Znd. Eng. Chem. Res. 1996,34, 640-655
640
Phase Equilibrium Calculations on an Indonesian Crude Oil Using Detailed NMR Analysis or a Predictive Method To Assess the Properties of the Heavy Fractions Jean-NoEl Jaubert,* Evelyne Neau, and Andre Pdneloux Laboratoire de Chimie Physique, Facult6 des Sciences de Luminy, 163,Avenue de Luminy, 13288 Marseille Cedex 9, France
Catherine Fressigne and Alain Fuchs Laboratoire de Chimie Physique des Matkriaux Amorphes, Universitk Paris-Sud, 91405 Orsay, France
A separation into aromatic and nonaromatic molecules was performed on a n Indonesian oil mixture with each cut from CS to C45. Each fraction was carefully analyzed using the NMR technique. NMR is not precise enough, however, to exactly determine the group composition of each fraction. Structural hypotheses were therefore developed to improve the efficiency of NMR as a n analytical method for use with petroleum fluids. Thanks to group contribution methods developed for this purpose, it has become possible to solve an equation of state and to predict the changes in the relative volume vs the pressure. These results are compared with those obtained using the predictive method recently developed by Neau, Jaubert, and Rogalski. There appears to be little or no advantage to be gained from performing the lengthy, difficult, and expensive NMR analysis.
Introduction The composition of petroleum reservoir fluids has usually been analyzed up t o Cll+ or C20+. To be able to perform phase equilibrium calculations (PVT calculations) on mixtures of this kind, it is necessary to estimate the physical properties (the critical parameters, the acentric factor, the Rackett compressibility factor) of the plus fraction with a view to solving the equation of state. It has recently been established (Neau et al., 1993) that the plus fraction can easily be represented by two or three molecules. Moreover, when the distillation is performed up to C20+, it is possible to group the cuts from C11 to C19 into a pseudocomponent called “C11-C1g”, which can be described with only three molecules. In this study, a true boiling point distillation was performed up to C45+. Thirty fractions were collected, and each of them was separated into “aromatic” (A) and “paraffin and naphthene” (P N) molecules. The 60 samples obtained (30 A and 30 (P N)) were analyzed by NMR in order to determine as precisely as possible their group composition, that is, the number of CH3, CH2, or CH in each sample. Using an equation of state with parameters established in terms of functional group composition, it is then possible to perform flash calculations and to predict the changes in the relative volume vs pressure. In this study, we investigated whether the PVT calculations could be improved using this detailed analysis in comparison with the predictive method previously described by Neau et al. (1993).
+
+
Experimental Data The molar composition of a reservoir fluid was determined from the compositional analysis of the gas and liquid phases in the separator (Figure 1). The composition of the liquid phase in the separator was determined from the gas and liquid phases obtained after a flash under atmospheric conditions. The analysis was per-
Y (
LIQUID 18ak 011 )
Aqalyseo
Figure 1. Determination of the molar composition of the reservoir fluid.
formed on the tank oil resulting from the atmospheric flash. The standard molar composition of the reservoir fluid, which is needed to apply the predictive method developed by Neau et al. (1993), is given in Table 1.The molar compositions extended to C45+ are given in Table 2. Table 3 gives the experimental data we wanted to predict: the relative volume during a constant mass expansion and during a differential vaporization, the density of the tank oil, and the saturation pressure at the depletion temperature. N M R Analysis. m e r performing the TBP distillation, each fraction was split into an aromatic and a paraffin naphthene sample. Each of the 60 samples obtained was carefully analyzed by NMR. A Bruker AM 400 spectrometer was used to record ‘H and 13C NMR spectra at 400.13 and 100.62 MHz, respectively. With each fraction, a lH spectrum and a proton-decoupled inverse gated (Freeman et al., 1972) 13Cspectrum (decoupling during acquisition only) were recorded. Partial 13C spectral editing was also undertaken, using the multiplet selection methods proposed by Cookson and Smith (1981,1983a,b, 1985,1989)and by Cookson et al. (1987). The Cquaternary, CH, CH2, (CH CH3) subspectra were recorded, using GAted Spin Echo (GASPE) and Conventional Spin Echo (CSE) pulse sequences with coupling constants Jc-Hof 160 Hz with
+
+
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 641 Table 1, Standard Molar Compositions of the Indonesian Oil Mixture compd
Nz
coz
methane ethane propane isobutane n -butane isopentanes n-pentane hexanes heptanes octanes nonanes decanes
Cll-cls czo+
separator
reservoir oil (molar %) 0.020 4.000 32.160 6.150 6.170 1.380 2.500 1.130 1.030 1.520 3.510 4.610 2.490 1.610 16.754 14.966
liquid phase 0.010 0.240 0.580 1.000 3.490 1.350 3.030 1.780 1.720 2.810 6.630 8.820 4.760 3.060 32.070 28.650
. I I
tank
gas phase 0.050 8.120 66.730 11.730 9.120 1.400 1.930 0.420 0.270 0.120 0.100 0.010 0.000
0.000 0.000 0.000
T-----r----r
liquid phase 0.000 0.028 0.033 0.149 0.650 0.266 0.603 0.359 0.348 2.063 4.918 6.235 5.589 3.756 39.613 35.390
--------
-T---
gas phase 0.052 1.141 2.906 4.620 15.564 5.958 13.347 7.820 7.552 5.986 13.912 19.806 1.237 0.099
0.000 0.000
r--T---
molar w t of cuts
density of cuts (dcm3)
98.0 111.0 124.0 137.0 150.0 218.5 385.0
0.6970 0.7845 0.8215 0.8315 0.8255 0.8822 0.8936
i r
---r---T----
i Figure 2. Example of a short-range heteronuclear shift correlation spectrum.
the aromatic carbons and 125 Hz with the aliphatic carbons, and different values of the parameters zJ (where r is the time delay between pulses). GASPE and CSE spectra were recorded with rJ, = 0.5 for the total aromatic 13C editing. GASPE and CSE spectra were recorded with zJd = 1.0 and the GASPE spectrum was recorded with zJd = 0.5 for the partial aliphatic editing. For all spectra, a digital phase correction, a baseline correction, and a digital integration were performed. In the 2D NMR analysis, direct (short-range) heteronuclear shift correlation 2D spectra were recorded with each intermediate fraction (from C11 to C14). The sequence used here (XHCORR.AUR in the Bruker
library of microprograms) was that developed by Bax and Morris (1981). The long-range heteronuclear shift correlation spectra were obtained by use of the unmodified COLOC sequence (correlation spectroscopy via longrange couplings, COLOC.AUR in the Bruker library). The analysis of short- and long-range 2D spectra was partly based on the assignment of 'H and I3C shift ranges to the various types of carbon and hydrogen atoms. (a) Analysis of the Aromatic Samples. We had no difficulty in interpreting the NMR spectra of the aromatic samples. A method using two-dimensional heteronuclear shift correlation spectra was developed
642 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 Table 2. Molar Percent Composition Extended to C a t compoundu
temp. range of distillation ("C)
N2 COZ methane ethane propane isobutane n-butane isopentane n-pentane c6
reservoir oil
separator liquid phase gas phase
tank liquid phase gas phase
0.020 4.000 32.160 6.150 6.170 1.380 2.500 1.130 1.030
0.010 0.240 0.580 1.000 3.490 1.350 3.030 1.780 1.720
0.050 8.120 66.730 11.730 9.120 1.400 1.930 0.420 0.270
0.000 0.028 0.033 0.149 0.650 0.266 0.603 0.359 0.348
0.052 1.141 2.906 4.620 15.564 5.958 13.347 7.820 7.552
molar wtb
density of cuts (g/cm3)
ARO P+N
36.0-70.0
1.230 0.289
2.276 0.534
0.097 0.023
1.671 0.392
4.849 1.137
78.0
0.6970
ARO P+N
70.0-100.0
1.544 1.966
2.917 3.713
0.044 0.056
2.164 2.754
6.121 7.791
80.5
0.7845
ARO P+N
100.0-127.0
1.421 3.189
2.719 6.101
0.003 0.007
1.922 4.313
6.106 13.700
96.0
0.8215
127.0-152.0
0.626 1.864
1.197 3.563
0.000 0.000
1.406 4.183
0.311 0.926
106.0
0.8315
152.0-176.0
0.601 1.009
1.142 1.918
0.000 0.000
1.402 2.354
0.037 0.062
115.0
0.8255
176.0-197.0
0.530 0.572
1.014 1.094
0.000 0.000
1.252 1.352
0.000 0.000
125.0
0.8260
197.0-219.0
0.687 0.756
1.314 1.448
0.000 0.000
1.623 1.789
0.000 0.000
135.0
0.8530
219.0-237.0
0.748 1.131
1.432 2.164
0.000 0.000
1.769 2.673
0.000 0.000
145.0
0.8765
ARO P+N
237.0-254.5
0.717 1.205
1.372 2.307
0.000 0.000
1.694 2.849
0.000 0.000
155.0
0.8945
ARO
254.5-271.5
1.080 1.621
2.068 3.103
0.000 0.000
2.554 3.833
0.000 0.000
166.0
0.8960
271.5-288.0
0.849 1.386
1.626 2.653
0.000 0.000
2.008 3.278
0.000 0.000
180.0
0.9070
288.0-303.0
1.313 1.028
2.513 1.967
0.000 0.000
3.104 2.430
0.00 0.000
194.0
0.8735
303.0-318.0
0.989 0.691
1.894 1.323
0.000 0.000
2.339 1.634
0.000 0.000
208.0
0.8765
318.0-332.0
0.801 0.651
1.533 1.246
0.000 0.000
1.893 1.539
0.000 0.000
222.0
0.8895
332.0-344.0
0.717 0.542
1.372 1.038
0.000 0.000
1.694 1.282
0.000 0.000
236.0
0.8850
344.0-357.0
0.836 0.578
1.601 1.106
0.000 0.000
1.978 1.366
0.000 0.000
251.0
0.8870
357.0-369.0
0.592 0.359
1.132 0.687
0.000 0.000
1.399 0.849
0.000 0.000
265.0
0.8825
369.0-381.0
0.871 0.414
1.667 0.793
0.000 0.000
2.059 0.979
0.000 0.000
279.0
0.8775
381.0-392.0
0.785 0.345
1.502 0.660
0.000 0.000
1.855 0.815
0.000
293.0
0.8680
392.0-402.0
0.695 0.296
1.331 0.567
0.000 0.000
1.644 0.701
0.000 0.000
307.0
0.8650
402.0-413.0
0.299 0.117
0.572 0.224
0.000 0.000
0.706 0.276
0.000 0.000
321.0
0.8725
413.0-423.0
0.775 0.305
1.484 0.584
0.000 0.000
1.833 0.721
0.000 0.000
335.0
0.8750
423.0-432.0
0.660 0.301
1.263 0.576
0.000 0.000
1.560 0.712
0.000 0.000
349.0
0.8750
432.0-441.0
0.871 0.356
1.667 0.681
0.000 0.000
2.059 0.841
0.000 0.000
364.0
0.8790
c7 CS
c9
ARO
P+N ClO ARO
P+N
c11
ARO P+N ClZ ARO P+N c13
ARO P+N
c14
c 15
P+N
c 16
ARO
P+N c17
ARO P+N
ClS
ARO P+N
c19
ARO P+N CZO ARO P+N CZl ARO P+N CZZ ARO P+N c23
ARO P+N
c24
ARO
P+N c25
ARO
P+N
0.000
c26
ARO
P+N
c27
ARO
P+N CZS
ARO
P+N c29
ARO
P+N
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 643 Table 2 (Continued) compound" c30
ARO P+N
c3l
ARO
ARO ARO
ARO
ARO
378.0
0.8840
1.149 0.509
0.000 0.000
392.0
0.8825
0.000 0.000
1.380 0.657
0.000 0.000
409.0
0.8885
0.656 0.405
0.000
0.810 0.500
0.000 0.000
439.0
0.8985
0.000
0.180 0.223
0.345 0.427
0.000 0.000
0.426 0.527
0.000 0.000
472.0
0.9320
0.092 0.198 0.678
0.177 0.379 1.298
0.000
0.219 0.469 1.603
0.000 0.000 0.000
512.0
0.9500
700.0
1.0150
0.000
0.000
1.317 0.492
450.0-460.0
0.486 0.215
0.931 0.412
0.000 0.000
460.0-480.0
0.583 0.278
1.117 0.532
480.0-500.0
0.343 0.211
500.0-525.0 525.0-550.0
P+N c45+
0.000 0.000
1.066 0.399
P+N c42-c46
density of cuts (g/cm3)
0.557 0.208
P+N c37-c41
molar wtb
441.0-450.0
P+N c35-c36
tank liquid phase gas phase
reservoir oil
P+N c32-cs4
separator liquid phase gas phase
temp. range of distillation ("C)
2550.0
0.000 0.000
+
4 ARO, aromatic molecules; P N, paraffin and naphthene molecules. The molar weight is available for the aromatic samples only; the molar weight of the (P N) fractions was determined by NMR.
+
t-
F
t t
1
I
Figure 3. Example of a long-range heteronuclear shift correlation spectrum.
644 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
Table 3. Experimental Data on the Fluid Studied“ constant mass expansion at T K = 360.95 pressure re1 volb (bar) (Vrel = VtotadVsat) 351.4 301.4 251.4 201.4 176.4 151.4 150.2 (Psat)
0.970 0.976 0.983 0.991 0.995 0.999 1.000
differential vaporization at T/K = 360.95 pressure re1 volc (bar) (Vrel = VfiqUidWref) 351.4 301.4 251.4 201.4 151.4 150.2 (Psat) 141.4
constant mass expansion a t TfK = 360.95 pressure re1 volb (bar) (Vrel = vt&dWsat)
1.346 1.355 1.365 1.376 1.386 1.388 1.374
148.9 145.9 142.4 136.9 115.9
1.004 1.012 1.022 1.040 1.122
differential vaporization at TfK = 360.95 pressure re1 volc (bar) (Vrei= VfiquidNref) 111.4 76.4 51.4 26.4 11.4 1.0
1.324 1.266 1.229 1.186 1.142 1.063
a The saturation pressure at T/K = 360.95 is Psat= 150.2 bars. The tank oil density under standard conditions is = 0.87850 g/cm3. In the case of a constant mass expansion, the relative volume is the total volume of the fluid divided by the liquid volume at saturation pressure (PSat).For a differential vaporization, the relative volume is the liquid volume of the fluid divided by the liquid volume at the final pressure, measured under atmospheric conditions (15 “C, 1atm).
Table 4. Results of the Analysis of the Aromatic Samples by NMR” compound MWam CH3ar CHzar CHar AROC6 AR0c.I AROCS ARoc9 AROClO AROCll AROCl2 ARoci3 ARoci4
moci5 AROC16
ARoc1.1 AROClS
ARoc19 AROCZO AROCZl AROCZ2 ARocz3 ARocz4 ARocz5 AROC26
ARocz7 AROCZS ARoc29 ARoc30 AROc31 ARoc32-c34 ARO&-c36 ARoc37-c41 ARoc42-c45 a
78.0 80.5 96.0 106.0 115.0 125.0 135.0 145.0 155.0 166.0 180.0 194.0 208.0 222.0 236.0 251.0 265.0 279.0 293.0 307.0 321.0 335.0 349.0 364.0 378.0 392.0 409.0 439.0 472.0 512.0
0.00 2.91 14.64 24.03 26.76 23.00 12.08 13.40 13.74 15.02 16.92 16.02 15.12 14.22 13.14 14.37 15.09 14.70 15.08 17.11 15.91 15.24 14.25 17.59 16.58 14.82 15.07 15.66 15.18 12.84
0.00 0.00 0.17 2.10 5.16 9.99 10.25 13.44 6.03 15.19 10.03 12.90 15.53 16.99 16.25 16.28 18.08 24.11 20.76 20.20 28.50 27.53 27.34 27.55 26.13 29.69 30.81 32.26 30.00 36.02
0.00 0.00 0.00 0.22 0.49 1.66 2.40 1.29 0.77 5.30 8.87 8.97 8.33 7.67 8.76 9.73 9.85 11.03 12.35 12.72 9.17 13.05 13.02 14.25 14.50 12.24 12.14 11.47 10.62 10.77
CHaro
Car0
Cjc
total sum
100.00 94.18 70.55 49.85 41.55 40.19 53.50 45.13 52.14 36.36 33.43 32.17 31.36 31.86 29.35 27.79 23.97 20.52 22.94 22.35 23.14 17.99 19.25 18.56 18.39 17.58 17.82 17.50 20.37 16.28
0.0 2.91 14.64 23.80 26.04 23.81 13.09 17.27 14.26 19.80 21.61 23.17 18.37 17.46 17.01 19.28 18.57 19.52 16.95 16.49 14.84 15.37 16.81 13.52 12.75 14.28 11.67 11.68 10.99 10.29
0.00 0.00 0.00 0.00 0.00 1.35 8.68 9.47 13.06 8.33 9.14 6.77 11.29 11.80 15.49 12.55 14.44 10.12 11.92 11.13 8.44 10.82 9.33 8.53 11.65 11.39 12.49 11.43 12.84 13.80
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
Results obtained on a total number of 100 carbons present in the sample.
for the study of the intermediates cuts (Fressigne, 1992). Correlations between carbons and their bonded protons were observed on the short-range heteronuclear shift correlation spectra from which all the alkyl chains belonging to the aromatic molecules could be determined. From the correlations found to exist on the longrange heteronuclear shift correlation spectra, between aromatic quaternary carbons Cqar and aromatic or aliphatic protons, it was possible to connect each Cqm to its bonded alkyl chain and thus to “reconstruct” the aromatic molecule (see Figures 2 and 3). For the other cuts (above CIS),the 13C spectral editing was sufficient t o determine the concentration of each type of carbon. Under these conditions, the NMR analysis makes it possible to count the exact number of carbon atoms of each type present in the sample. The results are summarized in Table 4, the notations employed are as follows (see also Figure 4): (i) CHsar, CHz,, and CH, are respectively a methyl, methylene, and methine group on an alkyl chain linked t o the aromatic cycle. With a group contribution method, they are taken to
C%*r
Figure 4. Illustration of the notations used to describe the aromatic samples.
be alkane-type carbons since they are sp3 hybridized. (ii) CH,, C, and Cj, are aromatic carbons, that is, carbons of the aromatic cycles (hybridized sp2). Cj, is a quaternary carbon belonging to more than one cycle (a carbon that joins cycles). The results in Table 4 are those obtained on a total number of 100 carbons present in the aromatic sample. In order to estimate the equation of state parameters by means of group contribution methods, it is necessary to calculate the number of each type of carbon per gram mole of aromatic sample. For a given sample, if the
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 645
+
Table 5. Noncorrected Results of the N M R Analysis of the (P N) Samples4 compound
CHAb
CH&
CHAC
CHsNb
CHzNd
CHNd
total sum
37.80 14.60 15.03 25.15 14.42 12.43 9.40 7.67 5.79 10.10 11.72 15.40 13.40 9.80 9.10 8.40 7.10 8.03 8.10 8.80 7.50 7.50 7.00 6.80 6.40 5.92 7.13 7.07 6.12 6.90
33.23 19.27 20.18 34.94 28.41 26.98 45.62 34.82 39.31 37.11 48.82 47.43 55.00 59.91 62.05 69.30 58.40 73.84 70.80 68.50 67.10 65.70 70.80 68.50 65.60 63.10 66.74 67.03 52.62 52.45
8.81 3.42 4.68 9.07 4.65 4.74 5.32 2.99 3.94 4.40 4.12 8.00 5.60 3.30 2.50 1.80 2.70 1.81 1.90 3.10 2.20 2.10 1.40 1.70 1.70 2.08 3.15 3.17 3.11 4.02
2.09 10.90 2.35 2.89 11.32 0.45 8.52 10.70 7.65 7.75 7.28 6.41 4.60 5.00 3.56 3.23 6.21 0.33 2.00 4.30 3.60 5.90 4.51 4.50 3.90 4.40 3.46 4.19 4.93 5.49
15.99 40.91 47.91 20.41 27.51 38.99 14.09 21.71 32.70 23.41 16.35 14.60 14.57 14.39 15.58 10.03 16.37 10.43 12.60 9.00 12.30 12.10 10.94 12.40 15.60 15.46 13.82 10.82 14.88 18.40
2.08 10.90 9.85 7.54 13.69 16.41 17.05 22.11 10.61 17.23 11.71 8.16 6.83 7.60 7.21 7.24 9.22 5.56 4.60 6.30 7.30 6.70 5.35 6.10 6.80 9.04 5.70 7.72 18.34 12.74
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
a Results obtained on a total number of 100 carbons present in the sample. With a group contribution method, C H D and C H A are taken to be identical. These values are underestimated. These values are overestimated.
u NMR tanes all these 9 carbons to be cyclic carbons
-
NMR takes til s molecule to have 8 cyclic carbons.
i
Figure 6. Explanation for the determination errors made with NMR. PARAFFIN MOLECULES
L
---
~
GI:
'
I
'
'
'
SO
1
40
, ,
'
,- - , , ,
30 PPIl
I
20
,
,
,
,
I
!D
.
NAPHTENE MOLECULES
-[--
0
Figure 5. Complex spectrum of a (P+ N) sample.
molar weight (MW,) is known, the number of gram moles present in 100 carbons is
n,,
+ 14.027CH2, + 13.019(CH, + CH,,) + 12.011(C,, + Cj,)yMwam = [15.035CH3,
(1) In the case of the aromatic samples, the MW,, (Tables 2 and 4) was directly measured aRer separating each cut into aromatic and nonaromatic molecules. (b) Analysis of Paraffin and Naphthene Samples. NMR Indetermination. Except for the very light cuts
h 3 N
Figure 7. Illustration of the notations used to describe the (P+ N) samples using NMR.
(CSand C,), it is not possible to exactly determine the structure of the (P+ N) samples, even with a very high-
performance spectrometer: the increase in isomer number with the boiling point of these samples makes the spectra very complex (see Figure 5) and causes overlaps between alkane resonances. The concentration of each
646 Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995
+
Table 6. Corrected Values of the NMR Analysis of the (P N)Samples compound CH& CHzAa CHAa CH3N CHzNb CHNb total sum (a)Corrections Corresponding to the High Hypothesis (See Appendix I) .. .. 37.80 14.60 15.03 25.15 14.42 12.43 9.40 7.67 5.79 10.10 11.72 15.40 13.40 9.80 9.10 8.40 7.10 8.03 8.10 8.80 7.50 7.50 7.00 6.80 6.40 5.92 7.13 7.07 6.12 6.90
33.23 19.27 20.68 35.85 30.77 27.10 45.74 35.90 41.15 40.39 52.23 49.17 57.23 62.50 65.31 71.02 61.40 75.83 73.99 70.49 70.13 77.94 81.54 74.86 70.00 66.94 70.67 70.26 55.63 57.69
8.81 3.42 5.18 9.98 7.01 4.86 5.44 4.07 5.78 7.68 7.53 9.74 7.83 5.89 5.76 3.52 5.70 2.14 3.90 5.09 5.23 2.10 1.40 3.29 4.60 5.92 5.38 6.40 6.12 6.90
2.09 10.90 2.35 2.89 11.32 0.45 8.52 10.70 7.65 7.75 7.28 6.41 4.60 5.00 3.56 3.23 6.21 0.33 2.00 4.30 3.60 5.90 4.51 4.50 3.90 4.40 3.46 4.19 4.93 5.49
15.99 40.91 47.41 19.50 25.15 38.87 13.97 20.63 30.86 20.13 12.94 12.86 12.34 11.80 12.32 8.31 13.37 8.44 9.41 7.01 9.27 0.00 0.20 6.04 11.20 11.62 9.89 7.59 11.87 13.16
2.08 10.90 9.35 6.63 11.33 16.29 16.93 21.03 8.77 13.95 8.30 6.42 4.60 5.01 3.95 5.52 6.22 5.23 2.60 4.31 4.27 6.70 5.35 4.51 3.90 5.20 3.47 4.49 15.33 9.86
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
molar&
avcycle sizec
81.46 94.00 103.48 122.42 131.80 144.92 161.59 170.58 182.22 198.24 215.39 231.90 246.28 258.24 271.61 288.10 296.93 316.83 329.40 343.92 355.10 374.53 389.30 400.77 411.01 420.57 453.38 478.64 515.13 587.29
5.83 5.50 4.82 4.50 4.50 5.09 5.09 4.50 4.50 4.50 4.50 4.50 4.55 4.50 4.79 4.50 4.50 4.50 5.58 4.50 4.51 4.68 6.00 5.63 5.56 4.51 4.50 4.50 4.50 4.50
81.46 94.00 103.00 122.42 133.19 143.49 160.11 171.04 183.07 201.22 218.93 233.40 248.69 260.88 275.49 289.64 300.47 317.41 332.83 346.30 359.67 375.57 390.59 403.36 415.71 427.68 457.14 485.15 522.37 595.52
5.83 5.50 4.51 4.50 5.21 4.50 4.50 4.50 4.94 4.50 4.50 5.94 5.78 4.81 4.50 4.50 4.86 4.51 4.87 5.06 4.50 6.00 6.00 6.00 6.00 6.00 6.00 6.00 5.84 6.00
(b) Corrections Corresponding to the Low Hypothesis (See Appendix I) .. 37.80 14.60 15.03 25.15 14.42 12.43 9.40 7.67 5.79 10.10 11.72 15.40 13.40 9.80 9.10 8.40 7.10 8.03 8.10 8.80 7.50 7.50 7.00 6.80 6.40 5.92 7.13 7.07 6.12 6.90
33.23 19.27 29.04 40.36 40.64 33.97 52.61 37.62 47.72 47.08 59.29 57.00 65.21 68.41 70.64 73.90 68.43 76.58 75.81 75.21 75.87 76.36 80.40 77.52 75.37 73.45 75.47 76.36 63.18 63.77
8.81 3.42 4.68 9.07 4.65 4.74 5.32 2.99 3.94 4.40 4.12 8.00 5.60 3.30 2.50 1.80 2.70 1.81 1.90 3.10 2.20 2.10 1.40 2.03 1.70 2.08 3.15 3.17 3.11 4.02
2.09 10.90 2.35 2.89 11.32 0.45 8.52 10.70 7.65 7.75 7.28 6.41 4.60 5.00 3.56 3.23 6.21 0.33 2.00 4.30 3.60 5.90 4.51 4.50 3.90 4.40 3.46 4.19 4.93 5.49
15.99 40.91 39.05 14.99 15.28 32.00 7.10 18.91 24.29 13.44 5.88 5.03 4.36 5.89 6.99 5.43 6.34 7.69 7.59 2.29 3.53 1.44 1.34 3.38 5.83 5.11 5.09 1.49 4.32 7.08
2.08 10.90 9.85 7.54 13.69 16.41 17.05 22.11 10.61 17.23 11.71 8.16 6.83 7.60 7.21 7.24 9.22 5.56 4.60 6.30 7.30 6.70 5.35 5.77 6.80 9.04 5.70 7.72 18.34 12.74
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
a C H A and CHA are the true alkane groups belonging to paraffin molecules or t o an alkyl chain linked to the cycles. CHzN and CHN are the true cyclic carbons. Calculated as described in Appendix I.
type of carbon can only be approximately determined by use of the aliphatic Cquaternary, CH2, and (CH CH3) subspectra. The real problem is due to the naphthene molecules. NMR takes into account like “cyclic carbons”, both carbons belonging to the cycle and the a, B, or y exocyclic carbons: (i) If there is a CH2 group in the y position, the a, and y exocyclic carbons are considered like cyclic carbons (belonging to the cycle). (ii) If there is a CH group in the y position, the a and /3
+
exocyclic carbons are assumed to be cyclic carbons. This error is illustrated in Figure 6. It can be readily understood from the above why NMR overestimates the number of cyclic carbons and underestimates the number of aliphatic carbons. This is why it is necessary to correct the NMR values before using group contribution methods. The noncorrected results directly obtained by NMR are listed in Table 5. The notations used are as follows (see also Figure 7): (i)
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 647 Table 7. Parameters Calculated by Use of Contribution Methods (a) Aromatic Samples compound
critical tempTJK
critical pressurepdbar
wa
Zub
AROC6 ARoc7 AROCs AROCg AROClO AROCll AROClZ ARoci3 ARoci4 ARoci5 AROC16 ARoci7 AROCl8 ARoc19 AROCZO
509.93 566.28 591.81 619.31 649.97 676.88 709.43 726.72 745.82 757.78 765.41 771.57 782.39 787.58 789.09
41.36 47.29 39.12 36.08 34.57 32.95 32.64 30.53 29.51 27.08 24.88 22.77 20.92 19.37 17.97
0.197 0.206 0.257 0.301 0.332 0.356 0.353 0.391 0.392 0.441 0.458 0.491 0.527 0.555 0.577
0.267 0.267 0.264 0.262 0.261 0.260 0.259 0.258 0.257 0.255 0.253 0.252 0.250 0.248 0.247
critical tempTdK
compound
AROCzi AROCzz AROczs ARoc24 ARoc26 AROC26 ARoc2-1 AROCzs AROCze AROC3o AROc31 AROC~Z-C~~ ARoc36-c36 ARoc37-c41 ARoc42-c45
786.92 796.75 805.00 809.01 816.17 828.70 831.87 825.31 845.16 844.50 841.43 863.84 874.85 872.31 906.73
(b)Paraffin and Naphthene Samples high hypothesis compound TdK Pdbar (P + N) c6 492.07 31.91 (P + N) C7 540.10 32.61 (P + N) Cs 577.82 32.19 (P + N) Cg 594.95 26.27 (P + N) Cio 626.75 25.45 (P + N) C i i 658.36 25.51 (P + N) Ciz 688.64 27.51 (P + N) c13 698.46 22.45 (P + N) c14 712.67 20.58 (P + N) c15 722.89 18.74 (P + N) c16 728.73 16.41 (P + N) c17 742.27 15.54 (P + N) Cis 750.03 14.27 (P + N) Ci9 763.24 13.75 (P + N) Czo 771.41 12.95 (P + N) C21 779.09 12.25 (P + N) C22 794.29 12.19 (P + N) c23 796.24 11.21 (P + N) c 2 4 804.96 10.64 (P + N) c 2 5 813.05 10.32 (P + N) c 2 6 820.58 10.00 (P + N) c 2 7 826.53 9.47 (P + N) Czs 830.95 9.03 (P + N) C29 838.38 8.84 (P + N) c 3 0 847.32 8.74 (P + N) c31 856.45 8.69 (P + N) c32-c34 862.59 8.03 (P + N) c35-c36 885.96 8.01 (P + N) c37-c41 909.47 7.97 (P + N) c42-c45 912.50 6.16 Acentric factor. b Rackett compressibility factor.
wQ
Zub
16.54 15.46 14.48 13.77 13.03 12.28 11.69 11.08 10.62 10.14 9.61 9.31 8.59 7.90 7.30
0.602 0.650 0.700 0.705 0.739 0.805 0.826 0.831 0.885 0.898 0.928 0.971 1.024 1.029 1.127
0.245 0.244 0.242 0.241 0.240 0.239 0.237 0.236 0.235 0.234 0.233 0.232 0.229 0.227 0.225
low hypothesis
WQ
ZRAb
TdK
Pdbar
0.262 0.271 0.294 0.367 0.395 0.387 0.419 0.474 0.528 0.571 0.654 0.690 0.749 0.785 0.826 0.868 0.880 0.935 0.977 1.004 1.029 1.075 1.112 1.128 1.139 1.147 1.202 1.224 1.224 1.316
0.265 0.266 0.265 0.262 0.258 0.257 0.257 0.254 0.252 0.253 0.248 0.247 0.245 0.244 0.243 0.242 0.241 0.239 0.238 0.237 0.236 0.235 0.234 0.233 0.232 0.231 0.229 0.228 0.226 0.226
492.07 540.10 579.88 596.98 632.37 658.68 689.51 699.74 717.29 729.06 735.50 747.92 756.66 768.26 776.85 781.49 800.46 797.14 808.65 816.88 826.21 828.46 832.68 842.42 853.61 863.64 867.94 883.07 909.05 909.11
31.91 32.61 33.03 26.69 26.38 26.03 28.15 22.68 21.12 19.43 17.24 16.02 14.85 14.22 13.49 12.47 12.70 11.28 10.95 10.58 10.39 9.57 9.12 9.04 9.06 8.98 8.23 7.85 7.82 6.05
C H A , CH&, and CHA are respectively a methyl, methylene, and methine group belonging either t o an alkyl chain that is linked to the cycle or to a paranin molecule. They are alkane-type carbons for the purposes of group contribution methods. (ii) CHzN and CHN are “cyclic” carbons. As discussed above, these carbons may be in fact exocyclic (in a, p, or y position); in this case, they should be treated like alkane-type carbons. Since NMR treats them like cyclic carbons, it will be necessary to correct them. (iii)CH3N are methyl groups close to the cycle, that is, a t a distance of less than four bonds. They are alkane-type carbons for the purposes of group contribution methods. Constraints due to the Group Contribution Methods. The application of group contribution methods requires expressing the values given in Table 5 for a gram mole of (P N) sample; it is thus necessary to know the molar weight of these samples. Moreover,
+
critical pressurepdbar
Wa
0.262 0.271 0.289 0.360 0.378 0.388 0.416 0.469 0.512 0.549 0.628 0.669 0.722 0.763 0.801 0.855 0.852 0.932 0.961 0.986 1.003 1.069 1.104 1.111 1.110 1.119 1.180 1.228 1.226 1.322
ZRAb
0.265 0.266 0.265 0.262 0.258 0.257 0.258 0.254 0.252 0.254 0.249 0.247 0.246 0.244 0.243 0.242 0.241 0.239 0.238 0.237 0.236 0.235 0.234 0.233 0.232 0.232 0.230 0.228 0.226 0.226
with group contribution methods, it is necessary to know the average size of the naphthene cycles. The method of correcting the values given in Table 5 as well as the manner of calculating the molar weight of the (P N) samples and the average cycle size is explained in detail in Appendix I. In fact, there are an infinite number of ways of obtaining these values. This is why it was decided to consider only two corrections leading to extreme values of the covolume used in the equation of state. These two corrections correspond to two different structures of the (P N) samples and will be called respectively “high hypothesis” (greatest value of the covolume) and “low hypothesis” (lowest value of the covolume). The results obtained with each of these two hypotheses are given in Table 6a,b. In the case of the (P N) samples, two different group compositions are thus available. The PVT calculations will be carried out with each of these compositions.
+
+
+
648 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 Table 8. Results of Predictions Performed with the Two Different Methods method used NMR high hypothesis low hypothesis predictive method developed by Neau et al. (1993)
depletion type
AVrell%a
constant mass expansion differential vaporization constant mass expansion differential vaporization
0.89 0.48 0.91 0.46
4.46 (6.7 bar)
10.01
constant mass expansion differential vaporization
0.52 0.49
-3.67 (-5.5 bar)
-0.24
hp$%b
a AVrell%,mean absolute percent deviation from the relative volume. A€'$% and A@/%are the percent deviations from the saturation pressure and the tank oil density under atomspheric conditions, respectively.
Table 9. Values of Group Parameters for T, and m, group (type of carbon)
mC,
Tj
j
0.05322 0.05484 0.02967
0.0608 0.0522 0.0091
T, = 0.04025 - 0.00233 (CY - 5P Ts = 0.03340 + 0 . 0 0 3 8 8 ( ~-~5P
m,, = 0.0378 - O.O03O(cy - 5) mes= 0.0219 - O.O046(cy - 5)
0.03586 0.04857 0.04185 a
+
cy, cycle size determined by NMR (4.5 5 cy 5 6). mcs= 0.0357 - 0.015[0.5G~ 0.75(Gs
Table 10. Values of Group Parameters for V,
D
D
gm = C,,gi
Vi
group ( t m e of carbon)
+
0.0325 0.0357 mcsb G7 - Gs - 6)].
c, = x x & € i i=l
i=l
Equation of State Flash calculations were performed using an equation of state of the Peng-Robinson type (Rauzy, 1982):
p=- R T
9 -6
-
a(T) with y = 2& Q(f y 6 )
+
+2
4.828 427; 6 = 0.045572(RTJPC)(2) ij is the pseudovolume related to the molar volume v and to the volume correction c (PBneloux et al. 1982) by
f =v
+c
with
with c = (RTJP,) x (0.083150 - 0.4406422,)
(3)
In eq 3, ,2 is the Rackett compressibility factor appearing in Spencer and Danner's (1973)modification of the Rackett equation. The a(T) function is
To solve the equation of state and perform a flash calculation, it is necessary to know for each component: the critical temperature T,,the critical pressure P,, the Rackett compressibility factor ZRA,the acentric factor w , and the binary interaction parameters E,. In this study, with the samples analyzed by NMR (from CSto C45), all these parameters were estimated using the group contribution methods described in Appendix 11. The binary interaction parameters E, were estimated using a group contribution method (Abdoul et al., 1992), even in the case of the light compounds not analyzed by NMR.
Results
+
with m = 6.812553 x [41.127539
We applied the group contribution methods described in Appendix I1 to the aromatic samples and to the high and low hypotheses of the (P N) samples. The results are summarized in Table 7a,b. It is now possible to predict the variation of the relative volume of the crude oil vs pressure in the case of each structural model previously described. Flash calculations were performed with 70 compounds (9 light pure compounds, 30 aromatic samples, 30 (P N) samples, and the TBP residue (C45+).The physical properties of the TBP residue C45+were assumed to be
+ 0 . 5 1 7 2 5 2 ~- 0 . 0 0 3 7 3 7 ~-~11 (5)
For a mixture containing p compounds of mole fraction xi, classical mixing rules were used:
+
Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995 649
1.2
1.4
1.0
1.2
t -.-
0.8
200.0
100.0
300.0
0.0
400.0
200.0
400.0
1.2
1.0
f
0.8
100.0 200.0 300.0 400.0 0.0 200.0 400.0 Figure 8. (a) Comparison between the very close results obtained with the high (-1 and the low (- - -) hypothesis resulting from an NMR
analysis (the fluid is described with 70 compounds). (b) Curves obtained by use of the predictive method developed by Neau et al. (1993) (the fluid is described with only nine components or pseudocomponents). (a and b, left) Constant mass expansion at T/K= 360.95of an Indonesian crude oil; (a and b, right) differential expansion at T/K = 360.95of an Indonesian crude oil.
I
icy
CH3N
CH3N
+
Figure 9. Illustration of the notations used to describe the (P N) samples.
similar to those corresponding t o the
c42-c45
fraction
(Tc= 910 K,Pc = 7 bar, w = 2.0, and Zw = 0.224). These results were compared with those obtained using the predictive method recently developed by Neau et al. (1993). In this case, the fluid is described as a mixture of the nine following components and pseudocomponents: N2, COZ,C a , C2H6, C3H8, butanes, CE-Clo, Cll-Clg, and C20+. The complete modeling requires only knowledge of the molar weight and the density of the single carbon
number (SCN)cuts between C11 and C20+. Comparisons can be made by using the results given in Table 8 and in Figure 8a,b. The most spectacular result was that the two structural hypotheses developed for correcting group compositions obtained with NMR yielded very similar results. Moreover, the prediction of the PVT properties was in very good agreement with the experimental data, except for the tank oil density. NMR is therefore a reliable method of analyzing SCN cuts of petroleum fluids, but it is a rather lengthy and expensive method. The result concerning the tank oil density may look surprising but may be explained since the tank oil density is not obtained directly. Indeed, a first flash is performed on the reservoir fluid under the separator conditions (Figure 1) and the resulting liquid phase is flashed under atmospheric conditions. The density of the last liquid phase is the tank oil density. Consequently, the errors become greater and greater after each flash calculation. In the present case, the flash calculation performed on the reservoir fluid does not allow us to estimate properly the experimental composition of the liquid phase of the separator. This is probably because the bottles of liquid and gas taken on
650 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
a
I I 4
long
chain
I
*I
I
I
a long chain Figure 10. Illustration of the notations used to describe the (P + N) samples. Definition of a long chain.
cl=
3 nL
C,= 3 nL
c,=
Ci= 3 nL
C1= 0.5 CH,N
0
r4-C = 3 nL+ Ch,N 1
C1=2 nL
C1= 2 nL
C,= 1.5 nL ( 8 ) !he
C,= 2.5nL
C,= 2 n L t CH,N
C1= 2 nL
Cl= 2 nL
( 0
=cy)
C,= CH,N
C1= Ct$N
C1= 1.5 CH,N
Ci= 2 CH3N
C1= CH,N
Figure 12. Values of CIbased on CH3N carbons.
t
c,,= CHcc + CH2CC
ewncncs of a m1-k of thl$ t p 16 highly xmprobabk due lo Dtenc effects
Figure 11. Estimations of C1 with long chains of different types.
the field from the separator were not really in equilibrium. A new flash on the calculated liquid phase of the separator leads to a calculated tank oil containing much more light components than the experimental one and explains why its density is lower by 10% than the experimental value. This deviation could be reduced by performing a flash calculation on the experimental liquid separator composition under atmospheric conditions. We did not perform this last calculation because with a predictive model all the calculated values must be obtained knowing only the reservoir fluid composition. Another important result is that knowing the structure of each SCN cut did not improve the PVT calculations obtained with the predictive method by Neau et al. (1993). This method describes the fluid as a mixture of nine components only and gives very satisfactory results on all the PVT properties. In this case, the tank oil density is perfectly predicted since the plus fraction characterization used in this method has been developed to correctly calculate this density. The differences between the experimental and calculated properties obtained with this Indonesian fluid are of the same magnitude as those obtained in a previous study for 14 different crude oils (Neau et al. 1993). For possible comparison, it is recalled that the method of Neau et
Cac 1
Figure 13. Plot of Clmi,, and
vs cat.
al. (1993) allows prediction of the evolution of the relative volume vs pressure during an isothermal depletion (constant mass expansion and differential vaporization), the saturation pressure and the tank oil density with overall deviations of respectively 2.5%, 2.7%,and 2.5%(Neau et al. (19931, Table IV).
Conclusion Using experimental molar compositions up to C45+ and after separating each SCN cut into aromatic and nonaromatic molecules, it was established that an NMR analysis of a crude oil could be used to satisfactorily predict the PVT properties of the fluid. These results were obtained thanks to the method developed in this
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 651
F-7 Extreme values
allowed values
Additional restrictions to the extreme values I
I
I
Cac Figure 14. Extreme and allowed values of C1.
study for correcting the raw data obtained by NMR. However, the calculations based on a compositional analysis up to C20+,using the predictive method of Neau et al., also yielded an accurate prediction of the PVT properties of the crude oil. Consequently, there appears to be no point in performing a detailed NMR analysis of the internal composition of each SCN cut between c6 and (245. This conclusion agrees with the results of Pedersen et al. (1992), who have studied whether it is necessary to obtain extensive analytical data up to C ~ O + .
Acknowledgment The authors gratefully thank the French petroleum company TOTAL, which sponsored this research.
Nomenclature a = equation of state parameter (temperature dependent) 6 = pseudocovolume (equation of state parameter) c = volume correction CH& = methyl group belonging either to a paraffin molecule or to an alkyl chain linked to a naphthenic cycle CH3, = methyl group belonging to an alkyl chain linked to an aromatic cycle CH3N = methyl group close to a naphthenic cycle CHA = methylene group belonging either to a paraffin molecule or to an alkyl chain linked to a naphthenic cycle CH2N = methylene group belonging to a naphthenic cycle or being close to a naphthenic cycle CHA = methine group belonging either to a paraffin molecule or to an alkyl chain linked to a naphthenic cycle CH2, = methylene group belonging to an alkyl chain linked to an aromatic cycle CHN = methine group belonging to a naphthenic cycle or being close to a naphthenic cycle CH,, = methine group belonging to an alkyl chain linked to an aromatic cycle CH,, = methine group belonging to an aromatic cycle C,, = quaternary aromatic carbon (belonging to an aromatic cycle) C,, = quaternary aromatic carbon belonging to more than one aromatic cycle cy = number of cycles in a naphthene molecule Ey = binary interaction parameter kG = binary interaction parameter
L = number of carbon atoms contained in an alkane molecule m = equation of state parameter for a pure component M A = molar weight of an alkane molecule M N = molar weight of a naphthene molecule MW,, = molar weight of an aromatic sample n~ = number of alkane molecules contained in 100 carbon atoms of a (P N) sample naro= number of gram moles contained in 100 carbons of an aromatic sample ney= number of cycles in a naphthene molecule nL = number of long chains n~ = number of naphthene molecules contained in 100 carbon atoms of a (P N) sample P = pressure P , = critical pressure Psat= bubble point of a crude oil at the depletion temperature R = ideal gas constant ( R = 8.314 411 Jmol-'0K-l) T = temperature Ti, = normal boiling temperature T,= critical temperature B = pseudo molar volume Y = molar volume u, = critical volume Vrel = relative volume during an isothermal depletion xi = mole fraction of component z Zm = Rackett compressibility factor Greek Symbols = tank oil density under standard conditions (15 "C, 1 atm) w = acentric factor
+
+
Appendix I. Correction of the NMR Data on the (P + N) Samples As previously mentioned, the problem is as follows: (1)to estimate the molar weight of the (P+ N) samples together with the average size of the naphthene cycles; (2) to correct the values given by the NMR, which overestimates the number of CH2N and CHN and underestimates the number of C H A and CHA (see (Figures 6 and 7). NMR assimilates CH2N and CHN to cyclic carbons. In this appendix (i) the carbon atoms of the cycle (true cyclic carbons) are noted CHzWand CH,, and (ii) the
652 Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995
carbon atoms that are in a,p, or y position on an alkyl chain linked to the cycle are denoted CHzccand CH,, (the subscript cc means “cyclic corrected”). These notations are illustrated in Figure 9. The real number of cyclic carbons (CH,, and CH,) is therefore CH,,
= CH,N - CH,,,
and CH,, = CHN - CH,, (AI-1)
The carbon atoms ending the side chains, besides CHzCc,CH,,, and CH3N, are indicated (Figure 10)by the subscript ac (alkane-type carbons on cyclane molecules). With NMR as with group contribution methods, these carbons are alkane-type carbons. The sum of all these carbons will be denoted Cac: Cac = CH3ac + CH,ac + CHac
+ CH,,,,
and
(AI-3)
Clmm= 3nL
+ 2CH3N
A = CH3A
(AI-6)
(AI-7)
where CH3 and CH are the number of methyl and methine groups, respectively, in the mixture. The number of alkane molecules contained in 100 carbon atoms of a (P N) sample is given by
+
nA
= [(CHZA - CH3,,) - (CHA - CHaC)Y2
+ CH& + CHA
(AI-11)
and L the carbon number of the alkane molecules in a (P N) sample, then
+
nA= (A - C,,)/L
(AI-12)
and TZL= CH3A -
CHA - 2-A -
(AI-13)
L
Finally, the extreme values of C1 (eq AI-5 and -6) are
+
Clmm= L -6C a c 3(CH3A - CHA -
sa, +
Clmh = 4
9)+ -)
2(CH3A - CHA - 2A L
2CH3N (AI-14) (AI-15)
+
In a (P N) sample C H d , CHA, A, and L are known; so that Clmmand Clminare linearly dependent vs Cac (Figure 13). (B) Selection of the Sums (CHs,, CK,) Depending on the Size of the Cycles. Let us write CO the number of cyclic carbons, that is
+
Co = CH,,
+ CH,,,
(AI-16)
and N , the number of carbon atoms experimentally determined by NMR:
N = CH3N + CHZN + CHN
(AI-17)
then N=CH,N+C,+C,
(AI-18)
C , = N - CH3N - Co
(AI-19)
which leads to
As n~ is a function of Cac (eq AI-21, we will investigate ways of estimating Clmin and Clmm with respect to Cat. The equations used were established as follows: for a mixture containing m molecules of alkane with the same number of carbon atoms
m = (CH, - CH)/2
(AI-10)
If we take t o denote A the number of carbons experimentally determined by NMR
(AI-5)
The minimum value will be Clmin = 2 n ~
(AI-9)
CH,
nL = CH3A - CHA - 2n,
nL = the number of long chains, which depends on the value of Ca, (eq AI-2) (AI-4) Figures 11 and 12 illustrate the influence of long chains and of CH3N groups on the value of C1 (eq AI3). If we group together the effects of long chains and of CH3N carbons, we can estimate the extreme values of c1. According to Figures 11and 12, the maximum value will be
-
by combining eqs AI-8 and -9, we obtain
(AI-2)
It is now possible t o define a long chain as an alkyl chain limited at one extremity by a CH3ac and at the other extremity by a CH,, or a CH, (in Figure 10, the molecule has four long chains). In the following section, we propose to investigate possible ways of estimating CHzccand CH,, (eq AI-1). (A)Possible Values of the Sum (CHzcc + C K C h The number of CHzccand CH,, can be estimated from the number of long chains and from the number of CH3N (that is, a methyl group branching an alkyl chain linked to the cycle but a t a distance of less than four bonds (see Figure 7)). We write
C, = CH,,
TZL= CH,,,
(AI-8)
Moreover, the number of CH3*, is equal to the number of CH,, plus the number of long chains; therefore
In petroleum fluids, the cycles are usually taken to have five or six carbon atoms. Assuming catacondensed cycles, the number of cyclic carbons in 100 atoms of a (P N) sample is
+
CO = nN[2
+ Ncy(cy - 2)1
(AI-20)
where NN is the molecule number of naphthenes contained in 100 carbon atoms of a (P N) sample, Ncyis the cycle number in one molecule, and cy is the carbon number per cycle (cy = 5 or 6). In the case of pericondensed cycles, however, the previous formula overestimates the number of cyclic carbons. To take this effect into account, we will assume that the cycle size can vary between 4.5 and 6. The two extreme values for COare thus
+
COmm= n,[2 COmin= “[2
+ 4N,,]
+ 2.5Nc,]
(CY = 6)
(AI-21)
(cy = 4.5) (AI-22)
Ind.Eng. Chem. Res., Vol. 34,No. 2, 1995 653
The extreme values of C1 based on the extreme values of COare (eq AI-19) = N - CH3N - CO-
(AI-23)
Cllow= N - CH3N - Coma
(AI-24)
Clhigh
We can demonstrate, as in the case of Cl- and Clmm, that COdn and C o m a are linear relationships of C,,. Indeed, assuming that the naphthenes in a (P N) sample have (L -1) carbon atoms, the number of cycles per molecule Ncy,which is equal to the number of unsaturated centers, is
+
Ncy= (14.02745 - 12.011 - M~)/2.016
(AI-25)
instance, we must have (i) Cac L nL L 0, which means according to eq AI-13 Cac 1 [(CH3A - CHA)L - 2AY (L - 21, or (ii)nA 2 0, that is, according to eq AI-30, Cac IA.
(C) Estimation of C H k and Cat. In the previous sections, we defined the possible values of the sum C1 = CHz,, CH,,. The problem is now how to split C1 into CHzccand CH,. For a given value of C1 we will consider two extreme values of CH,,. (a) Minimum Value of CH,,. It is obviously possible to consider molecules with no branching in a,p, or y of the cycle. Hence the minimum value of CH,, is
+
CH,, = 0
-
CH,,, = C,
(AI-26)
(b)Maximum Value of Cat. Due to steric considerations, it is not possible to assume that all the carbons in a,B, or y are of the CH, type. It seems reasonable to assume that each long chain leads to a CK,, this later being bonded to a CH3N. Thus
where Mass is the mass of 100 carbon atoms present in a (P N) sample:
CH,, = nL and CH,,, = C, - nL except if CH3N < nL
where MN is the molar weight of the naphthene molecules MN = (Mass - nAMA)/nN
+
+
Mass = 15.035(CH3A CH3N) 14.027(CHfi
+
In this case
+ CH,N) + 13.019(CHA + CHN)
CH,, = CH3N and CH,,, = C, - CH3N
(AI-27) and MA is the molar weight of the alkane molecules having L carbon atoms: MA = 14.0271; COmin
+ 2.016
(AI-28)
is thus given by the following relationship:
Comin = [2
25 + -(14.027L 2.016
-
12.011)]nN
+
2.5 MAnA - 2*5 Mass (AI-29) 2.016 2.016 since nN = (N
+ C,,)/(L - 1) and
nA= (A - C,JL (AI-30)
Co-
and C o m a are thus linear functions of As a partial conclusion, we have
Cat.
(D) Definition of the Low and High Hypotheses. The purpose of this study was to predict the changes in the relative volume vs pressure. In order to know the range of variations of this volume depending on the possible values of C1, we chose the covolume of the equation of state as the parameter serving to represent those variations. In line with the low and high hypotheses, we have taken the solutions leading to the lowest and highest values of the covolume b:
b = SZ$(TJP,)
(AI-32)
With each couple of values (C1, Cac) inside the polygon (Figure 14) and in each case (CH,, maximum or minimum), b was calculated using group contribution methods for T,and P, (eqs AII-1 and AII-6). These methods require knowing the cycle size and the total number of gram moles: nT = nA TIN. To estimate the cycle size, we assume a linear variation of cy with respect to C1 between Cllowand
+
clhigh:
cllow
Icl IClhigh
and
1‘
‘lma
With the four following relationships with respect to Cac
Cllow= N
The total number of gram moles is
- CH3N - nN[2 + 4Nw1
nT = nA
100 L - A L-1
C,,, = 2nL
Clm= = 3nL + 2CH3N
- C,, +-N +C, + nN = AL L-1
(AI-31)
The total molar weight of a (P
+ C,,
(AI-34)
+ N) sample is
MT = MasdnT
(AI-35)
It then becomes possible to plot the four straight lines c i i o w , clhigh, Clmin, and C l m m VS Cat. These lines define the domain of the extreme values of C1 (Figure 14). With some (P N) samples, it is possible to reduce the area of the extreme values of C1 (Figure 14). For
+
Mass is given by relation AI-27. With a given solution (characterized by C1, CH,,,, and CH,,), the number of each group was obtained as follows:
664 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
+ CH3N)/nT (AI-36) G(2) = ( C H A + CH,,,)/n,
number of CH,: G(1) = (CH,A number of alkane CH,:
(AI-37) number of alkane CH: G(3) = (CHA
(b) Estimation of the two corresponding values of b using b = QbR(TdP,): T, and P, were estimated with the group contribution methods described in Appendix I1 using the size of the cycles given by
+ CH,,)/n, (AI-38)
number of cyclic CH,:
G(4) = (CH,N - CH,,,)/n, (AI-39)
number of cyclic CH: G(5) = (CHN - CH,,)/n, (AI-40)
+
With each (P N) sample, we squared the allowed area for C1; for each value of C1, we have calculated the two values of b corresponding to the minimum and maximum values of CH,,. Finally, the extreme values of b led to the low and high hypotheses. The resulting groups are given in Table 6a,b. (E) Outline of the Calculations Used with a Given (P N) Sample Containing Alkane with L Carbon Atoms and Naphthene with (L- 1) Carbon Atoms. The method was applied using the following steps. (1)Preliminary calculations:
+
+ C H A + CHA N = CH,N + CH,N + CHN Mass = 15.035(CH3A+ CH,N) + 14.027(CH2A+ CH,N) + 13.019(CHA + CHN) MA = 14.027L + 2.016 A = CH,A
(2) Building of the polygon limiting the possible values of C1: Using two arbitrary values of C,,, it is possible to establish the h e a r relationships cliow, Clhigh, Clmin, and Clmaxvs C,,. The following relations were used for this purpose:
n,="
N + Ca,
MN =
Ncy
nA=-
7
number of alkane CH,: number of alkane CH:
number of cyclic CH,: G(4) = (CH,N - CH2,,)/nT number of cyclic CH: G(5) = (CHN - CH,,)/n, (4) Selection of the high and low hypotheses: Among all the previous estimated values of b, the highest and lowest values were selected. The corresponding cycle size and number of each group will be used for further calculations on the complete petroleum fluid.
Appendix 11. Estimating the Properties of the Samples Analyzed by NMR The critical properties (T,, P,), the acentric factor (o), and the Rackett compressibility factor (2,) of the aromatic and paraffin and naphthene samples analyzed by NMR were estimated using group contribution methods. The group contribution methods developed by Rogalski and Neau (1990) can be used to calculate the critical temperature (T,) and the critical volume (u,), given the normal boiling point Tb and the structure of the molecule. These methods have been slightly modified to be directly compatible with the NMR results. Tb = 0.6685
A - cac L
+ S - 0.17772S2 -
m, = 0.29942
+ S,
- O.21311Sm2 (AII-2)
with 8
nN
3
v,Jcm3 = CvjGj
+
+
(3) With each couple of values ((21, C,,) inside the allowed area, (a) Calculation of the two values of CH,, and CH2,, = C1 - CH,,:
-
CH,,, = C,
CH,, = nL if CH,N > nL CH,,, = C, - nL CH,, = CH3N if CH3N < nL* CH,,, = C, - CH,N
(MI-3)
j=1
j=l
14.027 - 12.011 - MN = 2.016
+
8
S = CT,Gj and S, = CmcjGj
Cllow= N - CH3N - nN[2 4NJ; Clhigh = N - CH3N - n,[2 2.5Ncy1; Clmin= 2nL;Clmm= 3n, 2CH,N
I
+ CH,N)/n, G(2) = (CHA + CH,,,)/n, G(3) = (CHA + CH,,)/n,
G(1) = (CH,A
0.1490 x 10-4Tb1.5- 0 . 4 3 6 8 ~ n , ~(AII-1) .~
Mass - nAMA
CH,, = 0
number of CH,:
TC
A - Cac
nL = CH3A - CHA - 2
and the following number of each group
+ 19.122 -
.j=l
5.47724 x 10-3Tb1.75- 5.88309Vst (AII-4) Gj is the number of groups j in 1 gmol of the sample and Tj,mcj,and uj are the values of group parameters j . These values are given in Tables 9 and 10. The calculation of Vst (eq AII.4) is quite easy: for the aromatic samples, V,t = C,,,, otherwise Vst = 0. The critical compressibility factor 2, and the critical pressure P , were calculated by use of the following relations:
=+
z,= z, + z
+
~ T ~z3Z/112, ~ . ~
(AII-5)
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 655
P , = Z,(RTJv,)
(MI-6)
for n-alkanes
2, = 0.512 73 2, = f0.81309 x Z , = -0.384 31 for aromatics 2, = 0.347 63 2, = -0.10032 x Z , = -0.101 15 for cyclanes 2, = 0.342 68 2, = -0.12249 x Z , = -0.083 21 The Rackett factor,2 given as
lod5 (MI-7)
and the acentric factor w were
for n-alkanes
,2
= 0.3098 - 0 . 0 0 6 3 2 5 ~ , ~ / ~
for aromatics
,2
= 0.3098 - 0 . 0 0 6 5 8 3 ~ ~ " ~
for cyclanes
,2
= 0.3098 - 0.006060~,1'~
L n o = 4.62301 - 4.91329m,-113
(MI-8) (MI-9)
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Received for review May 11, 1994 Revised manuscript received September 26, 1994 Accepted October 5, 1994@ IE9403030 Abstract published in Advance ACS Abstracts, December 15,1994. @
