In this chapter we will discuss relative permeabilities, relating their features to the pore-scale phenomena described previously. Both experimental measurements and predictions using different modelling approaches will be shown. However, this is not intended to be a comprehensive review of relative permeability, nor will it address measurement techniques: for a discussion of the latter see Honarpour et al. (1986) and Anderson (1987b).

Water-Wet Media

We show some example relative permeability curves for, unsurprisingly, our Bentheimer sandstone exemplar in Figs. 7.1, 7.2 and 7.3 (Ramstad et al., 2012; Alizadeh and Piri, 2014a). In the experiments shown in Fig. 7.1, the contact angle between water and oil was measured directly using X-ray imaging during primary drainage and waterflooding, with average values of 22° and 28° respectively, indicating strongly water-wet conditions (Aghaei and Piri, 2015).

Primary Drainage

In primary drainage, the rock is initially completely saturated with water: kro = 0 and krw = 1. The oil first traverses the largest throats in an invasion percolation process, as described in Chapter 3.4: this cuts off the most conductive flow paths for the water and krw drops sharply. There is a critical saturation when the oil phase will first span the sample. In the experiments of Alizadeh and Piri (2014a) the core is 3.81 cm in diameter and our pore length is 79 μm: putting these values in Eq. (3.29) gives an estimated critical saturation of around 5%, consistent with the results shown in Fig. 7.1. Percolation theory predicts a power-law rise in kro as a function of oil saturation with an exponent of around 4.8, Eq. (6.74).

The two relative permeabilities cross, krw = kro , at a saturation Sw ≈ 0.55 with a value of around 0.1 or lower. When there is a significant saturation of both phases, the sum of the relative permeabilities is much less than 1, indicating that the total flow of oil and water is impeded. This is caused by the presence of menisci which act as flow barriers to both phases; in particular, terminal menisci block pores and throats, while arc menisci have less of an impact, since they are confined to roughness and corners of the pore space.