Phase Equilibria in the Propane-Butane System Citation Nysewander, Cecil Wright (1938) Phase Equilibria in the Propane-Butane System. Master's thesis, California Institute of Technology. doi:10.7907/77pd-9657. https://resolver.caltech.edu/CaltechTHESIS:11252024-191022116 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemical Engineering) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Sage, Bruce H. (advisor) Lacey, William Noble (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1938 Record Number: CaltechTHESIS:11252024-191022116 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11252024-191022116 DOI: 10.7907/77pd-9657 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16876 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 26 Nov 2024 18:53 Last Modified: 26 Nov 2024 19:11 Thesis Files PDF - Final Version See Usage Policy. 9MB Repository Staff Only: item control page

PHASE E'?.UILI PRIA IN THE PROPANE- ;:i,UTANE SYSTEM Thesis by C. w. Nysewander In Partial Fulfillment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena, California 1938 TA BLE OF CO NTEN·rs Pa ge 1 Introduction - - - - - --- - - - - - - - - - - -4 Tempe r a ture Control 8 Apparatus ------------ Pre ss ure Measurement - - - - - - - 10 Volume Measurement ------------11 Purifica tion of Materi a ls - - - - - - ---14 Method of Adding Sample_ _ _ _ _ _ _ _ _ _ l5 Sxperimenta l Results - - - - - - - - - - - - - - - - -17 - - - - - - - - - - - - - - - - - -21 Bi b lio g r aphy - - - - - ----------37 Ack no wl edg e men ts - - - - - - - - - - - - - -38 PHASE EC,1 JILI BRI A I N THE PROPANE - BU TANE SYSTEM Introduction A very import ant f ac tor in th e design of equipment used in transforming , separating, or otherwise h a ndling of hydrocarbons is an exa ct knowled g e of the phys ical properties of the hydrocarbon mixtures themselves under v a rious tempera tures and pressures. A large store of informa tion concerning the physical properties of pure hydroca rbons a~d mixtures of the s e hydrocarbons has been amassed du ring the past fe w years but even so, there r ema ins mu ch to be done befor e the volumetric and pha se behavior of uninvesti ga ted mixtures ca n be quantitatively predicted from the p rop ert i e s of their components. Among the physical properties of intere s t are the P-V-T-N rel a tions. These rela tions a re of much v a lu e not only in themselves but a lso in the f a ct that ma ny other physical properties may b e calcul ated fro m such d a t a through the use of th e rmodynamic principles. At pres s ures in the nei ghbo rhood of 1-5 atmospheres, Raoult's Law and Dalton's Law may be used with fair accuracy to determine phase equilibrium da t a for hydrocarbon mixtures. At higher pressures and a t tempera tures a p p ro a ching the critica l temperatur~, however, deviations become large and these la ws ciust be supplanted with experimentally determined facts. _ Souders, Selheimer , and Brown (1), h a ve used fu ga city instea d of vapor pressure in an a ttempt to pred ict more a ccurately the equilibrium conditi ons at the hi gh er press ur es where experi- -2mental data we r e l ack ing . There hav e been de v e loped a t leas t t wo distinctly d ifferent types of apparatus for th e de termina tion of the P-V-T rel a tions of hydroca rbon mixtures. One of these, de s cri b ed in detail by Sage, Schaafsrna, a nd La cey (2), consists of a thermos t a t ed steel cell in wh ich the sample to be investiga ted is p l a ced. Suitabl e auxilliary a ppa ratus i s set u p in conjunction with th e s teel cell, so that th e vol ume of the s amp l e a nd the p r e s s ure may be chang ed by th e addition to or remova l of mercury from th e cell. The mercury l ev e l insid e the cell, a nd thus th e vol ume occupied by the sample, is a ccura t e ly meas ure d by a mo vabl e e l ectric conta ct. A different type of appara tu s has been used by Young Bah lke and Kay (3), (4), a nd Cumm ing s (5), s i mili a r to th e appa r a tus that was used to obtain the da t a p r esent ed in t h is thesis. It has a small di a meter thick wa ll ed g l ass tu b e in pl a ce of the steel cell for holdins t h e s a mple. The upper e nd of the g l ass tube is s ea l ed , wh il e th e lo wer end is f itt ed into th e steel b lock wh ich ha s connections for eva cua ting th e tu be , add ing th e sampl e , a nd a lso for a dding or removing mercury t o cha n g e t he vo l ume a nd p r ess ure on th e samp l e . I n t h i s cas e the v ol- ume ca n be measured by visua ll y n o tine; the he i gh t of t he me rcury l eve l i n t he g l ass t ube. Other de t a il s of construction a nd p rocedure will be f ound in th e se cti on devoted t o the a pparatus a nd experi menta l pro c edure. s ach t ype of a p para t us h as it s ad v a nta g e s a nd li mita tions. The v a ri a bl e vo l ume s t ee l cell may be us ed a t pr essur es u p to s ev e r a l thous a nd pound s , wh il e with th e g l ass tube about one -3thousand pounds per s qu a re inch a p pea rs to b e the upper limit. The steel cell may be ma de l arge e n o u e;h to hold e. sample we i ghinc,: 2 0 -50 e; r rtms whe reas the total sample for the gl ass tube used in these experime n ts was neve r over 0.1 g ram. l arg e sample may or may not be an advanta g e. The The l arg er sam- ple increases the accuracy with which the wei ghts of the different components of the sample ca n be determined but, at the same ti me, the larg er s a mple requir es a g r ea t deal more materi a l. It is usua ll y necess a ry to study seve ra l different compositions of a mixture. The amount of sample r equired ma y be quite im- portant where the purification is a prob l em. All the r e sults presented in this thesis r e qu ired l ess than 1 g ram of the finally purified propane and bute, ne. A further adva nta g e of th e 5 lass P-V-T appara tus is that the phase boundaries ma y b e determined q uite ac curately by dir e ct observation. The de w point a nd bubbl e points ma y be deter- mined by observing the pressure, volume, a nd temperature when a very small amount of the liquid or gas resp e ctively is in e quilibrium with the r e mainder of the sample in the other phase. With the steel cell, the de w points and bub bl e points may be obtained only by taking a g r ea t ma ny rea dine;s in the vicinity of the se points and determining the discontinuiti es in th e pressure- volum e curve at consta nt t empera ture. Another a dvant age of the g l a ss a pparatus i s the rapidity with which the temperature may be chang ed. The steel cell in a li quid bath with a larg e he a t capacity requires considerable time for cha n g ing tempera ture. The gl a ss tube is thermostated by a condensing vapor from a li quid boiling under reduced pres- -4sure. The temp e r a ture ma y be cha ng ed a n d th e a pparatus b rough t to equilibrium aga in in a few minutes mere ly by cha n g ing the pressure on th e boiling li quid. Apparatus 'rhe appara tus used a nd the procedure followe d will be described in detail with r efe renc e to Fi gure 1, which shows a schematic dia g r am of the, assembly, and Fi g ure 2, which show s the pressure tube a nd j ack e t in detail. The glass pressure tu be , A, was made of pyrex g lass cap illa ry tubing with 1. 88 mm. averag e inside di ame ter and a wa ll thickne ss of 3.1mm. The up- per end was sea led carefully , keeping the t h ick ness of g l as s over the end about the s a me as tha t of the wa lls. In th e p r e limina ry runs, the end was sealed in such a way tha t the in s i de of the tip was flat a nd a l a r ge amount of g l as s was a c cumul a ted a t the top. This sea l s at isfac torily withstoo d th e p r e ssure , after a nnealing , until it was cool ed to li quid air tempera ture. Apparently the cooling to li qui d a ir t empera ture ca us ed strains in the glass for it inva ri ably fra ctured in a pla n e a cross the fl a t surface at a lo wer pressure tha n tha t at wh ich it had been tested before cooling . By keeping the inner surface of the sea l ed end rounded a nd the wall t h ickness over the sealed end uniform, the pressure tube could be cool ed repeatedly with liq~id a ir, without fra cturing , when p res su r e was aga in applied. To the lo we r end of the p r e s s ure tube, A , Fi g ure 2, was sea l ed a 1.5 inch leng th of 1.2 inch diameter pyre x tubing in the sha pe of a thistle tube . This g l a ss assembly was t hen fitted into the upper r emo v a ble pa rt of the ste e l block, B , with a ru bber ga sket, C, h e ld in pl a ce by the g l and nut, D, -5- TO VACUUM PUMP t 6 ,@ - r __,L_I AIR H j· 8 FIG. I. -5- 11 11 II Ill 2 FIG. 2 -7When the steel parts we re fitted to ge ther the lower end of the thistle tube and the lower protective shield of steel slipped into the a nnula r cha nne l be low the level of the outlet from this enclosed space . After these parts h ad been assembled , the procedure was to evacuate the tube through valve 1, down to about . 001 mm . of mercury vacuum. Then by opening valve 3, shown in Fi gu re 1, mercury flowed into the annular channel, effectively sealing the inside of the pressure tube and the thistle tube from the annular space between the thistle tube and the steel block . Built into the lowe r part of the steel block were two needl e va lves, 1, in the vacuum line and 2, in the line to the sampling hook-up. Below this block was an electrical contact, E, with which the level of mercury could be kept in the app roximate vicinity whi l e adding the sample . C,::xtra heavy steel pipe connected the conta ct assembly with the mercury reservoirs, F and G, a nd the manometer , H. Reservoir G, was simply a junction between the mercury in the system and the oil in the pipe to the fluid pressure balance . An electrical contac t in- s i de this reservoir made it possible to keep the mercury level at a fixed point while taking pressure r ead ings . The r ese rvoir, F, was connect ed by a manifold with a source of a ir pr essure, a vacuum, and a vent . The a ir pr es sure was used to force mer- cury into the pre s sur e tube and thus chan3e the vol ume and pres sure on the s ampl e as des ired. pre ssure whe n desired . The vent a llowed the release of The vacuum was used to pull the mercury down out of the tube when the pressure in th e tube was less than one atmosphere . - 8The manometer, H , wa s useful in checkin?; the amount of s amp l e added , i n the calculation of the p r essure correction, and in indica ting d ir ectl y the pressures on th e s amp l es when they were in th e r a n g e of the manometer. The first two us es will be d escribed i n deta il l a t er . Temperature Control A va cuum j acke t, I, surrounded the pressure tube in the s ec ti on be t ween th e boiler, J, and the condenser a t th e top . This vacuu:n jacket wa s s ilve r ed ex cept for narrow v e r t ica l apertures, in front and ba ck, for obse rving the phenomena insid e the tube . The l eng t h of th e v acuum j a cke ted po rti o n was 27 . 5 inch es , th e insi de d i ame t e r, 1 . 1 inches , a nd t he outside diameter 1 . 5 inches. The li qui d providing the vapor was pull ed by suction into th e a nnul a r spa ce around th e p r essur e tube a nd up into th e bo iler spa ce, below th e va cuum j a ck e t, through the proj e ctin5 g l ass tub e , K. A rubb e r tubing connection p r 8vented li qui d from escaping be t ween t he l owe r e nd of the j acke t a nd pressure tube . To pre vent de t e riorat ion of this rubber con- nection b y the organic li qui ds used , a sma ll a :110unt of mercury was run into th e lo we r end of the jacket up to the l ev e l of the pro j e cting g l ass tube. Gl ass bead s were p l aced i n t he boi l e r section to prevent b ump ing . To prev ent the beads from wed g ing around th e pre ssure tube, the g l ass tubing thro ugh the small water condenser was ex t ended up several inches into th e boi ler section . A small hole, L , in th e wall of t h is tub e, just above the po int where it wa s sea led i nto the ou t er j acket , permitt ed th e liquid to be dra i ned out when des ired . Above the vacuum j acl{e t ed sec tio n a water condenser wa s pl aced t o condense the -10 the tube . The li qui ds used a nd the t empera t ur G r a n ge s for wh i ch th ey we r e f ound sati sfa cto ry a r e as fo llo ws : Ace t one , C . . P . 100-1 30° F . ~thy l Alcoho l, 96 % 1 40 -1 70° F. 1 To luene , (1 V o u • 1 80-220° F . .l. s . K. Pra cti ca l 230 - 265° F . Br omobenz ene , K. K. Bes t Gra de 265-300° F. Chlo ro benzen e , The junction of th e th e r mocou pl e was lo c.s ted s li ghtly a bove th e midd l e of th e l en p, th of th e pr e s s ur e tube , used in th e mea surements , a nd just to :) n e s i d e . 1:i: rror d u e t o r 3.d i a tio n was conside r ed neg li gibl e s inc e th e doub l e wa ll s of the jacke t we r e s ilve r ed except for th e na r r o w aper ture s for ob s e rva ti o n. Th e coppe r consta.n t a n th e rmocoupl e was ca li b r a t ed throughou t th e entire t emp era tur e r a n ~e r equ i r ed i n a t h e r mos t a t ed o ilba th or l ead bath a ga inst a s e t of Bureau Stc..nda r ds th e r mome t e rs whi ch coul d be r ead with a n a ccura cy of 0 . 03° F. Pressur e Measurement A fl u i d p r e s su r e bal a nc e with a n a ccuracy of 0 .1 pound per s qua r e inch was used t o mea s ure the pr e ssure s bel o w 300 pounds per s quare i nch a nd a p r e s s ur e ba l a nc e with a c curacy o f 1 pound pe r squa r e i nch w2-.s used t o mee. sure the h i ghe r pre s s ur e s . A numbe r of corre ction f acto rs we r e co ns i dered i n de t er mi ni n g the f i na l pr c~ssu r e on t he s ampl e . These correc t i ons incl uded th e ba r ome t e r correcti ons , cha n 6 e s i n th e h e i ght a nd d ensity of t he mercu r y i n th e pre s s ure tub e , o.nd th e corre c t i on du e to the d i ffer ence i n l ev e l of th e pr ? s sure ba l e.ne e a nd th e appara tus . -11correction d u e to th e capillary dep r ess i on of th e mercury wa s automa tica lly ma de i n t he constD.n t fo r th e appa r a.tus . This constan t was obta in ed by r ead i n g s e v e r a l press ure s b oth on th e pres s ur e ba l a nce a nd o n the manom e t e r, H. Aft e r corre cting t hese p r e ssure s for t he density of the mercury a nd th e he 1. ri:h t in t he p r e s s ur e tub e , th e A. Ve r ae;e d iff e r ence be t ween t he p r e s sure b a l a nc e r ead i n g and the ma nome t e r r ead ing was t aken as th e consta nt . I n a seri es of three d iff e r e nt p r essur e r ead- i n gs th e co nsta nt s fo u nd we re : - 20 . 0 3, -1 9. 94 , and -1 9 . 88 , ~nd th e a v e r age v a lu e of -1 9 . 90, was us ed . Th e corr ec ti on d ue to vapo r pressure of me rcury wa s s o sma ll as to be cons i de r ed ne g li g i b l e i n the temp e r atu r e r a n - e of these exp e r i men t s . The equat i o n for co rr e cti n g the p r e ssure s i s as f o ll o ws : P( corre ct ed ) = SP+ A + K (Ra- R) + B A i s th e consta nt for t he a ppa r a tus v1hen R = % a n d t he dens ity of th e mercury i n the p r e s s ur e tube is corrected t o 32 O• F. K i s a f a ctor conv e rting a co lumn (R0 -R) of mercury at the tempera ture of the expe ri m8nt to pounds per s quare inch . R0 is the r e fer e nc e po int a t th e uppe r most point i n th e inside of the t ube . R is th e a ctua l h e i gh t of me r cu r y i n th e p r e ssure tube . B i s t he ba r ome t e r r ea d ing i n po u nds pe r square i nch . Vo l ume Measurement Th e vo l ume of t he pre ssure tube as a function of the d i sta nce from th e sea l ed end , was ca lt b r a t ed by measur1ng t he l eng t h of a we i gh ed a mount of me r cur y as 1 t •na s mo v ed , i n a s i n5l e mass , u p a n d d o wn i ns i d e th e tube . Al l t he measu r ements -12of leng th or hei ,;;ht of mercury column or li q uid l eve l were made with a ca thetometer which was .s,ccura te to . 01 cm . Knowing the weight of the me rc ury and the temperature, its vo l um e could be obta ined . Then applying the meniscus corr ect ions to both ends, an averag e v o lume per cm. of tube leng th was obtained. By making a series of such r eading s over the por tion of the tu be used in the experiments a value for the volume of each cm. of the tube was obtained. Thes e va lues could have been integra t ed on a plot of volume v e rsus distance, but t o obta in g reater a ccura cy a method of plotting r es idua l vo l umes was us ed. A n ominal or b ase volume equal to .02785 cc . per cm . of tub e length was decided upon a nd this amount wa s subtracte d from the actual vol ume of each c m. of tube leng th . Then these r e sidua ls were plot- ted aga inst tub e leng th both as a ctua l r es idual for each c m. of leng t h and a l so as total cc . of r es idual from the sealed tip (ref. point) to each c ~ . distance from the seal ed tip. curves a r e shown in Fi g ure 3. These Thus the a ctua l volume at any dis- tance (R0 -R) from the reference point, R0 , equaled .02785 (Ra-R) p lus r e sidua l corresponding to tha t dista nce. The volumes were also corre cted for the me n iscus es of both the liqui d a nd the mercury a nd a lso for the vo lum e of the sma ll steel agitator us ed . Th e specific vo l ume of the ma t eri a l a ':Jove th e mercury l eve l, V :: [02785 (R0 -R) t Res idual - .013~ . 0 1 60 2 _, e i s ht of s a mpl e ( R -R ) i s the d i sta nce between the r e feren c e po i nt a nd the mero cury l evel. Then .02785 ( R0 -R ) i s the b ase vo l um e above R . Residual i s t he correct i on· between the ba e e vo l u me 'J.nd the a ctua l vo l ume and i s t aken fro m F i gure 3. The f i gur e , . 01331 , in- -1 3- . 125 100 100 80 u ::; er 2 w a. " ~ 0 2 u w ::, 60 u 75 u 3 w 0 ::; ..J 3 400 > <l'. :, 50 > 0 ..J iii w <l'. :, er ..J ;'! 0 ,- 0 iii . 20 ~ 25 0 0 10 20 DISTANCE 30 40 FROM REFERENCE POINT 50 CM. Fi g . 3. Residua l Volume Corrections f o r the Pressure Tube. -14cludes the volume of the steel agitator and the mercury meniscus correction. These volumes e. re in cubic centimeters. To convert the total volume in cubic centimeters into cubic feet per pound, the conversion fa,ctor, ( .01602 ~ weight of sample), is applied. Purification of Materials The propane and butane were obta ined from the Philgas Company. According to the specifica tions, the ori g inal propane contained les s than 0.1% impurities. It wa s further purified by fractional distillation in a glass-ring packed column (6), four feet long and 0.5 inches inside diameter, equipped with v a cuum jacket and with ade qu a te facilitie s for maintaining very consta nt reflux. The middle fraction, am:)l)_ntins to about three-fourths of the charg e, was collected in a liquid air cooled receiver connected with a hi gh vacuum deg.as sing apparatus. The material was then distilled under va cuum b a ck into the boiler of the fr:3 ctione,ting tower and refractiona ted. This time about 90% of the charge was collected in the li qu id a ir cool ed trap as before and later :-'tr.,i nsferred t -:) a steel stora.e; e bomb. An isotherm on this material throu gh the two phase r egi ::m indicated that its purity was satisfactory. The original butA.ne contained 0.3% isobutane. This material was purified by the s ame general procedure as described abov8 for the p ropa ne. -15Method of Adding Samp le Samples were a dded to the a9pa r a tus in th e following manner: samplBs of purif i ed p ropane a nd n-butane were kept in small steel wei p;hing bombs. Before attaching one of these bombs to the line l eading to va. l ve 2, the bomb was washeJ. in acetone , dried in a vacuum des i ca tor, and ca r8fully vrn i ghed. The mercury was pulled out of the pressure tube, lower chamb er, and manometer, H, down to the lBvel of the electrical contact, E, and valve 8 , clos ed . With the bomb valve closed, valve 2, was opened and the pr e ssure tube and connecting lines evacuated through valve , 1. The top of manometer , H, was connected to the same v acuum system. The vacuum was produced by a mercury vapor pump backed up by a Hi - Vac pump . When a va.cuum of .001 mm . was produced as measured b y a McLeod gage , va lve, 1, vvas closed and the bomb valve carefully opened, a llo wing the hydrocarbon sampl e to enter the pressure tube. This ga s caused the manometer to raise a nd the mercury a t the e l ectri ca.l contact to fall, but by e.ddins mercury through v a lve 8 , th e mercury l evel was kept at the contact . Y.lhen the desired amount of g?,s had been added as indicated. by the hei ght of the manometer l eve l, v alve , 2, was closed. Then the bomb was cooled in liquid air to reduce the amount of gas in the connecting lines to the vapor pressure of the hydrocarbon at li qui d air temperature. The bomb valve was closed, th e bomb warmed to ro om temperature, washed in acetone, dr i ed , and rewei ghed. The sample o f the other hydrocarbon was added in the sam e manner. It is admitted that the accuracy of this gravimetric method -16of de t ermining the amo unt of s ampl e mg,y not appea r to b e as ac cura te as some vo l ume tric me thod s wh ich h a v e been used. When the stra i z ht for wardness of the method and th e absence of a ny a ssumpt ions as to ga s volumes, etc., are considered, the ove r a ll a ccuracy was felt to be as good. Iri o nl y one run, No. 9, was the compo sition questiona b le, and this run was made with a very sma ll sample to obtain add itiona l dew po ints at lo we r temperatures. However in this ru n, several bubbl e points and dew points wer e taken at the hi g her t empe r a tures where the ph a se boundaries as functi o ns of p r essu r e a nd com position, and t ,3mperature a nd c ompo siti on had been definitely de t ermin ed by pre vious runs on l a. r e;er s a mples. Thus it was c-Jnsidered justifi abl e , in t h is ca se , to chan g e the c ompos iti on fr om tha. t det e rmined g r a vlmetrica lly, to one which woul d perm it t he dew points and bub ble points at the higher t emperatures to f a ll upon the definitely established curve s. This involved a sh ift of the mol percent of propane from 6 8 . 2% to 6 5 . 0%. Althoug~ the sim-olified diagram shows th e va lves, 1 and 2, some distance to either s ide o f t he vertical cent e r hole, the v a lve s were actua ll y pl a ced s o th at no ga s could be trapped when the mercury level WEts raised a '.JOve tha t point. Wh en the mercury level was r a is ed , c omp res s ing the s a mple into the portion of th e tube wher e the meas ur ements were made, fre quentl y at roo m tempera ture , the sample would begin to li quify below the boiler. It was f ound that an appre ci a ble amount of the li qu i d adh ered to the g l a ss wa lls. To preven t this, the sample -17was c onde nsed with liquid a ir into the upper tip of the tube while the mercury l eve l was raised u p above the boiler. The liqui d a ir trap, S, was slipped inside the vacuum jacket down around the tip of the pre ssure tube. After the mercury level was got ten above the boi l er, it was kept there until the measurements on the sample were comp l eted . Experimental The singl e phase measurements of the i sothe rms were simple to make, consisting merely of takin g r ead in5s of the pressure and th e corresponding volumes over the range desired . Since the in- vesti ga tion was l arge l y concerned o nly with the phase boundaries , the single phase measurements were limited to those in the nei ghborhood of the de w a nd bubble points . 'l'he measurements in the t wo phase region we re mor e difficult due to the d ifficulty with which equilibrium was attained be t we en the phases . The s ample was thoroughly azitated by means of a smal l iron stirrer which was moved up and down the inside of the tube with a ma e;net aro und the outside of th e jacket. All measurements were taken with valves, 3 and 8, open. Th is allowed the equilibrium to be reached before each r ead ing by an isobaric process. The p r essu r e having been set at the desired point by adding to or removi n p- a ir fr om the chamher , F, the s ample would be agitated, a t the constant pressure , until the tota l vol ume , occupied by bot:h phases ceased to chane;e with further a~itation. This ga ve a simple way of determininz when equilibrium had been reached. -18The bubble points were determined in the following manner: with the sample in the liquid phase at a pressure sli ghtly above the bubble point, the pressure was reduced very slowly by venting air while the liquid was continually and vi gorously agitated. At the first sign of a bub ble forming , the air release va lve was closed. If on further agitation the bubble did not become large r tha n being b a rely visible, this was considered to be the bubble point and the pressure and volume were recorded as such. If the bubble did become appreciably l a r ger on further a gitation the pressure was raised a few pounds a nd the process repeated. These points could be checked by approaching from the two phase re g ion but this method was much more dif f icult since it involved equilibrium in two phases instead of one just before the bubble point was reached. The most difficult measurements of all we re those of the dew points. The techni que finally developed was similar to tha t for bubble points. V'l i th a ll th e sample in the gas phase, the pressure was very slowly raised whil e the ga s was being thoroughly a g itated. At the first sign of li quid forming, the pressure valve was closed. If on further ag ita ting no more liquid was formed this was considered dew point. Al though these points co u ld b e checked from the opposite side, that is, from the two phase side, it was an a lmost endless task. It meant setting the pres sure a nd agita ting thorou ghly; if liquid rema ined, the p ressure was reset, lower, and the p roces s repeated. If one was fortunate, a fter a few tri a ls the exact pressure was found at which, a fter thorou a.;h agitation, only -19a very small amount o f li quid r emF.dned . Since pr e ssure and volume measu r ements were taken on both s i des of each of the phase boundari es for each isoth erm , the exact pos i ti.ons of the boundari es we re checked. by loca ting the discon tinuities in th e curves of p r e ssure v e rsus vo l ume at consta nt temp e r a tu.re . I n nearl y a ll th e determina t i on s, the dew po int a nd bubbl e point p r e s su res as de t e rmined by observation checked within . 5%of thes e p r e ssures as indica ted by the bre aks in th e i sotherms. Fi g ur e 4, shows th e isotherms ob t a. ined fr::,m run No . 5, on th e system conta ining 69 .8 mo l percent of p ropa ne and 30. 2 mo l per cent butane . I t was impossi b l e to o b t a in dew po ints over th e ent i re t emperature r a n g e unless very sma l l samples we re used , due to th e small volume o f the pressu r e tube. I t was f ound advisabl e to make runs with l a r Le s a mpl e s p rimaril y for bubble points over the en tire tempera ture r a n e;e and dew points a t the hi ghe r temperature s and then subsequently to fill in the dew po int data with runs o n sma ll er s amples. -20- 600 ~ d CJ) CI w a. 500 a:i ...J w CI :::J 400 Vl Vl w CI a. 164.2· 300 144,_4• 2oot--7~~1~2~J.s!'•4====t====+===+===1 ._ 0 .04 0 .08 SPECIFIC 0.12 VOLUME 0 .16 0 .20 CU. FT PER LB . F'i g . 4. Isotherms of System Containing 69 .8 r~ ol Percent Propane and 30.2 Mol Percent Butane -21- Results The experimental determinations incl uded the mea surements of the volumes of the phases under the different condi~ions of temperature and pressure, but these volumetric data have not been used in the preparation of this thesis other than to check, or in some ca ses to establish, the dew points and bubble points by the discontinuities in the re-lation, (j ¥) T' A numbe r of these isotherms for the system of composition, 69.8 mol percent propane and 30.2 mol percent butane are shown in Figure 4. Measurements were made upon nine different compositions in all, but the results of only the last five have been used. The measurements on the first two compositions were of a preliminary nature during which time a technique wa s being developed a nd certain improvements were being made in the a ppara tus. The results of the next two compositions studied were so fragmentary, due to the breaking of the pressure tube, that they were of no value. The compositions of the five r emaining runs are given in Table I, along with the pressures and temperatures at the critical point, the point of maximum pressure, and the point of maximum temperature for each composition. Figure 5, shows the phase boundaries of the five mixtures on a pressure-tempera ture diagr am , each loop representing a different mixture. From left to ri ght, these mixtures are No. 7, No. 5, No. 8, and No. 6, as numbered in Table I. The sample of mixture, No . 9, was too small to be studied satisfactorily in the critica l region. The broken line, t a ngent to - 22 - TEMPERATl iRF °F Fl g . 5 . Pre ssur e-Temp era t u r e Di a gr a ms a t Co nsta n t Compo sit i o ns -23TABLE I. Some Characteristics of the Mixtures Studied. Comoo si tion T~ol % Mixt. Point of Max.Pressure Press. Temp. #/s q. in. °F. No. C3 C4 5 69.8 30.2 638 242.6 6 20.8 79.2 584 288.6 7 85.5 14.5 630 223.2 8 33.8 66.2 610 279.2 9 65 .o ➔~ 35 .o Mixt. No. *Corrected va lue. Point of Max.Temp. Press. Temp. #/sq . 1 n. °F . Critical Po int • Press. Temp. #/sq. in. OF. 5 630 244.0 638 242.6 6 580 28 9.2 583 289.0 7 626 224.2 630 223.2 8 605 280.3 609 279.6 TABL"S II. Equilibri um Ratios for Propane and Buta ne Temperatures °F' . Propane Pressures #/sq. in. 100 280° 1.70 200 2.30 1.76 2.20 1. 24 1. 56 1. 87 400 1.25 1.46 1.69 500 1 . 04 1. 22 1. 36 1.31 300 1.50 Butane 100 0.57 o.84 o.64 o.89 o.47 e.65 o.85 4oo 0.53 0.71 0. 88 500 o.46 o. 66 o.so 200 300 o.47 o.95 -24these curves a nd whi ch e nds a t the critica l points of propane and butane, is th e loci of the critical po ints of a ll possible mixtures of propane and butane. It is evident from the fl a t- ness of this curve, especially as it a p p ro a ch es the critica l point of propa ne, that there is not much difference between the maximum pressures a nd the pressures at the critical points of th e different mixture s. As sho wn in Tab le I, for mixtures, No. 5, a nd No . 7, the d ifferences in these pressures a re neg li g ibl e, wh ile for mixtures, No . 6, and No. 8, the differences are barel y more than limits of the experimental error of the p r e s s ure measurements. to study experimentally Tha t it was found v e ry d if f icult the r ee;ion of r e tro g r 2.de cond ensa tio n . may be p a rtially explained by the facts tha t th e differences bet ween the maximum press ures and t he critica l p r essur es were s o small and tha t th e d ifferences be t ween t he maxi mum t empe ra tures and the criti ca l tempera tures we r e a l so qu it e small, the maximum be ing 1. 6 0 F., with mi xture No . 5, Tab le I. It is within th ese narrow limits t ha t th e phen omena of retro g r ad e c o n dens a tion o c curs. Fi gure 6 include s a number of p r essure- compo sition d ia- g r am s at consta nt temp e r a tur es r a n g ing f ro m 100° F. t o 2 80° F . This s et of d i a g rams was made up by following constant t empe ra ture lines on Fi gu re No. 5, and reading the p r essures a t t he phase boundar i e s of th e d iff e r e nt compositions. These pressures were th en p lot ted upon t h e pressure-co mpos iti o n coordinates a nd smooth curves drawn throue;h the points for each phase boundary a t ea ch tempera ture. Ea ch pa ir of con- stant tempera ture phase boundary cu rve s t erminates in common -2 5- 500 zd (f) a: w 400 Q. Cii ...J w a: 300 :::) (f) (f) w a: Q. 200 0. 2 0.4 MOL FRACTION 0 .6 0 .8 PROPANE Fi G. 6. Pressure -Co mpo sition Dia gr a ms a t Consta n t Tempe r a ture. -26points a t the vapor pressures of pure butane and propane a t tha t tempera ture . Consid e r, for examp l e , the curves at the co nsta nt temperature of 1 90° F. These cu~ves t e r minate a t the ri ght h a nd ordina te (100% propa ne) a t the va por pressure of pure propa ne a t 1 90° F. and terminate at the left hand ord ina te (100% butane ) at th e vapor pressure of pure butane. The reg ion enclosed by this p a ir of curve s i s the only reg ion in which t wo phases may exist in equilibrium a t 1 90° F. At a ll pressures above the upper curve, the l oci of bubble points at 190 0 F. for a ll mixture s of propane a nd butane, only the li quid phase may exist. At a ll pressures below the lo we r cu rve , th e loci of de w points a t 1 90°F. for all mixture s , -: m ly the gas ph ase may e xist. If no w a constant p r es - sure is taken, for example 300 pounds per s quare inch, it ls possible to determine the composition of th e coexisting phases at 190° F. by merely r eading t he composition of the li quid phase o n the bubbl e point curve and the composition of the gas ph ase on the dew point curve, both at 190°F. a nd 300 pounds per squa re inch pressure. The curvature of the bubbl e po int curves on this diag ram is a measure of the degree with wh ich mix t ures of butane and propane agre e with Raoul t I s Law and Dal ton's Law. Strai ght lines wo uld indica te tha t t he tota l vapor press ure of the liquid of any mixture a t a ny definite tempera ture is equa l to the sum of the mol fraction of butane tim es its va por pressure in the pure state, a t the tempe r a ture in ques tion, and th e mol fra ction of propane times its v apo r uressure at the -27same temperature. Since the bubble point curves a re not en- tirely strai ght, it is evident that mixtures of these hydrocarbons do not follow these 19.ws, al thou gh the deviations are not as large as is found with some pairs of other hydrocarbons with more widely va rying physical properties. Fi g ure 7, a temperature-composition diag ram at constant pressures, was prepared simil~rly to Figure 6, except that, in this case, constant pressure lines were followed on Figure 5, and the tempera tures of the phase boundaries of the different mixtures plotted on the tempera ture-com:o osi tion coordinates. On Fi gure 7, at the constant -pressure of 300 pounds per square inch, as an example, the phase boundary curves terminate at common points, the point on the right being the temperature at which pure propane has a vapor pressure of 300 pounds per square inch, and the point on the left being the temperature at which pure butane has a vapor pressure of 300 pounds per square inch. ·rhese two curves inclose the two phase region at 300 pounds per square inch for all mixtures of propane a nd buta ne. The upper curve is the loci of dew point temperatures for all mixtures a t this pressure and the lower curve is the loci of all bubble point temperatures at the same pressure. For any mixture at 300 pounds per square inch pressure, only the gas phase will exist above the dew point curve and only liquid phase will exist below the bubble point curve. If on this diag ram, a constant temperature line, for example 190° F., is followed, it is possible to determine the composition of the coexisting phases at 300 pounds per - 28- 0 .2 0.4 0 .6 0 .8 M OL FRACTI O N O F PRO PANE Fi g . 7. Tempe r a t ure - Co rnpo si ti o n Di a g rams a t Con s t a nt Pres s ure -29square inch pressure by r ead ing , as before, the composition of the ga s phase on the dew point curve and composition of the li quid phase on the bubble point curve. Since, on both dia g rams, the same pressure a nd tempera ture have been used, namely, 190° F. and 300 pounds per square inch, the composition of the coexisting phases as determined in both cases wil l be the same. The ratio of the mol fra ction of propane in the ga s phase to the mol frac tion of propa ne in the li quid phase is cal l ed the equilibrium ratio for propa ne. This quaptity, K, is frequently called the equilibrium consta nt although it va ries with temperature and pressure as well as the character a nd amounts of the other components present in the mixture. If at equilibrium, Xp is the mol fr a ction of propane in the li qu i d phase , a nd Yp is the mol fra ction in the coexistine; gas phase, then /(p ~ Y½P In a like manner, the equil i brium ratio for butane, )f 8 // I - Yp /. or in this binary sys t em, na-: /1-XP • -=- Y13/XB These values of K may be determined from the temperature-composition of the pressure com pos ition d i agr a m as explained previously. Equi librium r a tios t aken at different pressures from Figure 6, at each of the constan t temperatures indica ted there, were multiplied by the pressures a t which th ey were taken and then plotted aga inst these pressures in Fi g ure 8. The curves be low the dia gonal line represent consta nt tempera ture equilibrium r a tios for butane as functions of pressure. The curves · abo ve the dia e;onal line represent constant tempera ture equilibrium r a tios for propane as functions of pressure. If the equi- libriurn ratio for propane. i s desired, for e xample, at 190 o F. -30a nd 400 pounds per s qu a re inch p r e ssure, it may be de termined by dividing PK by P o r, in this case , K = 500/400; 1.25. Of cour se , for the sole purpose of obta ining equilibrium r a tios, a plot of equilibrium r a tios as functions of tempera ture or pres sure would be more convenient. This d iag r am , Fi g ure 8, was prepared to show more s a tisfa ctorily the beha vior of the s e ratios in the critica l re g ion. A numb er of equilibrium ratios t ak en from this di agr a m a re t abul a ted in Ta ble II for both propa ne a nd butane. The dia gona l line, Fi gu re 8, is the loci of points where the equili b rium r a tios a re e qu a l to unity, that is, where PK P. The equilibrium r a tios for e ither component a pproaches unity as the tota l p ressure on the system approa,ch e s the vapor pressure of tha t component a t the tempera ture of the s ystem. Where the tempe r ature is abo ve the critica l point of one of th e compone nt s , bo t h equili b rium ratios app ro a ch unity as the pressure app ro a ch e s the critica l pressure correspond ing to the temp e r a ture of the s ystem, which tempera ture be comes the critica l temp e r a ture of the s ystem. Thes e critica l va lu es , of co u rse, corre spond to de finite com positions. This is illustrated by th e consta nt temperature curves a t 220° F. , 250°F. , a n d 2 80° F. , and the correspo nd ing mixtures a re 88.8 mol percent propane, 64.6 mol percent propane, a nd 34.2 mol percent propane, r e spective l y , as may be as certained by noting the points, on Fi g ure 6, wh e re the ~hase boundary curves a t t hese tempera tures touch the loci of critical pressures. Thus a t tempe r atur es above th e critica l point of propane but b elo w th e critica l point fo r b uta ne, the butane equilibrium r a tios sta rt _a t unity a t the v apor pre s s ure - 31- / I / / fo0 ~ / 70 0 6 00 5 00 ~ CJ V) 5 a. 400 m _J '<. a. 300 200 I I I ,oo I I I I 100 200 300 PRESSURE 400 500 600 L B PER SQ IN Fi e . 8 . Pressur e Ti mes EQu ilib ri um Ra t i os a t Cons t a nt Tempe r a ture ve r sus Pressure . -32of butane and then return to unity a t the critica l pressure corresponding to the temperature o n t he system, wh ich becomes the critica l temp era tur e . At tempe r a tures be lo w the criti ca l points of either com- ponent, the equilibrium r a tios of either component become indetermina te as the pre s sure on the system becomes equ a l to the v a por pressure of the other component at the tempera ture of the sy s tem. The broken envelope curv es , starting a t the ori g in, a re the lo cl o f points a t wh ich the pressure on th e system becom e s equ a l to th e va.por pressure of the oth e r co mpo nent a t the t emp era ture of th e system . For examp l e , the upper broken envelope lin e is th e loci of points a t wh ich th e equili b rium ratios for propane becom es indet erm ina te, tha t is, the points a t which a t t he con s t a nt temp e r a ture s sho wn, the pressures become e qu a l to th e vapor p r e ssure of buta n e . The vertica l b ro ke n lines ind ica te the critica l p ressures of the pure compone nt s , t he upper one for buta n e a nd th e lo wer o ne f or propa n e . F i g ure 9, shows a compar i son of th e exper imentally d etermined equi li b rium ratios fo r bu t a ne and t hose ca lcula t ed by Rao ult's Law . It is e vident tha t the de vi a tion from Raoult's Law is not l a r ge a t 150 pounds p e r s qua re inch p r e ssure a nd increases only s li ghtly u p to 300 pounds pressure . Howe ver, a t 400 pounds pe r SQUa r e inch p r es sure the de vi a tion become s r e l a tively l a r ge as woul d be exp ec ted when the p r e ssure app ro a ch es th e critica l pressure . Wher e the n ec e ssary da t a have be en l a cking , va lu es for equili b rium r a tios have been ca l cula ted for eng ine eri n g de s i gn , not onl y through the us e of Rao ult' s La ··i 2,nd Dalton' s Lav; , but 1 a l so thro u gh th e u se of ce rta in co ncepts of i dea l sol u ti o ns. - 33 - f 0.75t - - -- "-1--'-----f-~- . t-+-'----,,.___,' - - - - - j - - - -7 K XPERIMENTAL AOULT'S LAW - - 150 250 200 TEMPERATURE °F F i g . 9 . Eq_uili b ri um Ra ti os for R'...lt a n e , Expe rimenta.l a nd Ca l cul 2. t ed . -34As defined by Lewis and Randall (8), "The ideal solution is one in which the fu ga city of e a ch component is proportional to th e mol fra ction of that component at every t empera ture a nd pressure." In :t-dea l solutions, the fu ga city of each component in a phase is equal to th e fu ga city of e ach component in the same phase in the pure state, at the same temperature, times its mol fr a ction in the idea l solution. If the propane-butane system was an ideal solution, the followin g e quations would be true: {,_' ::: PJ.. £PJ.. XP . Tp .L' .c v = tpc 1 J T p , J 6 ( { 1 refers to the fu ga ci ty of th e component in th e system and f to the fu ga city of the pure component. the liquid; 6' , to the ga s; The subscript ~, refers to r,to propa ne; a nd B, to butane. As used formerly, Xis the mol fra ction of the component in the liquid phase a nd Y, the mol fra ction in the ga s pha se). From these e qu a tions it is possible to determine the com positions of the phases in terms of fu gaciti e s. Then, since the fu gacity of e ach pure component is a function only of the tempera ture and pre ssure of the system, the compositions of the coexisting pha ses a t any tempera ture and. pre ssure ma y be determined with only the k no wled g e of the fu ga cities of the pure components a t the desired temperature a nd pre ssure. Considering the above e quations for pro pa ne, the follo wing rel a tion is obtained, Y,. fn; - f';v X P fi,'- r ', ,;. Since at e quilibrium, the fu gaci ty of the com po n en t i n the li quid is equ a l to the fu ga city of the com- ponent in the ga s YF-fPG ::-1, or )(Yt,.P = /{p= Xr-rn f:::,. It was throu gh the ,,., use of this r e l a tion tha t th e curve, No. 4, of Fi gure 10, wa s obta ined for p ropa n e a t 190° F. w ~ 0 8 t--- - - + -- -- + -- ---,.L-h,.<:'.___-,L,.c..._,jc__ _ ____J a: (/) s ~ 06,t--- - - + -- -----+'-44------"JL,~ -,¥..-- - - - 1 - - -- w z ~ Q_ ~0.4t-- ---+-w----,,...,,~ -,f--- -- +-- -- + - -- --I z 0 ~ du. 02'f---f,{ff---------,,!'------- - + - - - - + - - ' - '90::-___:_"f_----+--- - --l I - R/IOULT 'S ~ L AW 2- EXPERI MENTAL 3- IDEAL SOLUTION Il 4- 0.2 0.4 IDEAL SOLUTION I 06 08 MOL FRACTION OF PR)PANE IN LIQUID PHA SE F i e; . 1 0 . ~ x :pe ri ment a l a nd Ca lcul 2.t ed -Squili b ri um Cu r v es f o r Propa ne a. t 1 90° F' . -36Freque ntly there are insufficient P-V-T d a t a to perrni t the use of the la ws of i d e a l solutions since the se l aw s t ake into a ccount the volume of the li qui d ph ase a nd a lso the devi a tion of the gas pha se from perfect gas beh e. vior. Wher e no P-V-T data is ava ila ble, other tha n th e vapo r p r essure data of the pure compo nents, Raoult's and Dalton's Law s may be used. Curve No. 1, of Fi g ure 10, was obta ined by use of these l aw s. If only the fu gacities of the pure compo nent s are k nown, the volumes of the liqu id phase ma y be neg lected. Following this method, the curve, No . 3, of Fi gure 10, was obtained. For mixtures of p ropc1.n e a nd bu t a ne a t 190°F., this a d a ption of th e l a ws of id eal solutions a ppea rs to g ive ph ase equilibrium data nea r er the expe rimenta l r es ults, Curve 2, Fi g ure 10. Th e expe rimenta l curv8 i s nea rer the Rao~lt's Law cu rv e at hi ghe r concentra tions of p r opane , wh il e for the hi,:,:. .her concentra tions of buta ne, it is about equidista nt be t ween the Raoult's La w curve a nd th e curve prepa red b y the l aws of ideal solutions, ne g l e cting the volume of t h e li qu i d pha se . It is :proba ble that at hi ; her pr'J ssures . the l aw s of idea l solutions would more n ea rly fit th e experimenta l re sult s s ince the curves on Fi gure 9, indica te that, a t t he h i gh er p ressur es , th e de vi a tion from Raoult' s Law b e comes g r c&. ter. -37- Rr.:FERENC1:.: s (1) Soude rs, Se lhe imer, a nd Bro wn , Ind . Sng . Chem ., 24, 517 (1932) (2) Sa 5 e, S chaa fs ma , a nd La cey, Ind . Eng . Chem., 2 26, 1218 (1934) (3) Young , Sydney, J. Ch em . Soc., 47, 640 (1 885) (4) Bahlk e a nd Kay , Ind. Eng . Ch em., 24, 2 91 (1932) (5) Cumn1ing s, Stones , Vol a nte, Ind. Eng . Chem., 25, 728 (1933) (6) Young a nd J asa itis., J. Am . Chem. Soc., 58 , 377 (1936) (7) Be a tti e , Poff e nb e r g e r, a nd Had lock , J. Ch em . Phys ., .2. , F eb . , 193 5 (8) Lewi s a nd Ra nda,11, 11 Th e rmodynam ic s 11 , Pg . 2 23 .M cGr aw- Hill, 1923 -38- Acknowled g ement It is my pleasant duty to express my appreciation to Dr. B . H. Sage and Dr. W. N. Lacey for their ad vic e , cooperation, a nd kindly consideration throughout this research.