Modeling of Column Apparatus Processes

464 Pages·2018·9.16 MB·English

by  Christo Boyadjiev

Heat and Mass Transfer
Christo Boyadjiev · Maria Doichinova 
Boyan Boyadjiev
Petya Popova-Krumova
Modeling
of Column
Apparatus
Processes
Second Edition
Heat and Mass Transfer
Series editors
D. Mewes, Hannover, Germany
F. Mayinger, München, Germany
Heat and mass transfer occur in coupled form in most production processes and
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More information about this series at http://www.springer.com/series/4247
Christo Boyadjiev Maria Doichinova
(cid:129)
Boyan Boyadjiev Petya Popova-Krumova
(cid:129)
Modeling of Column
Apparatus Processes
Second Edition
123
Christo Boyadjiev Boyan Boyadjiev
Institute of Chemical Engineering (IChE) ChemEng Ltd.
BulgarianAcademy of Sciences (BAS) Sofia
Sofia Bulgaria
Bulgaria
PetyaPopova-Krumova
Maria Doichinova Institute of Chemical Engineering (IChE)
Institute of Chemical Engineering (IChE) BulgarianAcademy of Sciences (BAS)
BulgarianAcademy of Sciences (BAS) Sofia
Sofia Bulgaria
Bulgaria
ISSN 1860-4846 ISSN 1860-4854 (electronic)
Heat andMassTransfer
ISBN978-3-319-89965-7 ISBN978-3-319-89966-4 (eBook)
https://doi.org/10.1007/978-3-319-89966-4
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The logic and the intuition are the
foundation of the human knowledge and the
science
This book is dedicated to our Institute of
Chemical Engineering Bulgarian Academy of
Sciences
Christo Boyadjiev
Maria Doichinova
Boyan Boyadjiev
Petya Popova-Krumova
Preface
The complex processes in the column apparatuses have a combination of hydro-
dynamic processes, convective and diffusive mass (heat) transfer processes, and
chemical reactions between the reagents (components of the phases).
The fundamental problemin the column apparatuses modelingis a result ofthe
complicated hydrodynamic behavior in the columns, and thus, the velocity distri-
butions in the phases and the interphase boundaries in the columns are unknown.
Thisproblemcanbecircumventedifthephaseboundaryprocessesarereplacedby
equivalentvolumetricprocessesinthephasesandtheunknowndistributionsofthe
phase velocities are replaced by the average velocity of the cross section of the
columns.
The column apparatuses are possible to be modeled, using a new approach on
the base of the physical approximations of the mechanics of continua, where the
mathematicalpointisequivalenttoasmall(elementary)physicalvolume,whichis
sufficiently small with respect to the apparatus volume, but at the same time suf-
ficiently large with respect to the intermolecular volumes in the medium.
The mathematical models of the processes in the column apparatuses, in the
physicalapproximationsofthemechanicsofcontinua,willbethemassbalancesin
the phase volumes (phase parts in the elementary volume) between the convective
masstransfer(asaresultofthefluidmotions),thediffusivemasstransfer(asaresult
of the concentration gradients) and the volume mass sources (sinks) (as a result of
chemicalreactionsorinterphasemasstransfer).Inthecaseofbalancebetweenthese
three effects, the mass transfer process is stationary, or in the opposite case, the
process is non-stationary. These convection–diffusion-type models permit to be
madeaqualitativeanalysisoftheprocesses(models).Onthisbase,itispossibleto
obtain the main, small, and slight physical effects (mathematical operators). The
slight effects (operator) must be rejected because they are not experimentally
observable.Asaresult,theprocessmechanismidentificationispossibletobemade.
These models permit to determinate the mass transfer resistances in the gas and
liquidphasesandtheoptimaldispersionsystemfindingingasabsorption(gas–liquid
drops or liquid–gas bubbles). The convection–diffusion models are a base of the
ix
x Preface
average-concentrationmodels,whichallowaquantitativeanalysisoftheprocesses
incolumn apparatuses.
Theconvection–diffusionmodelsarepossibletobeusedforqualitativeanalysis
only, because the velocity distribution functions are unknown and cannot be
obtained.Theproblemcanbeavoidedbytheaverage-concentrationmodels,where
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
approximationsofthemechanicsofcontinua)willbeequivalenttoasmallcylinder
with a real 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 inter-
molecular distances in the medium.
Theconvection–diffusionmodelsandaverage-concentrationmodelsareusedfor
the qualitative and quantitative analyses of the processes in single phase (simple
and complex chemical reactions), two phase (absorption, adsorption, and catalytic
processes), and three phase (two-phase absorbent processes and absorption–ad-
sorption processes).
In many cases, the computer modeling of the processes in column apparatuses,
on the base of a new approach, using the convection–diffusion-type model and
average-concentration-typemodel,doesnotallowadirectuseoftheMATLAB.In
these cases, it is necessary to create combinations of MATLAB with appropriate
algorithms.
Practically, the new type models are characterized by the presence of small
parameters at the highest derivatives. As a result, the use of the conventional
software for solving of the model differential equations is difficult. This difficulty
may be eliminated by an appropriate combination of MATLAB and perturbation
method.
In the cases of countercurrent gas–liquid or liquid–liquid processes, the mass
transfer process models are presented in two-coordinate systems, because in
one-coordinate system one of the equations has not a solution by reason of the
negative equation Laplacian value. A combination of an iterative algorithm and
MATLABmustbeusedforthesolutionsoftheequationssetindifferentcoordinate
systems.
Inthecasesofanon-stationaryadsorptioningas–solidsystems,thepresenceof
mobile (gas) and immobile (solid) phases in the conditions of longtime processes
leadstothenon-stationaryprocessintheimmobilephaseandstationaryprocessin
themobilephase,practically.Asaresult,differentcoordinatesystemsmustbeused
in the gas- and solid-phase models. A combination of a multi-step algorithms and
MATLABmustbeusedforthesolutionsoftheequationssetindifferentcoordinate
systems.
The convection–diffusion and average-concentration models, where the radial
velocity component is equal to zero in the cases of a constant axial velocity radial
non-uniformity along the column height, are presented. There are many cases of
industrial columns, where these conditions are not satisfied. The models of
chemical, absorption, adsorption, and catalytic processes in the cases of an axial
Preface xi
modification of the radial non-uniformity of the axial velocity component, where
the radial velocity component is not equal to zero, are presented too.
Theabsorptionprocessintensificationofanaveragesolublegasisrealizedwith
anewpatentintwo-zonecolumn,wheretheupperzoneisphysicalabsorptionina
gas–liquid drops system (intensification of the gas-phase mass transfer) and the
lower zone is a physical absorption in liquid–gas bubbles system (intensification
of the liquid-phase mass transfer).
The solid fuel combustion in the thermal power plants, which use sulfur-rich
fuels, poses the problem of sulfur dioxide removal from the waste gases. This
problemiscomplicatedbythefactthatitisrequiredtopurifyhugeamountsofgas
with low sulfur dioxide concentration. The huge gas amounts need big apparatus
size, which is possible to be decreased if the removal process rate is maximized.
The purification of large amounts of waste gases from combustion plants used
countercurrentabsorbers,wherethegasvelocity(asaresultandabsorbersdiameter
too) is limited by the rate of the absorbent drops fall in an immobile gas medium.
A new patent avoids this disadvantage, where co-current sulfur dioxide absorption
is realized.
A new patent solves the problem of absorbent regeneration, using two-step
process—physical absorption of sulfur dioxide by water and adsorption of sulfur
dioxide from the water solution by synthetic anionite particles. The adsorbent
regeneration is made by ammonium hydroxide solution. The obtained ammonium
sulfite solution is used (after reaction with nitric acid) for concentrated sulfur
dioxide and ammonium nitrate solution production.
TheIntroduction(Chap.1)concernslinearmasstransfertheory(modeltheories,
boundarylayertheory,two-phaseboundarylayers),masstransferincountercurrent
flows (velocity and concentration distribution, comparison analysis), nonlinear
mass transfer (influence on the hydrodynamics, boundary conditions, boundary
layer theory, Marangoni effect), interphase mass transfer resistances (film theory
and boundary layer theory approximations), three-phase mass transfer processes
(physical, hydrodynamic, and interphase mass transfer models, absorption mecha-
nism and kinetics).
Part I focuses on the convection–diffusion-type models for qualitative analysis
of the column apparatus processes. Chapter 2 presents one-phase chemical pro-
cesses in column reactors (simple and complex chemical reaction kinetics),
approximations of the model (short-column and high-column model, effect of the
chemical reaction rate), effect of the radial non-uniformity of the velocity distri-
bution (conversion degree, concentration distribution, influence of the velocity
radialnon-uniformityshape,scaleeffect,backmasstransfermechanism),examples
(effect of the tangential flow, simultaneous mass and heat transfer processes, cir-
culation zones in column apparatuses, mass transfer in one-phase countercurrent
flow). Chapter 3 presents the convection–diffusion-type models of two-phase pro-
cesses (physical and chemical absorption, physical and chemical adsorption, cat-
alytic processes in the cases of physical and chemical adsorption mechanism),
examples (airlift reactors, airlift photobioreactor, moisture adsorption). Chapter 4
presents models of three-phase processes in the cases of two-phase absorbent