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Haris
Siampanis Degree:
Ph.D., Chemical Engineering
Advisor:
Christos Georgakis
Degree:
M.Sc.
Candidate, Chemical Engineering
Research
Project:
“Towards a Novel Approach in Solving
Population Balance Equations that account
for Crystal Size and Shape”
Project
Description: A wide range of
industries such as pharmaceuticals,
minerals, food and petrochemicals use
crystallization for separation and
purification purposes. Crystallization is
the process of formation of solid crystals
from a homogeneous solution. According to
Ramhkrisna, Population Balance Equation (PBE)
is the mathematical description of the
change in particle identities during a
process (such as crystallization). Although
a lot of research efforts have led to the
development of various numerical techniques
for the solution of PBEs a lack of a more
generalized approach which can be applied in
multi-dimensional PBEs is observed. Evidence
from previous research efforts, suggests
that the General Gamma Distribution may be
able to describe a PBE accurately. The
overall project goal aims to provide the
tools to solve PBEs by assuming the solution
form to be a linear combination of one or
two 3-parameter General Gamma Distribution.
In order to implement this idea it is
suggested to express the number density
function n(x, t) as the three-parameter
General Gamma distribution. This expression
gives the flexibility to extend the system
in a more general multi-dimensional system
that can be used to describe the crystal
shape. Starting from the fundamental
equation for 1-dimensional PBE, the number
density function n(x, t) is replaced by the
General Gamma three-parameter distribution.
The first parameter p1>0 is a
scale parameter, and the other two p2>0
and p3>0 are shape parameters. To
calculate the p1, p2,
p3 one needs to take three
moments and build a system of three
differential equations for the time
dependence of three parameters. At each time
t the external conditions of the overall PBE
will determine the value of supersaturation
and thus the crystal growth rate.
Runge-Kutta45 method is employed to
calculate the time evolution of p1,
p2, p3. The initial
used basis set consists of the simple
functions {1,x,x2,x3,…}.
After rescaling the method another set of
basis comprises of {1,ξ,ξ2,ξ3,…}
is used. A more accurate solution might be
possible by projecting the PBE along a third
set of basis that is orthogonal in the (0,+ )
interval and to this direction Laguerre
polynomials are the next to be explored.
The same procedure is to be followed for the
two gamma distributions that are set equal
to the number density function. The new
system with the 7 parameters is solved and
the models with one and two gamma
distributions are compared. The residuals
and real distribution data will define the
best appropriate model.
Education &
Experience:
National Technical
University of Athens (NTUA)
M.Sc, Organic
Industrial Engineering,
B.Sc. in Chemical Engineering
Funding:
Tufts University
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Graduate Students:
Fernando Lima
Foteini Makrydaki
Praveen Prasanna
Lisa Schupmann
Sze Wing Wong |
