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

A. Al-Sarihi; Z. You; A. Behr; L. Genolet; P. Kowollik; A. Zeinijahromi; P. Bedrikovetsky

doi:10.1007/s11242-019-01369-w

Transport in Porous Media

pp 1–41 | Cite as

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

Authors
Authors and affiliations

A. Al-Sarihi
Z. You
A. Behr
L. Genolet
P. Kowollik
A. Zeinijahromi
P. Bedrikovetsky

Article

First Online: 16 November 2019

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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 (m²)
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/m² 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
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

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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.

Appendix A: Mathematical Model for Two-Phase Immiscible Displacement

Following Rapoport and Leas (1953), Barenblatt et al. (1991), Lake et al. (2014), here we present the mathematical model for two-phase flow of immiscible incompressible fluids in porous media. The modified Darcy’s law expresses the momentum balance for each phase

$$u_{\text{w}} = - \frac{{kk_{\text{rw}} (s)}}{{\mu_{\text{w}} }}\frac{{\partial P_{\text{w}} }}{\partial x}\quad u_{\text{o}} = - \frac{{kk_{\text{ro}} (s)}}{{\mu_{\text{o}} }}\frac{{\partial P_{\text{o}} }}{\partial x}$$

(A.1)

where k is the permeability, u_w and u_o are the water and oil velocities, respectively, K_rw and K_ro are the relative permeability for water and oil, s is the saturation, μ_w and μ_o are the viscosity for water and oil and P_w and P_o are the phase pressures in water and oil.

Volumetric balance for water is:

$$\phi \frac{\partial s}{\partial t} + \frac{{\partial u_{\text{w}} }}{\partial x} = 0$$

(A.2)

Here ϕ is the porosity.

The total flux conservation follows from incompressibility of both phases:

$$u_{\text{w}} + u_{\text{o}} = U(t)$$

(A.3)

where U is the total velocity.

The difference between phase pressures is equal to capillary pressure

$$P_{\text{o}} - P_{\text{w}} = P_{\text{c}} (s) = \frac{\sigma \cos \theta }{{\sqrt {(k /\phi } )}}J(s)$$

(A.4)

Here P_c is the capillary pressure, σ is the interfacial tension, θ is the contact angle, and J is the capillary function.

Substituting Darcy’s law for both phases (1, 2) into the expression (4) for the total flux, expressing pressure in oil from Eq. (5) and also substituting it into Eq. (4) yield

$$U = - k\left( {\frac{{k_{\text{rw}} (s)}}{{\mu_{\text{w}} }} + \frac{{k_{\text{ro}} (s)}}{{\mu_{\text{o}} }}} \right)\frac{{\partial P_{\text{w}} }}{\partial x} - \frac{{kk_{\text{ro}} (s)}}{{\mu_{\text{o}} }}\frac{\sigma \cos \theta }{{\sqrt {\left( {k /\phi } \right)} }}\frac{\partial J(s)}{\partial x}$$

(A.5)

Expressing pressure gradient in water and substituting it into Eq. (1) yields

$$u_{\text{w}} = Uf(s) + \frac{{kk_{\text{ro}} (s)}}{{\mu_{\text{o}} }}\frac{\sigma \cos \theta }{{\sqrt {\left( {k /\phi } \right)} }}\left( {\frac{\partial J(s)}{\partial x}} \right)f(s),\quad f(s) = \left( {1 + \frac{{k_{\text{ro}} (s)\mu_{\text{w}} }}{{k_{\text{rw}} (s)\mu_{\text{o}} }}} \right)^{ - 1}$$

(A.6)

where f is the fractional flow for water.

Substituting expression for water flux (A.6) into volume balance equation for water (A.2) results in one equations for unknown saturation s(x, t):

$$\phi \frac{\partial s}{\partial t} + U\frac{\partial f(s)}{\partial x} = - \frac{\partial }{\partial x}\left[ {\frac{{kk_{\text{ro}} (s)}}{{\mu_{\text{o}} }}\frac{\sigma \cos \theta }{{\sqrt {\left( {k /\phi } \right)} }}\left( {\frac{\partial J(s)}{\partial x}} \right)} \right]$$

(A.7)

Introduce the following dimensionless variables and parameters:

$$x_{\text{D}} = \frac{x}{L},\quad t_{\text{D}} = \frac{1}{\phi L}\int_{0}^{t} {U(y){\text{d}}y,\quad P = \frac{kp}{{\mu_{\text{o}} UL}},\quad \varepsilon_{\text{c}} = \frac{{\sigma \cos \theta \sqrt {k\phi } }}{{\mu_{\text{o}} UL}}}$$

(A.8)

Here x_D is the dimensionless distance, L is the core length, t_D is the dimensionless time, P is the dimensionless pressure, and ε_c is the capillary-viscous ratio.

Equations (A.5, A.7) become

$$\frac{\partial s}{{\partial t_{\text{D}} }} + \frac{\partial f(s)}{{\partial x_{\text{D}} }} = \varepsilon_{\text{c}} \frac{\partial }{{\partial x_{\text{D}} }}\left( { - k_{\text{ro}} (s)f(s)J^{{\prime }} (s)\frac{\partial s}{{\partial x_{\text{D}} }}} \right),\quad f(s) = \left( {1 + \frac{{k_{\text{ro}} (s)\mu_{\text{w}} }}{{k_{\text{rw}} (s)\mu_{\text{o}} }}} \right)^{ - 1}$$

(A.9)

$$1 = - \frac{k\lambda (s)}{LU}\frac{\partial P}{{\partial x_{\text{D}} }} - \varepsilon_{\text{c}} k_{\text{ro}} (s)\frac{\partial J(s)}{{\partial x_{\text{D}} }},\quad \lambda (s) = \frac{{k_{\text{rw}} (s)\mu_{\text{o}} }}{{\mu_{\text{w}} }} + k_{\text{ro}} (s)$$

(A.10)

Here λ(s) is the total mobility of two phases.

Equations (A.1) and (A.3) are decoupled, which means that the saturation distribution during the displacement s(x_D, t_D) is determined from Eq. (A.1). Afterwards, the pressure distribution p(x_D, t_D) is determined from Eq. (A.2) for the obtained saturation distribution.

Water flux in continuity Eq. (A.1) consists on the advective and capillary components, defined by Eq. (A.9).

The core is initially saturated with oil and connate water, i.e. the initial condition for Eq. (A.1) is:

$$t_{\text{D}} = 0{:}\quad s = S_{\text{wi}}$$

(A.11)

Here S_wi is the initial water saturation.

Only water flows through the inlet cross section, so the boundary condition at the inlet of the core is:

$$x_{\text{D}} = 0{:}\quad f - \varepsilon_{\text{c}} k_{\text{ro}} \,f\,J^{{\prime }} (s)\frac{\partial s}{{\partial x_{\text{D}} }} = 1$$

(A.12)

The boundary condition at the core outlet after the breakthrough is given by the condition of continuity of pressures in the both phases across the outlet interface, from which follows the continuity of the capillary pressure also. At the right-hand side of the core outlet, we assume a segregated flow regime, so the capillary pressure is zero. Therefore, the capillary pressure is zero behind the core outlet too. Thus, the boundary condition at the outlet of the core corresponds to zero capillary pressure:

$$x_{\text{D}} = 1{:}\quad J(s) = 0$$

(A.13)

and the outlet saturation after the breakthrough is equal to its maximum value s⁰ = 1 − S_or. Here S_or is the residual oil saturation.

Appendix B: Large-Scale Approximation of the Buckley–Leverett Equations

For small values of ε_c, one can neglect terms with ε_c in right-hand sides of Eqs. (A.9, A.10):

$$\frac{\partial s}{{\partial t_{\text{D}} }} + \frac{\partial f(s)}{{\partial x_{\text{D}} }} = 0$$

(B.1)

$$1 = - \frac{k\lambda (s)}{LU}\frac{\partial P}{{\partial x_{\text{D}} }}$$

(B.2)

For this case, fractional flow function f(s) is the ratio between the water flux and the total flux.

Approaching ε_c > 0 in the boundary condition (A.6), we obtain:

$$x_{\text{D}} = 0{:}\quad f = 1$$

(B.3)

The solution s(x_D, t_D) of the 1 − D capillary–pressure–free displacement problem (B.1), (A.5)–(A.7) is self-similar, depending only on the group ξ = x_D/t_D, i.e. s(x_D, t_D) = s(ξ):

$$s\left( {x_{\text{D}} ,t_{\text{D}} } \right) = \left\{ {\begin{array}{*{20}l} {1 - S_{\text{or}} ,} \hfill & {0 < \frac{{x_{\text{D}} }}{{t_{\text{D}} }} < D_{\text{or}} = f^{{\prime }} \left( {1 - S_{\text{or}} } \right)} \hfill \\ {\frac{{x_{\text{D}} }}{{t_{\text{D}} }} = f^{{\prime }} \left( s \right),} \hfill & {D_{\text{or}} < \frac{{x_{\text{D}} }}{{t_{\text{D}} }} < D = f^{{\prime }} \left( {S_{\text{f}} } \right) = \frac{{\left( {S_{\text{f}} } \right)}}{{S_{\text{f}} - S_{\text{wi}} }}} \hfill \\ {S_{\text{wi}} ,} \hfill & {D < \frac{{x_{\text{D}} }}{{t_{\text{D}} }} < \infty } \hfill \\ \end{array} } \right.$$

(B.4)

The self-similarity of the solution is the only information which is required for inverse problem to have exact solution (see). In two following sections exact shape of s(x_D, t_D) will not be used, and only the fact of self-similarity will be exploited.

Appendix C: Welge’s Method for Determination of Fractional Flow Function

Let us discuss how to determine the fractional flow function f(s) from the water-cut history f(1, t_D) measured during the coreflood.

Let us integrate Eq. (B.1) over the region Δ on the plane (x_D, t_D) which is limited by the triangle ∂Δ: (0, 0) → (1, 0) → (1, t_D) → (0, 0) and apply the Green’s formula (Bedrikovetsky 2013):

$$0 = \iint\limits_{\Delta } {\left( {\frac{\partial s}{{\partial t_{\text{D}} }} + \frac{\partial f}{{\partial x_{\text{D}} }}} \right)}{\text{d}}x_{\text{D}} {\text{d}}t_{\text{D}} = \oint\limits_{{\delta\Delta }} {f{\text{d}}t_{\text{D}} - s{\text{d}}x_{\text{D}} }$$

(C.1)

Let us calculate the contour integral in (C.1) over the sides of triangle ∂Δ:

$$(0,0) \to (1,t_{\text{D}} ){:}\quad 0 \times 0 + ( - s_{i} \times 1) = - s_{i}$$

(C.2)

$$(1,0) \to (1,t_{\text{D}} ){:}\quad \int_{0}^{{t_{\text{D}} }} {f(1,\tau ){\text{d}}\tau } - s \times 0$$

(C.3)

$$(0,0) \to (1,t_{\text{D}} ){:}\quad f\left( {s\left( {1 /t_{\text{D}} } \right)} \right) - s\left( {1 /t_{\text{D}} } \right)f_{\text{s}}^{{\prime }} (s)$$

(C.4)

Substituting the expressions for the integrals over the sides of the triangle (C.2–C.4) into Eq. (C.1), we obtain the expression for the saturation on the core outlet:

$$s\,\left( {1,\,t_{\text{D}} } \right) = s_{i} + f\,\left( {1,t_{\text{D}} } \right)\,t_{\text{D}} - \int\limits_{0}^{{t_{\text{D}} }} {f\,\left( {1,t} \right)\,} {\text{d}}t$$

(C.5)

Corresponding the saturation values, calculated by (C.5), to the water-cut values, which have been measured at the same moments, we obtain the dependence f = f(s).

Appendix D: JBN Method for Determination of Relative Permeability

Following the works by Johnson et al. (1959) and Jones and Roszelle (1978), let us calculate the pressure drop on the core during the waterflood:

$$\Delta \,p\,\left( {t_{\text{D}} } \right) = \int\limits_{0}^{1} {\left( { - \,\frac{\partial p}{{\partial x_{\text{D}} }}} \right)\,{\text{d}}x_{\text{D}} = \frac{U\,L}{k}\,\int\limits_{0}^{1} {\frac{{{\text{d}}x_{\text{D}} }}{\lambda \,\left( s \right)}} } = \frac{{U\,L\,t_{\text{D}} }}{k}\,\,\int\limits_{0}^{1 /T} {\frac{{{\text{d}}\xi }}{\lambda \,\left( s \right)}}$$

(D.1)

Expressing the integral from (D.1) and taking its derivative with respect to the upper limit, we obtain the explicit expression for the total mobility

$$\lambda = \frac{\text{d}}{{{\text{d}}\xi }}\,\left( {\frac{{k\;\Delta \,p\,\left( \xi \right)\;\xi }}{U\;L}} \right),\quad \xi = \frac{1}{{t_{\text{D}} }}$$

(D.2)

Corresponding the values of total mobility calculated by (D.2) to the values of saturations calculated by (C.5) for the coherent moments, we obtain the dependence λ = λ(s).

From the expression for the fractional flow function (A.9), the formulae for determination of relative permeabilities for both phases are:

$$k_{\text{rw}} = f\,\lambda \;\mu_{\text{W}} ;\quad k_{\text{ro}} = \,\left( {1 - f} \right)\,\lambda \;\mu_{\text{o}}$$

(D.3)

It is important to emphasise that formulae (C.5) and (D.2), (D.3) deliver the solution f = f(s) and λ = λ(s) only for saturations which are realised during the displacement process. In the case of the displacement of oil with the connate water by water, the method provides with the fractional flow function and total mobility only for saturations higher than the frontal saturation s_f and below the s⁰ and also in the initial point S_wi.

Appendix E: Determination of the Frontal Saturation and Displacement Velocity from the Waterless Period Data

Let us calculate the pressure drop on the core, as in (D.1), but for the moment before the breakthrough. Acting by analogy to Eq. (D.1), we obtain

$$\Delta \;p\,\left( {t_{\text{D}} } \right) = \frac{U\,L}{k}\,\left( {t_{\text{D}} \;\int\limits_{0}^{D} {\frac{{{\text{d}}\xi }}{\lambda \,\left( s \right)} + \frac{{1 - D\,t_{\text{D}} }}{{\lambda \,\left( {s_{\text{i}} } \right)}}} } \right)$$

(E.1)

where initial saturation s_i can exceed connate water saturation S_wi.

Let us transform Eq. (E.1) to the form

$$\frac{{k\,\Delta \;p\,\left( {t_{\text{D}} } \right)}}{U\,L} = T\,\left( {\;\int\limits_{0}^{D} {\frac{{{\text{d}}\xi }}{\lambda \,\left( s \right)} - \frac{D}{{\lambda \,\left( {s_{i} } \right)}}} } \right) + \frac{1}{{\lambda \,\left( {s_{i} } \right)}}$$

(E.2)

Equation (E.2) gives the straight line versus t_D. The free constant in it is determined by the total mobility before the flood, which is known from the initial saturation process. The slope of the line together with the condition that the velocity D is the tangent of the fractional flow curve in the frontal saturation point makes it possible to determine the slope D and the frontal saturation s_f. The slope of the pressure drop as defined by Eq. (E.2) and calculated from the measured data is an additional information for relative permeability tuning from the coreflood data.

Appendix F: Determination of Pore Throat Radius from Permeability and Porosity

Following Barenblatt et al. (1991), here we derive permeability and porosity for cubic lattice with the tube radius r and the bond length l. One cube is adjacent to 12 bonds and one bond belongs to four cubes, so each cube includes three bonds. The porosity is equal to

$$\phi = 3\frac{{\pi r^{2} l}}{{l^{3} }}$$

(F.1)

Flow through a cube side corresponds to flow through a single tube. Comparing Darcy and Poiseuille laws

$$U = \frac{k}{\mu }\frac{\Delta p}{l} = \frac{1}{{l^{2} }}\frac{{\pi r^{4} }}{8\mu }\frac{{\Delta p}}{l},$$

(F.2)

we obtain the formula for permeability

$$k = \frac{{\pi r^{4} }}{{8l^{2} }}$$

(F.3)

From Eqs. (F.1) and (F.3) follows the expression for pore throat radius r

$$r = \sqrt {\frac{24k}{\phi }} .$$

(F.4)

References

Abbas, M.: An extension of Johnson, Bossler and Neumann JBN method for calculating relative permeabilities. In: SPE Annual Technical Conference and Exhibition 2016. Society of Petroleum Engineers (2016)Google Scholar
Adler, P.M.: Multiphase Flow in Porous Media. Springer, Amsterdam (1995)CrossRefGoogle Scholar
Adler, P.: Porous Media: Geometry and Transports. Elsevier, Amsterdam (2013)Google Scholar
Adler, P.M., Thovert, J.-F.: Fractures and Fracture Networks, pp. 103–162. Springer, Berlin (1999)Google Scholar
Akin, S.: Estimation of fracture relative permeabilities from unsteady state corefloods. J. Pet. Sci. Eng. 30(1), 1–14 (2001)CrossRefGoogle Scholar
Al Shalabi, E.W., Sepehrnoori, K., Delshad, M.: Mechanisms behind low salinity water flooding in carbonate reservoirs. In: SPE Western Regional & AAPG Pacific Section Meeting 2013 Joint Technical Conference 2013. Society of Petroleum Engineers (2013)Google Scholar
Arns, C., Adler, P.: Fast Laplace solver approach to pore-scale permeability. Phys. Rev. E 97(2), 023303 (2018)CrossRefGoogle Scholar
Arns, J.-Y., Arns, C.H., Sheppard, A.P., Sok, R.M., Knackstedt, M.A., Pinczewski, W.V.: Relative permeability from tomographic images; effect of correlated heterogeneity. J. Pet. Sci. Eng. 39(3–4), 247–259 (2003)CrossRefGoogle Scholar
Arns, C., Knackstedt, M., Mecke, K.: Boolean reconstructions of complex materials: integral geometric approach. Phys. Rev. E 80(5), 051303 (2009)CrossRefGoogle Scholar
Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publ. Ltd., London (1979)Google Scholar
Badalyan, A., Carageorgos, T., Bedrikovetsky, P., You, Z., Zeinijahromi, A., Aji, K.: Critical analysis of uncertainties during particle filtration. Rev. Sci. Instrum. 83(9), 095106 (2012)CrossRefGoogle Scholar
Banchoff, T.F., Lovett, S.T.: Differential Geometry of Curves and Surfaces. Chapman and Hall/CRC, London (2016)Google Scholar
Barenblatt, G., Entov, V., Ryzhik, V.: Theory of Fluid Flows Through Natural Rocks. Kluwer, Dordrecht (1991)Google Scholar
Barenblatt, G., Patzek, T.W., Silin, D.: The mathematical model of nonequilibrium effects in water–oil displacement. SPE J. 8(04), 409–416 (2003)CrossRefGoogle Scholar
Bartels, W.-B., Mahani, H., Berg, S., Hassanizadeh, S.: Literature review of low salinity waterflooding from a length and time scale perspective. Fuel 236, 338–353 (2019)CrossRefGoogle Scholar
Bedrikovetsky, P.: Mathematical Theory of Oil and Gas Recovery: With Applications to Ex-USSR Oil and Gas Fields, vol. 4. Springer, Berlin (2013)Google Scholar
Borazjani, S., Behr, A., Genolet, L., Van Der Net, A., Bedrikovetsky, P.: Effects of fines migration on low-salinity waterflooding: analytical modelling. Trans. Porous Media 116(1), 213–249 (2017)CrossRefGoogle Scholar
Borazjani, S., Behr, A., Genolet, L., Kowollik, P., Bedrikovetsky, P.: Ion-exchange inverse problem for low-salinity coreflooding. Trans. Porous Media 128(2), 571–611 (2019)CrossRefGoogle Scholar
Buckley, S.E., Leverett, M.: Mechanism of fluid displacement in sands. Trans. AIME 146(01), 107–116 (1942)CrossRefGoogle Scholar
Cao, J., James, L.A., Johansen, T.E.: Determination of two phase relative permeability from core floods with constant pressure boundaries. In: Society of Core Analysis Symposium, Avignon, France (2014)Google Scholar
Cao, J., Liu, X., James, L., Johansen, T.: Analytical interpretation methods for dynamic immiscible core flooding at constant differential pressure. In: Society of Core Analysis Symposium, St. John’s Newfoundland and Labrador, Canada, pp. 16–21 (2015)Google Scholar
Chatzis, I., Morrow, N.R., Lim, H.T.: Magnitude and detailed structure of residual oil saturation. Soc. Pet. Eng. J. 23(02), 311–326 (1983)CrossRefGoogle Scholar
Chen, Z.: Reservoir Simulation: Mathematical Techniques in Oil Recovery, vol. 77. SIAM, Philadelphia (2007)CrossRefGoogle Scholar
Chen, X., Kianinejad, A., DiCarlo, D.A.: An extended JBN method of determining unsteady-state two-phase relative permeability. Water Resour. Res. 52(10), 8374–8383 (2016)CrossRefGoogle Scholar
Civan, F., Donaldson, E.: Relative permeability from unsteady-state displacements with capillary pressure included. SPE Form. Eval. 4(02), 189–193 (1989)CrossRefGoogle Scholar
Dake, L.P.: Fundamentals of Reservoir Engineering, vol. 8. Elsevier, Amsterdam (1983)Google Scholar
Dos Santos, R.L., Bedrikovetsky, P., Holleben, C.R.: Optimal design and planning for laboratory corefloods. In: Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers (1997)Google Scholar
Farajzadeh, R., Ameri, A., Faber, M.J., Van Batenburg, D.W., Boersma, D.M., Bruining, J.: Effect of continuous, trapped, and flowing gas on performance of Alkaline Surfactant Polymer (ASP) flooding. Ind. Eng. Chem. Res. 52(38), 13839–13848 (2013)CrossRefGoogle Scholar
Farajzadeh, R., Lotfollahi, M., Eftekhari, A., Rossen, W., Hirasaki, G.: Effect of permeability on implicit-texture foam model parameters and the limiting capillary pressure. Energy Fuels 29(5), 3011–3018 (2015)CrossRefGoogle Scholar
Farajzadeh, R., Guo, H., van Winden, J., Bruining, J.: Cation exchange in the presence of oil in porous media. ACS Earth Space Chem. 1(2), 101–112 (2017)CrossRefGoogle Scholar
Honarpour, M., Koederitz, F., Herbert, A.: Relative permeability of petroleum reservoirs. CRC Press, United States (1986)CrossRefGoogle Scholar
Hussain, F., Cinar, Y., Bedrikovetsky, P.G.: Comparison of methods for drainage relative permeability estimation from displacement tests. In: SPE Improved Oil Recovery Symposium. Society of Petroleum Engineers (2010)Google Scholar
Hussain, F., Cinar, Y., Bedrikovetsky, P.: A semi-analytical model for two phase immiscible flow in porous media honouring capillary pressure. Trans. Porous Media 92(1), 187–212 (2012)CrossRefGoogle Scholar
Hussain, F., Zeinijahromi, A., Bedrikovetsky, P., Badalyan, A., Carageorgos, T., Cinar, Y.: An experimental study of improved oil recovery through fines-assisted waterflooding. J. Pet. Sci. Eng. 109, 187–197 (2013)CrossRefGoogle Scholar
Hussain, F., Pinczewski, W.V., Cinar, Y., Arns, J.-Y., Arns, C., Turner, M.: Computation of relative permeability from imaged fluid distributions at the pore scale. Trans. Porous Media 104(1), 91–107 (2014)CrossRefGoogle Scholar
Islam, M.R., Bentsen, R.: A dynamic method for measuring relative permeability. J. Can. Pet. Technol. 25(01), 39–50 (1986)Google Scholar
Johansen, T.E., James, L.A.: Solution of multi-component, two-phase Riemann problems with constant pressure boundaries. J. Eng. Math. 96(1), 23–35 (2016)CrossRefGoogle Scholar
Johnson, E., Bossler, D., Bossler, V.: Calculation of relative permeability from displacement experiments (1959)Google Scholar
Jones, S., Roszelle, W.: Graphical techniques for determining relative permeability from displacement experiments. J. Pet. Technol. 30(05), 807–817 (1978)CrossRefGoogle Scholar
Katika, K., Ahkami, M., Fosbøl, P.L., Halim, A.Y., Shapiro, A., Thomsen, K., Xiarchos, I., Fabricius, I.L.: Comparative analysis of experimental methods for quantification of small amounts of oil in water. J. Pet. Sci. Eng. 147, 459–467 (2016)CrossRefGoogle Scholar
Kianinejad, A., Chen, X., DiCarlo, D.A.: Direct measurement of relative permeability in rocks from unsteady-state saturation profiles. Adv. Water Resour. 94, 1–10 (2016)CrossRefGoogle Scholar
Kim, C., Lee, J.: Experimental study on the variation of relative permeability due to clay minerals in low salinity water-flooding. J. Pet. Sci. Eng. 151, 292–304 (2017)CrossRefGoogle Scholar
Krause, M.: Modeling and investigation of the influence of capillary heterogeneity on relative permeability. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2012)Google Scholar
Krause, M.H., Benson, S.M.: Accurate determination of characteristic relative permeability curves. Adv. Water Resour. 83, 376–388 (2015)CrossRefGoogle Scholar
Kuo, C.-W., Benson, S.M.: Numerical and analytical study of effects of small scale heterogeneity on CO2/brine multiphase flow system in horizontal corefloods. Adv. Water Resour. 79, 1–17 (2015)CrossRefGoogle Scholar
Kuo C.-w., Perrin J.-C., Benson, S.M.: Effect of gravity, flow rate, and small scale heterogeneity on multiphase flow of CO2 and brine. In: SPE Western Regional Meeting. Society of Petroleum Engineers (2010)Google Scholar
Lake, L.W., Johns, R., Rossen, W.R., Pope, G.A.: Fundamentals of enhanced oil recovery (2014)Google Scholar
Maplesoft™: Solver for a system of inequalities. https://www.maplesoft.com/support/help/maple/view.aspx?path=Task/SolveInequality (2019). Accessed 10 March 2019
MathWorks^®: Meshgrid, Surf Commands https://au.mathworks.com/products/matlab.html (2019). Accessed 10 March 2019
McPhee, C., Reed, J., Zubizarreta, I.: Core Analysis: A Best Practice Guide, vol. 64. Elsevier, Amsterdam (2015)Google Scholar
Miller, M.A., Ramey Jr., H.: Effect of temperature on oil/water relative permeabilities of unconsolidated and consolidated sands. Soc. Pet. Eng. J. 25(06), 945–953 (1985)CrossRefGoogle Scholar
Nasralla, R.A., Mahani, H., van der Linde, H.A., Marcelis, F.H., Masalmeh, S.K., Sergienko, E., Brussee, N.J., Pieterse, S.G., Basu, S.: Low salinity waterflooding for a carbonate reservoir: experimental evaluation and numerical interpretation. J. Pet. Sci. Eng. 164, 640–654 (2018)CrossRefGoogle Scholar
Odeh, A., Dotson, B.: A method for reducing the rate effect on oil and water relative permeabilities calculated from dynamic displacement data. J. Pet. Technol. 37(11), 2051-052058 (1985)CrossRefGoogle Scholar
Pereira, B.M.F., Shahverdi, H., Sohrabi, M.: Refinement of relative permeability measurements by accounting for viscous fingering in coreflood experiments. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2014)Google Scholar
Perrin, J.-C., Krause, M., Kuo, C.-W., Miljkovic, L., Charoba, E., Benson, S.M.: Core-scale experimental study of relative permeability properties of CO2 and brine in reservoir rocks. Energy Proc. 1(1), 3515–3522 (2009)CrossRefGoogle Scholar
Rabinovich, A.: Estimation of sub-core permeability statistical properties from coreflooding data. Adv. Water Resour. 108, 113–124 (2017)CrossRefGoogle Scholar
Rabinovich, A.: Analytical corrections to core relative permeability for low-flow-rate simulation. SPE J. (2018)Google Scholar
Rabinovich, A., Li, B., Durlofsky, L.J.: Analytical approximations for effective relative permeability in the capillary limit. Water Resour. Res. 52(10), 7645–7667 (2016)CrossRefGoogle Scholar
Rapoport, L., Leas, W.: Properties of linear waterfloods. J. Pet. Technol. 5(05), 139–148 (1953)CrossRefGoogle Scholar
Richmond, P., Watsons, A.: Estimation of multiphase flow functions from displacement experiments. SPE Reserv. Eng. 5(01), 121–127 (1990)CrossRefGoogle Scholar
Sigmund, P., McCaffery, F.: An improved unsteady-state procedure for determining the relative-permeability characteristics of heterogeneous porous media (includes associated papers 8028 and 8777). Soc. Pet. Eng. J. 19(01), 15–28 (1979)CrossRefGoogle Scholar
Sorop, T.G., Masalmeh, S.K., Suijkerbuijk, B.M.J.M., van der Linde, H.A., Mahani, H., Brussee, N.J., Marcelis, F.A.H.M., Coorn, A. Relative Permeability Measurements to Quantify the Low Salinity Flooding Effect at Field Scale (2015)Google Scholar
Tao, T., Watson, A.: Accuracy of JBN estimates of relative permeability: part 2-algorithms. Soc. Pet. Eng. J. 24(02), 215–223 (1984)CrossRefGoogle Scholar
Torsæter, O., Abtahi, M.: Experimental Reservoir Engineering Laboratory Workbook. Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology (NTNU), Trondheim (2003)Google Scholar
Toth, J., Bodi, T., Szucs, P., Civan, F.: Direct determination of relative permeability from nonsteady-state constant pressure and rate displacements. In: SPE Production and Operations Symposium. Society of Petroleum Engineers (2001)Google Scholar
Toth, J., Bodi, T., Szucs, P., Civan, F.: Convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs. J. Pet. Sci. Eng. 36(1–2), 33–44 (2002)CrossRefGoogle Scholar
Virnovsky, G., Guo, Y.: Relative permeability and capillary pressure concurrently determined from steady-state flow experiments. In: IOR 1995-8th European Symposium on Improved Oil Recovery (1995)Google Scholar
Virnovsky, G., Vatne, K., Skjaeveland, S., Lohne, A.: Implementation of multirate technique to measure relative permeabilities accounting. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (1998)Google Scholar
Welge, H.J.: A simplified method for computing oil recovery by gas or water drive. J. Pet. Technol. 4(04), 91–98 (1952)CrossRefGoogle Scholar
Zeinijahromi, A., Farajzadeh, R., Bruining, J.H., Bedrikovetsky, P.: Effect of fines migration on oil–water relative permeability during two-phase flow in porous media. Fuel 176, 222–236 (2016)CrossRefGoogle Scholar
Zhou, K., Hou, J., Fu, H., Wei, B., Liu, Y.: Estimation of relative permeability curves using an improved Levenberg–Marquardt method with simultaneous perturbation Jacobian approximation. J. Hydrol. 544, 604–612 (2017)CrossRefGoogle Scholar
Zou, S., Hussain, F., Arns, J.-Y., Guo, Z., Arns, C.H.: Computation of relative permeability from in situ imaged fluid distributions at the pore scale. SPE J. 23(03), 737–749 (2018)CrossRefGoogle Scholar

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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.Australian School of PetroleumThe University of AdelaideAdelaideAustralia
2.Wintershall Holding GmbH, EOT/RKasselGermany
3.The University of QueenslandBrisbaneAustralia

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

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