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Admissible Parameters for Two-Phase Coreflood and Welge–JBN Method

  • A. Al-Sarihi
  • Z. You
  • A. Behr
  • L. Genolet
  • P. Kowollik
  • A. Zeinijahromi
  • P. BedrikovetskyEmail author
Article
  • 44 Downloads

Abstract

The Welge–JBN method for determining relative permeability from unsteady-state waterflood test is commonly used for two-phase flows in porous media. We discuss the theoretical criteria that limits application of the basic Buckley–Leverett model and Welge–JBN method and the operational criteria of the accuracy of measurements during core waterflood tests. The objective is determination of the waterflood test parameters (core length, flow velocity and effluent sampling frequency) that fulfil the theoretical and operational criteria. The overall set of criteria results in five inequalities in three-dimensional Euclidian space of these parameters. For known rock and fluid properties, a formula for minimum core length to fulfil Welge–JBN criteria is derived. For cases where the core length is given, formulae for test’s flow velocity and sampling period are provided to satisfy the test admissibility conditions. The application of the proposed methodology is illustrated by two coreflood tests.

Keywords

Relative permeability Two-phase flow Welge–JBN method Coreflood parameters Mathematical model Laboratory waterflooding test 

List of Symbols

fk

Fractional flow during steady-state

fmin

Minimum measured value of fractional flow

J

Capillary J-function

k

Permeability (m2)

Kr

Relative permeability

Krowi

Relative permeability of oil at initial water saturation

Krwor

Relative permeability of water at residual oil saturation

L

Core length (m)

lg

Oil ganglion length (m)

Nc

Capillary number

Nmin

Minimum number of samples

no

Corey’s oil exponent

nw

Corey’s water exponent

Pc

Capillary pressure (Pa)

p

Pressure (Pa)

pmin

Minimum measured pressure (Pa)

P

Dimensionless pressure

qw

Water mass rate per unit area for linear flow (kg/m2 s)

R

Radius (m)

r

Pore throat radius

s

Water saturation

t

Time

sf

Frontal saturation during waterflooding

Sor

Residual oil saturation

Swi

Connate water saturation

U

Velocity

Vmin

Minimum distinguishable volume

x

Distance (m)

xD

Dimensionless distance

Greek Letters

εc

Capillary–viscous ratio

εw

Water-cut measurement accuracy

εp

Pressure drop accuracy

εs

Sampling period accuracy

Δt

Sampling period

σ

Interfacial tension (N/m)

ϕ

Porosity

μ

Viscosity (Pa s)

ρ

Density (kg/m3)

σ

Interfacial tension (N/m)

θ

Macroscopic contact angle

λ

Total mobility

ξ

Self-similar coordinate

Subscripts

c

Capillary

m

Maximum for velocity and for core length at maximum velocity

min

Minimum

w

Water

o

Oil

i

Initial

D

Dimensionless

Abbreviations

BL

Buckley–Leverett

BTC

Breakthrough curve

PDC

Pressure drop curve

RL

Rapoport–Leas

SS

Steady-state

USS

Unsteady-state

Notes

Acknowledgements

The paper is dedicated to the memory of Eng. C. Holleben (Petrobras) who initiated the work by Dos Santos et al. (1997). The authors are grateful to Dr. A. Badalyan (The University of Adelaide) for fruitful discussions. Deep gratitude is due to Profs. M. Lurie and A. Kurbanov (Moscow Oil–Gas Gubkin University), who introduced PB to waterflood mathematics.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • A. Al-Sarihi
    • 1
  • Z. You
    • 3
  • A. Behr
    • 2
  • L. Genolet
    • 2
  • P. Kowollik
    • 2
  • A. Zeinijahromi
    • 1
  • P. Bedrikovetsky
    • 1
    Email author
  1. 1.Australian School of PetroleumThe University of AdelaideAdelaideAustralia
  2. 2.Wintershall Holding GmbH, EOT/RKasselGermany
  3. 3.The University of QueenslandBrisbaneAustralia

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