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

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## 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

*f*_{k}Fractional flow during steady-state

*f*_{min}Minimum measured value of fractional flow

*J*Capillary

*J*-function*k*Permeability (m

^{2})*K*_{r}Relative permeability

*K*_{rowi}Relative permeability of oil at initial water saturation

*K*_{rwor}Relative permeability of water at residual oil saturation

*L*Core length (m)

*l*_{g}Oil ganglion length (m)

*N*_{c}Capillary number

*N*_{min}Minimum number of samples

*n*_{o}Corey’s oil exponent

*n*_{w}Corey’s water exponent

*P*_{c}Capillary pressure (Pa)

*p*Pressure (Pa)

*p*_{min}Minimum measured pressure (Pa)

*P*Dimensionless pressure

*q*_{w}Water mass rate per unit area for linear flow (kg/m

^{2}s)*R*Radius (m)

*r*Pore throat radius

*s*Water saturation

*t*Time

*s*_{f}Frontal saturation during waterflooding

*S*_{or}Residual oil saturation

*S*_{wi}Connate water saturation

*U*Velocity

*V*_{min}Minimum distinguishable volume

*x*Distance (m)

*x*_{D}Dimensionless distance

## Greek Letters

*ε*_{c}Capillary–viscous ratio

*ε*_{w}Water-cut measurement accuracy

*ε*_{p}Pressure drop accuracy

*ε*_{s}Sampling period accuracy

- Δ
*t* Sampling period

*σ*Interfacial tension (N/m)

*ϕ*Porosity

*μ*Viscosity (Pa s)

*ρ*Density (kg/m

^{3})*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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