Dynamic evolution of PSD in continuous flow processes: A comparative study of fixed and moving grid numerical techniques

Abstract The present study provides a comprehensive investigation on the numerical solution of the dynamic population balance equation (PBE) in continuous flow processes. Specifically, continuous particulate processes undergoing particle aggregation and/or growth are examined. The dynamic PBE is numerically solved in both the continuous and its equivalent discrete form using the Galerkin on finite elements method (GFEM) and the moving grid technique (MGT) of Kumar and Ramkrishna [1997. Chemical Engineering Science 52, 4659–4679], respectively. Numerical simulations are carried out over a wide range of variation of particle aggregation and growth rates till the dynamic solution has reached its final steady-state value. The performance of the two numerical methods is assessed by a direct comparison of the calculated particle size distributions and/or their moments to available steady-state analytical solutions.

[1]  B. Finlayson.  Nonlinear analysis in chemical engineering , 1980 .

[2]  J. Seinfeld,et al.  Numerical solution of the dynamic equation for particulate systems , 1978 .

[3]  Michael J. Hounslow,et al.  Finite-element methods for steady-state population balance equations , 1998 .

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

[5]  D. Ramkrishna.  The Status of Population Balances , 1985 .

[6]  Costas Kiparissides,et al.  Part II: Dynamic evolution of the particle size distribution in particulate processes undergoing simultaneous particle nucleation, growth and aggregation , 2005 .

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

[8]  Stelios Rigopoulos,et al.  Finite‐element scheme for solution of the dynamic population balance equation , 2003 .

[9]  Costas Kiparissides,et al.  Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation , 2004 .

[10]  Doraiswami Ramkrishna,et al.  Efficient solution of population balance equations with discontinuities by finite elements , 2002 .

[11]  M. Hounslow,et al.  A discretized population balance for nucleation, growth, and aggregation , 1988 .

[12]  Costas Kiparissides,et al.  Part III: Dynamic evolution of the particle size distribution in batch and continuous particulate processes: A Galerkin on finite elements approach , 2005 .

[13]  Adrian Sandu,et al.  A framework for the numerical treatment of aerosol dynamics , 2003 .

[14]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[15]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles , 1997 .

[16]  M. Hounslow,et al.  Adjustable discretized population balance for growth and aggregation , 1995 .