466
S. Schiele et al.
the crystals. This led to a higher supersaturation, which again led to higher growth
rates. These higher growth rates were therefore able to compensate for the error that
is made for the surface area.
In conclusion, a procedure to accurately model agglomeration and growth of
crystals with a 2D population balance was proposed. The population balance equation
considers the volume and surface area of the particles as internal coordinates and
was therefore able to conserve both of these values upon agglomeration. The growth
is also expressed with respect to growth of volume and area. The second subsection
summarizes how both of these rates can be determined. While the growth rate of the
volume was determined on a straightforward way, the growth rate of the surface area
needed to be estimated with a Monte Carlo based scheme. The scheme proposed
here was applied for potash alum crystals but is formulated in a way that it can be
applied to other material systems.
5 Integrated Crystallization Modelling in Dyssol
The crystallization models proposed in the previous sections are able to describe
the crystallization phenomena growth and agglomeration in an accurate way; however, they are computationally expensive. They are, therefore, with currently available hardware hardly suitable for process simulations that span long process times
and include complex flowsheets. There are, however, simpler crystallization models
available in the literature, that are able to describe several crystallization phenomena
simultaneously, and have less computational cost. A case study on the implementation of such a crystallization process within Dyssol was presented by Kulozik et al.
[7].
Kulikov et al. [50] study the performance of the dynamic flow sheet integration platform CHEOPS [51]—that is in some ways similar to Dyssol—based on an
integrated crystallization flowsheet. Therefore, a similar process was implemented
for Dyssol and compared to the results of Kulikov et al. [50]. The main difference
between CHEOPS and Dyssol is that CHEOPS is used to couple models that are
generated in different simulation environments. Dyssol now allows simulations in
one combined software package that can be used to model each unit operation and
couple different unit operations to form a flowsheet.
The flowsheet of Kulikov et al. [50] contains four units: (1) a mixed suspension
mixed product removal (MSMPR) crystallizer, (2) a hydrocyclone, (3) an evaporator
and (4) an ideal mixer. For all of the units a model was implemented in Dyssol. They
were then combined to an integrated flowsheet and Dyssol was used to simulate the
behavior of this exemplary process over a process time of 72 h. The first two of the
mentioned units will be briefly explained in the following sections. The mixer is
considered trivial and is not explained. It accepts two feed streams that are ideally
mixed to a product stream of the mixer. The evaporator is implemented in a way that
a constant ratio of pure solvent is withdrawn to concentrate its feed. It has a vapor
stream and a concentrate stream as outputs.
S. Schiele et al.
the crystals. This led to a higher supersaturation, which again led to higher growth
rates. These higher growth rates were therefore able to compensate for the error that
is made for the surface area.
In conclusion, a procedure to accurately model agglomeration and growth of
crystals with a 2D population balance was proposed. The population balance equation
considers the volume and surface area of the particles as internal coordinates and
was therefore able to conserve both of these values upon agglomeration. The growth
is also expressed with respect to growth of volume and area. The second subsection
summarizes how both of these rates can be determined. While the growth rate of the
volume was determined on a straightforward way, the growth rate of the surface area
needed to be estimated with a Monte Carlo based scheme. The scheme proposed
here was applied for potash alum crystals but is formulated in a way that it can be
applied to other material systems.
5 Integrated Crystallization Modelling in Dyssol
The crystallization models proposed in the previous sections are able to describe
the crystallization phenomena growth and agglomeration in an accurate way; however, they are computationally expensive. They are, therefore, with currently available hardware hardly suitable for process simulations that span long process times
and include complex flowsheets. There are, however, simpler crystallization models
available in the literature, that are able to describe several crystallization phenomena
simultaneously, and have less computational cost. A case study on the implementation of such a crystallization process within Dyssol was presented by Kulozik et al.
[7].
Kulikov et al. [50] study the performance of the dynamic flow sheet integration platform CHEOPS [51]—that is in some ways similar to Dyssol—based on an
integrated crystallization flowsheet. Therefore, a similar process was implemented
for Dyssol and compared to the results of Kulikov et al. [50]. The main difference
between CHEOPS and Dyssol is that CHEOPS is used to couple models that are
generated in different simulation environments. Dyssol now allows simulations in
one combined software package that can be used to model each unit operation and
couple different unit operations to form a flowsheet.
The flowsheet of Kulikov et al. [50] contains four units: (1) a mixed suspension
mixed product removal (MSMPR) crystallizer, (2) a hydrocyclone, (3) an evaporator
and (4) an ideal mixer. For all of the units a model was implemented in Dyssol. They
were then combined to an integrated flowsheet and Dyssol was used to simulate the
behavior of this exemplary process over a process time of 72 h. The first two of the
mentioned units will be briefly explained in the following sections. The mixer is
considered trivial and is not explained. It accepts two feed streams that are ideally
mixed to a product stream of the mixer. The evaporator is implemented in a way that
a constant ratio of pure solvent is withdrawn to concentrate its feed. It has a vapor
stream and a concentrate stream as outputs.