Solution of inverse problem for the kinetic equation
of mass crystallization
Fedorov S.P.
One of the bases of functioning any chemical production is a mathematical model of the
corresponding process which consists generally of a system of conservation equations describing the
process as a phenomenon and of kinetic coefficients and relations included into them, e.g.
for the rate of crystals growth and formation in mass crystallization processes. When the said
equations are based on the principles of physical modelling and have been sufficiently well
substantiated formally at present, then their ending kinetic relations should be set a priory and
found during the treatment of experimental data on the process kinetics, e.g. using methods of
mathematical planning. But the information obtained by these statistical methods is often incomplete
or distorted because of low resolution, i.e. an initial direct problem is not, in fact, closed
and thus it has no practical value for some specific production. To be able to carry out right
interpretation of experimental data and to have reliable information about kinetic relations
inverse problems on physical basis, are required, in which the main process mechanisms should be
taken into account, as well as their correct solution. At the same time it is necessary
to know that the more number of such mechanisms is considered in the problem, the less correct is it,
that’s why the level of generalization should have some reasonable limit.
For the practical solving of such return problem of the kinetics of mass crystallization
the program is developed, allowing to calculate the basic kinetic dependences for rate of crystals growth and
rate of formation on experimental data which acquisition does not demand too big efforts.
The theory of this problem explicitly is considered in the
// Журн. физ. химии (Journal of physical chemistry). 1990. V. 64. № 7. P. 1767.
