9364
Ind. Eng. Chem. Res. 2005, 44, 9364-9368
RESEARCH NOTES Pareto Profile Benchmark for Kinetics of Filtration and Extent of Dewatering of Fine and Colloidal Suspensions Sasanka Raha,† Kartic C. Khilar,‡ Pradip,*,† and Prakash C. Kapur† Tata Research Development and Design Centre, 54B Hadapsar Industrial Estate, Pune-411013, India, and Department of Chemical Engineering, Indian Institute of Technology, Powai, Mumbai-400076, India
The time scale of the process and the extent of dewatering are principal performance measures of high pressure filtration of fine and colloidal suspensions which give rise to compressible filter cakes. Analysis of numerous filtration tests conducted under a wide range of suspension chemistry and process conditions suggests that it is not possible to improve the two performance measures simultaneously. As stipulated by the Pareto optimum, any improvement in the filtration kinetics can occur only at cost of reducing the extent of moisture removed from the filter cake and vice versa. The unique Pareto profilesthe curve of filtration kinetics versus extent of dewaterings is the fingerprint of the filtration behavior of a particulate solid in suspension. Accordingly, any physical-chemical scheme, which purports to improve the overall filtration process, should be benchmarked against the Pareto curve. Introduction Solid-liquid separation is a common unit operation in the process industry. Pressure filtration, the focus of this work, is employed routinely for dewatering of fine and colloidal suspensions, which give rise to compressible filter cakes. This process has been studied experimentally and modeled theoretically by many investigators.1-20 In many instances, the theoretical treatment seeks to couple material-independent solid-liquid continuity-momentum balance equation with materialspecific constitutive relationships. The latter describe the characteristic rheological properties of the suspension that are relevant to dewatering, namely, cake compressibility and specific cake resistance. The cake resistance is substituted by permeability, hindered settling function, flux density function, diffusivity, etc, depending on the theoretical approach adopted. For analysis of the filtration process, it is necessary to characterize the suspension experimentally in terms of cake compressibility, as given by its compressive yield stress 3,6,11-13,20 and permeability, diffusivity, or specific cake resistance, etc.1,2,5-12,14-18 These functions determine the two core performance measures of the filtration process, equilibrium end moisture in the cake under a given applied pressure and time scale of the process, respectively. The equilibrium solid fraction φ∞ is the final volume fraction solids in filter cake when filtration ceases or, strictly speaking, effectively ceases. At this point, the compressive yield stress of filter cake P(φ∞), which rises steeply with increasing solid content, becomes equal to the applied pressure, and further consolidation of filter cake and dewatering stops. * Corresponding author. Tel.: +91 20 5608 6209. Fax: +91 20 5608 6399. E-mail:
[email protected]. † Tata Research Development and Design Centre. ‡ Indian Institute of Technology.
The performance of the filtration process can be altered greatly by manipulating one or more physicalchemical variables and parameters such as applied pressure, solid concentration, slurry preparation method, suspension pH, additives such as surfactants and polymers and their dosage, etc. A number of studies exist on the effect of pH and additives on the state of aggregation in a suspension and its filtration behavior.4,8,16-20 Appropriate manipulation of the suspension chemistry usually leads to either faster filtration rate or higher moisture removal and any improvement in one measure invariably results in deterioration in the other.4,9,14,19 In view of the empirical finding that, in general, it is not possible to improve both performance measures simultaneously, the interrelationship between dewaterability and filtration rate acquires considerable importance for establishing a benchmark for evaluating the effectiveness of a filtration process and providing a useful upper bound on its performance. On the basis of a large number of high-pressure filtration tests on model colloidal alumina suspensions under wide-ranging conditions, we demonstrate that it is apparently not possible to improve both dewaterability and rate at the same time and the two measures are uniquely related by a Pareto profile or curve,21,22 which provides an objective benchmark and upper bound for evaluating the performance of a particulate solid in a filtration process. Experimental Section Particulate suspensions for high-pressure filtration tests were prepared from A16 SG alumina (supplied by Aloca) having 9.3 m2/g BET surface area and 0.4 micron mean particle size, as measured by Horiba laser scattering particle size analyzer. Point of zero charge (pzc) for this powder was located at pH 6.5 by electrokinetic measurements on Zetameter 3.0 model.
10.1021/ie050605+ CCC: $30.25 © 2005 American Chemical Society Published on Web 10/25/2005
Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9365
Figure 1. Inverse of specific cake resistance of A16 SG alumina powder as a function of applied pressure.
Figure 3. Inverse of specific cake resistance of A16 SG alumina powder as a function of suspension pH for filtration under 100 kPa applied pressure.
Figure 2. Equilibrium solid volume fraction of A16 SG alumina powder achieved as a function of applied pressure.
For preparation of a suspension without any additive, the slurry was conditioned for 5 min and dispersed by a magnetic stirrer for 2 min (in some cases 24 h conditioning was carried out prior to magnetic stirring for 2 min). When required, pH was adjusted during conditioning with 4N HNO3 or 4N NaOH solution. The suspension was next ultrasonicated with a Branson 450 sonicator for 2 min using 50% duty cycle and 40 W power input. Two procedures were adopted for the addition of additives. In method A, the suspension was first mixed with polymer or surfactant with a magnetic stirrer for 2 min. Next, the suspension was ultrasonicated with a Branson 450 sonicator for 2 min using 50% duty cycle and 40 W power input. In method B, sonication was carried out first and then additive was added drop by drop with fast agitation with a magnetic stirrer for 2 min followed by slow agitation for 3 min. High pressure filtration experiments were carried out in a highly instrumented and programmable, computer-driven laboratory-scale test rig, which has been described in details elsewhere by its designers.11 Whatman filter paper No. 42 was used as the filter medium. The tests included the effect of various process parameters such as pH, pressure, initial slurry height (h0) in filtration chamber, solid volume fraction in feed (φ0), floccculant and surfactant type and concentration, different modes of polymer/surfactant addition, and slurry preparation methods used. Since pressure is an important, easy-to-
Figure 4. Equilibrium solid volume fraction of A16 SG alumina powder as a function of suspension pH for filtration under 100 kPa applied pressure.
manipulate process variable in filtration, tests were carried out over a wide range of pressures ranging from 1 to 250 kPa. Result and Discussions The specific cake resistance, Rc, for each experiment was computed from filtration data by the following equation14
ηRm Rcφ0Fsη t V+ ) V 2(1 - φ0)∆P ∆P
(1)
where V is cumulative filtrate volume collected at time t per unit filtration cross-sectional area during filtration under applied pressure, ∆P, φ0 is initial solid volume fraction in slurry, Fs is solid specific gravity, and η is fluid viscosity. The medium resistance, Rm, is assumed to be negligible. Figure 1 shows that the inverse of the specific cake resistance of alumina A16 SG, which is a measure of the rate of filtration, decreases with an increase in filtration pressure. Figure 2 shows that the end point solid volume fraction in the filter cake at equilibrium, that is, the extent of dewatering achieved, increases with an increase in pressure. As stated above, the applied pressure as a function of equilibrium solid
9366
Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005
Table 1. Details of Filtration Tests
fraction is, in fact, the compressive yield stress of the material.6,11-13,20 From Figures 1 and 2, we note that inverse of specific cake resistance decreases and solid content of filter cake (or extent of dewatering) increases with increasing pressure, and the two performance measures cannot be varied independently of each other. In the absence of a polymer or surfactant, the nature and magnitude of interactions between suspended particles and the resulting state of their aggregation are determined, in the first instance, by the pH of the suspension. In general, the suspension is fully aggregated or coagulated at or in the vicinity of the pzc of
the solid where the electrical double layer repulsion is switched off. It becomes increasingly dispersed as pH deviates from pzc. It is known that the filtration rate is higher (or specific cake resistance is lower) in coagulated suspensions than in dispersed ones. Figure 3 shows that, at 100 kPa filtration pressure, inverse of specific cake resistance of A16 SG alumina suspensions rises significantly as pH is increased from 3.3, reaching a maximum value at about pH 7.5. It falls once more as pH is increased further. This trend is in conformity with the phenomenon of dispersion/aggregation/dispersion of alumina suspensions with increasing pH, starting from
Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9367
is meaningful only if the Pareto profile is pushed upward and or to the right, the Pareto profile provides a useful benchmark for the dewatering of a suspension of a given material. Concluding Remarks
Figure 5. Pareto curve of A16 SG suspensions under widely different filtration conditions.
a low value. What is, however, more germane is that, as shown in Figure 4, end point solid volume fraction in the filter cake exhibits a trend with pH which is opposite to that of the inverse specific cake resistance in Figure 3. We conclude that filtration rate is highest in the vicinity of pzc but the extent of dewatering is the least, and any attempt to enhance the removal of water by pH control invariably leads to a drop in the filtration rate. In other words, in this instance also, the performance indices are interrelated and cannot be varied independently. It turns out that the two measures are more or less uniquely related by a Pareto curve for an exceptionally wide range of process conditions. This is illustrated in Figure 5 where inverse of specific cake resistance is plotted against end point solid volume fraction for 66 filtration tests. The process conditions, given in Table 1, encompassed (1) short (5 min) and long (24 h) conditioning of suspensions without any additive but with systematic variations in pressure, initial solid content, feed slurry height in filtration chamber, and pH, (2) addition of 100 and 10 ppm poly(acrylic acid) (PAA) by method A with systematic variations in molecular weight of the polymer, (3) addition of 100 ppm PAA of two molecular weights by method B with systematic variations in pH, and (4) addition of 100 ppm citric acid and sodium oleate surfactants. To a first approximation, the data in Figure 5 lie on a unique curve, which is seemingly independent of the suspension chemistry and physical process variables. It is also evident that it is not possible to improve filtration rate without paying a penalty in solid content of the filter cake and vice versa. This behavior exemplifies the Pareto optimum for a vector of two interrelated objective functions, which stipulates that no unique optimum solution is possible, but there exists a Pareto set of an arbitrary large number of solutions that are equally “good”. The solutions lie on the Pareto curve such that any attempt to improve one objective or performance measure must simultaneously result in loss in the second. Extensive filtration tests carried out by us on different materials suggest that the Pareto curve depends on the nature of particulate solid. It is sufficient to note here that the shapes of various material-specific Pareto profiles are similar to the curve in Figure 5. The permeability measure drops steeply in the lower solid volume fraction region, followed by a plateau where it changes only slowly. Since, an overall improvement in the filtration process brought on by modification of the physical-chemical variables, such as those listed above,
Unfortunately, the physical interpretation of the correlation between resistance and equilibrium solid fraction at a fundamental level is not obvious. The reason lies in the complexity of the filtration system, which is driven by the interplay of aggregates microstructure, hindered settling, compressibility of filter cake, and distribution of stress on liquid and solid phases. Indeed, it has not even been possible to satisfactorily model the compressive yield stress in terms of the interfacial phenomena operating in the concentrated suspensions, although empirical relationships between applied pressure and φ∞ have been presented in considerable details by the authors in a recent paper.20 On the basis of the analysis of a large amount of data, we have demonstrated that there are numerous optimized vectors of objective functions that belong to a unique Pareto set. Since every point on the Pareto curve represents a trade off between the two measures, there is no single global optimum in pressure filtration. Accordingly, any physical-chemical-based strategy, which purports to improve the overall filtration process, should be able to push back the performance envelop as given by the Pareto curve, which has not been demonstrated in the literature despite considerable research reported over the years. A similar situation is encountered in chemical reactions and material processing, also. For example, a grade-recovery curve in mineral processing (or yield-purity relationship in chemical synthesis) also conforms to the Pareto profile, as does the molecularweight-polydispersity index correlation in polymer reaction engineering.23 Acknowledgment Financial support for this work from Department of Science and Technology (DST), Government of India, is gratefully acknowledged. We are grateful to Prof. Mathai Joseph, Executive Director, Tata Research Development and Design Centre, for encouragement and support. Literature Cited (1) Shirato, M.; Murase, T.; Iwata, M. Deliquoring by expression theory and practice. Progress in Filtration and Separation, 4th ed.; Wakeman, R. J., Ed.; Elsevier: Amsterdam, 1986. (2) Tiller, F. M.; Kwon, J. H. Role of porosity in filtration. XIII. Behavior of highly compactible cakes. AIChE J. 1998, 44, 2159. (3) Buscall, R.; White, L. R. The consolidation of concentrated suspensions. Part 1: The theory of sedimentation. J. Chem. Soc., Faraday Trans. 1987, 83, 873. (4) Banda, S. M. H.; Forssberg, K. S. E. Structure variation in filter cakes from flocculated slurries. Scand. J. Metall. 1988, 17, 57. (5) Wakeman, R. J.; Sabri, M. N.; Tarleton, E. S. Factors affecting the formation and properties of wet compacts. Powder Technol. 1991, 65, 283. (6) Landman, K. A.; White, L. R.; Eberl, M. Pressure Filtration of Flocculated Suspensions. AIChE J. 1995, 41, 1687. (7) Lu., W. M.; Huang, Y. P.; Hwang., K. J. Methods to determine the relationship between cake properties and solid compressive pressure. Sep. Purif. Technol. 1998, 13, 9. (8) Sis, H.; Chander, S. Pressure filtration of dispersed and flocculated alumina slurries. Miner. Metall. Process. 2000, 17, 41.
9368
Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005
(9) Aziz, A. A. A.; de Krester, R. G.; Dixon, D. R.; Scales, P. J. The characterization of slurry dewatering. Water Sci. Technol. 2000, 14, 9. (10) Burger, R.; Concha, F.; Karlsen, K. H. Phenomenological model of filtration processes. 1. Cake formation and expression. Chem. Eng. Sci. 2001, 56, 4537. (11) de Krester, R. G.; Usher, S. P.; Scales, P. J.; Boger, D. V. Rapid filtration measurement of dewatering design and optimization parameters. AIChE J. 2001, 47, 1758. (12) Usher, S. P.; de Krester, R. G.; Scales, P. J. Validation of a new filtration technique for dewaterability characterization. AIChE J. 2001, 47, 1561. (13) Kapur, P. C.; Raha, S.; Usher, S.; de Krester, R. G.; Scales, P. J. Modeling of the consolidation stage in pressure filtration of compressible cakes. J. Colloid Interface Sci. 2002, 256, 216. (14) Tao, D.; Parekh, B. K.; Liu, J. T.; Chen, S. An investigation on dewatering kinetics of ultrafine coal. Int. J. Miner. Process. 2003, 70, 235. (15) Bai, R.; Tien, C. Further work on cake filtration analysis. Chem. Eng. Sci. 2005, 60, 301. (16) Besra, L.; Sengupta, D. K.; Roy, S. K.; Ay, P. Flocculation and dewatering of kaolin suspensions in the presence of polyacrylamide and surfactants. Int. J. Miner. Process. 2002, 66, 203. (17) Glover, S. M.; Yan, Y. D.; Jameson, G. J.; Biggs, S. Polymer molecular weight and mixing effects on floc compressibility and
filterability. Presented at 6th World Congress of Chemical Engineering, Institution of Chemical Engineers: Melbourne, Australia, 2001. (18) Glover, S. M.; Yan, Y. D.; Jameson, G. J.; Biggs, S. Dewatering properties of dual-polymer-flocculated systems. Int. J. Miner. Process. 2004, 73, 145. (19) Wu, C. C.; Wu, J. J.; Huang, R. Y. Floc strength and dewatering efficiency of alum sludge. Adv. Environ. Res. 2003, 7, 617. (20) Raha, S.; Khilar, K. C.; Pradip; Kapur, P. C. Rapid determination of compressive yield stress of dense suspensions by a mean-phi (φ h ) model of high pressure filtration. Powder Technol. 2005, 155, 42. (21) Miettinen, K. Nonlinear Multiobjective Optimization; Kluwer: Boston, MA, 1999. (22) Deb, K. Multiobjective Optimization Using Evolutionary Algorithms; Wiley: Chichester, U.K., 2001. (23) Raha, S.; Majumder, S.; Mitra, K. Effect of caustic addition in epoxy polymerization process: A single and multi-objective evolutionary approach. Macromol. Theory Simul. 2004, 13, 152.
Received for review May 21, 2005 Revised manuscript received October 7, 2005 Accepted October 12, 2005 IE050605+
