Settling velocities of particulate systems: 14. Unified model of sedimentation, centrifugation and filtration of flocculated suspensions

Abstract This paper presents a unified theory of solid–liquid separation of flocculated suspensions including sedimentation-thickening, centrifugation and filtration. After identifying the variables and equations for each of the operations, thickening, centrifugation and filtration, and establishing the compatibility between them, we show that these processes can be described by variants of one scalar hyperbolic–parabolic strongly degenerate partial differential equation with appropriate initial and boundary conditions. To complete the description, constitutive equations should be postulated for the solid–fluid interaction forces in the suspension and for the permeability and the compressibility of the porous medium, which is either a sediment or a filter cake. A particular unit operation can then be simulated by solving these equations numerically. The mathematical analysis of the resulting model confirms the well-posedness of the mathematical model and support the design of robust numerical simulation methods. These methods are employed to calculate a variety of examples from thickening, centrifugation and filtration, which illustrate the theory.

[1]  Ross G. de Kretser,et al.  Rapid filtration measurement of dewatering design and optimization parameters , 2001 .

[2]  Steinar Evje,et al.  On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes , 2000 .

[3]  Frank M. Tiller,et al.  The theory of sediment volumes of compressible, particulate structures , 1984 .

[4]  Kerry A. Landman,et al.  Solid/liquid separation of flocculated suspensions , 1994 .

[5]  Raimund Bürger,et al.  Settling velocities of particulate systems: 9. Phenomenological theory of sedimentation processes: numerical simulation of the transient behaviour of flocculated suspensions in an ideal batch or continuous thickener , 1999 .

[6]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[7]  W. Schneider,et al.  Application of the theory of kinematic waves to the centrifugation of suspensions , 1983 .

[8]  R. Font,et al.  Semi-batch test of sedimentation. Application to design , 2000 .

[9]  B. Fitch,et al.  Sedimentation of flocculent suspensions: State of the art , 1979 .

[10]  Knut-Andreas Lie,et al.  Numerical methods for the simulation of the settling of flocculated suspensions , 2000, Chemical Engineering Journal.

[11]  R. Font,et al.  Analysis of the Variation of the Upper Discontinuity in Sedimentation Batch Test , 1998 .

[12]  A. M. Duda,et al.  Addressing Nonpoint Sources of Water Pollution Must Become an International Priority , 1993 .

[13]  Raimund Bürger,et al.  Model equations for gravitational sedimentation-consolidation processes , 2000 .

[14]  Sedimentation test of metal hydroxides: hydrodynamics and influence of pH , 1999 .

[15]  Raimund Bürger,et al.  Applications of the phenomenological theory to several published experimental cases of sedimentation processes , 2000 .

[16]  Raimund Bürger,et al.  Sedimentation and suspension flows: Historical perspective and some recent developments , 2001 .

[17]  M. Ungarish,et al.  Hydrodynamics of Suspensions , 1993 .

[18]  Athanasios N. Papanicolaou,et al.  BATCH ANALYSIS OF SLURRIES IN ZONE SETTLING REGIME , 1997 .

[19]  P. T. Shannon,et al.  Batch and Continuous Thickening. Basic Theory. Solids Flux for Rigid Spheres , 1963 .

[20]  R. Font,et al.  Filtration with Sedimentation: Application of Kynchs Theorems , 2000 .

[21]  F. Tiller,et al.  Unifying the Theory of Thickening, Filtration, and Centrifugation , 1993 .

[22]  R. M. Bowen.  Part I – Theory of Mixtures , 1976 .

[23]  Kerry A. Landman,et al.  Compressive yield stress of flocculated suspensions: Determination via experiment , 1996 .

[24]  R. Bürger,et al.  Sedimentation and Thickening : Phenomenological Foundation and Mathematical Theory , 1999 .

[25]  K. J. Scott.  Experimental Study of Continuous Thickening of a Flocculated Silica Slurry , 1968 .

[26]  A. Michaels,et al.  Settling Rates and Sediment Volumes of Flocculated Kaolin Suspensions , 1962 .

[27]  Particulate flows : processing and rheology , 1998 .

[28]  P. T. Shannon,et al.  SETTLING OF SLURRIES—NEW LIGHT ON AN OLD OPERATION , 1965 .

[29]  Raimund Bürger,et al.  A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions , 2001 .

[30]  K. Landman,et al.  Scale-up procedures and test methods in filtration: a test case on kaolin plant data , 1995 .

[31]  R. Bürger,et al.  Mathematical model and numerical simulation of the settling of flocculated suspensions , 1998 .

[32]  Raimund Bürger,et al.  Phenomenological model of filtration processes: 1. Cake formation and expression , 2001 .

[33]  Raimund Bürger,et al.  Phenomenological foundation and mathematical theory of sedimentation–consolidation processes , 2000 .

[34]  Uwe Schaflinger,et al.  Centrifugal separation of a mixture , 1990 .

[35]  P. T. Shannon,et al.  Batch and Continuous Thickening. Prediction of Batch Settling Behavior from Initial Rate Data with Results for Rigid Spheres , 1964 .

[36]  Ross G. de Kretser,et al.  Validation of a new filtration technique for dewaterability characterization , 2001 .

[37]  Raimund Bürger,et al.  On a Free Boundary Problem for a Strongly Degenerate Quasi-Linear Parabolic Equation with an Application to a Model of Pressure Filtration , 2002, SIAM J. Math. Anal..

[38]  Raimund Bürger,et al.  Settling velocities of particulate systems: 12. Batch centrifugation of flocculated suspensions , 2001 .

[39]  B. Fitch,et al.  Kynch theory and compression zones , 1983 .

[40]  F. Tiller,et al.  Role of porosity in filtration: XIII. Behavior of highly compactible cakes , 1998 .

[41]  K. Landman,et al.  Pressure filtration technique for complete characterization of consolidating suspensions , 1998 .

[42]  Zone Settling of Concentrated Slurries in a Centrifugal Field , 1991 .

[43]  W. F. Eckert,et al.  Prediction of sedimentation and consolidation of fine tails , 1996 .

[44]  K. Karlsen,et al.  On some upwind difference schemes for the phenomenological sedimentation-consolidation model , 2001 .

[45]  E. M. Tory,et al.  Sedimentation of Small Particles in a Viscous Fluid , 1996 .

[46]  Richard J. Wakeman,et al.  Filtration : equipment selection, modelling and process simulation , 1999 .

[47]  R. Bürger,et al.  A Century of Research in Sedimentation and Thickening , 2002 .

[48]  G. J. Kynch.  A theory of sedimentation , 1952 .