0
Research Papers: Petroleum Engineering

Quantification of a Single Gas Bubble Growth in Solvent(s)–CO2–Heavy Oil Systems With Consideration of Multicomponent Diffusion Under Nonequilibrium Conditions

[+] Author and Article Information
Yu Shi

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

Daoyong Yang

Petroleum Systems Engineering,
Faculty of Engineering and
Applied Science,
University of Regina,
Regina, SK S4S 0A2, Canada
e-mail: tony.yang@uregina.ca

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received August 30, 2016; final manuscript received October 27, 2016; published online November 29, 2016. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 139(2), 022908 (Nov 29, 2016) (11 pages) Paper No: JERT-16-1353; doi: 10.1115/1.4035150 History: Received August 30, 2016; Revised October 27, 2016

A mechanistic model has been developed and validated to quantify a single gas bubble growth with considering multicomponent gas diffusion in solvent(s)–CO2–heavy oil systems under nonequilibrium conditions. Experimentally, constant-composition expansion (CCE) experiments are conducted for C3H8–CO2–heavy oil systems under equilibrium and nonequilibrium conditions, respectively. Theoretically, the classic continuity equation, motion equation, diffusion–convection equation, real gas equation, and Peng–Robinson equation of state (PR EOS) are integrated into an equation matrix to dynamically predict gas bubble growth. Also, the viscous term of motion equation on the gas phase pressure is included due mainly to the viscous nature of heavy oil. The newly proposed model has been validated by using the experimentally measured gas bubble radius as a function of time with good accuracy. Combining with the experimental measurements, the critical nucleus radius and gas bubble growth are quantitatively predicted with the newly proposed model. Effects of mass transfer, supersaturation pressure, mole concentration of each component, liquid cell radius, and pressure decline rate on the gas bubble growth are examined and analyzed. In general, gas bubble growth rate is found to increase with an increase of each of the aforementioned five parameters though the contribution of individual component in a gas mixture to the bubble growth rate is different. A one-step pressure drop and the unlimited liquid volume surrounding a gas bubble are considered to be the necessary conditions to generate the linear relationship between gas bubble radius and the square root of time.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Maini, B. B. , 1996, “ Foamy Oil Flow in Heavy Oil Production,” J. Can. Pet. Technol., 35(6), pp. 21–24. [CrossRef]
Maini, B. B. , 2001, “ Foamy-Oil Flow,” J. Pet. Technol., 53(10), pp. 54–64. [CrossRef]
Sarma, H. , and Maini, B. B. , 1992, “ Role of Solution Gas in Primary Production of Heavy Oils,” SPE Latin America Petroleum Engineering Conference, Caracas, Venezuela, Mar. 8–11, Paper No. SPE 23631.
Sheng, J. J. , 1997, “ Foamy Oil Flow in Porous Media,” Ph.D. dissertation, University of Alberta, Edmonton, AB, Canada.
Kamp, A. M. , Heny, C. , Andarcia, L. , Lago, M. , and Rodriguez, A. , 2001, “ Experimental Investigation of Foamy Oil Solution Gas Driven,” SPE International Thermal Operations and Heavy Oil Symposium, Porlamar, Venezuela, Mar. 12–14, Paper No. SPE 69725.
Smith, G. E. , 1988, “ Fluid Flow and Sand Production in Heavy-Oil Reservoirs Under Solution-Gas Drive,” SPE Prod. Eng., 3(2), pp. 169–180. [CrossRef]
Maini, B. B. , Sarma, H. K. , and George, A. E. , 1993, “ Significance of Foamy-Oil Behavior in Primary Production of Heavy Oils,” J. Can. Pet. Technol., 32(9), pp. 50–54. [CrossRef]
Sheng, J. J. , Hayes, R. E. , and Maini, B. B. , 1996, “ A Dynamic Model to Simulate Foamy Oil Flow in Porous Media,” SPE Annual Technical Conference and Exhibition, Denver, CO, Oct. 8–9, Paper No. SPE 36750.
Mastmann, M. , Moustakis, M. L. , and Bennion, B. , 2001, “ Predicting Foamy Oil Recovery,” SPE Western Regional Meeting, Bakersfield, CA, Mar. 26–30, Paper No. SPE 68860.
Bennion, D. B. , Mastmann, M. , and Moustakis, M. L. , 2003, “ A Case Study of Foamy Oil Recovery in the Patos-Marinza Reservoir, Driza Sand, Albania,” J. Can. Pet. Technol., 42(3), pp. 21–28. [CrossRef]
Uddin, M. , 2012, “ Modelling of Gas Exsolution and Transport in a Live Heavy Oil Reservoir,” SPE Heavy Oil Conference, Calgary, AB, Canada, June 12–14, Paper No. SPE 158257.
Firoozabadi, A. , Ottesen, B. , and Mikkelsen, M. , 1992, “ Measurements of Supersaturation and Critical Gas Saturation,” SPE Form. Eval., 7(4), pp. 337–344. [CrossRef]
Kashchiev, D. , and Firoozabadi, A. , 1993, “ Kinetics of the Initial Stage of Isothermal Gas Phase Formation,” J. Chem. Phys., 98(6), pp. 4690–4699. [CrossRef]
Sheng, J. J. , Maini, B. B. , Hayes, R. E. , and Tortike, W. S. , 1999, “ Critical Review of Foamy Oil Flow,” Transp. Porous Media, 35(2), pp. 157–187. [CrossRef]
Kumar, R. , 1999, “ Solution-Gas Drive in Heavy Oil-Gas Mobility and Kinetics of Bubble Growth,” M.Sc. thesis, University of Calgary, Calgary, AB, Canada.
Shi, Y. , Li, X. , and Yang, D. , 2016, “ Nonequilibrium Phase Behaviour of Alkane Solvent(s)–CO2–Heavy Oil Systems Under Reservoir Conditions,” Ind. Eng. Chem. Res., 55(10), pp. 2860–2871. [CrossRef]
Moulu, J. C. , 1989, “ Solution-Gas Drive: Experiments and Simulation,” J. Pet. Sci. Eng., 2(4), pp. 379–386. [CrossRef]
Wong, R. C. K. , and Maini, B. B. , 2007, “ Gas Bubble Growth in Heavy Oil-Filled Sand Packs Under Undrained Unloading,” J. Pet. Sci. Eng., 55(3–4), pp. 259–270. [CrossRef]
Jones, S. F. , Evans, G. M. , and Galvin, K. P. , 1999, “ Bubble Nucleation From Gas Cavities—A Review,” Adv. Colloid Interface Sci., 80(1), pp. 27–50. [CrossRef]
Scriven, L. E. , 1959, “ On the Dynamics of Phase Growth,” Chem. Eng. Sci., 10(1–2), pp. 1–13. [CrossRef]
Sheng, J. J. , Hayes, R. E. , Maini, B. B. , and Tortike, W. S. , 1995, “ A Proposed Dynamic Model for Foamy Oil Properties,” SPE International Heavy Oil Symposium, Calgary, AB, Canada, June 19–21, Paper No. SPE 30253.
Szekely, J. , and Martins, G. P. , 1971, “ Non-Equilibrium Effects in the Growth of Spherical Gas Bubbles Due to Solution Diffusion,” Chem. Eng. Sci., 26(1), pp. 147–159. [CrossRef]
Rosner, D. E. , and Epstein, M. , 1972, “ Effects of Interface Kinetics, Capillarity and Solute Diffusion on Bubble Growth Rates in Highly Supersaturated Liquids,” Chem. Eng. Sci., 27(12), pp. 69–88. [CrossRef]
Arefmanesh, A. , Advani, S. G. , and Michaelides, E. E. , 1992, “ An Accurate Numerical Solution for Mass Diffusion-Induced Bubble Growth in Viscous Liquids Containing Limited Dissolved Gas,” Int. J. Heat Mass Transfer, 35(7), pp. 1711–1722. [CrossRef]
Naderi, K. , and Babadagli, T. , 2016, “ Solvent Selection Criteria and Optimal Application Conditions for Heavy-Oil/Bitumen Recovery at Elevated Temperatures: A Review and Comparative Analysis,” ASME J. Energy Resour. Technol., 138(1), p. 012904. [CrossRef]
Shi, J. , and Leung, J. Y. , 2014, “ Semi-Analytical Proxy for Vapex Process Modeling in Heterogeneous Reservoirs,” ASME J. Energy Resour. Technol., 136(3), p. 032904. [CrossRef]
Li, H. , and Yang, D. , 2016, “ Determination of Individual Diffusion Coefficients of Solvent–CO2 Mixture in Heavy Oil Using Pressure-Decay Method,” SPE J., 21(1), pp. 131–143. [CrossRef]
Zheng, S. , Li, H. , Sun, H. , and 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), pp. 1533–1549. [CrossRef]
Sun, H. , Li, H. , and 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 Transfer, 74(7), pp. 173–184. [CrossRef]
Zheng, S. , Sun, H. , and 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 Transfer, 102, pp. 251–263. [CrossRef]
Zheng, S. , and 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,” SPE J. (preprint).
Zheng, S. , and Yang, D. , 2017, “ Experimental and Theoretical Determination of Diffusion Coefficients of CO2-Heavy Oil Systems by Coupling Heat and Mass Transfer,” ASME J. Energy Resour. Technol., 139(2), p. 022901. [CrossRef]
Cable, M. , and Frade, J. R. , 1987, “ Diffusion-Controlled Growth of Multi-Component Gas Bubbles,” J. Mater. Sci., 22(3), pp. 919–924. [CrossRef]
Gor, G. Y. , and Kuchma, A. E. , 2009, “ Steady-State Composition of Two-Component Gas Bubble Growing in a Liquid Solution: Self-Similar Approach,” J. Chem. Phys., 131(23), p. 234705. [CrossRef] [PubMed]
Amon, M. , and Denson, C. D. , 1984, “ A Study of the Dynamics of Foam Growth Analysis of the Growth of Closely Spaced Spherical Bubbles,” Polym. Eng. Sci., 24(13), pp. 1026–1034. [CrossRef]
Leung, S. N. , Park, C. B. , Xu, D. , Li, H. , and Fenton, R. G. , 2006, “ Computer Simulation of Bubble-Growth Phenomena in Foaming,” Ind. Eng. Chem. Res., 45(23), pp. 7823–7831. [CrossRef]
Payvar, P. , 1987, “ Mass Transfer-Controlled Bubble Growth During Rapid Decompression of a Liquid,” Int. J. Heat Mass Transfer, 30(4), pp. 699–706. [CrossRef]
Li, H. , Yang, D. , and Tontiwachwuthikul, P. , 2012, “ Experimental and Theoretical Determination of Equilibrium Interfacial Tension for the Solvent(s)−CO2−Heavy Oil Systems,” Energy Fuels, 26(3), pp. 1776–1786. [CrossRef]
Yarranton, H. W. , van Dorp, J. J. , Verlaan, M. L. , and Lastovka, V. , 2013, “ Wanted Dead or Live: Crude-Cocktail Viscosity—A Pseudocomponent Method to Predict the Viscosity of Dead Oils, Live Oils, and Mixtures,” J. Can. Pet. Technol., 52(3), pp. 176–191. [CrossRef]
Pedersen, K. S. , Christensen, P. L. , and Shaikh, J. A. , 2014, Phase Behavior of Petroleum Reservoir Fluids, 2nd ed., CRC Press, Boca Raton, FL.
Tharanivasan, A. K. , Yang, C. , and Gu, Y. , 2006, “ Measurements of Molecular Diffusion Coefficients of Carbon Dioxide, Methane, and Propane in Heavy Oil Under Reservoir Conditions,” Energy Fuels, 20(6), pp. 2509–2517. [CrossRef]
Peng, D. , and Robinson, D. B. , 1976, “ A New Two-Constant Equation of State,” Ind. Eng. Chem. Fundam., 15(1), pp. 59–64. [CrossRef]
Li, H. , and 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,” Energy Fuels, 25(1), pp. 215–223. [CrossRef]
Li, H. , Yang, D. , and Li, X. , 2013, “ Determination of Three-Phase Boundaries of Solvent(s)-CO2-Heavy Oil Systems Under Reservoir Condition,” Energy Fuels, 27(1), pp. 145–153. [CrossRef]
Li, H. , and Yang, D. , 2013, “ Phase Behaviour of C3H8/n-C4H10/Heavy-Oil Systems at High Pressures and Elevated Temperatures,” J. Can. Pet. Technol., 52(1), pp. 30–40. [CrossRef]
Li, H. , Zheng, S. , and Yang, D. , 2013, “ Enhanced Swelling Effect and Viscosity Reduction of Solvent(s)/CO2/Heavy-Oil Systems,” SPE J., 18(4), pp. 695–707. [CrossRef]
Li, H. , Sun, H. , and Yang, D. , 2016, “ Effective Diffusion Coefficients of Gas Mixture in Heavy Oil Under Constant-Pressure Conditions,” Heat Mass Transfer (preprint).
Li, X. , Li, H. , and Yang, D. , 2013, “ Determination of Multiphase Boundaries and Swelling Factors of Solvent(s)–CO2–Heavy Oil Systems at High Pressures and Elevated Temperatures,” Energy Fuels, 27(3), pp. 1293–1306. [CrossRef]
Li, X. , Yang, D. , Zhang, X. , Zhang, G. , and 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, pp. 77–86. [CrossRef]
Chueh, P. L. , and Prausnitz, J. M. , 1967, “ Vapor-Liquid Equilibria at High Pressures: Calculation of Partial Molar Volumes in Non Polar Liquid Mixtures,” AIChE J., 13(6), pp. 1099–1107. [CrossRef]
Yortsos, Y. C. , and Parlar, M. , 1989, “ Phase Change in Binary Systems in Porous Media: Application to Solution-Gas Drive,” SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8–11, Paper No. SPE 19697.
Claridge, E. L. , and Prats, M. , 1995, “ A Proposed Model and Mechanism for Anomalous Foamy Heavy Oil Behavior,” SPE International Heavy Oil Symposium, Calgary, AB, Canada, June 19–21, Paper No. SPE 29243.
Ward, C. A. , and Levart, E. , 1984, “ Conditions for Stability of Bubble Nuclei in Solid Surfaces Contacting a Liquid–Gas Solution,” J. Appl. Phys., 56(2), pp. 491–500. [CrossRef]
Kamath, J. , and Boyer, R. E. , 1995, “ Critical Gas Saturation and Supersaturation in Low-Permeability Rocks,” SPE Form. Eval., 10(4), pp. 247–253. [CrossRef]
Kennedy, H. T. , and Olson, C. R. , 1952, “ Bubble Formation in Supersaturated Hydrocarbon Mixtures,” J. Pet. Technol., 4(11), pp. 271–278. [CrossRef]
Firoozabadi, A. , and Kashchiev, D. , 1996, “ Pressure and Volume Evolution During Gas Phase Formation in Solution Gas Drive Process,” SPE J., 1(3), pp. 1–9. [CrossRef]
Geilikman, M. B. , Dusseault, M. B. , and Dullien, F. A. L. , 1995, “ Dynamic Effects of Foamy Fluid Flow in Sand Production Instability,” SPE International Heavy Oil Symposium, Calgary, AB, Canada, June 19–21, Paper No. SPE 30251.

Figures

Grahic Jump Location
Fig. 1

The schematic of cell model

Grahic Jump Location
Fig. 2

Flowchart of numerically solving the equation matrix

Grahic Jump Location
Fig. 3

Comparison of the measured and calculated bubble radius for n-C5H12n-C14H30 systems

Grahic Jump Location
Fig. 4

The calculated radius of a gas bubble for C3H8–CO2–heavy oil systems

Grahic Jump Location
Fig. 5

Bubble radius as a function of time with varying two gas diffusion coefficients

Grahic Jump Location
Fig. 6

The relationship between the bubble radius and time with varying individual diffusion coefficient of (a) CO2, (b) C3H8 with the 100% original mole fraction of both gases, and (c) CO2 and C3H8 with 50% C3H8 original mole fraction

Grahic Jump Location
Fig. 7

The relationship between the bubble radius and time with different supersaturation pressures

Grahic Jump Location
Fig. 8

The relationship between the bubble radius and time with varying (a) both two gases mole fractions, (b) CO2 mole fraction, and (c) C3H8 mole fraction

Grahic Jump Location
Fig. 9

The relationship between the bubble radius and time with different liquid cell radius

Grahic Jump Location
Fig. 10

The relationship between the bubble radius and time with different pressure decline rates

Grahic Jump Location
Fig. 11

The relationship between the bubble radius and square root of time

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In