| Summary: | Thesis (MSc (Mathematics))--University of Stellenbosch, 2009. === ENGLISH ABSTRACT: Packed beds are widely used in industry to improve the total contact area between two
substances in a multiphase process. The process typically involves forced convection of
liquid or gas through either structured or dumped solid packings. Applications of such
multiphase processes include mass transfer to catalyst particles forming the packed bed and
the adsorption of gases or liquids on the solid packing.
An experimental study on the determination of air flow pressure drops over different
packingmaterialswas carried out at the Telemark University College in Porsgrunn,Norway.
The packed bed consisted of a cylindrical column of diameter 0.072m and height 1.5m, filled
with different packingmaterials. Air was pumped vertically upwards through a porous distributor
to allow for a uniform inlet pressure. Resulting pressure values were measured at
regular height intervals within the bed. Due to the geometric nature of a Raschig ring packing
wall effects, namely the combined effects of extra wall shear stress due to the column
surface and channelling due to packing adjacent to a solid column surface, were assumed to
be negligible.
Several mathematical drag models exist for packed beds of granular particles and an
important question arises as to whether they can be generalized in a scientific manner to
enhance the accuracy of predicting the drag for different kinds of packing materials. Problems
with the frequently used Ergun equation, which is based on a tubular model for flow
between granules and then being empirically adjusted, will be discussed. Some theoretical
models that improve on the Ergun equation and their correlation with experimental work
will be discussed. It is shown that a particular pore-scale model, that allows for different geometries
and porosities, is superior to the Ergun equation in its predictions. Also important
in the advanced models is the fact that it could take into account anomalies such as dead
zones where no fluid transport is present and surfaces that do neither contribute to shear
stress nor to interstitial form drag. The overall conclusion is that proper modelling of the
dynamical situation present in the packing can provide drag models that can be used with
confidence in a variety of packed bed applications. === AFRIKAANSE OPSOMMING: Gepakte materiaal strukture word in die industrie gebruik om die kontak area tussen twee
stowwe in meervoudige faseprosesse te vergroot. Die proses gaan gewoonlik gepaard met
geforseerde konveksie van ’n vloeistof of ’n gas deur gestruktureerde of lukrake soliede
gepakte strukture. Toepassings van sulke meervoudige faseprossese sluit onder andere in
die massa-oordrag na katalisator partikels wat die gepakte struktuur vorm of die absorpsie
van gasse of vloeistowwe op die soliede gepakte elemente.
’n Eksperimentele ondersoek oor die drukval van veskillende gepakte elemente in ’n
kolom is gedoen by die Telemark University College in Porsgrunn, Noorweë. Die gepakte
struktuur het bestaan uit ’n kolommet ’n diameter van 0.072m en ’n hoogte van 1.5m. Lug is
vertikaal opwaarts gepomp deur ’n poreuse plaat wat gesorg het vir ’n benaderde uniforme
snelheidsprofiel. Die druk is toe op intervalle deur die poreuse struktuur gemeet. In die
studie is die effekte van die eksterne wande, nl. die bydrae van die wand se wrywing en die
vorming van kanale langs die kolom wand, as weglaatbaar aanvaar.
Daar bestaan baie wiskundige dempingsmodelle vir gepakte strukture wat uit korrels
saamgestel is. ’n Belangrike vraag kan dus gevra word, of laasgenoemde modelle veralgemeen
kan word op ’n wetenskaplike manier om die demping deur verskillende gepakte
strukture akkuraat te kan voorspel. Probleme wat ontstaan het met die wel bekende Ergun
vergelyking, wat gebaseer is op ’n kapillêre model en wat toe verder aangepas is deur empiriese
resultate van uniforme sfere, sal bespreek word. Teoretiesemodelle wat verbeteringe
op die Ergun vergelyking voorstel sal bespreek word en vergelyk word met eksperimentele
data. Daar word ook gewys dat ’n spesifieke porie-skaal model, wat aanpasbaar is vir verskillende
geometrieë en porositeite, in baie gevalle beter is as die Ergun vergelyking. ’n
Ander baie belangrike aspek van gevorderde modelle is die moontlikheid om stagnante gebiede
in die gepakte strukture in ag te neem. Laasgenoemde gebiede sal die totale kontak
area sowel as die intermediêre vorm demping verlaag. Die gevolgtrekking is dat wanneer
deeglike modulering van dinamiese situasies in die industrie gedoen word kan dempings
modelle met vertroue op ’n verskeidenheid gepakte strukture toegepas word.
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