RDC extraction column simulation using the multi-primary one secondary particle method: Coupled hydrodynamics and mass transfer

Abstract Based on the multivariate population balance equation (PBE) and the primary secondary particle concept a mathematical model is developed for liquid extraction columns. It is extended to include the momentum balance for the dispersed phase. The resulting model is complicated by the integral source term of the PBE. To reduce this complexity, while maintaining most of the information from the continuous PBE, the concept of the primary secondary particle method is used. The effect of the number of primary particles (PP) on the final predicted solution is investigated. Numerical results show that the solution converge fast as the number of PP is increased. The terminal droplet velocity is found to be the most sensitive model parameter to the number of PP. The predicted steady state profiles (droplet diameter, holdup and the concentration profiles) along a pilot RDC extraction column are compared to the experimental data where good agreement is achieved.

[1]  Themis Matsoukas,et al.  Constant-number Monte Carlo simulation of population balances , 1998 .

[2]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[3]  Menwer Attarakih,et al.  LLECMOD: A Windows-based program for hydrodynamics simulation of liquid–liquid extraction columns , 2006 .

[4]  G. S. Laddha,et al.  Transport phenomena in liquid extraction , 1978 .

[5]  Richard V. Calabrese,et al.  Drop breakup in turbulent stirred‐tank contactors. Part I: Effect of dispersed‐phase viscosity , 1986 .

[6]  Hans-Jörg Bart,et al.  Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid¿liquid extraction columns , 2006 .

[7]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[8]  Malcolm H. I. Baird,et al.  Handbook of Solvent Extraction , 1991 .

[9]  Daniel Garthe,et al.  Fluiddynamics and Mass Transfer of Single Particles and Swarms of Particles in Extraction Columns , 2006 .

[10]  John D. Thornton,et al.  Science and practice of liquid-liquid extraction , 1991 .

[11]  Ernest J. Henley,et al.  Separation Process Principles , 1998 .

[12]  Hans-Jörg Bart,et al.  The Droplet Population Balance Model – Estimation of Breakage and Coalescence , 2003 .

[13]  M. Slater,et al.  Studies of drop break‐up in liquid‐liquid systems in a rotating disc contactor. Part I: Conditions of no mass transfer , 1991 .

[14]  Hans-Jörg Bart,et al.  LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns , 2008 .

[15]  A. Kumar,et al.  Correlations for Prediction of Mass Transfer Coefficients in Single Drop Systems and Liquid–Liquid Extraction Columns , 1999 .

[16]  Rosner,et al.  Monte Carlo Simulation of Particle Aggregation and Simultaneous Restructuring. , 1999, Journal of colloid and interface science.

[17]  D. R. Lewin,et al.  Modeling, simulation and control of liquid-liquid extraction columns , 1998 .

[18]  Ian T. Cameron,et al.  Process systems modelling and applications in granulation: A review , 2005 .

[19]  Hans-Jörg Bart,et al.  Solution of the population balance equation using the sectional quadrature method of moments (SQMOM) , 2009 .

[20]  Hans-Jörg Bart,et al.  Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions , 2004 .

[21]  Markus Kraft,et al.  Simulation of coalescence and breakage: an assessment of two stochastic methods suitable for simulating liquid–liquid extraction , 2004 .

[22]  J. F. Richardson,et al.  Sedimentation and fluidisation: Part I , 1997 .

[23]  Mamoru Ishii,et al.  Two-fluid model and hydrodynamic constitutive relations , 1984 .

[24]  J. Wesselingh,et al.  Single Particles, Bubbles and Drops , 1999 .

[25]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[26]  Vanni,et al.  Approximate Population Balance Equations for Aggregation-Breakage Processes. , 2000, Journal of colloid and interface science.

[27]  Mark W. Hlawitschka,et al.  One-Group Reduced Population Balance Model for CFD Simulation of a Pilot-Plant Extraction Column , 2010 .

[28]  Christian Drumm,et al.  Process intensification with reactive extraction columns , 2008 .

[29]  D. Marchisio,et al.  Drop breakage in liquid-liquid stirred dispersions : Modelling of single drop breakage , 2007 .

[30]  S. Hartland,et al.  Unified Correlations for the Prediction of Drop Size in Liquid−Liquid Extraction Columns , 1996 .

[31]  Eckhart Blaß,et al.  Dynamic behaviour and simulation of a liquid‐liquid extraction column , 1991 .

[32]  Lawrence L. Tavlarides,et al.  Description of interaction processes in agitated liquid-liquid dispersions , 1977 .

[33]  Robert McGraw,et al.  Description of Aerosol Dynamics by the Quadrature Method of Moments , 1997 .

[34]  R. Fox,et al.  Application of the direct quadrature method of moments to polydisperse gas–solid fluidized beds , 2004 .

[35]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[36]  M. Goodson.  Stochastic Solution of Multi-Dimensional Population Balances , 2007 .

[37]  Solution of the droplet breakage equation for interacting liquid–liquid dispersions: a conservative discretization approach , 2004 .

[38]  Hans-Jörg Bart,et al.  Droplet population balance modelling—hydrodynamics and mass transfer , 2006 .

[39]  M. J. Slater,et al.  Liquid-liquid extraction equipment , 1994 .

[40]  Simulation of the transient behaviour of a stirred liquid/liquid extraction column , 1996 .