Surface Tension of Reservoir CrudeOil/Gas Systems Recognizing the Asphalt in the Heavy Fraction

Abstract

Summary. Improvements in predicting surface tensions for crude-oil/gas systems at reservoir conditions has been attributed to new parachors for distillation cuts of crude oil and the recognition that the last fraction or residue of distillation has a parachor not continuous with the distillation cuts. For such reservoir gas/oil systems as condensates, which normally do not contain asphalt materials, the new parachors for the crude cuts would suffice for the surface-tension computation. For a reservoir fluid containing asphaltic substances, the calculation procedure should include a single measurement of the surface tension. Introduction Proper estimation of surface tension for oil/gas systems is important in many reservoir engineering calculations. There is a special need for accurate surface-tension estimates when predicting the performance of fractured reservoirs. In many of these reservoirs. gravity drainage is the most important mechanism for oil recovery. Surface tension is required to predict capillary pressure and hence the ultimate gravity-drainage recovery. The following illustrates the sensitivity of predicted oil recovery resulting from what might seem to be normal variations in surface tension. Consider a fractured reservoir with a typical block height of 10 ft 13.05 mi. For this block, assume a capillary threshold height of 8 ft 12.44 mi. Consider two alternative procedures for predicting surface tensions of 1 and 0.5 dyne/cm 11 and 0.5 mn/ml, respectively. If the capillary threshold height of 8 ft 12.44 mi corresponds to a surface tension of 1 dyne/cm ( 1 mN/m]. the threshold height for 0.5 dyne/cm 10.5 mN/m] would be reduced to 4 ft 11.22 mi. Differences in ultimate drainage recovery performance for the surface tensions of 1 and 0.5 dyne/cm (1 and 0.5 mNm/nil for Bo = 1.25 and Sor, = 0. 15 are about 14 and 41 % of- stock-tank oil content otther block. respectively. A limited number of papers have discussed computational procedures for predicting surface tension for gas/oil systems. The use of these procedures, as is discussed later, leads to large errors in estimating the surface tension of reservoir crude-oil/gas systems. In the following. we review the available correlations and pertinent literature. Macleod and Sugden proposed an empirical relationship between the surface tension and density of pure substances in the form of the following equation: ..........................................(1) where a is the surface tension and P is the parachor. Other parameters arc defined in the Nomenclature. The parachor value is very nearly constant for a substance over a wide range of temperatures. Eq. 1, based on the work of Macleod and Sugden, assumes a relationship between decreasing surface tension and decreasing density difference between liquid and gas phases as one approaches the critical temperature. Macleod and Sugden determined the exponent of 4 in Eq. 1 by examining measured surface tensions of several pure substances. Fowler later derived the value of 4 for the exponent on the basis of statistical mechanics and thermodynamics. Weinaug and Katz extended Eq. 1 to compute mixture gas/ liquid surface tension in the form of ..........................................(2) where PC is the parachor of a substance established from pure component surface-tension measurements with Eq. 1. Weinaug and Katz used Eq. 2 to compare measured and computed surface tension of a C I /C3 system for a wide pressure and temperature range. The agreement between computed and measured values was within the accuracy of experimental data. Hough and Stegemcier later suggested an exponent of 3.66 for Eqs. 1 and 2 to provide a correlation that could better match their measured surface tensions of the C1 /nC5 and C1 /nC10 systems in the critical region. Deam and Maddox compared the measured surface tension of the C1 1C,) binary with computed values from the Weinaug-Katz and HoughStegemeier equations. They concluded that the Weinaug-Katz equation (Eq. 2) generally gives better reproducibility of their surfacetension measurements than the Hough-Stegemeier correlation. Lee and Chien recently presented a surface-tension correlation that is based on scaling theory. They obtained a value of 3.91 for the exponent in Eq. 1 instead of 4, as originally proposed by Macleod. Lee and Chien expressed the parachor in terms of critical properties such as critical volume, critical pressure, and critical temperature. An approach was suggested to obtain first the pseudocritical properties of the mixture. and then use the correspondingstates equation to compute the mixture parachor. A comparison of surface-tension data of C1 1C3 - C1 /C5. and C1 1C9 with the computed values from the Weinaug-Katz and Lee-Chien approaches shows that both methods predict surface-tension values with about the same accuracy. For the C1 1C 10 surface tension comprising four data points, however. the predictions of Lee and Chien are closer to measurements than those of Weinaug and Katz. For reservoir fluid systems. both the Weinaug-Katz and Lee-Chien approaches have had limited verification because of a scarcity of data in the literature. Katz et al. compared the measured surface tension of a reservoir gas/oil system at 115deg.F 146deg. Ci and 2,700 psia [ 18.62 MPa] of 1.1 dyne/cm 11. 1 mN/m] with a computed value of 0.85 dyne/cm 10.85 mN/m] from Eq. 2. Parachor of the C7, fraction of the reservoir fluid system was obtained from a graph showing a linear relationship between the heptane-plus fraction and the molecular weight. Katz et al. 10 prepared this graph by measuring the surface tension for the C7, residue of various crudes. P. 265^