Effect of Pressure on Viscositv of rzrButane and Isobutane J
B. H. SAGE, W.D.YALE, AKD W.N. LACEY California Institute of Technology, Pasadena, Calif.
The prediction of the viscosity of multicomponent hydrocarbon gases under the conditions that are encountered in the production, refining, and transportation of petroleum is of importance to the petroleum technologist. Information concerning the viscosity of each of the components of such gases is necessary before it will be possible to prepare a satisfactory correlation of these viscosities as a function of the prevailing pressure, temperature, and composition of
the fluid in question. In the present investigation the viscosity of n-butane and isobutane was measured throughout the gaseous region at temperatures from 100' to 220' F. The viscosity of these hydrocarbons of the liquid phase was also determined throughout this temperature interval from vapor pressure up to 2,000 pounds per square inch. These data are recorded in tabular form and several diagrams illustrating the behavior are included.
T
value of 74.4 micropoises a t 68" F., which is in good agreement with the measurement of Ishida a t 73.4" F. The effect of pressure upon the viscosity of hydrocarbon gases has not been extensively investigated. Day (8) d e termined the viscosity of n-pentane and isopentane gas at pressures from 2 pounds per square inch to vapor pressure a t 77" F. The effect of pressure upon the viscosity of methane and two natural gases was measured (14) a t temperatures from 100" to 220" F. for pressures up to 2,500 pounds per square inch. The viscosity of propane (13) was studied throughout the gas and liquid regions a t pressures up to -2,000 pounds per square inch for temperatures between 100 and 220 " F. These data included information upon the viscosity in the vicinity of the critical state.
HE viscosity1 of n-butane gas a t atmospheric pressure was measured by Titani (18) who reported a value of 68.9 micropoises a t 32" F. In a later investigation Titani (19) obtained a value of 73.9 micropoises at 68" F. for the viscosity of this hydrocarbon. Kuenen and Visser (8) measured the viscosity of a sample of n-butane, which contained approximately 1 per cent ethane, a t several temperatures. These measurements by Kuenen and Visser indicated a higher viscosity (14 per cent) than was obtained by Titani. Because of the impurities in Kuenen's sample and the possibly better technique employed by Titani, the latter's values 'for n-butane gas were used in connection with the comparisons prew sented in this paper. ?! The viscosity of iso2 butane gas was deter8 mined a t atmospheric 125 pressure by Ishide (6) , who employed the rotating cylinder method in this work. He obtained o 100 a value of 75.5 micropoises for the viscosity > of i s o b u t a n e gas a t 73.4" F. Titani (19) 3 75 measured the viscosity of SIm this gas and reported a 1 All viscosities reported in this paper ar0 absolute viscosities unless otherwise indicated. These values are given in terms of the poise which is a c. g. 8 . unit. This is inconsistent with the units of pressure but was employed because of the frequent use of the poise in engineering literature. All pressures reported are absolute and are expressed in pounds per square inoh.
O
Method 150
125
100
100
50
100
PRESSURE
I50
200
LB PER S Q IN
FIGURE 1. VISCOSITY OF GASEOUS B-BUTANE 223
The apparatus employed in this investigation was recently described ( 1 3 , 1 4 ) . I n principle the method consists in measuring the time necessary for a closely fitting steel ball to roll through a fixed distance in a closed inclined cylindrica1 tube. In the range of conditions where the flow of the fluid passing the ball is laminar, the time of roll is directly proportional to the absolute viscosity of the fluid when a
INDUSTRIAL AND E N G I K E E R I N G CHEMISTRY
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VOL. 31, NO. 2
urements of Nasini and Pastonesi (10) for air indicated a somewhat larger dependence (6 per cent) of the calibration of the instrument upon the flow conditions. Because of the excellent agreement of the measurements by Stakelbeck (16) and Phillips (11) for the viscosity of carbon dioxide a t elevated pressures, this material was employed to establish this part of the calibration of the instrument. Although the precision of measurement was as good here as in the laminar region, it is believed that the use of the Reynolds criterion as a quantitative measure of the type of flow existing within the instrument may have introduced an added uncertainty. For this reason it is estimated that the gas viscosities may be in error, by as much as 5 per cent. On the other hand, the viscosity of the liquids was measured under such conditions that the probable uncertainty was not greater than 3 per cent.
Materials The n-butane used in this investigation 50
100 PRESSURE
150 200 LB PER SQ IN
was obtained from the Phillips Petroleum
250
Company. Their special analysis indicated that it contained 99.7 mole per cent nbutane and 0.3 mole per cent isobutane; it was not further purified. The isobutane was obtained from the same source and contained less than 0.03 mole per cent impurities. The n-pentane used in the calibration of the instrument contained 99.3 mole per cent n-pentane and 0.7 mole per cent isopentane. The hydrogen was obtained from the electrolysis of dilute sulfuric acid and was purified by passing it through granular sodium hydroxide and magnesium perchlorate in order to remove entrained acid and water. The carbon dioxide was a commercial product which was purified by successive sublimations and partial solid&cations a t liquid air temperatures. As an indication of its purity, the vapor pressure was measured at 32" F. and found to be 505.4 pounds per square inch, which compared favorably with a value of 505.55 pounds per square
FIGURE2. VISCOSITY OF GASEOUS ISOBUTAXE
.
correction has been made for the buoyant effect of the fluid. Flowers (6) proposed this type of instrument for the measurement of the viscosity of liquids. For this purpose it is satisfactory since the flow conditions around the ball do not change in character during the course of a given set of measurements. However, in the case of gases there is approximately a hundred fold change in the Reynolds number within the instrument due to an increase in pressure from atmospheric to 3,000 pounds per square inch for a gas such as nitrogen. Under these conditions large discrepancies from the linear relation between the time of roll and the absolute viscosity are encountered which necessitate the calibration (19)of the instrument as a function of the flow conditions existing within the instrument. Within the laminar range, which included only the measurements in a part of the liquid region, there is a single-valued functional relation between the time of roll and the absolute viscosity. The calibration of the instrument in this region for the lower viscosities was established from known values of the viscosities of air (7), hydrogen (WI), and carbon dioxide (11) at atmospheric pressure. At the higher viscosities, liquid n-pentane (17, 20) was employed in the calibration of the instrument. The consist.ent nature of the calibration curve, as established by these materials, indicated that the uncertainty of measurement in the laminar region was not more than 2 per cent. The calibration ( I S ) of the instrument in the turbulent regime was established by measurements upon gases whose viscosities were known at elevated pressures. Carbon 75 IO0 I25 I50 175 ,200 dioxide (11,16),nitrogen (I,@, and air ( I O ) TEMPERATURE F were employed for this purpose. The agreemerit Of ;he data for air and carbon dioxide FIGURE3. EFFECTOF TEMPERATURE UPON THE VISCOSITY O F GASEOUS ISOBUTANE was satisfactory (2 per ,cent), but the measij
INDUSTRIAL AND ENGINEERING CHEMISTRY
FEBRUARY, 1939
inch reported by Bridgeman (2). I n addition, it was found that a twofold change in volume caused a change in vapor pressure of only 0.15 pound per square inch. The nitrogen was a commercial product, and density measurements indicated that it did not contain more than 1per cent impurity. w The air employed in connection with the calibration of the f? 0 instrument was taken from the atmosphere of the laboratory. 0 a It was passed over ascarite and magnesium perchlorate at elevated pressures in order to remove carbon dioxide and iI, water.
225
I600
1400
>
k
v, 0 0
Results
'
The experimental measurements obtained for n-butane > gas are presented in Figure 1. The dual ordinate scale was w employed in order to keep the curves separated sufficiently for t clearness. The volumetric data required for the interpre- 3 tation of the experimental measurements mere taken from a % m study of the thermodynamic behavior of n-butane (16). The a measurements of Titani (18, 19) at atmospheric pressure are in satisfactory agreement with these data. Extrapolation of the present measurements to the temperatures at which Titani's data were obtained (32" and 68" F.) indicates a discrepancy of approximately 1 per cent between the two sets of measurements. In general, the effect of temperature upon the viscosity of n-butane gas a t atmospheric pressure was found to be approximately the same from the two sets of measurements. The data of Kuenen and Viaser (8) were approximately 14 per cent higher than the r~aluesof Titani. Discrepancies of this magnitude between the different investigations may be an indication of the difficulty encountered in the accurate experimental evaluation of the viscosity of gaseous hydrocarbons of relatively high molecular weight. Day (3) experienced difficulty in determining the viscosity of n-pentane and isopentane gas by the rotating cylinder method, which was more suitable for this purpose than the rolling ball viscometer employed in the present investigation. Figure 1 indicates that there is an increase in the isothermal viscosity-pressure coefficient as the vapor pressure is
TABLEr. ABSOLUTEVISCOSITY OF GASEOUSAND LIQUID BUTANES Abs. Pressure 100e F. L~I./~ in.Q .
Abs. Visoosity, Micropoises 130° F. 160' F. 190° F.
220° F.
n-Butane Satd.gas Satd. liquid 14.7 20 40 60
100 150 200 400 600 1000 1500 2000 Satd. gas Satd. liquid 14.7 20
40 60 100 150
83.8 1470 78.4 78.7 82.1
..
103 1024 86.9 87.4 89.1 91.7 98.3
1248 1272 1295 1332 1370 1398
1034
..
1058 1081 1120 1165 1190
84.1 1320 76.5 77.5 79.2 82.1
Isobutane 103.8 91.3 1058 890 79.5 82.6 80.2 83.1 81.8 85.2 84.2 87.3 89.8 92.5
1344
ioii
13f6 1404 1456 1506 1554
1102 1132 1186 1252 1297
..
z5u
400 600 1000 1500 2000
93.7 1232 82.6 83.1 85.3 88.2
101 896
I
928 956
'*loll
1065 1106
121 834 91.0 91.4 93.3 95.8 101 112 836 862 887 930 979 1009 134.4 753 85.7 86.6 88.7 91.1 95.7 103 117 7% 81 1 862 913 954
148
...
94.7 95.3 97.5 99.8 104 113 125
.. ..
... .
..
.. .. 88.7 89.8 92.1 94.2 99.4
106
114 131
.. .. .. ..
..
1200
IOOC
400
800
I 400 800 PRESSURE
1600
I200
I
I
I200 LB PER S Q
1600
IN
F I G ~4. E VISCOSITY OF LIQUIDBUTANE (above) AND LIQUID ISOBUTANE (below)
approached. The data indicate a minimum in the isobaric viscosity-temperature relation a t the higher temperatures which is in accord with the predictions of Ewell (4) concerning the pressure and temperature coefficients of viscosity. It was necessary to extrapolate the experimental data to vapor pressure in order to establish the viscositv of the saturated gas. In general, this extrapolation was short, and it is believed that no uncertainties greater than those involved in the experimental work resulted from this procedure. The values have not been extended to pressures much below atmospheric since there is some doubt as to the value of the viscosity-pressure coefficient at infinite attenuation. A similar diagram for isobutane is presented in Figure 2. I n this instance the values at atmospheric pressure indicate a slightly lower viscosity (1 per cent) for this gas than would be predicted from the measurements of Titani (19) and of Ishida (6). I n general, the viscosity-pressure coefficient of
INDUSTRIAL AND ENGINEERING CHEMISTRY
226
isobutane is smaller than that for n-butane except at the highest pressures and temperatures encountered in this investigation, where the reverse is true. This type of behavior is due primarily to the proximity of the critical state of isobutane under these conditions. This results in large values of the viscosity coefficients of both pressure and temperature,
VOL. 31, NO. 2
Table I and the volumetric data relating to n-butane which are available in the literature (16). Curves for the lower pressures are not included because of the rapid increase in the kinematic viscosity with a decrease in pressure. Behavior analogous to that indicated in Figure 5 was found for isobutane. The data reported in this paper for the viscosity of n-butane and isobutane gases are not of high accuracy, owing to the inherent limitations of the rolling ball viscometer when used for the measurement of the viscosity of gases a t elevated pressures. It is believed, however, that they are of sufficient engineering value to justify their use until such a time as more accurate information is available. The measurements upon the viscosity of the liquid phases of these hydrocarbons are more dependable and their accuracy should suffice for most engineering purposes.
Aclmowledgment This work was done as a part of a general program of research being conducted by Research Project 37 of the American Petroleum Institute. The financial assistance and cooperation of this institute made i t possible. The assistance of Mrs. R. L. Prescott id connection with the preparation of the experimental results is acknowledged.
Literature Cited (1) Boyd, Phys. Rev., 35, No. 2, 1284 (1930). I
IO0
I25
150
TEMPERATURE
I75
200
F'
FIQURE 5. KINEMATICVISCOSITY
OF
n-BUTANE
since both of these are infinite a t the critical state. The effect of temperature upon the viscosity of isobutane is indicated in Figure 3. The measurements of Titani and Ishida at atmospheric pressure are included. Figure 4 depicts the experimental findings for liquid n-butane and isobutane. The volumetric data required for the interpretation of the experimental results were obtained from the investigations ( l a , 16) relating to the thermodynamic behavior of these hydrocarbons. Figure 4 indicates a progressive increase in the isothermal viscosity-pressure coefficient with an increase in temperature which is again in accord with the predictions of Ewell (4). The behavior indicated in this figure for n-butane and isobutane is analogous to that found for propane (19). The experimental results for liquid and gaseous n-butane and isobutane were interpolated graphically to even values of temperature and pressure and are recorded in Table I. It is believed that these tabulated values do not involve uncertainties greater than 5 per cent in the gaseous region and 2.5 per cent in the condensed liquid region. For many purposes it is desirable to employ the kinematic viscosity-i. e., the ratio of the absolute viscosity to the density-instead of the absol employ p consistent set of matic viscosity. In the pressed in grams per cubic centdeter in order that it may be consistent with the absolute sity, expressed in micropoises. Both of these quantit involve the fundamental units of mass, length, and time, and are inconsistent with the unit of pressure used here, which involves force, length, and time.) Figure 5 presents the kinematic viscosity of liquid and gaseous n-butane as a function of temperature. These values are based upon the absolute viscosities recorded in
(2) Bridgeman, S. Am. Chem. Soc., 49, 1174 (1927). (3) Day, Phys. Rev., 40,281 (1932). (4) Ewell, J . Chem. Phys., 5, 571 (1937). (5) Flowers, Proc. Am. SOC.Testing MateriaEs, 14,565 (1914). (6) Ishida, Phys. Rev., 21, 550 (1923). (7) Kellstrom, PhiZ. Mag., 171 23,313 (1937). (8) Kuenen and Visser, VersEag K. Akad. Wetenschappen,22, 336 (1913). (9) Michels and Gibson, Proc. Roy. SOC. (London), A134, 288 (1931). (10) Nasini and Pastonesi, Cazz. chim. {tal., 63,821 (1933). (11) Phillips, Proc. Roy. SOC.(London), A87, 48 (1912). (12) Sage and Lacey, IND. ENQ.CEEM.,30, 673 (1938). (13)Ibid., 30, 829 (1938). (14) Sage and Lacey, TTans. Am. Inst. Mining Met. Engra. (Pet. Div.), 127, 118 (1938). (15) Sage, Webster, and Lacey, IND. ENQ.CHEM.,29, 1188 (1937) (16) Stakelbeck, 2. ges. Kalte-Ind., 40,33 (1933). (17) Thorpe and Roger, Trans. Roy. SOC.(London), A185,397(1895). (18) Titani, Bull. Inst. Phys. Chem. Research (Tokyo), 8 , 433 (1929). (19) Ibid., 9,98 (1930). (20) Tousa and Staab, Petroleum Z., 26, 1117 (1930). (21) Yen, Phil. Mag., 151 38, 582 (1919). RECE~IVED July 2 5 , 1938.
