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An Improved CO2−Oil Minimum Miscibility Pressure Correlation for Live and Dead Crude Oils Huazhou Li,† Jishun Qin,‡ and Daoyong Yang†,* †

Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, Canada, S4S 0A2 State Key Laboratory of Enhanced Oil Recovery, Beijing, China, 100083

‡

S Supporting Information *

ABSTRACT: An improved CO2−oil minimum miscibility pressure (MMP) correlation has been successfully developed to more accurately determine the CO2−oil MMP for a wide range of live and dead crude oils. Experimentally, slim-tube tests have been conducted to determine the CO2−oil MMPs for four crude oil samples with high molecular weights of C7+ fraction. Theoretically, the newly developed CO2−oil MMP correlation is originated from a CO2−oil MMP database from the literature that covers 51 CO2−oil MMP data for various live and dead oil samples, especially those with high C7+ molecular weights. The new CO2−oil MMP correlation is expressed as a function of reservoir temperature, C7+ molecular weight, and mole fraction ratio of volatile components (N2 and CH4) to intermediate components (CO2, H2S, and C2−C6). Compared to nine commonly used CO2−oil MMP correlations in the literature, it is found that the new CO2−oil MMP correlation provides the best reproduction of the literature CO2−oil MMP data with a percentage average absolute deviation (% AAD) of 8.08% and a percentage maximum absolute deviation (% MAD) of 22.99%, respectively. To further examine its predictive capability, the new CO2−oil MMP correlation is then validated with the four experimentally measured CO2−oil MMPs in this study. The newly developed CO2−oil MMP correlation leads to the best prediction accuracy of the four measured CO2−oil MMPs with a % AAD of 4.18% and a % MAD of 7.01%, respectively.

1. INTRODUCTION CO2 injection is considered as the most promising enhanced oil recovery (EOR) technique for recovering light to medium oils in the near future. CO2 injection also plays a more important role in reducing the greenhouse emissions by sequestrating the emitted CO2 into depleted oil reservoirs. As for a successful CO2 injection project, it is desirable to achieve miscibility between crude oil and CO2 in the formation because a recovery factor of 100% can be theoretically obtained under miscible conditions. The minimum miscibility pressure (MMP) at which the crude oil and CO2 becomes miscible is a key factor because, in general, CO2 is not miscible at first contact with reservoir oils, but may achieve dynamic miscibility through multiple contacts.1 Currently, various experimental, theoretical, and empirical methods have been made available to determine the CO2−oil MMP. The existing experimental methods can be time-consuming and expensive, while theoretical models require an accurate characterization of the fluid systems by using an equation of state. In addition, empirical correlations have their own limitations for each specific scenario, though they are extremely useful for fast prescreening reservoir candidates for potential CO2 injection. Therefore, it is of fundamental and practical importance to develop reliable and accurate correlations for determining the MMP for a given crude oil−CO2 system. In the petroleum industry, the most widely used experimental methods are the rising-bubble apparatus (RBA) test2 and the slim-tube test.3 Theoretical methods mainly include the analytical key tie-line methods,1 mixing-cell simulation method,4 and EOS modeling approach.5 Various CO2−oil correlations have been made available, each of which © 2012 American Chemical Society

is correlated with different parameters that are associated with reservoir conditions and/or oil properties.6−17 The CO2−oil MMP correlation proposed by Alston et al.15 has been widely used in the oil industry due to its simplicity and accuracy. Recently, Emera and Sarma16 provided a modified version of the Alston-type CO2−oil MMP correlation by using the genetic algorithm. It is worthwhile noting that the database used by Emera and Sarma16 includes oil samples with C7+ molecular weight of up to only 268. It is not certain whether the extrapolation of the Emera-Sarma correlation16 to a higher C7+ molecular weight is accurate or not for MMP determination. A comprehensive review of the existing CO 2 −oil MMP correlations can be found in the Appendix at the end of this paper. In this paper, slim-tube tests have been conducted to experimentally determine the CO2−oil MMP for four crude oils, all of which have high C 7+ molecular weights. Theoretically, accuracy of the original Alston correlation15 and the Emera−Sarma correlation16 is first examined by predicting the CO2−oil MMPs for eight oil samples including the four oil samples studied in this work. It is found that both the original Alston correlation15 and the Emera−Sarma correlation16 cannot be extrapolated to accurately determine the CO2−oil MMP for such crude oils with high C7+ molecular weights. A modified CO2−oil MMP correlation is accordingly proposed on the basis of a CO2−oil MMP database that Received: Revised: Accepted: Published: 3516

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Table 1. Compositional Analysis Results of Eight Crude Oil Samples with High C7+ Molecular Weights in Mole Percentage component

oil A

oil B

oil C

oil D

oil E

oil F

oil G

oil H

N2 CO2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7+ total

1.77 0.63 27.12 2.11 0.88 0.07 0.66 2.07 0.47 0.93 63.29 100.00

1.971 0.343 16.739 5.901 3.843 0.401 1.295 1.769 0.604 1.576 65.558 100.000

2.129 0.481 24.691 3.718 1.626 0.170 0.805 0.650 1.328 1.223 63.179 100.000

1.01 7.17 16.29 2.89 1.29 0.13 2.16 0.45 1.40 1.63 65.58 100.00

1.252 0.897 37.543 5.476 4.196 1.104 2.902 1.360 1.875 2.734 40.661 100.000

0.166 0.166 17.195 5.892 4.528 0.892 1.441 1.053 0.650 0.206 67.811 100.000

0.39 1.41 6.35 7.43 7.13 0.89 3.73 0.74 3.50 2.67 65.76 100.00

0.96 0.07 24.05 3.72 4.36 0.00 3.38 0.00 1.55 0.72 61.19 100.00

MWC5+

301

254

283

265

285

276

263

391.0

MWC7+

310

265

293

275

327

282

281

402.7

References

this work

this work

this work

this work

21

22

23

24

includes crude oils with high C7+ molecular weight up to 402.7. The new MMP correlation takes into account the reservoir temperature, molecular weight of C7+ fraction, and mole fraction ratio of volatile components (N2 and CH4) to intermediate components (CO2, H2S, and C2−C6). The new CO2−oil MMP correlation is then validated with the four CO2−oil MMPs measured in this study. Compared to the other commonly used ones in the literature, the newly developed CO2−oil MMP correlation is not only able to most accurately reproduce the CO2−oil MMPs for the live and dead oils documented in the literature, but also leads to the best prediction of the experimentally measured CO2−oil MMPs for the four oil samples examined in this study.

2. EXPERIMENTAL SECTION In this study, the CO2−oil MMPs of four crude oil samples (i.e., oil A, oil B, oil C, and oil D) with high C7+ molecular weights are measured by using the slim-tube test method. Table 1 shows the compositional analysis results of these four oil samples together with those of another four oil samples documented in the literature. It can be seen from the compositional analysis results that all these four oil samples used in this study have a large amount of volatile components (N2 and CH4) and C7+ fraction. The molecular weights of C7+ fraction for oil A, oil B, oil C, and oil D are measured to be 310, 265, 293, and 275, respectively. The slim-tube apparatus used in this study has an outer diameter of 0.25 in, a length of 60 ft, and a total pore volume of 128 cm3. The packing material for the slim tube is 180−220 mesh quartz sand. The slim-tube tests are performed on the recombined reservoir fluid with CO2 at the given reservoir temperature. Prior to each run of the slim-tube test, the whole slim-tube apparatus is maintained at the desired reservoir temperature. Once the slim tube is saturated with the crude oil sample, CO2 is introduced to displace the oil at an injection rate of 10.0 cm3/h. For each test pressure, the hydrocarbon pore volume of CO2 injected, produced oil volume, and produced gas volume are recorded, respectively. The CO2 displacement experiments are carried out at several pressures with the temperature being maintained constant at the reservoir temperature. Figure 1 plots the oil recovery factors measured at 1.20 hydrocarbon pore volume of CO2 injected as a function of operating pressure for

Figure 1. Variation of the oil recovery factor measured at 1.20 hydrocarbon pore volume of CO2 injected at various operating pressures for oil sample A.

oil sample A. With the conventional method for a typical slimtube test,3,18 the CO2−oil MMP for oil sample A is determined to be 31.30 MPa by pinpointing the breakpoint of the oil recovery curve (See Figure 1). By applying the same methodology as for oil A, the CO2−oil MMPs for oil B, oil C, and oil D are determined to be 22.30, 27.90, and 24.10 MPa, respectively. A conservative error of 5% can be applied to the experimentally measured MMPs, though it is difficult to estimate the errors associated with the experimental measurements due to its complexity.

3. MATHEMATICAL FORMULATION 3.1. Factors Influencing the CO2−oil MMP. Reservoir temperature and oil composition have been considered to be the most important factors that affect the CO2−oil MMP.7 All the correlations in the literature suggest that the calculated MMP should increase with the reservoir temperature, while most of them employ different parameters to address the effect of oil compositions on CO2−MMP. The initial work of Rathmell et al.19 recommended that CO2 miscibility be related to the fractions of volatile components (e.g., CH4) and intermediate components (i.e., C2−C6). In general, it has been 3517

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original Alston correlation15 are employed to predict the CO2− oil MMPs for the eight oil samples (see Table 2). As can be

well-recognized that a higher volatile fraction tends to increase the CO2−oil MMP, while a higher intermediate fraction tends to decrease the CO2−oil MMP.19 Holm and Josendal7,8 argued that CO2 miscibility development does not depend on the presence of C2−C4 in the reservoir oil and that fraction of CH4 in the reservoir oil does not affect the MMP appreciably. Subsequently, a graphic CO2− oil MMP correlation that only considered reservoir temperature and C5+ molecular weight was proposed.7,8 Metcalfe and Yarborough,20 in their comment to the Holm−Josendal correlation,7,8 pointed out that any correlation for predicting CO 2 miscibility must consider the presence of light components, intermediate components in the reservoir fluids, and temperature before it can be considered sufficient for prediction purposes. The opinion of Metcalfe and Yarborough20 is supported by the experimental study of Alston et al.,15 i.e., the slim-tube recovery factor at gas breakthrough is reduced by an increased ratio of volatile to intermediate fraction in the reservoir oil, and consequently leading to a higher MMP. In addition, Alston et al.15 found that C5+ molecular weight is a better correlating parameter than API gravity. The above discussion suggests that, in addition to the reservoir temperature, an accurate CO2−oil MMP correlation should take into account the presence of volatile components, intermediate components, and heavier components in the reservoir oil. The correlation proposed by Alston et al.15 considers reservoir temperature, C5+ molecular weight, and mole fraction ratio of volatile components (N2 and CH4) to intermediate components (CO2, H2S, and C2−C4). It has been widely used in petroleum industry due to its simplicity and good accuracy. The Alston correlation shows that all three factors have a positive effect on the calculated CO2−oil MMP, which is consistent with the experimental measurements.15,19 Emera and Sarma16 used the genetic algorithm to obtain a modified version of the Alston CO2−oil MMP correlation, which is found to be superior to the other correlations in terms of its prediction accuracy. The 4-coefficient Emera−Sarma correlation16 is found to have a comparable prediction accuracy, compared to the 16-coefficient CO2−oil MMP correlation developed by Shokir.17 It is worthwhile noting that the predictive capability of any empirical CO 2 −oil MMP correlation is highly dependent on the form of the mathematical expression itself together with the database that is used to optimize the coefficients in the correlations. A CO2−oil MMP database that covers various oil samples and a broad range of temperatures is desirable for developing a versatile empirical CO2−oil MMP correlation. The database used by Alston et al.15 for developing the CO2−oil MMP correlation includes oil samples with C5+ molecular weight of up to only 240.7, while the database used by Emera and Sarma16 includes oil samples with C5+ molecular weight of up to only 247.8. The modified Alston correlation by Emera and Sarma16 is not guaranteed to be applicable to oil samples with C5+ molecular weights that are larger than 247.8. 3.2. Improved CO2−Oil Correlation. Table 1 shows the compositional analysis results of the eight medium oil samples that are examined in this study. It can be seen from Table 1 that all the eight oil samples have high C7+ molecular weights, among which oil sample H has the largest C7+ molecular weight of 402.7. To examine their applicability for crude oils with high C7+ molecular weights, the Emera−Sharma correlation16 and the

Table 2. Predicted CO2−Oil MMPs for the Eight Medium Oil Samples with the Emera−Sarma Correlation16 and the Original Alston Correlation,15 Respectively oil A B C D E F G H

TR (°C)

EXP (MPa)

Emera− Sarma16 (MPa)

101.6 99.0 108.4 101.6 104.4 85.65 82.22 115.56 66

31.30 22.30 27.90 24.10 27.121 20.6122 21.9923 25.5423 2024

46.94 31.58 43.75 33.39 40.77 29.99 23.22 32.45 38.52

%AAD

% AD

Alston et al.15 (MPa)

% AD

46.96 41.63 56.82 38.56 50.43 45.52 5.59 27.07 92.59

59.98 35.65 53.09 38.17 49.25 35.59 25.88 35.11 56.38

91.62 59.88 90.30 58.38 81.75 72.70 17.70 37.48 181.92

45.02

76.86

seen, the Emera−Sharma correlation16 predicts the CO2−oil MMP with a percentage average absolute deviation (% AAD) of 45.02% for the eight oil samples, while the original Alston correlation15 provides an even larger % AAD of 76.82%. In addition, both the Emera−Sharma correlation16 and the original Alston correlation15 overestimate the CO2−oil MMP for all the eight oil samples, which is probably due to the dominant dependence of the two correlations on the C5+ molecular weight. Therefore, neither the Emera−Sharma correlation16 nor the original Alston correlation15 is appropriate for predicting MMP for oil samples with such high C5+ molecular weights. This implies that the form of Alston model itself may need to be modified or the database used for developing the correlations should include the CO2−oil MMP data for medium oils with high C5+ molecular weights. It is essential that the Alston-type correlation be modified for achieving a better prediction of CO2−oil MMP for oil samples with high C5+ molecular weights. The original Alston correlation15 takes the following form, ⎞d ⎛x MMP = a(1.8TR + 32)b (MWC5 +)c ⎜ VOL ⎟ ⎝ x INT ′ ⎠

(1)

where TR is the reservoir temperature in °C, MWC5+ is the molecular weight of C5+ fraction, xVOL is the mole fraction of volatile components including N2 and CH4, xINT′ is the mole fraction of intermediate components including CO2, H2S, and C2−C4, and a, b, c, and d are empirical coefficients. The original Alston-type MMP correlation is accordingly modified as follows, MMP = f [ln(1.8TR + 32)]g [ln(MWC7 +)]h ⎞k ⎛ x ⎜1 + VOL ⎟ x INT ⎠ ⎝

(2)

where MWC7+ is molecular weight of C7+ fraction, xINT is the mole fraction of intermediate components including CO2, H2S, and C2−C6, and f, g, h, and k are empirical coefficients. The term ln(1.8TR + 32) is used to suppress temperature effect on the CO2−oil MMP when the reservoir temperature is relatively 3518

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relatively low temperatures, the CO2−oil MMP is strongly correlated with the reservoir temperature. At high temperatures, the strong relationship between CO2−oil MMP and reservoir temperature seems to deteriorate. This implies that other factors, such as the presence of volatile components, intermediate components, and heavier components in the reservoir oil, must be taken into account in order to more accurately predict the CO2−oil MMP, in particular, for hightemperature reservoir oils. The empirical coefficients in eq 2 are obtained with the leastsquares regression method. Consequently, the modified CO2− oil MMP correlation is finalized as follows,

high. The reason why MWC7+, instead of MWC5+, is used in the modified correlation is partially because MWC7+ is a routine measurement item in a typical compositional analysis report, while MWC5+ normally needs to be calculated from MWC7+. In addition, it is found in this study that the use of MWC7+ rather than MWC5+ even leads to a slightly better performance of the resulting eq 2 in terms of the correlation coefficient R2. The use of term ln(MWC7+) is to suppress the dominant dependence of the CO2−oil MMP correlation on the C7+ molecular weights, especially on high C7+ molecular weights. Further comparison between eq 1 and 2 reveals that the term (1 + xVOL/xINT), rather than xVOL/xINT′, is used in the modified correlation. The underlying rational for using such a modified term is to correct the inconsistent variation of the calculated MMP when the mole fraction ratio of volatile components to intermediate components is approaching zero. Equation 1 leads to a zero MMP if the mole fraction ratio is zero, which is, however, physically incorrect. Since dead oils normally do not have volatile components, that is, the volatile to intermediate ratio is zero, the term (1 + xVOL/xINT) can be deemed as a correction term that quantifies the deviation of CO2 MMP for live oils from dead oils. Supporting Information, Table S1 shows the CO2−oil MMP database which is all obtained from the literature. The CO2−oil MMP database used in this study includes a total of 51 MMP measurements, among which five data points are obtained for the four oil samples with high C7+ molecular weights (i.e., oil E, oil F, oil G, and oil H as listed in Table 1). In addition, it should be noted that 10 out of the 51 measurements are obtained for dead oil samples, while the remaining 41 measurements are obtained for live oil samples. The CO2−oil MMPs in Supporting Information, Table S1 are used to determine the coefficients in eq 2 by regression. It is worthwhile mentioning that the four experimentally measured CO2−oil MMPs are excluded in the database (see Table 2) that is used to develop the new correlation, though they are solely used to validate the newly developed CO2−oil MMP correlation. Figure 2 illustrates a scattered plot of the experimental CO2− oil MMP versus reservoir temperature. It can be seen from

MMP = 7.30991 × 10−5[ln(1.8TR + 32)]5.33647 −1

2.08836

[ln(MWC7 +)]

⎞2.01658 × 10 ⎛ x ⎜1 + VOL ⎟ x INT ⎠ ⎝

(3) 2

Equation 3 generates a fit with R = 0.9501. Table 3 listed the standard errors of the fitted coefficients. The low standard Table 3. Standard Errors of the Fitted Coefficients Appearing in Equation 3 coefficient f g h k

value

standard error −5

7.30991 × 10 5.33647 2.08836 2.01658 × 10−1

5.75 2.73 3.95 1.78

× × × ×

10−5 10−1 10−1 10−2

errors indicate a robust fit. Similar to the methodology adopted by Alston et al.15 and Emera and Sarma,16 if the predicted MMP is lower than the saturation pressure for an oil sample, the saturation pressure should be used as the MMP instead.

4. RESULTS AND DISCUSSION The newly developed CO2−oil MMP correlation, that is, eq 3, is compared with nine commonly used ones documented in the literature. Supporting Information, Table S2 shows the comparison results of the calculated CO2−oil MMPs in the literature by using the newly developed CO2−oil MMP correlation and the other nine existing ones. As can be seen from Table S2, eq 3 provides the most accurate CO2−oil MMP reproduction in comparison with the other popular correlations with an overall % AAD of 8.08% and an overall percentage maximum absolute deviation (% MAD) of 22.99%, respectively. More specifically, for the five data points of four medium-toheavy oil samples that have C7+ molecular weights larger than 281 as bolded in Table S2, the new CO2−oil MMP correlation outperforms the other nine correlations examined with a % AAD of 6.03% and a % MAD of 15.40%, respectively. The % AAD and % MAD for the light oil samples (i.e., all the oil samples excluding the four medium-to-heavy oil samples that have C7+ larger than 281) obtained with the new correlation are 8.30% and 22.99%, respectively, which are found to be far lower than those provided by the other nine correlations. As for the dead oil samples (i.e., the oil samples with zero volatile components), the new correlation leads to a % AAD of 6.50% and a % MAD of 12.85%, respectively. It is worthwhile noting that, among the other nine correlations examined, only the Yellig−Metcalfe correlation12 provides a comparable accuracy

Figure 2. Scattered plot of experimental CO2−oil MMP as a function of reservoir temperature.

Figure 2 that, in general, the experimentally determined CO2− oil MMP increases with an increase in reservoir temperature. At 3519

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14.58 34.86

34.86 12.94 6.67 3.84

46.74 56.82

20.39 25.19 26.04 25.03 75.05 91.62 13.10 22.96 9.10 18.06 28.68 41.27 8.28 21.57

MPa % AD

49.96 41.63 56.82 38.56 46.94 31.58 43.75 33.39

MPa % AD

91.62 59.88 90.30 58.38 59.98 35.65 53.09 38.17

MPa % AD

19.95 7.80 22.96 1.69 37.54 24.04 34.31 24.51

MPa % AD

18.06 10.77 1.17 6.42 25.65 24.70 28.23 25.65

MPa % AD

41.27 19.34 30.38 23.73 18.38 17.99 19.42 18.38

MPa % AD

21.57 6.17 3.51 1.86

Glaso Orr−Jensen Yellig−Metcalfe

18.83 22.29

14.40 18.72 22.29 19.92

14.15 27.07 4.18 7.01 % AAD % MAD

MPa % AD MPa

35.81 26.47 34.12 28.90 27.07 8.50 15.77 5.28

% AD MPa

22.83 24.20 23.50 22.83 2.39 7.01 6.45 0.88

% AD MPa

30.55 23.86 29.70 24.31 31.30 22.30 27.90 24.10 A B C D oil oil oil oil

EXP MMP MPa oil sample

24.55 23.68 26.92 24.55

Lee Cronquist Yuan et al.

5. CONCLUSIONS In this paper, the original Alston correlation15 for determining CO2−oil MMP has been improved and successfully applied to accurately predict oil−CO2 MMP for various oil samples. Such improvement is made possible by using a CO2−oil MMP database that covers 51 data points measured for various dead and live oil samples, in particular, including five MMPs for four oil samples with high C7+ molecular weights up to 402.7. The newly developed CO2−oil MMP correlation considers the reservoir temperature, molecular weight of C7+ fraction, and mole fraction ratio of volatile components (N2 and CH4) to intermediate components (CO2, H2S, and C2−C6). In comparison with the other nine commonly used correlations in the literature, it is shown that the newly developed CO2−oil MMP correlation provides the best reproduction of the literature CO2−oil MMP data with a % AAD of 8.08% and a

this work

Table 4. Comparison of the Predicted MMPs for the Four Oil Samples by This Work and the Other Nine Existing Correlations

Alston et al.

Emera−Sarma

Shokir

with a % AAD of 5.94% and a % MAD of 13.05% for the dead oil samples, respectively. Table 4 compares the predicted CO2−oil MMPs by using the newly developed CO2−oil MMP correlation and the other nine existing ones. It can be seen from Table 4 that, compared to all the other existing correlations, the new correlation is able to provide the most accurate prediction of the CO2−oil MMPs for these four oil samples that have high C7+ molecular weights with a % AAD of 4.18% and a % MAD of 7.01%, respectively. An accurate empirical MMP correlation should provide a prediction error that is within or close to the experimental error. As can be seen from Table 4, the prediction error of 4.18% provided by the proposed MMP correlation lies within the experimental error. This supports the predictive capability of the proposed correlation. It can be seen from the above discussion that the new CO2−oil MMP correlation expressed by eq 3 is the most suitable correlation for estimating CO2−oil MMP for various live and dead oils in comparison to the other nine popular correlations investigated. In summary, the improved performance of the new CO2−oil MMP correlation developed in this paper has been achieved through modifying the mathematical form of the original Alston correlation and expanding the CO2−oil MMP database by including the MMP measurements for crude oils with high C7+ molecular weights. It is also demonstrated in eq 3 that the C7+ molecular weight only imposes a modest impact on the CO2−oil MMP, which is contrary to the fact that most of the correlations in the literature that take the C5+ or C7+ molecular weight into account overemphasize the contribution of the C5+ or C7+ molecular weight to the CO2−oil MMP. Figure 3 shows variation of the calculated CO2−oil MMP for oil sample A as a function of the mole fraction ratio xVOL/xINT by using the new correlation eq 3. It can be observed from Figure 3 that the calculated CO2−oil MMP decreases smoothly to a certain point as the mole fraction ratio xVOL/xINT is gradually reduced to zero. Hence, the newly proposed CO2−oil MMP corrects the inconsistent variation of the CO2−oil MMP calculated by using either the original Alston correlation15 or Emera−Sarma correlation16 when the mole fraction ratio is approaching zero. The CO2−oil MMP is predicted to be zero by using either the original Alston correlation15 or Emera− Sarma correlation16 if the mole fraction ratio is zero (i.e., the oil sample is a dead oil sample). A zero CO2-MMP for a dead oil sample is physically incorrect from an experimental point of view, as is also proved by the measured CO2−oil MMPs for the dead oil samples listed in Supporting Information, Table S1.

% AD

Correlation

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The Yellig−Metcalfe correlation is shown as the following form:12 MMP = 12.6472 + 0.01553(1.8TR + 32) + 1.24192 × 10−4(1.8TR + 32)2 716.9427 − (1.8TR + 32)

The Orr−Jensen correlation is provided as

(A-3)

13

⎡ MMP = 0.101386 exp⎢10.91 ⎣ −

% MAD of 22.99%, respectively. Compared to the other nine commonly used ones, the newly developed CO2−oil MMP correlation leads to the best prediction accuracy of the CO2−oil MMPs for the four oil samples measured in this study with a % AAD of 4.18% and a % MAD of 7.01%, respectively.

MMP = 5.5848 − 2.3470 × 10−2MWC7 + + 1.1721 × 10−11MWC7 +3.73 −1.058

e786.8MWC7 +

APPENDIX

MMP Correlations for Pure CO2−Oil Systems

(1.8TR + 32)

(A-5)

where MWC7+ is C7+ molecular weight. If xINT < 18%, the Glaso correlation is expressed as follows,

In this appendix, nine commonly used MMP correlations for pure CO2−oil systems are reviewed and presented, one of which are in graphical form, while the remaining are in mathematical form. Holm and Josendal7 developed a graphical correlation for CO2−oil MMP that took reservoir temperature and molecular weight of C5+ fraction into account. The Holm−Josendal correlation is only applicable to oil samples with MWC5+ less than 240. Subsequently, Mungan9 extended the Holm− Josendal correlation to crude oils with MWC5+ as high as 340. However, it should be pointed out the Holm−Josendal correlation with Mungan’s extension has strict pressure and temperature limitations for each MWC5+, which constraints its extensive use. The Cronquist correlation10 correlates CO2−oil MMP with reservoir temperature, C5+ molecular weight, and mole fraction of the main volatile component, that is, CH4, and is expressed as follows,

MMP = 20.3251 − 2.3470 × 10−2MWC7 + −1.058

3.73 e786.8MWC7 + + 1.1721 × 10−11MWC 7+

(1.8TR + 32) − 8.3564 × 10−1x INT

(A-6)

The Alston CO2−oil MMP correlation considers the effect of reservoir temperature, C5+ molecular weight, and mole fraction ratio of volatile components (CH4 and N2) to intermediate components (CO2, H2S, and C2−C4). The original Alston correlation is expressed as follows:15 15

MMP = 6.0536 × 10−6(1.8TR + 32)1.06 (MWC5 +)1.78 ⎛ x VOL ⎞0.136 ⎟ ⎜ ⎝ x INT ′ ⎠

(A-7)

where xVOL is mole fraction of volatile components including N2 and CH4, and xINT′ is mole fraction of intermediate components including CO2, H2S, and C2−C4. Two bubblepoint pressure (Pb) corrections are also included in the original Alston correlation. If Pb < 0.345 MPa, the following alternative equation, obtained by removing the volatile to intermediate ratio term, is used,

MMP = 0.11027 (1.8TR + 32)0.744206 + 0.0011038MWC5 + + 0.0015279C1 (A-1)

where TR is reservoir temperature in °C, MWC5+ is C5+ molecular weight, and C1 is mole fraction of CH4 in the reservoir oil. The Lee correlation,11 Yellig−Metcalfe correlation,12 and Orr−Jensen correlation13 all correlate CO2−oil MMP only with the reservoir temperature. The Lee correlation is given by11 MMP = 7.3924 × 102.772 − [1519/(492 + 1.8TR )]

(A-4)

Glaso14 proposed a CO2−oil MMP correlation that considered the effect of reservoir temperature, C7+ fraction molecular weight, and mole fraction of the intermediates (C2−C6) if the mole fraction of the intermediates is less than 18%. If the mole fraction of the intermediates xINT > 18%, the Glaso correlation is expressed as follows:

Figure 3. Variation of the calculated MMP for oil sample A with mole fraction ratio xVOL/xINT by using eq 3.

■

⎤ 2015 ⎥ 255.372 + 0.5556(1.8TR + 32) ⎦

MMP = 6.0536 × 10−6(1.8TR + 32)1.06 (MWC5 +)1.78 (A-8)

In addition, if the calculated MMP by the original Alston correlation is lower than Pb, the Pb will be chosen as the MMP instead. Subsequently, Emera and Sarma16 modified the original Alston correlation by re-optimizing the coefficients based on an

(A-2) 3521

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expanded CO2−oil MMP database. The modified Alston correlation by Emera and Sarma16 is presented as follows:

10−2. For y4 = MWC5+, A34 = −3.1604 × 10−6, A24 = 1.9860 × 10−3, A14 = −3.9750 × 10−1, and A04 = 2.5430 × 101.

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MMP = 5.0093 × 10−5(1.8TR + 32)1.164 (MWC5 +)1.2785

Table S1 shows the CO2−oil MMP database used for developing the new CO2−oil MMP correlation. Table S2 compares the calculated CO2−oil MMPs for crude oils in the literature by this work and the other nine existing correlations. This material is available free of charge via the Internet at http://pubs.acs.org.

(A-9)

Similarly, if Pb < 0.345 MPa, the following equation should be used, MMP = 5.0093 × 10−5(1.8TR + 32)1.164 (MWC5 +)1.2785

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(A-10)

Also, Pb will be chosen as the MMP instead if the calculated MMP by using either eq A-9 or eq A-10 is lower than Pb. Yuan et al.6 developed a CO2−oil MMP correlation by using an analytical theory from an equation of state. The correlation, taking into account the reservoir temperature, C7+ molecular weight, and mole fraction of the intermediates (C2−C6), is given by

*Tel.: 1-306-337-2660. Fax: 1-306-585-4855. E-mail: tony. [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge a Discovery Grant awarded to D. Yang from the Natural Sciences and Engineering Research Council (NSERC) of Canada and permission from EHR Enhanced Hydrocarbon Recovery Inc. and the Research Institute of Petroleum Exploration and Development (RIPED), PetroChina to publish this paper.

+ (a7 + a8 MWC7 + − a9 MWC7 +2 − a10x INT)

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(A-11)

where values of the empirical coefficients a1−a10 are a1 = −9.8912, a2 = 4.5588 × 10−2, a3 = −3.1012 × 10−1, a4 = 1.4748 × 10−2, a5 = 8.0441 × 10−4, a6 = 5.6303 × 101, a7 = −8.4516 × 10−4, a8 = 8.8825 × 10−6, a9 = −2.7684 × 10−8, and a10 = −6.3830 × 10−6, respectively. More recently, Shokir 17 proposed a CO2−oil MMP correlation based on the alternating conditional expectation algorithm. The Shokir correlation, which is a function of reservoir temperature, C5+ molecular weight, mole fraction of the volatiles, and mole fraction of intermediates (CO2, H2S, and C2−C4), is expressed as follows,17 MMP = − 0.068616z3 + 0.31733z 2 + 4.9804z + 13.432 (A-12)

where, for pure CO2−oil system, 4

z=

∑ zi i=1

(A-13)

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and z i = A 3i yi3 + A 2iyi2 + A1i yi + A 0i

AUTHOR INFORMATION

Corresponding Author

MMP = a1 + a2 MWC7 + − a3x INT ⎛ ⎞ x INT ⎟ ⎜ + a4 + a5MWC7 + + a6 (1.8TR + 32) ⎜ MWC7 +2 ⎟⎠ ⎝ (1.8TR + 32)2

ASSOCIATED CONTENT

S Supporting Information *

⎛ x VOL ⎞0.1073 ⎟ ⎜ ⎝ x INT ′ ⎠

NOMENCLATURE a, b, c, d = empirical coefficients defined in eq 1 % AD = percentage absolute deviation % AAD = percentage average absolute deviation EXP = experimental f, g, h, k = empirical coefficients defined in eq 2 % MAD = percentage maximum absolute deviation MMP = minimum miscibility pressure, MPa MWC5+ = molecular weight of C5+ fraction, g/mol MWC7+ = molecular weight of C7+ fraction, g/mol Pb = bubble point pressure, MPa R2 = correlation coefficient RBA = rising-bubble apparatus TR = reservoir temperature, °C xVOL = mole fraction of volatiles in the reservoir oil including N2 and CH4, mol % xINT′ = mole fraction of intermediates in the reservoir oil including CO2, H2S, and C2−C4, mol % xINT = mole fraction of intermediates in the reservoir oil including CO2, H2S, and C2−C6, mol % REFERENCES

(1) Wang, Y.; Orr, F. M. Jr. Analytical calculation of minimum miscibility pressure. Fluid Phase Equilib. 1997, 139 (1−2), 101−324. (2) Christiansen, R. L.; Haines, K. H. Rapid measurement of minimum miscibility pressure with the rising-bubble apparatus. SPE Res. Eng. 1987, 2 (4), 523−527. (3) Jarrell, P. M.; Fox, C. E.; Stein, M. H.; Webb, S. L. Practical aspects of CO2 Flooding; SPE Monograph Series, Vol. 22; Society of Petroleum Engineers: Richardson, TX, 2002. (4) Jaubert, J.-N.; Wolff, L.; Neau, E.; Avaullee, L. A very simple multiple mixing cell calculation to compute the minimum miscibility pressure whatever the displacement mechanism. Ind. Eng. Chem. Res. 1998, 37 (12), 4854−4859.

(A-14)

where yi denotes the ith input variable (y1 = TR, y2 = xVOL, y3 = xINT′, and y4 = MWC5+), A3i, A2i, A1i, and A0i represents the polynomial coefficients for yi. The values of coefficients in the above Shokir correlation are provided as follows: For y1 = TR, A31 = 2.3660 × 10−6, A21 = −5.5996 × 10−4, A11 = 7.5340 × 10−2, and A01 = −2.9182. For y2 = xVOL, A32 = −1.3721 × 10−5, A22 = 1.3644 × 10−3, A12 = −7.9169 × 10−3, and A02 = −3.1227 × 10−1. For y3 = xINT′, A33 = 3.5551 × 10−5, A23 = −2.7853 × 10−3, A13 = 4.2165 × 10−2, and A03 = −4.9485 × 3522

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