15 Compartmental Population Balances by Means of Monte Carlo Methods
545
As a second step, the combination of the findings above in an operator splitting
approach for the full simulation of a compartmental network has been sketched. It
has been found that:
• the computationally advantageous event-driven simulation technique can be also
used for the simulation of smaller time steps than the intrinsic MC time step—
making this method applicable for a network of PBE compartments (like already
discussed in [51]).
• the merging techniques introduced in [23] can be used for the simulation of particle transport between single compartments. (These findings have already been
presented on a more complicated system in [57], the here presented description
of the simulation algorithm is, however, far more detailed.)
• out of 4 case studies of a flow-sheet with increasing degree of complexity,
4 conventional MC methods can simulate the 3 simplest cases while merging techniques
are needed for the simulation of the most complex case (this finding has not been
published prior to this work).
Acknowledgements This work is supported by the DFG (Deutsche Forschungsgemeinschaft)
within the priority program SPP 1679 “Dynamic flowsheet simulation of interconnected solids
processes” [KR 1723/15–1,2&3].
References
1. Ramkrishna, D.: In: Population Balances: Theory and Applications to Particulate Systems in
Engineering, 1st edn., Academic (2000). ISBN 978–0-12-576970-9
2. Ramkrishna, D., Singh, M.R.: Population balance modeling: current status and future prospects.
Ann. Rev. Chem. Biomol. Eng. 5, 123–146 (2014)
3. Schwarzer, H.-C., Peukert, W.: Combined experimental/numerical study on the precipitation
of nanoparticles. AIChE J. 50(12), 3234–3247 (2004)
4. Sommer, M., Stenger, F., Peukert, W., Wagner, N.J.: Agglomeration and breakage of nanoparticles in stirred media mills−a comparison of different methods and models. Chem. Eng. Sci.
61(1), 135–148 (2006)
5. Peglow, M., Kumar, J., Heinrich, S., Warnecke, G., Tsotsas, E., Mörl, L., et al.: A generic
population balance model for simultaneous agglomeration and drying in fluidized beds. Chem.
Eng. Sci. 62(1–2), 513–532 (2007)
6. Kraft, M.: Modelling of particulate processes. KONA Powder Particle J. 23, 18–35 (2005)
7. Kiparissides, C.: Challenges in particulate polymerization reactor modeling and optimization:
a population balance perspective. J. Process. Control. 16(3), 205–224 (2006)
8. Bhole, M.R., Joshi, J.B., Ramkrishna, D.: CFD simulation of bubble columns incorporating
population balance modeling. Chem. Eng. Sci. 63(8), 2267–2282 (2008)
9. Schütz, S., Gorbach, G., Piesche, M.: Modeling fluid behavior and droplet interactions during
liquid–liquid separation in hydrocyclones. Chem. Eng. Sci. 64(18), 3935–3952 (2009)
4 The four case studies comprise: (1) a flowsheet without recycle stream and screen units, (2) a
flowsheet with one recycle stream and without sieve unit, (3) a flowsheet with one sieve unit and
without recycle stream and (4) a flowsheet with a recycle stream and a sieve unit.
545
As a second step, the combination of the findings above in an operator splitting
approach for the full simulation of a compartmental network has been sketched. It
has been found that:
• the computationally advantageous event-driven simulation technique can be also
used for the simulation of smaller time steps than the intrinsic MC time step—
making this method applicable for a network of PBE compartments (like already
discussed in [51]).
• the merging techniques introduced in [23] can be used for the simulation of particle transport between single compartments. (These findings have already been
presented on a more complicated system in [57], the here presented description
of the simulation algorithm is, however, far more detailed.)
• out of 4 case studies of a flow-sheet with increasing degree of complexity,
4 conventional MC methods can simulate the 3 simplest cases while merging techniques
are needed for the simulation of the most complex case (this finding has not been
published prior to this work).
Acknowledgements This work is supported by the DFG (Deutsche Forschungsgemeinschaft)
within the priority program SPP 1679 “Dynamic flowsheet simulation of interconnected solids
processes” [KR 1723/15–1,2&3].
References
1. Ramkrishna, D.: In: Population Balances: Theory and Applications to Particulate Systems in
Engineering, 1st edn., Academic (2000). ISBN 978–0-12-576970-9
2. Ramkrishna, D., Singh, M.R.: Population balance modeling: current status and future prospects.
Ann. Rev. Chem. Biomol. Eng. 5, 123–146 (2014)
3. Schwarzer, H.-C., Peukert, W.: Combined experimental/numerical study on the precipitation
of nanoparticles. AIChE J. 50(12), 3234–3247 (2004)
4. Sommer, M., Stenger, F., Peukert, W., Wagner, N.J.: Agglomeration and breakage of nanoparticles in stirred media mills−a comparison of different methods and models. Chem. Eng. Sci.
61(1), 135–148 (2006)
5. Peglow, M., Kumar, J., Heinrich, S., Warnecke, G., Tsotsas, E., Mörl, L., et al.: A generic
population balance model for simultaneous agglomeration and drying in fluidized beds. Chem.
Eng. Sci. 62(1–2), 513–532 (2007)
6. Kraft, M.: Modelling of particulate processes. KONA Powder Particle J. 23, 18–35 (2005)
7. Kiparissides, C.: Challenges in particulate polymerization reactor modeling and optimization:
a population balance perspective. J. Process. Control. 16(3), 205–224 (2006)
8. Bhole, M.R., Joshi, J.B., Ramkrishna, D.: CFD simulation of bubble columns incorporating
population balance modeling. Chem. Eng. Sci. 63(8), 2267–2282 (2008)
9. Schütz, S., Gorbach, G., Piesche, M.: Modeling fluid behavior and droplet interactions during
liquid–liquid separation in hydrocyclones. Chem. Eng. Sci. 64(18), 3935–3952 (2009)
4 The four case studies comprise: (1) a flowsheet without recycle stream and screen units, (2) a
flowsheet with one recycle stream and without sieve unit, (3) a flowsheet with one sieve unit and
without recycle stream and (4) a flowsheet with a recycle stream and a sieve unit.