J . Phys. Chem. 1986, 90, 1692-1 700
1692
CONDENSED PHASES AND MACROMOLECULES Pressure (1-1000 bars) and Temperature (20-100 "C) Dependence of the Viscosity of Liquid Hydrocarbons D. Ducoulombier, H. Zhou, C. Boned, J. Peyrelasse, H. Saint-Guirons, and P. Xans* Laboratoire de Physique des MatPriaux Industriels,t Institut Universitaire de Recherche Scientifque, 64000 Pau, France (Received: June 25, 1985: In Final Form: November 21, 1985)
This study deals with the determination, using a falling body viscosimeter, of the viscosities of n-alkanes (n-Clo,n-C,,, n-C,,. n-C,,, n-C,,, and n-CI8),alkylbenzenes (butyl, hexyl, and octyl), and some alkane mixtures, between 20 and 100 O C and from 1 to 1000 bars. A phenomenological equation has been derived from the experimental viscosity values. These have also been compared with the values obtained numerically from some models. We have more specially studied the corresponding-states model. A semiempirical relation is given for n-alkanes, taking n-CI4as a reference. This relation also accounts for the results obtained for alkane mixtures and alkylbenzenes. The limits of the method are also indicated.
Introduction When the behavior of the fluid of oil fields (mainly made of hydrocarbons) is simulated, one of the most important parameters is the fluid viscosity. Parameters of distribution of the components are generally introduced in modeling. The viscosity depends on such parameters as well as the component viscosities on temperature and pressure. Therefore, the systematic experimental determination of the viscosity of the components as a function of temperature and pressure should be the starting point for the derivation of the constitutive equations of a n oil fluid. T h a t is why we have proceeded as follows: the systematic determination of solid-liquid diagrams as a function of pressure and temperature by differential scanning calorimetry (DSC) for several pure components (n-alkane and alkylbenzene) ; the measurement of the viscosity of the above-mentioned materials and some mixtures, vs. pressure (1-1000 bars) and temperature (20-100 "C), which partly covers the conditions found in oil fields: the study of a phenomenological representation with a n empirical law. enabling an easy interpolation within the experimental range; the testing of some method of frequently used to simulate the behavior of oil field fluids, considering first of all the simple case of a pure component, then considering some typical mixtures. Experimental Techniques Pressure differential scanning calorimetry (DSC) allowed the systematic determination of phase diagrams of the pure components. A technical article' gives all the details of the experimental apparatus developed in our laboratory. Determination of the viscosity coefficient was carried out by using a guided falling body ( u p to 4000 bars and from -10 to 100 "C). Figure 1 represents the different parts of the system. The dynamic viscosity 11 of the studied fluid a t pressure P and temperature T is given by 'If 7
=K
(PEOI
- Pl,q)Af
where At represents the falling time. K is a parameter depending on the shape and on the nature of the falling body whose variations as a function of P and T a r e negligible; psol represents the density = 8.700 g/cm3). pllqrepresents the density of the falling body (p501 of the fluid. For the studied liquids, pllq is well-known up to 400
'ChRS-GRECO "Micanique des Contacts-Tribologie". 0022-3654/86/2O90- I692$0 I .50/0
bars (literature data) in this temperature range. As variation of P is very small and linear from 1 to 400 bars, we have extrapolated piIqvalues up to 1000 bars. As an example, the n-C,, density a t 40 "C reaches 0.718 g/cm3 a t 1 bar and 0.744 g/cm3 a t 400 bars, and, from extrapolation, can reach 0.783 g/cm3 a t 1000 bars. Consequently, the psol- pllq difference shows little variation within the experimental range (n-C,,,, from 7.982 g/cm3 a t 1 bar to 7.917 g/cm3 a t 1000 bars). Repeated tests show that the average differences for the At falling time remain less than 1%. Temperature is set at f 0 . 5 O C and pressure a t f l bar. A microcomputer is in charge of the data processing and controls the cell rotation. All samples a r e purum quality from Fluka A.G. pl,q vs.
Experimental Results ( 1 ) Alkanes. T h e following alkanes have been studied: ndecane (Cl0),n-dodecane (C12),n-tetradecane (C,,), n-pentadecane (C,s), n-hexadecane (C16),and n-octadecane (C18). The heaviest alkanes are not in the liquid state a t all pressures and temperatures. T h e DSC analysis has allowed us to precisely determine the liquid-state domain for each of these samples. Figure 2 shows the results. Table I gives the values of viscosities of alkanes between 20 and 100 "C and from 1 to 1000 bars. As a comparison, Figure 3a,b gives our results relative to the n-decane as well as those found in the Figure 4a-c represents the viscosity variations that we found vs. the number of carbon atoms, a t various temperatures and pressures. Figure 5a,b represents the viscosity variations vs. temperature for the alkanes, at 1 and 1000 bars. ( 2 ) Alkylbenzenes. W e have measured the viscosit) of three alkylbenzenes (butyl, hexyl, and octyl). Table I1 gives the values obtained from 20 to 100 "C and from 1 to 1000 bars. ( 3 ) Alkane Mixtures. We have studied five mixtures of pure alkanes with several weight ratios. Table 111 gives the obtained
(1) Saint-Guirons, H.; Xans, P. J . Phys. E: Sci. Instruni. 1981, 14, 1332-1336. (2) Ducoulombier, D. Thtse de 3" Cycle, Universiti de Pau, 1984. (3) Ducoulombier, D.; Lazarre, F.; Saint-Guirons, H.; Xans, P. Reu. Phys. Appl. 1985, 10, 735-740. (4) Lazarre, F.; Ducoulombier, D, Brevet No.
8211550, 1982.
(5) Gouel, P. Thbe, Inst. Nat. Pol. Toulouse, France, 1979. (6) Lee, A. L.; Ellington, R. T.; Eakin, B . E. J . Chem. Eng. Data 1965,
IO,
101.
( 7 ) Carrnichael, L. T.; Berry, V . M.; Sage B. H. J . Chem. Eng. Data 1969,
14,
27-31.
(8) "Creps Geopetrole"; Editions Technip.: Paris, 1970
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1693
Viscosity of Liquid Hydrocarbons
I
I
I
.
Pressurization
MEASURING
Temporized rotation
CELL
command A
I
I '
--
c
*
+
Data processing
'
VISCOSITY
(P,T)
Figure 1. Measuring system flow diagram.
tI
PHAY
DIAGRAM
OF
becomes infinite at 0 K and not at T , > 0 K, following our results. That is why we have used the following equation:
STUDIED ALKAFES
First of all, we have checked that the variation of 17 vs. T was well represented by this relation, a t a given pressure. In order to introduce the pressure parameter, we have considered two alternatives: (i) W e have first expanded the Ao, Bo, T , quantities as a polynomial in P. Then we have checked the following relation:
I
7 = exp
[
aP2 + 6P + c
+
d p
+ eP3 + fP2+ gP + h T - (iPz + j P + k )
]
(1)
The coefficients a-k are derived by using a least-squares method. Deviations will be characterized by -20
smrt LIQUID
DV =
501 ID
P(bor)
1
7)calcd
- Vexptl
/loo
(DV in %)
Vexpti
where qCalcdrepresents the calculated value and qexptlthe experimental value. The average of DV has been established as less than 1% (Table IV) for the alkanes. Table V indicates the values of coefficients a-k in the case of the n-tetradecane. We can notice that the experimental results are most often confirmed for each pure body, yet there is no existing correlation between the coefficients and the number of alkane carbons. This situation certainly comes from the high number of involved constants ( 1 1 constants). Therefore, the obtained parameters (such as Table V parameters) are purely phenomenological and valid for a given alkane. The denominator T - (iP2 j P k ) has roots in P for each T value, but we have checked that, in any case, they were outside the pressure range (1-1000 bars) and that the a s / d P derivative is always positive. (ii) W e have also checked the following relation
+ +
7=
exp[[(alP2 + 6 , P
+ c l ) T + (aoP2 + boP + c o ) ] / [ T- T,]] (2)
1694
Ducoulombier et al.
The Journal of Physical Chemistry, Vol. 90, IVO.8 , 1986
TABLE I: Measured Viscosities (7,cP) of n-Alkanes vs. P no. of carbon atoms r. o c IO 12 14 15 16 P = I bar 1.50 2.33 20 0.924 1.07 1.60 1.95 0.696 40 2.23 1.15 1.36 0.546 0.81 60 1.56 0.441 0.634 0.878 1.02 80 1.16 0.363 0.510 0.692 0.785 0.896 IO0
20 40 60 80 100
20 40 60 80 100
0.892 0.701 0.555 0.477
P = 200 bars 1.91 2.94 1.33 1.94 0.987 1.39 0.763 1.04 0.640 0.853
1.46 1.07 0.853 0.676 0.594
P = 400 bars 2.35 3.86 1.62 2.42 1.21 1.72 0.930 1.28 0.790 1.06
I .21
P 20 40 60 80 100
1.75 1.29 1.01 0.801
2.88 1.96 1.44 1.11
0.706
0.930 3.48 2.35 1.69 1.30
100
2.06 1.50 1.17 0.934 0.819
20 40 60
2.41 1.71 1.35
80
1.08
100
0.936
=
600 bars 4.73 2.91 2.06 1.54 1.26
and T
TABLE 11: Measured Viscosities (7,cP) of Alkylbenzenes vs. P and T T , ‘C
18
20 40 60 80
3.10 2.10 1.51 1.14
100
2.43 1.70 1.27 0.990
3.03 2.10 1.56 1.22
3.73 2.55 1.88
1.46
3.01 I .96 1.44 1.13
3.61 2.43 1.77 I .37
4.56 2.95 2.13 1.64
4.40 2.77 1.98 1.49
80
1.08
3.47 2.44 1.81 1.46
4.27 2.82 1.96 1.48 1.17
P = 600 bars 2.08 3.29 1.42 2.18 1.14 1.64 0.90 1.26 0.74 1.01
5.19 3.34 2.33 I .76 I .37
P = 800 bars 2.45 3.90 1.67 2.54 1.32 1.90 1.oo 1.44 0.83 1.15
4.55 3.07 2.23 1.72
P = 1000 bars 4.09 2.81 4.10 5.47 1.97 2.86 3.65 1.51 2.10 2.61 1.25 1.66 1.99
5.68 3.53 2.52 1.92
6.20 3.87 2.74 2.06 1.60
40 60
0.99 0.83 0.68 0.55
20 40
5.62 3.45 2.44
60 80 100
1.81
20 40 60
7.00 4.22 2.95 2.17
80
100 20 40 60
5.09 3.50 2.56
80 100
1.73 I .24 0.94 0.74
P = 400 bars 1.76 2.74 1.19 1.83 0.98 I .39 0.79 1 .08 0.65 0.87
I .47
100
2.58
1.63 1.24 0.97
20 80
oct1l
200 bars 2.25 1.52 1.16 0.92 0.73
P
P = 800 bars
20 40 60
butyl hexyl P = I bar 1.07 1.70 0.79 I .20 0.63 0.895 0.51 0.697 0.42 0.57 =
3.43 2.32
P = 1000 bars 6.93 4.16 2.93 2.23
20 40 60
6.06 4.10 2.98
where T , is supposed to be constant, for a given body, in the considered pressure interval. Seven constants are to be determined. T h e representation is still very good. Table IV shows that the DV average deviation remains less than 1.3%. Here again, we have recorded no correlation of the equation coefficients with the number of alkane carbons. So, with the first or second relation, we obtain a suitable phenomenological representation of the experiment data. Such equations allow an easy interpolation between experimental points. Figure 7 represents the three-dimensional diagram (p,P,T) that has been obtained for n-octadecane, from eq 1. (2) Comparison with Existing Models. Two typical models have been tested on pure alkanes. The Kouzel model’ applies to hydrocarbons with a very high molecular weight. T h e Lohrentz-Bray-ClarkiO model allows us to calculate the viscosity p from the coordinates of the involved fluid critical point. ( i ) Kouzel Model. A comparison with our results appears to be satisfying for all studied alkanes, up to about 200 bars. For higher pressures, the Kouzel model overestimates the viscosity. See Figure 8 for n-octadecane a t 40, 60, and 100 OC, as an example. (ii) Lohrentz-Bray-Clark Model. Figure 9 enables us to compare the values obtained for the n-decane a t 20 and 100 O C . A discrepancy can be noted (generally a n underestimation by the model). However, this can be related to the “gaslike” hypothesis put forward by the authors of the model (for the heaviest alkanes, the discrepancy is mugh higher). (9) ”A.I.P. Technical Data Bsok, Petroleum Refining”; American Petroleum Institute: Washington, DC, 1970; Chapters I and 11. (10) Lohrenz. J . ; Bray, B. G.; Clark, C. R. J . Per. Technol. 1964, 1171-1176.
80
100
2.87 1.96 1.48 1.11 0.90
4.58 2.94 2.17 1.63 1.28
7.30 4.39 3.18 2.39 1.84
( 3 ) Corresponding-States Model. (i) This model tries to estimate fluid behavior from another fluid behavior taken as a reference, introducing a reduced pressure and temperature. This model has just been discussed by Pedersen et al.” who suggest the following procedure:
The index c is related to the critical point and index 0 to the reference. M represents the molecular weights (expressed in grams) and p represents the density. , T h e a quantity is the “rotational coupling coefficient” initially introduced by Tham and Gubbins.12 (The three involved coefficients are adjusted by using the experimental viscosity data.) Therefore, we must know the variations of the viscosity and density of the reference vs. pressure ( 1 1) Pedersen, K. S.; Fredenslund, A,; Christensen, P. L.; Thomassen. P. Chem. Eng. Sei. 1984, 39, 1011-1016. (12) Tham, M . J . ; Gubbins, K . E. Ind. Eng. Chem. Fundam. 1970, 9.
63-69.
The Journal of Physical Chemistry, Vol. 90, No. 8, I986
Viscosity of Liquid Hydrocarbons TABLE 111: Measured Viscosities (7,cP) vs. P and T for Various Alkane Mixtures" T, "C P, bars 40 60 80 Mixture 75% n-Clo-25% n-CI6 0.90 0.69 0.55 1 1.13 0.86 0.68 200 1.38 1.04 0.82 400 1.66 1.24 0.97 600 1.97 1.45 1.15 800 2.31 1.67 1.33 1000
200 400 600 800 1000
Mixture 50% n-CIo-50% n-C16 1.18 0.89 1.51 1.12 1.86 1.38 2.24 1.66 2.64 1.97 3.07 2.3 1
0.69 0.87 1.07 1.27 1.49 1.72
1 200 400 600 800 1000
Mixture 25% n-Clo-75% n-C16 1.60 1.17 2.07 1.50 2.59 1.87 3.16 2.27 3.77 2.70 4.44 3.16
0.89 1.11 1.36 1.63 1.93 2.25
1
Mixture 25% n-Clo-25% n-C12-25% n-C14-25%n-C16 1 1.21 0.91 0.71 200 1.60 1.19 0.89 1.09 2.00 1.48 400 600 2.43 1.78 1.31 800 2.89 2.09 1.55 1.81 3.36 2.41 1000 T, "C 20 Mixture 40% n-Clo-60% n-C, 1 0.506 200 0.614 400 0.742 600 0.888 800 I .os 1000 1.23
P, bars
40 0.393 0.483 0.575 0.685 0.800 0.920
"Proportions are given in weight ratios. TABLE IV: Average Value of the DV Absolute Deviation between Experimental and Calculated Viscosities for the Pure Bodies av value of the abs dev system
n-decane n-dodecane n-tetradecane n-pen tadecane n-hexadecane n-octadecane n-butylbenzene n-hexylbenzene n-octylbenzene
eq 1 1.o 0.9 0.7 0.2 0.8 0.5 1.7 0.8 0.7
eq 2 1.3 1.1 1.3 0.3 1.5 1.1 2.5 1.3 1.4
TABLE V: Calculated Values for the n-C1, Coefficients from 8 to If a = -4.868729 k 10" g = -2.527380 b = 6.162691 X h = 874.0397 c = -3.461585 i = -2.985316 X d = 1.545022 X j = 0.3435125 e = -3.443880 X IOd k = -182.6151 f = 4.187426 X lo-'
" P in bars, T in degrees Celsius, 7 in centipoise (eq 1). and temperature. If we choose methane as a reference, like Pedersen et al. ( T , = -82.62 " C and P, = 45.96 bars), the comparison of theoretical values obtained with n-Cls ( T , = 471.75 "C and P, = 11.9 bars), within the scope of Hogenboom resultsI3
1695
TABLE VI: Viscosity Values (7, cP) vs. P and T from the Literature Data for n-C,,* n-C,,8 and (1 atm = 1.013 bar) n-C,
T , OC 0
10 20 30 40 50 60 70 80 90 100
T, OC 0 20 40 60 80 100
T, OC -173 -163 -153 -133 -113 -93 -73
1
0.5175 0.4625 0.4145 0.3740 0.3380 0.3080 0.2825 0.2580 0.2360 0.21 70
15 0.2020 0.1680 0.1410 0.1178 0.0972
1
0.1445 0.1065
100 0.5610 0.5045 0.4530 0.4105 0.3730 0.3405 0.3120 0.2860 0.2630 0.2435 0.2250
P. atm 200 300 0.6165 0.6780 0.5550 0.6115 0.5000 0.5525 0.4535 0.5025 0.4130 0.4560 0.3775 0.4165 0.3460 0.3820 0.3170 0.3505 0.2920 0.3235 0.2710 0.3000 0.25 15 0.2790
50 0.2100 0.1755 0.1480 0.1247 0.1045 0.0974
n-Ca P, atm 100 200 0.2215 0.2450 0.1860 0.2070 0.1580 0.1765 0.1342 0.1512 0.1135 0.1302 0.0963 0.1125
100 0.1761 0.1314 0.1010 0.0702 0.0530 0.0405 0.02884
n-C, P, atm 200 300 0.2215 0.2489 0.1606 0.1888 0.1210 0.1434 0.0798 0.0897 0.0609 0.0685 0.0485 0.0553 0.0390 0.0457
400 500 0.7440 0.8 125 0.6710 0.7340 0.6060 0.6625 0.5505 0.6015 0.4990 0.5455 0.4560 0.4960 0.4185 0.4550 0.3840 0.41 80 0.3540 0.3855 0.3290 0.3580 0.3060 0.3330
300 0.2670 0.1945 0.1680 0.1458 0.1275
400 0.2865 0.2450 0.2105 0.1830 0.1603 0.1415
400 0.2839 0.2179 0.1677 0.1021 0.0763 0.0616 0.051 3
500 0.3197 0.2531 0.1954 0.1184 0.0841 0.0676 0.0566
(up to 3600 bars and from 60 to 135 "C), implies that the methane density is well-known up to 13 900 bars from -168 to -198 "C. (It should be noted that Pedersen et a1.l' make the comparison with two n-C,8 nonspecified points.) Changing the reference and, for example, choosing the n-Cl4 ( T , = 420.85 OC and P, = 16 bars),14 we see therefore that we must know its density up to 4850 bars from 107 to 37 OC to be able to compare the model with the data obtained on n-CI8.l3 As part of our results (from 20 to 100 O C and from 1 to 1000 bars) the n-CI4 properties have to be identified from 1.344 to 1344 bars and from 18.56 to 74.45 "C. Conversely, if we know the n-C,, properties from 20 to 100 " C and from 1 to 1000 bars, the mCl8 properties shall be deduced from relation 4 from 0.744 to 744 bars and from 41.5 to 127.4 "C. As for qo(P',T'), the range of P,Texperimental values has a n effect over the P',T' range which must be known for the reference (besides, here is involved the ratio a,/a). Therefore, it becomes necessary to use a reference whose viscosity and density variations are perfectly known with P and T . T h a t is why it is better to avoid extrapolating the values of the reference too much and, if we indulge in this type of extrapolation, a comparison within a n important experimental P,T range shall be made to be sure of the validity of the representations. (ii) As for us, we have searched for the best representation of experimental results through the relation
P' = P(P,,/P,) T' = T( TCJT,) where the coefficients A , B, and C can easily be determined by (13) Hogenboom, A. L.; Weebb, W.; Dixon, J. P. J . Chem. Phys. 1967, 46,2586-2598. (14) Reid, R.; Prausnitz, J.; Sherwood, T. "The Properties of Gases and Liquids", 3rd ed.; McGraw-Hill: New York, 1977.
1696
The Journal of Physical Chemistrv, Vol. 90, No. 8, 1986
0
Ducoulombier et al.
GOUEL (1979) : 1 9 - 4 4 - 6 2 - 8 1 ° C
(0)
0
P(bars)
I
I
I
I *
ib) 0
P(bars1 I
I
I
Figure 3. Comparison of our results with literature data concerning n-decane:
adjustment when the other values are known. W e have taken as reference n-CI4whose viscosity is represented by eq 1 (and Table V) with a 0.7% average deviation. A , B, and C can be calculated for each alkane. Unfortunately, no correlation appears with the number of alkane carbons. That is why we made the analysis on all the alkanes including literature values for n-C,,n-C4,8 and ) ' ~ VI). methane ( ~ I - C , (Table (1 5 )
"Encqclopidie des gar. L'air liquide"; Elsevier: Ne%,York, 1976.
+, our experimental data; -,
I
*
calculated with eq 1 ,
Taking into account the observation that it is better not to extrapolate relation 1 for n-C,,, we must have 1 C P'C 1000 bars and 20 OC C T'C 100 OC. It implies limitations on the possible values of P and T . T h a t is why only the 11 1 points complying with the previous conditions have been kept for the n-alkanes from C,* to C,. (The values of P, and T, are indicated on Table VII). (No couple (P,T) of n-C, can be accepted and the values at 100, 200, 300, 400, and 500 a t m for T = -173 O C can alone be used for methane.) These are the best values we have obtained: A
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1697
Viscosity of Liquid Hydrocarbons Tl
'rP; (n-ALKANS) PrPiiiirP
/
: 1 bar / /
/
+
+
/
/
/ 20'C
/ /
f
(a)
/
12.5 for alkanes and we cannot use the chart). W e have also applied the corresponding-state model. While keeping n-C,, as a reference and the coefficients previously determined with the alkanes, we get an average deviation of 8.2% (maximum deviation for the butylbenzene: 21.3% with P = 1000 bars and T = 60 "C). The numerical results are given in Tables VI11 and 1X. T h e agreement is reasonable. If an alkylbenzene had been selected as reference, the correlation would have most likely been better. As we had experimental values for three alkyls only, we have not been able to reuse the process used for alkanes. Discussion of Results Obtained on the Alkane Mixtures W e have first compared our experimental results with mixtore laws of the 7 = F ( q i . a i )type where @, characterizes the volume
Figure 7. q,P,T diagram obtained from eq 1 for n-octadecane.
fraction of component i with an q iviscosity. W e have noticed that Lobe's law16
a2 = 0.27 In
(g2/q1)
+ (1.3
;n
(:))"*
for binary blends and the cubic law q 1 ~ 3=
~@,~,ii'
(6)
give excellent results. Table X gives the average and maximum (16) Lobe. V . M. Thesis, University of Rochester, NY. 1973
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1699
Viscosity of Liquid Hydrocarbons
4
TABLE VII: Values of the Molecular Weight, the Critical Pressure, and the Critical Temperature for the Various Systems" critical critical press., system mol wt, g temp, OC bars 245.52 471.85 11.9 n-Cl8 14 226.448 443.85 n-C16 212.421 433.85 15 n-CI 5 198.394 420.85 16 n-C14 385.15 18 170.34 n-C1* 142.286 344.45 20.8 n-Go 100.205 267.05 27 n-C7 58.124 152.05 37.5 n-C, 16.043 -82.55 45.4 n-C, 28.47 134.222 387.39 butylbenzene 424.39 23.48 hexylbenzene 162.276 190.33 455 20.07 octylbenzene 365.38 19.2671 CIO + cl6 (75% clO) 156.861 388.496 17.6268 clo+ c16 (50% c l o ) 174.762 414.379 15.8732 ClO + cl6 (25% clO) 197.276 24.7258 113.65 294.642 CIO + c7 (40% CIO) 395.293 17.3305 C l o+ C 1 2+ C I 4+ C16(25%) 178.929
nfcPl
From ref 14 for pure bodies and from eq 7 for mixtures. TABLE VIII: Average and Maximum Deviations between Experimental and Calculated Viscosities Obtained with Eq 4 When Values Are Not Extrapolated by Using Eq 1 relation 4 system no. of exptl points av max n-Cl8 16 4.1 9.4 n-C16 20 4.7 12.9 n-C,, 20 4.0 6.5 4 2 20 4.0 10.7 n-C,o 15 8.9 13.6 n-C7 15 5.5 15.9 n-C, 5 14.2 29.2 total 111 5.5 29.2
octylbenzene hexyl benzene butylbenzene total
20 25 20 65
6.4 7.2 13.5 8.9
12.1 13.0 21.3 21.3
CIO +
10 15 5 15 63
10.1 12.0 10.8 5.9 10.9 10.6
15.9 16.6 14.8 10.9 14.2 16.6
239 234
7.8 7.6
29.2 21.3
c 1 6 (75% CIO) C I O+ C16 (50% CIO) CIO + c16 (25% CIO) CIO + c7 (40% C,O) C I O+ c12 c14+ c16(25%) total
total except n-C,
18
deviations for both laws; represents the weight fraction (for n-C7 we have only taken the six experimental points corresponding to P C 500 bars: see Table VI). Figure 6a,b shows typical results. We have also compared the results with the corresponding-state model. To define T , and Pc of the mixture we have used"
OCTADECANE (n-C,)
PIC.)
0 0
I
1
I
500
-
KKX)
Figure 8. Comparison of our results with Kouzel's model in the case of n-octadecane: +, our experimental data. TABLE IX: Average and Maximum Deviations between Experimental and Calculated Viscosities Obtained with Eq 4 When the Values Obtained with Eq 1 are Extrapolated relation 4 system no. of exptl points av max 22 8.5 30.9 n-Cl8 24 4.8 12.9 n-C16 24 4.0 7.2 n-C15 10.7 30 3.6 n-C12 30 7.7 13.6 n-C,o n-C7 65 4.2 19.1 34 10.5 17.1 n-C, 37 12.5 52.2 n-C, 52.2 6.9 total 266
octylbenzene hexylbenzene butylbenzene total
+ cl6 (750/0clO) + c16 (50% clO) CIO + c16 (25% CIO) clo+ c7(40% c l o ) CIO + c12 + cl4 + c16 (25%) total total except n-C, c10
c10
30 30 30 90
8.1 7.9 13.1 9.7
18.9 19.5 21.4 21.4
18 18 18 12 18 84 440 403
7.7 10.6 10.8 7.3 9.2 9.2 7.9 7.5
15.9 16.6 14.8 18.9 14.2 18.9 52.2 30.9
TABLE X: Comparison of the Experimental Data on Alkanes Mixtures with Theoretical Results Given by Eq 5 and 6 (Lobe and Cubic Law with @ Mass Fraction)
no. of exptl points
where x represents the mole fraction. W e have chosen Mmi,=
Lobe av dev Lobe max dev cube root av dev cube root max dev
54 1.6 5.6 2.9 8.0
6 15.6 18.4 18.8 20.1
18 4.2 7.3
J . Phys. Chem. 1986, 90, 1700-1706
1700
f I I
lished (we would have needed to know n-C14properties from 91.5 to 455.3 OC and from 0.35 to 176 bars). As for n-C4, we d o not have to extrapolate so much and thus the representation is mofe satisfactory. Table IX gives for relation 4 an average deviation less than 8% on 440 points.
ICP
DECANE
Conclusions
I
0
500
1000
Figure 9. Comparison of our results with the Lohrentz-Bray-Clark model in the case of n-decane: +, our experimental data.
C x i M , to define the equivalent molecular weight. The values obtained are indicated in Table VII. Tables VI11 and IX indicate that, here again, the agreement is satisfactory when eq 4 is used. Therefore, eq 4, which is obtained from pure alkanes, with n-C14 as reference, seems to work satisfactorily with alkane mixtures. W e have also used the following relations to determine T, and
P,: T, = Cx,T,,, P, = c x , P , ,
(8)
An effect of T,, P, definitions has been noticed concerning the obtained values. From Table 111, relation 4, and eq 8, we have obtained for the 63 experimental points 16.2% average deviation (10.6% with eq 7) and 24.3% maximum deviation (16.6% with eq 7). Finally, we have indicated in Tables VI11 and IX the results obtained for all the points. Table VI11 shows that when the reference values are not extrapolated, the average deviation reaches 7.8% with a maximum deviation of 29.2% (on 239 points). If we extrapolate the reference, Table IX shows that n-C, is the only one with a bad representation, although the n-C, average deviation reaches 12.5% from relation 4 (yet, with a maximum of 52.2%). This comes from the large extrapolation affecting n-Cl4 a t temperatures very far from the ones for which relation 1 was estab-
In this study, we have given values for the viscosity v(P,T)of the alkanes (from n-C,,, to n-C,*),some typical mixtures of alkanes, and three alkylbenzenes within the range of pressures and temperatures usually found in oil fields. This data completes recent works made on the following samples: n-C,, n-C,, n-C12,n-C,,, alkane blends, cyclohexane, and aromatic hydro~arbons.l'-'~ From a phenomenological point of view, the results are very well represented by the empirical relation 1; this relation, however, unfortunately requires 11 constants which have to be determined for each sample. W e have also shown the interest and the limits of a relation based on corresponding states and requiring a reference. The advantage lies in the fact that we just need to know well the properties of the body chosen as a reference, as well as the critical temperatures and pressures of the studied bodies. It is interesting to see that taking the alkane n-C14as a reference gives satisfactory results even if the corresponding states relation is applied to alkylbenzenes. However, reduced temperatures and pressures should be used carefully since it can lead to extrapolations for the reference (for example application of relation 4 to methane). Finally, we have noted that the corresponding-states method applies to mixtures as well, though in this case there are blending laws (Lobe's law and cubic law) which can be as precise. Acknowledgment. We thank the SNEA(P) Co. for its financial support as part of a n Industry/University contract. Registry No. n-C,,, 124-18-5;n-C,,, 112-40-3:n-C,,, 629-59-4;n-C,,, 629-62-9; n-C,,, 544-76-3; n-C,,, 593-45-3: OCBZ, 21 89-60-8: HEBZ, 1077- 16-3; BUBZ, 104-51-8. (17) Dymond, J. H.; Young, K. J.; Isdale, J. D. I n t . J. Thermophys. 1980, l , 345-373.
(18) Dymond, J. H.; Robertson, J.: Isdale, J. D. I n t . J . Thermophys. 1981, 2, 133-154. (19) Kashiwagi, H.: Makita, T. I n t . J. Thermophys. 1982, 3, 289-305.
A Dynamlc Light Scattering Study of the terf -Butyl Alcohol-Water System Thomas M. Bender and R. Pecora* Department of Chemistry, Stanford University, Stanford, California 94305 (Received: August 9, 1985; In Final Form: November 21, 1985)
The hypersonic speed of sound (C,) has been measured in the tert-butyl alcohol-water system (TBA/water) from 0.0 to 0.16 mole fraction of TBA at 10-45 "C by Brillouin scattering. Considerable dispersion in the C, as compared to that found in the zero frequency and ultrasonic range is observed. The isentropic compressibilities in the hypersonic range are also presented for IO, 20, and 25 " C . Photon correlation spectroscopy (PCS) gave no evidence of the presence of oligimers in the system and depolarized interferometry measurements detected no rotational diffusion by species in the system. The acoustic relaxation times calculated at mole fraction of TBA equal to 0.105 were found to be in agreement with literature values of both NMR and dielectric relaxation measurements on this system. The results obtained were interpreted from the viewpoint that the relaxation time observed was due to a structural relaxation.
Introduction The system of terr-butyl alcohol-water (TBA/water) has been the subject of numerous investigations in the past 50 years, In the water-rich region, this system shows a wide variety of seemingly anomalous physical properties. In the 0.05-0.10 mole fraction
of T B A (XTBA) range a t 25 O C the partial molar volume ( Vm) of TBA goes through a minimum while the partial molar heat capacity (Cp,,) of the system goes through a maximum.'-s Is( I ) Nakanishi, K . Bull. Chem. SOC.Jpn. 1960. 33, 793.
0022-3654/86/2090-1700$01.50/0 0 1986 American Chemical Society
