AMERICAS ISSTITUTE 01' MINIS(> AN11 METAI,I,UR(;ICAI, ENGISREIIS Technical Publication No. 1599 (CLASS G, PETROLEUM DIVISION, KO. IYI) DISCUSSION OF THIS PAPER IS INVITED. Discussion in writing (z copies) may be sent to the Secretary. American Institute of Mining and Metallurgical Engineers. 29 West 39th Street. New York. N. Y. Unless special arrangement is made, discussion of this paper will close Sept. jo, 1943. Any discussion r)ffcred thereafter should preferably be in the form of a new paper. Viscosity of Natural Gases.% CORRELATION is presented for predicting th'e viscosities of light paraffin hydrocarbon mixtures such as natural gases for temperatures from o0 to 400 F'. and for pressures from atmospheric to 10,000 lb. per sq. in. The correlation is based on the viscosity data for the methane-propane system and requires only a knowledge of the molecular weight of the natural gas. The viscosities of natural gases reported in the literature up to 2 Ib. were reproduced by the correlation with an average deviation of 5.8 per cent. The viscosity of a natural gas is required whenever calculations are made of the pressure drop that occurs while the gas flows through pipes or porous media. Methods of predicting the viscosities of gases at the present operating pressures are not available. This paper presents a simple method of predicting the viscosity of a natural gas in the single-phase region from its molecular weight, temperature, and pressure. The viscosity of methane, propane, and four of their binary mixtures, 20,40,60, and 80 mol per cent, have been determined for pressures from 400 to 0 lb. per sq. in. and temperatures from 77' to 437'F., with an experimental accuracy of 3.2 per cent.2 The apparatus used in the investigation * University of Michigan. t Associate Professor of!chemical Engineering. University of Michigan. References are at the end of the paper. (New York Meeting. February 194.3) was a modification of that employed in previous studiess,'hn the viscosity of normal parafin hydrocarbons. It consists of a viscosimeter of the rolling-ball, inclined-tube t ~pe,"~,~ with auxiliary equipment for making up and charging binary mixtures into the visco~imeter.~ The viscosity data on the methane-propane mixtures have been plotted as a function of molecular weight with lines of constant pressure, charts of constant temperature in Figs. I to 3. These charts are extrapolated at temperatures below 77OF and at pressures above 0 lb. per sq. inch. At atmospheric pressure the viscosity of light hydrocarbon gases,increased with increased temperature, contrary to the change of viscosity of liquids with temperature. The atmospheric viscosities of the normal paraffin hydrocarbons have been determined by several investigators%~,9,1o,l2,l~.l6,17,19 and are plotted in Fig. 4 as a function of molecular weight, with extrapolation to 896OF. and to 220 molecular weight. Data for isopentane and normal pentane show less than 2 per cent difference in viscosity, indicating that Fig. 4 can be used for isomeric paraffin hydrocarbons with an accuracy of approximately 2 per cent.. Trautz and Sorg17 determined the atmospheric viscosities of methane-propane mixtures and showed that they are proportional to the molecular weight. The viscosities of these mixtures Copyright. 1943, by the American Institute of Mining and Metallurgical Engineers, Inc. TECHNOLOGY. P~~nor.n!rx July 1943. Printed in U. S. A.
2 VISCOSITY OF NATURAL GASES calculatetl from Fig. 4 represent the experi- 3.5 per cent, comparable with their rxperimental data with an average deviation of mental accuracy, for gases containing less 0.44 per cent, as tabulated in Table I, than 7 per cent of nitrogen. For gases conindicating that Fig. 4 can be used for taining higher percentages of nitrogen, FIG. I.-CHART FOR PREDICTING VISCOSITIES OF NATURAL GASES FROM DATA FOR METHANE- PROPANE MIXTURES. obtaining the atmospheric viscosities of light paraffin hydrocarbon mixtures such as natural gases. Berwald and Johnson1 determined the atmospheric viscosities of natural.gases containing various amounts of nitrogen. Their data are represented by Fig. 4 with an average deviation of about a molecular average of the viscosity for nitrogen-free gas as read from Fig. 4 and for pure nitrogen gave satisfactory agreement with the experimental data. Since the viscosity of light paraffin hydrocarbon mixtures is a function of molecular weight at atmospheric pressure,
LEO H. BICHEK, JR. AND DONALD L. KATZ 3 it might be cxpcctctl that the same relation- the experimental accuracy of "approxiship would hold for higher pressures. mately j per cent." reported by Sagc ant1 To test the applicability of Figs. I to 3 Lacey.13 for predicting the viscosities under pres- The two-phase region indicated in Figs. W C U U R WUGM FIG. 2.-CHART FOR PREDICTING VISCOSITIES OF NATURAL GASES FROM DATA FOR METHANE- PROPANE MIXTURES. sure of light hydrocarbon mixtures such as natural gases from the molecular weights or gravities of the gases, a comparison is made between the predicted viscosities and the experimental values reported for natural gases in Table I. The predicted viscosities compare with the reported values with an average deviation of 5.8 per cent. This accuracy is comparable with I to 3 is the two-phase region fo~ the methane-propane system. It is known that the two-phase region is a function of the concentration of the constituents in the gas as well as of the molecular weight. For this reason, and because the physical properties of fluids are known to change rapidly near the critical region, Figs. I to 3 should not be used for predicting the viscosity of a
4 VISCOSITY OF NATURAL G,\SES Gas near its critical region, or at a tempera- Lure and pressure whcrc two phascs exist. The methane-propane data may bc correlated on the basis of molecular weight, the neighborhoocl uf the two-phase region, it tlocs not reproducc the data on natural gases any more closely than the simple molecular-weight plots. MOLECULAR mkiwt FIG. 3.-CHAKT FOR PRXDICTINC VISCOSITIES OF NATURAL CASES FROM DATA FOR METHANII- PROPANE MIXTURliS pseudocritical temperature, and pseudo- EXAMPLE CALCULATION critical press~re.~ The prediction of the For purposes of illustration, the viscosity viscosity of a natural gas by this relationof the lean natural gas reported by Sage ship requires the analysis of the gas from which the pseudocriticals may be computed. and Lacey13 will be calculated from its Although this correlation based on pseudoweight, at 1600F. and 2S00 lb. critical temperature and pressure has per sq. in. In this case, the analysis is givcn advantages for predicting viscosities of but a measured gas gravity (air = 1.0) miscellaneous hydrocarbons, especially in would have been sufficient.
LEO D. BIClfl~,l<, JK..!ND 1)ONALL) L. KATZ 5 'I'ABLE I.-C'otrtparison of Calcl~laled Viscosilies wilh Keporled Values Gases Investigated Mol Per?$: Molec- &ght Temper- :;:* Viscosity. ~{FE: micro poise.^ ~ b per.- Sq. In. Calcd. Exptl. Trautz and Sorgl7 CHI-C~HB mixture CHI-CsHs mixture.. CHI-CaHs mixture.... I Sage and Lacey" Lean natural gas................ 83.19 Rich natural gas............... I Berwald and Johnson1 Natural gas No. 2................. 98.4 69'74 ~ 20.4 zj o 16.2 3d2 464 32 104 248 392 464 32 IOA z46 392 464 100 160 200 160 200 60 14.7 14.7 14 7 1. 2, 1. 2. 1, 2, 1,000 1, 2.000 1,000 1, 2,000 103.2 304.6 499.8 109.8 129.8 139.2 122 163 214 129 161 205 133 160 I92 146 I74 203 144 166 183 108 113 118 109.i 129.0 138.5 I33 180 219 136 172 200 145 174 I92 150 I70 191 146 I57 169 103 103 103 +o.si f 0.62 fo.52 8.3 9.5 2.3 5.2-6.4 + 2.0 8.3-8.1 * 0.0-2.6 f2.4 + 6.3-1.4 +5.7 + 8.3 + 4.9 + 9.7 f14.6 Calculated average molec- pressure and molecular weight could be ular weight = 20.42 plotted as a function of temperature, as a Viscosity at loo0f., 2 Ib. per sq. in. = 214 micropoises means of interpolation. (from Fig. 2) TABLE 2.-The Iriscosily of Nitrogen Viscosity at 2oo F., 2 lb. I - - - per sq. in. = 192 micr~poises Temperature. Deg. F. (from Fig. 2) Pressure. kb' E: o I 60 1 IOO 1 zoo 1 300 khs. - Assuming straight-line interpolation between the temperature plots, the viscosity of the lean natural gas at 160 F. and 2 lb. per sq. in. is 14.7 1,000 2,000 3v000 4,000 6.000 8.000 10,000 156 163 176 203 259 328 Viscosity. Micropoises 172 I79 188 208 257 315 373 433 182 188 196 213 257 308 358 405 206 213 217 229 242 261 299 337 377 227 238 247 256 268 295 323 351 The corresponding experimental value reported by Sage andlacey is 200 micropoises. If the viscosity is changing rapidly with temperature, the viscosities at any given GASES CONTAINING NITROGEN Figs. I, 2 and 3 are based on methanepropane mixtures without the presence of
6 \'ISCOSITY OF NATUKAL GASES
~ -- LEO B. BICHER, JR. AND DONALD L. KATZ 7 nonparaftin hydrocarbons. Although the. 34: ~~i;~~~;pjh;fi";2;2~~bjh'y~.23;935) 6, 71. relationships presented may apply for un- 5. Flowers: p1.06. Amer. SOC. Test. Mat. (1914) 14, 565. saturated the of 6. M. D. Hersey: Jnl. Wash. Acad. Scj. gases containing more than about 5 per (1916) 6, 525-530. cent nitrogen should not be obtained by 7. Hoppler: Chem. Zeit. (1933) 57, No. 7. 62. 8. R. M. Hubbard: Thesis. Univ. of Mich. using Figs. I to 3 directly. Since at atmos- (194.0). pheric pressure the molal average viscosity 9. Y. Ishlda: Ph~s. Rev. (1923) 21, 550-563. : 10. Klemenc and Remi: Monatsh. Chem. (1923) of nitrogen and the nitrogen-free hydro- 441 307. carbon gas reproduces the experimental 11. A. Michels and R. 0. Gibson: Proc. Roy. SOC. (1931) A-134, 288. a procedure gases under 12. A. 0. Rankine and C. J. Smith: Phil. &fag. pressure should be the best approximation (1921) 42, 615-200. now available. Table 2 presents viscosity 13. B. A.I.M.E. H. Sage (1938) and 127,118-133. W. N. Lacey: Trans' values for nitrogen interpolated and extra- 14. A. S. Smith: Thesis, Univ. of Mich. (1940). 15. Titani: Bull. Chem. polated from literature~,~g data at Sot. Japan (1933) 8, 250, 7CC -.,.,- and 75 C for pressures to 10,000 pounds. 16. Trautz and Kurz: Ann. Physik (1931) 9, REFERENCES 081., 17. M. Trautz and K. G. Sorg: Ann. Physik (1931) 10, 81-96. I. W. B. Berwald and T. W. Johnson: U. S. 18. Trautz and Zink: Ann. ~hysik (1~30) [51 7, Bur. Mines Tech. Paper 555. 427. 2. L. B. Bicher, Jr., and D. L. Katz. Ind. 19. H. Vogel: Int. Crit. Tables (1929) 5, 3; and Eng. Chem. (1943) 35. Ann. Physik (1914) 43, 1235.