PHASE EQUILIBRIA IN
least approximately, the total mixtures coming from the well for a series of gasoil ratios. On the other hand, a study of the properties of a series of such mixtures may be of v a l u e i n c o n n e c t i o n with the general problem of hydrocarbon behavior.
Properties of Samples
HYDROCARBON
SYSTEMS B. H.SAGE:AND W. N. LACEY California Institute of Technology, Pasadena,
XI. Thermodynamic Properties of Mixtures of a Crude Oil and a Natural Gad
M
ANY of the important problems of the
petroleum production kngineer call for a knowledge of the energy relations involved in the processes which he must control as well as a n understanding of the changes in physical condition of the complex mixtures of hydrocarbons which accompany those processes. Upon reaching the surface of the ground, the hydrocarbons flowing from the well are separated, for convenience of handling, into natural gas and crude oil by means of "traps." One possible method of obtaining a representative sample of the mixture produced by a given well is to sample carefully each stream of material leaving this separation system, measure as accurately as feasible the rates of production of these streams, and then reblend the samples in the laboratory in the proportions indicated by the field measurements. In many fields where well-head pressures are high, two sets of traps produce two streams of natural gas a t different pressures and one stream of crude oil. When variations in the conditions of production for a given well occur, it is probable that the relative quantities of gas and oil vary more widely than do the compositions of the oil and gas produced. It is therefore advantageous to blend the samples of the gas streams in proper proportions to give a sample representative of the total natural gas produced. This procedure has the advantage that this gas can then be added to the oil in varying proportions t o reproduce, a t 1 Previous articlea i n thia series appeared during 1934 and 1936, and in January, 1936.
The present paper deals with results obtained from a study of such a set of samples obtained from a well producing from the fifth Callender zone of Dominguez Field in the Los Angeles basin of California. The well was producing a t an average gas-oil ratio of 1400 cubic feet of gas per barrel of oil (both measurements were made at 60" F. and 14.73 pounds per square inch). (Absolute p r e s s u r e s a r e g i v e n t h r o u g h o u t this paper.) The gas was separated from the oil by means of two traps, At the time of sampling, the highpressure trap was maintained a t a presCalif. sure of 82 pounds per square inch and the low-pressure trap, from which the oil sample and the second gas sample were obtained, was operated a t about 10 pounds per square inch absolute. The two gas samples were blended as described, care being taken to prevent loss by condensation or in other ways. The sample of oil was dehydrated to remove approximately 2 mass per cent of water produced with it. The sample of blended gas, the sample of oil, and several mixtures of the two were subjected to a study of their thermodynamic properties over a pressure range from 400 to 3000 pounds per square inch and a t temperatures varying from 70" to 220" F. The properties reported are specific values (per pound of mixture) of volume, heat content, and entropy. A low-temperature fractionation analysis of the blended gas sample showed it to contain, in terms of mole per cent: 1.50 oxygen and nitrogen, 0.60 carbon dioxide, 87.78 methane, 3.82 ethane, 3.36 propane, 0.74 isobutane, 1.26 nbutane, 0.38 isopentane, 0.26 n-pentane, and 0.30 heavier, calculated - as hexane. The physical p r o p e r t i e s of t h e oil sample were Specific volumes and as follows: gravity, specific heats were ex33.9" A. P. I . a t p e r i m e n t a 11y deter60" F.; flash point, below 80" F.; pour mined for several mixpoint, 10" F.; vistures of a crude oil and c o s i t y , 42 s e c o n d s natural gas from DoSaybolt U n i vers a1 minguez Field, Calif. at 100" F.; w a t e r From these data were a n d s e d i m e n t by c e n t r i f u g e , 0.1 per calculated the values of cent by volume. A the therm o d y n a m i c sample of this oil was properties, heat con fractionally distilled, t e n t , and entropy. using a r e c t i f y i n g Illustrative diagrams c o l u m n containing twelve p e r f o r a t e d indicate some features plates, separate conof the behavior of such secutive o v e r h e a d mixtures with changes fractions of 5 volume of temperature and per cent being colpressure. lected. For each of
-
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250 AVERAGE BOILING POINT
Methods and Apparatus
DEG. F
DEG.
AVERAGE BOILING POINT
FIGURE1. RESULTS FROM ANALYTICAL DISTILLATION OF CRUDEOIL
The methods and apparatus used for this work were described previously (4,5,8). The specific volumes for a series of compositions were measured as functions of pressure and temperature by changing isothermally the pressure on each sample in a steel cell by addition or withdrawal of mercury. This process was repeated for each composition at each of a series of temperatures. The attainment of equilibrium was assured by a mechanical agitator within the equilibrium chamber and was verified by the agreement of pressure readings for a given specific volume, when approached from a higher and a lower pressure. The temperature was maintained within 0.1’ F. of the desired value (recent addition of an improved thermostat has made this more feasible), the pressure was measured to 1 pound per square inch, and the volume measurements were correct to 0.1 per cent of the reading. The specific heats of the oil, the gas, and a series of their mixtures were determined over the entire temperature range. A constant-volume calorimeter (5) was used for the oil and its mixtures with the gas, and an adiabatic expansion method (6) was utilized for the determination of the specific heat a t constant pressure of the gas at 1 atmosphere pressure. It is believed that the results for the crude oil alone are accurate within 1 per cent, and that those for the gas and for mixtures up to 15 mass per cent of gas are accurate within 2 per cent. The viscosity of the saturated liquid solutions of these same samples of gas and oil for the same temperature and pressure ranges have been previously reported (6).
Thermodynamic Properties Since over one thousand equilibrium measurements were recorded, space does not permit a complete report. A portion of these experimental points is shown in Figure 2, illustrating the isothermal variation in specific volume with pressure for one of the mixtures-namely, that containing 5.61 mass per cent of gas. I n Figure 2 only those experimental points lying in the condensed region and those immediately below the bubble-point pressure are shown, although the measurements were carried down to a minimum pressure limit of 400 pounds per square inch.
I
I
1250
I
1500
1
1750
PRESSURE
I
2000 LBS.
I
2250 PER
I
2500
I 2750
Sa IN.
FIGURB2. SPECIFIC VOLUMES NEAR BUBBLEPOINT FOR MIXTURECONTAINING 6.61 MASSPER CENT OF GAS
A
these fractions there were made determinations of specific 4 gravity,a absolute viscosity, and molecular weight, and an Engler distillation was also carried out. Some results of this analysis are given in Table I. To aid in visualizing the results, the specific gravity, absolute viscosity, average molecular weight, and cumulative mass fraction distilled were plotted in Figure 1 as functions of the average boiling points of the fractions as determined by the results of the Engler distillations. 2 The term “sueoifio aravitv” - i s here wed to denote the ratio of the weight of a given volume of the material at speoified temperature and pressure to the weight of the same volume of water at its maximum density for atmospheric pressure.
/
TEMPERATURE
DEG.
F.
FIGURE3. SPECIFIC HEATSAT CONSTANT PRESSURE OF NATURAL GAS AND OF CRUDEOIL
FEBRUARY, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
251
&
d
DISTILLATION OF DOMINGUEZ CRUDEOIL TABLEI. ANALYTICAL Gr. of Still Vapor --Distn. RecoveryFraction C. A. S. T. M. Engler Distn. Temp. Temp. Fraction Total at 60' F. Initial 10% 60% 90% Max. A. B. P. Type of Engler Distn. ' F. Per cent by 002. A . P.I . F. O F. O F. O F. 'F . F. 1 5.16 161 214 Natural gasoline 196 6.16 72.0 217 5.05 60.3 2 10.21 198 246 Gasoline 238 5.11 66.2 15.32 218 258 3 Gasoline 6.11 4 267 53.3 20.43 246 281 Gasoline 298 5.13 60.7 25.66 278 Gasoline 5 3 10 5.05 326 48.0 30.61 Gasoline 333 6 308 364 6.06 45.3 36.66 7 342 Gasoline 361 5.08 8 406 42.6 40.74 384 Gasol/ne 402 444 6.02 46.76 9 40.6 428 443 Gasoline 479 6.02 38.0 60.78 466 482 10 Kerosene 350a 66.94 11 6.16 36.1 518 662 Kerosene 12 369a 5.27 33.6 61.21 548 680 Kerosene 504a 13 28.3 71.59 10.38 641 686 Gas oil Residue in still: 28.41% by vol. of the crude charged; gravity, 13.90° A. P. I. at 60' F.; viscosity, 532 aec. Saybolt Universal at 210° F.
Fraotion No.
Absolute pressure of 50 inm.; all other fractions distilled at approximately 760 mm. i
The upper curve of Figure 3 shows the change of specific heat at a constant pressure of 1 atmosphere for the natural gas as a function of temperature. The points marked with squares were calculated from data taken from several sources, (1, 2, 3, 6 ) on the assumption that the specific heats of the individual components of the gas were additive to give the specific heat of the mixture. The two sets of points are in agreement within the limits of error of either set. The lower curve of Figure 3 is for the crude oil, showing the specific heat at constant pressure for the condensed liquid; for each point of the curve the process is started at a pressure infinitesimally higher than bubble point and is ended a t the same pressure but with the liquid a t bubble-point condition. The pressure will, however, vary from point to point along the curve. By the methods previously described (8), specific values (per pound of material) were calculated for the heat content and the entropy of each mixture studied below 18.75 mass per cent of gas a t various temperatures and pressures within the experimental range. Values for mixtures of higher percentage of gas could not be calculated because of lack of specific heat data. The calorimeter bomb in use could not be subjected safely to the pressures necessary in using a sufficient mass of these mixtures with high gas content. The results of these calculations, together with corresponding specific volume values, are given in Tables I1 and 111. In the
I 75
100
,
125
TEMPER AT U R E
I 150
175
BUBBLE
POINT
PRESSURE
POUNDS
PER S B
IN.
FIGURE 6. VARIATION OF BUBBLE-POINT PRESSURE WITH TEMPERATURE FOX MIXTURES OF DIFFERENT COMPORITION
I 200
DEG. F.
FIQURE4. CHANGE OF SPECIFIC VOLUME WITH TEMPERATURE FOR A MIXTURE CONTAININQ 5.61 MASSPER CENTOF GAS
BUBBLE
POINT
PRESSURE
L B S . PER Sa. IN.
FIGURB6. ISOTHERMAL CHANGESOF BUBBLE-POINT PRESSURE WITH VARIATION IN COMPOSITION OF MIXTUREB
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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FEBRUARY, 1936
case of each composition, both the heat content and the entropy were arbitrarily taken as zero for 60" F. a n d a p r e s s u r e of 3000 p o u n d s p e r square inch. This choice of datum results in a few n e g a t i v e v a l u e s of h e a t content. The values for heat content and entropy are given to one more figure than is warranted by the specific heat data, in order to show t h e i s o t h e r m a l changes with suitable a c c u r a c y . Table I11 gives the comp o s i t i o n s a n d specific v o l u m e s of bubble-point liquids for various combinat i o n s of temperature and pressure. Several illustrative graphs have been prepared from the data of Tables I1 andIII. Figure 4 shows a series of constant-pressure lines indicating the changes of specific v o l u m e w i t h change of temperature for a constant compositionwith 5.61 mass per cent of gas. The linear v a r i a t i o n of specific volume f o u n d i n t h e t w o - p h a s e region of Figure 4 was found to hold within experimental error throughout the p r e s s u r e , temperature, and composition range investigated except for the mixture containing 10.94 mass per cent of gas near its bubble point. Such curvature, indicating c h a n g e with temperature of the thermal e x p a n s i o n coefficient, is not surprising because nearness to critical state is becoming evident. The constancy of thermal expansion for a given pressure throughout most of the two-phase region furnishes a welcome simplification of behavior. T h e above mentioned approach to critical region is also indicated in Figure 5 by the rapid r i s e i n solubility with increase of equilibrium pressure a t the h i g h e r pressures, and in Figure 6 by the small change in bubblepoint pressure with change in temperature a t the higher temperatures. T h e c h a n g e in specific gravity of b u b b l e - p o i n t l i q u i d w i t h increasing
1000
500
1500
2500
2000
LBS
PRESSURE
PER
S Q
IN
OF RUBBLE-POINT LIQUIDS FIGURE7. SPECIFICGRAVITY
equilibrium pressure is shown for a series of temperatures in Figure 7. The rapid decrease in specific gravity a t the highest pressures shown is due to the rapid increase in solubility of the gas in this region. As will be noted in Figure 5, this rapid increase in solubility becomes apparent a t lower pressures for the lower temperatures and thus causes the crossing of the curves in Figure 7. In this higher pressure region, for a given equilibrium pressure the bubble-point liquid corresponding to a higher temperature may have a higher specific gravity than that for a lower temperature. The inversion of curvature of the lines in Figure 7 is due to the shift in the balance between two different effects having opposite influence upon the specific gravity of the bubblepoint liquid. The increase of solubility with pressure (Figure 5) tends to lower the specific gravity while the increased compressibility of the resulting solution tends to cause an increased specific gravity. Figure 8 shows the effect of changes in composition upon
W
I
2.5 MASS
I
5.0
I
I
7.5
PERCENT
10.0 OF
I
12.5
GAS
VOLUME OF MIXTURES AS FIQURE 8. SPECIFIC TION OF COMPOSITION AT 160" F.
A
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AND SPECIFIC VOLUMES OF BUBBLE-POINT LIQUID MIXTURESOF NATURAL GAS AND CRUDEOIL TABLE111. COMPOSITIONS
Abs. -70.0' Pressure Compn. Lb./8q. in. 1.42 2.14 2.87 3.68 4.61 5.62
F . Vol.
--
(Compositions expressed a8 mass per cent gas, specific volumes as cubic feet per pound) 7 100.Oo F . 7 ~ 1 3 0 ..F 0 ~ ----160.0° F.---190.0° F . Compn. Vol. Compn Vol. Compn. Vol. Compn. Vol.
7 -220.O0
Compn.
F.Vol.
6.66 7.96 9.47 11.24 13.27
aoc
0.9c
I-
ae:
0.8(
0.7:
the specific volume of the material a t various pressures but a t the one temperature of 160' F. The same sort of inversion in curvature of the bubble-point liquid curve as was shown in Figure 7 appears here. The nearly straight lines shown in the two-phase region of Figure 8 were found to be characteristic of a large portion of the region beyond that shown in Figure 8. The compressibility of the sample of natural gas is shown in Figure 9 for a series of temperatures. These curves indicate, i t is believed, that the gas is above its cricondentherm (critical condensation temperature) at the lowest temperature here investigated. The thermodynamic behavior of this gas is summarized in the temperature-entropy chart shown in Figure 10. The shape of the lines of constant heat content at the higher pressures and temperatures indicates approach to the condition a t which inversion of the Joule-Thomson coefficient of the gas occurs. The thermodynamic data for the mixtures of crude oil and natural gas cannot be satisfactorily presented with ordinary scale on the temperature-entropv plane, the temperature-heat content plane, br the heat content-entropy piane. Thk is &
PRESSURE
LBS
P E R SQ IN.
FACTOR OF THE NATURAL GAS RQURE 9. COMPRESSIBILITY
"
ENTROPY BTU. PER DEG. F. P E R POUND DIAQRAM FOR THE NATTJRAL GAS FIGURE 10. TEMPERATTJRE-ENTROPY
FEBRUARY, 1936
i
I
2.5
INDUSTRIAL AND ENGINEERING CHEMISTRY
I 10 MASS
I
1 10.0
z5 PERCENT
I 12.5
I
255
I
I
I
I
I
25
5.0
75
la0
126
OF G A S
MASS
FIQURIQ11. INTERPOLATION CHARTFOR ENTROPY OF MIXTURESAT 160" F.
due to the fact that the isothermal changes in entropy and in heat content are small compared to those occurring with change of temperature. This results in long narrow diagrams. The small isothermal changes in heat content in the twophase region result from rather flat maxima in the values of this function. The temperature-entropy chart for the crude oil alone was found to be entirely similar to that for another crude oil presented in a previous paper of this series ( 7 ) . Although it was not feasible to present here thermodynamic charts of the types mentioned above, all the necessary data for their construction are contained in Tables I1and 111. Since the values of entropy and heat content given are only relative values based upon an arbitrary datum state a t 60" F. and 3000 pounds per square inch for each separate composition, the values for different compositions are not directly related and cannot be so related or brought to h comparable basis without a knowledge of the heats of solution involved in the changes of composition. Even though the values of entropy and heat content are not calculated upon a common basis, nevertheless variations in these values are systematic and it is feasible to use graphs of these values against composition for interpolation to obtain corresponding values for
PERCENT
OF
I
GAS
FIQURE12. INTERPOLATION CHART' FOR HEATCONTENT OF MIXTURESAT 160' F.
compositions between those studied experimentally. Figure 11 shows such a graph for interpolation of entropy values a t 160" F., and Figure 12 is the corresponding graph for heat content values. These figures give no direct indication of actual changes of entropy and heat content with composition. Figure 13 presents Joule-Thomson coefficients for the gas, the crude oil, and three mixtures. These values were calculated from the thermodynamic data. An inversion or change of sign of the coefficient occurs in the two-phase region, The discontinuities shown in the curves for the mixtures occur at the bubble points and indicate a sudden change in the slope of the lines for constant heat content-constant total composition upon crossing the bubble-point curve on a temperature-pressure plane. Thus a given mixture of the crude oil and the natural gas may either fall or rise in temperature upon throttling, depending upon the pressure range in which the process occurs.
Acknowledgment Financial assistance for this work was given by the American Petroleum Institute. The Union Oil Company of California cooperated by furnishing the samples used and the analyses of them, except the determinations of molecular weights. The assistance of Howard Pyle, of that company, is particularly acknowledged. J. E. Sherborne and H. S. Backus carried out many of the laboratory determinations reported.
Literature Cited (1) Eucken, A.,and Lude, K., von, 2.phya. Chem., B5,413 (1929). (2) Eucken, A.,and Parts, A., Ibid.,B20,184 (1933). (3) International Critical Tables, Vol. V, p. 81,New York, McGrawHill Book Co., 1929. (4) Sage, B.H., and Laoey, W. N., IND.ENG.CHEM.,26,103 (1934). and Lacey, W. N., Ibid.,27,1484(1935). (5) Sage, B.H., (6) Sage, B.H., and Lacey, W. N., Oil Weeklv, 77, No. 10,29 (1935); Oil Gas J.,34, No. 1, 16 (1935). (7) Sage, B. H.,Lacey, W. N., and Schaafsma, J. G., IND. ENG. CHEM.,27,162 (1935). (8) Sage, B. E., Sohaafsma, J. G., and Lacey, W. N., Ibid., 26, 1218 (1934). RIWBIVIPD July 8, 1985.
~
500
1000 PRESSURE
I
1500 LBS PER
i
I
2000
2500
SQ IN
FIGURE13. JOULE-THOMSON COEFFICIENTS AT 160" F.
