Viscosity Evaluation for NMR Well Logging of Live Heavy Oils1gjh/Consortium/resources/Viscosity Evaluation for NMR Well Logging...22 PETROPHYSICS February 2012 Viscosity Evaluation

PETROPHYSICS22 February 2012

Viscosity Evaluation for NMR Well Logging of Live Heavy Oils1

Zheng Yang2, George J. Hirasaki3, Matthias Appel4, Daniel A. Reed5

Well log NMR T2 measurements of heavy oil and bitu-men appear to be significantly longer than from laboratory results. This is likely due to gas dissolved in heavy oil and bitumen at reservoir conditions. In this work, the viscosity and laboratory NMR measurements were made on recom-bined live heavy oil and bitumen samples and on synthetic Brookfield oil as a function of dissolved gas concentra-tions. The effects of CH4, CO2, and C2H6 on the viscosity and T2 responses of these two heavy oils at various satura-tion pressures were investigated. In this work, measured T2 of live heavy oil is signifi-cantly larger than T2 of dead oil, even at the lowest pressure level (≈100 psia). Live oil T2 is found to have linear corre-

lations with both saturation pressure and gas concentration on semi-log scale for all three gases. The investigations on live oil viscosity show that, regardless of the gas type used for saturation, live oil T2 correlates with viscosity/tempera-ture ratio on log-log scale. More importantly, the changes of T2 and viscosity/temperature ratio caused by solution gas follow the same trends as those caused by temperature variations on dead oil. This conclusion holds for both bitu-men and for the synthetic Brookfield oil. In this manner, the viscosity of live heavy oil can be evaluated from the NMR response to dead oil and the correlation of T2 with viscosity/temperature.

ABSTRACT

PETROPHYSICS, VOL. 53, NO. 1 (fEBRuaRY 2012); PaGE 22–37; 39 fIGuRES

Manuscript received by the Editor June 10, 2011; revised manuscript received January 4, 2012.1Originally presented at the SPWLa 52nd annual Loggin Symposium, Colorado Springs, CO, uSa, May 14–18, 2011.2Chevron, Richmond, Ca; Email: [email protected] university, MS-362, 6100 Main St., Houston, TX 77005, uSa; Email: [email protected], 3737 Bellaire Blvd., Houston, TX 77025, uSa; Email: [email protected] Energy, 10000 Ming ave., Bakersfield, Ca 93309, uSa; Email: [email protected]©2012 Society of Petrophysicists and Well Log analysts. all Rights Reserved.

INTRODUCTION Heavy oil and bitumen are characterized by their high viscosity, and represent a worldwide known oil reserve of 6 trillion barrels (Deleersnyder, 2004). as the conventional oil reserves of the world continue to decline and the explora-tion and production technologies keep improving, heavy oil and bitumen deposits have attracted great attention from the energy industry, and will be the focus of the oil industry for years to come. Low field NMR has displayed great potential in many heavy oil well logging case studies (e.g., California, Ven-ezuela and China) (Deleersnyder, 2004). However, due to the extremely high viscosity of heavy oil, the T2 relaxation distribution has a significant component that is shorter than what can be measured by current NMR logging tools. New methods for both NMR measurement and subsequent raw data interpretation have been developed in previous work (Yang and Hirasaki, 2008), to correct the T2 relaxation times of heavy oil and bitumen. This method involved supple-menting CPMG measurements with fID measurements. Recently, laboratory NMR measurements have shown that the laboratory T2 results of bitumen samples (extracted from cores with dichloromethane solvent) appear to be remarkably shorter than the corresponding well log T2. This

is likely due to gas dissolved in heavy oil and bitumen at reservoir conditions. The T2 distribution depends on oil viscosity and dissolved gas concentration, which may vary throughout the heavy oil field. Thus, a method to determine the gas solubility and the in-situ viscosity from NMR logs would be very useful in heavy oil and bitumen reservoir development. In this work, viscosity and laboratory NMR measure-ments as a function of dissolved gas concentrations were performed on recombined live heavy oils. The effects of three different gases (CH4, CO2, and C2H6) on the viscos-ity of two different samples were investigated in a series of saturation pressures. The correlations between the saturation pressure, gas solubility, NMR T2 and live oil viscosity are established to resolve the differences between NMR log and laboratory data. The findings constitute a method for evalua-tion of in-situ heavy oil viscosity through NMR well logging.

EQUIPMENTS AND MATERIALS

The NMR spectrometer used in this work was a low field Maran-II operating at a proton resonance frequency of 2.0 MHz. a 40-mm NMR probe with a 40-mm sweet spot in length and minimum echo spacing of 0.2 ms was used for

Viscosity Evaluation for NMR Well Logging of Live Heavy Oils

PETROPHYSICS 23February 2012

most NMR measurements. The typical applied width of π/2 pulse was ≈8.3 μs and that of π pulse was ≈15.5 μs. Another 50-mm NMR probe with a minimum echo spacing of 0.4 ms was used for static gradient measurements. The temperature of the magnetic field system was controlled at 30°C with an error of ± 0.1°C. a pressure vessel manufactured by TEMCO was used for all high pressure experiments. The main body of this pressure vessel was made with PEEK and was customized to fit the 40 mm probe and the compatible temperature control system. It had an internal diameter of 22 mm and the total volume of its sample chamber was 82 ml. The synthetic heavy oil sample used in this work was the Brookfield viscosity standard #B360000 (100 percent PaO oil, commercially available from the Brookfield Com-pany), which has a viscosity of 361,700 cP at 25°C. This is even more viscous than the athabasca bitumen used in our previous work (Yang et al., 2008). The three pure gases (CO2, CH4 and C2H6) used in this work were provided by Matheson Tri-Gas with product grade of ultra High Purity.

EXPERIMENTS AND RESULTS

Viscosity of heavy oil samples

The viscosities of the bitumen sample and the Brook-field viscosity standard #B360000 were measured at differ-ent temperatures by using the Brookfield viscometer LVDV-III+. The sample temperature was controlled by an oil bath (HaaKE K35) connected to the viscometer sample holder. The temperature for the viscosity measurements ranged from 10°C to 90°C. Specifications of the Brookfield viscom-eter LVDV-III+ limited the lowest temperature that the bitu-men sample viscosity measurement could be performed at to 20°C. When the sample temperature was further lowered to 10°C, the bitumen viscosity was beyond the capability of Brookfield viscometer (≤ 3.0 × 106 cP). CPMG measurements were performed on the two heavy oil samples at temperature from 10°C to 90°C, at 10°C inter-

vals. at each temperature, the measurements were repeated three times to ensure the reliability of experimental data. The T2 values at different temperatures were evalu-ated with the interpretation method developed in our pre-vious work (Yang et al., 2008). The relationship between the viscosity/temperature ratio and T2 of the two heavy oil samples is shown in fig. 1. although the correlations are still linear on a log-log scale, they clearly deviate from pre-viously reported correlations (Morriss et al., 1997; Zhang et al., 1998; Lo et al., 2002).

Investigations on recombined live oils at differentpressures

The investigations on the recombined live oils satu-rated with CO2, CH4, and C2H6 were performed at different pressures. During the experiments with each gas, the procedure was generally divided into two stages, the pressurization stage and the depressurization stage. first, the highly pres-surized gas was introduced into the closed pressure vessel. after the gas-oil system reached equilibrium at the highest pressure level, the system pressure would be depressurized to several lower levels, step by step. at each lower pressure, the equilibrium was achieved as well. During the entire process, NMR measurements were performed periodically to track the T2 change. Proper num-ber of scans (NS) was chosen to make the signal-to-noise ratio (SNR) equal to 100. Each measurement was repeated 6 times to ensure reliability of experimental data. The system pressure inside the vessel was monitored by using Senso-Metrics pressure transducer (Model 602008, Max. 5000 psig). The investigations on the recombined live oils first started with Brookfield oil.

CO2 saturated Brookfield oil

The Brookfield oil was first recombined with CO2. In this case, the gas pressure inside the vessel was initially raised to 892 psia by injecting CO2 from the top of the pres-

Fig. 1 Relationship between T2 and viscosity/tempera-ture ratio for the two heavy oils.

0.01

0.1

1

10

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

T 2(m

sec)

Viscosity/Temperature (cP/K)

Brookfield oil

Bitumen

T2 = 37.92*(T / Visc)0.6815

R2 = 0.9956

T2 = 4.252*(T / Visc)0.4493

R2 = 0.9972

Fig. 2 T2 distribution of Brookfield oil with CO2 as a func-tion of time.

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4

0.1 1 10 100 1000 10000

Am

plitu

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T2 Relaxation Time Distribution (msec)

0 hr

21 hr

71 hr

116 hr

260 hr

568 hr

PETROPHYSICS24

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sure vessel. Then, the gas source was cut off and no more gas was added into the system afterwards. The oil sample volume was 15 ml.

The pressure vessel was vertically placed in the 30°C air bath after gas injection. In this manner, gas transferred into the oil without generated convection. The T2 distribution of Brookfield oil with dissolved CO2 was measured as a func-tion of time and the results are displayed in Fig. 2. as shown in fig. 2, the oil T2 peak markedly moves to larger values with time. It indicates that a significant amount of CO2 is dissolved into the heavy oil, even without any generated convection. The CO2 is dissolved at the gas-liq-uid interface, increases the oil density, and creates a natural convection pattern until the oil is gas saturated (Haugen et al., 2009). The recorded system pressure and the change of T2during the pressurization stage are displayed in fig. 3. as CO2 gradually dissolved into the oil, the pressure in the vapor phase kept decreasing, while the oil T2 continuously increased as more CO2 was dissolved. as shown in fig. 3, both vapor pressure and oil T2 started leveling up after 400 hours. Theoretically, the ultimate pressure at equilibrium can be measured when the Brookfield oil is completely saturated with CO2. However, in practice, the 2 phases may take an extremely long time to really reach the equilibrated state. Therefore, as an approximation, we assumed that the CO2-Brookfield oil system reached quasi-equilibrium after 568 hours and then, moved to the next stage – depressurization. The recorded pressure at 568 hours was 780.4 psia, while the T2 of Brookfield oil saturated with CO2 was 4.91 ms. afterwards, the depressurization was conducted by decreasing the pressure by 200 psi at a time till the pressure inside the vessel reached approximately 100 psia. The pres-sure vessel was kept vertical inside the 30°C air bath during the entire depressurization process. The changes of pressure

and live oil T2 were monitored in a similar way to the pres-surization phase. The NMR T2 and pressure measurements were extended for at least an extra two days after the CO2 saturated oil first reached its equilibrated value at each pressure level. This ensured that the T2 and pressure measurements were are at equilibrium. The evolutions of oil T2 and gas pressure for the CO2saturated Brookfield oil as a function of time at four differ-ent lower pressure levels are displayed in fig. 4. The values of pressure and live oil T2 at equilibrium are shown in each subplot, respectively. The time when the CO2 saturated oil first reached equilibrium at each pressure level is indicated by the vertical dashed line. The T2 distributions for the CO2 saturated oil at different pressures are shown in fig. 5. as the CO2 was depressur-

Fig. 5 T2 distribution of CO2-Brookfield oil system at dif-ferent pressures.

0

1

2

3

4

0.1 1 10 100 1000 1000

Am

plitu

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780 psia

638 psia

452 psia

273 psia

122 psia

14.7 psia

0

Fig. 3 Vapor pressure decay and oil T2 increase with time, for the CO2-Brookfield oil system.

0.1

1

10

760

780

800

820

840

860

880

900

0 200 400 600

T2 of CO

2 Dissolved Brookfield Oil

(msec)

Syste

m P

ress

ure

(psia

)

Time (Hour)

Pressure

T2

Fig. 4 Evolution of T2 and pressure for CO2 saturated Brookfield oil as a function of time at different pressures during depressurization stage.

600

700

1

10

0 50 100 150 200

Pressure (psia)

T2

of B

rook

field

Oil

(mse

c)

Time (Hour)

T2 Pressure

Peq = 638.1 psiaT2 = 3.06 msec

60

160

0.1

1

0 50 100 150

Pressure (psia)

T2

of B

rook

field

Oil

(mse

c)

Time (Hour)

T2 Pressure


400

500

1

10

0 50 100 150 200

Pressure (psia)

T2

of B

rook

field

Oil

(mse

c)

Time (Hour)

T2 Pressure


200

300

0.1

1

10

0 20 40 60 80

Pressure (psia)

T2

of B

rook

field

Oil

(mse

c)

Time (Hour)

T2 Pressure




ized from 780 psia to 122 psia, the oil T2 peak significantly decreases from large to smaller values. Moreover, even when the gas pressure is only 122 psia, the T2 of live oil is still markedly different from the oil without CO2.

CH4 saturated Brookfield oil

In the case of CH4-Brookfield oil, the gas pressure inside the closed vessel was initially 896 psia, and the oil sample volume was 15 ml. The pressure vessel was vertically placed in the 30°C air bath after the introduction of pressurized CH4. In this manner, only diffusion occurred between gas and oil. The T2 distribution of Brookfield oil with CH4 was measured as a function of time and the results are displayed in fig. 6. as shown in fig. 6, the position of the live Brookfield oil peak did not change significantly during the entire 168 hour measurement time. The extremely slow dissolution of CH4 is due to the small diffusivity of CH4 into heavy oil (Zhang et al., 2000; upreti et al., 2002). Consequently, if it occurred only by diffusion between the oil and gas phases, CH4 saturation would take an unreasonably long time. Therefore, it was necessary to boost the saturation pro-cess by generating convection on the CH4-oil system. In order to generate convection, the pressure vessel was placed on a support stand at room temperature and repeatedly turned from vertical to horizontal and then back to vertical, as shown in fig. 7. The interval between each action (from vertical to horizontal, or from horizontal to vertical) was about 60 minutes. The vessel was put back into the Maran spectrometer every night and vertically placed in the 30°C air bath over-night. The system pressure and the T2 of CH4 dissolved oil were measured every subsequent morning. The T2 distribution of CH4 dissolved Brookfield oil was measured as a function of time in the period of convection and is displayed in fig. 8.

In contrast to the observations from fig. 6, with the assis-tance of convection, the oil T2 peak increases to larger val-ues. In fig. 8, the T2 distribution has a small peak at around 1 sec. This is believed to be the response of high pressure CH4 vapor inside the pressure vessel. The T2 of pressurized CH4 was found to be around 1 sec at 1000 psia (private com-munication with Dr. arjun Kurup). The T2 of CH4 dissolved oil first reached equilibrium plateau value after 206 hours, as shown in fig. 8. The experiments continued for two extra days, and no significant changes for either pressure or T2 were observed. Therefore, the system was considered to be equilibrated at that point. During the 206 hours, the generated convection made the pressure decrease by about 34 psi, from 886 psia to 852 psia. Correspondingly, the solution of CH4 increased the oil T2from 0.36 ms to 0.69 ms.

In comparison with the observations from the case of CO2-Brookfield oil, the dissolution of CH4 increased T2 much less than CO2 did. The T2 rose from 0.36 ms to 0.69 ms at 852 psia in the case of CH4-oil, while the equilibrated T2 was 4.91 ms at 780 psia for CO2-oil. Therefore, in order to create enough difference for reliable measurement, we depressur-ized the CH4-Brookfield oil mixture directly from 852 psia to 100 psia. We followed the same experimental procedures as in the CO2 case. The pressure change was recorded and the T2 measurement was performed periodically.

Fig. 6 T2 distribution of Brookfield oil with CH4 as a func-tion of diffusion time.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.1 1 10 100 1000 100

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0hr

4hr

19hr

42hr

101hr

168hr

00

Fig. 7 Demonstration of generating convection

Fig. 8 T2 distribution of Brookfield oil with CH4 as a func-tion of time in convection.

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0.5

1.0

1.5

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0.1 1 10 100 1000 10000

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plitu

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0 hr

9 hr

85 hr

129 hr

177 hr

206 hr

251 hr

PETROPHYSICS26

Yang et al.

February 2012

The changes of T2 and the recorded pressure for the CH4saturated Brookfield oil at 111 psia are displayed in fig. 9. The shift of live oil T2 distribution at three different pressure levels is displayed in fig. 10. as the CH4 was depressurized from 852 psia to 111 psia, the T2 peak significantly shifted to shorter values. However, the T2 of CH4 saturated Brookfield oil at 111 psia still is remarkably different from the T2 of dead oil.

C2H6 saturated Brookfield oil

In the case of C2H6-Brookfield oil, the gas pressure inside the vessel was first raised to 551 psia by injecting C2H6 from the top of the pressure vessel. This pressure was less than the critical pressure of C2H6, which is 706.7 psia. The oil sample volume was 13 ml. after the initial gas injection, the diffusion behavior of C2H6 inside the Brookfield oil at 30°C was first investigated. The T2 distribution change as a function of time during the diffusion period is shown in fig. 11.

an interesting finding was that when C2H6 gradually dissolved into the oil, the T2 distribution of oil became bi-modal. This is because the dissolved C2H6 decreases the vis-cosity of oil, significantly increasing T2 of oil with C2H6 to 10 ms. Meanwhile, the T2 of oil without gas still remained at its original value of < 1 ms. as more C2H6 dissolved into the Brookfield oil, the area of the peak representing the C2H6saturated oil increased, while the area of the peak of oil with-out gas shrank correspondingly.

The explanation for the bi-modal of T2 distribution shown in fig. 11 was verified by the static gradient CPMG measurement (slice measurement) on the oil sample with the 50-mm probe. The applied echo spacing was 0.4 ms. The sample volume in this case was 13 ml, resulting in 3.4 cm in length in the pressure vessel. a regular CPMG measurement was first made on the entire sample. afterwards, the slice measurements were performed at three different positions along the sample. The available slice thickness was approxi-mately 1 cm. The midline position of each slice is displayed in fig. 12. Position #1: center of the entire sample; position #2: 1.5 cm

Fig. 9 T2 and pressure for CH4 saturated Brookfield oil as a function of time during depressurization stage.

40

90

140

0.1

1

0 20 40 60 80 100 120

Pressure (psia)

T 2of

Bro

okfie

ld O

il (m

sec)

Time (Hour)

T2 Pressure

Peq = 111 psia

T2 = 0.39 msec

Time (Hour)

Fig. 10 T2 distribution of CH4 saturated Brookfield oil at different pressure levels.

0.0

0.5

1.0

1.5

2.0

2.5

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3.5

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14.7psia

111psia

852psia

Fig. 11 T2 distribution of Brookfield oil with C2H6 as a function of time in diffusion.

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0 hr

45 hr

109 hr

132 hr

300 hr

468 hr

733 hr

Fig. 12 Static gradient T2 measurements on C2H6 dis-solved oil sample.

0

0.5

1

1.5

0.1 1 10 100 1000 10000

Am

plit

ude

f

T2 Relaxation Time (msec)

T2 Distribution of Entire Sample

Slice at Sample Center

Slice 1.5cm Down from Center

Slice 2.1cm Down from Center

#1

#2#3



down from the sample center; and position #3: 2.1 cm down from the sample center. In position #2, part of the bottom part of the slice was outside of the sample region, while in position #3, only a small part at the top of the slice was within the sample region. The results of the sliced T2 mea-surements are displayed in fig. 12, where the area for each peak approximately indicates the sample size for each slice measurement. Comparing the T2 distribution from each slice measure-ment with the T2 distribution of the entire oil sample, it is clearly shown that the sample in position #1 was the C2H6 saturated oil, while the sample of position #3 was the oil without C2H6. The T2 distribution resulting from position #2 represents the combination of C2H6 saturated oil and dead oil. after 733 hours of diffusion, convection was introduced to the C2H6-Brookfield oil system by using the same method as for the CH4 case. The change of T2 distribution as a function of time during the convection stage is displayed in fig. 13. The last measurement made during diffusion, which lasted 733 hours, is also plotted in fig. 13 as a benchmark. Comparing fig. 11 and fig. 13, we find that the convec-tion significantly boosted the dissolution of C2H6 into Brook-field oil. as shown in fig. 13, 167 hours after the generation of convection (900 hours in total after the initial pressuriza-tion), the T2 peak for dead oil completely disappeared, as the entire oil sample was saturated by C2H6. The experiment continued for another 96 hours and no significant change for either pressure or T2 was observed. In fig. 11 and fig. 13, the relatively smaller peaks located at approximately 1 sec are believed to be the T2 response of dissolved C2H6 inside the oil sample at the pres-ent pressure level. The T2 of pressurized C2H6 was found to be 10.4 sec at 560 psig and 8.7 sec at 485 psig (private com-munication with Dr. arjun Kurup). Parameters of the NMR measurements were carefully selected to avoid T2 contribu-tion from C2H6 vapor (fig. 11 and fig. 13).

after the Brookfield oil was saturated with C2H6 at 480 psia, the depressurization was conducted by decreasing the pressure by 100 psi at a time, until the pressure inside the vessel reached approximately 100 psia. The pressure vessel was kept vertical inside the 30°C air bath during the entire depressurization process. The changes of pressure and live oil T2 were monitored in a similar way to the previous two cases. The measured T2 and recorded pressure changes as a function of time for the C2H6 saturated Brookfield oil at four lower pressure levels are displayed in fig. 14. The T2 peak shift of C2H6 saturated oil at different pressures is shown in fig. 15. It is clear that the live oil T2 is significantly larger than that of the dead oil, even at the lowest pressure level. The T2 peak from dissolved C2H6, approximately at 1 sec at 480 psia, decreases to smaller values as equilibrium pressure decreases (fig. 15). Meanwhile, the area of the dis-

Fig. 13 T2 distribution of Brookfield oil with C2H6 as a function of time in convection.

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3

0.1 1 10 100 1000 10000

Am

plitu

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733 hr

757 hr

805 hr

900 hr

Fig. 14 T2 and pressure for C2H6 saturated Brookfield oil as a function of time at different pressures during depressurization stage.

220

320

1

10

0 50 100 150

Pressure (psia)

T 2of

Bro

okfie

ld O

il (m

sec)

Time (Hour)

T2 Pressure

Peq = 287 psiaT2 = 3.45 msec

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430

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T 2of

Bro

okfie

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T 2of

Bro

okfie

ld O

il (m

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Time (Hour)

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0.1

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0 50 100 150 200

Pressure (psia)

T 2of

Bro

okfie

ld O

il (m

sec)

Time (Hour)

T2 Pressure


Fig. 15 T2 distribution of C2H6 saturated Brookfield oil at different pressure levels.

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14.7 psia

106 psia

189 psia

287 psia

393 psia

480 psia

PETROPHYSICS28

Yang et al.

February 2012

solved C2H6 T2 peak shrinks as well, indicating the decrease of dissolved amount of C2H6 inside the oil sample.

Solubilities of three different gases in Brookfield oil

using appropriate pressure changes, vapor phase vol-ume and temperature, the solubility of each gas in Brook-field oil at each pressure level was calculated by using the Eq. (a.1) or Eq. (a.2) shown in appendix a. The compress-ibility factor z for each gas can be found in reference books (IuPaC, 1973; NBS, 1974; NBS, 1976). Meanwhile, an extrapolation was performed at each pressure level (as shown in appendix B) for all three gases in order to correct the effect of temperature change on the initial pressure reading. The relationship between the solubility of each gas, which was calculated with either the corrected pressure data via extrapolation or the original recorded data, and the cor-responding T2 is plotted in Fig. 16. The T2 of dead Brook-field oil is indicated by X symbols. Here, the solubility is expressed in the unit of mole gas/ml oil. as displayed in fig. 16(a) and fig. 16(b), solubilities of CO2 and CH4 calculated from the corrected pressure data are significantly smaller than those calculated from the origi-nally recorded data at each pressure level. Obviously, for both CO2 and CH4, the solubilities calculated with uncor-rected pressure trends deviate further from the value of dead oil T2, than the results calculated with corrected pressures. fig. 16(c) shows the relationship between the solubil-ity of C2H6 in Brookfield oil and its corresponding T2. The extrapolation of C2H6 solubility calculated from the cor-rected data is much closer to the value of dead oil T2, while the trend of solubility calculated from the original pressure

data deviates significantly. Especially at 106 psia, the solu-bility calculated from the originally recorded pressure data is near zero. However, as shown in fig. 15, the C2H6 satu-rated oil T2 is markedly larger than the dead oil T2. This is unreasonable and also implies that correction of the recorded pressure data is necessary. The relationship between the gas concentration in oil and the corresponding pressure at equilibrium is displayed in fig. 17 for different gases. The calculation results are from the corrected pressure data. Henry’s law is employed to fit the pressure vs. gas concentration data and the esti-mated Henry’s constant for each gas in the Brookfield oil is displayed by the corresponding fitted function in the plot. as shown in fig. 17(a), the calculated solubility val-ues in the cases of C2H6-oil and CH4-oil follow Henry’s law well. However, the originally calculated solubility of CO2 deviates significantly. The extrapolation of the CO2 data does not pass through the origin. Instead, at x-axis (y = 0), it has an intercept of 0.00109 mol gas/ml oil (indicated by the red solid dot). Similar deviation was also observed for the relationship between live oil T2 and solubility for CO2, as shown in fig. 16(d). The proposed explanation for this deviation is that, dur-ing the pressurization stage in the case of CO2-oil (800 psia at 30°C), besides the original two phases (vapor CO2 and liquid oil), a third phase, which is CO2-rich liquid with presence of heavy-hydrocarbon components, may be formed inside the CO2-heavy oil system. The L-L-V three-phase-equilibrium has been observed in both CO2/alkane system (Orr et al., 1981; Enick et al., 1985) and CO2/Crude oil system (Orr et al., 1981; Syegh et al., 1990) at near-critical condition. The extraction of heavy hydrocarbon components (as heavy as C24) into CO2-rich phase was reported by Orr et al. (1981). More importantly, the coexisting three phases were found to be able to form more easily with heavier component in the CO2/oil binary mixture (Orr et al., 1981). During the pressurization stage of CO2-oil system in this study, after the injection of the pressurized CO2 had ceased, the stripping of hydrocarbons from the oil by CO2 and the

Fig. 16 Relationship between the solubility in Brookfield oil and its corresponding T2 for three different gases.

y = 0.28e1820.9x

R² = 1

y = 0.25e1556x

R² = 1

0.1

1.0

0.E+00 2.E-04 4.E-04 6.E-04 8.E-04

T 2of

Liv

e Br

ookf

ield

Oil

(mse

c)

Solubility in Brookfield Oil (mol gas/ mL oil)

Dead Oil T2

with corrected data

with original dataCH4

(b)

y = 0.49e1404.3x

R² = 0.997

y = 0.94e1007.8x

R² = 0.992

0.1

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10

100

0.E+00 1.E-03 2.E-03 3.E-03

T 2of

Liv

e Br

ookf

ield

Oil

(mse

c)


Dead oil T2

with corrected data

with original data

C2H6(c)

y = 0.11e1192.6x

R² = 0.9923

y = 0.09e991.37x

R² = 0.996

0.1

1

10

0.E+00 1.E-03 2.E-03 3.E-03 4.E-03 5.E-03

T 2of

Liv

e Br

ookf

ield

Oil

(mse

c)

Solubility in Brookfield Oil (mol / mL oil)

Dead oil T2with corrected datawith original data

CO2

(a)

y = 0.49e1404.3x

R² = 0.997

y = 0.28e1820.9x

R² = 1

y = 0.94e1007.8x

R² = 0.992

0.1

1

10

100

0.E+00 1.E-03 2.E-03 3.E-03 4.E-03

T 2of

Liv

e Br

ookf

ield

Oil

(mse

c)


Dead oil T2C2H6-OilCH4-OilCO2-Oil

(d)

Fig. 17 Relationship between the gas concentration in Brook-field oil and the equilibrated pressures. Here, (a) solubility data in the case of CO2-Oil deviates from Henry’s law; (b) solubility data for CO2-Oil is corrected to follow Henry’s law.



dissolution of CO2 into oil occurred simultaneously. as more heavy hydrocarbon components were present in the CO2vapor phase, a CO2-rich liquid phase could have gradually formed inside the pressure vessel. However, simply by moni-toring the pressure change in vapor phase, we cannot tell the difference between the pressure decay from the dissolution of CO2 into oil and the pressure decay caused by condensation of CO2 into the CO2-rich liquid phase. The justification of the proposed interpretation of the two liquid phases is dem-onstrated in appendix C, by showing that the z factor of CO2with the adjustment matches with Henry’s law.

The recorded pressure decay due to the condensation of CO2 in the second liquid phase was mistaken as that caused by the solution of CO2 into the oil phase. as a result, the cal-culated solubility of CO2 at the highest pressure level could be significantly larger than its “true” value. Subsequently, as the pressure decreases, the CO2-oil system moved away from the three-coexisting-phases region, and the data for the pressure difference at each lower pressure level could be correctly obtained. However, based on the method for solubility calculation in this work (appen-dix a), any impact on the solubility at the highest pressure will uniformly affect the calculation of solubility at each lower pressure. Consequently, as shown in fig. 17(a), the calculated solubility of CO2 in Brookfield oil appears to be overestimated with a constant value at each pressure level, but still linearly correlates the pressure at equilibrium and the solubility in the oil. In order to correct the overestimation of CO2 solubility, we uniformly subtracted the excess value at the intercept of x-axis from the originally calculated solubility at each pres-sure and re-plotted the corrected CO2 data in fig. 17(b). It is clear that the corrected CO2 data now follows the Henry’s law well.

The corrected CO2 data are also employed in the rela-tionship of live oil T2 and CO2 solubility. Comparing fig. 16(d) and fig. 18, as the solubility of CO2 was corrected via the method demonstrated in fig. 17, the data trend of T2vs. corrected solubility of CO2 now extrapolates well to the dead oil value. The relationship between live oil T2 and its corresponding gas solubility is closely linear on a semi-log scale for all three gases. furthermore, an interesting finding in fig. 18 is that the relationship between live oil T2 and gas solubility appears to closely follow a similar trend, regard-less of the gas type used for saturation.

Viscosity measurements on live Brookfield oil

The viscosity of live Brookfield oil with different gases was measured at different pressures by using a capillary viscometer. all the measurements were performed at room temperature (22°C). The relationship between fluid viscosity and flow rate, measured pressure drop and tube dimension is governed by the Hagen-Poiseuille equation

Here, μ is oil viscosity, Q is flow rate, L is length of tube, and R is inner radius of the tube. The capillary viscometer was first tested with dead Brookfield oil at four different flow rates. The average value obtained by using the capillary viscometer was 468,996 cP at room temperature. Meanwhile, the viscosity measured with the Brookfield viscometer at the same temperature was 481,000 cP, only a 2.5 percent difference from the average value from the capillary viscometer. The viscosity of live Brookfield oil saturated by C2H6 was measured at five different pressure levels. In the case of

Fig. 18 Relationship between the solubility of CO2 in Brookfield oil and its corresponding T2. Here, the cor-rected data for CO2-Oil extrapolates well to dead oil value.

T2 o

f Liv

e B

rook

fi eld

Oil

(mse

c)

Fig. 19 Relationship between the T2 of Brookfield oil and the viscosity/temperature ratio.

0.1

1

10

100

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

T 2R

elax

atio

n Ti

me (

mse

c)


C2H6-Oil

CO2-Oil

CH4-Oil

Dead Oil at 22C

Dead Brookfield Oil at Different T

µ =P0 − PL( ) ⋅π ⋅R4

8 ⋅Q ⋅ L .

PETROPHYSICS30

Yang et al.

February 2012

either CO2-oil or CH4 -oil, the live oil viscosity measurement was performed at one pressure level. The measured viscos-ity values of Brookfield oil under different conditions are summarized in fig. 19 and the data of dead oil viscosity at different temperatures are also plotted for comparison. The investigation on the viscosity of live Brookfield oil shows that, regardless of the gas type used for saturation, the live oil T2 correlates with viscosity/temperature ratio on a log-log scale. More importantly, as displayed in fig. 19, the changes of T2 and viscosity/temperature ratio caused by solution gas follow the same trend as those caused by tem-perature variations on the dead oil. The investigations on the recombined live bitumen were conducted with the same procedures developed in the case of Brookfield oil.

C2H6 saturated bitumen

The recombination experiments on bitumen first started with C2H6. The total bitumen sample volume in this work was 13 ml. The vessel containing bitumen and C2H6 was first placed vertically in the 30°C air bath so that only diffusion occurred to the C2H6 dissolution into bitumen. The pressure change during the diffusion stage was recorded and was used for the extrapolation required to remove the tempera-ture effect on the initial pressure reading (appendix B). as shown in fig. 20, the pressure decreases sharply within the initial 40 minutes. This is mainly due to the sig-nificant temperature change after pressurized gas injection. after the first 60 minutes, the recorded pressure started to level out. The diffusion stage lasted for 130 minutes and the convection was introduced to the C2H6-bitumen system immediately afterwards. The T2 response of C2H6 dissolved bitumen during the entire pressurization stage was measured as a function of time and is displayed in fig. 21. The experi-mental procedures are similar to those used in the Brookfield oil case.

Similar to the observations in the work on C2H6-Brook-field oil, the bimodal peak for the T2 distribution of bitumen also appeared as the dissolution of C2H6 gradually proceeded. The relatively small peaks at approximately T2 = 2 sec are the responses from the dissolved C2H6 inside the bitumen sample at the present pressure level. Here, the selection of NMR parameters was the same as for the work on Brook-field oil; therefore, the contribution from C2H6 vapor to T2 is negligible. as shown in fig. 21, the dissolution of C2H6 in bitumen reached saturation after 308 hours. The measurements for both T2 and pressure continued for an extra 121 hours there-after and no significant changes were observed. The T2 peak of C2H6 saturated bitumen is much broader than in the T2 distribution of C2H6-Brookfield oil. further-more, even after complete saturation of C2H6, the bitumen

Fig. 20 Pressure change of C2H6- bitumen during the diffusion stage.

515

520

525

530

535

0 20 40 60 80 100 120 140

Pres

sure

l (ps

ia)

Time (min)

Initial diffusion stage

Fig. 21 T2 distribution of bitumen with dissolved C2H6 during pressurization stage.

0.0

0.5

1.0

1.5

0.1 1 10 100 1000 10000

Am

plitu

de f


Dead Oil

23 hrs

120 hrs

141 hrs

213 hrs

308 hrs

391 hrs

429 hrs

Fig. 22 T2 and pressure for C2H6 saturated bitumen dur-ing depressurization stage.

330

350

370

390

1

10

0 20 40 60 80 100 120

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 370 psia

160

180

200

220

0.1

1

10

0 20 40 60 80

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 200 psia

60

80

100

120

0.1

1

10

0 20 40 60 80 100 120

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 106 psia

230

250

270

290

1

10

0 20 40 60 80 100

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 278 psia



still has a certain amount of components relaxing faster than the first applied echo spacing (0.2 ms). This is because the bitumen sample has much more complex components and even higher viscosity than synthetic Brookfield oil. after the bitumen was saturated with C2H6 at ≈ 475 psia, the depressurization was conducted by decreasing the pres-sure by 100 psi at a time till the pressure inside the vessel decreased to approximately 100 psia. The measurements of pressure and T2 during the depressurization stage were per-formed in the same way as for the work on the Brookfield oil. The recorded pressure and T2 for the C2H6 saturated bitu-men at different pressure levels are displayed in Fig. 22. The T2 values shown in each plot are evaluated through regular CPMG data without specified M0 and lognormal distribution model. [The mean value of T2 for each pressure was supple-mented with fID measurements (Yang et al., 2008)]. The T2distributions of C2H6 saturated bitumen from regular CPMG data interpretations are displayed in fig. 23. as crude oil, the major bitumen T2 spectra peaks are much broader than those of the synthetic Brookfield oil.

CO2 saturated bitumen

The gas-oil mixing experiments for the CO2 saturated bitumen were conducted in the same way as for the C2H6-bitumen. Due to sample loss during the previous measure-ments, the total bitumen volume used in the CO2-bitumen case was 9.5 ml. at the beginning of the mixing experiment, the pressure vessel was placed in the 30°C air bath until no significant temperature-related pressure decay was observed. In this manner, enough pressure data was collected for extrapola-tion during the diffusion stage. afterwards, the convection was introduced to the CO2-bitumen system via rocking of the vessel as shown in fig. 7. The T2 distribution changes of bitumen during the CO2dissolution process are shown in fig. 24. The number of scans (NS) was adjusted to reach SNR = 100. The applied

width of π/2 pulse and π pulse were tuned before each mea-surement. as shown in fig. 24, the CO2 dissolved in bitumen reached equilibrium after 391 hours. Thereafter, the gas dis-solution experiment continued for an extra 79 hours and no significant change of either T2 distribution or pressure in the vapor phase was observed. Equilibrium was confirmed at this point. after the bitumen sample was saturated with CO2 at 709 psia, the depressurization was conducted by decreasing the pressure by 150 psi at a time till the pressure inside the ves-sel decreased to approximately 100 psia. The recorded pres-sure and T2 for the CO2 saturated bitumen at different pres-sure levels are displayed in fig. 25. The vertical dashed lines in the plot indicate the time when CO2-bitumen first reached equilibrium at each pressure. The T2 distributions of CO2 saturated bitumen at differ-ent pressure levels are displayed in Fig. 26. All the distribu-tions shown in the plot are from regular CPMG data inter-pretations.

Fig. 23 T2 distribution of C2H6 saturated bitumen at dif-ferent pressure levels.

0.0

0.5

1.0

1.5

0.1 1 10 100 1000 10000

Am

plitu

de f


Dead oil

106psia

200psia

278psia

370psia

475psia

Fig. 24 T2 distribution of bitumen with dissolved CO2 during pressurization stage.

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000 1000

Am

plitu

de f


Dead Oil

21 hrs

97 hrs

174 hrs

284 hrs

391 hrs

470 hrs

00

Fig. 25 T2 and pressure for CO2 saturated bitumen dur-ing depressurization stage.

380

390

400

410

420

0.1

1

10

0 10 20 30 40 50

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 414 psia

90

100

110

120

130

140

0.1

1

0 10 20 30 40 50 60 70

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 120 psia

270

280

290

300

310

0.1

1

10

0 10 20 30 40 50 60 70

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 300 psia

550

560

570

580

590

1

10

0 10 20 30 40 50 60

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 583 psia

PETROPHYSICS32

Yang et al.

February 2012

The T1 distributions of the CO2 saturated bitumen at the same equilibrated pressures were also obtained, and shown in fig. 27. an inversion recovery sequence with 20 differ-ent recovery times logarithmically spaced between 30 μsec and 5 sec was employed for the measurements. The T1 dis-tributions for live bitumen at different pressure levels are displayed in fig. 27. The variations of T1 distribution with pressure are much smaller than the T2 change of live bitumen, as shown in Fig. 26. In other words, the change of bitumen viscosity (caused by the change of CO2 solubility at different pres-sure) has much more effect on the T2 response than on T1. This observation matches the results obtained in previous work on other heavy oil samples (Hirasaki et al., 2003).

CH4 saturated bitumen

The same experimental procedures for both diffusion and convection were applied in the case of CH4-bitumen. The total sample volume used in measurements was 7.6 ml.

The T2 distributions measured during the CH4 dissolu-tion process are shown in fig. 28 as a function of time. The number of scans (NS) was adjusted to reach SNR = 100. The applied width of π/2 pulse and π pulse were tuned before each measurement. as shown in fig. 28, the T2 changes caused by the dis-solved CH4 are significantly smaller than those observed with the other two gases. CH4 reached saturation in bitumen after 331 hours. The measurements continued for an extra 97 hours thereafter and no significant changes of T2 distribu-tion and pressure were observed. as mentioned in the CH4-Brookfield oil, the smaller T2 peaks at approximately 1 sec are from the CH4 vapor inside the vessel. Due to the much smaller solubility of CH4 in bitumen, the depressurization was only conducted at two pressures (fig. 29). The T2 distributions of CH4 saturated bitumen at different pressure levels are displayed in fig. 30. all the dis-tributions are from regular CPMG data interpretations. The minor peaks between 100 ms and 1000 ms are from free CH4in the vapor phase. as the pressure decreases, the gas peak moves to smaller T2 value and shrinks to smaller area.

Solubilities of three different gases in bitumen

The solubility of each gas in the bitumen was calculated by using Eq. (a.1) and Eq. (a.2). The relationship between

Fig. 26 T2 distribution of CO2 saturated bitumen at differ-ent pressure levels.

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000 10000

Am

plitu

de f


Dead oil

120 psia

300 psia

414 psia

583 psia

709 psia

Fig. 27 T1 distribution of CO2 saturated bitumen at differ-ent pressure levels.

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000 10000

Am

plitu

de f

T1 Relaxation Times (msec)

T1 at 709 psia

T1 at 583 psia

T1 at 414 psia

T1 at 300 psia

T1 at 120 psia

Fig. 28 T2 distribution of bitumen with dissolved CH4 dur-ing pressurization stage.

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000 10000

Am

plitu

de f


Dead oil

19 hrs

141 hrs

263hrs

331hrs

428hrs

Fig. 29 T2 and pressure for CH4 saturated bitumen dur-ing depressurization stage.

490

500

510

520

530

540

0.1

1

0 20 40 60 80

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 517 psia

110

120

130

140

150

0.1

1

0 20 40 60 80

Pressure (psia)

T 2of

bitu

men

(mse

c)

Time (Hour)

T2 Pressure

Peq = 131 psia



gas concentration in bitumen and its corresponding equili-brated pressure is plotted in Fig. 31. Henry’s law is employed to fit the pressure vs. gas con-centration data for all three gases. The two solid lines are the fitted curves to the C2H6-bitumen and CH4-bitumen data, respectively. The dashed line is the fitting to the CO2-bitu-men data. The fitted functions are displayed in the plot. as shown in fig. 31(a), the behaviors of the three gases in the bitumen are quite similar to those in Brookfield oil (fig. 17). C2H6 and CH4 closely follow Henry’s law while, CO2 signifi-cantly deviates from it. The calculated solubilities for CO2 in bitumen appear not to extrapolate to zero. The proposed explanation for this phenomenon has been discussed in the work on Brookfield oil. The justifica-tion of the interpretation is shown in appendix C. In order to correct the overestimation for the calculated CO2 solubil-ity in bitumen, we uniformly subtract the excess value at the intercept of x-axis from the originally calculated solu-bility at each pressure and re-plot the corrected CO2 data in fig. 31(b). It is clear that the corrected CO2 data follows the Henry’s law well. The corrected CO2 data are also employed in the rela-tionship of live bitumen T2 and CO2 solubility. as shown in fig. 32(a), the originally calculated data from CO2-bitumen significantly deviate from the dead oil values. However, as the solubility of CO2 was corrected via the method shown in fig. 31, the data trend of T2 vs. corrected solubility of CO2 extrapolates well to the dead bitumen value. The rela-tionship between live bitumen T2 and its corresponding gas solubility is closely linear on a semi-log scale for all three gases. furthermore, similar to the observations in the work on Brookfield oil, the relationship between the live oil T2 and gas solubility shown in fig. 32(b) appears to closely follow similar trend, regardless of the gas type used for saturation.

Viscosity measurements on live bitumen

The viscosity of live bitumen with different gases was measured using the same method as for Brookfield oil. The

viscosity measurements on the C2H6 saturated bitumen were performed at three pressure levels. However, due to the lim-ited volume of available bitumen sample, the viscosity of live bitumen saturated by either CH4 or CO2 was only mea-sured at one pressure level. The results for live bitumen vis-cosity with three different gases are shown in fig. 33.

Comparing fig. 33 with fig. 19, we can find that, although the crude bitumen sample is totally different from synthetic Brookfield oil, the live oil T2 still correlates with the viscosity/temperature ratio on a log-log scale, regardless of the gas type used for saturation. as in the case of Brook-field oil, we observe that the changes of T2 and viscosity/temperature ratio caused by solution gas follow the same trend as those caused by temperature variations on the dead bitumen. Data from other reference papers (Vinegar et al., 1991; LaTorraca et al., 1998; McCann et al., 1999; Zhang, 2002) are employed to compare the bitumen and Brookfield oil data obtained in this work and shown in fig. 34. Here, the relaxation time and viscosity/temperature ratio are normal-ized with respect to 2 MHz (Yang et al., 2008, Hirasaki, et al., 2003).

Fig. 30 T2 distribution of CH4 saturated bitumen at differ-ent pressure levels.

0

0.2

0.4

0.6

0.8

1

0.1 1 10 100 1000 10000

Am

plitu

def


Dead oil

131 psia

517 psia

914 psia

Fig. 31 Relationship between the gas concentration in Bitu-men and the equilibrated pressures. Here, (a) solubility data in the case of CO2-Bitumen deviates from Henry’s law; (b) solu-bility data for CO2-Bitumen is corrected to follow Henry’s law.

Fig. 32 Relationship between the gas solubility in bitumen and its corresponding T2. Here, (a) data from CO2-bitumen is deviated from dead oil value; (b) corrected data for CO2-bitumen well extrapolates to dead oil value.

PETROPHYSICS34

Yang et al.

February 2012

The bitumen data are highlighted in red, while the data from Brookfield oil are highlighted in blue. as shown in fig. 34, the T2 data from the synthetic Brookfield oil devi-ate from the crude oil data. However, either T2 or T1 data obtained from the bitumen follow well the trend of reference data from other crude oils.

Relationship between pressure and live oil T2

The equilibrium pressure correlates well with the live oil T2 of the two heavy oils. It is found that the relationship between pressure and T2 is closely linear on a semi-log scale for all three reservoir gases, as shown in fig. 35. It is clear that C2H6 has the most significant influence on T2, while CH4exerts the least T2 change at the same pressure level. More-over, the data trends from any of the three gases extrapolate well to the dead oil T2 value (indicated by an X).

CONCLUSIONS

The T2 of live oil is significantly larger than the T2 of dead oil, even at the lowest pressure level in this work (≈100 psia). The relationships between equilibrium pressure and live oil T2 of both two heavy oils are found to be closely linear on a semi-log scale for all three reservoir gases. C2H6has the most significant influence on the T2, while CH4 exerts the least T2 change at the same pressure level. The calculated solubilities of both CH4 and C2H6 in the two different heavy oils follow Henry’s law well. However, the calculation for CO2 is significantly overestimated. This may be due to a CO2-rich liquid phase where heavy-hydro-carbon components could have formed inside the vessel at the highest pressures. The relationship between calculated gas solubility and the corresponding live oil T2 is found to be closely linear on a semi-log scale for all three gases. With the correction by Henry’s law in the cases of CO2, the relationship between the live oil T2 and gas solubility appears to closely follow similar trend for each oil, regardless of the gas type used for saturation. The changes of T2 and viscosity/temperature ratio caused by solution gas follow the same trend as those caused by temperature variations on dead oil. Moreover, this finding holds for both synthetic and crude oils. In this manner, the viscosity of live, heavy oil can be evaluated from the NMR response of dead oil with the correlation of T2 with viscosity/temperature.

ACKNOWLEDGMENTS

The authors are grateful to Shell E&P Company and the Rice Consortium of Processes in Porous Media for their financial support, and gratefully acknowledge Harold Vin-egar for proposing this research.

Fig. 33 Relationship between the T2 of bitumen and the viscosity/temperature ratio.

0.01

0.1

1

10

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

T 2Re

laxa

tion

Tim

e (m

sec)


C2H6-Bitumenl

CO2-Bitumenl

CH4-Bitumen

Dead Bitumen at Different T

Fig. 34 Relationship between normalized T2 and nor-malized viscosity/temperature ratio for different oils.

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05

Nor

mal

ized

Rel

axat

ion

Tim

e (m

sec)

Normalized Viscosity/Temperature (cP/K)

T2[LaTorraca et al](2 MHz)

T1[LaTorraca et al](2 MHz)

T2[McCann et al](2MHz)

T1[McCann et al](2 MHz)

T2[Vinegar et al](2 MHz)

T1[Vinegar et al](80 MHz)

T2[Zhang et al](2 MHz)


T2[Zhang et al](7.5 MHz)

T1[Zhang et al](7.5 MHz)



Corr. by Morriss et al

Dipole-dipole Corr.

T2[Bitumen, Dead](2 MHz)

T2[Bitumen, Live](2 MHz)

T1[Bitumen, Live](2 MHz)

T2[Brookfield, Dead](2 MHz)

T2[Brookfield, Live](2 MHz)

T1

T2

Fig. 35 Relationship between equilibrium pressure and the corresponding live oil T2 for different gases.

y = 0.1369e0.0065x

R² = 0.9984y = 0.2064e0.0027x

R² = 0.9887

y = 0.2367e0.0006x

R² = 0.9775

0.1

1

10

0 200 400 600 800 1000

T 2of

Liv

e Bi

tum

en (m

sec)

Pressure (psia)

CO2-Bitumen

CH4-Bitumen

C2H6-Bitumeny = 0.43e0.0071x

R² = 0.9967 y = 0.40e0.0032x

R² = 0.9998

y = 0.36e0.0008x

R² = 1

0.1

1

10

100

0 200 400 600 800 1000

T 2of

Liv

e B

rook

fiel

d O

il (m

sec)

Pressure (psia)

CO2-Oil

CH4-Oil

C2H6-Oil



REFERENCES

Deleersnyder, M., 2004, In-Situ heavy-oils viscosity determinationusing NMR and conventional logs: application to a real exam-ple, Paper 86939: Society of Petroleum Engineers, presented at the SPE International Thermal Operations and Heavy Oil Sym-posium and Western Regional Meeting, Bakersfield, California, March 16–18.

Enick, R., Holder, G. D. and Morsi, B. I., 1985, Critical and threephase behavior in the carbon dioxide/tridecane system: Fluid Phase Equilibria, vol. 22, no. 2, p. 209–224.

Haugen, K. B. and firoozabadi, a., 2009, Mixing of two binarynon-equilibrium phases in one dimension: AIChE Journal, vol. 55, no. 8, p. 1930–1936.

Hirasaki, G. J., Lo, S. W. and Zhang, Y., 2003, NMR propertiesof petroleum reservoir fluids: Magnectic Resonance Imaging, vol. 21, no. 3–4, p. 269–277.

IuPaC, 1973, International Thermodynamic Tables of theFluid State Carbon Dioxide: Pergamon Press, London, uK.

LaTorraca, G. a., Dunn, K. J., Webber, P. R. and Carlson, R. M.,1998, Low-field NMR determinations of the properties of heavy oils and water-in-oil emulsions: Magnetic Resonance Imaging, vol. 16, no. 5, p. 659–662.

Lo, S., Hirasaki, G. J., House, W. V. and Kobayashi, R., 2002, Mixing rules and correlations of NMR relaxation time with viscosity, diffusivity and gas/oil ratio of methane/hydrocarbon mixtures: SPE Journal, vol. 7, no. 1, p. 24–34.

McCann, K. E., Vinegar, a. and Hirasaki, G. J., 1999, NMR analysisof crude oil and pure hydrocarbon fluids (private communica-tion).

Morriss, C. E., freedman, R., Straley, C., Johnston, M., Vinegar, H. J. and Tutunjian, P. N., 1997, Hydrocarbon saturation and viscosity estimation from NMR logging in the Belridge Diato-mite: The Log Analyst, vol. 38, no. 2, p. 44–59.

NBS, 1976, The thermophysical properties of ethane, from 90 to600K at pressures to 700 bar: NBS Technical Note 684, Boulder, Colorado.

NBS, 1974, The thermophysical properties of methane, from 90 to500K at pressures to 700 bar: NBS Technical Note 653, Boulder, Colorado.

Orr, f. M. Jr., Yu, a. D. and Lien, C. L., 1981, Phase behavior ofCO2 and crude oil in low-temperature reservoirs: SPE Journal, 480–492.

Syegh, S. G., Rao, D. N., Kokal, S. and Najman, J., 1990, Phase beha-viour and physical properties of Lindbergh heavy oil/CO2 mix-tures: Journal of Canadian Petroleum Technology, vol. 29, no. 6, p. 31–39.

upreti, S. R. and Mehrotra, a. K., 2002, Diffusivity of CO2, CH4,C2H6, and N2 in athabasca Bitumen: Canadian Journal of Chemical Engineering, vol. 80, p. 116–125.

Vinegar, H. J., Tutunjian, P. N., Edelstein, W. a. and Roemer, P. B.,1991, Whole core analysis by 13C NMR, SPE Formation Evalu-ation, vol. 6, no. 2, p. 183–189.

Yang, Z. and Hirasaki, G. J., 2008, NMR measurement of bitumenat different temperatures: Journal of Magnetic Resonance, vol. 192, no. 2, p. 280–293.

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APPENDIX A

Gas solubility calculation

The method for calculating gas solubility from pressure data is described as follows:

Pressurization stage

after pressurization, the pressure inside the closed sys-tem decreases due to the dissolution of gas into the oil. In this stage, according to mass balance, the gas amount removed from the vapor phase equals the gas amount transferred into the oil phase. In this manner, the gas solubility sg in the oil can be calculated by the following equation:

Here, Vg is the volume of vapor phase inside the pressure vessel, and Voil is the volume of oil sample inside the pres-sure vessel. assuming the swelling effect of oil in this work is negligible, both Vg and Voil are constant. P0 is the start-ing pressure, and Peq is the pressure at equilibrium. z0 is the compressibility under the starting pressure P0, and zeq is the compressibility under the equilibrium pressure Peq.

Depressurization stage

after each depressurization, the pressure inside the closed system increases due to the release of dissolved gas from inside the oil into the gas vapor. In this stage, according to mass balance, the gas amount transferred into the vapor phase after each depressurization equals the gas amount removed from the oil phase. In this manner, the gas solubil-ity sg in the oil can be calculated by the following equation:

Here, sg,i is the solubility at current pressure level, sg,i−1 is the solubility at previous pressure level right before the depres-surization, Vg is the volume of vapor phase inside the pres-sure vessel, and Voil is the volume of oil sample inside the pressure vessel. assuming the swelling effect of oil in this work is negligible, both Vg and Voil are constant. P0 is the

sg =P0 ⋅Vgz0 ⋅R ⋅T

−Peq ⋅Vgzeq ⋅R ⋅T

⎛

⎝⎜

⎞

⎠⎟ Voil . (a.1)

sg , i = sg , i−1 −Peq ⋅Vgzeq ⋅R ⋅T

−P0 ⋅Vgz0 ⋅R ⋅T

⎛

⎝⎜

⎞

⎠⎟ Voil . (a.2)

PETROPHYSICS36

Yang et al.

February 2012

starting pressure, and Peq is the pressure at equilibrium. z0 is the compressibility under the starting pressure P0, and zeq is the compressibility under the equilibrium pressure Peq.

APPENDIX B

Extrapolation for initial pressure

at the beginning of each pressurization or depressuriza-tion, a big pressure change inside the pressure vessel within a relatively short time inevitably occurs. Consequently, the system is temporarily either heated by the pressurization or cooled by the depressurization, and then return to the tem-perature of the air bath (30°C). In this manner, significant pressure fluctuation is caused by the temperature change and displays non-realistic P0 for solubility calculations. There-fore, the removal of the temperature influence on pressure reading at the start of each pressure level is necessary. In this work, extrapolation was employed to make the correc-tion. The case of C2H6-Brookfield oil is taken to illustrate the extrapolation for the pressure data during the initial period of either pressurization or depressurization stage. fig. B.1 shows the analysis and extrapolation of recorded pressure data for the pressurization stage of C2H6-Brookfield oil. The recorded data within the initial period, which were considered to be significantly influenced by temperature change, are shown by open triangles. The pressure data after this initial period are displayed by open rectangles and used for extrapolation. The fitted function for extrapolation is also displayed in Fig. B.1. Similar analysis and extrapolation were also performed on the pressure data recorded in the stage of depressuriza-tion, and shown in fig. B.2. The extrapolation is shown with a solid line and the extrapolated value at each pressure level is highlighted with a red solid dot in each subplot. The fitted functions and the corresponding R2 values are also displayed. It is clearly shown that, with the additional effect of temperature rise-up after each rapid depressurization, the

pressure within the initial period (open triangles) increases significantly faster than those thereafter (open rectangles).

APPENDIX C

z Factor of CO2 at 30°C with the adjustment to match Henry’s Law

In Brookfield Oil

The gas solubility is calculated via an equation of state with compressibility factor z, as shown in appendix a. In order to remove the overestimation of CO2 solubility, the compressibility factor z was re-adjusted to correct the pres-sure vs. solubility curve of CO2, to match Henry’s law (fig. 17). The solubility calculation method during the pres-surization stage is expressed by Eq. (a.1). The adjustment on z factor can be made on either z0 (initial point) or zeq(equilibrium point).

The adjustment on z0 at the initial pressure was first per-formed and the re-evaluated value is indicated as z0 in Fig. C.1. In order to correct the calculated solubility by chang-ing the z factor at the initial pressure, the re-evaluated value needs to move up to a value of 0.83. This value is very unlikely for the compressibility factor of CO2 at 873 psia. The adjustment on ze at the equilibrium pressure shows that, in order to correct the calculated solubility to match Henry’s law, the corrected z factor value needs to move down to a value of 0.51 (indicated as ze in fig. C.1) at 780 psia. as we discussed in the previous paragraphs, the pro-posed explanation to the deviation of CO2 data from Henry’s law is the coexistence of a CO2-rich liquid phase with the CO2 vapor and oil phase. Therefore, the estimated value of ze is contributed by both ze,v (z factor for CO2 vapor phase)

Fig. B.1 Extrapolation for the pressurization stage of C2H6-Brookfield oil.

y = -0.3244x + 540.5R² = 0.9951

520

530

540

550

560

0 5 10 15 20 25

Pres

sure

(psia

)

Time (Hour)

Fig. B.2 Extrapolations for the depressurization stage of C2H6-Brookfield oil at different pressures.

y = 2.2414x + 155.5R² = 0.9955

150

160

170

0 1 2 3 4 5 6

Pres

sure

(psia

)

Time (Hour)

Peq = 189 psia

y = 1.6257x + 78.9R² = 0.9514

70

80

90

0 1 2 3 4 5 6

Pres

sure

(psia

)

Time (Hour)

Peq = 106 psia

y = 1.6301x + 267.2R² = 0.9608

250

260

270

280

290

0 5 10 15 20

Pres

sure

(psia

)

Time (Hour)

Peq = 287 psia

y = 1.3881x + 374.9R² = 0.9257

350

360

370

380

390

400

0 5 10 15 20

Pres

sure

(psia

)

Time (Hour)

Peq = 393 psia

*

*

*



and ze,l (z factor for CO2-rich liquid phase). as shown in fig. C.1, the extrapolated value of ze,l at 780 psia is highlighted by a red asterisk, while ze,v is indicated by a black asterisk. ze can be calculated by Eq. (C.1) and (C.2).

Here,

The sum of mole fraction of CO2 in non-oil phase is consid-ered as 1.

Given the values for all three z factors shown in Eq. (C.1) and combining Eq. (C.1) and Eq. (C.2), the mole fraction of CO2 in vapor phase and CO2 in CO2-rich liquid phase can be calculated. The calculated mole fraction of CO2 in vapor phase is 0.58; correspondingly, the mole fraction in CO2-rich liquid phase is 0.42. Here, on the basis of available data in the reference book (IuPaC 1973), the estimated density for CO2 vapor is 0.1431 g/ml and the density for CO2-rich liquid is 0.5421 g/ml. In this manner, the volume fraction of CO2 in either vapor phase or CO2-rich liquid phase is calculated to be 0.84 and 0.16, respectively.

In Bitumen #10-19

The gas solubility is calculated via an equation of state with compressibility factor z, as shown in appendix a. In

order to remove the overestimation of CO2 solubility, the compressibility factor z was re-adjusted to correct the pres-sure vs. solubility curve of CO2 to match the Henry’s law (fig. 31). The solubility calculation method during pressur-ization stage is expressed by Eq. (a.1). The adjustment on zfactor can be made on either z0 (initial point) or zeq (equilib-rium point) to serve the purpose. adjusting z0 at the initial pressure to follow Henry’s law gives the re-evaluated value z0 (as shown in fig. C.2) to be 0.96. This value is very unlikely for the compressibility fac-tor of CO2 at 745 psia. The adjustment on ze shows that, in order to correct the calculated solubility to follow Henry’s law, the corrected z factor value needs to move down to a value of 0.55 (indi-cated as ze in fig. C.2) at 709 psia. as we discussed in the section “In Brookfield Oil”, the estimated value of ze is contributed by both ze,v (z factor for CO2 vapor phase) and ze,l (z factor for CO2-rich liquid phase). as shown in fig. C.2, the extrapolated value of ze,l at 709 psia is highlighted by a red asterisk, while ze,v is indicated by a black asterisk. Given the values for all three z factors shown in Eq. (C.1) and combining Eq. (C.1) and Eq. (C.2), the mole frac-tion of CO2 in vapor phase and CO2 in CO2-rich liquid phase can be calculated. The calculated mole fraction of CO2 in vapor phase is 0.54, and the mole fraction in CO2-rich liquid phase is 0.46. In this case, based on the available data in the reference book (IuPaC, 1973), the estimated density for CO2 vapor is 0.1223 g/ml and the density for CO2-rich liquid is 0.4586 g/ml. In this manner, the volume fraction of CO2 in either vapor phase or CO2-rich liquid phase is calculated to be 0.82 and 0.18, respectively. These values are close to the calcula-tions in the case of CO2-Brookfield oil.

Fig. C.1 Analysis of compressibility factor z of CO2 for adjusting the calculated solubility of CO2 in Brookfield oil to follow Henry’s law.

Fig. C.2 Analysis of compressibility factor z of CO2 for adjusting the calculated solubility of CO2 in bitumen #10-19 and match Henry’s law.

*

ze∗ = ze, v ⋅ xv + ze, l ⋅ xl (C.1)

xv , mole fraction of CO2 in vapor phase;xl , mole fraction of CO2 in CO2-rich liquid phase;

xv + xl = 1 (C.2)

*

*

*

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