December, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
1085
ENOINE OF HIGHEST EFFICIENCY
.
In a broader view this is only one phase of the problem of the fuel-engine relation. The important point is to get the most from the fuel by suitable treatment before use and then by burning it in an engine made to fit the prior treatment. As to what type of engine to build a t any one time, it does not matter whether i t be carburetor, injection, Diesel two-cycle, four-cycle, nonreciprocating, or whatever, so long as the over-all economies are right. Engines are all made from metal and brains, and what we want to do is to put as much of the latter in as possible. When that is done, we get the most and the cheapest power from a pound of fuel. What the engine problem looks like with relation to fuels is a circle, as shown in Figure 11. If we think of a barrel of crude oil entering the circle at some point, we can refine it around one direction to increase the octane number or around the other direction to increase the cetane number. But the two processes meet at the same point in a very high compression engine which has about the same thermal efficiency, since efficiency is largely determined by compression ratio. But one important difference is that our present octane-number (gasdine) engine can be run about a third faster than the cetane number (Diesel) engine. This barrier may be removed soon after the war. The combustion process is the place where the fuel and the engine meet, and that mechanism is what we are trying to utilize to best advantage. The future development of automobile aircraft, and Diesel engines will depend upon how well management, as well as engineers and chemists, understand the fun& mentals of the relation between the fuels and proper engines. We are studying fuels from the standpoint of the engine builder and not as fuel producers. We do similar researches in metallurgy, fabrics, rubber, and many other materials which we use. From this research we will know the practical limitations of the material we use and not ask our suppliers to do things which are outside of the bounds of technical and commercial practicability. It also helps us determine the road which our future researches
Figure
11. Oil Refining and Engine Design
should take because what may be technically and commercially impractical today may easily be an everyday product in the not too distant tomorrow.
Calingsert, George, IND.ENO.CHSM..35, adv. p. 6 (Oot., 1943). Chavanne, G.,and Lejeune, B., BdL doc. A i m . Belg., 31,98-102 (1922).
Edgar, Graham, Calingaert, George, and Marker, R. E., J . Ana. Chem. SOC.,51, 1483 (1929). Kettering, C. F..J . Soe. Automotive En#re., 4, 263 (1919).
Zbid., 5, 197 (1919). Lovell, W. G., Campbell, $. M., and Boyd, T. A., IND.ENB. C8E%f.,23, 26 (1931). Zbid., 23,666 (1981). Zbid., 25, 1107 (1933). Zbid., 26, 476 (1934). Zbid., 26, 1106 (1934). Midgley, Thomas, Jr., J. SOC.Automotive Engre., 7, 489 (1920). Midgley, Thomas, Jr., and Boyd, T. A., IND.ENB.C ~ M 14, ., 894 (1922).
Blending Aviation Gasoline Components S. STANLEY LUKOFSKY Eastern States Petroleum Company (of Texas), Houston, Texas
A
N IMPORTANT part of aviation gasoline manufacture consists in the proper blending of available gasoline components to meet the three primary specifications of vapor pressure, 1-C octane rating, and a third specification which we call “property C”. For the purposes of this discussion the actual specifications are unimportant provided we realize that, whatever they are they must be met in our final blend. Let us call the 1-Coctane number K I , the adjusted or true initial vapor and the property C number Ka. pressure K2, The 1-C octane number and property C number, as given, are understood to be the indices chosen by Petroleum Administration for War to be volumetrically proportional to the blending effect of the component in mixtures; the laboratory or Reid vapor pressure must be translated into true initial vapor pressure via well known conversion data. It is recognized that vapor pressure,
as so defined, is proportional to molar ratios. Thus we must urive a t the correct values for Kt, KI, and KIin the final blend. K 1 and Ka are determined by the volumetric proportions; KSia determined by the molar proportions in the mixture. The symbols used in the mathematical discussion are as follows:
z y z w
u D
M F
R
-----
component 1 in blend, gal. component 2 in blend, gal. component 8 in blend, gal. component 4 in blend, gal. = component 5 in blend, gal. density of subscribed component, lb./gal. molecular weight of subscribed component, lb./mole volumetric proportion of subscribed component, dimensionless mole fraction of subscribed component, dimensionless 1-C octane number of subscribed component, dimensionlass
logs
INDUSTRIAL AND ENGINEERING CHEMISTRY
S = property C number of subscribed component, dimensionless T = true initial vapor pressure. lb./sq. in. abs. K 1 = 1-C octane number desired in final blend, dimensionless K z = true initial vapor pressure desired in final blend, lb./sq. in. abs. K3 = property C number desired in final blend, dimensionless a = ( K 1 - R] of subscribed component, dimensionless (Le., a2 = KI - &) b = (K2 2') of subscribed component, lb./sq. in. abs. c = ( K 3 - S) ( D I M ) of subscribed component, consider dimensionless
-
Except with respect to K whose subscripts are implicit in the symbol, subscripts 1 through 5 refer to components 1 through 5, respectively
.
We may write immediately:
=x
VI
2
-
2
V 2= x
+ y + + w + u;
Moles component 1 =
Y
**
+y +z + w +
B
, etc.
(1)
Mz
(2)
moles component 2 = Dsy
MI
Vol. 36, No. 12
Equations 4, 8, and 10, which are the conditional equations to be met by the final blend, have been transformed into the more readily handled, homogeneous simultaneous Equations 7, 9, and 12 which may be assembled in the set: alx 612 C15
+ + bg2 a3z + a4w + a5u = 0 + ab2y~ y+ + b4w + = 0 + C2y + + + 0 C32
C4W
bgV C6U
i
(13)
In this form the three conditions are susceptible to rapid solution by the laws of determinants. In addition the conditions for the existence of a solution are well known. I n general, a t least four components must be used to give a solution. Three components or less are not enough to satisfy the three conditions. With three components given, two conditions can be met; the third condition will be whatever it may and will not, in general, be the desired figure. With more than four components the solution will be in terms of two or more arbitrarily selected components. Thus, in Equation 13 let us determine x , y, z in terms of w and v:
-
DIX .r
(3)
Or
(x
+ y + Xz + w + u
+ zY + w + u ) R 2 +
( Z + Y
2
+ y + + + u ,) R4 + W
+ (x
(x+y+s+w+u
ZL!
2
Clearing fractions and collecting terms:
(K1
- R I ) X+ (KI - ZfJY alx
or
+
+ nsg +
+ (K1 - R ~ ) =u 0
a32
+ udw +
By definition of the property C> index, VISI v2s2 r a s 3 3484
+
+
(KI - & ) z (Kj - RJw
+
+
W J
+
=
vbs5
(7)
0
=
(6)
K3
(8)
which becomes c1x
+ c*u +
Ca2
+
C*fO
+ c5u = 0
I n the application of this theory certain facts soon become apparent. First, negative results mean that the components cannot be blended together to give the desired specifications. This is illustrated by the fact that 80-octane gasoline cannot be obtained by blending a 60-octane stock with a 75-octane stock. Secondly, a minimum.of four components is required to allow for mathematical solution a t all. This is illustrated by the fact that no amount of blending of two different stocks will satisfy more than one specification in general. With these restrictions and, of course, the essential need for accurate laboratory results, this theory is perfectly general and affords a powerful technique in the practical problem of blending. A numerical example of the preceding theory follows in which three fictitious properties of a blend and its components are used
(9)
13y Raoult's law,
PIT1
+ FtTe + 1"17'3 + F47'4 + 1''5T&= h'?
which hecomes
or
(10)
Mathematical principles are discussed which underlie the blending of liquid components to meet simultaneously the specifications for three extensive properties of the mixture when the volume of one of the components is known to be limiting. Reference is made particularly to blending aviation gasoline although the treatment is entirely general. The physical properties in question are assumed to be linearly dependent upon either the volumetric or molar proportion of the coniponents in the mixture.
December, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
1007
instead of the aviation gasoline specificaTABLE I. DATAON EXAMPLE 1 tions (Table I). This is done in order not to reveal restricted data. Property A is Corn 0- -Pro ertyRelative Symbol nent ho. A C M D D/M DIM a b C linearly dependent on molar proportions, e . 1 26.96 18.30 76.60 102 6.77 0.0666 1.000 + 1.66 -8.3 -16.SO whereas properties B and C are dependent Y 2 23.64 1.20 70.00 96 6.67 0.0684 1.210 + 6.12 + 8 . 8 -10.00 I a 40.80 19.00 66.00 72 6.18 0.0719 1.270 -16.60 -9.0 6.00 on volumetric proportions. W 4 28.26 1.00 6.00 88 6.16 0.0699 1.236 + 0.43 +9.0 +64.00 I t is desired to have property A of the mixture equal to 28.60, property B equal to 10.0, and property C equal to 6.0. Equation 16 is easier if a calculator is available; Equation 17 Then the following set of equations must be solved: is emier if a slide rule is used. -8.32 8 . 8 ~ 9.02 9 . 0 ~ 0 Using a numerical example, say Equation Set 14: -16.5~ 10.0~ 6.02 54.h 9 0
-
c
+- - - ++ f1.65~+ 6.12~ - 15.52 + 0 . 4 3 ~ 0 5
80,
Voi.
%
Mole
Gallono
1 2 3 4
1.910 1.710 0.906 1.000 6.626
34.6 30.9 16.4 18.1
30.0 32.0 18.0 20.0
Corn onent
%
L
P
A
8.08 7.68 7.34 8.66
28.60
r
o rty-
+
%
C
6.32 0.37 8.12 0.18 9.99
26.4 21.7 10.8
;1
bic
e12
-
++ abrYr ~++ aaz + &w 00 bat + b4w + a v + ciz + c4w = 0 }
--
8.8 9.0 -10.0 6.01 6.12 -15.5
Common denominator = -16.5 :5
+
1.1
60.0
Multiply column 2 by -0.6 and add the k u l t to column 8,
1;
For completeness we note briefly methods of solution of simultaneous equations in three unknowns. Given the following set of equations: 011:
-- + +
+-
-8.32 8 . 8 ~ 9.02 9.0p ~ 0 -16.5s 1O.w 6.02 f 5 4 . 0 ~= 0 +1.65~ 6.12y 15.52 0 . 4 3 ~p 0
Solution gives x = 1.91w, y = 1.71w,z = 0.905~:
-16.5 (15)
In determinant array, solution for z, y, and L in terms of 10 is:
-ma81
-14.28 -19.17
1 + -19.171-
+ 1.65
-
8.8 +-10.0 6.12
-16.5 5:::
+
-10.0
8.3 8.81 -16.5 -10 = -3166
6.12
Numeratarx 9.0 / 8.8
-- 9.0 - 9.0 -10.0 8.8 -14.M p 4 . O 6.01 = 1-54.0 - 0.43 +-10.0 6.12 -16.5 - 0.43 + 6.12 -19.17 -64 -14.28
- 0.43
Thewfore c
9
I
-10
-1:'8
+ 6.12 -19.17 -= 1.91w
1-
-6050
In expanding the determinant as &own, the signs of the coefficients of the aecond-order determinant are determined as follows: The coefficient (- 14.28) is in the first row and third column. The sum of 1 3 is even, hence the sign is not changed. If the Bum were odd, the sign should be changed.
+
-
Numerator y
- 8.3 --549.0 -- 6.01 9.0 - 8.3 -54 - 9.0 = 1-16.5 1-16.5 + 1.65 - 0.43 -15.5 + 1.65 - 0.43 -15.07 - 8.3 -9.0 -15.07 8.3 - 9.0 = -5394
1-
1
+1.65 -0.43
1
-16.5
-54
Hencey = 1.70~ Numerator2 =
Or we can expand by the method of minors: c
IO
a
aal
+ +
-8.3
8
-
1-1 1 1
- 8.3 8.8 9.0 1-16.5 -10 -54 1.65 6.12 - 0.43
1
51.2
8.8 - 9.01 +1.65 0.43 51.2 -58.3
-58.3
6.12 Hence z = 0.900~
+ +
1-
-8.3 8.8 0 +51.2 -58.3 +1.65 6.12 - 9 0.43 *0
-
-
-2866
Where routine calculations of this nature are required, it is relatively easy to set up a tabular scheme of coefficientswhereby these multiplications can be done almost automatically by anyone who can use a calculator.
