ARTICLE pubs.acs.org/EF
Evaluation of Different Methodologies to Determine the Molecular Weight of Petroleum Fractions Juan J. Espada, Cristina Almendros, and Baudilio Coto* Department of Chemical and Energy Technology, ESCET, Universidad Rey Juan Carlos, c/Tulipan s/n, 28933 Mostoles (Madrid), Spain ABSTRACT: The correct characterization of petroleum fractions is crucial to correctly describe the processes in which they are involved. Most of the properties required to complete the characterization of these mixtures can be determined by well established methods. However, in the case of molecular weight, it is frequently determined by empirical correlations because of the scarcity of reliable methods. This work aims at evaluating the suitability of different techniques to calculate the molecular weight of petroleum mixtures. Cuts from three different crude oils within the whole range of boiling temperatures were analyzed by gel permeation chromatography (GPC) and high temperature gas chromatography (HT-GC). The former is a direct methodology to obtain the molecular weight. The latter, however, requires a process calculation as it yields the distillation curve, which must be converted into composition distribution. In this work, this calculation was performed by means of two continuous distribution models of different complexity. The molecular weight values obtained by GPC and HT-GC-based models were in good agreement, despite their different approach.
1. INTRODUCTION To optimize the design and operation of the processes in which petroleum mixtures are involved, a good knowledge of the process is necessary. However, experimental determination is time and money consuming, and therefore, modeling is a good tool to simulate changes in the operation conditions or feed quality.13 The key of a simulation model is to properly describe the phase equilibrium involved, and consequently, a consistent thermodynamic model based on accurate experimental information is crucial. The accuracy of a model to describe equilibrium properties depends not only on the thermodynamic basis but also on the number of pseudocomponents taken into account to describe the extremely high number of compounds in petroleum fractions. These mixtures are usually described by conventional pseudocomponent definition procedures based on distillation curves, effective in vaporliquid equilibrium processes (VLE).48 However, other schemes as model molecule approaches are required to describe liquidliquid equilibrium processes (LLE) because chemical structure has much bigger effect than boiling temperatures.9,10 The correct characterization of the pseudocomponents requires the accurate estimation of the bulk properties (boiling point, density, and molecular weight), which are seldom available. The determination of boiling point and density is well reported in the literature.11,12 However, the determination of molecular weight is not well established, and it is still an active research area, 13,14 as this parameter is required for the use of simulation programs. The molecular weight can be experimentally determined, but most of the available methods are time-consuming and show important uncertainties when heavy petroleum mixtures are involved.15 For that reason, the molecular weight of petroleum fluids is commonly determined using empirical correlations, as reported in the literature, 1620 although their application to r 2011 American Chemical Society
heavy petroleum fractions is limited. To overcome these limitations, different authors have developed methodologies to calculate the molecular weight of heavy petroleum fractions using continuous distribution models.2123 This approach allows the estimation of different properties, such as boiling temperature, molecular weight, density, or refractive index, using few experimental data. This work aims at developing reliable methodologies to determine the molecular weight of petroleum fractions within the whole boiling temperature range. The petroleum fractions obtained from three different crude oils were analyzed by gel permeation chromatography (GPC) and high temperature gas chromatography (HT-GC). Although GPC analysis is a standard procedure and has been widely used to determine the molecular weight of polymers, it has to be modified to be applied to petroleum mixtures. In this work, a calibration from low molecular weight n-alkanes (C8C50) was checked with good results. HT-GC was used to obtain the ASTM D2887 distillation curve (simulated distillation curves (SDA)).11 Even when boiling temperature and molecular weight are directly related, there was not described any method to directly determine the average molecular weight from SDA. In this work, these curves were fitted using two continuous models, one developed by Riazi22 and other supplied by Repsol,24 to obtain a distribution of boiling temperature for each mixture. Thereafter, the boiling temperature distribution was converted into composition and, finally, yielded the average molecular weight of the mixture. Both models yielded similar results, showing differences in the light and heavy Received: June 9, 2011 Revised: September 26, 2011 Published: October 07, 2011 5076
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Table 1. Characteristics of the Crude Oils Used in This Work
origin
crude oil A
crude oil B
crude oil C
West Africa
Mediterranean
America
API classification
light
light
heavy
specific gravity
0.8315
0.8489
0.9544
Table 2. Average Molecular Weight Values Obtained by GPC for the Analyzed Fractions GPC Mw (g/mol) fraction boiling range (°C)
crude oil A
crude oil B
105130
115
113
130160
125
126
130
160190 190216
137 150
138 154
137 151
216240
166
240299 299335
2. EXPERIMENTAL SECTION 2.1. Materials. Petroleum fractions (covering the boiling temperature range 105565 °C) obtained from three different crude oils provided by Repsol were used in this work. The main features of the crude oils used are summarized in Table 1. 2.2. Gel Permeation Chromatography (GPC). The average molecular weight of the different mixtures was determined by gel permeation chromatography (GPC). A Waters Alliance GPCV 2000 equipped with refractive index and viscometer detectors and three different columns (two PLgel 10 μm MIXED-B, 300 7.5 mm and a PLgel 10 μm 106 Å, 300 7.5 mm) was used. The mobile phase was 1,2,4-trichlorobenzene; the flow rate was set at 1 mL/min, and the temperature was set at 145 °C. Samples were dissolved in 1,2,4trichlorobenzene, and the concentration was around 1.21.5 mg/mL. Calibration was carried out using pure n-paraffin within the range C10C50. 2.3. Distillation Curve (SDA). The simulated distillation curves were obtained according to the ASTM D-2887 method.11 The equipment was a 3900 Varian GC with an automatic injector, a cryogenic system, a flame ionization detector (FID), and an on-column injection system. Column was a 10 m length 0.53 mm internal diameter with a 0.17 mm width silicone stationary phase. The studied mixtures were dissolved in CS2 (5 wt %) and analyzed. A mixture of n-alkanes (C5C80) was used as calibration. The distillation curve of each sample was obtained by using specific software (STARSD) provided by Varian. The analyses of the samples were performed in different conditions regarding their nature (light or heavy) as follows: • Light samples (Tb e 335 °C): Injector: 40400 °C (10 °C/min). Hold time at maximum temperature: 10.5 min. Column Oven: 35400 °C (10 °C/min). Hold time at maximum temperature: 10.5 min.
172
169
202
197
241
234
335370
264
240
272
370427
317
339
334
427538
430
433
441
538565
619
580
760
Detector: 420 °C • Heavy samples (Tb g 335 °C): Injector: 40425 °C (10 °C/min). Hold time at maximum temperature: 10.5 min. Column Oven: 35425 °C (10 °C/min). Hold time at maximum temperature: 10.5 min. Detector: 450 °C.
Figure 1. GPC calibration curve obtained from pure n-paraffin compounds.
ends of the distillation curve. These results were compared to those obtained by GPC, showing reasonable agreement.
crude oil C
3. CALCULATION PROCEDURE 3.1. Gel Permeation Chromatography (GPC). Molecular weight determination by GPC is usually based on the Universal Calibration obtained from a set of standard monodisperse polystyrene (PS) samples. The molecular weight covered by these PS samples ranges between 2 and 2000 kg 3 mol1, but depending on the application, it can be extended to 6000 kg 3 mol1. The application of such procedure to petroleum mixtures has to deal with some difficulties: • Petroleum fractions are expected to have molecular weight under 1 kg 3 mol1, and the extension of the molecular weight calibration range to those low values is difficult by means of polymeric samples. • The nature of petroleum fractions is very different from polymeric solutions, and usual calibration can lead to unconfident values. • Very often, it is not possible to obtain confident values for viscosity for non-polymeric samples by means of the GPC viscosimeter. Consequently, a different calibration procedure was carried out. As indicated, calibration was carried out using pure n-paraffin within the range C10C50, thus covering a molecular weight range of 0.140.70 kg 3 mol1. Universal Calibration was not used because of the difficulty to obtain reliable values for intrinsic viscosity. A direct correlation between retention time and molecular weight was tested. Figure 1 shows calibration results by considering both the first and second order polynomial curves. It is clearly shown how linear approach deviates systematically at low molecular weights. Standard deviations obtained by comparing bibliographic molecular weight values for the C10C50 pure n-paraffin to those calculated by linear and second-order polynomial equations were 10 and 1.2 g 3 mol1, respectively. Consequently, the second order polynomial was considered more 5077
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Table 3. Fitting Parameters and Obtained Deviations for Boiling Temperatures Calculated by the SDA-Based Models for the Analyzed Fractions Riazi P0
fraction boiling range (°C)
A
Repsol δ (%)
B
P0
A
B
C
δ (%)
Crude Oil A 105130
55.00
7.67
3.72
3.63
55.00
12.00
0.42
0.06
1.84
130160
77.80
4.31
5.44
1.04
75.00
28.52
0.24
0.09
0.79
160190
98.00
2.06
5.52
0.64
99.00
33.24
0.20
0.17
0.62
190216
150.00
0.14
3.28
1.12
133.00
27.75
0.21
0.33
0.84
216240
170.00
0.14
3.19
0.38
174.00
10.81
0.38
0.76
0.32
335370 370427
234.92 364.55
0.03 0.05
8.80 1.92
0.48 0.11
300.00 363.00
13.78 5.42
0.35 0.48
0.15 3.17
0.15 0.21
427538
366.46
0.13
2.79
0.18
382.00
12.08
0.48
1.60
0.22
538565
459.20
0.02
3.31
0.14
459.00
25.13
0.29
0.63
240299 299335
avg
0.86
0.16 0.57
Crude Oil B 4.92
10.49
5.50
35.28
0.30
0.08
7.00
6.43
1.85
57.00
35.91
0.23
0.05
0.98
0.36
4.76
0.9
111.00
21.09
0.27
0.13
0.62
140.00 146.96
0.09 0.10
5.58 7.80
0.48 0.28
155.00 145.00
14.44 46.38
0.30 0.14
0.16 0.06
0.45 0.31
240299
204.37
0.13
3.49
0.4
215.00
10.89
0.42
0.66
0.34
299335
232.60
0.02
6.10
0.46
265.00
13.62
0.36
0.11
0.11
335370
293.60
0.00
4.68
0.20
302.00
15.13
0.30
0.24
0.15
370427
358.51
0.06
1.95
0.14
355.00
7.27
0.44
2.49
0.25
427538
380.05
0.12
2.29
0.21
375.00
16.58
0.39
1.49
0.32
538565
496.09
0.07
1.46
0.90
470.00
19.54
0.26
1.61
105130
5.00
130160
50.00
160190
112.00
190216 216240
27 106 590.9
avg
1.48
0.79 1.03
Crude Oil C 105130
7.00
50.71
0.21
0.07
5.48
130160
77.80
4.31
5.44
3.35
54.50
36.05
0.24
0.02
1.03
160190
98.00
2.06
5.52
4.03
87.00
34.21
0.22
0.11
0.79
190216
65.00
6.57
4.18
65.00
53.31
0.23
0.00
2.74
216240
140.00
0.28
7.64
0.35
148.00
40.93
0.16
0.10
0.26
240299
190.00
0.19
3.63
0.42
195.00
17.27
0.35
0.42
0.53
299335 335370
228.47 286.63
0.02 0.00
6.42 6.48
0.42 0.74
228.00 299.00
44.33 17.68
0.18 0.28
0.10 0.26
0.26 0.11
370427
259.32
0.44
4.98
1.26
259.00
83.57
0.11
0.31
0.61
427538
229.05
6.34
4.17
0.89
45.00
246.97
0.12
0.11
0.8
538565
106.50
8.09
2.63
106.00
238.79
0.14
0.08
884.2
106
avg
1.83
accurate, and any further calculation was carried out by using such a calibration curve. For a given mixture, the average molecular weight was calculated from the following average definition: Mw ¼
∑ ∑
ni Mi 2 ¼ nj Mj
∑ ∑
c i Mi ¼ cj
∑ Xi Mi
and Xi is the mass fraction for the i-slice. In the above equation, it was used as the next relationship for the slice mass fraction: Xi ¼
ð1Þ
Where Mi is the molecular weight for the i-slice as determined from the retention time and the calibration curve; ci is the mass concentration measured by the refractive index detector,
2.49 1.37
ci cj
∑
ð2Þ
which represents the possibility to obtain the mass fraction distribution in terms of i-slices with molecular weight M i. To carry out further comparisons, slice mass fraction was converted into the pseudo-n-paraffin mass fraction, x, following 5078
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Figure 2. SDA for two different crude oil fractions, crude oil A 130160 °C (a) and crude oil C 370427 °C (b): experimental values (symbol) and calculated by Riazi (_____) and Repsol (............) models.
Table 4. Average Molecular Weight Values Obtained by SDA-Based Models for the Analyzed Fractions crude oil A
crude oil B
crude oil C
fraction boiling range (°C)
Riazi Mw (g/mol)
Repsol Mw (g/mol)
Riazi Mw (g/mol)
Repsol Mw (g/mol)
Riazi Mw (g/mol)
Repsol Mw (g/mol)
105130 130160
109 126
107 124
107 125
106 123
126
111 122
160190
142
142
141
138
142
136
190216
160
160
160
161
155
156
216240
178
178
178
178
177
177
240299
217
217
209
209
299335
257
255
256
256
335370
292
292
293
293
292
293
370427 427538
370 476
370 475
367 469
367 468
360 453
367 451
538565
629
626
594
624
610
587
A different equation, developed and provided by Repsol,24 was also considered in this work:
the next expression: xk ¼
Mj ¼ Mkþ1
∑ Xj
ð3Þ
Mj ¼ M k
Where the sum range covers from the j-slice whose Mj is equal to M of the k n-paraffin, M(k), to the j-slice whose Mj is equal to M of the k + 1 n-paraffin, M(k + 1). 3.2. Distillation Curves. In this work, two equations were used to obtain the molecular weight of each fraction from the SDA results. In both cases, the procedure involves the fitting of SDA, the determination of distribution function, and the averaging of molecular weight. Riazi reported a two-parameter distribution model to describe the SDA curve, given by the following equation:22 1=B A 1 ln P ¼ B x
P0 P P0 x ¼ 1 xw P ¼
P ¼ P0 þ A½ð100xw ÞB C lnð1 xw Þ
where xw is the cumulative mass fraction and P denotes the absolute boiling point (Tb). P0, A, B, and C are specific parameters of each sample obtained by fitting SDA data. Although both equations are based on similar approaches, the equation developed by Repsol requires an additional parameter to be adjusted. Specific parameters were obtained for each sample by minimizing next objective function: δð%Þ ¼ 100
ð4Þ
where xw is the cumulative mass fraction and P is the absolute boiling point (Tb). P0, A, and B are specific parameters for each sample. Values for these parameters were obtained by fitting the SDA data.
ð5Þ
1 n
∑
jPi Pi, calc j Pi
ð6Þ
which represents the percent average relative deviation, where Pi is the SDA absolute boiling point for a given xw,i, P i,calc is the corresponding absolute boiling point calculated by eq 4 or 5, and n is the number of experimental points of the SDA curve. 5079
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Figure 3. Molecular weight values calculated for the analyzed fractions: GPC (0), Riazi model (4), and Repsol equation (O).
3.3. Distribution Function. The distribution function, F, can be obtained from each analytical equation considered: ! df 1 1 P ¼ f ðxw Þ w xw ¼ f ðPÞ w dxw ¼ dP dP
¼ FðPÞ dP
ð7Þ
From Riazi, eq 4, an analytical expression is straightforwardly obtained for the distribution function, as published elsewhere.22 However, eqs 5 and 7 lead to a nonanalytical expression for the distribution function of the Repsol equation, and therefore, it was evaluated numerically by means of the mathematical commercial software Maple. A more useful relation can be obtained when the variable P, boiling temperature, is converted into molecular weight, M. The equation proposed by Marano and Holder25 for the correlation of the boiling point of n-paraffin with the number of carbon atoms was considered, and any true component was interpreted in terms of a pseudo-n-paraffin with the same boiling temperature. Consequently, any further interpretation was carried out in terms of pseudo-n-paraffin components. From eq 7, a new distribution function G(M) can be defined
according to df 1 dP
dxw ¼
!
dP dM ¼ GðMÞdM dM
ð8Þ
From the G distribution function, the mass fraction for a given pseudo-n-paraffin k can be obtained by Z Mkþ1 G dM M ð9Þ xk ¼ Z kM∞ G dM M1
Combining eqs 1 and 9, average molecular weight can be determined by Z M∞ MG dM M1 M w ¼ Z M∞ ð10Þ G dM M1
eqs 9 and 10 are equivalent to the previous eqs 3 and 1, respectively. 5080
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Figure 4. Plot of the composition given in terms of the mass fraction of n-paraffin vs the number of carbon atoms for crude oil A 130160 °C (a) and crude oil C 370427 °C (b): calculated from GPC (symbol) and calculated from the SDA with Riazi (_____) and Repsol (............) models.
4. RESULTS AND DISCUSSION 4.1. GPC Molecular Weight Values. Values for the molecular weight obtained by GPC following the procedure described are given in Table 2. As expected, similar values of molecular weight were obtained for fractions with the same boiling temperature range regardless the crude oil. A similar conclusion is obtained all along the whole boiling temperature range. This result is of special relevance because it shows the versatility of the proposed method to calculate the molecular weight of both light and heavy petroleum fractions. 4.2. SDA Molecular Weight Values. First step in this procedure is the determination of specific parameters by fitting each SDA distillation curve. Table 3 lists values for the obtained parameters and for δ(%), defined by eq 6, obtained for the fitting of all the samples. As shown in Table 3, the heavier the analyzed fraction is the better the fitting, probably as a result of the use of relative deviation. Figure 2 shows typical obtained results for the boiling temperature against the cumulative mass fraction (SDA). Experimental values and those calculated for both Riazi and Repsol equations are presented for two different crude oil fractions. Figure 2a shows the results for a low molecular weight fraction (crude oil A 130 160 °C) and reveals that both models provide a good description, but the Riazi model yields the highest differences in the low boiling temperature range. Figure 2b shows typical results for a higher molecular weight fraction (crude oil C 370427 °C), and the conclusions are similar to those given for Figure 2a. In this case, the Riazi model also yields higher differences both in the low and high boiling temperature ranges. Similar results were obtained for the rest of crude oil fractions analyzed. These results are in good agreement with those shown in Table 3, where less deviation was found for the values calculated by Repsol model, as this equation allows a better description of both the lowest and highest boiling temperature range. From eqs 4 to 10, values for average molecular weight can be calculated using the distribution function models. Table 4 summarizes the obtained values by this procedure for all the fractions. Values of average molecular weight obtained by GPC agree quite well with those calculated by SDA-based models for most of the analyzed fractions, despite the fact that both approaches are different. Likewise, similar results were obtained by both SDA
models. The difference between the molecular weight values obtained by the proposed models increases for the heavier fractions, although it should be carefully considered because of the uncertainties in the description of the highest boiling temperature range, as commented earlier in the paper. Figure 3 displays the molecular weight values calculated by GPC and the SDA models for the analyzed fractions to check the variation of the molecular weight as a function of boiling temperature. It can be observed how the obtained values for molecular weight increase as the temperature does in all cases regardless of the crude oil and the calculation method, as expected. 4.3. Mass Fraction Distribution. eqs 3 and 9 allow the obtaining of the distribution of pseudo-n-paraffin compounds in terms of mass fractions for each sample from both GPC and from SDA analyses. Figure 4 shows the obtained results for the mass fraction of a single n-paraffin vs the number of carbon atoms for two different crude oil fractions. Mass fractions calculated from GPC experimental results through eqs 2 and 3 are presented together with those calculated from the SDA with Riazi and Repsol models through eq 9. The light fraction exhibits a narrow distribution (Figure 4a) showing a good agreement between the distributions calculated by both SDA models. However, a slight displacement from the distribution obtained by GPC analysis was observed. The distribution of the heavy fraction is wider (Figure 4b); that is, the results obtained by the SDA models are similar, although higher discrepancies with respect to the GPC results were observed. The good agreement achieved between GPC and SDA-based model results reveals their suitability to calculate the average molecular weight and the distributions of the analyzed fractions, despite the differences between both approaches. The similarity between the molecular weight values calculated by the proposed models, in spite of the uncertainties observed, to describe the lowest and the highest boiling temperature range is remarkable.
5. CONCLUSIONS GPC and distillation curve analysis allows for calculating the average molecular weight of petroleum fractions within the whole range of boiling temperatures, obtaining similar results. The analysis of the distillation curves can be carried out by means of equations with different complexity yielding different 5081
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accuracy for the SDA fitting. However, the obtained molecular weight values are similar in all cases and insensitive to the quality of the SDA fitting.
’ AUTHOR INFORMATION Corresponding Author
*Phone: 34 91 4887089. Fax: 34 91 4887068. E-mail: baudilio.
[email protected].
’ ACKNOWLEDGMENT The authors thank Repsol for providing the samples used in this work. ’ REFERENCES (1) Eckert, E.; Vanek, T. Comput. Chem. Eng. 2005, 30, 343–356. (2) Van Grieken, R.; Coto, B.; Romero, E.; Espada, J. J. Ind. Eng. Chem. Res. 2005, 44, 8106–8112. (3) Espada, J. J.; Coto, B.; Pe~na, J. L. Energy Fuels 2009, 23, 888–893. (4) Coto, B.; Van Grieken, R.; Pe~na, J. L.; Espada, J. J. Chem. Eng. Sci. 2006, 61, 4381–4392. (5) Briesen, H.; Marquardt, W. AIChE J. 2004, 50, 633–645. (6) Beer, E. Nafta 1994, 45, 617–627. (7) Miquel, J.; Castells, F. Hydrocarbon Process. 1993, 72, 101–105. (8) Hariu, O. H.; Sage, R. C. Hydrocarbon Process. 1969, 48, 143–148. (9) Vakili-Nezhaad, G. R.; Modarres, H.; Mansoori, G. A. Chem. Eng. Technol. 1999, 22, 847–853. (10) Espada, J. J.; Coto, B.; Pe~na, J. L. Fluid Phase Equilib. 2007, 259, 201–209. (11) ASTM Standard D-2887-99. Annual Book of Standards; American Society for Testing Materials: West Conshohocken, PA, 2003; Vol. 5. (12) ASTM Standard D-2892-99. Annual Book of Standards; American Society for Testing Materials: West Conshohocken, PA, 2003; Vol. 5. (13) Boozarjomehry, R. B.; Abdolahia, F.; Moosavian, M. A. Fluid Phase Equilib. 2005, 231, 188–196. (14) Retzekas, E.; Voutsas, E.; Magoulasn, K.; Tassious, D. Ind. Eng. Chem. Res. 2002, 41, 1695–1702. (15) El-Hadi, D.; Bezzina, M. Fuel 2005, 84, 611–617. (16) Kesler, M. G.; Lee, B. I. Hydrocarbon Process. 1976, 55, 153– 158. (17) Riazi, M. R.; Daubert, T. E. Hydrocarbon Process. 1980, 59, 115– 116. (18) Riazi, M. R.; Daubert, T. E. Ind. Eng. Chem. Res. 1987, 26, 755–759. (19) API Technical Data Book: Petroleum Refining, American Petroleum Institute: New York, 1997. (20) Maroto, J. A. J. Pet. Sci. Eng. 2009, 69, 89–92. (21) Vakili-Nezhaad, G. R.; Modarres, H.; Mansoori, G. A. Chem. Eng. Process. 2001, 40, 431–435. (22) Riazi, M. R. Ind. Eng. Chem. Res. 1997, 36, 4299–4307. (23) Whitson, C. H. Soc. Pet. Eng. J. 1983, 23, 683–694. (24) Pe~na, J. L. Repsol Report. Personal communication. (25) Marano, J. J.; Holder, G. D. Ind. Eng. Chem. Res. 1997, 36, 1887–1894.
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