I5
(5
15 SULFURIC 4CID
-s-” to -
- IO
6’
8 IO c
c
-
3
3
c
I
0 “
0“
m 2 5
s 5
0
m 3 5 0
0 0
5
40
15
20
0
0
IO
5
uo2so,
UO2SO4Iwt%)
15
20
0
(wt %I
15
---
29lImole.I.EXCESS
$\$
5
IO
I5
20
0
uo2so, Iu t % I Figure
5
10
15
to uozso, ( w l %I
15
20
TEMPERATURE CONTOUR LINES O ~ o t i - e r m ~ l FOR APPEARANCE OF T W O LIQUID PHASES REGION OF BLUE-GREEN CRYSTALLINE SOLIDS
11111
0
5
1’11
REGION OF RED SOLIDS
A
REFERENCE COMPOSITION OF 0 1 m CuSOq 0 I m uOzS04
+
REFERENCE COMPOSITION
20
OF HRT FUEL
0 005 m CuSO, 0 0 4 m UOzS04 (PLUS ca 0 0 2 5 m H2SOe1(55%1
uo2s04( w t % l
1. P h a s e t r a n s i t l o n temperatures I n solutions containing cupric sulfate, uranyl sulfate, a n d sulfuric acid
against o n e of t h e composition variables yields smooth curves from which interpolation values may b e obtained. Figure 1 s h o w s temperature contour plots obtained i n t h i s manner for e a c h of the five acidity values. T h e regions in which solid p h a s e s were encountered a r e indicated. A comparison s h o w s that a s the amount of e x c e s s sulfuric a c i d is increased the s c o p e of t h e precipitation regions s h r i n k s a n d t h a t t h e temperature a t which liquid p h a s e separation occurs for a specific concentration is elevated. If sufficient a c i d is present to prevent precipitation of a solid, pure copper sulfate-sulfuric acid solutions will yield a second liquid p h a s e i n a manner completely analogous to t h e behavior o r uranyl s u l f a t e solutions. Solution compositions falling within t h e precipitation regions a r e probably of n o interest for reactor use, b e c a u s e of t h e temperature limitation. T h e d a t a i n t h e two-liquid p h a s e region provide a n upper temperature limit for reactor u s e for any composition within t h e s c o p e of t h i s study. Relying on p a s t experimental data (4), t h e two liquid phase appearance temperatures for t h e heavy water system a r e
expected to b e of the order of 5‘’ t o 10°C. lower than for t h e corresponding ordinary water system. LITERATURE C I T E D (1) McDuffie, H. F., Compere, E. L., Stone, H. H., Woo, L. F . . Secoy, C. H., “Homogeneous Catalyais for Homogeneous Reactors. C a t a l y s i s o f the Reaction Between Hydrogen and Oxygen, ” Southwide Chemical Conference, ACS, Memphis, Tenn., Dec. 6, 1956. (2) Posnjak, E., Tunell, G., Am. J. Scf. 218, 1-34 (1929). (3) Secoy, C H., J . Am. Chem. SOC.72, 3343 (1950). (4) S e m y , C. H., others, “The Reactor Handbook AECD-3646,” Vol. 2, 1st ed., Chap. 4.3, p. 559, Technical Information Service, U. S. Atomic Energy Commission. Oak Ridge, T e n n , May 1955. R e c e i v e d for review May 24, 1 9 5 8 Accepted October 9 , 1958. Division of Industrial and Engineering Chemistry, Symposium on Chemistry and R e p r o c e s s k g of Circulating N u d e a r Reactor F u e l s , 133rd meeting, ACS, San Francisco, Calif., Aprii 1958. Based on work performed at Oak Ridge National Laboratory, operated by Union Carbide Corp. for the Atomic Energy Commission. Other articles from t h i s symposium will be published in the February 1959 i s s u e of Industrial and Engineering Chemistry.
Diffusion Coefficients in Hydrocarbon Systems. Methane
in the Liquid Phase of the Methane-Santa Fe Springs Crude Oil System H. H. R E A M E R and
0 . H. SAGE California institute of Technology, Pasadena, Calif.
L i t t l e experimental work i s available concerning the molecular transport of methane in t h e liquid p h a s e of hydrocarbons except t h e earlier work of Pomeroy (10) and of Lacey and others (1, 4, 5, 7. More recently, interest in t h i s field h a s revived and a t the present time some information i s available concerning the transport of methane in binary systems made up of t h i s hydrocarbon and the paraffin hydrocarbons from propane through n-decane, with the exception VOL. 4, NO. 1, JANUARY 1959
of o c t a n e and nonane (11, 13-16). Kirkwood (6) h a s s e t forth some of t h e basic relationships of molecular transport and t h e s e have been extended t o a number of situations of particular interest t o petroleum production (9). T h e work of Drickamer h a s made a marked contribution to an understanding of transport in liquid and g a s phases at elevated pressures. H i s studies, directed toward an understanding of the behavior at a gas-liquid interface (24, 29,
15
i
.-i m
0
s
6
m
.m
0
.m
2 :3
..C
m
3 ._I
u1
a
z
:4
o m m
Gdr; UJww
r.0
Ym.3
m22
m m o -30
NNCI
: : :
...
.9 'z1 m 0
La E
8
._I
.e
m
0 7 N
s
d 16
a
g
0.93
0.9 2
1000
2000
PRESSURE Figure
3000
4000
LE. PER SO. IN.
2. Volumetric correction factor for methane-Santa F e Springs crude a i l system
methane in t h e liquid phase of t h e methane-crude oil system a s a function of pressure and temperature. T h i s factor i s the first bracketed term of Equation 1. Similar information for the weight correction factor for methane in t h i s system i s shown in Figure 3. T h i s factor i s t h e l a s t bracketed term of Equation 1. T h e deviation of t h e s e correction factors from unity i s much smaller for t h e methanecrude oil system than i s encountered with such systems a s methane-n-butane (1.5). T h e necessary values of concentration of the two components were obtained from t h e original volumetric study (21). EXPERIMENTAL DATA
Information similar t o that shown in Figure 1 w a s obtained a t other temperatures between 40' and 280'F. A sample of the detailed experimental results obtained for t h e measurements covered in Figure 1 i s s e t forth in T a b l e 11, which includes approximately 25% of t h e tabular information obtained. T a b l e 111 records the experimental information obtained from the application of a l e a s t squares fit to the linear relationship between the weight of methane crossing the interf a c e and the square root of time, together with t h e associ-
18
ated experimental conditions. In addition, t h e values of t h e volumetric correction factors have been included. From t h e s e the Fick diffusion coefficient a s described by Equation l w a s computed. Values both with and without consideration of t h e effect of hydrodynamic velocity a r e reported in T a b l e 111. T h e standard errors of estimate reported in T a b l e I11 a r e based upon t h e assumption that all of t h e error i s associated with t h e weight of methane crossing t h e interface and none in connection with t h e time. T h e experimental results obtained in t h i s investigation a r e presented a s a function of pressure in Figure 4. L i n e s of constant composition have been included a s a matter of interest. T h e experimental points shown i n Figure 4 were located a t a linear average of t h e initial and final pressures used in each measurement. A substantial part of t h e deviation of the experimental data from the smooth curves may b e ascribed t o uncertainties in t h e equilibrium data, particularly in values of t h e partial volumes of methane and of t h e crude oil. Likewise,, uncertainties in t h e values of t h e concentration required for t h e solution of Equation 1 add to t h e
0
U
: I2 5 Y L IL
10 o
8
s-
7 5
-u
8. Y
50
z 0
?
-
2 5
0
U x
-
IL
500
loo0
1500 PRESSURE
Figure 4.
2000
3000
2500
L B PER SO
3500
IH
Effect of pressure upon Fick diffusion coefficient for methane
JOURNAL OF CHEMICAL AND ENGINEERING DATA
Toble II. Somple of Experimental Measurements ot 22O0F. Pressure, P S I . A.
Weight Fraction Methane Liquid P h a s e
125.66 424.W
0.0012 0.0068
Time, Sec.
0 2 170 2229 2319 2369 2419 2469 2769 2949 3499 3699 3789 3809 4169 4269 4319 4619 4819 5019 5719 6019 6269 6869 7019 7219 7369 7669 7819 8019 8119 8469 8819 8919 9119 9219 9819 10019 10219 10269 10719 11068 11518 12068 12368 12718 13568 14068 14568 14968 15468
Methane Addede, Lb. X lod
... ... 1.952 3.905 5.857 7.810 9.762 11.715 15.620 21.477 23.429 25.382 27.334 29.287 31.239 33.191 35.144 37.096 39.049 44.906 48.811 50.763 56.621 58.573 60.526 62.478 64.431 66.382 68.335 70.288 72.240 74.193 76.145 78.098 80.050 82.002 83.955 85.907 87.860 89.812 91.765 95.670 97.622 99.574 101.527 107.384 109.33 7 111.289 115.194 117.146
TEMPERATURE
Figure 5.
OF
Influence o f temperature upon F i c k diffusion coefficient for methone
upon s t u d i e s of the transport of methane in the liquid phase of t h e methanepropane (16), methane-n-butane (15), methane-n-pentane (11), methane-n-heptane ( 1 4 , methane-nd e c a n e (13), and methane-white oil systems (12). It i s not surprising that t h e methane-crude oil system yields slightly smaller F i c k diffusion coefficients than would be obtained for s y s t e m s containing no aromatic or naphthenic compounds. T h e accumulation of experimental data upon t h e diffusion coefficients of t h e lighter hydrocarbons h a s not a s yet progressed to the point where a generalization of the r e s u l t s to permit estimation of t h e diffusion coefficients i s worthwhile. T h e s e diffusion coefficients a r e somewhat smaller than those for methane in a binary hydrocarbon system involving a paraffinic, l e s s volatile component of t h e same molecular weight. ACKNOWLEDGMENT
T h i s work constitutes a contribution from Project 37 of t h e American Petroleum Institute a t the California Institute of Technology. T h e methane w a s supplied through t h e courtesy of T h e T e x a s Co. Virginia Berry prepared the data in a form suitable for publication. B. Lawson Miller ass i s t e d in t h e preparation of t h e manuscript, which was reviewed by W. N. Lacey.
8Weight added to heterogeneous isochoric system. bInitial equilibrium pressure. CConstant operating pressure during diffusion.
l a c k of agreement of t h e experimental data with t h e smooth curves presented. T h e standard deviation of t h e experimental measurements shown i n Figure 4 from t h e smooth curves w a s 0.6 x 10-* s q u a r e foot per second, when i t w a s assumed that all of t h e uncertainty lay i n t h e F i c k diffusion coefficient and none i n t h e determination of t h e temperature, pressure, or composition. Smoothed v a l u e s of t h e F i c k diffusion coefficient a r e reported in T a b l e IV as a function of s t a t e , after correction for t h e hydrodynamic velocity. T h e effect of temperature upon t h e F i c k diffusion coefficient for methane in t h e m e t h a n e c r u d e oil system is shown i n Figure 5. A s would be expected, there i s a significant i n c r e a s e in t h e coefficient with a n i n c r e a s e i n temperature. T h e Fick diffusion coefficient i s presented a s a function of t h e molecular weight of t h e less volatile component for three temperatures in Figure 6 . I t is apparent that the coefficient in t h e methane-crude oil system is slightly lower than that estimated for a paraffin hydrocarbon system involving a l e s s volatile component of t h e same molecular weight. T h e d a t a included i n Figure 6 a r e based VOL. 4,
NO.
1, JANUARY 1959
MOLECULAR WEIGHT OF LESS VOLATILE C O W O N E N T
Figure 6.
Effect of moleculor weight of less volatile component upon F i c k diffusion coefficient for methane in the liquid phase
19
sa::
9+.Y
mmm
282
'SN
.
o m m
V
4t.m am-
% g8; mmlnm
0 0 0
0 0 0 0
0146
dddd
????
???
9
9
2
5 X
X
k
k X
wwm ? ? :
Q
Y E1
4
Q
s
2
I
2
s
X
X
,. _I
b
Ili
?!
a
f
4
t
X
3 L.
f
4
a. .
6 c)
W
E
E
LI
P
c)
d
0
!i
r
Y
u
24
I
c)
'2
J6
C
p
.5 c C
4 - N 0
9
0 0 0
'C c)
z
d
>
.s6 d
N N 6
(4
20
JOURNAL OF CHEMICAL AND ENGINEERING DATA
= t o t a l weight of component k crossing t h e interface, pounds specific volume of component k , cubic feet per pound A = difference in 6 = time, s e c o n d s uk = concentration of component k, pounds per cubic foot
Ek
Table IV.
Fick Diffusion &efficient
Methane i n Liquid P h a s e Pressure, P.S. 1. A.
Concn. lb./cuft.
Compn. weight fraction
for Methane
F i c k Diffusion Coefficient, Sq.Ft./Sec., XIOd
v k = partial
Superscript
* = average
40’ F.a 500 1000 1500 2000 2 500 3000 3500
0.013 0.026 0.038 0.05 1 0.063 0.074 0.084
500
0.011 0.022 0.034 0.046 0.058 0.07ob 0.083
0.687 1.379 2.004 2.578 3.123 3.619 4.069
1.8 1.8 1.8 1.8 1.86 1.8b 1. 86
100’ F.
1000 1500 2000 2500 3000 3500
0.568 1.160 1.730 2.280 2.828 2.3616 3.901b
3.3 3.2 3.1 3.1 3.0 2.96
2.e
160’ F. 500 1000 1500 3000 3500
0.009 0.020 0.03 0 0.042 0.053 0.066b 0.08Ob
500 1000 1500 2000 2500 3000 3500
0.008 0.018 0.028 0.03 8 0.050 0.063 0.077b
500
0.007 0.017 0.026 0.036 0.047 0.059 0.073
2000 25 00
0.489 0.982 1.491 2.012 2.544 3.O9Ob 3.681b
5.0 4.7 4.6 4.4 4.3 4.1b 4.0b
220’ F. 0.409 0.858 1.319 1.800 2.282 2.816 3.379b 280’
1000 1500 2000 2500 3000 3500
7.3 6.9 6.6 6.3 6.0 5.7 5.46
F.C
0.348 0.759 1.189 1.636 2.052 2.560 3.024
11.6 11.2 10.7 10.3 9.9 9.5 9.0
‘Values of composition and concentration extrapolated from data a t higher temperatures. bExtrapolated from d a t a a t lower pressures. CValues of composition and concentration extra?olated from data a t lower temperatures.
NOMENCLATURE DF,k
= F i c k diffusion coefficient of component k. square f e e t /
Q
second = w e i g h t of component k added per unit area of interface, pounds /square foot
VOL. 4, NO. 1, JANUARY 1959
condition
Subscripts
e = conditions a t equilibrium g = gas phase i = conditions a t interface j = component j , stagnant component k = component k,diffusing component I = liquid phase o = initial conditions
LITERATURE CITED (1) Bertram, E. 4., Lacey, ‘4. N., Ind. Eng. Chem. 28, 316 (1936). (2) Botkin, D. F., Reamer, H. H., Sage, 6. H.. Lacey, W. N., “Fundamental Research on Occurrence and Recovery of Petroleum 1943,” 4merican Petroleum Inst., pp. 62-70. (3) Emmert, R. E., Pigford, R. L., Chem. Eng. Progr. 50, 87 (1 9 5 4). (4) Hill, E. S., Lacey, ‘.A‘. N., Ind. Eng. Chem. 26, 1324 (1934). ( 5 ) Ibid., p 1327 (6) Kirkwood, J. G , Crawford, E , Jr., J. Phys. Chem. 56, 1048 (1952). L a c e y , W. N., Oil G a s 1. 30, No. 8, 15; No. 9, A8 (1921). Meyers, C. H., Bur. Standards J. R e s e a r c h 9. 807 (1932). Opfell, J. 6.,Sage, 6. H., Ind. Eng. Chem. 47, 918 (1955). Pomeroy, R. D., Lacey. ‘4. N., Scudder, N. F., Stapp, F. P., Ibid., 25, 1014 (1933). (11) Reamer, H. H., Duffy, C. H., Sage, 6. H., Ibid., 48, 2 8 2 (1956). (12) Ibid....D. 285. , .~ (13) Reamer, H. H., Opfell, J. E, Sage, 6. H., Ind. Eng. Chem. 48, 275 (1956). (14) Reamer, H. H., Sage, 6. H., A.1.Ch.E. Journal 3, 449 (1957). (15) Reamer, H. H., Sage, R H., Ind. Eng. Chem., Chem. Eng. D a t a Series 1, 71 (1956). (16) Reamer, H. H., Sage, R H., Ibid., 3, 54 (1958). (17) Reamer, H. H., Sage, €3. I{., Rev. Sci. Inslr. 29, 709 (1958). (18) Reamer, H. H., Sage, E H., “Transport Properties in Gases. Measurement of Diffusion Coefficients i n G a s e s and Liquids a t Elevated P r e s s u r e s , ” pp. 62-74, Northwestern University P r e s s , Evanston, Ill., 1958. (19) Sage, EL H., Hicks, R L., Lacey, ’4. N., “Drilling and Production P r a c t i c e 1938,” 4merican Petroleum Institute, pp. 402-20. (20) Sage, €3. H., Lacey, W. N., Trans. Am. Inst. Mining Met. Engrs. 136, 136 (1940). (21) Sage, 6. H., Webster, D. C , Lacey, W. N.. Ind. Eng. Chem. 28,984 (1936). (22) Schlinger, W. G., Reamer, H. H., Sage, 6. H., Lacey, W. N., “Fundamental Research on Occurrence and Recovery of Petroleum, 1952-1953,” 4merican Petroleum Institute, pp. 70-106. (23) Schrage, R. W., “Theoretical Study of Interphase Mass Transfer,” Columbia University P r e s s , New York, 1953. (24) Tung, L. H., Drickamer, H. G., I . Chem. Phys. 20, 6 (1952). (25) Ibid., p. 10. Received for review December 13, 1957.
Accepted May 5, 1958.
21
