Theoretical Analysis of Fractionating Process of Adsorption BEVERIDGE J. MAIR, JAMES W. WESTHAVERl, AND FREDERICK D. ROSSINP National Bureau of Standards, Washington, D. C.
T h i s report gives the results of a theoretical study of the fractionating process of adsorption made on the basis of the concepts used in the theoretical analysis of fractionating processes in general, as, for example, the process of distillation. Equations are derived for determining separation factor for binary solutions and for determining height equivalent to unit theoretical stage of separation. Experimental results are given for the separation factor as a function of concentration for the following solutions: benzene plus n-propylbenzene, benzene plus ethylbenzene, benzene plus n-hexane, and benzene plus cyclohexane. Experimental results are also given for the height equivalent to unit theoretical stage of separation.
P
REVIOUS reports from this laboratory (2-12) have de-
scribed the experimental development and use of the process of adsorption as a fractionating tool for separations in the liquid state. These experimental developments have included the removal of aromatic hydrocarbons from paraffins and cycloparaffins, including hydrocarbons of both low and high molecular weight; the removal of water and other nonhydrocarbon impurities from purified hydrocarbons; the quantitative separation of aromatic from nonaromatic hydrocarbons, including those of the gasoline, kerosene, gas-oil, and wax fractions of petroleum; the separation of mixtures of pure hydrocarbons of different types; the separation of hydrocarbons of the same type but of different molecular weight; and the separation of isomeric hydrocarbons of the same type. The present report gives the results of a theoretical study of the fractionating process of adsorption made on the basis of the concepts used in the theoretical analysis of fractionating processes in general, as, for example, the process of distillation. Consider an equimolecular mixture of substances A and B which are t o be separated by reason of differences in volatility in a vertical distilling column in which A and B are present in two phases, gas and liquid, with the entire charge of materials being in the rectifying section. At the moment of starting, the average composition of the gas and liquid phases in the rectifying section is everywhere 50 mole % in A. Before the molecules can be separated it is necessary to provide for the transport of molecules A and B through the system from one end t o the other and t o provide for the interchange of molecules from one phase t o another. 1
Present address, Division 19, U. S. Patent Office, Washington 25, D . C. Present address, Carnegie Institute of Technology, Pittsburgh, Pa.
These requirements are met by providing a heater a t the bottom end of the rectifying section and a condenser a t the top end. By this means, molecules A and B in the liquid phase a t the bottom are vaporized, and the vapors travel upward through the length of the column. On reaching the condenser a t the top, the vapors are returned t o the liquid phase and the liquid material flows by gravity down the rectifying section t o the bottom end. As the vapors pass upward and the liquid phase flows downward, a continual interchange of molecules between the two phases occurs. Finally after a certain time, a state of equilibrium in the given system will be substantially attained with a higher concentration of the more volatile molecules, A, at the top of the column and a higher concentration of the less volatile molecules, B, a t the bottom. I n the fractionation of liquids by adsorption, a similar picture may be developed. Consider an equimolecular mixture of substances A and B which are t o be separated by reason of differences in adsorbability in a vertical column packed with suitable adsorbent. I n this column, A and B are present in two phases, liquid and solid-adsorbed, and the entire charge of material is in the fractionating section. At the moment of starting, the average composition of the adsorbed and liquid phases in the adsorption column is everywhere 50 mole % ’ in A. Before the molecules can be fractionated, it is necessary t o provide for their transport through the system and for their interchange from one phase to another. This may be accomplished by introducing fresh adsorbent a t the bottom of the column, letting i t pass upward through the column, and placing a suitable desorbent a t the top of the column in order t o keep the charge of material in the column. I n this way, the molecules in the liquid phase at the bottom of the column pass t o the solidadsorbed state as fresh adsorbent is introduced a t the bottom, and the molecules in the solid-adsorbed phase a t the top of the column 1279
~~~~~~~~~~
AND ENGINEERING CHEMISTRY
Vod. 42,
No, 7
cross section between A and R in the liquid phase and A and J3 in the adsorbed phase. The mole fractaons of A and B will become, AN: and N g 4- A N : , in the liquid phase respectively, AT; and ti'i AN; and N ; Ai\'; in the adsorbed phase. Because for either phase the sum of the mole fractions a t any time i q unity, it follows that
+
+
Si
+
+ A,Vi A'%-;
4-
(3)
f AATg == I
= - an-;
(4)
Similar relations hold for the liquid phase, so that AY' AAh~ 1
(5)
I
Therefore, the difference in mole fractions of ,component h between the liquid and adsorbed phases, A~VA,will be the same a s the difference in mole fraction of component €3 between the liquld and adsorbed phases, - A N B P A N A = AX;
-- AN:
+ AXi
= -- AN;
-^
ASB
(6)
Relations similar to the foregoing equations may be obtained using the volume fractions of B and B, V Aand Bs, instead of the mole fractions, Na and Y B . The corresponding equations are as follows :
MOLE FRACTION OF COKPOVEFIT A
Figure 1 Schematic Diagram of Progressive Changes i n Composition Occurring in Fractionation of Equimolecular Mixture of A and B
I=,
+ 'I%=
1
4- A T A
+ v', $-
A!':
AVA = AVA = 4V; - AVh
are returned to the liquid phase as the desorbent meets the adsorbent as the latter is on its way out of the column. I n actual practice, of course, the adsorption exyieriment is more easily performed by using a long column of adsorbent and having the zone of molecules A and B move downward over fresh adsorbent with a suitable desorbent following. The length of column of adsorbent required is that corresponding to the volume of fresh adsorbent which is required to be introduced a t the bottom of the stationary zone of material being separated in order to reach equilibrium. The volume oi fresh adsorbent Vequired is that volume which will convert, from the liquid to the adsorbed state, a volume of material that corresponds in principle to the volume of material that, in the distillation process, is converted from the liquid to the gas state in the boiler. With the foregoing picture of the adsorption fractionating process, one can, in working out the mathematical relations involved, use the concept of the separation factor, a , defined as = (h'A/lVB)"/(Na/ivs)'
1
AT7i = - A V a
I
01
(7) =
(1)
I n Equation 1, N indicates mole fraction, and the superscripts, a and 1, refer to the adsorbed phase and the liquid phase, respectively. In the adsorption process, as with the distillatiohi process3,a may vary with the composition of the liquid phase, Similarly, one can, as in distillation, use the concept of the height equivalent to one theoretical stage of separation, z
(9)
-Avb
= -AVB
(8)
+
(10) A v b = --AVB
(la)
Provision is suitably made for ths transport of molecules A and B from one end of the fractionating section So the other, as by introducing f ~ e s hadsorbent a t the bottom of tdie column and maintaining a desorbent a t the top. In this way, molecules A and B travel in the adsorbed phase from the bottom to the Lop of the column and in th? liquid phase from the tog to the bottom. A t the
"I t
THEORY TRANSPORT
Suppose a solution of b o liquid substances, A and B, is t o be fractionated by adsorption, with the entire charge of material in a vertical cylindrical fractionating section. Let A be more strongly absorbed than B over the entire range of composition, and assume no significant change in volume on mixing At the beginning of the experiment, the average of the compositions of the liquid and adsorbed phases is the same throughout the fractionating section. This average composition 1s that of the original hquld solution, in which the mole fraction of component A is N ; and that of B is ivg. The sum of the mole fractions is unity:
Nk
-j-
NB= P
(2)
Consider a horizontal cross section near the middle of the frstctionating section, and assume equilibrium to be ~stablisheda t this
Figure 2. Results of Three Adsergtien Experiments wit Equivolume Mixture of Benzene and n-Hexane Scale of spdinates gives t h e refraotive index, n ~ at , 25' C., and scale' sf abracissas percentage by volume of hydrocarbora f i l t p e t d
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1950
1281
is the density (for the liquid a t the standard temperature), the net number of moles of component A transported upward across the givcn cross section in unit time is Ana = A ? j ~ / ( ~ ? f /=p )Z~L A V A / ( ; \ [ / ~ ) A (18)
Similarly, the net number of moles of component B transported downward across the given cross section in unit time is AnB = A u B / ( M / ~ ) = B - u A v i s / ( M / p ) ~ (19)
It follows that Ana
(n!f/p)A
=
AnB ( h I / p ) ~
(20)
If the molecular volumes of A and B are equal, then, across the given cross section in unit tirnr, the net number of moles of component A transVOLUME OF FILTRATE 1Y ML ported upward is equal to the net number of moles Figure 3. Results of Three Adsorption Experiments with Solutions of component I3 transported downward. of Benzene and n-Hexane Figure 1 is a schematic diagram of the eomposiExperiments 3, 5, and 7 refer to solutions containing, respectively, 0.25, 0.50, and 0.75 of a mivture of A and B along the length of the tion volume fraction of benzene fractionating section a t various stages of the process. It is assumed that the molecular volumes of bottom of the column, the molccules in the liquid phase pass to A aiicl I), ale equal and that the initial composition of the system is the adsorbed phase, while at the top of the column the molecules equimolecular in A and 1%. The average composition of the adin the Mdsorbed phase pass to the liquid phase. At the given crosssorbed and liquid phases in the system a t the start is given by t h r sectional level, the two phases are moving in opposite directions, vertical straight line, i j , a t N A = 0.5. After flow of material and equilibrium is continually maintained between the two phases through the system has started, and fractionation and transport of material occur acoording to the picture previously given, there at the given level. The flow of molecules -A and 1%in the two phases, upward in the will be a iict amount of component -4transported upward and nn equal net amount of component I3 transported downward. After adsorbed phase and downward in the liquid phase, is such that fractionation has been under way for some time, with a certain across any cross section of either phase the volume of material flowing is the same throughout the system. Let the rate of flow of quantity of material having circulated through the system, the materid be equal to u , i n volume per unit time, where the volume composition of the material may be represented by the lines OF the material is t o be measured not in the adsorbed or liquid a,h,c,d. At this stage, the areas cdj and abi are proportional, restate in which the material happens to exist in the actual process, spectively, to the net amounts of component A transported upbut in the liquid state a t a standard temperature. I n this and ward and to the net amouiit of component B transported downsubsequent places in this paper, the voluine of a substance always ward. At this stage, the bulk of the material, represented by the i~efersto the volume measured in the liquid state a t the standard line be, has the same composition as the original mixture. temperature. Then the volume of component A transported upAt successive later stages of the fractionation, the composition \yard in the adsorbed phase across thc given cross section in unit may be represented by the lines a'b'c'd' and a"b"c"d". It may be noted that the corresponding areas a t the ends, c'd'j, a'b'i, time is equal to and c"d"nj, a"b"im, are becoming larger and that the quantity v: = (T'X AVA)1L (12) of material in the middle having the initial composition, represented by the lines b'c' and b"c", is becoming smaller and :ind the volume of component A transported downward in the sma~ler. liquid phase across the given ci'oss section in unit time is equal to Finally, a stage will be reached when the quantity of material ak = ( P Af A v L ) u (13) a t the middle having the initial composition becomes infinitesimal and points h"' and e'" coincide. The resulting curve of composiThe net volume of component h transported upward across the tion is represented by ma"b"(c"')d"'i, At this final stage, given cross section in unit time, AUA,is the difference of the two areas nd'"c"'j and 7nu"'b'''i are proportional to the total net foregoing quantities: amounts of A transported upward and B transported downward, AVA = u ( A v ~- A V : ) = U A V A respectively. (14) I
+
In a similar way, one obtains the corresponding relation for the net volume of component 13 transported downward across the given cross section in unit t'imc:
- &le
=
?LAVE
(15)
Because AVa = - A V s
(16)
it, follows that ALIA= AYB
(17)
Equation 17 shows that, across the given cross section in unit time, the net volume of component A transported upward ii equal to the net volume of cornponent B transported downward. If t'he molecular volume of A (in the liquid state a t the standard t,emperature) is ( M / P ) A ,where M is the molecular weight and 0
VOLUME OF F I L T R A T E IN ML.
Figure 4. Results of Three Adsorption Experiments with Solutions of Benzene and n-Propylbenzene Experiments 10, 12, and 13 refer to solutions containing. respectively, 0.25, 0.50, and 0.78 volume fraction of benzene
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1282
-
N
Vol. 42, No. 7
1 = (J-iN; -:Y.;A-;)/Lv;.v;
(26)
Substituting in each of the two terms in the nuinerator on the right side 1 - N A for A-B,
c ”
N
- 1
[Si(l - A-i) - lVL(1 - X i ) ] / -I-.;:\-$= (A-; - Lv;)/Nilv; ( 2 7 )
=
But L90
0
400
50
10
,OO
0
VDLUNE
Figure 5.
ZOC
300
0
50
100
-1-1- y;
110
C F F ’ L T R L T E I N NL.
Results of Three Adsorption Experiments with Solutions of Benzene and Ethylbenzene
a - 1
Experiments 15, 16, a n d 17 refer to solutions containing, respectively, 0.25, 0.50, and 0.75 volume fraction of benzene
The total volume of component -4,transported upward across a given cross sect’ionwhere t’heinitial composition exists, is obtained by multiplying both sides of Equation 14 by the time, t , during which the experiment has been proceeding:
t AVA = ut AT‘a
(21)
This equation is valid only so long ae some material with the same composition as the original mixture remains. When the stage is reached where none of the original material remains, any additional increase in the time t,he experiment proceeds does not increase the quantity of material transported. Letting the total volume of coniponent 9 transported be represented by Z AVA,and the tot,al volume of material which has flo.lved through the system be represented by li, Equation 21 becomes ZAVA = UAVA
(28)
= ASA
so that (29)
A~\-A/’-V:++~;
=
Similarly, one ohtaiiis t,he following relations in teimq of volume hactions: a
-
1
130)
AV-A/T~LAI’~U
=
Equations 29 and 30 are the fundamental equations expressing the separation factor in terms of the difference in mole fraction or volume fraction of one component in the two phases and the composition of the t u o phases. Iff is the ratio of the quantity of material in the adsorbed phase to the total quantity of material in both phases, the quantity being measured in each case as the volume of the liquid a t a standard temperature, then it may be shown that
VA= fV,?
+ (1 -S)
(31)
v ! 4
(22)
For a given experiment, such as that represented by curve u”b”c”d” in Figure I, the term Z A U A in Equat,ion 22 may be evaluated from the area c”d”nj or equivalent area a”b”im. The value of U on the right side of Equation 22 is proportional to the total quantit,y of fresh adsorbent introduced at the bottom of the fractionating section and may be evaluated experimentally. The value of U is the t,ot’alvolume of material which has passed across a given cross section in one of the phases during the experiment’. This is also the total volume of material which, a t the top of the fractionating sect,ion, has been desorbed from the adsorbed to the liquid state, or which, a t the bottom of the fractionating section, has passed from the liquid t o the adsorbed state. If t,he amount of material adsorbed per unit quantity of adsorbent is known and if the total amount of adsorbent introduced a t the bottom of the fractionating section during the given experiment is known, t’he product gives the value of U.
c
SEPARATION FACTOR 111 the preceding section, the separation factor for the fractionating process of adsorption has been defined as OL
= (~\-~/l~-~)/(-~;/~~~)
EEVZENE
013s
ll-IEXANE
(23)
where a and 1 refer to the adsorbed and liquid phases, respectively. It can be shown that the ratio of the ratios of the volume fractions of A and B in the two phases is equal to the ratio of the ratios of the mole fractions of -4and B in the two phases: ( p A / T . ’ B ) /(
va/vk )
=
[ n A ( ~ ~ / f ) A / n B ( J l I”/ / P )[ B n A ( - l f / f )A/nB(nf/f 151’ = ( Y I A / ~ B ) ~ / ( Y I A / ~= E ) (’ ~ A / ~ B ) . / ( ‘ ~ - A / ~ \ ’ B ) ‘
(24) e-hl0LE
F Q A C - Oh
Therefore, the separation factor is also equal to a =
(v:/v;)/(v!4/v;)
I
(25)
By subtracting unity from both sides of Equation 23 and simplifying, one obtains the relation
0
I
I
c 1
C 2 h’0.P
I
I 36
I
I
I
GB
FRACT’OU CF BE‘IENE
Figure 6. Separation Factor for System Benzene Plus n-Hexane from Fractionation Experiments
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1950
Similarly,
Vi
=
7% + ~ A V A (36)
Table I. Characteristics of Adsorption Columns Used in Experiments Reported in This Investigation Adsorbent (Silica Gel) in Fully Packed Section Total void Total Total volume bulk void per unit Mass, volume, volumea, length, grams cc. cc. sq. cm. 2.16 4970 3460 3590 1.87 2120 1475 1532 1.92 2180 1317 1575 2400 1670 2.12 1732
and =
vi - (1 - f ) A v a
(37)
- 1=
Fractionating Section Inside Material diameter, of NO. em. om. construation 1600 2.0 Stainless steel 1, 2 - 6 790 1.9 Borosilicate glass 10 1.9 Borosilicate glass 12 790 2.0 Borosilicate glass 790 13 a Total void volume taken as volume of liquid required to fill packed rectifying section.
Column
I n terms of the difference in volume fraction of one component in the two phases and the composition of the original m a t e r i a l , E q u a t i o n 30 becomes a
Length,
-fAv~)[v;,- (1 - f ) A v A ]
A ~ A / ( ~ A
(38)
Equation 30 may be expressed in terms of the difference in volume fraction of one component in the two phases and the composition of the liquid phase, as follows:
Ti; = V', - AVA
(39)
Then 01
1283
- 1 = AVA/VL(V', - AVA)
(48)
n = L/Z
Taking the logarithm of the terms in Equation 47, rearranging, and substituting for n bv Equation 48, one obtains
(40) log (NA/NB)L - log
But from Equation 22, AVA = (ZAVA)/I;
Let z equal the height of the given fractionation section equivalent to one theoretical stage of separation, and let L represent the length of the fractionating section. Then
(41)
(NA/LvB);o
= (l/z)(log
cU)L
(49)
If the ratio N A / N Bis known as a function of the length of the fractionating section, a plot of
so that AVA is evaluated from the experimental observations. Therefore, the separation factor, a , is evaluated completely from the experimental observations, using Equations 30, 38, or 40, as appropriate. HEIGHT EQUIVALENT TO UNIT THEORETICAL STAGE OF SEPARATION
When all the original mixture has been resolved and an equilibrium state attained in the column, a simple relation can be derived among the composition, the number of stages of separation, and the value of the separation factor, a, over the range of composition over which 01 is substantially constant, by considering the fractionating system m equivalent to a succession of discrete stages of fractionation in a manner similar to that employed by Fenske (1) for the distillation process a t total reflux. In the first stage, the liquid phase is in equilibrium with the adsorbed phase, such that
a(NA/ivi?): = ( N A / L $ ~ B ) ;
(42)
The adsorbed phase in the first stage has the same composition as the liquid phase in the second stage, so that (Wa/NBj: = ( h T a / N B ) :
(43)
In the second stage,
CX(NA/NB)\= (NA/~\'B)~
(44)
~ ( N A I I V B= ): (IVA/NB)~
(45)
so that Continuing for n stages, and eliminating all the intermediate compositions by means of the relations, similar to the foregoing, one obtains an( N A / N B ) = (N A / N B ) :
(46)
or
~ " ( N A / N B= ) ;(NA/NB)!,+I
(47)
If the compositions in the liquid phase of the first stage and the (n stage are known, and if the separation factor, a, is constant over the range of composition, then Equation 47 may be used to evaluate a. Conversely, if the separation factor is already known from other experiments, Equation 47 may be used to evaluate the number of stages required to produce a given change in composition.
+
against length L gives, over the range of composition over which 01 is substantially constant, a straight line beginning at the origin and having a slope equal to (l/z) log a. Since a is known, this yields a value for z, the height equivalent to one theoretical stage of separation. Similarly, the equation log ( V A / V B )-~ log (VA/VB)L,= (I/z)(log a ) ~ (SO) may be used to obtain z
EXPERIMENTAL RESULTS APPARATUS AND METHOD
The apparatus for the fractionating experiments was the same as previously described (3,6, 8). Table I gives the characteristics of the several adsorption columns used. The adsorbent was silica gel having a distribution of particle size such that about 60% of the material was between 200- and 325-mesh (Davison Chemical Corporation, Baltimore, Md., No. 22-08). Isopropyl alcohol was used as the desorbing liquid. All the experiments were performed a t room temperature, which was within several degrees of 25' C. I n the fractionating experiments, the procedure used was essentially the same as previously described. The charge of the two components to be fractionated is introduced a t the t o p of a packed column and caused to pass downward over fresh adsorbent followed by a desorbing liquid. As soon as the introduction of solution begins, the more adsorbable component is preferentially adsorbed, with a consequent reduction in the concentration of this component in the liquid phase. As more solution is introduced the top layer of adsorbent comes into contact with successive portions of solution with the original composition and soon comes to equilibrium with a solution of this composition. In the meantime the first portion of solution passes over fresh adsorbent and the concentration of the more adsorbable component is progressively reduced in this portion. Both the length of the zone of adsorbent which has come t o equilibrium with solution of the original composition and the volume of solution a t the leading front which has become depleted in the more adsorbable component increase as more solution enters the adsorbent a t the top of the column. When the volume of the charge is larger than the capacity of the fractionating section, liquid will issue from the bottom of the column and eventually the zone of adsorbent which has come to equilibrium with solution of the original composition will extend to the bottom of the column. At this point solution of the original composition will begin to issue from the bottom of the column
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1284
VOLUME F P A C T I O N O F
0.4
0 2
6
I
1
I
BEhZENL 06
I
I
0.8
I
I
1 .O
EENZEhE PLUS CYC-OdEXANE
@:-VOLUME FRACTIOV .-MOLE FRACTiON
I
C
1
i c 2
1
1
04 '3LF
hAk-31 0
1
I
06 BE\Z;tJ-
I O B
Figure 7. Separation Factor for System Benzene Plus Cyclohexane, from Fractionation Experiments
At this stage of he oper:ttioii, the volunic~-conipo~itioii diagi,aiii of the material that has already p:isscd out of the column may be represented by curve 7nu"b"b"' in Figure 1. \\'hen the introtiuction of material into the column at the top is halted and a suitahle desorbent is introduced to caause all t,he remaining material in the column to issue from the bot tom, the volume-composition dingram of the final portion of inaierinl may be represented 1-, c"'c"d"n. The quantity of mi~terialtransported toward ewli end is measured by areas inzu"0'' and jndl'c", which are supposegl to be symmetrical and in at~tualpractice are substantially so. In the calculation of the scpartitioii factor from experinit~iit~ 01' the kind mentioned above, Equation 40 wa,s used, with T'il :Liid V k taken as equal t o the volume fractions of h and H i n thc original mixture. QUANTITY O F MATERIAL IN ADSORBED PHASE
In order to evaluak the separat>ionE:ictor, 01, there is requirctl to be known t,he value of U , the total amount of material under fractionation h n s p o r t e d through the system. The total ainount of material t,ransported is proportional to the quantity of fre& adsorbent used in the experinimt. If the quantity of material in the adsorbed phase per unit amount of adsorbent is substantially constant, then the total aillourit, of material transported, U , is equal to the product of the total mass, J f , of fresh adsorbent used in the experiment, niultiplied hy ? L , ) ~ , the quantity of mitterial revidelit in the adsorbed phase per unit mass of adsorbent, the material being measured in tho liquid state at 25" C.: L T
= JIll,,L
(51 j
The total quantity of fresh :Ldsorl,riit, ;lI! is readily determinctl for each experiment. It is required t o knon. the quantity of m:iterial resident in the adsorbed plinsc pcr unit m:~ss of the ailsorbent. It, is not feasible to tleteriuine thc quantity of materid a t i sorbed by bringing the material as liquid tiircctly in contact xitli the adsorbent, because, after cquililji,iuni is established, there is no way of removing the excess liquid from the adsorbent without affect,ing the quantity of niateri:il atlsorhd. However, the same result can be obtained nithout, physical contact of the adsorherit Jvith the material in the liquid phase by letting the adsorbent con10 to equilibrium with the given material in the gas phase, n-hi~*lii n turn is in equilibrium with the smie material in the liquid pb After equilibrium is established in such a system, the esc:ipirig tendency of the given matekil .r~-ill be the same in all threi. phases, liquid phase, gas phase, and adsorbed phase, and thc quantity of material in t'he adsorbed phase \ d l be the s:iiiic :I; that a h e n in direct contact 11-ith tlic liquid.
Experimental Procedure. A known mass, approximat el!. 100 grams, of fresh silica gel was placed in a flat dish (10 cm. in diameter) with cover glass. The dish and contents, with cover glass removed, were placed in a vacuum glass desiccator, containing in the lower section, as liquid, an excess of t,he compound to be adsorbed. The evacuation of the desiccator was continued until
Vol. 42, No. 7
the air ir-as substa.ntially all rcniovcti irom the system. At intervals of 24 to 72 hour?, the inc in iiiav of the adsorbent \vas determined by removing thc d nd contents, covering, neighing, and ret'urning it t o the dcsiccator, which mas again evacuatctl. \Vith benzene, n-heptane, and n'atei,, it ir-as found tha.t constant, weight, was reached n-ithin 24 hours or lees. The espcrimcnts were performed at room temperature, which was 25" * 2" C. From such expei,iments pcrforiiied on three liquids liaviiig very great differenecs in adsorb~il)ility-namely, n-hcptmc, benzene, and water-thc following results were obtained for thc quantity of material (expressed in terms of the volunicx iii til(: liquid state at 25 C,.) in the atlsorlxd pli per unit n i a s of the given adsorbent, silica gcl (Davisori (Ihcniicd Corporation. 13:tltiinore, >Id., S o . 22-08) : wlicptaiic, 0.343: Ixnzene, 0.363; ir-it~er, 0.307 ml. (substance adsorbed) per gram (adsorbent). Within the requirements of the present' invcatigation, these result's arc substantially constant,, with an average value of 0.358 ml. per gram. SEPARATION FACTOR BY FRACTIONATING METHOD
Table I1 gives the results of the csgeriments perforiiic:tl to evaluate the separation factor for the binnrg systems of i)cnzeiie plus n-hexane, benzene plus cyclohcsane, iwnzene plus rL-propylbenzene, and benzene plus ethylbenxcnc. Also includctl i w t 1 1 lit; results of one experiment on the systcin cthyl alcohol plus 12heptane. In these expcrimeiits, t'hc qumir'ity of adsorlxwt i n i s licpt below the amount which noulrl have resulted in tho wsolu-. tion of all the original mat I , so that in c>:whof the e x p c ~ r i i n e n i ~ there always resulted some quantity of the original ni:itcri:il unresolved. Figure 2 shows the rc,suIts of tlircc espcriments (n'os. 4, 3, :uid 19) with original charges itorisisting oi' mi equivolume mixt1u.c: oi' lienzene and n-hexanc. Thcse thrtte cqxriments shoiv clwrly hon. the quantity of the pure coniponcnts A 2nd B producwi :it ( end increases with the quantity of :idsolbent, which est:tlilishc,+ the total flow of material through the system during the give11experiment. The curves in Figure 2 are siiiiilar to the corrcrpoiitliiig theoretical curves in Figure 1. In the experiments listed in Tablc 11.for t,he hydrocarboil iems, the net amount of transport, of each component in ii giveii experiment was evaluated using values of refractive indm as :t measure of the composition. Jrorn measurements of irfractivc index made on known mixtures of I~ciizciic:tiid n-hexane, c:ont:ii 11ear 0, 25, 50, 75, and 100 vol 70bcwz~ne,the following lid thc composition of this tioii between t,he refriictivc in( tcm was obtained:
ng (mixture) - n::(n-hcxane)
= 0.1149
SimiltLrly, f o the ~ niixtuyc of hcnzenc
xiid
V
+ 0.0108 l-y
n~j(mixture)- n~(c!-ciohoziiii(,)= 0.0603 T7
'
I
%-VOLUME
.--HOLE 3
(32)
cyclohexane,
+ 0.014 1
(Si{,
FRACTICh FRACTION
I 0 2
I
I
04
06
I
I
C 8
,
J
I O
'/OLE F R A C T I O U O F fiE\.ENE
Figure 8. Separation Factor for Systems Benzene Plus n Propylbenzene and Benzene Plus Ethylbenzene, from Fractionation Experiments
Table 11. Col-
Expt. No. 1 2 3
umn No. 10 10 10 13 13 13 13 12 13 10 13 12 13 13 12 1 12 10 12 10 6 10 10
4
5 6 7 8 30 31 32 33 34 9
L
10 11 12 13 14 15 16 17 18
Summary of Experimental Results for Determination of Separation Factor Composition, Volume Fraction
Conipononts
9 Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene . ~ Benzene Benzene Benzene Heptane ~~
~
B n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Ilexsne n-Hexane Cyclohexane Cyclohexane Cyclohexane Cycloliexanc n-I’~oliylbenzene n-Propylbenzone n-Proiiylbenzone n-Propylbensene n-Propylbenaene n-Pronvlbenzene ~ ~ ~ .” . Ethylbenzene Ethylbensene Ethylbenzene Ethyl alcohol
A
B
0.05 0.10 0.25 0.50 0.50 0.50 0.75
0.95 0.90 0.75 0.50 0.50 0.50 0.25 0.10 0.10 0.80 0.75 0.50 0.20 0.90 0.75 0.50 0,50 0.25 0.10 0.75 0.50 0.25 0.5
0.90 0.90 0.20 0.25 0.50 0.80 0.10 0,25 0.50 0.50 0.75 0,90 0.25 0 . 50 0.75 0.5
I2.Iass of Ad3orbent, G. *291 59 1 591 668 1002 1336 668 608 600 59 1 668 608 668 1732 1575 3590 1575 1532 1575 1532 3590 1532 383
Quantity of Mixture,
MI. 1800
1000 600 600 600 600 480 1000 2000 650 540 400 300 400 280 500 300 280 400
200
400 200
I n Equations 52 and 53, V is the volume fraction of benzene in the mixture a t 25” C. For the binary mixtures of benzene plus ethylbenzene and berizenr plus n-propylbenzcne, the refractive index was assumed t o be linear with the volume fraction, an assumption that is adequate for these systcins for the purposes of the present investigation. It will be noted from the results in Table I1 that the quantities of components A and I3 transported in caeh experiment, ZAVA and I:AVB, are substantially equal, as required b y the theory. I n Figure 3 are plotted the results of experiments 3, 5, and 7, showing the existence of material of the original composition for the several experiments in which the original composition varied from 0.25 t o 0.75 volume fraction in the svstem benzene d u s nhexane. Figures 4 and 5 show, respectively, similar results for 1.521 I expcrimen ts on the binary systems hcnzene plus n-propylb e n z e n e and benzene plus ethylbenzene. BENZENE
z
EXPT 19
Y
z
1285
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1950
, 10,
140
U, MI.
I’;A*
ii11.
47’~,
MI.
212 239 218 239
73.2 71.8 57.5 24.20
73.2 72.8 55.5 25.16
548 1286 548 137
24.05 58.65 17.5
24.98 61.26 19.2 63.44
,
..
a
.56.0 73.1 83.3 64.8 96.7 123.7 34.53 11.82 12.44 73.2 72.3 56.5 24.68
24.51 d9 95 18.35 (63.44)
’
0.264 0.345 0.393 0.271 0.270 0 259 0.144 0.0542 0.0578 0.345 0 . a03 0.259 0.103
0.0447 0.0466 0.0335 0.463
8.7 7.2 5.4
3.4 3.4 3.2 2.8 2.3 2.5 4.8 3.7 3.2 2.3 1.46 1.44 1.38 1.41 1.35 1.28 1.25 1.21 1.21 26
In Figure 6 are plotted the values of the separation factor as a function of composition for t,he systein bcnzenc plus rL-hexane. For this system, the separation factor decreases from a value near 8 a t 10% benzene to near 2.3 a t 90% benzene. I n Figure 7 are plotted the values of the separat’ion factor as a function of composition for thc system benzene plus eyclohexane. The separation factor for this system is a little less than for the system benzene plus 12-hexane, the vnriat’ion with composition being similar. In Figure 8 are plotted the values of the separation factor as :t function of composition for the systems benzene plus etliylbenzeiie and benzene plus n-propylbenzene. As would be expected, the separation factor is greater for the latter system. I n each of the two systems, the separation factor decreases slightly wit,h increase in the concentration of benzene. For equivolume mixtures of each of the pairs of component’s, the smoothed and rounded values of the separation factor, determined from the fractionating experiments, are as follows: benzene plus ethylbenzene, 1.2; benzene plus n-propylbenzene, 1.4; benzene plus n-hexane, 3.4; benzene plus cyclohexane, 3.0; ethyl alcohol plus n-heptane, 26.
1
SEPARATION FACTOR BY STATIC METHOD
Lz
Y 1.36
0
150 300 450 VOLdNE OF FILTRATE IN ML
Values of the separation factor were also determined a t three concentrations for the system benzene plus 12-hexane and for the system benzene plus cyclohexane by an independent static method.
600
BENZENE WHEXANE VOLUME IN ML
.,
n
The procedure was, in part, the same as that described lor the dctermination of the quaiitit! of material in the adsorbed phase and consisted in allowing an excess of the solution under investigation t o come to equilibrium, by transfer through thc vapor phase, with 100 grams of fresh silica gel in a “vacuum” desiccator from which substantially all the air had been removed. After standing for 1 week t o be sure t h a t equilibrium was attained, the material which constituted the adsorbed phase was recovered by transferring the adsorbent t o a short column and desorbing the adsorbed material with ethyl alcohol. The material from the adsorbent, together with some ethyl alcohol, was collected as a single fraction and the ethyl alcohol was removed by washing with iced water. The compositions of the adsorbed phase and of the liquid phase with which it was in equilibrium were determined from measurements of refractive index.
.f’ou .1.5 290
295
300
305
310
VOLUME OF FILTRATE IN ML
Figure 9. Results of Adsorption Experiment with Equivolume Mixture of Benzene and n-Hexane
VOLUME IN M L
Figure 10. Results of Adsorption Experiment with Equivolume Mixture of Benzene and n-Propylbenzene
By means of the static method, values of the separation factor were determined for the svstem benzene plus n-hexane to be 5.6, 4.1, and 3.2, for mixtures in which the volume fraction of benzhne was 0.212, 0.506, and 0.820, respectively. The corresponding smoothed values for the same compositions by the fractionation method are 5.6,3.4, and 2.4, respectively.
1286
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 42, No. 7
Table 111. S u m m a r y of Experimental Results for Evaluation of Height Equivalent t o U n i t Theoretical Stage of Separation Composition,
Expt.
Column
KO.
No.
A
19 20 21 22 23 24 25 26 27 28 29
13
Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene
b
1
1 13 13 6 12 1 2 6 1
Quantity of Miutriie,
Volume
Piaction ______
Components
A
B hexane n-Propylbenaene n-Propylbenzene n-Propylbenaene n-Propylbenzene n-Propylhenzene n-Propylbenaene n-Propylbenzene Ethylbenzene Ethylbenzene Ethylbenzene
MI.
B 0.50 0 50 0 30 0,50 0 . 30 0 . 50 0.50 0,50 0.50 0.50 0.50
0.50 0.50 0.50
0,50
0.50 0.50 0 50 0.30 0 50 0.50 0.50
600 200 200 50 30 100 2d 100 100 300 200
Mass of Idrorbent, G. 1666 3520 3590 866 423 3500 197 3500 3520 3.590 3590
c-,
AIL 596 1260 1285 310 155 12.54 70.5 1254 1260 128.5 1285
Rate of Flown,
Cm / H o u r 7.30 17.96 15.50 5.24 6.51 7.13 7.81 5.65 17.30 13.15 12.50
LI
sb
3.40 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.21 1.21 1.21
0.558 0,128 0.087 0.238 0.188 0.166 0.256 0.123 0.075 0.078 0.076
I ,
Cni. 0.95 1.12 1.61 0.60 0.76 0.86 0.56 1.14 1 10
1.0'3 1.09
Rate of f l o refers ~ t o that at end of experiment. s = d[log(T/A/VB)L - 1 o g ( V A / 1 7 B ) L = O ] / ~ L .
,
5c0,
Similarly, for the system benzene plus cyclohexane, values of the s e p a r a tion factor were determined b y the static m e t h o d to be 5.9, 3.5, and 2.7, for miytures in JT h i c h the BENZENE' ETHYLBEYZihE volume fraction .0 5 EXPT 2 8 of benzene was 7 0.132,0.450, and P 00 . 7 7 2 , respec0 tively. The corresponding smoothed values iZ0 130 140 150 I60 I70 103 for t h e same VOLUME IN HL compositions by Figure 11. Results of Adsorption Exthe f r a c t i o n a p e r i m e n t w i t h Equivolume Mixture of tion method are Benzene a n d Ethylbenzene 5 . 2 , 3.2, and 2.4, respectively. At this early stage of the development of the theory of the fractionating process of adsorption, the above agreement hetween the two widely different method- is considered satisfactory. P'LI
J
HEIGHT EQUIVALENT TO UNIT THEORETICAL STAGE OP SEPARATION
In Table 111are presrnted the results of experiments performed t o determine the height equivalent to unit theoretical stage of separation. In these experiments the quantity of adsorbent was larger than the amount required for the resolution of all the original material. Figures 9, 10, and 11 show the results of three experiments (Kos. 19, 20, arid 28) with original charges consisting of equivolume mixtures of benzene and n-hexane, benzene and npropylbenzene, and benzene and ethylbenzene, respectively. The plot of the logarithm of the ratios of the volume fractions with respect to t'he volume of filtrate, for t'he system benzene plus n-hexanc (Figure 9), shows curvature, as would be expected from the fact that the separation factor for this system changes appreciably with concentration. For the systems benzene plus n-propplbenzene (Figure 10) and benzene plus ethylbenzerie (Figure 1l ) ,the corresponding plots are substantially linear. Figure 12 shows a plot of t,he calculated values of z as a funct,ion of the rate of flow. The values of the rate of flow plotted are those a t the bottom of the column, in centimeters per hour. In t,erms of the flow of material through the system, 1 cm. per hour is approximately equal to 2.1 ml. (liquid) per hour. For the lower rates of flow, the value of z is near 1 cm. ACKNOWLEDGMENT Grateful acknowledgment is made to Albert J. Sweetman for assistance in performing the experiments reported in this paper. LITERATURE CITED (1) Fenske, 41.R.. IND. ENG.CHEM.,24, 482 (1932).
it
0
em
eo
(3
n
i 1i 1
BEhZELE plus n-PEXAYE @ BEYZEhE PIUS ETHYLBENZEhE BEhZEYE O I L S 8-PROPYLBE"IZEVE
0 O q I
I
I
4
I
I
8
1
I
12
I
I
I6
0 20
R C E OF F L O h IU C C I H O U Q
Figure 12. Height Equivalent to Unit Theoretical Stage of Separation i n Relation t o R a t e of Flow
(2) Forsiati, A. P.,Willingham, C. B., Mair, B. J., and Rossini, F.D., J.Research N a t l . Bur. Standaids, 32, 11 (1944). (3) hlair, B. J., Ibid., 34, 435 (1945). (4) Slair, B. J., and Foraiati, A. F.,Ibid., 32, 151 (1944). ( 5 ) Ibid., p. 165. (6) Mair, B. J., Gaboriault, A. L., and Rossini, F. D., IND.EXG. C H E h f . , 39, 1072 11947). (7) Mair, B. J., Schicktana, S. T., and Rose, F. W., Jr., J . Reseaich S a t l . Dur. S t a n d a r d s . 15. 557 '1935). (8) hlair, B. J., Sweetman. -4.J., and Rossini, F. D., IND. ENG. CHEM.,41, 2224 (1949). (9) hlair, B. J., and White, J. D., J . Research N a t l . Bur. Standards,
15, 51 (1935). (10) Rossini, F. D., Mair, B. J., Forziati, A. F., Glasgow, A. R., Jr., and Willingham, C. B., Proc. 47n. Petroleum Inst., 23, 111, 7 (1942); Oil Gas J . , 41, KO.27, 106 (1942); Petroleum Refiner, 21, No. 11,73 (1942). (11) Khite, J. D., and Rose, F. W.,J r . , J . Research iYatZ. Bur. Staizdards, 21, 151 (1938). (12) Willingham, C. B., Ibid.,22, 321 (1939). RECEIVED February 23, 1950. Investigation performed a t the National Bureau of Standards as part of the work of the American Petroleum Institute Pioiect 6 on " l n a l y s i c , Purification, and Properties of Hydrocarbons."
