Non-uniqueness in capillary pressure–saturation–relative permeability relationships for two-phase flow in porous media: Interplay between intensity and distribution of random micro-heterogeneities

Abstract

8The two-phase flow behaviour in porous media is determined on the basis of capillary pressure-saturation-relative 9 permeability relationships (P c -S-K r ). These relationships are highly non-linear and obtained by laboratory 10 experiments on porous samples, typically around 10-12cm in length. It is normally assumed that these samples are 11 homogenous; however it is well known that this is in fact not the case and that even at this scale micro-scale 12 heterogeneities exist. Two-phase flow experiments on soils with different properties (e.g., particle and pore size 13 distribution, permeabilities, etc) result in different P c -S relationships. These cause non-uniqueness in the P c -S 14 curves. Recent work has shown that the presence of these micro-heterogeneities has a significant effect on the 15 measured P c -S-K r relationships and they also cause non-uniqueness in these relationships. In the previous work in 16 this area, the micro-heterogeneity effects on the P c -S-K r relationships have been analysed in a number of contexts, injecting on horizontal plane. On the other hand, injection from the bottom (vertically upwards) leads to a higher 31 iw S . As expected, the distribution of heterogeneity has a significant effect on the saturation distribution and the 32 shape of the P c -S-K r curves. However, we show that if the heterogeneities are distributed in such a way that they 33 are closer to the boundary of injection, the irreducible wetting phase saturation is higher.

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

“…Hou et al [13] explored the influence of measurement sensor's response on the magnitude of the dynamic capillary effects at scale of a representative elementary volume (REV) and argue that the effects may be due to the experimental measurement artifacts. Their acknowledgement of the impact of the micro-heterogeneities on the dynamic capillary effects, at larger scales, is in agreement with the earlier submission of Das et al [12] and Mirzaei and Das [14].…”

“…Das et al [12] investigated the effects of grain size, amount and distribution of micro-heterogeneities on the K r -S w relationship and found that water relative permeability was higher in coarse grain sand, while oil relative permeability was higher in fine grain sand. The effects of gravity were neglected in earlier work [42] but these were included in the latter work [12]. They [12] further showed that larger intensity of heterogeneity led to higher irreducible water saturation in addition to having significant effect on K r -S w relationship.…”

“…But, the non-uniqueness in these relationships is well acknowledged. For example, for the P c -S w relationships and their saturation-rate dependency, depend on factors such as fluid properties like viscosity and density ratios [2][3][4][5], domain scale [6][7][8][9], media permeability [7,10,11], micro-heterogeneities [9,12], and hysteresis in P c -S w relationships [9], among others. Hou et al [13] explored the influence of measurement sensor's response on the magnitude of the dynamic capillary effects at scale of a representative elementary volume (REV) and argue that the effects may be due to the experimental measurement artifacts.…”

Artificial Neural Network to Determine Dynamic Effect in Capillary Pressure Relationship for Two-Phase Flow in Porous Media with Micro-Heterogeneities

“…These heterogeneities have specific two-phase flow properties and affect the P c -S w relationships (Das et al 2004;Das and Mirzaei 2013). To quantify how the heterogeneities affect the P c -S w relationships, a number of studies have been conducted (Ataie-Ashtiani et al 2002;Das et al 2004Das et al , 2006Manthey et al 2005;Mirzaei and Das 2007;Das and Mirzaei 2013). For example, Ataie-Ashtiani et al (2002) have shown that, because of the presence of micro-heterogeneities, P c -S w relationships measured in laboratory-scale domain may be sensitive to the imposed boundary conditions.…”

“…For example, Ataie-Ashtiani et al (2002) have shown that, because of the presence of micro-heterogeneities, P c -S w relationships measured in laboratory-scale domain may be sensitive to the imposed boundary conditions. The micro-heterogeneity effects on the P c -S w relationship have been analysed in a number of other contexts too, e.g., effects of uniformly and randomly distributed heterogeneities, hydraulic parameters (e.g., entry pressure, intrinsic permeability), heterogeneity in particle size and intensity of the heterogeneities (e.g., Das et al 2004Das et al , 2006Ataie-Ashtiani et al 2003). It is clear that the heterogeneity effects on the twophase flow properties are significant and they must be accounted for in the P c -S w relationships.…”