ¼ c(1 DC) þ hDC c(1 DC)jt2 þ hDCjt2 ¼ c(1 DC) þ (Kc þ K0 )DC (Kc þ K0 )DCjt2 (15) where DC is the dry content of the fibres. If K is close to zero, the relationship between Dc and c can be simplified as Dc ¼ c(1 DC)
(16)
RESULTS AND DISCUSSION Validation Experiment A washing experiment with a material forming relatively homogeneous filter cakes, calcium silicate (CaSiO3), was performed in order to evaluate the measurement technique used. The median size of a calcium silicate particle was measured with laser diffraction (Malvern 2600 series) and found to be 10.4 mm. Washing a calcium silicate cake takes more time than washing a paper pulp cake. This makes it possible to measure for a longer time at each measurement point, hence reducing the measurement error. It is also possible to measure at several heights in the cake during the same washing experiment. An example of this can be seen in Figure 2, where the concentration of CsCl has been measured at two heights, i.e., at the top of the bed (h L21 ¼ 0.14) and at the bottom of the bed (h L21 ¼ 0.83), during one washing experiment. Figure 2 shows that it is possible to obtain local displacement curves with this new technique.
Figure 2. Local washing curves for calcium silicate.
Figure 3. Washing curves for experiments in Group A; L 30 mm.
Evaluation Based on Measurement on the Filtrate The experimental conditions and results for paper pulp cakes are summarized in Table 1. The bed height is the only variable that has been varied. In group A, the bed height is approximately 30 mm, in group B it is 40 mm and, in group C, it is 50 mm. The velocity in all the experiments is quite low. The Reynolds number is at most 6 1023 (for Experiment 6), which is well within the laminar range. If the experimental conditions are identical, then the washing curves for beds with the same height should also be identical. The washing curves can be seen in Figures 3– 5. In Figure 3, the curves match each other perfectly and the experimental conditions are, indeed, the same. In Figure 4, the slopes of the curves differ slightly. The curves are, however, not all that different; it may, therefore, be assumed that the experimental conditions are approximately identical. In Figure 5, however, there is a significant difference between the shapes of the curves for Experiments 10, 11 and 12 and Experiments 13 and 14. The variation in shape is a result of that the slurry was pumped into the equipment with a much higher pressure (1 bar) for Experiments 10 to
Figure 4. Washing curves for experiments in Group B; L 40 mm.
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DETERMINING LOCAL DISPERSION COEFFICIENT IN DISPLACEMENT WASHING
Figure 5. Washing curves for experiments in Group C; L 50 mm.
12 than for Experiments 13 and 14, where the pressure was 0.2 bar. The bed was hence more compressed for Experiments 10 to 12; leading to more ideal washing. Another explanation for the difference between the experiments could be that the pulp has been taken from the pulp mill on different occasions. Even though the properties of the pulp do not fluctuate to a large extent, the samples will never be exactly the same. The Peclet number and the coefficient K were estimated by fitting the dispersion model, equation (6), to the experimental data by using a non-linear least-square algorithm. The Peclet number; uL/DL, is a dimensionless number that describes the degree of mixing between the displaced and the displacing fluid in the bed and describes the shape of the washing curve. The Peclet number and the dispersion coefficient can be found in Table 1. As could be expected from Figure 3, the Peclet number and the dispersion coefficient are essentially the same for Experiments 1 to 5. The Peclet number and dispersion coefficient are more varied for Experiments 6 to 14. The Peclet number ranges from 29 to 135. Gra¨hs (1976) obtained Peclet numbers between 99 and 378 in his experiments on sulphate pulp. Poirier et al. (1988) obtained Peclet numbers between 3 and 47. The high Peclet number in Gra¨hs (1976) can be attributed to the high bed heights used in his experiments (10–17 cm). In Poirier et al. (1988), the bed height is approximately the same (2.5–8.5 cm) but the velocity is much higher and the consistency is lower. It is however difficult to be certain about the cause if the difference in Peclet number since, as too often with pulp washing experiments, a number of factors that could influence washing (such as pH, formation pressure and fibre length) are unknown. The coefficient K is set to zero since the pH was low and it is well known that the adsorption of metal ions on pulp fibres is substantially lower at low pH than at high pH (Rosen, 1975) as the acidic groups in the pulp are protonized at low pH values: the pKa values of the two characteristic acidic groups are 4.5 and 10. The cesium content is, however, not zero. The cesium content in the washed cakes was measured and found to be between 3.5–5 g kg21 dry pulp, but as it was found that the amount of cesium adsorbed did not change significantly during washing, it is the same as K is equal to zero.
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Figure 6. A comparison between the measured washing curve and the calculated washing curve for Experiments 3 and 11.
The residuals from the curve fitting are shown in Table 1. The residual is the squared 2-norm divided by number of measurements. The residuals for all the cases are small. Two examples are illustrated in Figure 6, where the measured washing curves for Experiments 3 and 11 are compared with the fitted displacement model. Experiment 3 has the smallest residual of all the experiments whilst Experiment 11 has the largest. In both cases, the fit to the slope of the curve is excellent. However, for Experiment 11, there are some variations in concentration during the initial washing period. This variation may be explained by the fact that the cake has not been compressed to equilibrium and inlet mixing has therefore occurred.
Local Measurements Local displacements curves for Experiments 10 to 14 are shown in Figure 7. The dispersion effect is not pronounced, which is apparent from the lack of increasing deviation from a step function as the wash water moves through the bed. Nonetheless, it can be clearly seen how the wash front
Figure 7. Local displacements curves at different heights for experiments in Group C; L 50 mm.
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Figure 8. Local displacement curves at different heights for experiments in Group B; L 40 mm.
Figure 9. Local displacement curves at different heights for experiments in Group A; L 30 mm.
moves through the bed. In Figures 8 and 9, the local displacement curves for Experiments 1 to 4 and Experiments 5 to 9 are shown. The curves are not very smooth, but as with Figure 7, Figures 8 and 9 show how the wash fronts propagate through the bed, providing another example of how local measurements of displacement washing are possible using this new measurement technique. The slopes are also comparable with the ones in Figures 3– 5 showing that the different measuring techniques give the same response. When examining the results it should also be remembered that paper pulp is a difficult material when it comes to making measurements due to its heterogeneous nature and the fact that the washing phase is relatively fast. Another complicating factor is that different cakes have been used in each experiment. Considering the experimental difficulties involved, the results are very promising. The reason for why it was not possible to notice a change of the slopes of the breakthrough curves is probably a combination of measurement error and the fact that the dispersion effect is small in the experiments made in this investigation. Figure 10(a) is the result of a simulation of local breakthrough curves with a dispersion coefficient similar to the ones obtained in this investigation (4 1028 m2 s21). It can be seen that the change in slope is very small in this case. This should be compared with the case when the dispersion coefficient is one order of magnitude higher (i.e., 4 1027 m2 s21), Figure 10(b). For this case the slope changes quite a lot. As mentioned earlier the intensity was measured at several bed heights after each experiment. The measured intensity was used to calculate the porosity profile within the bed and it was concluded that the porosity did not change significantly within the bed. This was an expected result since the beds had been highly compressed in order to avoid changes in porosity. The Peclet number and K values previously determined (based on the filtrate) were used to calculate the theoretical washing curves within the bed. The measured curves agreed in general well with the calculated curves. An example of the good agreement is found in Figure 11 that shows the calculated and measured local displacement curves for Experiments 7 and 8.
Figure 10. Calculated displacement curves at different bed heights when, k ¼ 0.01, L ¼ 40 mm, u ¼ 4.76 10–5 m s21. (a) Pe ¼ 47.7 and DL ¼ 4 10– 8 m2 s21. (b) Pe ¼ 4.77 and DL ¼ 4 10–7 m2 s21. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 357– 364
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and the resulting displacement curves are smooth. Although the experimental technique could be refined somewhat as far as pulp washing is concerned, the results are very promising; the new measurement technique provides new insight in the filter cake washing process.
NOMENCLATURE
Figure 11. Calculated and measured local displacement curves for Experiments 7 (h L21 ¼ 0.88) and 8 (h L21 ¼ 0.60).
c d DC DL h I K L m Pe t u w xi
concentration, kg dm23 diameter of the washing cell, m dry content longitudinal dispersion coefficient, m2 s21 height from the piston, m intensity, s21 constant length of bed, m 1/(1 2 1) Peclet number, uL/DL time, s velocity, m s21 wash ratio, ut L21 length of species i in the path of the g-rays
Greek symbols 1 porosity h amount of sorbed solute per unit volume of solid, kg dm23 l 1/(1 2 K þ K/1) m attenuation coefficient, m21 r density, g L21 Subscripts CsCl p w 0 1 2
Cesium chloride paper pulp water initial value value at time t1 value after washing
REFERENCES Figure 12. Measured and calculated displacement curves for Experiments 6 (h L21 ¼ 0.25) and 1 (h L21 ¼ 0.52).
Even at the top of the bed, as seen in Figure 12, the agreement is acceptable even though the measuring time is too long to capture the wash front perfectly. That the calculated curves agree well with the measured curves shows that the local dispersion coefficients are approximately the same as the overall dispersion coefficients. In this case, where there are no changes in porosity within the bed, this is an expected result.
CONCLUDING REMARKS This work has shown that it is possible to measure displacement curves at different heights within a filter cake. The calculated curves based on the dispersion model agree well with the measured curves. A difficulty with measuring inside the pulp bed is that pulp washing is a relatively fast process; the measurement error is therefore not negligible, resulting in washing curves that are not smooth. When the washing process is slower, as was in the case of the calcium silicate bed, the measurement error is very small
Bertin, E.P., 1975, Principles and Practice of X-Ray Spectometric Analysis (Plenum Press, New York, USA). Gre´n, U. and Stro¨m, K.H.U., 1985, Displacement washing of packed beds of cellulose fibres, Pulp & Paper Canada, 86(9): 261–264. Gra¨hs, L.-E., 1975, Displacement washing of packed beds of cellulose fibres. Part 1. Mathematical model, Svensk Papperstidning, 78(12): 446– 450. Gra¨hs, L.-E., 1976, Displacement washing of packed beds of cellulose fibres. Part 2. Analysis of laboratory experiments, Svensk Papperstidning, 79(3): 84– 89. Johansson, C. and Theliander, H., 2003, Measuring concentration and pressure profiles in deadend filtration, Filtration Solutions, 3(2): 114– 120. Lapidus, L. and Amundson, N.R., 1952, Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, J Phys Chem, 56: 984– 988. Lee, P.F., 1979, Optimizing the displacement washing of pads of wood pulp fibers, TAPPI, 62(9): 75– 78. Poirier, N.A., Crotogino, R.H. and Douglas, W.J.M., 1988, Axial dispersion models for displacement washing of packed beds of wood pulp fibres, The Canadian Journal of Chemical Engineering, 66: 936–944. Rosen, A., 1975, Adsorption of sodium ions on kraft pulp fibers during washing, TAPPI, 58(9): 156– 161. Sedin, P., Johansson, C. and Theliander, H., 2003, On the determination and evaluation of pressure and solidosity in filtration, Chem Eng Res Des, 81(A10): 1395–1405. Sherman, W.R., 1964, The movement of a soluble material during the washing of a bed of packed solids, AIChEJ, 10(6): 855–860. Sjo¨stro¨m, E., 1993, Wood Chemistry Fundamentals and Applications (Academic Press, San Diego, USA).
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Trinh, D.T., Poirier, N.A., Crotogino, R.H. and Douglas, W.J.M., 1989, Displacement washing of wood pulp – an experimental study, Journal of Pulp and Paper Science, 15(1): 28–35. Wakeman, R.J., 1990, Simulations of dispersion phenomena in filter cake washing, Chem Eng Res Des, 68: 162 –171. Wakeman, R.J. and Attwood, G.J., 1988, Developments in the application of cake washing theory, Filtration and Separation, 25(July/August): 272– 275.
ACKNOWLEDGEMENTS The financial support of the Swedish Energy Agency is greatly appreciated. We would also like to thank So¨dra Cell for their assistance in this project. The manuscript was received 13 June 2006 and accepted for publication after revision 1 November 2006.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 357– 364
Abstract: A new experimental technique has been developed in order to study the washing characteristics in a filter cake during displacement washing. The test material primarily used was paper pulp which forms highly heterogeneous filter cakes where the local values of, for example, porosity may be assumed to differ substantially from the average values. The experimental equipment used was a piston filter press equipped with a g-radiation source and a scintillation detector that was used to measure concentrations of different species inside the filter cake at different bed heights. In these experiments, Csþ ions were used as the tracer compound for studying displacement washing. The filtrate was also collected and, from the displacement curves based on the concentration in the filtrate, the dispersion coefficients and the Peclet number could be determined; these values were used to calculate local displacement curves. The calculated local displacement curves agreed well with the measured local displacement curves showing that local measurement of the dispersion coefficient is a very valuable tool for studying the washing of filter cakes. Keywords: cake washing; paper pulp; experimental technique; dispersion; local properties.
INTRODUCTION
Correspondence to: Professor H. Theliander, Chalmers University of Technology, Chemical Engineering and Biological Engineering, Kemiva¨gen 10, Gothenburg 412 96, Sweden. E-mail: [email protected]
DOI: 10.1205/cherd06059 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, March 2007 # 2007 Institution of Chemical Engineers
The washing of filter cakes is a commonlyused industrial operation in, for example, the paper pulp and mineral industries. A cake is washed in order to separate the filtrate from the cake, thus removing impurities or recovering valuable liquor. In some cases, both the cake and the filtrate are considered valuable: one example of this is washing of paper pulp. In an ideal washing operation, all of the original liquor is displaced by one void volume of wash water. This is, however, not the situation in reality. There are several different phenomena responsible for the deviation from the ideal case, e.g., adsorption and various phenomena related to the structure of the cake and the flow conditions, which are normally included with diffusion and called dispersion. Even though the ideal case cannot be achieved, it is nonetheless important to try to make the process as ideal as possible, and thereby minimize the amount of wash liquid used. In order to make the process as ideal as possible, it is important to have a solid understanding of the washing process and the factors influencing it. This is, however, far from a trivial task. Displacement washing is a complex process which is influenced by a number of factors as mentioned above; a complete model has not yet been presented. The
most commonly-used model is the dispersion model where the diffusion coefficient in the transport equation is replaced by a dispersion coefficient (Lapidus and Amundson, 1952; Sherman, 1964; Poirier et al., 1988). In the case of pulp washing, a more advanced model was proposed by Gra¨hs (1975). He assumed that the bed consists of three different zones: the fibre material, a zone with stagnant liquor and a zone with flowing liquor. He then devised a set of differential equations to describe the mass transfer between these zones. Even though several different models have been used to describe displacement washing, the experimental technique used is more or less the same: some specie of interest is washed out from the cake and the concentration of the specie in the wash water is measured. This technique has been used, with some modifications, by e.g., Sherman (1964); Gra¨hs (1976); Lee (1979); Gre´n and Stro¨m (1985); Wakeman and Attwood (1988) and Trinh et al. (1989). Even though many interesting conclusions have been drawn from the resulting washing curves, this measurement technique has several drawbacks. One is that the concentrations of the measured species in the filtrate are the averaged values of the local concentrations in the bed, and not the actual local 357
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concentrations. Another drawback is that this technique only provides implicit information about what happens inside the bed. If data could be attained from within the bed during the washing process, more detailed knowledge of the washing process could be gained. The aim of this work has therefore been to develop a new experimental method that makes it possible to measure concentrations inside the bed during the washing stage. The materials used to develop this new technique are paper pulp and calcium silicate. Pulp is an interesting material: not only is the material heterogeneous in itself, it also forms heterogeneous beds due to its tendency to form flocs. A softwood pulp fibre is approximately 2–4 mm long and 20–40 mm wide (Sjo¨stro¨m, 1993); such a heterogeneous material makes local measurements especially interesting. Calcium silicate is less heterogeneous and has therefore been used to perform a validation experiment.
EXPERIMENTAL Equipment The experimental equipment used is a test filter piston press as shown in Figure 1. The experimental equipment has earlier been described in more detail (Johansson and Theliander, 2003; Sedin et al., 2003). The filter chamber is made of Plexiglas and has an inner diameter of 6 cm. The bottom of the chamber consists of a perforated plate through which the filtrate can exit. Munktell filter paper number 5 was
Figure 1. Experimental set-up.
used as the filter media. The bed can be compacted to any desired height of up to 10 cm and the height of the bed is measured by a position sensor mounted on the piston’s rod. The piston press is equipped with a concentration measuring system consisting of a NaI(TI) scintillation detector with a g-radiation source. The attenuation of g-rays is proportional to the density of the medium and the atomic number. A suitable tracer substance is therefore one that has an atomic number as different from the atoms present in the system as possible. The Csþ ion was therefore chosen as the measured specie instead of Naþ, which is more commonly used in pulp washing experiments since it is one of the key species that is washed out in a pulp mill. It is, however, reasonable to assume that the dispersion effect is similar for Csþ and Naþ since they are both alkali metals and exhibit similar chemical behaviour. It has been difficult to circumvent the fact that, in washing experiments, the wash fluid mixes with the fluid at the inlet of the bed. This problem has been discussed e.g., Sherman (1964) and Wakeman (1990). In order to minimize this problem, a sintered metal plate has been used to separate the wash fluid from the pulp cake. The wash fluid does not penetrate the sintered plate until pressure has been applied. Using a sintered plate is also an efficient way of distributing the wash water evenly over the cake.
Methodology The paper pulp used is bleached sulphate softwood pulp taken from a Swedish pulp mill. The fibre length was on average 2.45 mm and the average width was 30.2 mm. The pulp was washed several times with an acidic solution (HCl) in order to remove metal ions. Twenty grams of CsCl was then added to 25 g of pulp. The pulp was suspended in 7 L of deionized water, which gave a pulp consistency of 3.6 g L21 and a pH of 4. The slurry was mixed thoroughly and pumped into the washing equipment. When 5 L of slurry had been pumped through the device, the inlet was closed and the pulp mat was compacted to the desired bed height. After measuring the attenuation of CsCl at different bed heights pressure was applied to the wash fluid and the washing process began. The wash water pressure was 0.4 bar for Experiments 1 to 5 (see Table 1), 0.15 bar for Experiments 6 to 9 and 0.2 bar for Experiments 10 to 14. Deionized water was used as the wash fluid. During the washing run,
Table 1. Experimental condition and results Group
Exp.
A
1 2 3 4 5 6 7 8 9 10 11 12 13 14
B
C
2
L 10 (m)
h L21
u 105 (m s21)
1
Pe
DL 108 (m2 s21)
Residual 104
3.11 3.18 3.12 3.08 3.10 4.02 4.07 3.81 4.10 4.95 5.00 5.00 5.00 5.04
0.52 0.69 0.84 0.35 0.19 0.25 0.88 0.60 0.39 0.09 0.90 0.30 0.50 0.70
5.54 4.19 4.77 4.62 3.70 6.00 4.83 4.86 5.12 3.20 3.80 3.87 3.65 4.41
0.838 0.837 0.833 0.837 0.833 0.872 0.872 0.883 0.876 0.898 0.899 0.898 0.896 0.896
47.6 36.2 39.5 43.2 34.7 58.5 28.4 107 48.7 94.6 135 107 64 53.3
3.63 3.69 3.77 3.29 3.30 4.12 6.92 1.74 4.31 1.65 1.41 1.81 2.85 4.16
3.27 4.31 1.64 4.20 3.91 5.86 3.60 2.97 3.35 5.97 6.19 5.75 3.14 3.77
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DETERMINING LOCAL DISPERSION COEFFICIENT IN DISPLACEMENT WASHING the filtrate was collected at one minute intervals; the attenuation of CsCl, at a predetermined height, was measured at two minute intervals. The ideal situation would be to measure the concentration of CsCl at several different heights in the same pulp cake. However, since a pulp washing experiment only takes 30 min, and the measuring time has to be at least 2 min in order to obtain an acceptable measurement error, this is not possible; several experiments with identical experimental conditions but different measurement heights were performed instead. The attenuation of CsCl was also measured after the washing stage. The measurement error was less than 0.1% for the measured intensity before and after the washing stage. The measured intensity during the washing stage has a larger error, the exact value of which is difficult to determine: the intensity fluctuates not only as a result of the measurement error but also from an actual change in CsCl concentration. However, the measurement error at the end of the experiment where the CsCl concentration does not change can be estimated to be about 1%. There are also additional errors due to the heterogeneous characteristics of the pulp fibre cakes formed. The washing run lasted between 25 and 40 min, corresponding to two to three void volumes of water. The concentration of Csþ in the filtrate was measured with an atomic absorption spectrometer. The measurement error was, on average, 1.5%. The cake was dried in an oven and weighed. It was thereafter wet-digested and the Csþ content was measured. A washing experiment with a more homogeneous material, calcium silicate (CaSiO3), was performed, in order to make an initial test of the measurement technique using a material forming relatively homogeneous filter cakes. In this experiment, 344 g calcium silicate was added to 3656 g of water. Forty grams of CsCl was subsequently added to the mixture. The filtrate was collected at ten minutes intervals. The CsCl concentration was measured at two different heights at five minute intervals.
EVALUATION OF EXPERIMENTS Washing Experiment The dispersion model, with a source term accounting for the sorption of solute on the fibres, was used to evaluate the experimental data. @c @c @2 c 1 @h þ u DL 2 ¼ @t @z @z m @t
(1)
where m ¼ 1=ð1 1Þ is the volumetric void to solid ratio. In order to solve the partial differential equation, a relationship between the concentration of the solute in the liquid phase and the sorbed solute is needed. Several different relationships have been used in earlier investigations (Sherman, 1964; Gra¨hs, 1975). Here, a linear relationship will be used:
h ¼ Kc þ K0
(2)
where K is a constant that can be determined from measurements. K0 does not have to be determined: it does not appear in the final equation since the derivative of a constant is zero.
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The following boundary and initial conditions have been used: c(0, t) ¼ c0 ¼ 0
(3)
c(1, t) ¼ ci (1) c(z, 0) ¼ ci (z) ¼ ci
(4) (5)
Equation (1) has together with boundary conditions (3) and (4) and an initial condition (5) been solved by Lapidus and Amundson (1952). The solution is: sffiffiffiffiffiffi! " c 1 1 lw uL ¼1 erfc pffiffiffiffiffiffiffi ci 2 2 lw DL sffiffiffiffiffiffi!# 1 þ lw uL ðuL=DL Þ þe erfc pffiffiffiffiffiffiffi 2 lw DL
(6)
where
l¼
1 1 K þ ðK=1Þ
Intensity Measurements The attenuation of g-rays in a medium can be expressed as I ¼ I0 emx
(7)
where I is the measured intensity, I0 the background intensity and m the attenuation coefficient of the medium of length x. For a multicomponent system, equation (7) can be rewritten as X N I mi xi ln ¼ I0 i¼1
(8)
In this experiment, there are three major species present: pulp, water and CsCl. Equation (8) can therefore be written as I (9) ln ¼ mw xw mp xp mCsCl xCsCl I0 The intensity was measured at a time t1 (I1) and after the pulp was washed (I2). The pulp is not removed during the washing phase and xp1 is therefore equal to xp2. If I2 is subtracted from I1 the pulp contribution is eliminated, resulting in equation (10): I1 I2 ln ln ¼ mCsCl (xCsCl,1 xCsCl,2 ) I0 I0 mw (xw,1 xw,2 )
(10)
The decrease in CsCl is equal to the increase in water, i.e., (xCsCl,1 xCsCl,2 ) ¼ (xw,1 xw,2 )
(11)
This leads to the following equation: I1 I2 ln ¼ mCsCl (xCsCl,1 xCsCl,2 ) ln I0 I0
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þ mw (xCsCl,1 xCsCl,2 )
(12)
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The length difference can then be expressed as DxCsCl ¼
lnðI2 =I0 Þ lnðI1 =I0 Þ mCsCl mw
(13)
The concentration difference is finally DcCsCl ¼
DxCsCl rCsCl d
(14)
where d ¼ 0.06 m is the diameter of the filtration chamber and rCsCl ¼ 3988 g L21. The values of mw and mCsCl have been measured and found to be 19 m21 and 2598 m21, respectively. The calculated values for mw and mCsCl based on Bertin (1975) are 18.18 m21 and 2803 m21, respectively at 59.94 keV. In order to compare the washing curves based on the filtrate with the local washing curves a relationship between c in equation (6) and Dc in equation (14) is needed. The relationship can be written in the following way: Dc ¼ c(1 DC) þ hDC c(1 DC)jt2 þ hDCjt2 ¼ c(1 DC) þ (Kc þ K0 )DC (Kc þ K0 )DCjt2 (15) where DC is the dry content of the fibres. If K is close to zero, the relationship between Dc and c can be simplified as Dc ¼ c(1 DC)
(16)
RESULTS AND DISCUSSION Validation Experiment A washing experiment with a material forming relatively homogeneous filter cakes, calcium silicate (CaSiO3), was performed in order to evaluate the measurement technique used. The median size of a calcium silicate particle was measured with laser diffraction (Malvern 2600 series) and found to be 10.4 mm. Washing a calcium silicate cake takes more time than washing a paper pulp cake. This makes it possible to measure for a longer time at each measurement point, hence reducing the measurement error. It is also possible to measure at several heights in the cake during the same washing experiment. An example of this can be seen in Figure 2, where the concentration of CsCl has been measured at two heights, i.e., at the top of the bed (h L21 ¼ 0.14) and at the bottom of the bed (h L21 ¼ 0.83), during one washing experiment. Figure 2 shows that it is possible to obtain local displacement curves with this new technique.
Figure 2. Local washing curves for calcium silicate.
Figure 3. Washing curves for experiments in Group A; L 30 mm.
Evaluation Based on Measurement on the Filtrate The experimental conditions and results for paper pulp cakes are summarized in Table 1. The bed height is the only variable that has been varied. In group A, the bed height is approximately 30 mm, in group B it is 40 mm and, in group C, it is 50 mm. The velocity in all the experiments is quite low. The Reynolds number is at most 6 1023 (for Experiment 6), which is well within the laminar range. If the experimental conditions are identical, then the washing curves for beds with the same height should also be identical. The washing curves can be seen in Figures 3– 5. In Figure 3, the curves match each other perfectly and the experimental conditions are, indeed, the same. In Figure 4, the slopes of the curves differ slightly. The curves are, however, not all that different; it may, therefore, be assumed that the experimental conditions are approximately identical. In Figure 5, however, there is a significant difference between the shapes of the curves for Experiments 10, 11 and 12 and Experiments 13 and 14. The variation in shape is a result of that the slurry was pumped into the equipment with a much higher pressure (1 bar) for Experiments 10 to
Figure 4. Washing curves for experiments in Group B; L 40 mm.
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Figure 5. Washing curves for experiments in Group C; L 50 mm.
12 than for Experiments 13 and 14, where the pressure was 0.2 bar. The bed was hence more compressed for Experiments 10 to 12; leading to more ideal washing. Another explanation for the difference between the experiments could be that the pulp has been taken from the pulp mill on different occasions. Even though the properties of the pulp do not fluctuate to a large extent, the samples will never be exactly the same. The Peclet number and the coefficient K were estimated by fitting the dispersion model, equation (6), to the experimental data by using a non-linear least-square algorithm. The Peclet number; uL/DL, is a dimensionless number that describes the degree of mixing between the displaced and the displacing fluid in the bed and describes the shape of the washing curve. The Peclet number and the dispersion coefficient can be found in Table 1. As could be expected from Figure 3, the Peclet number and the dispersion coefficient are essentially the same for Experiments 1 to 5. The Peclet number and dispersion coefficient are more varied for Experiments 6 to 14. The Peclet number ranges from 29 to 135. Gra¨hs (1976) obtained Peclet numbers between 99 and 378 in his experiments on sulphate pulp. Poirier et al. (1988) obtained Peclet numbers between 3 and 47. The high Peclet number in Gra¨hs (1976) can be attributed to the high bed heights used in his experiments (10–17 cm). In Poirier et al. (1988), the bed height is approximately the same (2.5–8.5 cm) but the velocity is much higher and the consistency is lower. It is however difficult to be certain about the cause if the difference in Peclet number since, as too often with pulp washing experiments, a number of factors that could influence washing (such as pH, formation pressure and fibre length) are unknown. The coefficient K is set to zero since the pH was low and it is well known that the adsorption of metal ions on pulp fibres is substantially lower at low pH than at high pH (Rosen, 1975) as the acidic groups in the pulp are protonized at low pH values: the pKa values of the two characteristic acidic groups are 4.5 and 10. The cesium content is, however, not zero. The cesium content in the washed cakes was measured and found to be between 3.5–5 g kg21 dry pulp, but as it was found that the amount of cesium adsorbed did not change significantly during washing, it is the same as K is equal to zero.
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Figure 6. A comparison between the measured washing curve and the calculated washing curve for Experiments 3 and 11.
The residuals from the curve fitting are shown in Table 1. The residual is the squared 2-norm divided by number of measurements. The residuals for all the cases are small. Two examples are illustrated in Figure 6, where the measured washing curves for Experiments 3 and 11 are compared with the fitted displacement model. Experiment 3 has the smallest residual of all the experiments whilst Experiment 11 has the largest. In both cases, the fit to the slope of the curve is excellent. However, for Experiment 11, there are some variations in concentration during the initial washing period. This variation may be explained by the fact that the cake has not been compressed to equilibrium and inlet mixing has therefore occurred.
Local Measurements Local displacements curves for Experiments 10 to 14 are shown in Figure 7. The dispersion effect is not pronounced, which is apparent from the lack of increasing deviation from a step function as the wash water moves through the bed. Nonetheless, it can be clearly seen how the wash front
Figure 7. Local displacements curves at different heights for experiments in Group C; L 50 mm.
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Figure 8. Local displacement curves at different heights for experiments in Group B; L 40 mm.
Figure 9. Local displacement curves at different heights for experiments in Group A; L 30 mm.
moves through the bed. In Figures 8 and 9, the local displacement curves for Experiments 1 to 4 and Experiments 5 to 9 are shown. The curves are not very smooth, but as with Figure 7, Figures 8 and 9 show how the wash fronts propagate through the bed, providing another example of how local measurements of displacement washing are possible using this new measurement technique. The slopes are also comparable with the ones in Figures 3– 5 showing that the different measuring techniques give the same response. When examining the results it should also be remembered that paper pulp is a difficult material when it comes to making measurements due to its heterogeneous nature and the fact that the washing phase is relatively fast. Another complicating factor is that different cakes have been used in each experiment. Considering the experimental difficulties involved, the results are very promising. The reason for why it was not possible to notice a change of the slopes of the breakthrough curves is probably a combination of measurement error and the fact that the dispersion effect is small in the experiments made in this investigation. Figure 10(a) is the result of a simulation of local breakthrough curves with a dispersion coefficient similar to the ones obtained in this investigation (4 1028 m2 s21). It can be seen that the change in slope is very small in this case. This should be compared with the case when the dispersion coefficient is one order of magnitude higher (i.e., 4 1027 m2 s21), Figure 10(b). For this case the slope changes quite a lot. As mentioned earlier the intensity was measured at several bed heights after each experiment. The measured intensity was used to calculate the porosity profile within the bed and it was concluded that the porosity did not change significantly within the bed. This was an expected result since the beds had been highly compressed in order to avoid changes in porosity. The Peclet number and K values previously determined (based on the filtrate) were used to calculate the theoretical washing curves within the bed. The measured curves agreed in general well with the calculated curves. An example of the good agreement is found in Figure 11 that shows the calculated and measured local displacement curves for Experiments 7 and 8.
Figure 10. Calculated displacement curves at different bed heights when, k ¼ 0.01, L ¼ 40 mm, u ¼ 4.76 10–5 m s21. (a) Pe ¼ 47.7 and DL ¼ 4 10– 8 m2 s21. (b) Pe ¼ 4.77 and DL ¼ 4 10–7 m2 s21. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 357– 364
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and the resulting displacement curves are smooth. Although the experimental technique could be refined somewhat as far as pulp washing is concerned, the results are very promising; the new measurement technique provides new insight in the filter cake washing process.
NOMENCLATURE
Figure 11. Calculated and measured local displacement curves for Experiments 7 (h L21 ¼ 0.88) and 8 (h L21 ¼ 0.60).
c d DC DL h I K L m Pe t u w xi
concentration, kg dm23 diameter of the washing cell, m dry content longitudinal dispersion coefficient, m2 s21 height from the piston, m intensity, s21 constant length of bed, m 1/(1 2 1) Peclet number, uL/DL time, s velocity, m s21 wash ratio, ut L21 length of species i in the path of the g-rays
Greek symbols 1 porosity h amount of sorbed solute per unit volume of solid, kg dm23 l 1/(1 2 K þ K/1) m attenuation coefficient, m21 r density, g L21 Subscripts CsCl p w 0 1 2
Cesium chloride paper pulp water initial value value at time t1 value after washing
REFERENCES Figure 12. Measured and calculated displacement curves for Experiments 6 (h L21 ¼ 0.25) and 1 (h L21 ¼ 0.52).
Even at the top of the bed, as seen in Figure 12, the agreement is acceptable even though the measuring time is too long to capture the wash front perfectly. That the calculated curves agree well with the measured curves shows that the local dispersion coefficients are approximately the same as the overall dispersion coefficients. In this case, where there are no changes in porosity within the bed, this is an expected result.
CONCLUDING REMARKS This work has shown that it is possible to measure displacement curves at different heights within a filter cake. The calculated curves based on the dispersion model agree well with the measured curves. A difficulty with measuring inside the pulp bed is that pulp washing is a relatively fast process; the measurement error is therefore not negligible, resulting in washing curves that are not smooth. When the washing process is slower, as was in the case of the calcium silicate bed, the measurement error is very small
Bertin, E.P., 1975, Principles and Practice of X-Ray Spectometric Analysis (Plenum Press, New York, USA). Gre´n, U. and Stro¨m, K.H.U., 1985, Displacement washing of packed beds of cellulose fibres, Pulp & Paper Canada, 86(9): 261–264. Gra¨hs, L.-E., 1975, Displacement washing of packed beds of cellulose fibres. Part 1. Mathematical model, Svensk Papperstidning, 78(12): 446– 450. Gra¨hs, L.-E., 1976, Displacement washing of packed beds of cellulose fibres. Part 2. Analysis of laboratory experiments, Svensk Papperstidning, 79(3): 84– 89. Johansson, C. and Theliander, H., 2003, Measuring concentration and pressure profiles in deadend filtration, Filtration Solutions, 3(2): 114– 120. Lapidus, L. and Amundson, N.R., 1952, Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, J Phys Chem, 56: 984– 988. Lee, P.F., 1979, Optimizing the displacement washing of pads of wood pulp fibers, TAPPI, 62(9): 75– 78. Poirier, N.A., Crotogino, R.H. and Douglas, W.J.M., 1988, Axial dispersion models for displacement washing of packed beds of wood pulp fibres, The Canadian Journal of Chemical Engineering, 66: 936–944. Rosen, A., 1975, Adsorption of sodium ions on kraft pulp fibers during washing, TAPPI, 58(9): 156– 161. Sedin, P., Johansson, C. and Theliander, H., 2003, On the determination and evaluation of pressure and solidosity in filtration, Chem Eng Res Des, 81(A10): 1395–1405. Sherman, W.R., 1964, The movement of a soluble material during the washing of a bed of packed solids, AIChEJ, 10(6): 855–860. Sjo¨stro¨m, E., 1993, Wood Chemistry Fundamentals and Applications (Academic Press, San Diego, USA).
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Trinh, D.T., Poirier, N.A., Crotogino, R.H. and Douglas, W.J.M., 1989, Displacement washing of wood pulp – an experimental study, Journal of Pulp and Paper Science, 15(1): 28–35. Wakeman, R.J., 1990, Simulations of dispersion phenomena in filter cake washing, Chem Eng Res Des, 68: 162 –171. Wakeman, R.J. and Attwood, G.J., 1988, Developments in the application of cake washing theory, Filtration and Separation, 25(July/August): 272– 275.
ACKNOWLEDGEMENTS The financial support of the Swedish Energy Agency is greatly appreciated. We would also like to thank So¨dra Cell for their assistance in this project. The manuscript was received 13 June 2006 and accepted for publication after revision 1 November 2006.
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