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Correlation of Surface and Interfacial Tension of Light Hydrocarbons in the Critical Region

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Correlation of Surface and Interfacial Tension of Light Hydrocarbons in the Critical Region Correlation of Surface and Interfacial Tension of Light Hydrocarbons in the Critical Region E.W.HOUGH* THE U. OF TEXAS MEMBER AIME AUSTIN. TEX. G. L. STEGEMEIER SHELL DEVELOPMENT CO. JUNIOR MEMBER AIME HOUSTON. TEX. Downloaded from http://onepetro.org/spejournal/article-pdf/1/04/259/2152696/spe-197-pa.pdf by guest on 28 September 2021 ABSTRACT Interfacial tension is defined as the specific Empirical equations for surface tension of propane surface-free energy between two phases of unlike and normal butane as functions of reduced temper­ fractional composition, while surface tension is ature are obtained from experimental data. Another defined as the specific surface-free energy between correlation relating surface tension to enthalpy of two phases of the same fractional composition. The vaporization is given for these two compounds. In usual definitions relating interfacial tension to a addition, new parachor numbers are calculated for liquid-liquid interface and surface tension to a the normal paraffin hydrocarbons. These numbers gas-liquid interface are not clearly defined when are utilized for the calculation of interfacial tension the critical regi~n is included, and there is no sharp of two-component systems as functions of pressure distinction between a gas and a liquid phase. and Jemperature, using a modified form of Weinaug­ Interfacial tension is probably the most important Katz equation. The experimental data for two binary single force that makes one-half to one-third of the systems are approximated by the correlation. From total oil actually in place in a reservoir rock un­ these results it is found that the interfacial tension recoverable by conventional gas-drive or waterflood in the high-pressure region remains extremely low methods. A rough estimate of this figure for the at large pressure decrements below the critical United States is 100 billion bbl. Interfacial tension pressure. Thus, it appears that condensate systems presently is used by petroleum engineers in the may have flow characteristics almost like single­ estimation of saturation gradients at the gas-oil phase conditions even though the pressure is within contact and at the oil-water contact. The data in the two-phase region. this paper should prove useful for estimates of Experimental data have shown that interfacial reserves involving gas-oil contacts. Relative per­ tension divided by density difference approaches meability undoubtedly is influenced by interfacial zero as the critical pressure is approached. A tension, for sufficiently small values. These data calculation of wetting-phase saturations indicates should be useful in determining how small the that the saturation gradient at the two-phase contact values are. In addition, these data should eventually becomes increasingly abrupt as the critical pressure add to our fundamental knowledge of surfaces. At is approached. the critical point, all surface excesses approach zero and the thickness becomes very large. DISCUSSION SINGLE-COMPONENT SYSTEMS Prediction of the surface and interfacial tension l of the light hydrocarbons and of two-component It has been observed that the following relation­ hydrocarbon mixtures at various temperatures and ships are good approximations to the physical pressures may be made i£ other physical properties properties of propane and n-butane. are known. Extensive experimental work on single­ For propane, I'lp = 0.80 (l_TITc )O.326, Y = 49.5 component and binary systems 1 is the basis for (I-TITc )l.20, y/i"J.p = 61.9 (I-TITc )O.874, and the correlations outlined in this paper. y = 112.5 i"J.,,-3.68. For n-butane, i"J.p = 0.86 (1-TIT c)O.333, Y = 52.5 Original manuscript received in Society of Petroleum Engi­ neers office June 12, 1961. Revised manuscript received Sept. (1 ~TITc)1.22, y/i"J.p = 61.0 (I-TITc )O.887 and 29, 1961. Acknowledgment is made with thanks to API Grant­ y = 91.2 1'lp3.66. in-Aid 45, to the Shell Oil Co. for a fellowship which supported 0 .... of us, and to The U. of Texas which purchased much of Guggenheim's2 values for these constants not the equipment used on a special grant. specifically for hydrocarbons, are i"J.p = C,' (1- -Now head of Petroleum Enaineering Dept. at Mississippi State U. TITc)l/3, Y = C"(I-TITc)11/9, y/I'lp = C"'(l­ TITc)8/9, and y = Ci"J.pll/3. lReferences given at end of paper. SPE 197 DECEMBER, 1961 259 Reprinted from the December. 1961. Issue of SOCIETY OF PETROLEUM ENGINEERS JOURNAL The symbols and units are and ethane appear to diverge slightly from this !':!p = difference in density of the liquid pattern. Some of this divergence is probably caused and vapor phases, gm/cc, by the measurement of surface tension against air rather than its own vapor, and by the neglect of the y = surface tension, dynes/em, vapor density. T = absolute temperature, oR or oK, A correlation suggested by Magaril7 relates the Tc critical temperature (absolute), oR = enthalpy of vaporization at constant pressure to the or oK, and surface tension. Tables 2 and 3 and Figs. 2 and 3 C: C'~ C'" = constants. express this relation for propane and for n-butane. The exponents for propane and n-butane are taken The straight-line relationship on log-log paper from log-log plots. The last equation may be recog­ appears to deviate slightly as the critical point is nized as the surface tension-density difference re­ approached. lationship leading to Sugden's parachor,3 with the exponent "3/11" rather than "1/4". That is, TWO-COMPONENT SYSTEMS P = MC3/11 = M y3/11 Prediction of interfacial tension in two-component /1p systems is much more difficult than in the single­ component systems because of the added composition Downloaded from http://onepetro.org/spejournal/article-pdf/1/04/259/2152696/spe-197-pa.pdf by guest on 28 September 2021 where P = parachor, and variable. The correlation suggested by Weinaug and M = molecular weight. Katz 8 has been used with the new exponent and From this modified equation, new values of slightly modified for use with molal volumes rather parachor were calculated for some of the normal than specific gravity. The relation is paraffin hydrocarbons. Surface-tension and density­ difference data for methane, ethane, n-decane and y ={ 6/43 fl (xliV x - yl/Vy ) n-e icosane were taken from Rossini,4 for n-pentane from Sage and LaceyS and from Katz,6 and for pro­ + P2 (x2 /Vx - Y2 IVy ~ pane and n-butane from Sage and Lacey and from r experimental work'! The values are shown in Table where y interfacial tension, dynes/em, 1. Because the parachor is (ideally) independent = of temperature, the values of surface tension and PI "" parachor of the first component, density difference were selected at the temperature P 2 = parachor of the second component, at which the best data were obtainable or at the 1000 temperature at which the vapor density is negligible if this latter data were not available. Fig. 1 shows 900 II a regular increase in the parachor with an increase I in molecular size from 3 to 20 carbon atoms. Methane II 800 TABLE 1 - PARACI:IOR OF NORMAL PARAFFIN HYDROCARBONS V Density Surf. or 700 Carbon Temp. Diff. Intf. Tens. Compound Atoms ~ (gm/cc) (dynes/cm) Parachor V 600 II Methane - 256 0.4218 R 13.7R 77.9 0:: R R o V Ethane 2 - 238 0.620 26.34 118.0 :r: 8 V Propane 3 100 0.443 5.47 158. 1 ~ 500 5.45 K 158 0:: ~ D C~I E n-Butane 4 120 0.5328 9.27 200.5 V~ 9.20 200 400 n-Pentane 5 100 0.603 8 14.0K 246 II ; R R i n-Decane 10 68 0.730 23.92 463 300 I n-Eicosane 20 100 0.7754 R 27.2 R 899 I P~N TIN R=Rossini (Ref. 4); S=Sage and Lacey (Ref. 5); and K=Katz II n (Ref. 6). 200 I .~ R )1 !A.I~E ! TABLE 2 - ENTHALPY OF VAPORIZATION AT H,,~ E CONSTANT PRESSURE - PROPANE 100 VaT T~t N Enthalpy of ~'E Temperature Vaporization* Surface Tension** (0 F) (calorieslgm-mol) (dynes/cm) o 3 5 7 9 (( 13 15 17 19 100 3271 5.48 2 4 6 8 10 12 14 16 18 20 3.66 130 2878 NUMBER OF CARBON ATOMS 2366 1.97 160 IN MOLECULE 190 1660 0.58 *Sage and Lacey (Ref. 5). FIG. I - PARACHOR, NORMAL PARAFFIN **Current paper. HYDROCARBONS. 260 SOCIETY OF PETROLEUM ENGINEERS JOURNAL TABLE 3 - ENTHALPY OF VAPORIZATION AT critical loci is also the line of zero interfacial CONSTANT PRESSURE - NORMAL BUTANE tension; hence, the subsequent iso-interfacial Enthalpy of tension lines must roughly parallel this boundary. Temperature Vaparizatian* Surface Tensian** These data and assumptions allow extrapolation (0 F) (calaries/gm.moll (dynes/em) and interpolation to all points within the two-phase 100 4816 10.49 region. It is evident from these plots that the inter­ 130 4566 8.67 facial tension of a binary mixture in the temperature 160 4266 6.88 range in which the critical pressure is high increases 190 3912 5.14 220 3498 3.48 much more slowly with a decrease in pressure than 250 2980 2.02 either of the pure components. In the case of the 280 2307 0.80 methane-normal pentane system, a pressure drop *Sage and Lacey (Ref. 5). of 450 psi from the critical pressure is required **Current paper. at lOOoF before the interfacial tension reaches 1 dyne/cm. The same increase for the pure components = mol fraction in the liquid phase, Xv X2 occurs with a pressure drop of about 120 psi.
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