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An Analytical Model for Determination of the Solvent Convective Dispersion Coefficient in the Vapor Extraction Heavy Oil Recovery Process

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Abstract

In this article, a new model is developed to determine the solvent convective dispersion coefficient in a solvent vapor extraction (VAPEX) heavy oil recovery process. It is assumed that solvent mass transfer by convective dispersion takes place along the transition zone between the solvent chamber and untouched heavy oil, whereas solvent mass transfer by molecular diffusion occurs in the direction normal to the transition zone. It is also assumed that the solvent-diluted heavy oil gravity drainage through the transition zone has a linear or quadratic velocity profile in order to obtain analytical solutions of the solvent convective dispersion coefficients for the solvent chamber spreading and falling phases. As a result, this analytical model correlates the solvent convective dispersion coefficient to the maximum apparent oil gravity drainage velocity at the interface between the solvent chamber and transition zone, solvent molecular diffusion coefficient, transition-zone thickness, and porosity of the porous medium. To determine the solvent convective dispersion coefficient, the maximum apparent oil gravity drainage velocity is calculated by using Darcy’s law and the transition-zone thickness is obtained either from a previous study or by using a time similarity between the solvent molecular diffusion and oil gravity drainage. It is found that such a determined solvent convective dispersion coefficient is two to five orders larger than the solvent molecular diffusion coefficient, depending on the detailed experimental conditions of a specific VAPEX test.

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Abbreviations

c :

Solvent mass fraction in the solvent-diluted heavy oil, g solvent/g heavy oil (g solvent/g heavy oil)

C max :

Maximum solvent volume concentration at the interface between the solvent chamber and transition zone (vol.%)

D :

Solvent molecular diffusion coefficient (m2/s)

D app :

Apparent solvent molecular diffusion coefficient along x-axis (m2/s)

D x :

Apparent solvent molecular diffusion coefficient along x-axis (m2/s)

D y :

Solvent convective dispersion coefficient along y-axis (m2/s)

g :

Local gravitational acceleration (m/s2)

H :

VAPEX physical model height (m)

J x :

Solvent mass flux by molecular diffusion along x-axis (kg/m2 s)

J y :

Solvent mass flux by convective dispersion along y-axis (kg/m2 s)

k :

Absolute permeability of the VAPEX physical model (m2)

L :

VAPEX physical model length (m)

P :

Constant operating pressure during the VAPEX test (kPa)

P v :

Propane vapor pressure at T = 20.8°C (kPa)

Q s :

Solvent mass flow rate (kg/s)

T :

Constant operating temperature during the VAPEX test (°C)

t :

Time (s)

v :

Interstitial gravity drainage velocity of the solvent-diluted heavy oil along the transition zone (m/s)

v ave :

Average apparent gravity drainage velocity of the solvent-diluted heavy oil along the transition zone (m/s)

v max :

Maximum apparent gravity drainage velocity of the most diluted heavy oil at the interface between the solvent chamber and transition zone (m/s)

x :

x-coordinate (m)

y :

y-coordinate (m)

δ :

Transition-zone thickness (m)

μ o :

Viscosity of the heavy oil (Pa s)

μ o(C max):

Viscosity of the most diluted heavy oil at the interface between the solvent chamber and transition zone with the maximum solvent volume concentration C max(Pa s)

ρ :

Density of the solvent-diluted heavy oil (kg/m3)

ρ o :

Density of the heavy oil (kg/m3)

ρ s :

Density of the liquid solvent (kg/m3)

ρ o(C max):

Density of the most diluted heavy oil at the interface between the solvent chamber and transition zone with the maximum solvent volume concentration C max (kg/m3)

ΔA x :

Cross-sectional area of the finite control volume along x-axis (m2)

ΔA y :

Cross-sectional area of the finite control volume along y-axis (m2)

ΔV :

Volume of the finite control volume (m3)

θ :

Inclination angle of the transition zone (°)

\({{\phi}}\) :

Porosity of the VAPEX physical model

χ s :

Solvent solubility in the heavy oil, g solvent/100 g heavy oil (g solvent/g heavy oil)

Ω :

Cementation factor

app:

Apparent

ave:

Average

c:

Convection

d:

Diffusion

max:

Maximum

o:

Oil

s:

Solvent

x :

x-axis or at any x value

x + Δx :

at x + Δx

y :

y-axis or at any y value

y + Δy :

at y + Δy

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Correspondence to Yongan Gu.

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Derakhshanfar, M., Gu, Y. An Analytical Model for Determination of the Solvent Convective Dispersion Coefficient in the Vapor Extraction Heavy Oil Recovery Process. Transp Porous Med 92, 495–507 (2012). https://doi.org/10.1007/s11242-011-9916-5

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Keywords

  • Heavy oil recovery
  • Solvent vapor extraction (VAPEX)
  • Convective dispersion
  • Molecular diffusion
  • Gravity drainage
  • Solvent-based oil recovery