Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: CHR. BOYADJIEV
Pages: [131] - [150]
Received Date: December 12, 2012; Revised January 26, 2013
Submitted by:
The column apparatuses are main devices for solution of technological
and ecological problems in chemical engineering. A new approach of the
column apparatuses modelling on the base of two steps models -
diffusion type of model (for qualitative analysis) and average
concentration model (for quantitative analysis) is presented.
The diffusion type of models are obtained on the base of the physical
approximations of the mechanics of continua, where the mathematical
point is equivalent to a small (elementary) physical volume, which is
sufficiently small with respect to the apparatus volume, but at the
same time sufficiently large with respect to the intermolecular
volumes of the medium. As a result, the mathematical model is mass
balance in this elementary volume in convection-diffusion equation
form.
The diffusion type of models describe chemical and mass transfer
processes in column apparatuses in the cases of one, two or three
phases systems, where the solid phase is reagent, catalytic or packed
bad. A qualitative analysis of these models is presented, using
generalized (dimensionless) variables, where the characteristic
(inherent) scales are the maximal or average values of the variables.
As a result is possible to be identified the main physical effect, the
small physical effect and the very small (negligible) physical effect,
which must be neglected because it is not possible to be measured
experimentally. The diffusion type of models are the base for the
creation of the average concentration models.
The using of the diffusion type of models for quantitative analysis of
the processes in column apparatuses is not possible because the
velocity function in the convection-diffusion equation is unknown. The
problem can be avoided if the average values of the velocity and
concentration over the cross-sectional area of the column are used,
i.e., the medium elementary volume (in the physical approximations of
the mechanics of continua) will be equivalent to a small cylinder with
radius equal to the column radius and a height, which is sufficiently
small with respect to the column height and at the same time
sufficiently large with respect to the intermolecular distances in the
medium.
The average concentration models permit to analyze the effect of the
radial nonuniformities of the velocity and the concentration on the
process efficiency in the column and to solve the scale-up problem.
The new approach of the column apparatuses modelling is used for
modelling of physical and chemical absorption, chemical adsorption,
homogeneous and heterogeneous (catalytic) chemical reactions, airlift
reactors for chemical and photochemical reactions.
mathematical modelling, mechanics of continua, column apparatus, diffusion type of model, average concentration of model.
