N° d’ordre: 308-96 Annee 1996 ECOLE DU PETROLE ET DES MOTEURS UNIVERSITE CLAUDE BERNARD (LYON I) THESE PRESENTEE A L’UNIVERSITE CLAUDE BERNARD (LYON I) POUR L'DETENTION DU DIPLOME DE DOCTORAT DE L’UNTVERSITE CLAUDE BERNARD (LYON I) EN GENIE DES PROCEDES PAR LOH KONG MING Master ofScience — University of Manchester Institute of Science and Technology (UK) Speciality “Petrochemicals and Hydrocarbon Chemistry" Sujet de la these: RECEIVED 0CT *51998 ETUDE DE LA COMPETITION D’ADSORPTION ENTRE LES COMPOSES OXYGENES ET LES HYDROCARBURES SUR LES TAMIS MOLECULAIRES \S ^ Soutenue le 29 novembre 1996 devant la commission d’examen: B. BERNAUER Rapporteur D. CLAUSSE Rapporteur M. GAILLARD C. JALLUT S. JULLIAN J. LIETO President
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N° d’ordre: 308-96 Annee 1996
ECOLE DU PETROLE ET DES MOTEURS
UNIVERSITE CLAUDE BERNARD (LYON I)
THESE
PRESENTEE A L’UNIVERSITE CLAUDE BERNARD (LYON I)POUR L'DETENTION DU DIPLOME DE
DOCTORAT DE L’UNTVERSITE CLAUDE BERNARD (LYON I)EN GENIE DES PROCEDES
PAR
LOH KONG MING
Master of Science — University of Manchester Institute of Science and Technology (UK) Speciality “Petrochemicals and Hydrocarbon Chemistry"
Sujet de la these:
RECEIVED
0CT *51998
ETUDE DE LA COMPETITION D’ADSORPTION ENTRE LES COMPOSES OXYGENES ET LES HYDROCARBURES
SUR LES TAMIS MOLECULAIRES
\S ^
Soutenue le 29 novembre 1996 devant la commission d’examen:
B. BERNAUER RapporteurD. CLAUSSE RapporteurM. GAILLARDC. JALLUT S. JULLIAN J. LIETO President
DISCLAIMER
Portions of this document may be illegible electronic image products. Images are produced from the best available originaldocument.
N° d’ordre: 308-96 AnnSe 1996
ECOLE DU PETROLE UNIVERSITE CLAUDE BERNARDET DES MOTEURS (LYON I)
THESE
PRESENTEE A L’UNTVERSITE CLAUDE BERNARD (LYON I)POUR L’OBTENTION DU DIPLOME DE
DOCTORAT DE L’UNIVERSITE CLAUDE BERNARD (LYON I)EN GENIE DES PROCEDES
PAR
LOH KONG MING
Master of Science - University of Manchester Institute of Science and Technology (UK) Speciality "Petrochemicals and Hydrocarbon Chemistry’’
Sujet de la thkse:
ETUDE DE LA COMPETITION D’ADSORPTION ENTRE LES COMPOSES OXYGENES ET LES HYDROCARBURES
SUR LES TAMIS MOLECULAIRES
Soutenue le 29 novembre 1996 devant la commission d’examen:
B. BERNAUER RapporteurD. CLAUSSE RapporteurM. GAILLARDC. JALLUT S. JULUANJ. LIETO President
Distributeur exclusifEditions Technip, 27 rue Ginoux, 75737 PARIS CEDEX 15
ACKNOWLEDGEMENT
I wish to express my heartfelt thanks and appreciation to the following who had in one way or the other made this work possible.
• Professor J. Lieto from the University of Claude Bernard (Lyon I) who had consented to be the President of the Examination Committee.
• Professor D. Clausse, Dr. J.F. Gaillard, Dr. C. Jallut and Dr. S. Jullian who had kindly agreed to be members of the Examination Committee.
• Staff of Petronas Research and Scientific Services Sen. Bhd. (PRSS) for their contribution towards this project.
• MTBE (Malaysia) Sdn. Bhd. for their assistance and support in the successful completion of this project.
• Staff of Institut Frangais du Petrole (IFP), especially Mr. A. Rojey, Dr. A. Deschamps, Dr. S. Jullian (who was my co-supervisor), Dr. A. Methivier, Mr. B. Tavitian and Mr. A. Barrou which had provided facilities, expert advice and technical support during the course of the work.
• Mr. Mohamad Nor Hashim, a staff of Process Technology Group, Petronas Research and Scientific Services Sdn. Bhd. who had assisted in collecting and analysing the products.
Petronas, PRSS Management and the French Government for the scholarship and encouragement.
2.3.1. Flow modelling 272.3.2. Mass transfer between fluid and solid 29
2.4. PRINCIPLES OF COLON 303. EXPERIMENTAL 37
3.1. DETERMINATION OF THE ADSORPTION ISOTHERM OF 37A BINARY MIXTURE ON AN INDUSTRIAL ZEOLITE3.1.1. Description of the Isotherm Determination Apparatus 3 8
3.1.2. Experimental Procedure 393.1.3. Method of Calculation 43
TABLE OF CONTENTS
3.2. DETERMINATION OF BREAKTHROUGH CURVES OF A 46BINARY OR TERNARY MIXTURES USING COMMERCIAL MOLECULAR SIEVES3.2.1. Description of the Adsorption Breakthrough Curves 46
Determination Apparatus
3.2.2. Experimental Procedure 504. RESULTS AND DISCUSSION 54
4.1. ADSORPTION ISOTHERMS 544.1.1. Adsorption Isotherm of Methanol in n-Hexane 54
4.1.2. Adsorption Isotherm of 1 -Hexene in n-Hexane 614.1.3. Modelling of Isotherms 67
4.2. BREAKTHROUGH CURVES 68
4.2.1. Breakthrough Curves of Methanol or 1-Hexene in 68n-Hexane at Various Operating Conditions
4.2.2. Breakthrough Curves of Methanol and 1-Hexene in 85n-Hexane at Various Operating Conditions
4.3. MODELLING 994.3.1. Simulation of Elution Profile 99
5. CONCLUSION 1036. REFERENCES 141
APPENDICES
Appendix A GC calibration curve for methanol in n-hexane 105
Appendix B To calculate the concentration of adsorbate in the adsorbed and 106fluid phases (method A)
Appendix C To calculate the concentration of adsorbate in the adsorbed and 108fluid phases (method B)
Appendix D Photograph of experimental apparatus 113
Appendix E Sample data sheet of surface analysis 114Appendix F Data sheet of vapour phase adsorption 120Appendix G To calculate volume fractions 130
Appendix H Sample data sheet of simulation results 132
1 INTRODUCTION
The purpose for conducting the study is to investigate the application of molecular
sieves in removing methanol and other oxygenated compounds and to compare
simulated results using a proprietary Institut Francais du Petrole (IFF) computer
programme against experimental data.
Molecular sieves are crystalline aluminosilicates. They are similar to clays and
belonging to a class of minerals known as zeolites. For a long time, their main use
has been restricted to the remove of water from hydrocarbon fractions.
In recent years, the use of molecular sieves for other applications has been
developed particularly in the separation of oxygenated compounds (alcohols, ether,
etc) from hydrocarbon process streams.
With increasing gasoline demand and as a result of lead phase-out programs being
implemented in many countries, alternative octane enhancer such as Methyl
Tertiary Butyl Ether (MTBE) is increasingly being used. MTBE is synthesized
from isobutene and methanol in the presence of a strong acidic ion exchange resin
catalyst. A typical chemical MTBE reaction is as shown below.
CH3 ch3
HjC = C + CH3OH----- *-CH3- C - O -CH3
ch3 ch3
1
Generally, MTBE units are designed with two reactors in series. Most of the
etherification reaction is achieved at elevated temperature in the first reactor and
then partially finished in the second reactor with 90% of the isobutene conversion
taking place in the first and 50% conversion of the remaining isobutene in the
second. 99% conversion can be attained by installing a catalytic distillation
downstream of the second reactor where product MTBE is recovered in the
bottoms and unreacted C4 hydrocarbons and methanol are recovered overhead.
Unreacted methanol is recovered for recycle via a water wash of the C4-methanol
stream followed by a methanol-water distillation.
The near methanol-free C4 raffinate leaves the top of the distillation tower and goes
to the oxygenates remover tower. In the oxygenates removal tower, dimethyl
ether (DME), tertiary buthyl alcohol (TEA), MTBE and residual methanol are
separated from the C4-methanol raffinate stream. These components are
concentrated in the top of the tower and are drawn off with the light ends. The
product C4 raffinate leaves the tower bottom. A schematic flow diagram of a
conventional MTBE process is shown in Figure 1.
2
REACTION PRODUCT SEPARATION OXYGENATE REMOVAL
MeOHMETHANOLRECYCLER
1st 2nd Reactor Reactor
Water
OXYGENATEC4'S
C4'S
MTBE
Isobutylene Rich C4 Feed
MTBE MTBE WATER WASH OXYGENATEREACTORS COLUMN SYSTEM STRIPPER
Figure 1. Conventional MTBE process
REACTION METHANOL RECOVERY SYSTEM OXYGENATE REMOVAL SYSTEM
Isobutylene Rich 04 Stream
ADSORPTION
REGENERATION
METHANOLRECYCLE
MeOH
OXYGENATE FREE C4'S
SPENT REGENERATION FLUID
REGENERATIONFLUID
MTBEMTBE MTBE METHANOL
REACTORS COLUMN ADSORBERSOXYGENATEADSORBERS
Figure 2. UCC's raffinate treatment process
3
Instead of the water wash system, proprietary adsorption processes have been
developed by Union Carbide Corporation (UCC) which use molecular sieves to
adsorb the oxygenates. A schematic diagram of the UCC process is as given in
Figure 2. By using this scheme several advantages are achieved.
For the case of water wash and distillation, two costly towers, expensive ancillary
equipment (pumps, condensers, reboiler) are required. A purge is also required to
remove heavy components or corrosion products that may build up in the closed
extraction-fractionation loop creating potential disposal problems. Likewise during
the striping operation to remove oxygenates, in addition to high capital and utility
costs, the conventional oxygenate stripper often experiences excessive losses of
C4's in the overhead.
From the advantages shown above, it is obvious that a study of the competitive
adsorption between methanol, MTBE, C4 stream, DME, water, and TEA is useful
in understanding both the theoretical as well as the practical aspect of oxygenates
removal and it was the subject of our PhD work.
4
2 BIBLIOGRAPHY
2.1 ADSORPTION
2.1.1 Definition
Adsorption is a surface phenomenon which involves the separation of a substance
from one phase and its accumulation at the surface of another. The adsorbing
phase is termed the adsorbent and the adsorbed material at the surface is called the
adsorbate. Adsorption is differentiated from absorption, a process in which the
substance becomes distributed throughout the solid or liquid. Frequently, it is
difficult to distinguish which is more dominant since both processes can take place
simultaneously and hence the general term sorption is used to described them.
2.1.2 Adsorption Principles
Adsorption may be either a physical or a chemical process and in some cases both
occur simultaneously. Physical adsorption results from the relatively weak Van der
Waals forces comprising both the London dispersion forces and the classical
electrostatic forces (polarization, dipole and quadrupole interactions). Chemical
adsorption involves valency forces whereby a reaction takes place between the
adsorbent and an adsorbate resulting in the formation of a new compound.
Generally, physisorption is differentiated from chemisorption by the following
characteristic:
5
Physical Adsorption Chemisoption
Low heat of adsorption
* approximately equal to heat of
High heat of adsorption
• approximately equal to heat ofcondensation.
Reversible, non-activated and fast.
Monolayer or multilayer.
reaction.Irreversible, activated and slow.
Monolayer only.
2.1.3 Factors Affecting Adsorption
Basically, an adsorption system comprises of the adsorbate, the fluid phase, and the
adsorbent. The extent of adsorption relates to certain properties of the adsorption
system elements and also to conditions they are subjected to e.g. pressure,
temperature, feed velocity, etc.
For adsorbate, properties such as molecular size, molecular structure, polarity and
steric form have significant influence. For adsorbent, characteristics such as surface
area, the physicochemical nature of the surface, porosity and particle size are
important. The composition of the fluid phase in terms of competitive adsorption
can also interact greatly with adsorption capacity.
2.1.4 Industrial Adsorbents
In principle, all microporous materials can be used as adsorbents for purification
and separation. The microporous structure can be characterized by standard
techniques, the most important characteristic being surface area, pore volume and
6
For surface area determination, the most commonly used is the gas adsorption or
the Brunaur-Emmett-Teller (BET) method. Assuming liquid density and hexagonal
close-packing and given that the area of a N2 molecule to be 16.2 A2, the surface
area is taken as the area for monolayer coverage.
The total pore volume is usually determined by helium and mercury densities
displacements. Helium because of its small size and negligible adsorption, gives
total voids; whereas mercury, which do not penetrate into the pores at ambient
pressure gives interparticle voids. The difference between the both gives the total
pore volume.
The pore size distribution is measured by mercury porosimetry for pores larger
than 100 - 150A and by N2 desorption (or adsorption) for 10 - 250 A. For still
smaller pores, molecular sieving is used [1, 2, 3],
Various methods of determining the physical resistance of adsorbent to
degradation are available. Stirred Abrasion and Ro-Tap Abrasion are two such
examples.
Amongst the many types of material which exhibit adsorbent properties, four very
important and industrially used are activated carbon, molecular sieve carbon,
activated alumina and silica gel. However, another class of adsorbents which is
pore size distribution as well as mechanical properties such as bulk density, crush
strength, and attrition resistance.
7
gaining attention is zeolitic molecular sieves. This will be the subject of the present
study.
2.1.5 Zeolites
Zeolites are crystalline aluminosilicates of alkaline or alkaline earth and can be
represented stoichiometrically by
AW(A10),(Si02)y] zHzO
where x and y are integers, n is the valence of cation M and z is the number of
water molecules.
Structurally, zeolites framework consists of a three dimensional network of Si04
and A104 tetrahedra, joined together in various regular arrangements through
shared oxygen, to form an open crystal lattice containing pores of molecular
dimensions into which guest molecules can penetrate this is why they are known as
molecular sieve. Although pure analogs such as silicalite has been prepared, the
Si/Al ratio is commonly between one to five. Each aluminium atom present in the
structure would require an exchangeable cation to balance the negative charge on
the framework. By reducing the number of aluminium atom through substitution
with a silicon atom a systematic transition in adsorptive properties from the
aluminium-rich sieves, which have very high affinities for water and other polar
molecules, to the microporous silicas which are essentially hydrophobic and adsorb
n-paraffin in preference to water. Thus by varying the Si/Al ratio and cationic form,
8
11.3
A
it is possible to alter the adsorptive properties to achieve the selectivity required for
a specific separation.
Intracrystalline difiusivities are determined by the free diameters of the windows.
The size of the windows depends on the number and type of exchanged cations.
Sodalite which has six-membered oxygen ring has a free diameter of about 2.8 A
which allows small polar molecules such as H20 and NH3 to penetrate. Zeolite
with eight-membered oxygen including type A, chabazite and erionite have free
diameter of 4.2 A. Large port zeolites such as type X, Y, and mordenite having
twelve-membered oxygen rings have free diameters of 7 - 7.4 A. The pentasil
zeolites which include ZSM-5, ZSM-11, and silicalite are characterized by an
intermediate channel size formed by ten-membered oxygen rings falls around 5.7
A. Figure 3 provides some illustrated examples of the zeolites framework
w
Figure 3. Schematic representation showing framework structures of (a) zeolite A (b)zeolites X and Y, (c) erionite and (d) chabazite.
a
VIII
2.1.6 Zeolite A
Socialite units are made up with 24 tetrahedra which are arranged in six four-rings
(or square faces) and eight six-rings (or hexagonal-faces). An octahedral
arrangement of sodalite units joined by oxygen bridges through six square faces,
gives the zeolite A framework structure. This arrangement forms a large polyhedral
cage of free diameter of about 11.4 A with eight-membered oxygen windows. A
three dimensional isotropic channel structure constricted by eight-membered
oxygen rings is obtained by stacking these units in a cubic lattice. Zeolite A has a
Si/Al ratio closed to 1 with 12 univalent exchangeable cations per unit cell. Three
distinct cation sites are identified given by Type L, H, and HE as illustrated in Figure
4(a) Depending on the cation types, a 3A sieve is obtained with potassium and a
4A sieve with sodium. The 3A sieve is widely used for drying reactive
hydrocarbons such as olefins in view of its small pores, which exclude the larger
olefin molecules thus preventing reactions.
Figure 4. (a) type A (b) types X and Y
10
2.1.7 Zeolites X and Y
The framework structure of zeolites X and Y consists of an array of eight cages
containing a total of 192 A102 and Si02 tetrahedral units. Sodalite units are linked
via oxygen bridges through four of the eight hexagonal-faces in a tetrahedral
arrangement like carbon atoms in diamond. The resulting structure has a large
cavity or supercage with twelve-membered oxygen rings of free diameter around 7
- 8 A. Depending on the Si/Al ratio, a X zeolite has a ratio between 1-1.5 and a Y
between 1.5 - 3.0. Also the number of exchangeable univalent cations varies from
about 10-12 per cage for X to as low as 6 for high silica Y. The cation
distribution is much more complex with six different sites being identified. Through
ion-exchanged of the cation present, the adsorptive properties as well the
selectivity of zeolites X and Y could be improved.
2.1.8 Pentasil Zeolite
These zeolites have structures characteristic of stacking of double five-ring unit.
ZSM-5 and ZSM-11 are end members of a series of pentasils. Both ZSM-5 and
ZSM-11 have three-dimensional pore systems comprising 10- tetrahedron rings,
intermediate in size between the windows for zeolites A, X, and Y. Wide variation
in the Si/Al ratio is possible, however, typical value of a ZSM-5 zeolite is given in
Figure 5. They are characterized by 2 types of pore system, one consisting of
zig-zag channels of near circular cross-section and the other of straight channels
with elliptical cross-section as in the case of ZSM-11 structure. Adsorptive
properties are determined by the different framework structure and pore size.
11
Figure 5. Schematic diagram of the channel structures of (a) ZSM-5 and (b) ZSM-11 [4]
2.1.9 Characteristics of Major Commercial Zeolites
Table 1 gives the characteristics of some major commercial zeolite adsorbent in the
pelletized form.
Table 1. Characteristics of some major synthetic zeolite sorbents [5]Zeolite Type Major Cation Norminal
Aperture Size, ABulk Density,
kg/m3Water Capacity.
Wt °o
3 A (Linde) K 3 641 203 A (Davidson) K 3 737 21
4A (Linde) Na 4 657 22
4A (Davidson) Na 4 705 23
5 A (Linde) Ca 5 721 21.55 A (Davidson) Ca 5 705 21.7
10X (Linde) Ca 8 641 31.6
13X (Linde) Na 10 609 28.5
13X (Davision) Na 10 689 29.5
Table 2 gives a list of the molecular dimensions of some molecules which are
smaller than the apertures of the zeolite types. Separation of a mixture from the
12
different groups via molecular sieving is theoretically possible. However, in general
separation is normally based on different strengths of different equilibrium amounts
adsorbed rather than on molecular sieving.
Table 2. Molecular dimensions and zeolite aperture sizes [6]
Molecular size incr&zsfcg ~=
He. Nc, Ar. CO Kr.Xc C,H, SF.Oj, CH. uo-C»H,0
C,H. «-C,H„ CF,a," iso-CjH,,CH,OH
Size limit for CH.CN «-C,4Hle CF,C1 iso-C.H,,Ci- ind Bi- CH,NH, etc CHFCl, etc.mordcnitci and CH,Q c,H,a chq,levynite about CH.Br C,H,Br CHBr,here (3-8 A) CO, C.H.OH CHI,
Type 5--------------------------- C,H, C.H.NH, (CH,),CHOHcs, CH,a, lCH,),CHa
.CH,Br, n-C,F,Siae limit for Ni- CHF.G o-C.F.o
mordenite and Linde CHFr n-C,F,.sieve 4A about here tCHjIjNH 8,H.(5:4-0 A) CH,I
Type 4—---------------------- 3,H.Size limit for Ca-rich
chabazxtt Unde sieve5A. Ba-zrolite and{melinite about here(=4-9 Al
Coke formation or slow loss of crystallinity often result in adsorbent deactivation
involving either a loss of equilibrium capacity or an increase in mass transfer
resistance. When sieve is exposed to high temperature and high moisture during
thermal regeneration a slow and irreversible degradation of crystals structure may
occur as in the case of zeolite X which has limited hydrothermal stability. In the
case of zeolite A, under similar conditions, increase in mass transfer resistance
results in partial pore closure.
13
When reactive species such as olefins are present, they form polymeric compounds
which eventually become coke on thermal regeneration resulting in reduced
adsorbent capacity.
2.1.11 Characteristics of the Adsorbate
The physical and chemical character of an adsorbate have significant influence on
adsorption selectivity and rate . For a homologue series of organic molecules in an
aqueous system solubility decreases with increase in chain length due to
hydrophobicity of the hydrocarbon portion [7], A material which has low solubility
in water will have a higher tendency to concentrate on the adsorbent surface.
However, large molecular size could result in slow diffusion through the pore or
worse completely block the pore entrance.
In addition, the molecular form, be it ionic or neutral, branched or linear, has
significant impact on adsorption.
14
2.2 ADSORPTION ISOTHERMS
2.2.1 Adsorption Isotherms From Solutions
In contrast to gaseous phase adsorption, liquid phase adsorption involves the
formation of a compact layer on the adsorbent surface. As there are no vacancies in
the surface layer and the bulk solution, the number of molecules of a given
component may increase in the surface layer only by displacement of an equal
number of molecules of another component.
While the determination of the gaseous phase adsorption isotherm is a straight
forward procedure, liquid phase adsorption isotherm is a much more difficult,
hence some simplication have to be made.
In order to derive a relationship between adsorption at the solution/solid interface
and the solution composition, consider adsorption from a completely miscible
binary solution whose components are 1 and 2 on a homogeneous adsorbent
surface. At thermodynamic equilibrium :
111 = Hi , ti = U2 (1)
where Hi and H2 are the chemical potentials of the components 1 and 2
respectively, in the surface phase, and Hi and H2 are the corresponding potentials
in the bulk phase.
Given that |i, = H? +RT\nx(fi , equation 1 can be rewritten in the form :
p-i'1 +RTln xSfi = |ii +RT]nxlf1 (2)
15
H-2* +RT\nxs2f2 = p,® +RT\nx2f2 (3)
where {Xj’s and p®’* are the standard chemical potential of component 1 and 2 in
the surface phase, p.® and p® are those in the bulk phase, x[ and xi, and xs2 and
x2 ;/^and/i, and f2 and/2 are the mole fractions and activity coefficients of
component 1 and 2 in the surface and bulk phases.
Combining equations 2 and 3,
*1*2 _fif2 xix2 j\fi exp (4)
Denoting
c=f
K= exp 1RT Hi"' - 111
# = CK=a (5)
Given x£ = 1 - X* and x2 = 1 - xi
S _ Cttl _ 0=11 OOC1+X2 ! + («-!)*:, (6)
16
The above equation is often referred to as the individual adsorption isotherm of
component 1 from solution. The quantity a is known as the distribution coefficient
or distribution function. It depends on bulk phase composition.
Assuming both surface and bulk phases to be ideal and adsorption takes place on a
uniform adsorbent surface
C = 1 and K, = constant
which implies that
4*2*i4 = a = Ki
where K, is the adsorption equilibrium constant.
Hence,
c _ K\Xl 1
(7)
This equation, is widely used in studies of adsorption from solution.
Assuming adsorption from non ideal solution; C and a varies with x,
For all values of a; when x, —> 0 ; 1 + (a - 1) x, —M
17
Hence,
x\ = ax i
When x, = 1; 1 + (a - l)x, —> a
hence, x\ = Xi = 1
Case X
When component 1 is strongly adsorbed which implies that
- — Hi j » RT , hence K, » 1 and a » 1 for slight deviation of C from
unity.
Therefore,
s o%,xi ~ 1+0%, (9)
Case 2
When component 1 is weakly adsorbed which implies that, K,« 1, hence K, « 1
and a «1 for slight deviation of C from unity.
Therefore,
V5 *»!i-%, (10)
18
Case3
When both component 1 and 2 has approximately equal adsorbabilities which
implies that, K, ~ 1 and a is a function of K, and C. a can be greater than unity for
small values of x, and smaller than unity for larger values of x, or vice versa.
Cases 1, 2 and 3 can be graphically representated by curves 1, 2 and 3 in Figure 6.
x0s is given in mole fraction.
Figure 6. Individual adsorption isotherms from a binary solution : 1. positive adsorption, 2- negative adsorption, 3- limited adsorption, a - the adsorption azeotropic point.
Equation 6 can also be rewritten in terms of number of moles of the components
per gram of adsorbent in the surface solution. In this instance,
T\\ = l+(ay-l)*i (11)
2where J = is the coefficient of surface displacementTlm,l
Tj^ i and Tj^2 are the number of moles of component 1 and 2 at saturation.
19
The expression can also be rewritten in terms of excess adsorption (reduced
adsorption)
a(n) _ •n£,,iY(«-l)*i(l-*i) ^1 1 + (ay-l)%i (12)
or
(h) _ <i7(a-l)»i(l-*i)* 1 + (CCjf-l)*! (13)
where s being the specific surface area.
Depending on the value of a, all possible cases can be represented graphically by
curves 1,2, and 3 of Figure 7
Figure 7. Excess adsorption isotherms for a binary solution: 1- positive adsorption, 2- negative adsorption, 3 - limited adsorption, a - the adsorption azeotropic point.
20
2.2.2 Classification Of Adsorption Isotherm For Non Electrolyte Binary Solution.
The first classification of excess adsorption isotherm for binary mixture was made
by Ostwald and Izaguirre [8], Schay and Nagy [9, 10] subsequently proposed a
more detailed classification as shown in Figure 8.
Type 1 Type 2 Type 3
Type 5Type 4
Figure 8. Classification of excess adsorption isotherms for a binaiy solution
2.2.3 Adsorption From Binary Solutions Of Substances Of Limited Miscibility
The adsorption isotherms of binaiy solutions of liquids of limited miscibility often
have the shape shown in Figure 9. The adsorption increases rapidly as its solubility
limit is approached and tends asymptotically to a line parallel to the adsorption
axis. The rapid increase of adsorption at these concentrations indicates multilayer
adsorption. However, recent studies attribute this behavior to phase separation
which starts earlier than in bulk because of the effect of the porous structure of the
adsorbent, this process is therefore similar to the capillary condensation observed
in vapour adsorption.
21
35
30
E
0 0.5
C/Cn1.0
Figure 9. Excess adsorption isotherm of methanol on silica gel from n-heptane. [11]
2.2.4 Adsorption from Multicomponent Solutions
Adsorption from multicomponent solutions is a very complex process and presents
many difficulties. Oscik [12, 13] considered the thermodynamics of adsorption
from multicomponent systems. He derived an expression to calculate the mole
fraction of a given substance in the surface layers on the basis of its adsorption
isotherms from suitable binary solutions.
(14)
where n is the number of components in the multicomponent solution.
2.2.5 Adsorption Isotherm Models
Adsorption isotherm can be mathematically represented by an expression relating
the amount adsorbed q to the concentration c in the equilibrium fluid phase
such as q = f(c). This is a generalized adsorption isotherm model.
Although there exist a number of adsorption isotherm models of varying degree of
complexity, the most widely used are those of Langmuir (15), Freundlich (16) and
Langmuir-Freundlich (17). These isotherm equations are often used to predict the
amount adsorbed in a specific system . In the present study, only the Langmuir and
Langmuir-Freundlich isotherm models will be reviewed for the purpose of
simulating the experimental data.
a. Langmuir Model
The Langmuir model is based on the following assumptions:
• Molecules are adsorbed on a fixed number of localized sites.
• Each site can accommodate only one adsorbate molecule.
• All the sites are energetically equivalent.
• There is no adsorbed molecule-molecule interaction.
The adsorption isotherm expression is obtained by considering dynamic equilibrium
between the rates of adsorption and desorption.
For a pure substance,
23
(15)? _ kx Qm 1 +kx
where q is the quantity adsorbed.
qm is the quantity adsorbed at saturation,
k is the adsorption constant,
x is the molar fraction in the fluid phase.
For a multicomponent system,
(jj _ faQ™ l+'LkjXj
where i represents the component i.
b. Langmuir- Freundlich Model
This model was developed by Koble and Corrigan (17). It was derived from the
Langmuir and Freundlich expressions taking into consideration the heterogeneity
of surface sites.
(16)
For a pure substance,
9 _ kxa 1 +kxa
where a is an empirical coefficient.
For a multicomponent system, it gives :
(17)
24
(18)q{ _ kjxf‘ qm 1 +Z,kjXjJ
25
26
2.3 DYNAMICAL MODELLING OF ADSORPTION COLUMNS
The length of an adsorption column is generally much greater than its diameter so
that one can consider the fluid and solid concentration being only function of z, the
position along the column. There are three main phenomena to model in such
system:
- the flow of the fluid through the packed bed of adsorbent,
- the mass transfer between the fluid and the adsorbent
- the thermodynamical equilibrium properties.
The latter has already been treated in the previous chapter. We will focuss here on
flow modelling and mass transfer. The following discussion is based on reference
[23], the basical one in the adsorption domain.
2.3.1 Flow modelling
If the flowrate through the packed adsorbent is sufficently high, one can consider
that the flow is a plug flow but it is more convenient to take into account the axial
dispersion due to molecular diffusion and turbulent mixing.
One way to represent axial diffusion is to define an axial dispersion coefficient Da
such as the mass balance of component i is as follows :
r» d2C,- d(v-C,) dC,- , 1-SjT+~sT+lT+— (19)
27
where v is the fluid interstitial velocity
Q the fluid concentration
e,, the bed porosity, supposed to be uniform
q; the mean solid concentration of component i
^ the mean flux of i per unit of particle volume
Sometimes, v is approximative^ constant along the column : this is the case for
adsorption processes from liquids or when the adsorbable components
concentrations are sufficiently low (the so-called "trace system" in Ref. 23). If v is
not constant, its variation with z is calculated by using the global mass balance :
Ct- 1+^-2, t=0 (20)
where Ct = X, C, the total fluid concentration is supposed to be constant
Another way to model axial dispersion, which has been extensively used in
chromatography modelling [25], is to consider the bed void fraction as a serial
arrangement of Np perfectly mixed cells. If one consider that the interstitial velocity
or the volumetric flowrate are constant, the mass balance of component i over the
cell number j is :
g-cr'-C-ci+tV^+Fy.Tr (2i)
where Q is the fluid volumetric flowrate
Ft' and VJ are the bed voidage and solid volumes of cell j.
28
Generally, the cells are identical so that Vb' =Vb and Vp ~Vp . For high Peclet
number or if Np is sufficiently large, the plug flow with axial dispersion and the
cells in series models are equivalent.
2.3.2 Mass transfer between fluid and solid:
If the mass transfer efficiency is very high, one may consider that thermodynamical
equilibrium between solid and fluid is reached at each time and position in the
column. In this case q^q*, the solid concentration of the adsorbent at equilibrium
with the interstitial fluid.
If mass transfer efficiency has to be taken into account, one must consider the
different following step:
- mass transfer between the fluid and the surface of the pellets : one define an effective mass transfer coefficient A^such that:
= kf-a-(Ci~ C*) where a is the external surface area per unit particle volume
and C* is the fluid concentration of component i holding at the particle surface. It
is possible to evaluate kf by using correlation between non dimensional numbers.
-mass transfer inside the pellets : a pellet of zeolite is made of a great
number of very small crystals so that it may be seen as a porous media which
porosity is ep. Basically, one must describe mass transfer within the intercrystalline
macropores of the pellet and within the crystals. If Cpi is the concentration of
29
component i within the macropores and if the pellet is considered as a sphere, the
component i balance over the pellets leads to :
R2V j
BRdCpi l-£p dcci —+—'~ (22)
8c”where is the component i flux per unit of crystal volume between the macropores and the crystals, Cci is the mean concentration of component i in the
crystal, R is the radius within the pellet and Dp is the apparent diffusion coefficient
through the macropores.
8C~-In order to calculate -^r, one must solve the following mass balance over the
crystal:
J. 3C„r2 " dr 3r (23)
where Cd is the concentration of component i in the crystal, r is the radius within
the crystal and Dc is the diffusion coefficient through the microporous crystal.
The crystal surface is supposed to be at equilibrium in this so called bi-dispersed
model. Simplification occurs if one or another step is controlling the overall
process [23],
2.4 PRINCIPLES OF "COLON"
The simulation program "COLON" is an IFP propetary computer program
developped to simulate adsorption processes for the liquid phase separation of C8
aromatic isomers as orthoxylene, metaxylene and paraxylene [18]. This model can
be used to simulate breakthrough curves or SMB ( simulated moving bed)
30
processes. We will compare our experimental breakthrough curves to thoose given
by "COLON".
The "COLON" model is based on the following assumptions :
- the adsorbent repartition in the column is uniform
- the temperature is constant
- the liquid flowrate is constant
The liquid flow through the column is represented by a serial arrangement of Np
identical perfectly mixed cells and the thermodynamical equilibrium being supposed
instantaneous, each of these cells is in fact a theoretical plate.
The volume corresponding to each plate is divided in four zones:
- the fluid volume Vb corresponding to the bed voidage
- the fluid volume Vmp corresponding to the macro and mesoporous volume
of the pellet
- the volume Vgp corresponding to the microporous volume of the pellet or
the adsorbent capacity
- the solid volume
31
The mass balance over each cell number j for a component i is given by the
ordinary differential similar to equation (21). This equation is discretized according
to the time in order to solve it. If one choose a step time equal to the fluid mean
time residence 4+1 = hi the bed voidage of each cell, the component i mass
Table 17 Adsorption data of 1.48 wt % methanol in n-hexane on molecular sieves at_____________313 K and flowrate of 31.0 gram/min (3 column, 13X) - run no 4________Density @313 K (g/cm3), MeOH
n-C6Density of Mixture (g/cm3)Initial Concentration (wt %)
Pump SettingFlow Rate (g/min)Empty Bed Volume (cm3)Weight of Catalyst (g)
0.77330.64250.64441.4800
1.531.0574.8384
Sample Time Bal. Rdg. WtDiffi Cum. Wt Bed Vol. EfE ConeNo (min) (8) (g) (g) (wt%)
Start 0.00 119701st Drop 8.71 11700 270 270 2.19 0.000
Figure 30 Comparison of normalized breakthrough profiles of methanol in n-hexan
Nor
mal
ized
conc
entr
atio
n
Bed volume at stoichiometry
Figure 31. Comparison of normalized breakthrough profiles of 1-hexene in n-hexane
4.2.3 Breakthrough Curves of Methanol and 1-Hexene in n-Hexane at Various
Operating Conditions
The breakthrough curves determination for methanol and 1-hexene in n-hexane
were carried out at different flowrates, temperatures and adsorbents. The results
obtained are as given in Table 24 to 27 and is illustrated in Figures 33 to 36. A
summary of the operating conditions used are as given in Table 28. From the data,
it can be seen that the breakthrough points obtained for run nos lb, 2b and 3b were
36.09, 31.44 and 33.48 bed volumes processed respectively. The increased in
flowrates from 12. lg/min to 32.6 g/min which is about 2.7 times resulted in a 2.61
reduction in bed volume processed for methanol. 1-hexene which was initially
adsorbed together with n-hexane was eventually displaced by methanol which is
more polar, resulting in an early breakthrough of 1-hexene.
A change in temperature from 313 K (run no 2b) to 323 K (run no 3b) results in an
improvement in 2.04 bed volumes processed which is not in agreement with known
behavior i.e. higher temperature normally results in an earlier breakthrough.
However, if experimental errors were to be taken into considerations, the
difference was not significant.
Finally, a comparison of the effect of adsorbent type was carried out. Run no 3b
carried out with a 13X zeolite was compared with run no 4b which used a 5A
zeolite. The breakthrough points were found to be 33.48 and 26.55 bed volumes
processed respectively. The reduction in bed volume processed was expected
since 5A zeolite has a lower capacity for methanol compared to 13X as determined
earlier in the adsorption isotherm. If a reduction factor of 0.21/0.22 = 0.95 was
85
offered by the 5 A due to the smaller aperature size of the window. Desorption and
readsorption runs were carried out in both cases. Desorption was carried out at
383 K using a 45:55 ratio of 1-hexene to n-hexane for 100 minutes , followed by
readsorption. A typical desorption curve is as shown in Table 29 and Figure 37.
The readsorption breakthroughs for run no 3b and 4b are shown in Tables 30 and
31 and illustrated in Figures 38 and 39. The breakthrough points were found to be
7.95 and 5.43 bed volumes processed indicating a serious reduction in processing
capacities by about 76.3 % and 79.5 % respectively.
used, the amount of bed volume processed for 5A should be 31.81 instead of
26.55. The differences could be attributed to higher mass transfer resistance
Table 24. Adsorption data of 1.48 wt % methanol and 1.49 wt% 1-hexene inn-hexane on molecular sieves at 323 K and flowrate of 12.1 gram/min (3 column, 13X) - run no lb____________________________________
Density @ 323 K (g/cm3), MeOH
1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)
Pump Setting
Flow Rate (g/min)Empty Bed Volume (cm3)
Weight of Catalyst (g)
0.7637
0.64300.63300.6351
1.48301.5118
0.5
12.1574.8384
Sample Time Bal. Rdg. Wt. Diff. Cum. Wt. Bed Vol. Eff. Cone Eff. Cone1C6 MeOH
Table 25. Adsorption data of 1.52 wt % methanol and 1.49 wt% 1-hexene inn-hexane on molecular sieves at 313 K and flowrate of 31.5 gram/min(3 column, 13X) - run no 2b
Density @ 313 K (g/cm3), MeOH1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)Pump SettingFlow Rate (g/min)Empty Bed Volume (cm3)Weight of Catalyst (g)
0.77330.65290.64250.64461.52481.4896
1.531.5
574.8384
Sample Time Bal. Rdg. Wt. Dig. Cum. Wt Bed Vol. Eff. Cone Eff. Cone
Table 26. Adsorption data of 1.49 wt % methanol and 1.50 wt% 1-hexene in n-hexane onmolecular sieves at 323 K and flowrate of 32.6 gram/min (3 column, 13X) -run no 3b
Density @ 323 K (gZcm3), MeOH1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)Pump SettingFlow Rate (g/min)Empty Bed Volume (cm3)Weight of Catalyst (g)
0.76370.64300.63300.63511.48901.5014
1.532.6574.8384
Sample Time Bal. Rdg. Wt. Diff. Cum. Wt Bed Vol. Eff. Cone Eff. Cone1C6 MeOH
Table 27. Adsorption data of 1.49 wt% methanol and 1.49 wt% 1 -hexene in n-hexane on molecular sieves at 323 K and flowrate of 30.9 gram/min (3 columns, 5A) - run no 4b
Density @ 323 K (g/cm3 ), MeOH
1-C 6
n-C6
Density of Mixture (g/cm3)
Initial Concentration MeOH (wt %)
Initial Concentration 1-C6 (wt %)
Pump Setting
Flow Rate (g/min)
Empty Bed Volume (cm3)
Weight of Catalyst (g)
0.7637
0.6430
0.6330
0.6351
1.4860
1.4915
1.5
30.9
574.8
395
Sample Time Bal. Rdg. Wt. Diff. Cum. Wt Bed Vol. E£f. Cone EfF. Cone1C6 MeOH
No (min) (g) (g) (g) (wt%) (wt%)
Start 0.00 11816
1st Drop 8.74 11546 270 270 2.22 0.000 0.000
2 10.61 11488 58 328 2.70 0.001 0.000
3 12.61 11424 64 392 3.22 0.003 0.000
4 14.61 11368 56 448 3.68 0.006 0.000
5 16.61 11308 60 508 4.17 0.012 0.000
6 18.61 11249 59 567 4.66 0.019 0.000
7 20.61 11190 59 626 5.14 0.031 0.000
8 22.61 11132 58 684 5.62 0.046 0.000
9 24.61 11070 62 746 6.13 0.067 0.000
10 27.61 10981 89 835 6.86 0.117 0.000
11 30.61 10894 87 922 7.58 0.176 0.000
12 33.61 10806 88 1010 8.30 0.267 0.000
13 37.61 10688 118 1128 9.27 0.427 0.000
14 41.61 10569 119 1247 10.25 0.580 0.000
15 46.61 10414 155 1402 11.52 0.473 0.000
16 51.61 10263 151 1553 12.76 0.889 0.000
17 56.61 10111 152 1705 14.01 1.159 0.000
18 66.61 9810 301 2006 16.49 1.488 0.000
19 76.61 9508 302 2308 18.97 1.665 0.000
20 86.61 9204 304 2612 21.47 1.738 0.000
21 96.61 8902 302 2914 23.95 1.794 0.000
22 106.61 8592 310 3224 26.49 1.849 0.006
23 110.61 8469 123 3347 27.51 1.837 0.093
90
Sample Time Bal. Rdg. WtDiff. Cum. Wt. Bed Vol. Eff. Cone 1C6
EfF. Cone MeOH
No (min) (g) (g) (g) (wt%) (wt%)
25 112.61 8406 31 3410 28.02 1.824 0.167
26 113.61 8375 31 3441 28.28 1.813 0.203
27 114.61 8344 31 3472 28.53 1.811 0.248
28 115.61 8313 31 3503 28.79 1.801 0.280
29 116.61 8281 32 3535 29.05 1.796 0.313
30 118.61 8220 61 3596 29.55 1.754 0.361
31 120.61 8155 65 3661 30.09 1.739 0.439
32 122.61 8092 63 3724 30.60 1.753 0.570
33 124.61 8028 64 3788 31.13 1.739 0.606
34 126.61 7967 61 3849 31.63 1.724 0.627
35 129.61 7872 95 3944 32.41 1.702 0.746
36 132.61 7778 94 4038 33.18 1.685 0.788
37 135.61 7683 95 4133 33.96 1.664 0.818
38 138.61 7589 94 4227 34.74 1.647 0.901
39 142.61 7462 127 4354 35.78 1.628 1.071
40 146.61 7338 124 4478 36.80 1.608 1.056
41 150.61 7213 125 4603 37.83 1.587 1.110
42 154.61 7087 126 4729 38.86 1.573 1.155
43 158.61 6962 125 4854 39.89 1.556 1.197
44 162.61 6836 126 4980 40.93 1.538 1.235
45 166.61 6708 128 5108 41.98 1.548 1.301
46 171.61 6549 159 5267 43.28 1.537 1.334
47 176.61 6389 160 5427 44.60 1.527 1.426
48 181.61 6226 163 5590 45.94 1.532 1.343
49 186.61 6063 163 5753 47.28 1.512 1.337
50 191.61 5900 163 5916 48.62 1.515 1.379
51 196.61 5735 165 6081 49.97 1.523 1313
Table 28. Bed volume processed of methanol-1 -hexene-n-hexane at various operating conditions
Run No Pump Set Flowrateg/min
Cone, wt % Temp. K Column Stoi. Bed Vol. Processed (MeOH)
igure 33. Breakthrough curves of methanol-1 -hexene in n-hexane - ran no lb
1-Hexene Methanol0.5 -
■0—0 10—0—$■
Bed Volume
Figure 34. Breakthrough curves of methanol-1 -hexene in n-hexane -ran no 2b
92
Effl
uent
Conc
entr
atio
n (w
t%)
^ Ef
fluen
t Con
cent
ratio
n (w
t%)
2.5
1.5
0.5 - 1-Hexene
'0 0 0 -C-' 0—^30
Bed Volume60
igure 35. Breakthrough curves of methanol-1 -hexene in n-hexane - run no 3b
Methanol1-Hexene
Bed Volume
Figure 36. Breakthrough curves of methanol-l-hexene in n-hexane -run no 4b
93
Table 29 Desorption data of 1.49 wt % methanol and 1.50 wt% 1-hexene inn-hexane on molecular sieves at 383 K and flowrate of 28.2 gram/min(3 column, 13X) - run no 3b
Density @383 K (g/cm3 ), 1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)Pump SettingFlow Rate (g/min)Empty Bed Volume (cm3)Weight of Catalyst (g)
0.56270.55610.5591
45.000055.0000
1.528.2574.8384
Sample Time Bal. Rdg. WtDiff. Cum. Wt. Bed Vol. EfF. Cone EfF. Cone1C6 MeOH
Table 30. Readsorption data of 1.49 wt % methanol and 1.50 wt%1-hexene in n-hexane on molecular sieves at 323 K and flow rate of 37.9 gram/min ( column, 13X) - run no 3b___________
Density @ 323 K (g/cm3), MeOH1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)Pump Setting
Flow Rate (g/min)
Empty Bed Volume (cm3)
Weight of Catalyst (g)
0.76370.64300.63300.63501.47111.4896
1.5
37.9
574.8
384Sample Time Bal. Rdg. Wt. Dig Cum. Wt Bed Vol. Elf. Cone Eff Cone
1C6 MeOHNo (min) (g) (g) (a (wt%) (wt%)Start 0.00 8137
Table 31. Readsorption data of 1.49 wt % methanol and 1.49 wt%1-hexene in n-hexane on molecular sieves at 323K and flowrate of 37.1 gram/min (3 column, 5A) - run no 4b
Density @ 323 K (g/cm3), MeOH1-C6n-C6
Density of Mixture (g/cm3)Initial Concentration MeOH (wt %)Initial Concentration 1-C6 (wt %)Pump SettingFlow Rate (g/min)Empty Bed Volume (cm3 )Weight of Catalyst (g)
0.76370.64300.63300.63511.48601.4955
1.5
37.1574.8395
Sample Time Bal. Rdg. Wt. Dig. Cum. Wt Bed Vol. Eff. Cone 1C6 Eff. ConeMeOH
No (min) (g) fe) (g) (cm3) (wt%) (wt%)Start 0.00 11404
Figure 41. Comparison of simulated and experimental breakthrough curves of methanol in n-hexane - run no. 2
Simulated Experimental
tlmlimt.tiiltimtinliii ,,, I ,,,,,,,,, I L) i iinlnni
Bed volume
Figure 42. Comparison of simulated and experimental breakthrough curves of 1-hexene in n-hexane - run no. 6
102
5 CONCLUSION
In the design of an adsorber or understanding the adsorber behavior, it is necessary to
acquire information on adsorption equilibrium and rate. For this purpose, the
adsorption isotherms of methanol in n-hexane and 1-hexene in n-hexane were
determined. The capacity of methanol in n-hexane at 313 K and 323 K in 13X was
found to be 0.23 and 0.22 g/g and in 5A, 0.21 g/g for both temperatures. In the case
of 1-hexene in n-hexane, the capacity was found to be 0.19 g/g and 0.17 g/g
respectively. All the isotherms exhibited Langmuir-type pattern with methanol
exhibiting near-step change behavior indicating an extremely favourable adsorption.
Modelling of the isotherm data was carried out using the Langmuir and
Langmuir-Freundlich expressions. Both models fitted the experimental data well.
However, the Langmuir model is preferred expression in view of its simplicity and it
involves only one parameter, k
The "macro" approach in which the total resistances is represented in the form of a
breakthrough curve necessitate a number of breakthrough experiments to be carried
out at various conditions. The various parameters studied were concentration,
flowrate, column length, temperature and zeolite type. It was observed in the case of
methanol in n-hexane that there were small differences in the profiles when
concentration, column length and temperature were varied. However, variation in
flowrate caused the profile to be more dispersed. For the case of 1-hexene in
n-hexane some differences in the breakthrough profiles were noted. This may be due
to experimental difficulties in controlling the flowrates at the start of the experiment
rather than inherent adsorption behavior. In the 3-component system
103
to methanol. Readsorption under various conditions showed marked reduction in the
amount of feed processed.
Breakthrough curves simulated using the "COLON" computer programme which is
based on an estimation of selectivity and theoretical plates predicted reasonably well
in terms of bed volume processed for the 1-hexene in n-hexane system. However, it
failed for the methanol in n-hexane system. To predict better the results, it is believed
that the numerical analysis needs to be refined.
(1-hexene-methanol-n-hexane), 1-hexene breakthrough was much earlier compared
104
Act
ual (
wt/w
t%)
Appendix A
GC calibration curve for methanol in n-hexane
Y - MO + Ml *x + M8*xe + M9*xs
2.1102-0.76470.15288
l M t I
0 0.5 1 1.5 2 2.5 ... 3GC (wt/wt%)
GC calibration curve for 1-hexene in n-hexane
y = -0.32342 + 1.0244% R= 0.99994 -
0 .20 40 60 80 100GC Results (wt/wt%)
105";
To Calculate the Concentration of Adsorbate in the Adsorbed and Fluid Phases
Appendix B
(Method A)
Let,
We know,
f f fmm + m ^ — rrif
f f fmm — mt x Cm
By substituting equation (2) into equation (1), we have,
f f f fmt x cm + mh = mt
Given,
mh = mt (1 - cm)
By rearranging equation (4),
m\ = ----- I h-T
1 — Cm
By substituting equation (5) into equation (2), we have,
mm =f f
mh Cm
1 — Cm
(1)
(2)
(3)
(4)
(5)
(6)
Amount of methanol adsorbed per gram of molecular sieve is given by,
Q mm — mmz (7)
Concentration of methanol (g/cm3) remaining in the solution,
f = mmPmfm (8)
+ m
106
where /77m mass of methanol in the fluid phase (g).
mh " mass of n-hexane in the fluid phase (g).
rrft total mass of the fluid phase (g).
m% initial mass of methanol before adsorption (g).
of mass fraction of methanol in the fluid phase (g).
p density of fluid(g/cm3).
z amount of molecular sieves(g).
107
Appendix C
To Calculate the Concentration of Adsorbate in the Adsorbed and Fluid Phases (Method B)
Surface Excess
Consider a binary mixture A and B which are adsorbed on a molecular sieve. The surface
excess of A and B is given by,
rA = ^ X - xaJ (1)
r6 = ^ X (XB - *b) (2)
Hence,
rA + r ms xD - Z
- xa) + (xg - Xg)(3)
= ^ X [*S + Xg - XA - xg] (4)
The amount of adsorbate adsorbed on a molecular sieve is given by,
T(A =mA " mA
(5)
TIB =mB - mB
(6)
where m^, mB, ma, and mg are respectively the masses of A and B in the initial and
final mixture.
.. 108
Given,
XAmAmt
and
x0B XB
mBmt
where mf = m°A + m°B
mt = itia + itiq
We know by manipulation,
rA r\AxB ~ t\BxA (7)
Consider,
a) at saturation
Vp = t\ava + t\avb
1 M + M Vp VpVA VB
where Vp = adsorbent micropore volume
Va = molar volume of A
(8)
(9)
109
Vg = molar volume of B
b) Gurvistch rule
Gurvistch rule states that the number of moles of A (or B) adsorbed at saturation is equal to
the micropore volume of the adsorbent divided by the molar volume of A (or B).
VPVA
VpVB (10)
1 JTA + na(ii)
To change to molar mass, multiply the numerator and denominator by the respective molar
mass.
TIA mA 'Hb MB
nf ma i|af Mb
1 (12)
where mA = mass of A adsorbed = - m a
mB = mass of B adsorbed = mB - mg
mA = molar mass of A
mg = molar mass of B
110
c) The hypothesis that in a gaseous phase, the amount adsorbed is equal to that of the liquid
phase at saturation.
. Ma = Mmf
M9B Mm sat
B
/ /. _ ^B
M9a M9 (13)
where = concentration of A in the gaseous phase at saturation and
M9B = concentration of B in tha gaseous phase at saturation.
d) Also,
TlA =muA - mA m,
(14)
•ns =mB - mB m B (15)
By substituting equations (14) and (15) into equation (13),
1 =A ZHB
MB
i = m + m z M9A m%
(16)
111
Finally, the individual isotherm can be written as,
IIF Ta + M9bxa1 - XA + &BXA
ns =rB + m%xB
1 - xb + &AXB
u o mbwhere (3 g = °
ma' ^ " Mg
112
113
Appendix E
ANALYSE : 18571 DATE : 4 May 1984
SAMPLE NAME : org b ma1 ays
USER NAME : jol'iao
4p„n TVoj
PNTFHPNTR- SAMPL E-MERC DRY
WEIGHT* 102.2 100
PNTR NUMBER = I 15 THETA = 1 4 0 . 0 000PNTR WEIGHT = 71.0282 G GAMMA = 485 . 0000PNTR VOLUME = 2.8500 CC MERCURY DENSITY = 1 5 < -< =.PNTR CONSTANT* 1 0.0 0 0 0 MICRO L? EQUILIBRATION = < ri fififmSTEM VOLUME = . 580 0 CC HP EQUILIBRATION = .0000
SAMPLE WEIGHT* . 5 9 0 9 G INITIAL PRESSURE ; . 8 5 80SAMPLE WEIGHT* 71.4171 G
G/CCSECSEC
INTRUSION (PRESSURISATION) DATA SUMMARY
TOTAL INTRUSION VOLUME(V)= TOTAL PORE AREA(A) =MEDIAN PORE DIAMETER(VOLUME) MEDIAN PORE DIAMETER(AREA)= AVERAGE PORE DI AMETE.R( 4 V/A ) = BULK DENSITY*SKELETAL DENS ITY*