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Effective diffusion coefficients of gas mixture in heavy oil under constant-pressure conditions

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Abstract

We develop a method to determine the effective diffusion coefficient for each individual component of a gas mixture in a non-volatile liquid (e.g., heavy oil) at high pressures with compositional analysis. Theoretically, a multi-component one-way diffusion model is coupled with the volume-translated Peng-Robinson equation of state to quantify the mass transfer between gas and liquid (e.g., heavy oil). Experimentally, the diffusion tests have been conducted with a PVT setup for one pure CO2-heavy oil system and one C3H8–CO2-heavy oil system under constant temperature and pressure, respectively. Both the gas-phase volume and liquid-phase swelling effect are simultaneously recorded during the measurement. As for the C3H8–CO2-heavy oil system, the gas chromatography method is employed to measure compositions of the gas phase at the beginning and end of the diffusion measurement, respectively. The effective diffusion coefficients are then determined by minimizing the discrepancy between the measured and calculated gas-phase composition at the end of diffusion measurement. The newly developed technique can quantify the contributions of each component of mixture to the bulk mass transfer from gas into liquid. The effective diffusion coefficient of C3H8 in the C3H8–CO2 mixture at 3945 ± 20 kPa and 293.85 K, i.e., \(18.19 \times 10^{ - 10} {\text{m}}^{ 2} / {\text{s}}\), is found to be much higher than CO2 at 3950 ± 18 kPa and 293.85 K, i.e., \(8.68 \times 10^{ - 10} {\text{m}}^{ 2} / {\text{s}}\). In comparison with pure CO2, the presence of C3H8 in the C3H8–CO2 mixture contributes to a faster diffusion of CO2 from the gas phase into heavy oil and consequently a larger swelling factor of heavy oil.

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Abbreviations

A :

Cross-sectional area of PVT cell, cm2

a :

Attraction parameter in PR EOS model, kPa·m3/kmol

a c :

Factor in correlation of attraction parameter in PR EOS model

b :

Van der Waals volume, m3/kmol

C i :

Dimensionless concentration of solvent, i = 1, 2

c i :

Concentration of ith solvent in heavy oil, mole fraction, i = 1, 2

c i,sat :

Saturated concentration of ith solvent in heavy oil, mole fraction, i = 1, 2

D eff, i :

Effective diffusion coefficient of ith solvent, m2/s, i = 1, 2

k :

kth time step

L :

Updated liquid phase height, m

L 0 :

Initial heavy oil height, m

MW :

Molecular weight, g/mol

m :

mth node along the diffusion direction

n j :

Molar mass of jth component in liquid phase, mol, j = 1, 2, 3

nc :

Number of components in the diffusion system

ng :

Number of solvent components

O(c):

Objective function

P :

Pressure, kPa

P c :

Critical pressure, kPa

R :

Universal gas constant, kPa·m3/(K·kmol)

SF X :

Swelling factor

SG :

Specific gravity

T :

Temperature, K

T c :

Critical temperature, K

T r :

Reduced temperature, K

t :

Time, s

V :

Molar volume, m3/kmol

V corrected :

Corrected molar volume, m3/kmol

V 1, V 2 :

Molar volume of heavy oil and solvent-diluted heavy oil at the test temperature and pressure, m3/kmol

X :

Dimensionless distance

x :

Coordinate direction, m

x j(h) :

Composition of j(h)th component in liquid phase, mole fraction, j(h) = 1, 2 and 3

y i,cal :

Calculated composition of ith solvent in gas phase, mole fraction, i = 1, 2

y i,exp :

Measured composition of ith solvent in gas phase, mole fraction, i = 1, 2

Z RA :

Rackett parameter

α :

Alpha function in PR EOS model

δ :

BIP matrix

ρ :

Density, kg/m3

τ :

Dimensionless time

ω :

Acentric factor

µ :

Dynamic viscosity, cP

References

  1. Fatemi SM, Sohrabi M (2013) Experimental investigation of near-miscible water-alternating-gas injection performance in water-wet and mixed-wet systems. SPE J 18(1):114–123

    Article  Google Scholar 

  2. Rivero JA, Mamora DD (2005) Production acceleration and injectivity enhancement using steam-propane injection for Hamaca extra-heavy oil. J Can Pet Technol 44(2):50–57

    Article  Google Scholar 

  3. Alkindi AS, Al-Wahaibi YM, Muggeridge AH (2011) Experimental and numerical investigations into oil-drainage rates during vapor extraction of heavy oils. SPE J 16(2):343–357

    Article  Google Scholar 

  4. Varte G, Montel F, Nasri D, Daridon J-L (2013) Gas solubility measurement in heavy oil and extra heavy oil at VAPEX conditions. Energ Fuels. doi:10.1021/ef400266t

    Google Scholar 

  5. Badamchi-Zadeh A, Maini BB, Yarranton HW (2008) Applicability of CO2-based VAPEX process to recover Athabasca bitumen. In: Paper SPE 117855, presented at the SPE international thermal operations and heavy oil symposium, calgary, AB, October 20–23

  6. Talbi K, Maini BB (2008) Experimental investigation of CO2-based VAPEX for recovery of heavy oils and bitumen. J Can Pet Technol 47(4):1–8

    Article  Google Scholar 

  7. Luo P, Zhang Y, Wang X, Huang S (2012) Propane-enriched CO2 immiscible flooding for improved heavy oil recovery. Energ Fuels 26(4):2124–2135

    Article  Google Scholar 

  8. Li H, Zheng S, Yang D (2013) Enhanced swelling effect and viscosity reduction of solvent(s)-CO2-heavy oil systems. SPE J 18(4):695–707

    Article  Google Scholar 

  9. Li H, Yang D, Tontiwachwuthikul P (2012) Experimental and theoretical determination of equilibrium interfacial tension for the solvent(s)-CO2-heavy oil systems. Energ Fuels 26(3):1776–1786

    Article  Google Scholar 

  10. Li H, Yang D (2013) Phase behaviour of C3H8-n-C4H10-heavy oil systems at high pressures and elevated temperatures. J Can Pet Technol 52(1):30–40

    Article  Google Scholar 

  11. Etminan SR, Maini BB, Chen Z, Hassanzadeh H (2010) Constant-pressure technique for gas diffusivity and solubility measurements in heavy oil and bitumen. Energ Fuels 24(1):533–549

    Article  Google Scholar 

  12. Yang Y, Hyndman CL, Maini BB (2000) Measurement of gas diffusivity in heavy oils. J Pet Sci Eng 25(1–2):37–47

    Google Scholar 

  13. Upreti SR, Mehrotra AK (2000) Experimental measurement of gas diffusivity in bitumen: results for carbon dioxide. Ind Eng Chem Res 39(4):1080–1087

    Article  Google Scholar 

  14. Upreti SR, Mehrotra AK (2002) Diffusivity of CO2, CH4, C2H6, and N2 in Athabasca bitumen. Can J Chem Eng 80(1):116–125

    Article  Google Scholar 

  15. Sheikha H, Pooladi-Darvish M, Mehrotra AK (2005) Development of graphical methods for estimating the diffusivity coefficient of gases in bitumen from pressure-decay data. Energ Fuels 19(5):2041–2049

    Article  Google Scholar 

  16. Wen Y, Bryan J, Kantzas A (2005) Estimation of diffusion coefficients in bitumen solvent mixtures as derived from low field NMR spectra. J Can Pet Technol 44(4):29–35

    Google Scholar 

  17. Tharanivasan AK, Yang C, Gu Y (2006) Measurements of molecular diffusion coefficients of carbon dioxide, methane, and propane in heavy oil under reservoir conditions. Energ Fuels 20(6):2509–2517

    Article  Google Scholar 

  18. Guerrero-Aconcha U, Kantzas A (2009) Diffusion of hydrocarbon gases in heavy oil and bitumen. In: Paper SPE 122783, presented at the SPE latin american and caribbean petroleum engineering conference, Cartagena, Colombia, May 31–June 3

  19. Saboorian-Jooybari H (2012) A novel methodology for simultaneous estimation of gas diffusivity and solubility in bitumens and heavy oils. In: Paper SPE 157734, presented at the SPE heavy oil conference, Canada, Calgary, AB, June 12–14

  20. Yang C, Gu Y (2006) Diffusion coefficients and oil swelling factors of carbon dioxide, methane, ethane, propane, and their mixtures in heavy oil. Fluid Phase Equilib 243(1–2):64–73

    Article  Google Scholar 

  21. Nguyen TA, Farouq Ali SM (1998) Effect of nitrogen on the solubility and diffusivity of carbon dioxide into oil and oil recovery by the immiscible WAG process. J Can Pet Technol 37(2):24–31

    Article  Google Scholar 

  22. Riazi MR (1996) A new method for experimental measurement of diffusion coefficients in reservoir fluids. J Pet Sci Eng 14(3–4):235–250

    Article  Google Scholar 

  23. Yang D, Gu Y (2008) Determination of diffusion coefficients and interface mass-transfer coefficients of the crude oil − CO2 system by analysis of the dynamic and equilibrium interfacial tensions. Ind Eng Chem Res 47(15):5447–5455

    Article  Google Scholar 

  24. Yang D, Tontiwachwuthikul P, Gu Y (2006) Dynamic interfacial tension method for measuring the gas diffusion coefficient and the interface mass transfer coefficient in a liquid. Ind Eng Chem Res 45(14):4999–5008

    Article  Google Scholar 

  25. Yang C, Gu Y (2005) New experimental method for measuring gas diffusivity in heavy oil by the dynamic pendant drop volume analysis (DPDVA). Ind Eng Chem Res 44(12):4474–4483

    Article  Google Scholar 

  26. Luo H, Salama D, Kryuchkov S, Kantzas A (2007) The effect of volume changes due to mixing on diffusion coefficient determination in heavy oil and hydrocarbon solvent system. In: Paper SPE 110522, presented at the SPE annual technical conference and exhibition, Anaheim, CA, November 11–14

  27. Baehr HD, Stephan K (2006) Heat and mass transfer. Springer, New York, NY

    Book  MATH  Google Scholar 

  28. Jamialahmadi M, Emadi M, Müller-Steinhagen H (2006) Diffusion coefficients of methane in liquid hydrocarbons at high pressure and temperature. J Pet Sci Eng 53(1–2):47–60

    Article  Google Scholar 

  29. Upreti SR, Lohi A, Kapadia RA, El-Haj R (2007) Vapor extraction of heavy oil and bitumen: a review. Energ Fuels 21(3):1562–1574

    Article  Google Scholar 

  30. Li H, Yang D (2015) Determination of individual diffusion coefficients of solvent-CO2 mixture in heavy oil using pressure-decay method. SPE J 21(1):131–143

    Article  MathSciNet  Google Scholar 

  31. Zheng S, Li H, Sun H, Yang D (2016) Determination of diffusion coefficient for solvent-CO2 mixtures in heavy oil with consideration of swelling effect. Ind Eng Chem Res 55(6):1533–1549

    Article  Google Scholar 

  32. Sun H, Li H, Yang D (2014) Coupling heat and mass transfer for a gas mixture-heavy oil system at high pressures and elevated temperatures. Int J Heat Mass Trans 74(7):173–184

    Article  Google Scholar 

  33. Zheng S, Yang D (2016) Experimental and theoretical determination of diffusion coefficients of CO2-heavy oil systems by coupling heat and mass transfer. J Energy Res Tech 139(2):022901

    Article  Google Scholar 

  34. Zheng S, Sun H, Yang D (2016) Coupling heat and mass transfer for determining individual diffusion coefficient of a hot C3H8–CO2 mixture in heavy oil under reservoir conditions. Int J Heat Mass Trans 102:251–263

    Article  Google Scholar 

  35. Zheng S, Yang D (2016) Determination of diffusion coefficients of C3H8-n-C4H10-CO2-heavy oil systems at high pressures and elevated temperatures by dynamic volume analysis (DVA). In: Paper SPE 179618, presented at the SPE improved oil recovery conference, Tulsa, OK, April 9–13

  36. Peng D, Robinson DB (1976) A new two-constant equation of state. Ind Eng Chem Fundam 15(1):59–64

    Article  Google Scholar 

  37. Tharanivasan AK, Yang C, Gu Y (2004) Comparison of three different interface mass transfer models used in the experimental measurement of solvent diffusivity in heavy oil. J Pet Sci Eng 44(3–4):269–282

    Article  Google Scholar 

  38. Fadaei H, Scarff B, Sinton D (2011) Rapid microfluidics-based measurement of CO2 diffusivity in bitumen. Energ Fuels 25(10):4829–4835

    Article  Google Scholar 

  39. Baker LE, Pierce AC, Luks KD (1982) Gibbs energy analysis of phase equilibria. SPE J 22(5):731–742

    Article  Google Scholar 

  40. Teja AS, Sandler AI (1980) A corresponding states equation for saturated liquid densities. II. Applications to the calculation of swelling factors of CO2-curde oil systems. AIChE J 26(3):341–345

    Article  Google Scholar 

  41. Péneloux A, Rauzy E, Freze R (1982) A consistent correction for Redlich–Kwong–Soave volumes. Fluid Phase Equilib 8(1):7–23

    Article  Google Scholar 

  42. Li H, Yang D (2011) Modified α function for the Peng-Robinson equation of state to improve the vapor pressure prediction of non-hydrocarbon and hydrocarbon compounds. Energ Fuels 25(1):215–223

    Article  Google Scholar 

  43. Li X, Yang D, Zhang X, Zhang G, Gao J (2016) Binary interaction parameters of CO2-heavy-n-alkanes systems by using peng-robinson equation of state with modified alpha function. Fluid Phase Equilib 417:77–86

    Article  Google Scholar 

  44. Shi Y, Li X, Yang D (2016) Nonequilibrium phase behaviour of alkane solvent(s)-CO2-heavy oil systems under reservoir conditions. Ind Eng Chem Res 55(10):2860–2871

    Article  Google Scholar 

  45. Li X, Li H, Yang D (2013) Determination of multiphase boundaries and swelling factors of solvent(s)-CO2-heavy oil systems at high pressures and elevated temperatures. Energ Fuels 27(3):1293–1306

    Article  Google Scholar 

  46. Li X, Yang D, Fan Z (2014) Phase behaviour and viscosity reduction of CO2-heavy oil systems at high pressures and elevated temperatures. In: Paper SPE 170057, presented at the SPE heavy oil conference, Calgary, AB, June 10–12

  47. Spencer CF, Danner RP (1972) Improved equation for prediction of saturated liquid density. J Chem Eng Data 17(2):236–241

    Article  Google Scholar 

  48. Rasmussen ML, Civan F (2009) Parameters of gas dissolution in liquids obtained by isothermal pressure decay. AIChE J 55(1):9–23

    Article  Google Scholar 

  49. Luo P, Yang C, Gu Y (2007) Enhanced solvent dissolution into in situ upgraded heavy oil under different pressures. Fluid Phase Equilib 252(1–2):143–151

    Article  Google Scholar 

Download references

Acknowledgments

The first author acknowledges a Discovery Grant from Natural Sciences and Engineering Research Council of Canada to H. Li. The authors also acknowledge a Discovery Grant and a Collaborative Research and Development (CRD) Grant from the NSERC to D. Yang and EHR Enhanced Hydrocarbon Recovery Inc. for financial support.

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Authors and Affiliations

  1. School of Mining and Petroleum Engineering, University of Alberta, Edmonton, T6G 1H9, Canada

    Huazhou Andy Li

  2. Petroleum Systems Engineering, Faculty of Engineering and Applied Science, University of Regina, Regina, S4S 0A2, Canada

    Huijuan Sun & Daoyong Yang

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  1. Huazhou Andy Li
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Correspondence to Huazhou Andy Li.

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Li, H.A., Sun, H. & Yang, D. Effective diffusion coefficients of gas mixture in heavy oil under constant-pressure conditions. Heat Mass Transfer 53, 1527–1540 (2017). https://doi.org/10.1007/s00231-016-1919-x

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