Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Relative Permeability

Three Phase Relative Permeability: Conclusions

Relative permeability for water wet and oil wet systems is distinctively different for two-phase flow.  In water oil system, as the system becomes more oil wet, relative permeability of water increases, relative permeability of oil decreases and the cross over point occurs at smaller water saturation.  In three-phase systems where the medium is strongly wetted, the relative permeability of the wetting phase is a function of its saturation only.  There is also some evidence that the relative permeability of the wetting phase and the non-wetting phase is a function of its own saturation only in strongly wetted medium.  This indicates that the relative permeability of the wetting and non-wetting phase is a function of its own saturation only.  This means that there is little or no hysteresis between drainage and imbibition relative permeability of the wetting phase and the non-wetting phase.  However, for the intermediate wetting phase, its relative permeability has been seen to be a function of other saturations, as well as saturation history.  Thus significant hysteresis in relative permeability of this phase is seen.

The steady state and unsteady state method can be used to evaluate relative permeability of each phase.  However, the steady state method yields more reliable data.  Most people recommend that this method should always be used.

The experiment to find relative permeability of three-phase systems is very complex, thus many models were developed.  Corey et al. published the first three-phase relative permeability model in 1956.  This model was based on the assumptions that the pore space in the medium can be represented by a bundle of capillary tubes.  Other methods that made the same assumption include: Naar and Wygal, Land, Parker et al.  Stone’s models are based on the channel flow theory.  He published method 1 in 1970 and method 2 in 1973.  Since then many people have modified these models.  These people include: Dietrich and Bondor, Hirasaki, Aziz and Settari, Fayers and Mathews, Aleman, and Parker et al.  There were also other models published by Pope, Baker, Blunt and Moulu et al.

Baker compared the models of Stone, Hirasaki, Corey et al., Naar and Wygal, Land Aleman and Parker et al.  He found that Stone’s method 1 could fit data better if the estimation of S_om is good.  However, he found that his own method, which is a simple interpolation between the various set of data, yields the best fits.  Delshad and Pope evaluated the predictions of Corey, Naar and Wygal, Land, Stone, Baker, Parker and Pope.  They found that Pope’s model fits better than the rest.  Up to this point, an extensive comparison of all the models with all the experimental data is not seen in literature, so it cannot be concluded which model is best.  However, Stone’s methods are the most commonly used.

There are some parameters that researchers have seen to affect relative permeability characteristics (of two-phase systems).  Many have seen that as interfacial tension decreases, the relative permeability of water and oil increases.  The reduction in IFT reduces the interference between two phases, making them able to flow better.  The relationship between relative permeability and saturation of low IFT system is still a point of debate; many say that this relationship is linear, while others say that it is not.

When temperature changes, the relative permeability also changes.  Handy et al. reported that the effect of temperature is more significant in low IFT systems.  In both high and low IFT, Sor decreases and S_wir increases with increasing temperature.  The cross over point also shifts to higher S_w values.  Thus Handy et al. believed that as temperature increases, the system becomes more water wet.  Nakornthap et al. explained that this increase in water wetness is due to the breakdown of the organic layer on the surface of the rock.  Sufi et al. disagree with this.  They believe that the change in relative permeability is due to the change in viscous forces, not a change in wettability.

Flow rate was seen to affect relative permeability.  Handy et al., Sandberg et al. and Sufi et al. reported that as the flow rate increases, relative permeability of water increases, while relative permeability of oil decreases.  However, Handy and Sufi disagree with the critical stable flow rate.

The effect of viscosity on relative permeability is also investigated.  Sandberg said that oil viscosity has no effect on relative permeability.  However, Odeh reported that the effect of viscosity is most significant at connate water saturation.  Also, Sufi et al believed that changes in viscosity lead to changes in relative permeability.

The studies of relative permeability and the effects of other parameters were mainly done on sandstones (or sandpacks) with conventional oil.  For carbonate systems, if the rock properties are uniform, the same flow characteristics seen before can be expected.  However, carbonates usually are oil wet while the majority of the models assumed that the medium is water wet.  Thus care must be taken when choosing a model to predict three-phase flow.  Also, carbonates have vugs, so the core sample evaluated might not be representative.  With heavy oil systems, the flow characteristics might be different.  The effects of these parameters on relative permeability may be different as well.  More experiments must be conducted to investigate the effects of each parameter on relative permeability.  The selection of an appropriate model to predict relative permeability of viscous oil should be made with care.