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Research Papers: Petroleum Engineering

A Power-Law Mixing Rule for Predicting Apparent Diffusion Coefficients of Binary Gas Mixtures in Heavy Oil

[+] Author and Article Information
Hyun Woong Jang

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

Huazhou Li

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

1Corresponding author.

2Present address: School of Mining and Petroleum Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 20, 2017; final manuscript received October 23, 2017; published online December 5, 2017. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 140(5), 052904 (Dec 05, 2017) (15 pages) Paper No: JERT-17-1375; doi: 10.1115/1.4038386 History: Received July 20, 2017; Revised October 23, 2017

A power-law mixing rule has been developed to determine apparent diffusion coefficient of a binary gas mixture on the basis of molecular diffusion coefficients for pure gases in heavy oil. Diffusion coefficient of a pure gas under different pressures and different temperatures is predicted on the basis of the Hayduk and Cheng's equation incorporating the principle of corresponding states for one-dimensional gas diffusion in heavy oil such as the diffusion in a pressure–volume–temperature (PVT) cell. Meanwhile, a specific surface area term is added to the generated equation for three-dimensional gas diffusion in heavy oil such as the diffusion in a pendant drop. In this study, the newly developed correlations are used to reproduce the measured diffusion coefficients for pure gases diffusing in three different heavy oils, i.e., two Lloydminster heavy oils and a Cactus Lake heavy oil. Then, such predicted pure gas diffusion coefficients are adjusted based on reduced pressure, reduced temperature, and equilibrium ratio to determine apparent diffusion coefficient for a gas mixture in heavy oil, where the equilibrium ratios for hydrocarbon gases and CO2 are determined by using the equilibrium ratio charts and Standing's equations, respectively. It has been found for various gas mixtures in two different Lloydminster heavy oils that the newly developed empirical mixing rule is able to reproduce the apparent diffusion coefficient for binary gas mixtures in heavy oil with a good accuracy. For the pure gas diffusion in heavy oil, the absolute average relative deviations (AARDs) for diffusion systems with two different Lloydminster heavy oils and a Cactus Lake heavy oil are calculated to be 2.54%, 14.79%, and 6.36%, respectively. Meanwhile, for the binary gas mixture diffusion in heavy oil, the AARDs for diffusion systems with two different Lloydminster heavy oils are found to be 3.56% and 6.86%, respectively.

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Figures

Grahic Jump Location
Fig. 1

(a) Typical phase diagram of a pure substance [28] and (b) vapor pressure lines of six gas solvents N2, CH4, CO2, C2H6, C3H8, and n-C4H10. Bold dots denote the critical points [30].

Grahic Jump Location
Fig. 2

(a) Phase envelopes of CO2–C3H8 mixtures for three different mole composition ratios between CO2 and C3H8 [32] and (b) phase envelope of CO2–C3H8 mixture used by Zheng et al. [21] showing three different vapor quality lines with total gas mixture mole composition of 84.38 mol % CO2 and 15.62 mol % C3H8 [32]

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Fig. 3

Flowchart for calculating apparent diffusion coefficient of a binary gas mixture in heavy oil

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Fig. 4

Parity chart of the measured diffusion coefficients and calculated diffusion coefficients using Eq. (2) for pure-gas/heavy-oil systems tested by Sun et al. [22], Zheng et al. [21], and Zheng and Yang [24]

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Fig. 5

Parity chart of the measured diffusion coefficients and calculated diffusion coefficients using Eq. (2) for pure-gas/heavy-oil systems tested by Marufuzzaman [19]

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Fig. 6

Parity charts of the measured diffusion coefficients and calculated diffusion coefficients using Eq. (4) for pure-gas/heavy-oil systems tested by Yang and Gu [18]

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Fig. 7

Comparison of (a) the measured and calculated drop volume by Eq. (D1) and (b) the measured apparent diffusion coefficients [18] of a CO2–C3H8 mixture (70 mol % CO2, 30 mol % C3H8) in heavy oil and calculated apparent diffusion coefficients by using Eqs. (4) and (8) at 297.05 K

Grahic Jump Location
Fig. 8

Comparison of (a) the measured and calculated drop volume by Eq. (D1) and (b) the measured apparent diffusion coefficients [18] of a CH4–C3H8 mixture (70 mol % CH4, 30 mol % C3H8) in heavy oil and calculated apparent diffusion coefficients by using Eqs. (4) and (8) at 297.05 K

Grahic Jump Location
Fig. 9

Comparison of (a) the measured and calculated drop volume by Eq. (D1) and (b) the measured apparent diffusion coefficients [18] of a C2H6–C3H8 mixture (70 mol % C2H6, 30 mol % C3H8) in heavy oil and calculated apparent diffusion coefficients by using Eqs. (4) and (8) at 297.05 K

Grahic Jump Location
Fig. 10

Parity chart of the measured apparent diffusion coefficients by Sun et al. [22], Zheng et al. [21], and Zheng and Yang [23] and calculated apparent diffusion coefficients using Eqs.(2) and (8) for gas mixtures

Grahic Jump Location
Fig. 11

Parity chart of the measured apparent diffusion coefficients and calculated apparent diffusion coefficients for gas mixtures under the constant pressure and constant temperature. Equations (4) and (8) are used for Yang and Gu's [18] data measured at 297.05 K, while Eqs. (2) and (8) are used for the data measured by Li et al. [45] at 294.55 K.

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