INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1951
and head at tlic. v i i d - . 'fhe i,eflus flon,. 21s a I'alliiig film ou the inner surface of thf tulw, and at each of the heated zones a fraction entering the zoiic i i l,evaporized. Conversely, at each of the vooled zone,%.a fraction of the vapor is condensed. The vapors :mil contlrn.;:itr+ .n f o r m i 4 join and mi\- n-ith the main vapor ant1 iwfliis q t t w i i i - i i i tlii3ir zotlr's of origin.
Fipure 1.
1003
iiieut, inechanisiii itscil'. Slust of t h e art' i.oiisequenL t o ttiv increase of the diffusion constants in the vapor phase and to the decrease of the absolute vaporization and condensation rates at the interface. Increase of thr diffusion conztants introducca t1r.o opposing effects. First, the Iiiixiiig txtc nornial t o tlie interface is increased or, in other \vorcls, the v:tpor "film rcsistance" is reduced, this increases the interphase t ransfcr rates and is t':rvorat)lp. 0 1 1 t h e other h i i d , mixing j i i t h i , tIirc3ction oi Ho\v of the. ~ a p o t ' .tiwni also brc.oiiic~srapitl; this c31fec.t inay l i e htt,oiigly uiif':ivtii :ti JII'. \>c(;auW the Vapor Strcalll ~ l ( Y 0 1 1 l ~ 1Si l l i L l J l I ' 1 0 h n ~ ) l ) I l ~ ': It \,tbrtic.:il concentration gr a cl'ICIII. Reduction of the absolute vaporization aiiti coiidensation rittc 1:' aln.a>-sunfavoral)lc, liecause it directly reduces the net intei iihasr transfer rates. A t even modvratr \mxum the romposit r c niay lie f:tr froni l)eing i n iquililiriiini \vi1 11 1.ac.11othlT. (&alitRtivc,l!., tlic. i ~ o i i t r i b u t i o i iof ~ thesc t l i r w iLlfcLcts to tlw t ~ v ~ r - a acparation ll :irt illustrated in Figure 2. :irtion of transversi. ditTu9ion is aliprosiniately in lional to thr prcsaurc over tlw \vholr pressure range. Tmigitudinal diffusion is unfavorablc 1 o :t limited m t r n t a t high vtwuuni. hut its cffcc-t on separatioii ilisapprarr asymptotically :is t h i , pressurc inrreawn. Finally, the absolutr vaporization and icondensation ratcs exert a favorahle infliiencc proportional to thr, pressnrr at low pressures. but. ah t h o pressui~ris incrcascd ahovi, the low rrgion?t h e gain rrnciirs :I tli>tinitrlimit :isymptoticall~..
The Volcott Cascade
Figure 2.
Kffects of Pressure on Contact Rectification Curve I = transverse diffusion Curve I1 = absolute vaporization rate Curve 111 = longitudinal ditrusion
r 1
I Iir nuin o f tlic tlirvi. c~flcc~ts--thittis, thc: dcpentieniv of t 111, o\-c.r-all separation-is illustrated by curve 1 in Figure 3, agaiil qualitatively. The vanishing of t h r vaporization and condcri,tition rates as thc pressure approaches zero more than offsets t,hi :idvantage of high transverse diffusion, hecause the latter i n proves the transfer rate by action on the vapor phase only. Consequently the separation approaches zero with tho pressurv. .It t,hc high end of the pressurc range, enrichnimt, is liniitivl 1)rincipally Iiy the transvrrsc diffusion, so that t h r separatioi, again approaches zero as t h r prcaxure incrraaw to vt:ry IarEi, values. Of these effects, only longitudinal diffusion influences thermal rectification, and the dependence is similar to t h a t for contaci rectification-that is, the effect is harmful, but t o a limited extent, at lon- pressures. Therein lies t,he great advantage of thermal over contact rectification: i t can be emplo:-ed t o yield sharp separations at high vacuum, and contact rectification c,annot.
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1951
totically t o a limit as the number of heated-cooled zone pairs is increased ; the present column theoretically realizes t h a t limit. Effects of Pressure. As pointed out in the introduction, t,hermal rectification is inherently independent of most of the pressure effects that destroJ- the usefulness of contact rectification at lorv pressures. Specific thermal rectification devices, however, are subject to pressure dependence in secondary waysfor example, as discussed in the preceding section. The present concentric tube arrangement is dependent on pressure t o a minor extent on]!-, but analysis of the mechanism of the dependence is necessary before hypotheses for theoretical treatment of performance can be set down. The influence3 of pressure on the action of the present type columns fall into two distinct categories: effects on mixing in the vapor stream and effects on efficiency of partial condensation. T h e mixing phenomena, in turn, fall into two types: mixing by diffusion and mixing by turbulence. Under practical operating conditions, turbulence prevails at pressures above atmospheric and down t o somewhat below and provides a state which may be idealized, for theoretical purposes, a s uniform composition of the vapor stream throughout a horizontal section. At the other extreme, a t low pressures, the same condition is established, because the large values of the diffusivities provide rapid mixing even xvith laminar flow. I n the intermediate pressure range, however, where laminar flow and Ion diffusion rates prevail, little mixing occurs. Partial condensation is well known to be an inefficient enrichment process at pressures of the order of atmospheric and above. This is a consequence of the low diffusion rates XThich do not allow tjhe light component,s t o diffuse away from the interface as they t’end to concentrate there. If the diffusivities are large, however, large concentration gradients cannot be maintained normal t o and near the interface where condensation occurs, and separation nearly equal to the simple theoretical ideal can be obtained; such conditions are evidently met a t low pressures. THEORY
The equations of perforniance for the present column, as well as all others, can be derived by the method described in a previous paper ( 2 ) by proper inclusion of the secondarily formed vapor and condensate in the interphase transfer rate function. Let the number of moles of condensate and vapor formed per unit length of column per unit time h e Q c and Qr, respectively. and the compositions of the condensate and vapor be p ( y ) and ~ ( 2 ) .Taking a material halance over each of the streams over an element of column length yields, for binary systems at steady at.ate,
1005
Corresponding equations for the liquid and for the section below the feed are similarly obtained. After assumption of explicit functional forms for p and q2 x can be eliminated from Equation 4 with the aid of 2, and the equation of performance can be obt ained immediately by integration. Graphical methods can, of course. be used \There p and y are known only from empirical data not easily expressible analyticall>-. .4n important and useful simplification occurs in the special cases where Qc = Q,,; L and V are constant throughout the csoluniii and t h r general solution Equation 4 reduces t o
Such operation will be termed adiabatic. The left-hand member of this equation is dimensionless and has a simple physical interpretation. Since Qs is the total vaporization rate in the column. Q ~ D IisVthe ratio of the vaporization rate to the vapor flow rate or, statistically, the number of times that the material is redistilled in passing through the column: it will be termed t h e heat ratio, Y , because, in ideal batch distillation, it is equal t o t h e ratio of the gross heat input to the column t o the heat input to t h e pot. T h e heat ratio is the proper parameter for characterizing the performance of columns of the present type. The use of an equivalent number of theoretical plates or transfer units is unsatisfactory for characterizing thermal columns, because the performance of such columns is quite different from t h a t of eontactors, and neither plates nor transfer units are invariants with respect, to composition. Actually, however, as will be shown later, the heat ratio required for a given separation is nearly equal numerically t o the number of theoretical plates or transfer unit,?i required for the same separation in contactor columns, for most conditions of operation. The analogy between heat ratio for thermal coluinns and theoretical plates for contactor columns is a close one. .4 theoretical plate may b r rrgarded a$ a step in composition corresponding to passing from a liquid t o a vapor in equilibrium with it, and in t.his sense corresponds to a single simple distillation in xvhich a n infinitesimsl amount is taken overhead. The heat ratio, on the other hand, also meeeures the number of equivalent single simplc distillations, but on the basis of heat rather than composition. Minimum Reflux. The minimum reflux ratio, corresponding t o infinite heat ratio, is easily obtained by setting the denominator of the integrand of Equation 4 or 4a a t zero. Hence, generally, Qrq
- Q ~ P=
(Qm
- Qc)y
ij)
and for adiabatic operation p = 9
General Solution for Steady State. Subtraction of one of the preceding equations from the other, followed by integration, yields the conventional operating line, exactly as in contact rolumns: T’y
- Ls
=
(V - L ) Z P
(2: If the Q’s are constant along t h e height of the column, as in the concentric tube c o l u n i ~ then ~.
V
=
F’o
+ (Q.
- &r)z
(3)
by which the variable V can be eliminated from the vapor material balance equation, giving, above the feed,
(5a)
give formulae for the minimum reflux. Actually, of course, p and y are funct,ions of y and 1, and where PO expressed do not depend on the reflux ratio. The desired formula can be obtained, however, b y eliminating either y or z from Equation 5 or 5a with the operating line, Equation 2, which does involve the reflux rat,io. Though the operating lines are the same for thermal and contact rectification, the minimum reflux values are not necessarily so. I n the following sections, equations of performance are derived for specific sets of hypotheses. The relatively simple cases for high and moderately low pressure8 will be solved first, after which the difficult problem of operation at intermediate pressure and the trivial one of operation a t extreme high vacuum will be discussed. High Pressure. At pressures of the order of atmospheric and above, mixing in the vapor stream is rapid because of turbulence and may be idealized as instantaneous. Partial condensation,
1006
INDUSTRIAL AND ENGINEERING CHEMISTRY
however, is nearly nonselective, and its contribution to the enrichment can be neglected. For constant relative volatility. a , t h w e conditlons lead to p = y and y =
(YX
1
+ ( a - 1:s
11 1
Vol. 43, No. 4
this rase: it is because of large diffusion rates. This example diti’ers from t h a t of high pressure, however, because the large diri’nion rates permit the partial condensation action t o coritri!)iLte an efficient part to the enrichment. .\gain assuming constant relative volatility, the secondarily fornieti vapor? and condensates have the compositions
The simplest case, adiabatic operation a t total reflux. foilom immediately from the operating line x = 1 and substitution o f expressions (Equation 6) in Equation 4a. The result i.5
which gives explicitly and exactly the heat ratio requirtd to cti‘wt a given separation )There the volatility ratio is known. Surprisingly, the right-hand menibcr of this equation oi performance is identical with Lewis’ approsinlatioil ( 6 ) for hui-\l\lcplate column performanre; it is also identical to t h r cwrre,qx)nt!ing result for packed columns derived from transfer unit thror!., where the vapor diffusional resistance is controlling. Thes!: identities are purely coincidental, however, because the prewrit result rests on entirely different hypotheses than either of tht’ others. For other conditions of thermal rectification :io ;uc,l: relationships exist. Equation 6 can readily be compared with the corresponding ones for packed and bubble-plate columns by Lvriting it in the form =
__ 1 In CY
-
1
&-3) + Ill YO
(1 -
{/D)
I
2
-
( i u 1‘
0
YD
and noting t h a t the second term on the right is negligible relative t o the first for all ordinary conditions of operation. For h u h h l p plates
The equation of performance can he obtained as beforr, t)y .SUI)atitutinq these in Equation 4 or 4a, eliminating 1: with the operating line and integrating. For adiabatic operation a t total r(stlux this yields
.\g:+in there is a small second t e r m on the right-hand side wtiic,ti ni:i>. l>eneglected in comparing this equation of performance with othixrl. .is the volatility ratio approaches unity, the ratios of t h r coefficient of the logarithm, a / ( a ? - 11, t o t h e corresponding roef5cients for plate, packed, and high pressure thermal columns apprnarhes 1 2 . In other words, a heat ratio unit at high v a ~ i i i i n i;i equivalent t o two theoretical plates. This increased separating power is not surprioing, hecause at high priwure only tlie addition of heat contributes enrichment,, the alistrwtion merely serving to maintain uniform flow, whereas at high vacuum both artions are favorahle with respect to compocit iou. The higli w c u u n i equations of perforriiance for partial reflux, nonadialmtic operation, or both can be obtained 1 3 elementary ~ methods, but again these are complicated algrtiraically and inc*onvt.iiit,nt for practical problems. The niininiuni reflux for adiabatic operation, however, is easily and is of interest: c~:il~~ulatt~ti
and for packed colunins (C)
The ratios of the characterization indews for tlw thiee type;. ot rectification are therefore P1ate:packcd:Iiigh pressure therninl::
1 l a 7 1 1 -- . - __ __IIrn’2ol- 1 ’ a - 1 ~
As the volatility ratio approaches unit>-, all three ratios : t i ~ o approach unity. Consequently, all three types of c for contart t,olumii,< esc’ept that a ? replaces a . Since the minirnuni reflus rxtio decreases with increasing a and since CI is taken grtLater than unity, t h e minimum reflus is rctluced by tlie partial cond$nsing action. .i pinch point in high pre>aure thermal columns a n d in all ct ones is a point at \~-hichthe liquid and vapor are i n ibriuiii with e a r h other-that is. have their compositions separated kiy oiit’ theoretical plate. In high vacuum thermal re!\tifii‘:ition. lion-ever. a piueh point occurs only where the liquid and v:ipor compositions are separated by two theoretical plates. L-niler high vacuuni operation a remarkable condition (‘anprevail near a pinch point. If the reflux ratio is less than the nl niiriimuni for contact (7oiumns hut greater than given by ion 13, a s can Iw easily realized in pracmtice with l o ~ vreflux and high lirat ratio. there is a region a t the bottom of the caolunin actually richer than the cornposition whirh !>rium with the liquid. Further, the vapor fornizd 1)- partial vxporizxtion of the refluy is poorer than tlie m x i n vapor strrani which it joins. Conversely, the liquid is poorer th:iri that which would t w i n equilibrium with the vapor, and the (*ontiensatefrom the vapor is rirher than the liquid whir-h . . . i t J C ~ ~ : I S . Severthelc,ss enrichment is obtained, because the vapor forriird from the reflux is riclier than the condensate formed f r o m the vapor. resulting iri a net interphaae transfer .diich is favorable. The condition is peculiar because either the partial revaporizatie!) or tht’ p:trtial recondensation would b e harmful alone. im.. povetiahiiig rwthcr than enric)hirig thr, vapor stream. brit in (*ombination excellent rectificzation is attxiued. Pritler these conditions. contact enrichment effects would reverse and impoverish the vapor.
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1951
Intermediate Pressure. In the pressure range intermediate between the extremes treated in the two preceding sections. the mechanism of operation of the present thermal rcctif>-ingcolumn is physically simple and readily idealized hypothetically. but the mathematical analysis of the performance is very difficult. I n this pressure range the flon- of the vapor stream is laminar, a n d the diffusion constants are small. Consequently it is proper t o assume t h a t no mixing occurs in that stream. but t h a t the composition is uniform along a ytream line from the reflus film t o the rotary condenser. Partial condensation niust i)e neglected as an enrivhing action under these conditions. Sinre the vapor composition is now no longer uniform acre:" a horizontal section, as was assumed in the two preceding sections, UPC of the liquid material balance (Equation 1 ) is much more convenient than the vapor one (Equation l a ) . Though the analysis will deal n-ith L instead of y, any desired value of y can he obtained aftrrward from the operating line equation: such a calculated value of y will be a mean one, weighted across the section by flow rate. Kinematically, vapor formed from a point on the reflus surface will flow radially inward a t a rate dependent on Q and upward a t a rate dependent on 1.. I t will then t)e condensed and thrown outward, back into the reflux stream. a t a point higher than t h a t of its origin by a distance equal to the vert::.al component of its travel as vapor. Thus y is the compos; ion of the vapor in equilibrium with the reflux a t its point of origin, a n d p is the composition of vapor in equilibrium with the reflus at a point below the point of origin by the height of a single vaporizstion-condensation cycle. Calculation of thp height of a cycle, or the height gained by a vapor molecule in passing from the evaporator to the condenser, , can br made by superposing the inward and upward f l o ~ s tvith regard to the equation of continuity. Such analysis proves t h a t the stream lines in the vapor lie radially on a paraboloid of revolution coaxial with the column and t h a t the difference in height between the ends of any one of them is K'Q. T h e quantity V 'Q is exactly the height of one heat ratio unit, a result that might have been expected because one vaporizationcondensation cycle should he statistically equal t o a heat ratio unit. For adiabatic operation, the differential equation (1) for the liquid composition can be n-ritten
if Y is taken a s the independent variable of height, instead of z. \\.ith this independent variable, the origins of the secondarily formed vapor and condensate differ in height by unity, and the values for p and p become p = -
ar l + ( a - l i r
" - 1
and q
=
1
+ ( a - lh N2
'1
(15)
where the bar notation designates evaluation a t the subscript. Substituting these into the differential equntion, introduring the refluu ratio. and making use of the identity
yirltis
I? R 1 a
+
01
1 lis tlv
1
+ ( a1
-
l).r
This can be siniplified further by pendent variable. Putting
R
Iv
- 1
+
1
+(CY
-
1)r
'
Y
=
transformation on the de-
R 4 R
+ 1)
""
1007
yields
du-_ _ _ _1 - u(u - 1)
du
1
(19)
U(")
which is a differential-difference equation, involving both derivatives and finite differences. It may be transformed into an integral equation by multiplying by du and integrating between 0 and Y : t h r result is
wherein the constant K is fixed bv (21) Equations 10 and 20 appear t o be the simplest relationr between the simplest canonical variables. Ynfortunately neither of these is amenable to elementar?. mathematical analysis, and further 5tuily is required before solutions useful for numerical romputation can be derived. 3luch can be learned about the process. hoivever, by examination of t h e equations and the transformations leading to them. 1Iost important, perhaps, is the fact t h a t Equations 19 and 20 are explicitly independent of R and cy. For given distributions of u , the interrelations betxeen R , a , and x are fixed by Equation 18. Before diwussing the form of the general solution for u, an examination of the limiting cases is helpful. I n the neighborhoods of the ends of an infinite column, (L must be constant. The values of these constants can be obtained from Equation 20, which gives the roots u(--33j
=
K -
4
~
- 11 a n d u ( m ) =
K
+-
4
~
- 12
(22)
These are the only constant values of u which will satisfy Equation 20. At total reflux, the limiting end compositions are zero and unity, and c y 1 / * , which proand the corresponding values of u are vide an interesting check on the roots (Equation 221; both pairs are mutually reciprocal. The second of Equations 22 provides a more convenient evaluation of the constant K than Equation 21. With it, Equation 20 k~eco~nes
(23) and I ( ( = ) appears as one of the explicit parameters of the solution. I t is only a hypothetical constant for finite columns but is easily calculated for all practical examples, as will be shown later. Qualitatively, the general form of the solutions of Equation 23 can be olitained by graphical considerations similar to Cauchy's proof of the esistence theorem for solutions of ordinary differential equations of the first order. Assume t h a t for large negative values of Y the function U ( V ) is a straight line of height 1 4 0 ) and very small slope. Continuation in the positive direction of Y n-ith the aid of Equation 23 indicates t h a t the slope increases to a point of inHection and then decreases again as I L ( Y ) approaches the constant u( I) asyniptoticdly for large values of u . T h e general s h a m of the curve is therefore much like 0 (17) the conveniional hyperbolic tangent function for ordinarv rectification. Samoles are illustrated schematically in Figure 5. Su(*hanalysis proves that the principal solution of Equation 23 contains one arhitrar>- conatant. -4s iq evident from the conitrurtion or from thy equation itself, this constant is merely
INDUSTRIAL AND ENGINEERING CHEMISTRY
1008
additive to v-that is, it permits a translation in the direction of the v-axis. Complete solution of any rectification problem under t h r present hypotheses could then be obtained from a one parameter family of solutions of Equation 23 for varying u( m ) , all passing through a point, preferably (0, 1). Such u-curves would give all possible relations between zO, 21, R , and (Y.
I Figure 5 .
Function of ~ ( v ) Schematic ,
Unfortunately, the graphical continuation method descrihed is not suitable for quantitative computation. The steps integrated must be very small relative to a v-unit, and practical problems generally require large values of Y. Even more serious than the labor involved, however, is the fact that the errors are cumulative. An alternative and more illuminating derivation of Equation 20 can be based on the operating line, Equation 2 . The flux of light component in the vapor stream a t any height, v , is t.he amount vaporized in the interval, Y to Y - 1. Therefore,
Substituting this expression into the operating line, Lquation 2 yields, after suitable transformation, Equation 20, with
This last relation permits direct determination of constant K from the operating variables. and from it, the intrrcrpts of the asymptotes of u can be determined by Equations 2 2 . The pinch point will occur where the liquid and vapor ~0111positions are constant over a finite length of tlie column. ,Setting y and z constant in Equation 2 1 shows that the pinrh po:'ilt coiupositions are identical t o those of ordinary rounterixrrr'nt cwntact rectification-that is, liquid and vapor are in equi1ibriu:n with each other. This is the same law that prevails for tlie rotary thermal colun~na t high pressure but differ? from that for the rotary column under vacuum. Equation 13. Extreme High Vacuum. I n all the idealized type. of operation treated aboTe, mixing in the vapor stream in the direction of flow has been neglected. This is a justifiable assumption un1es.s the pressure is so low that the mean free path of the molecules in the vapor is comparable with the length of the colun~n. If the latter condition is reached, mising in the vapor stream becomes very
Hypotheses Vapor mixing sepn.b y Valid f o r Radial Vertical partial cond. Pressures Complete S o n e Sone High h'one None None Intermediate Complete None Theoretical Low Complete Complete Theoretical Yery low
Vol. 43, No. 4
rapid indeed, and the vapor stream is no longer able to support a concentration gradient in the direction of flow; in other words. its composition may be idealized as uniform throughout its volume. Under such conditions the efficiency of separation by partial condensation is substantially ideal. The equation of perforniance for such operation can be derived easily froin the material balance equation for the liquid (Equation l I by taking p and q as in Equations 11. regarding ?/ as constant, and integrating between 20 and y. The iced composition can then be obtained from xo by the operating line; the distillate composition is, of course. the constant,, y. The resulting formula is, however, of little practical value, because such operation yields poor separations, as t h e following analysis will show. Consider operation a t infinit,eY . The pinch point a t the bottom is identical with that calculated for an infinite column a t ordinary high vacuum-that is, the liquid and vapor at the bottom differ by two theoretical plates. The vapor, however, has the same compoPition as the distillate, and the performance can be calculated from the operating line and pinch point relations alone. Nom- let the reflux also become infinite. The feed and waste compositions then become equal, and the vapor is then two plates richer than the feed. The over-all performance of a thermal column under extreme high vacuum conditions is therefore exactly two plates if both thc heat and reflux ratios are infinite, and reduction of either or both ratios to practical values would reduce the separation t,o even lese. Practicall>-,therefore, there must exist a critical minimum pressure below which thermal columns of the present type do not operate satisfactorily. SUMMARY OF THEORETICAL RESULTS
.4t atmocphcric pressure and above, the present thermal r e d fying column chould perform much like convent,ional contactors. .4~the pressure is reduced, the mechanism of operation becomes difficult to analyze, but the performance at high reflux is probably not greatly changed. Further reduction gives a considerable increase in separating power. up t o about double that of contactors, arid finally, a t extreme high vacuum, the separation falls again and beconies very poor. These results are plotted, again qualitatively BF curve 111 of Figure 3. The abscissa scales of Figure 3 are not even relative, because no study has been made of the limit,s of pressure within which the four idealized cases treated in this paper approximate reality; the relative positions of the maximum oii the contact rectification curve and the transition from high t o intrrmediatcs prwsure operation on the thermal rectification are merely reasonable guesses. .it partial reflux the differences between thermal and contart rrctificatioii are even more pronounced: these are punimarizcd in Table I. DESIGN A 3 D CONSTRUCTIO\ O F COLUMSS
Figure 6 is a photograph of the complete still and associated apparatus; the structural details, however, are more clearly presented in the diagrammatic assembly drawing, Figure 7. Basic dimensions are listed in Table 11. The motor-rotor-condenser assembly is ail metal. The rotor proper has a serrate profile with the outer edges sharp, t o aid in throwing off the condensate droplets. It fits snugly outside a heavier-walled, rigid, st,ationary tube, Fhich serves as a guide bearing and extends upward through a h o l l o ~shaft motor, being
Performance a t Total reflux Low reflux Nearly same a s contactors Kearlg same as contactors Excellent Unknown, probably good Twice t h a t of contactors Better t h a n contactors Very poor \ ery poor
Pinch Point Same a s for contactors Same a s for contactors Contactor value for as Only finite e v i c h m e n t finite heat ratio
Minimum Reflux Same as f o r contactors Same a s for contactors Less t h a n for contactor at total reflux a n d in-
April 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
T ~ B L11. E BASICDI.\fEXsIOXS
O F CoI.L-\IS
Culurrm proper: 1 in. long, 45 nim. outside diameter, joint to pot 6 5 , 4 0 spherical Roror: 1-in. long, 25 mm. diameter .Tacker: i 5 inm. outside diameter
firinlJ- anchored on the top of the motor housing. T h e sinall radial clearance between the rotor and its internal guide tube is filled with oil: for lubrication and thermal (,ontact. The guide tuhe thus obviates the need for external lieariiiga on the rotor:
it also serves as a chamber for the coolant, without requiring any packing glands. The voolant water flows into and out of the guide tube through sriiall copper tuties; each of these extends to the bottom of the yuiclr tuht,, is closrtl a t the lotver end. and i.: providrtl xvith nuiiierous sniall holes along its side. Thr flow of cwolaiit is therefor? luli,tantially transverse, rather than verticd, anti heat can be tli*sipated at a high rate without introducing aii appreciable temperature gradient vertically. Tlieriiiocouples are provided in the coolant inlet arid out let lines immediately above the top of the rotor, anti a n e d e valve :illti flowmeter are placed in the inlet h i e . so that the rate of heat trarisfrr to the rotor can lie measured an(1 controllrd. The main esternal bearing for the rotor also. ii v a w u n i +aI. T h i a hearing is a simple journal typc. I)ut accurately i i x t ~ ~ h i n t t~oi l u ;;mall radial clrarance. T ~ Iiushiiig P is counterI i c i w c i a t the uIJpfJr end to provide ari aniiuhr oil cup. Ivhich is kcbpt filled to constant level during vacuum operation. 1111nic~tliatel>~ helow the hearing, the rotor carries :i conical splash ritig, 1vIiic.h thro\vs the oil off and into an annular trough a t thrs tali of the coluniii proper. .i coiitinuous Hon. of oil through the tii.:iring is thwehy niaintaitird, foriiiiiig a p r f w t v:wuuiii wal. So other packing is nrwlccl. The remaiitiiig structural part3 of t h r atill are glass. The r,riluiiiii roper is fitted to t h c h i r i n g w i l a greirsed joint, t l i c s out.sicle of tlic latter lit4iig machined to thcx c>ortwttapcxr for tlir [iur]iosr. Thcl caoluiiin proper is heated I)? a Iiifilar IirLlical \viiicliiig of I i i ~ i v ySic*hroiiie ribtimi aplilietl tlirectly t o thcx tube and prot i ~ ~ . t c tiy ~ r l a11 outer jacket of glass tuliinp. T h r heatrd irngth t~\-ttwtlrtu oppo4tr the tiottom elid of the rotor but does not t.t~:i(.li thc top. Thrl resulting unhc~atedpot,tioti at t h e top swvtx :i- ~4 total c-ondenser, eliminatiiig the iirrll ior onf1 of c*onvcwtionaI t > J)I..
Thc~tlistillxtca titkc-off linr i.- nicfir(,l\. a riclr tube. ,sralt~,li i i t o t h r veiluiiiii at the top of the heated z o n e . Sinc.t. the coiirltwatt~ ft.oiii t l i v wgion above must flow ilonm the iiinczr * u r ~ i i r eof thv voluiiiu. a definite fractiou of it \vi11 enter this ttii)tl. This limit:. ttit. 1 ~ 4 u ratio x ot)tainal)le to a l i o v ~ii u i i i i i i i i u i n . l i u t tho w. critical: especially at, high heat ratios, a n d requires coiisitlerable experience on the p a r t of the, operator. T h e heat r a t i c v a l u e s reported in Table 11I were all computc~l from coolant f l ( ~ \ v and tcmperatut,c, rise., togc'tlii'r. \\-it11 thcj ~ ~ < ~ t - h ( , :ivattwyca ttrr :iliij visual control of the atliabativ .state. T h e equivalmt nunilirr of theoretical plates was coniputc~~l from t h e relativp volatility data of Bragg and Riclrardn ( 3 arid U-ard (91, using the equatiori of Dodge and IIuffnian Thr, results prrsentrtl in Table 111 show t h a t a hcsat riitil) unit is allout vilual t o or better than a theorctical plate; this in iicatrs that thc high pressure h>.potIiesrs are good apprijxini:ttion. for operation a t atniospheric pressure. T?St I'UnS \VC'l'e also 111ade at 0.01 111111. (Jf IllC'I'C'Ul'>- ~ J l ' ~ ' > * l l l ' ( ' , usirig thi> niistures of nirta- anti parat ricresyl phospliwtc:~\vliic,li ~ver(3studied by Bishop ( 1 j . Ewii a t Ion. heat ratios, hlI\\r.vc,t.. rlj. coinplcJti3that IICJ ciu:intitativc t>v:ili~ation of the cduniri raould b c m:tdc. TliiJsc rwult:: i i i c ~ ~ ~wpvis el~re range is still safely abovt, tlie 11y~10uum ca8e d i s c u w d thwrvticzill>~, An interesting series of phciiornena were obsrrved as t h i s lie;it input to the column \\-as inereascd during a run. :it lo\v h c 3 : t r inputs, a uniform film is observPd, somewhat stippled by the riiiii of droplets striking it. .I?the 1ie:tt input is incre the film rather suddenly lieconies uneviLn i i n d soon b r e a k u p iiitr, separate droplrts which slide do\vnivard and rapidly disapprvir, under these conditions the liquid does n o t wet the l3';ijJIJratlJl surfaw. Finally, at very high hcat inpiit. the reflux d o e i r i o t even adhere t o the hot surface; vaporization is so rapid that t l r , , droplets appear to bounce froni thct \\-all and never w r i i i , i i i r o actual contact with it,. These effects limit the heat ratio ol)t:iiiiat)le \vitIi a giveti column; there is a masimuni heat input Cor \\-Iiichthe condensate will flou- on the heated surface and there is, of iwurw. a prac-tic.ii1 minimum throughput. For t,he column descritwd tlir niasiniuni heat input was about 1 vatt pvr square cni. ~\-Iiich,f o r i'rinvenient throughputs, limits the hfai, ratio to a1)out :30. .41 lo\v I
St.\lXI,iRY
I . .I clistirictiori is niadc tretwrii contact, and thernial rtvrific.:itiori : iri contact rwtification, interphase transfer arises froni t i 1 1 3 spontaneouP approach toward equilibrium; in thermal rcctif i w t i v n , interphase transfer is effected by addition of heat t.o the i.csflus. or abstraction of heat from t h r vapor, or both, causing p:ii,tial vaporization, partial condensation, or both, reym!tivcBly. 2 . . The effects of pressure on contart rwtification are a n a l ~ z c ~ i l cluditatively. T h e argument indicates t h a t the proce,ss raiiiioi i'nnction usrfully at pressures belo~vthe moderate vacuum rmigc. at.? of nonadiabatic operation on contact rrc.tific.:iare also analyzed. The phenonirna arc complier certain conditioiis, ilonadiahatic operation ma>>.icbltiI ~ e t t e rnricahment r t ndiatJntiv, 1)c:cause of thr addition:tl t lic~rni:tl rtsctification rffe 1. .\ new t,hermal rect ig eolurriii is described; it eo1 t \vi.r cwnc:eritric tubes, the outer one tiring heated and the in (.oolrd :trid rotated. .i. The perforninnce of the n?w columil is calculated for toiir itleall\- rralizrd in different pressure r:irigc+. the perforinaricr is much like t h a t of ortlinarr nirdiatc and low pressures i t is b e t t w ; iiiiil t l i w r > . indicates that it fails to t'unvtion ur;efully only at cstrrnwl?. low p I ~ ~ , ~ : " u r c ~ . ti. I k t a i l r cwilcc,riiing they dwign aiid construction of t , h c , iwlu t i i r i arts p r w m t e d . A fen. j~erforniancefigures are prrscntrtl ai111 d. Thrse g j w i i i o d e ~ a t r gl ~ ~ support ~ d tCJ the t h t v i r ~ . Iti.ii11y pri.iiic,tc,d pi~i?'ornianrr,
