Modeling Particle-Size Distribution Dynamics during Precipitative Softening
Publication: Journal of Environmental Engineering
Volume 136, Issue 1
Abstract
A population balance model was developed to simulate simultaneous precipitation and flocculation during precipitative softening. Rate coefficients for nucleation, crystal growth, and flocculation were extracted from experimental particle-size distribution (PSD) data based on changes in the total number and total volume of particles. Three models of flocculation were evaluated: rectilinear, curvilinear, and an empirical size-independent model. Model simulations were compared with experimental PSD data to test which model was most appropriate. The curvilinear precipitative flocculation model was superior when seeded precipitation occurred at moderate mixing intensities . However, the curvilinear model overpredicts the formation of very large particles and requires values of the collision efficiency greater than 1.0, suggesting a more complicated dependence of the PSD dynamics on mixing intensity and saturation ratio than presently included in the model. At higher mixing intensities , flocculation exhibited size-independent behavior, indicating that physical/chemical aspects of the precipitation process are altering or overshadowing the physics described in the curvilinear flocculation model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the American Water Works Association, the U.S. EPA STAR Graduate Fellowship Program (Grant No. UNSPECIFIEDFP 91640701-0) and the National Water Research Institute through graduate fellowships awarded to JAN. The abovementioned agencies have not officially endorsed this publication and the views expressed herein are those of the writers and may not reflect the views of these agencies.
References
Andreassen, J. P., and Hounslow, M. J. (2004). “Growth and aggregation of vaterite in seeded-batch experiments.” AIChE J., 50(11), 2772–2782.
Bramley, A. S., Hounslow, M. J., and Ryall, R. L. (1996). “Aggregation during precipitation from solution: A method for extracting rates from experimental data.” J. Colloid Interface Sci., 183(1), 155–165.
Chapra, S. C., and Canale, R. P. (1988). Numerical methods for engineers, 2nd Ed., McGraw-Hill, New York.
Collier, A. P., and Hounslow, M. J. (1999). “Growth and aggregation rates for calcite and calcium oxalate monohydrate.” AIChE J., 45(11), 2298–2305.
David, R., Marchal, P., Klein, J. P., and Villermaux, J. (1991). “Crystallization and precipitation engineering—III. A discrete formulation of the agglomeration rate of crystals in the crystallization process.” Chem. Eng. Sci., 46(1), 205–213.
Han, M. Y., and Lawler, D. F. (1992). “The (relative) insignificance of G in flocculation.” J. Am. Water Works Assoc., 84(10), 79–91.
Hostomsky, J., and Jones, A. G. (1991). “Calcium-carbonate crystallization, agglomeration and form during continuous precipitation from solution.” J. Phys. D: Appl. Phys., 24(2), 165–170.
Hounslow, M. J., Mumtaz, H. S., Collier, A. P., Barrick, J. P., and Bramley, A. S. (2001). “A micro-mechanical model for the rate of aggregation during precipitation from solution.” Chem. Eng. Sci., 56(7), 2543–2552.
Hounslow, M. J., Ryall, R. L., and Marshall, V. R. (1988). “A discretized population balance for nucleation, growth, and aggregation.” AIChE J., 34(11), 1821–1832.
Ilievski, D., and White, E. T. (1994). “Agglomeration during precipitation-agglomeration mechanisms identification for crystals in stirred caustic aluminate solutions.” Chem. Eng. Sci., 49(19), 3227–3239.
Kramer, T. A., and Clark, M. M. (1999). “Incorporation of aggregate breakup in the simulation of orthokinetic coagulation.” J. Colloid Interface Sci., 216(1), 116–126.
Kumar, S., and Ramkrishna, D. (1996). “On the solution of population balance equations by discretization—I. A fixed pivot technique.” Chem. Eng. Sci., 51(8), 1311–1332.
Kumar, S., and Ramkrishna, D. (1997). “On the solution of population balance equations by discretization—III. nucleation, growth and aggregation of particles.” Chem. Eng. Sci., 52(24), 4659–4679.
Lawler, D. F., and Nason, J. A. (2005). “Integral water treatment plant modeling: improvements for particle processes.” Environ. Sci. Technol., 39(17), 6337–6342.
Lawler, D. F., O’Melia, C. R., and Tobiason, J. E. (1980). “Integral water treatment plant design: From particle size to plant performance.” Advances in chemistry series. 189. Particulates in water, M. C. Kavanaugh and J. O. Leckie, eds., American Chemical Society, Washington, D.C., 353–388.
Lee, D. G., Bonner, J. S., Garton, L. S., Ernest, A. N. S., and Autenrieth, R. L. (2000). “Modeling coagulation kinetics incorporating fractal theories: A fractal rectilinear approach.” Water Res., 34(7), 1987–2000.
Li, J. (1996). “Rectilinear vs. curvilinear models of flocculation: Experimental tests.” Ph.D. dissertation, The Univ. of Texas at Austin, Austin, Tex.
Li, X. Y., and Logan, B. E. (1997a). “Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid.” Environ. Sci. Technol., 31(4), 1237–1242.
Li, X. Y., and Logan, B. E. (1997b). “Collision frequencies of fractal aggregates with small particles by differential sedimentation.” Environ. Sci. Technol., 31(4), 1229–1236.
Liew, T. L., Barrick, J. P., and Hounslow, M. J. (2003). “A micro-mechanical model for the rate of aggregation during precipitation from solution.” Chem. Eng. Technol., 26(3), 282–285.
Lister, J. D., Smit, D. J., and Hounslow, M. J. (1995). “Adjustable discretized population balance for growth and aggregation.” AIChE J., 41(3), 591–603.
Marchal, P., David, R., Klein, J. P., and Villermaux, J. (1988). “Crystallization and precipitation engineering—I. An efficient method for solving population balance in crystallization with agglomeration.” Chem. Eng. Sci., 43(1), 59–67.
McCabe, W. L. (1929a). “Crystal growth in aqueous solutions I—Theory.” Ind. Eng. Chem., 21(1), 30–33.
McCabe, W. L. (1929b). “Crystal growth in aqueous solutions II—Experimental.” Ind. Eng. Chem., 21(2), 112–119.
Mumtaz, H. S., and Hounslow, M. J. (2000). “Aggregation during precipitation from solution: An experimental investigation using Poiseuille flow.” Chem. Eng. Sci., 55, 5671–5681.
Mumtaz, H. S., Hounslow, M. J., Seaton, N. A., and Paterson, W. R. (1997). “Orthokinetic Aggregation during precipitation: A computational model for calcium oxalate monohydrate.” Chem. Eng. Res. Des., 75(A2), 152–159.
Nason, J. A. (2006). Particle aspects of precipitative softening: Experimental measurement and mathematical modeling of simultaneous precipitation and flocculation, The University of Texas at Austin, Austin, Tex.
Nason, J. A., and Lawler, D. F. (2008). “Particle size distribution dynamics during precipitative softening: Constant solution composition.” Water Res., 42(14), 3667–3676.
Nason, J. A., and Lawler, D. F. (2009). “Particle size distribution dynamics during precipitative softening: declining solution composition.” Water Res., 43(2), 303–312.
Privman, V., Goia, D. V., Park, J., and Matijevic, E. (1999). “Mechanism of formation of monodispersed colloids by aggregation of nanosize precursors.” J. Colloid Interface Sci., 213(1), 36–45.
Ramkrishna, D. (2000). Population balances: Theory and applications to particulate systems in engineering, Academic, San Diego.
Sajo, E. (2008). “Evaluation of the exact coagulation kernel under simultaneous Brownian motion and gravitational settling.” Aerosol Sci. Technol., 42(2), 134–139.
Simons, S., Williams, M. M. R., and Cassell, J. S. (1986). “A kernel for COMBINED Brownian and Gravitational coagulation.” J. Aerosol Sci., 17(5), 789–793.
Smoluchowski, M. (1917). “Versuch einer mathematischen theorie der koagulations-kinetic kolloider losungen.” Z. Phys. Chem., 92, 129.
Thomas, D. N., Judd, S. J., and Fawcett, N. (1999). “Flocculation modelling: A review.” Water Res., 33(7), 1579–1592.
Veerapaneni, S., and Wiesner, M. R. (1996). “Hydrodynamics of fractal aggregates with radially varying permeability.” J. Colloid Interface Sci., 177(1), 45–57.
Zhang, J. J., and Li, X. Y. (2003). “Modeling particle size distribution dynamics in a flocculation system.” AIChE J., 49(7), 1870–1882.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 136 • Issue 1 • January 2010
Pages: 12 - 21
Copyright
© 2010 ASCE.
History
Received: Dec 2, 2008
Accepted: Jul 6, 2009
Published online: Jul 17, 2009
Published in print: Jan 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.