» V X J . t » l . -L \ V_/. ¿J tJ X J . A p r i l 1 9 4 5 .
IMPROVED ACCURACY OF C.F.R. MOTOR METHOD TEST FOR HIGH OCTANE RATING; W ITH CONTINUOUS SCALE FROM 40 TO 120 O.N.
B y L. B. Sw e e t l a n d * (Member) a n d P. Dr a p e r * (Fellow).
In t r o d u c t i o n.
Th e desirability of an u n in te rru p ted scale of octane num bers from th e low est to th e highest anti-knock values in current use has always been evident, an d it was in order to fill this need th a t th e “ 17° M otor M ethod ” was in tro d u ced a n d standardized by th e In s titu te of Petroleum in 1941.1 This m ethod has been in use in th e U n ited K ingdom up to th e presen t tim e in conjunction w ith th e C .F.R . M otor M ethod, em ploying a carefully set bouncing-pin for determ ining sta n d a rd knock intensity.
A bout tw o years ago th e A.S.T.M. approved th e following som ew hat drastic alteratio n s to th e M otor M ethod.
(a) R em oval of th e c arb u re tto r th ro ttle plate.
(b) Use o f “ Guide Tables for M icrometer setting (compression ratio) for S ta n d ard K nock In te n s ity .”
The fact t h a t these m odifications rendered th e 17° m ethod extension of th e octane scale non-linear, p rom pted th e work described in th is report.
Now th a t th e In s titu te of P etroleum M otor M ethod has been brought into line w ith th e A.S.T.M. regarding (a) an d (b) above, th e work will be of general interest.
Su m m a r y.
1. R atin g s w e re 'o b ta in e d on tw enty-one engines on tw o In s titu te of P etroleum m o n th ly correlation samples by th e old an d th e new A.S.T.M.
M otor M ethod. T he results indicated no appreciable change in ratings, b u t th e re was a red u ctio n in “ spread ” of h alf an octane num ber by th e new m ethod.
2. A brief exam ination of th e 17° M otor M ethod w ith o u t th e th ro ttle p late led to th e finding th a t th ere was a break in con tin u ity of te s t condi
tions a t 100 O.N. The Guide Tables for m icrom eter settin g for stan d ard knock in te n sity below 100 O.N. could n o t be ex trapolated to cover ratings in th e higher octane range because excessively high compression ratios and knock in te n sity w ould be encountered.
3. A n investigation has been m ade on th e relationship of octane num ber to com pression ra tio a t sta n d a rd knock in ten sity w ith various ignition settings.
I t was established th a t th e A.S.T.M. ignition setting a t high compression ratio s creates unstable conditions of engine operation, w ith th e result th a t slight fluctuations in spark tim ing have a very m arked effect on th e knock in ten sity . This condition probably accounts for m uch of th e rough- ru n n in g a n d difficulty of octane ra tin g which are experienced on fuels of
* A sia tic P e tr o le u m Co.
1 0 6 SW E ET EA N D AN D D R A PE R : IM P :
100 O.N. a n d over. This can be overcom e by settin g th e sp ark for m ax i
m um knock, as th is allows a considerably lower com pression to be used with sta n d a rd knock in ten sity . A sm ooth curve th e n relates octane num b er and com pression ra tio from 40 to 120 O.N., a n d a sep arate m eth o d above 100 O.N. is n o t necessary.
4. I t is recom m ended t h a t a fixed spark settin g of 25° advance be con
sidered for th e I.P . a n d A.S.T.M. M otor M ethod th ro u g h o u t th e ran g e from 40 to 120 O.N. T he 17° M otor M ethod w ould th e n become obsolete.
De t a i l s o f Te s t.
I n th e absence of d a ta from A m erica to show th e effect of th e changes in th e A.S.T.M. M otor M ethod on th e ra tin g of fuels, m em bers of th e I.P . m o n th ly correlation scheme agreed to te s t th e tw o sam ples for N ovem ber 1942 by th e existing a n d th e modified A.S.T.M. M otor M ethod, so th a t a com parison of ratin g s could be m ade. A sum m ary of th e results obtained from te sts on tw en ty -o n e engines is as follows :—
N o . o f C .F .R . en g in es 21.
S a m p le N o . 67. S a m p le N o . 68.
W ith th r o ttle
p la te .
W ith o u t th r o ttle
p la te .
W ith t h r o ttle
p la te .
W ith o u t th r o ttle p la te .
A v e r a g e O .N . 78-2 78-2 .99-5 99-6
S p rea d O .N . . . . . 2- 3 1- 8 2- 1 1-7
A v e r a g e d e v ia tio n . 0-55 0-47 0-42 0-37
W hen th e A.S.T.M. Guide T a b le 2 figures of o ctane num ber and com pression ratio for sta n d a rd knock in te n sity are p lo tted , a curve is o b tain ed (Fig. 1) which is v ery flat in th e high-octane range a n d e x tra polation above 100 O.N. suggests im possibly high com pression ratios for fuels up to 120 O.N. A stu d y of th e d a ta on th e developm ent work of th e 17° M ethod (i.e. w ith th e th ro ttle plate) indicated t h a t lower compression ratio s should be em ployed for sta n d a rd knock in ten sity .
P relim in ary te sts w ith o u t th e th ro ttle p late on one engine confirmed t h a t th ere was a decided k in k in th e curve a t 100 O.N. w hen ex trap o latin g i t to cover th e 17° M ethod. A fixed se ttin g of 19° advance above 90 O.N.
showed an im provem ent in th e shape of th e curve. This is shown graphically in Fig 1, a n d it will be observed t h a t changing th e ig n itio n advance from 17° to 19° a t 100 O.N. alters th e com pression ra tio req u irem en t for sta n d a rd knock in te n sity from 8-5 to 8-07 : 1.
I n order to o b ta in some fu rth e r d a ta on th e effect o f spark-tim ing, some investigational w ork was carried o u t on th ree engines, one o f w hich was arran g ed for pow er o u tp u t readings, to determ ine :—-
(a) T he ignition settin g for m axim um knock a t m axim um knock m ix tu re stre n g th a n d sta n d a rd knock in te n sity on fuels ranging from 40 to 120 O.N.
(b) The ignition setting for m axim um power a t m axim um knock m ix tu re stre n g th a t various com pression ratio s from 4-5 to 1 up to th e highest ratio possible w ith o u t detonation.
120
C .F .R , MOTOR METHOD TEST FO R H IG H OCTANE RA TIN G , 1 0 7
KNOCKINTENSITYAT VAKIOTTSIGNITIONSETTINGS.
1 0 8 SW EETLA N D AN D D R A PE R : IM ____ _
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C.F.R. MOTOR METHOD(WITHOUTTHROTTLEPLATE).COMPRESSIONRATIO-IGNITIONADVANCEFORA.S.T.M. MAXIMUMKNOCK ANDMAXIMUMPOWER.
O .F .R . MOTOR M ETHOD TEST FO R H IG H OCTANE RATIN G . 1 0 9
The sta n d a rd knock in ten sity was obtained th ro u g h o u t th e te sts by setting th e compression ratio for th e O.N. of th e fuel according to th e A.S.T.M. Guide Table a n d obtaining a mid-scale knock-m eter reading.
W hen altera tio n s in th e spark advance changed th e knock-m eter reading, th e compression ra tio was ad ju sted to re-establish a midscale reading. On high-octane fuels advance of spark-tim ing from A.S.T.M. tow ards th e m axi
m um knock po in t caused heavy detonation, which was beyond th e record
ing lim it of th e knock-m eter.
The results of th e w ork on (a) an d (b) are shown graphically in Fig. 2, an d it will be noticed th a t th ere is a very wide discrepancy n o t only betw een th e m axim um knock a n d th e m axim um power ignition settings, b u t also betw een these settings a n d th e M otor M ethod ignition tim ing. In th e high-octane range th e sta n d a rd an d th e m axim um -pow er ignition settings are sim ilar, a n d it is here t h a t th e operation of th e engine is decidedly unsteady. This is very ap p a re n t w hen using a dynam om eter u n it, b u t it is p a rtly obscured on a synchronous m otor u n it.
In order to check th e effect of using m axim um knock ignition setting, four sensitive types of fuel were te sted on one engine using th is setting, and th e ratin g s were sim ilar to those obtained by th e latest A.S.T.M. M otor M ethod.
Ta b l e I .
Mi c r o me t e r Set t i ng f o r S t a n d a r d K n o c k I n t e ns i t y f o r Bar omet ri c Pressure of
■ 29-92 i n. of Me r c u r y a n d ^ i n. Vent uri .
M icrom eter se ttin g s u p t o 70 O .N . as for A .S .T .M . M otor M ethod.
25° M otor m e th o d
o c ta n e n u m b er.
M icrom eter se ttin g ,
in .
25° M otor m e th o d
o c ta n e n u m b er.
M icrom eter se ttin g ,
in .
25° M otor m e th o d
o c ta n e n u m b er.
M icrom eter se ttin g ,
in.
70 0-533 90 0-303 110 0-068
71 0-523 91 0-290 111 0-059
72 0-513 92 0-277 112 0-051
73 0-503 93 0-264 113 0-043
74 0-492 94 0-251 114 0-034
75 0-482 95 0-238 115 0-026
76 0-471 96 0-226 116 0-018
77 0-460 97 0-214 117 0-011
78 0-449 98 0-201 118 0-004
79 0-436 99 0-189 119 - 0 - 0 0 3
80 0-424 100 0-177 120 - 0 - 0 1 0
81 0-412 101 0-165
82 0-400 102 0-154
83 0-388 103 0-143
84 0-376 104 0-132
85 0-364 105 0-121
86 0-352 106 0-110
87 0-340 107 0-099
88 0-328 108 0-088
89 0-316 109 0-078
B a r o m etric co rrectio n . F o r e a c h 0-1 in . m ercu ry ad d or su b tr a c t 0-003 in . to th e m icro m e ter s e ttin g . A d d for h ig h b arom eter, su b tr a c t for lo w barom eter. A s for
A .S .T .M . M otor M eth od . s,
As th e m axim um knock sp ark se ttin g for all com pression ra tio s above 7 to 1 (octane num bers above 70) was 28°, it seem ed logical to determ ine th e effect of a fixed advance of 28° a t th e lower ratio s. T he results, as show n in Fig. 1, indicate t h a t th e effect is sufficiently sm all to allow th is se ttin g to be used from 40 to 120 O.N.
I n th e high-octane range th e effect o f th e first increm ents of advance of sp ark from A.S.T.M. is to enable v ery m uch lower com pression ra tio s to be em ployed. This becomes a ra p id ly dim inishing effect as th e sp ark tim ing approaches 28°. A t 100 O .N., for instance, a 3° advance from th e A.S.T.M.
se ttin g o f 16° lowers th e ra tio b y 0-5, b u t from 25° to 28° th e ra tio change is only 0T . B eyond th e optim um settin g fu rth e r advance causes rap id changes in perform ance. The above suggests t h a t a fixed ig n itio n se ttin g should be ad o p ted w hich is w ithin th e zone of least influence from ab o u t 24° to 28°. The guide curve resulting from te sts on tw o engines w ith a fixed se ttin g of 25° advance is shown in Fig. 1. This is reproduced in term s of m icrom eter setting, as in th e A.S.T.M. m ethod, in Table I.
Pr a c t i c a l Te s t s i n Ot h e r En g i n e s.
I n order to te s t th e behaviour o f a num b er of C .F.R . engines operating u n d er th e proposed 25° m odifications, p a rtic ip a n ts in th e I.P . C.F.R.
correlation scheme agreed to te s t fuels for several m o n th s w ith o u t th e th ro ttle p late, first using th e A.S.T.M. guide curve, th e n w ith 25° advance a n d th e 25° guide curve in Fig. 1.
E leven fuel sam ples of w idely v ary in g ty p es were te ste d b y th e tw o m ethods in each of tw e n ty engines over a period of four m o n th s, from w hich it was n o te d t h a t th ere was no sensible difference in th e average o ctane num bers in th e range teste d—i.e., 79 to 103 O.N.— a n d th e m a x i m u m
spread a n d average deviation were slightly less b y th e 25° m ethod. T h at th e spread on tw e n ty engines w as less w ith th e 25° m eth o d dem onstrates t h a t th e m eth o d is acceptable to th e in d iv id u al engines.
I t is recom m ended t h a t a fixed sp ark settin g o f 25° advance be con
sidered for th e I.P . an d A.S.T.M. M otor M ethod th ro u g h th e range from 40 to 120 O.N. The 17° M otor M ethod w ould th e n become obsolete.
I t is felt t h a t th is investigation should be given prom inence a t th e p resen t tim e, as it provides a m eans for increasing th e accuracy of ra tin g h ig h o cta n e fuels.
References.
1 K n o c k -R a tin g o f F u e ls o v e r 100 O .N .— t h e 17° M otor M eth o d . T h e I n s t it u t e o f P e tr o le u m . S t a n d a r d Me t ho d s f o r Te s t i ng Pe t r o l e u m a n d i t s Produc t s, fo u r th e d itio n , 1942, I .P . 4 3 /4 2 (T ), p . 158.
2 A . S . T . M . S t a n d a r d s on Pe t r o l e um P r o d u c t s a n d Lubr i c ant s , October 1942. K n o c k c h a r a c te r istic s o f M otor F u e ls , D .3 5 7 —4 2 (T ).
1 1 0 IM PRO V ED ACCURACY OE E .C .R . MOTOR M ETHOD T E S T .
I l l
FRACTIONAL DISTILLATION OF TERNARY MIXTURES. PART I.
B y A. J . V. Un d e r w o o d, D.Sc., M .I.Chem .E., A.M .I.M ech.E., F.R .I.C ., F .In st.F ., F .In st.P e t.
Su m m a r y.
A n a n a ly tic a l m e th o d is p r e se n te d for c o m p u ta tio n s r e la tin g to th e fra c
tio n a l d istilla tio n o f te r n a r y m ix tu r e s . I t is a lso sh o w n t h a t t h e p rin cip le o f t h e m e th o d c a n b e e x te n d e d to m ix tu r e s o f m o re th a n th r e e co m p o n e n ts.
Fo r te rn a ry m ixtures w ith com ponents denoted by x, y, z th e composi
tio n s o f th e liquids on adjacent plates of a fractionating column are con
nected by th e following relations, derived from m aterial balances.
m x0 + b = --- — ■... (1) y* i + l i / i + Pi
m 2/o + c = y x 1 + §yx + z 1r u w — ,... (2)
m z0 • j- d = - , (3)
0 T y x 1 + py i + z , w
F o r a rectifying column, m = -n——R where R is th e reflux r a t i o ; b = R - j- 1
Xd -; c = ■; d = - Zd . y and [i are th e relative volatilities of com ponents x an d y to com ponent z and y > ¡3 > 1.
| I j
F o r a stripping column, m = — ^ — , where S is th e “ reboil ra tio ,” i.e.
th e num ber of moles of vapour retu rn ed by th e reboiler to th e stripping colum n per mole of b ottom pro d u ct w ithdraw n. F or a stripping column on which a rectifying column is superim posed, S — ^ --- — ; b =
— ; c = — Ah’; d = —Adf. F or b o th rectifying a n d stripping columns b + c + d = l — m ...(4) C onstant m olal reflux an d co n stan t relative volatilities thro u g h o u t th e colum n are assum ed.
E q u atio n s (1), (2), an d (3) can be used to calculate compositions from p la te to p late. I t will be shown th a t, by suitably transform ing them , th e com position on an y p late can be calculated w ith o u t using a stepwise p ro cedure from plate to plate. Previously such a direct calculation has been possible only for th e special case of to ta l reflux where m — 1 an d b — c = d = 0.
The m ethod of transform ation which can be applied to equations (1),
1 1 2 U N D ER W O O D : FRACTIONAL D ISTILL A TIO N OF
(2), a n d (3) to m ake th em suitable for a direct calculation depends on th e use o f a p a ram eter </> w hich is defined in th e following m an n er. L e t h, Jc, a n d I be th e values of x, y, a n d z, respectively, w hich correspond to th e com positions on tw o a d ja c e n t p lates w hen th ere is no change in com position betw een these tw o plates, h, Jc, a n d I represent th e com position a t which no fu rth e r fra c tio n a tio n tak es place—t h a t is, th e com position for which m inim um reflux conditions o b ta in w ith th e given reflux ratio . T hey are defined b y th e equations
m h + b = —t—r vn— ...(5) yh + p* + I ^
mJc + c = —— — ... (6)
^ yh + |3A + I w
m l + d — —f—— ,... (7)
yh + p i + I w
L e t m (yh + -)- I) — <f>... (7a) ,, , 1 m h 4 - b mJc 4- c m l 4 - d '
so t h a t T = ---=— = —— =— — — ... (8)
<P g ym ti p'tuJc ini
Then h — ^ • L ^ - 7 |q\
— m (y — <j>)’ to(P — <j>)’ m ( l “ <j>) ‘ ( ) Now h, Jc, an d I are p articu la r values of x, y, a n d z, a n d x -f- y -f- z = 1 for all values, so th a t, also, h -f- Jc -j- I = 1. S u b stitu tin g from equations (9),
+ • • • • (10)
This is a n e q u atio n o f th e th ird degree, so t h a t th ere are th ree values of <f>
which satisfy it.
R etu rn in g to equations (1), (2), an d (3), an eq u atio n can be derived in th e form
m x0 + b + + c) + \ ( m z 0 + d) + X3 =
y x i + \ 1$y1 + X2Zl + X3(ya;1 + pyx-4- Zi) n n y x i + P2/i + «i
This equation is o b tain ed by m ultiplying eq u atio n (2) b y X1; eq u atio n (3) b y X2, an d adding th em to eq u atio n (1), a n d also adding X3 to b o th sides.
E q u a tio n (11) is satisfied by all values o f x, y, z w hich satisfy eq uations (1), (2), (3). The in d eterm in ate m ultipliers Xx, X2, X3 can be given a n y values desired.
R earranging eq u atio n (11),
m x0 + \ m y 0 - f X2m z0 + b + X1c + X2d -f- X3 =
y ( l + *3 ) ^ 1 + P(xx + X3) y x + (X2 + X3)z1 + P2/x + »1
X1; X2, X3 are now chosen so t h a t th e function of x 0, y 0, z0 on th e left-h an d
(13)
TERNARY MIXTURES. PART I. 113
sid e o f t h e e q u a tio n b e c o m e s e x a c t ly th e sam e fu n c tio n , e x c e p t for a c o n s t a n t m u ltip lie r , a s th e fu n c tio n o f aq, y v z v w h ic h c o n s titu te s th e n u m e r a to r o f th e r ig h t-h a n d sid e o f e q u a tio n (12). T h is req u ires t h a t
y ( i + h ) _ P (x t + x3) _ x2 + x3
m Xxm X2m
a n d t h a t b -f- Xxc -f- X2cZ -f- X3 = 0 ...(14) U s in g e q u a tio n s (13) a n d (14), e q u a tio n (12) b eco m es
/ . n y ( l + X3)(aq + X1y 1 + X ^ )
( ° + 0 + X^ 0) - --- y x x + "p y T + "z l ' ' ( } S in ce th is e q u a tio n is sa tisfied b y a ll v a lu e s o f x 0, y 0, z0 a n d aq, y x, z v w h ich s a t is f y e q u a tio n s (1), (2), (3), it is also sa tisfied b y a;0 = aq = h ; y 0 = y x = Jc; z 0 = z x = I, w h ic h are p a rticu la r so lu tio n s as d efin ed b y e q u a tio n s (5), (6), (7). S u b s titu tin g th e s e v a lu e s in e q u a tio n (15), th erefore
/j, i -i 7. i *\ 7\ y ( i + x3)(/j + x-jc + x2Z) m ( h + X jc + X2Z) = y h + ---
a n d y ( 1 + _ Xj l = y h 4 - Bfc 4- Z = — from e q u a tio n (7a). E a c h o f th e
m m
th r e e term s in e q u a tio n (13) is th erefore eq u a l to — an d , so lv in g for Xx, X2 a n d X3,
± - l + - 1
^ = y ~ 1 ’ Xl = f r i ‘ h ~ r~ ' ' ' (I6) p
T h e se v a lu e s o f Xx, X2, X3 also s a tis fy e q u a tio n (14) for
" - 1 - - 1
b + Xxc - f X2d + X3 = b + c . f d . ^ + - — 1 P ~ 1
- ( l - £ \ J + — _____ l \
~ \ y / \ y — ^ P — ^ 1 — $ 1
= 0 from eq u a tio n (1 0) S u b s titu tin g t h e v a lu e s o f Xx, X2, X3 in eq u a tio n (15) g iv e s
</> -, $ i r t — 1 £ — 1
T here are th re e values of <f> given by eq u atio n (10). D enoting th ese by
<f>i, <f>2> 0a > th ere are th ree equations corresponding to e q u atio n (17), nam ely, 0 i f 7 X i , Pÿi . « i 1
. y^o P2/o _j_ z0 = m I y </>-, 1 - 0 x 1 _ • (18a)
1 1 4 U N D ERW O O D : FRAC TIONAL D ISTILL A TIO N OF
y — <f>1 p — l — ^ i 7^1 + P*/i + Zi
0 2 [ r 3*! _|_ Pyi _[_ zi ] yxo + Py0 + Zq = m \ y - ^ 2 p - 0 2 i — fa ) _ y — 0 2 P — 02 1 — ^ 2 y * i + P y i + z i
f a f v x i + Pyi + zi 1
y ^ ° Py0 + 2o = w l y - ^ 3 P - 0 3 i -
y 03 P — 03 i 03 y * i “I- P y i ^ 2 i D ividing eq u atio n (18a) b y eq u atio n (186),
_ .y * o + Py0 + z0 ya?i ■ P y i +
y — f a P — f a i — <fi = f i y — f a P — 0 i i — 0 i y^o ! P^o | z0 <f>2 • yaq • ^ Pyx | z x
7 — 0 2 P — 02 1 — ^2 Y — f a P — 0 2 1 — 02
(1 9 )
Applying th is relatio n to successive pairs of plates, th e re is readily obtained for th e n th p late th e equation
Yx o + Py0 + z0 y x n + p y n j§ zn
y — 0 i P - 0 i i — ^ i = i f a \ n y — <f>i P — 0 i i - ^ x - ,2Q ,
7*0 , Py0 , z0 \<f>J ' y x n $yn Zn a)
y — <f> 2 P ~ 02 1 — f>2 7 — ^ 2 P ~ 02 1 — 02
B y following th e sam e procedure w ith th e o th er pairs o f eq u atio n s (18a), (186), (18c) th ere are also o b tain ed th e eq uations
y - 0 2+
P $2 +
l 02
y x o I P Vo I z0
y - 03 1
P — fa 1 l — 03 a n d
y x o I Py0 I z0
y - f a 1
P 03 1
l 03
y x 0
+ Py0
+ z0
Yx n + $Vn
■<f>2\n y — f a P — f a 1 — 0 2 f a ' ’ Yx n , P*/» . Zn
' 1
(206) y — 0 s P — <l>3
y xk + Py«
M * y — 03 P — 03
i/ ’ y x n , Py» (20c)
y — ^ p — <f>1 + 1 — 0 X
E q u a tio n s (20a), (206), (20c) provide a m eans for calculating th e com positions on p late n w hen th e com positions on p la te 0 are given. W hen given values of x 0, y 0, z0 are su b stitu ted , th e re are o b tain ed th ree sim ul
taneous equations of th e first degree in x n, y n, zn. These th re e eq uations are only equivalent to tw o independent equations, as an y one of equations (20a), (206), (20c) can be o b tain ed from th e o th er tw o b y division. There
TERN A R Y M IX TU RES. PA RT I . 1 1 5
is, however, also th e equation x n -f- y n + zn = 1, so th a t three equations are available for solving for th e th ree unknow ns x n, y n, zn.
The left-hand side of equations (20a), (206), (20c) becomes u n ity when x 0 = x D, y 0 = yD, z0 = zD.
_ b e d
XD = T~ 1 - r a W D ~ > Vd 1 1 - m71 > ZD’ D 1 - TO
T hen
y z D , , PyD PyD , , 2d = _ i 1 I bv / ¿>y , , CPCP , d \
P — </q 1 — ^! 1 TO \ y </q P — <Ai
from equation (10).
T he same relation holds good for all three values of (f>. A sim ilar sim pli
fication is obtained for a stripping column by p u ttin g x n = xw, y n — y w, zn = zw, and th e right-hand side of equations (20a), (206), (20c) th en reduces to u n ity . The simplified equations facilitate calculation of th e com position on th e n th plate from th e to p of a rectifying column or th e n th plate from th e b ottom of a stripping column.
C onstant m olal reflux an d co n stan t relative v olatility have been assumed.
V ariations in th em can be ta k en into account by applying equations (20a), (206), (20c) successively to sections of th e column in which appropriate values are used.
E q u atio n s (20a), (206), (20c) are sim ilar in ty p e to th e equations for th e usual calculation in th e special case of to ta l reflux. In th a t case, equations (1), (2), (3) give
* 0 = f y \ n x_n a n d Vo = Vn
Vo 'P ' Vn z0 Zn
E q u atio n s (20a), (206), (20c) correspond, therefore, to a case of to ta l reflux in which th e com ponents are
Y x , Py , 2 N / Yx I P V I 2 \
'M - <I>1 1 — <t>J’ \ y — 4>2 P — 02 1 ~ w and
y x p y z
y — 4> 3 P — (f>3 1 — </>■ respectively a n d th e relative volatilities are <f>±, </>2, cf>3 respectively.
E q u atio n s (20a), (206), (20c) can also be w ritte n in another form. D en o t
ing by 6j, 1cv l x th e values corresponding to 4>} a n d sim ilarly for <f>2 and <f>3, th e use of equations (9) in equation (20a) gives
P^i l-t y 61 . P^x , h
-^ % x° + — -yo + d - z° T~ • + V Vn + d • (21) yh2 S kt L \<f>2J ‘A , # 2 _r h z
~b 0 + V ' y ° + d 0 6 ■ " + c • Vn + d ' "
to g eth er w ith tw o sim ilar equations.
1 1 6 U N D ERW O O D : ERACTIONAL D ISTILL A TIO N OE
I t has been m entioned t h a t h, 1c a n d I represent th e lim iting com position for w hich th e reflux ra tio represents conditions of m inim um reflux. There are th ree such lim iting com positions corresponding to th e th re e sets of values of h, Tc a n d I. T he significance of these th ree com positions will be discussed in th e second p a r t of th is paper.
The m ethod w hich has been outlined requires th e solution of th e cubic eq u atio n (10) to find <f>v (f>2, (f>3. The process o f solution is facilitated by the following considerations. E q u a tio n (10) can be w ritte n
6y(P — <£)(1 — <t>)+ cP(l — <j>)(y — </>) + d(y — <f>)($ — <f>)
- ( y - m - M l - <t>) = 0 • • (22) D enoting th e expression on th e left-h an d side of th e eq u atio n by E and giving to <f> th e values 0, 1, p, y successively it is seen th a t
w hen <f> = 0, E = fiy (b c + d — 1)== — mpy, i.e. negative,
<j> = 1, E = dfiy, i.e. positive,
<f> — p, E = — cp(p — l)(y — ¡3), i.e. negative,
<f> = y, E = by(y — p)(y — 1), i.e. positive.
T hus E m u st become zero for a value of </j betw een 0 a n d 1, for a value betw een 1 a n d ¡3 a n d for a value betw een (3 a n d y. D enoting these values b y <f>v <f>2 an d <f)3 respectively th e n
0 < <f>! < 1 ; 1 < <^2 < p ; (3 <4>3 < y
This gives a read y indication of th e values of <f> w hich satisfy eq u atio n (10).
A fu rth e r in dication can also be obtained. I f eq u atio n (22) is m ultiplied o u t, it becomes
¿3 _ ^2{(1 _ d) + p(1 _ c) + y(1 _ &)} + ^ + y +
— b(y - f (3y ) — c((3 + P y ) — d([3 + y ) } — (1 — b — C — d)$y Since <j>v (f>2, (f>3 are th e ro o ts of th is equation,
4>i + ^ 2 + ^ 3 = (1 — d) - f p( 1 — c) + y (l — d) . 4>l4)2 + ^2^3 + =
P + y + Py — b(y + (3y) — c(p - f (3y) — d (p + y) . a n d ^ i^2^3 = (1 — 6 — c — d ) P y ...
I f we now assum e as ap p ro x im ate solutions,
= 1 _ d ; cj>^== p (l — c) ; = y ( l — b)
•these values satisfy eq u atio n (24). T hey also ap p ro x im ately satisfy equation (25) since, to a first a p p ro x im a tio n ,.
(1 — d)(p(l — c)y(l — d) = Py(l — b — c — d)
as b, c a n d d are fairly sm all com pared w ith u n ity and, for a first ap p ro x i
m ation, powers above th e first m ay be neglected. W ith th e sam e ap p ro x i
m ation, e q u atio n (24a) is also satisfied. The procedure for solving eq u atio n (10) or (22) is therefore to assum e th e values given b y eq u atio n s (26) as a first ap p roxim ation a n d th en to o b tain a closer ap p ro x im atio n by a n y of th e usual m ethods.
= 0 (23)
. (24)
. (24a) . (25)
(26)
I n m any cases th e process of solution is facilitated through one or more o f th e coefficients b, c, d in equation (10) being approxim ately zero when th e com ponent in question is present in very small am o u n t in th e product.
In th e second p a r t of this paper it is p lanned to show th e application of th e m ethods here presented to num erical cases.
Mix t u r e s o f More t h a n Th r e e Co m p o n e n t s.
The m ethod of transform ing th e basic equations which has been described can also be applied to m ixtures of more th a n three com ponents an d th is application is briefly indicated below. Consider a four-com ponent m ixture.
U sing th e sam e sym bols as before, le t w be th e fo u rth com ponent, more volatile th a n x a n d having a relative volatility of 8 referred to z. Then, as before,
s „ , , , ■ • ■ • <2 , )
+ „ r - i » „ + , - ■ ■ - (28>
m y° + 0 — 8w, + y x 1 + ^
m z0 + d = —-- -—— . . . . (30)
8wq + yaq + (3y1 + z4 Using th e indeterm inate m ultipliers X4, X2, X3, X4, then {mw0 + a) + -k^mxo + b) + X2(m y0 + c) + X3(raz0 + d) + X4
_ Sag -j~ ^ jy x i + ^3zi d~ 74(8w1 -f- y x 1 -f- (ly1 -j- z4) Sug + y x 1 U py4 + z4
or
TERN A RY M IX TU RES. PA RT I . 1 1 7
m w 0 + X1m x 0 + \ m y 0 + 73raz0 + a + Xyb + X2c -f- X3d - f X4 _ 8(1 + + y U i + 74)aq -f- (3(X2 -f- X4)y4 -(- (X3 -f- X4)z4
Swq + y x l + Py1 + z 1 Choose X4, X2, X3, X4 so th a t
(31)
8(1 -f- X4) _ y ( x 4 -f- X4) _ ft(X2 -j- x4) _ x3 -f~ x4 (32)
m X4m x2m X3m
and
a -{- X-J) d- ^2^ d~ 73d X4 = 0 . . . . (33)
<f> ii now defined by th e equations
mg + a m h - \ - b m k + c m l -(- d 1 8 mg ym h pmfc m l <j> (34) w here g is th e corresponding value for com ponent w and
(j> = m(8g -)- yh -f- $k -f- I ) ...(35)
Since g th e equation for <f> corresponding to eq u atio n (10) is
a</> , b t + c t _ + d± _ = m = 1 - a - b - c - d
1 1 8 FRACTIONAL D ISTILL A TIO N OF TER N A R Y M IX T U R E S. FA RT I.
8 '— <f> y — <f> p — <f> 1 — <j>
or
aS_ + J y + cp + d = 1 . . . (36) 8 — <j> y — (f> p — <f> 1 — (f)
This is a n equation of th e fo u rth degree giving four values of <f>-
As before it can be shown t h a t each of th e term s in e q u atio n (32) is equal to —.
to
h _ <t> i . x4 _ i . x.
T h e n ¡ J - , - ! .
These values of Xx, a2, X3, a4 will be seen to satisfy eq u atio n (33).
E q u atio n (31) becomes
8wo , y x o , P2/o , zo _ 8 — 1j> y — cf> p — (/> 1 — </>
<f> r $w1 y x x py x
ft r SWj y x x $ yx z x ]
to 18 — ft y — ft P — ft 1 — ftJ
• • (3 7 )
8nq + y x x + p y x + z x
There are four of these equations corresponding to th e fo u r values of ft.
F rom th em can be derived four eq uations sim ilar to eq u atio n s (20a), (206), (20c) an d th e y are equivalent to th ree in d ep en d en t eq uations. T he fo u rth eq u atio n required is«> + a ; + i / + « = l , an d th e final solution involves th e solution of four linear sim ultaneous equations.
The general procedure can obviously be applied sim ilarly to m ixtures of m ore th a n four com ponents.
Al e x a n d e r Dt t c k h a m, 18 7 7 -1 9 4 5 .
OBITUARY.
A L E X A N D E R DUCKHAM.
It is w ith great regret th a t we have to record th e d eath of Mr. A lexander D uckham , w hich occurred on F eb ru ary 1st, in a London nursing home, following an operation.
A lthough n o t a Founder Member,. D uckham was one of th e oldest m em bers of th e (then) In stitu tio n of Petroleum Technologists, having joined a t its inception in 1914. He gave m any years of useful service to th e In s titu tio n as a Member of Council (1919-1934) and as a V ice-President (1925-1934), and his passing will be felt keenly by all th e older members who were associated w ith him in those v ita l early days o f th e In stitu tio n .
More p articu larly is th e In stitu te indebted to D uckham ’s foresight in having first suggested th a t th e work of S tandardization of Tests should be undertaken. I n 1917, a t th e T w enty-fourth General Meeting, th e th e n President, Mr. Charles Greenway (later Lord Greenway) read a letter from D uckham in which he said :—
“ My suggestion is th a t th e In stitu tio n should appoint a S ta n d a rd ization Com m ittee, whose reference should be to investigate m ethods of testing and to recom m end Standards for adoption in this co u n try .”
The first m eeting of th e S tandardization Com m ittee was held on 17th Ju n e , 1921, an d a few m onths later Mr. D uckham was elected Chairm an (in succession to Mr. Jam es Kewley, who h ad resigned), a n d w ith his accustom ed energy he presided over th e m any m eetings of th e Com m ittee prep ara to ry to th e publication of th e first R ep o rt on th e S tandardization of Tests. In 1925 he h ad to resign th e Chairm anship owing to illness following an operation. All th e m em bers of this first Com m ittee an d its several Panels will rem em ber th e w holehearted support th e work received from Mr. D uckham .
D uring th e first W orld W ar he was busily engaged w ith th e M inistry of M unitions, being successively D irector of Sm all Arm s Supply, Con
troller of N ational A ircraft Factories, and of American A ircraft Assembly in th is country, in m uch of th e w ork being closely associated w ith a P a st P resident of th e In stitu tio n , th e late Sir F rederick Black.
F rom th e beginning of aviation D uckham took th e keenest interest in th e new venture, and this led to an in tim ate friendship w ith Blériot. H e provided a m em orial stone near D over Castle to m ark th e spot where B lériot landed after th e first successful Channel flight. This interest was m aintained th ro u g h o u t his fife in his activities on behalf of th e R .A .F, Benevolent F u n d , to which he was a generous contributor, an d moreover was th e m eans of collecting considerable sums. In addition to financial support, D uckham gave his house, V anbrugh Castle, B lackheath, as a home for R .A .F. orphan boys and, later, his charm ing residence, Rooks Hill, near Sevenoaks, w ith a generous endow m ent tow ards upkeep.
1 2 0 OBITUARY.
A lexander D uckham was b orn on M arch 11th, 1877, th e son of F rederick D uckham , M anager an d E ngineer of th e Millwall D ock C om pany. H is younger brother, Sir A rth u r D uckham , was w ell-known as a p rom inent figure in th e gas in d u stry . A lexander was edu cated a t th e old B lack h eath School, a n d afte r m atricu latin g stu d ied u n d er R am say a t U n iv ersity College, w here he won th e G oldsm iths Scholarship, th e E x h ib itio n of th e C lothworkers Com pany, an d th e Senior Gold Medal. H is s ta r t in a career was largely influenced by his godfather, A lfred Y arrow (later Sir Alfred), th e well-known shipbuilder, who, appreciating th e coming im portance of oil, especially as a n a v a l fuel, suggested to D uckham th a t here he m ight find a p ractical application o f his chem ical knowledge, an d in 1899, w orking alm ost single-handed, he laid th e fo undation of th e well-known firm bearing his nam e.
A few years la te r he becam e in terested in th e im p o rta n t question of oil supplies from w ithin th e E m pire, an in terest stim u lated b y th e clearly forthcom ing change to oil as th e n av a l fuel, an d in 1905 he founded T rin id ad C entral Oilfields, L td ., of w hich he was C hairm an an d M anaging D irector.
In itia tiv e , an exceptional ab ility to grasp new ideas, w ith energy an d
“ drive ” to p u t th e m in to practice a n d o b tain th e co-operation of his staff in carrying th em to a successful issue were th e o u tstan d in g characteristics o f A lexander D uckham . N or m u st his generosity be forgotten. As V iscount T renchard w rote :—
“ Y ou do w onderful work, an d I m u st say you are th e m ost generous m an I know to th e R .A .E . B enevolent F u n d .”
A M emorial Service was held on 12th F e b ru a ry a t St. M ichael’s, Cornhill, w hen a large num ber of friends, representatives of th e R .A .F . B enevolent F u n d (including L ord T renchard), a n d em ployees of th e firm, p aid a last trib u te to A lexander D uckham , th e In s titu te being represented b y th e Secretary, Mr. F . H . Coe.
J . S. S. B.
