Fundamentals of Fluid Flow in Porous Media


Chapter 2

Relative Permeability

Three Phase Relative Permeability: Effects of Flow Rate on Relative Permeability

Theoretically, relative permeability is not a function of flow rate.  However, there has been experimental data which shows that the relative permeability changes as the flow rate changes.  In general, the relative permeabilities for both phases were found to increase with increasing flow rate.

Leverett et al. were the first to report about the influence of flow rate on relative permeability, however they later attributed this to capillary end effects.  Crowell et al. and Greffen et al. found that injection rate has no affect on the viscous flow of water and gas. Also, Labastie et al. reported that relative permeabilities were independent of flow rate except near residual oil saturation

[25].  However, there are many others who reported that relative permeability does change as flow rate changes.

Heaviside et al. believed that for an intermediate wettability medium, at low flow rates the oil segments would exist in the center of pores, and blocks the flow of water.  However, at high pressure gradients or high flow rates water would be forced through the throats with the oil coating the pore surface.  Thus relative permeability can change with flow rate[7].

Heaviside et al. also found that the viscous force does not affect residual oil saturation for strongly water wet chalk.  In the experiment, the pressure gradient is increased but no change in production rate is seen[7].

Handy et al. reported that rate affects relative permeability below 120 cc/hr.  Above this rate, no significant rate effect was observed[21].  Also, they have seen that the rate effect does not significantly affect Sor or end point relative permeabilities

Sandberg et al., however, reported that the relative permeability of the water phase increased very slightly with flow rate.  In contrast, the oil phase relative permeability increases significantly.  He reasoned that the rate effect on the oil phase may be a result of some tendency for the oil phase to flow in slugs[6].

Sufi et al. performed a more in depth study regarding the effects of flow rate on relative permeability.  They noticed a trend in the relative permeability curves from the experimental results, which is shown in Figure 2‑95.

Effects of Flow Rate on Relative Permeability (After 22)
Figure 2-95: Effects of Flow Rate on Relative Permeability (After 22)

This figure shows that the relative permeabilities for oil remain unchanged, while the water relative permeability curves are low at low flow rate, and become independent of rate when the flow is high (greater than 240 cc/hr).  Therefore, it was assumed by Sufi et al. that the rate of 240 cc/hr represents the minimum rate required for front stability.  As mentioned before, Handy said that in their experiment when the flow rate is larger than 120 cc/hr, no effect is seen.  Thus Sufi and Handy disagree about the value of the critical stability flow rate.

It was found by Akin et al. that gas relative permeability increases with increasing total flow rate.  They have also seen that the effects on brine and hexane relative permeability are much more compared to gas relative permeability.  The oil and water capillary pressure values for higher flow rates were also greater at high brine saturation data.  Thus it is expected that relative permeability should change with flow rate[25].

Heaviside et al. reported that for strongly wetted systems, at high IFT, there is a negligible rate dependency, even at very high flow rate.  However, in cases of low IFT, rate dependency can be seen[7].


[6] Sandberg, C.R. and Gournay, L.S., “The Effect of Fluid-Flow Rate and Viscosity on Laboratory Determinations of Oil-Water Relative Permeabilities”, Trans., AIME (1958) 213, 36-43.

[7] Heaviside, J., Brown, C.E., and Gamble, I.J.A., “Relative Permeability for Intermediate Wettability Reservoirs”, SPE 16968.

[21] Torabzadeh, S.J. and Handy, L.L., “The Effect of Temperature and Interfacial Tension on Water/Oil Relative Permeabilities of Consolidated Sands”, SPE 12689.

[25] Akin, S. And Demiral, B., “Effects of Flow Rate on Three-Phase Relative Permeabilities and Capillary Pressures”, SPE 38897.


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