Article,
Modeling and simulation of crystallization processes using parsival
Chemical Engineering Science, 56 (7): 2575-2588 (2001)
Abstract
Mathematical models describing particle-size distributions in crystallization
processes are of a challenging complexity. Depending on the considered
physical phase system and the considered process, mathematical models
of crystallization processes include phenomena such as primary nucleation,
crystal growth, fines dissolution as well as agglomeration and/or
breakage (attrition) of crystals. From a numerical point of view,
agglomeration and breakage of crystals add particular (quadratic)
complexity, since all particle sizes are connected by integral terms.
A new powerful algorithm for the treatment of all these structures
is presented in this paper. The method -- called Galerkin h-p method
-- is based on a generalized finite-element scheme with self-adaptive
grid- and order construction and is connected to a time discretization
of Rothe's type. The algorithm can be applied to all combinations
of the phenomena discussed above and needs no additional information
on the form of the particle-size distribution. The numerical algorithm
and the user-interface was implemented using object-oriented concepts
leading to the simulation package P (Pticle Sze euation). The paper
presents some basic features of P and the numerical algorithm as
well as one illustrating example.
