364
INDUSTRIAL AND ENGINEERING CHEMISTRY
s=------= AF (m)(0)(C)
50 (0.0064) (12.5) (500)
=
1.25 lb./sq. in. per in.
From Equation 5 the reset rate should be:
(d~),,,
Vol. 38, No. 4 gal./min./min.
=
For the proportional plus reset controller,
The controller limit stops should be set a t 4 and 64 inches of level. Figure 5 shows that after a sudden change in inflow the level will return t o mid-tank in a time of about (5) (C)/( A F ) or 50 minutes. The settings for the proportional plus reset controller can be 'stated as follows: Sensitivity is set so that a level change equivalent to C moves the valve enough to make a flow change equal to A F . Reset rate is set equal to 1.5 divided by the time required to fill the tank at a rate of flow equal to A F .
SUMMARY OF EQUATIONS
For the proportional response controller,
Temperature-Density Relation for Gasoline-Range Hydrocarbons JOHN GRISTOLD %NUJU-NARI CHEW' ?'he Cnicersity of Texas,
A u s t i n . Zexas
+
T h e teniperature coefficient of density ( a ) in the equation, d: = d:' a ( t - 20). for pure hydrocarbons from c', to C12 is correlated with hydrocarbon structure o r type and molecular weight a t temperatures near 20' C. by the formula, - a = rn(l/M - 0.002) 6 X lo-:. where .M is molecular weight and m is a constant depending only on structural t)pe. This permits an exact coiiFersion of d:' to i.P.1. gravity whenerer the type of compound is k n o w n . For application to wider temperature range+, ralues of B in the equation, d f = d:' a(t - 20) 3 ( t - 20)2, are calculated for the few compounds on whivh data of sufficient accurac: and range are available. The balues of B \arj with structure in an unknown manner.
+
+
ACCURATE temperature-density relation for pure liydrocarbons is needed for conversion of dk to various temperatures and to degrees A.P.I. (60/GO0 F,).Several correlations of density and of volume with temperature already have been presented. The most general seems t o be that of Lipkin and Kurtz (8). For the relat,ion, pi
d6 where d
t
= =
d:'
+ a(t - 20) + S(f
- 20)*
(1)
density, grams/ml. temperature, C.
these authors plotted a against niolccular \?-eightfor various types of hydrocarbons, and p ,against molecular weight for normal paraffins. X single curve gave a fairly good representation of a for all types of hydrocarbons, although only a fraction of t,he values fell exactly on the curve. CORRELATIOS O F ALPHA
The Lipkin and Kurtz plots show that the shape of the curves is a t least approximately hyperbolic. If this is h e , a plot of 01 against the reciprocal of molecular n-eight will yield a straight line. This was found to be the case, and Figure 1 shows values of a calculated from the most recent and reliable data (enumerated later). Figure 1 shows that divergence from a single straight line is greatest a t the lowest molecular weight,s, t,hat the data tend 1
Present address, University of Michigan. Ann Arbor, M i c h .
+
to converge st higher molecular weights, arid that d l arornaticn fall above the line and all n-paraffins fall below the line; therefore, by dif'fcrentiating between the-e types, a more accurate correlation is obtainable. Calingaert et al. ( 1 ) reported obtaining a linear correlation for paraffins on the coordinates of aJ4 us. 'V, where S is the number of carbon atoms from heptane to eicosarie (C, to C20). A type form equation linear in a M arid S may be transformed algebraically into an equation linear in a and 1 / X for any given series of hydrocarbons. Recent data for the individual types vcre plot tad separately with the results shown on Figure 2. The data include n-paraffins from Cs to (216, isoparaffins through Cs, naphthrnes through C h , olefins and aromatics through Clz,and a feT7 heavier compounds. On the isoparaffin and olefin plots, points for several isomera of the same molecular weights sometimes superimpose. The data for each individual t,ype are best represented by a straight line. With the exception of isoparaffins, the best lines for all series extrapolate through a hypothetical common point a t 500 molccular weight and 01 = -60 X 10-5. The isoparaffins may also he represented by a line through this common point m-ith less error than occurs between certain isomers of the same molxular weight in ot,her types. Isoparaffins, naphthenes, olefins, diolefins, and acetylenes may all be represented by the same line. A general equation for all types may be viritten in t'erms of molecular weight, and slope: -a =
m(l/iM
- 0.002) + 60 X 10-
(2)
April, 1946
INDUSTRIAL A N D ENGINEERING CHEMISTRY
365
stants now available, and partly to the improved method of correlation. SCOPE OF EQUATION 1
' x MW Figure 1. Values of
CY
Since values of p are known for relatively few compounds and no p correlation is indicated between various types, the scope of Equation 1 reduced to linear form by omission of the squared term should be defined. Values of p for the n-paraffins cover a range; using the constants for pentane through decane, values of P ( t - 20)2 were set equal to 0.0001, 0.0002, and 0.0005, and solved for (t - 20). The resulting figures are the number of degrees above and below 20" C. a t which the stated density error occurs if the squared term in Equation 1 is dropped entirely. The results (Table 111) show that the density error accruing from neglect of the B term is negligible between 15"and 25" C., and frequently between much wider temperature limits. This agrees with the conclusion of Deanesly and Carleton (2) that for n-paraffins the temperature coefficient of density is substantially linear over the range 20" C. * 20' C.
103
Calculated from Recent Data
where CY is the coefficient in Equation 1, ill is molecular weight, and m is the slope that depends on structure: Hydrocarbon Type n-Paraffins Isoparaffins, naphthenes, olefins, diolefins, acetylenes Aromatics
'
Slope m 0.0315 0 0333 0 0383
EVALUATION OF p
Data of a high order of accuracy and covering a fairly wide temperature range are needed for oalculation of p. Very few of the temperature-density data reported in the literature are adequate for this purpose. The only data comprehensive for a series are on n-paraffins. These form a straight line from Cj to C,e when p is plotted against the reciprocal of molecular weight (Figure 3). The equation for the line is:
-Pn.=. =
(800/M
- 3.0)10-'
(3)
Calingaert et al. (1) calculated p for n-paraffins from pentane through dodecane, and also p for several isoparaffins' using data from other sources (3, 12). It was noted that values for isoparaffins were different from those for n-paraffins, but this was ascribed to inaccuracies of the data. Lipkin and Kurtz (8)recommended that p values of n-paraffins be used for all hydrocarbons. Data have appeared since which show that p for n-paraffins should not be implicitly used for other types, even for isoparaffins. Data on styrene (II), on 2,3dimethylbutane ( 7 ) , and on undecyne may be used to obtain values of p of a t least approximate accuracy. Table I gives the calculated values. The styrene reference data are presented only as a calculated table, and the value of p may not be accurate. For all other compounds the values range from equal to several times greater than those for the corresponding n-paraffins. As far as the authors know, Equation 1 is merely the conventional power series type of empirical equation commonly used to represent physical data. It docs not correlate densities accurately over wide temperature ranges without the addition of a cubic term as used in International Critical Tables (6). Therefore no simple and general correlation of p may be expected. However, a rough' value may be selected from Table I for use with compounds other than n-paraffins. Table I1 compares the present values of CY and p with those of Lipkin and Xurtz. The differences are appreciable in many places and are due partly to the later and more accurate con-
GRAVITY CONVERSION TABLE
Densities of pure hydrocarbons are commonly reported in the literature as die, whereas the petroleum industry favors A.P.I. gravity (at 60"/60" F.). A rapid and exact conversion between the two is of great convenience. The data required for the conversion are temperature coefficients of density for the hydrocarbons and for water. For the more common pure hydrocarbons, Equation 1 with the p term omitted was used with the proper a value to convert d:' to density a t 15.56" C. (SO0 F.) relative to water a t 4" C. This was then converted to density a t 15.56' C. relative to water a t 15.56' C. by dividing by the relative dcnsity of water a t 15.56' C. t o water a t 4" C. The A.P.I. gravities corregponding to these densities were then obtained from a table
TABLEI. VALUESOF p FOR HYDROCARBOXS OTHERTHAN ~-PARAFFIKS ,.B
x . , ins ..
Subject hydrocarbons 0 -2.4 -2.17 -0.89
%-Paraffin" 1 0 to 145 -0.47 Satn. 0 t o 200 -0.63 1 10 t o 100 -0.40 1 -0.50 -20 to 90 1 -20 to 80 -0.50 -0.50 1 I5 to 90 -0.4 -0.21 a From Figure 3 at mol. wt. of subject compound. (For compounds other than isoparaffins, these molecular weights are not those of actual paraffins. This rocedure gives slightly better correlation than the basis of equal number oE)oarbon atoms.) Compound
Pressure, Atm.
TABLE 11. COMPARISON OF
Temp.,
c.
AND
(Y
p
WITH
LIPKINA N D KURTZ
VALUES
x
106 B Authors Lipkin Mol. n-ParAroand Wt. affins matics Othersa Kurtz 72 97.5 99.6 -8.1 85 90.8 -6.4 92.5 97.4 100 85.2 86.6 -5.0 90.6 120 80.0 84.3 -3.7 81.1 140 76.2 -2.6 79.7 77.2 -1.8 76.3 73.4 74.2 160 -1.2 71.2 180 73.6 71.8 69.4 200 -0.7 71.5 70.0 225 -0.2 69.4 67.7 68.2 67.7 66.3 66.7 250 +0.2 65,l 65.4 275 66.3 .+0.5 64.2 300 66.8 65.1 +0.8 64.4 Isoparaffins, na hthenes, olefins, diolefins, and acetylenes. Recommended for n-paraffins only. -a
Lipkin and Kurtz 97.4 91.5 86.7 82.0 78.5 75.8 73.7 71.9 70.3 69.0 67.9
.
I
.
.
.
-
*- -
.
I _
x
10'
Autborsb -8.8 -6.4 -5.0 -3.7 -2.7 -2.0 -1.4 -1.0 -0.6 -0.2 +0.1
+0.3
m .
INDUSTRIAL AND ENGINEERING CHEMISTRY
366 I
I
I
I
I
I
Vol. 38, No. 4
r
..
2
4
8
6
I x
12
IO
14
16
103
MW
Figure 2.
V d i i e s of 01 Separated ‘ r pe ~ of Hydrocarbon
According tn
I x MW
103
(IS). Values of N read from tlie curvcH of Figure 2 werc u d for calculating thu .i.I’.I. gravity, except for benzene for which the actual experimental value used. Benzenc is tlic only commoil pure hydrocarbon not satisfactorily correlated. The bcst curve (as noted on Figurc 2) T T ~ used S for isoparaffins. Table IV lists tlie conversion values. The dciisity range includes all known hydrocarbons in t,hc clttsses indicated, from CS through thc CScompound. Intermediate values may bc rcadily found by interpolation, so tlic table is usable for hydrocsrbons of various degrees of purity. SOURCES OF DATA AYD PROCEDURES
I n ail cffort lo rise tlw iiio\t dependable density data, thosc from the Katiorinl I3urcau of Standards ( I O ) werc iircd a h c n
possible. For the noinial p a i a f h i tlic Bureau of St:iiidai(k data \\ere used for pcmtane tlirough nonanc; froin dcc-aric on, those of Deancil) and Cai lct on ( 2 ) u ere used. The temperatuic rocficicril of density (ddldt) i i g i w n :Lt various temperatul c c , t l i t 01 values were calculattd by l h e abbreviated form of ICqua tion 1 ( p term o m i t i d ) cind rhta near 20” C. (uwally valuti\ at 20” and 25’ (2.). A reI-’resentativenumbci of ibomriic compounds OF tlic vdi Ious classes were sclectcd, arid theii OL values calculatcd and plot t ccl One point on a plot inny reprcqcnt more than one isomci. T1:Lt:i for high-molcculai-nciglit c.ompound\ not reported by the 1 3 r i 1 ( > ~ ~ 1 i
(t I--
Compound n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane
0X
10’
-7.9
-6.3 --5.0 -4.0 -3.25 -2.5
*0.0001 1 1 . 3 ’ C.
12.0 14.1 15.9 17.8 20.0
-
20) for Error of
.~.0.0002 1 5 . 9 0 c. 17.8
=to 0005 23.2’ ( ”
28.3
4’1.7
20.0 22.5 25.2
28.2
31.0 35.7 39.0
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1946
367
“of Standards (above 9 carbon TABLE FOR HYDROCARBONS TABLE IV. GRAVITYCONVERSION atoms in most cases) were obA.P.I. ,Gravities tained mostly from Egloff (4, 6). Olefins Olefins Olefins Olefins In the selection of values, care and and and . Alkyl and cycloPenBennaphHexnaphHeparonaphwas taken to use those on difthenes Octanes tanes rnatics anes Toluene thenes zene thenes pentane tanes Density, fcrcnt samples only where data C8 C’ c’ cB c’ C6 c’ CS CS CS CS d’: , (70)” (72) (78) (84) (86) (92) (98) (100) (106) (112) (114) by different investigators agreed .. 0.6100 98.5 .. .. .. .. or where data from different .. 0.6200 94:9 94.9 .... .. .. .. .. .. ... . .. .. .. 0.6300 91.3 91.3 sources gave the same value of 0.6400 87.8 .. .. 87:s .. .. a. This was necessary becausc .. 0.6500 84.6 .. .. 84’6 84.6 .. .. 0.6600 81.2 .. ... . 81.3 81.3 .. .. .. 78:3 . . much ’of the density data lacked .. 0.6700 78.1 .... 78.2 78.2 the necessary accuracy, and .. .. 75:3 0.6800 75.0 . . 75.1 ., 75:2 75.2 . . 72.3 .72.2 0.6900 72.0 . . . . 72.1 . . . . 72.2 cvcn an error of *0.0001 in 69.3 ,. G9:4 69.4 69.2 .. .. 69.3 0.7000 69.1 .. .. density produces an appreciable .. 66.6 66.6 66.5 66.3 . . .. 66.4 .. .. 0.7100 .. 63.8 63.9 .. 63.6 .. .. 63.7 .. . . 63.8 0.7200 error in the calculated value of a. .. 61.2 61.2 61.1 .. 61.0 .. .. 61.1 .. ,. 0.7300 58.5 *. .... 58.6 .. 58.4 .... .... 58.5 .. .. .. 0.7400 Requirements of accuracy and 56.1 .. 55.9 56.0 . . ’ 56.0 ... 0.7500 temperature range covered are .. 53.6 0.7600. .. . . . . ‘53.5 .. .. 63.6 .. .... .. 51.2 ,. 0.7700 .. .. .. 51.1 .. .. .. 51.2 more rigorous for the calculation .. 48.9 .. 0.7800 .... .. 48.8 48.8 of p than for calculation of a. .. .. 46.6 .. .. 0.7900 .. *. * * . . . . .. 44.4 . . 0.8000 . , .. .. .. .. . . . . T h e data suitable for calculation 0.8100-0.8500(no compounds) of P have already been noted. .. .. 32.1 0.8600 *. .... ,. 32.1 .. .. .. *. 30.3 .. 0.8700 ... *. 30:1 .. 30.2 .. From these, 6 was found by the *. 28.4 *. *. 0.8800 ,. 28.3 . . .. *. graphical procedure used by .. 26.6 .. 0.8900 * * .. .. .. .. 0.9000 , . *. *. .. .. .. Calingaert (1). 4 Figures in parentheses are molecular weights. Density data are available for G and lighter gaseous hydrocarbons. These were not included. to CISwas 0.565 a t temperatures near 20” C. Equation 5 is usesince the liquid density depends on pressure, and the gaseous ful in connection with Equations 1, 2, and 3 to correct refractive hydrocarbons under high pressures do not correlate well with the indices for temperature. While Equation 5 was developed from higher hydrocarbons a t atmospheric pressure. data near 20’ C., the temperature limits over which it is valid are unknown.
.
.
I
.
I
I .
..
..
I
. ..
....
..
....
.
..
TEMPERATURE-DENSITY-REFRACTIVE INDEX
Temperature, density, and refractive index are fundamentally rclated to molecular structure. For n-paraffins (and their mixtures) a t 20’ C. the density-refractive index relation (%)is:
n = 0.52167d
+ 1.03104
(4)
Ward and Kurtz (14, 15) discussed the theoretical relations and noted that the ratio of differences of refractive index to den: sity between two temperatures was substantially constant, or
An
= CPd
I
(5)
For hcavy petroleum fractions (A.S.T.M. groups 0 and 1) the value of C was 0.59, and for all lighter petroleum oils and wax, C mas 0.60. Mibashan (9) found that C for n-paraffins from CS
.
.
- 8 _NORMAL PARAFF 0
LITERATURE CITED
(1) Calingaert, G.,Beatty, H. A., Kuder, R. C., and Thornson, G. W., IND. ENQ.CHEM.,33, 104 (1941). (2) Deanesly, R. M., and Carleton, L. T., J . Phys. Chem., 45, 1104 (1941). ( 3 ) Dornte, P. W., and Smyth, C. P., J . Am. Chem. SOC.,52, 3546 (1930). (4) Egloff, G. “Physical Constants of Hydrocarbons”, Vola. I and 11, Ned York, Reinhold Publishing Corp., 1939. (5) Egloff, G., and Grosse, A. V., U.0.P. BookEets, 217,219 (1938). (6) International Critical Tables, Vol. 111, p. 27 (1928). (7) Kelso, E. A,, and Felsing, W. A,, IND.ENQ.CHEM.,34, 161 (1942). (8) Lipkin, M.R.,and Kurtz, S. S., IND. ENQ.CHEM.,ANAL.ED., 13,291(1941). (9) Mibashan, A.,Tram. Faraday SOC.,41,34 (1945). (10) Natl. Burzof standards, “Selected VBlues of Properties of Hydrocarboqs”, A.P.I. Research Project 44 (1943). (11) Patnode, W., and Scheiber, W. J., J . Am. Chem. SOC.,61, 3449 (1939). (12) Srnyth, C. P., and Stoops, W. N., J . A m . C h e i . SOC.,50, 1883 (1928). (13) Tagliabue, C. J., Mfg. Co., Tag Manual for Inspectors of Petroleum, 26th ed., 1942. (14) Ward, A. L.,and Kurtz, 8. S., IND. ENQ.CHEM.,ANAL.ED., 10, 659 (1938). (15) Ward, A. L., and Kurtz, 9. S., in “Science of Petroleum”, Vol. 11, p. 1137,Oxford Univ. Press, 1938.
x
‘
4
6
Figure 3.
8
I x MW
IO
12
I4
103
Values of @ for n-Paraffins
16
Liquid Holdup and Flooding in Packed Towers-Correction
6
Attention is called t o a n inconsistency in the units specified for the quantity ULin the table of nomenclature page 445) of this article by J. C. El in and F. B. Weiss [IND.! E h . CHEM., 31, 435 (1939)l. UL,&e superficial liquor velocity based on entire cross section, should be correctly ft./sec. rather than ft./hr. as printed. With this change the superficial mass velocity of liquor, lb./(hr.) (sq. ft.) = 3600 ULp ~ . The chart of Figure 10 as printed is correct, as long as consistcnt time units are employed.
