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Transport in Porous Media

, Volume 96, Issue 2, pp 397–417 | Cite as

Sensitivity Analysis for Dynamic Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

  • Saddam K. Yazzan
  • Ramon G. BentsenEmail author
  • Japan Trivedi
Article

Abstract

Dynamic spontaneous imbibition (DSI) plays an important role in oil reservoir characterization. Conventional equations used to characterize DSI consider neither interfacial coupling effects (ICE) nor variable inlet saturation (S*) for DSI. Yazzan et al. (Transp Porous Media 87(1):309–333, 2011a; 86(3):705–717, 2011b) developed a set of equations, and a numerical solution scheme, to take into account ICE and variable S* for DSI. Based on these, a graphical user interface (GUI) simulator was built. A sensitivity analysis has been conducted to study the effect of the fluid and rock properties on DSI. The results reveal that including a variable S* has no significant impact; however, neglecting ICE results in an overestimation of the imbibition flow rate. Moreover, it is shown that the capillary and relative permeability curves determine the type of frontal advance, and that the imbibition recovery is proportional to the square root of time.

Keywords

Dynamic spontaneous imbibition Interfacial coupling Transport equations Two-Phase flow Immiscible flow 

List of symbols

Variables

a

Experimentally determined parameter in definition for R 12

ai, bi, ci, di

Fitting coefficients i = 0, 1, 2

c

Experimentally determined parameter which controls amount of viscous coupling

\({\hat{A}}\)

Slope obtained from plot of \({\overline Q}\) versus \({\sqrt{\tau}}\)

Ac

Area under the capillary pressure curve

C(S)

Capillary function

F1

Non-capillary fractional flow function, \({F_1 = \frac{R_{12} \lambda _1^0}{R_{12}\lambda _1^0+\lambda _2^0}}\)

G(S)

Gravity function

kr1

Relative permeability to the wetting phase

kr2

Relative permeability to the non-wetting phase

L

Length of porous medium

Mr

End point mobility ratio

Ng

Gravity number, \({N_{\rm g} = \frac{\Delta \rho^{\prime}g {\rm sin} (\theta )L}{A_{\rm c}}}\)

Pc

Capillary pressure

\({\overline{q}}\)

Dimensionless normalized imbibition flow rate

\({\overline{q}}\)

Dimensionless normalized cumulative imbibition production

R12

Hydrodynamic factor, R 12 = 1− a (1 − S)

S

Normalized wetting phase saturation

S*

Normalized variable inlet saturation

Greek symbols

αi

Interfacial coupling factor, α i = α c i · α v i, i = 1, 2

αci

Capillary coupling parameters, i = 1, 2; α c1 = α c2 = α c = 1 − φ

αvi

Viscous coupling parameters, i = 1, 2; \({\alpha _{v1} = 1 - \frac{c}{R_{12}} \frac{\lambda _2^0}{\lambda _m^0}}\) ; \({\alpha _{v2} = 1 - cR_{12} \frac{\lambda _1^0}{\lambda _m^0}}\)

Δρ′

Difference in density without hydrodynamic effect

λ (S)

Average coupling effect, \({\lambda (S) = ( {\frac{\alpha _1+\alpha _2}{2}})}\)

\({\lambda_i^o }\)

Mobilities measured in a steady-state co-current (SSCO) flow experiment, i = 1, 2

λ1r

Effective mobility to the wetting phase at its residual saturation to the non-wetting phase

λ2r

Effective mobility to the non-wetting phase at its irreducible saturation to the wetting phase

\({\lambda_m^0 }\)

Parameter to ensure dimensional consistency, \({\lambda _m^0 = S\lambda _{1r}^0 + (1 - S)\lambda _{2r}^0 }\)

ξ

Normalized distance measured from the inlet surface of a core

πc (S)

Dimensionless capillary pressure

θ

Angle of inclination of the core to the horizontal

ρ

Fluid density

τ

Dimensionless time

φ

Porosity of the porous medium

Superscripts

0

Denotes the parameter is for co-current flow

Subscripts

1

Wetting phase

2

Non-wetting phase

nw

Non-wetting phase

w

Wetting phase

r

Residual

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Saddam K. Yazzan
    • 1
  • Ramon G. Bentsen
    • 1
    Email author
  • Japan Trivedi
    • 1
  1. 1.Department of Civil and Environmental Engineering, School of Mining and Petroleum EngineeringUniversity of AlbertaEdmontonCanada

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