Citation: MIRZAEI, M. and DAS, D.B., 2006. Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3D porous media: implications of micro-heterogeneities. Chemical Engineering Science, 62 (7), pp. -1947Additional Information:• This article was published in the journal Chemical Engineering

in Wiley Online Library (wileyonlinelibrary.com).Well defined experiments and numerical analyses are conducted to determine the importance of dynamic effect in capillary pressure relationships for two-phase flow in porous media. Dynamic and quasi-static capillary pressure-saturation (P c -S w ) and, qS w /qt-t curves are determined. These are then used to determine the dynamic effects, indicated by a dynamic coefficient () in the porous domains which establishes the speed at which flow equilibrium (qS w /qt ¼ 0) is reached. s is found to be a nonlinear function of saturation which also depends on the medium permeability. Locally determined s seems to increase as the distance of the measurement point from the fluid inlet into the domain increases. However, the functional dependence s-S w follows similar trends at different locations within the domain. We argue that saturation weighted average of local s-S w curves can be defined as an effective s-S w curve for the whole domain which follows an exponential trend too.

in Wiley InterScience (www.interscience.wiley.com).Traditional descriptions of multiphase flow in porous media rely on an extension of Darcy's law along with relationships between capillary pressure (P c ), saturation (S), and relative permeability (K r ). New theories have been proposed which suggest that P c relationships should include a dynamic coefficient (s) (Hassanizadeh and Gray, Water Resour Res. 1993;29:3389-3405) to indicate how ''quickly'' or ''slowly'' flow equilibrium is reached. While validity of these theories must be examined, it is also necessary to determine the significance of s and its range of values. In this article, we analyze the significance of s depending on fluid properties. We address the ways in which they cause nonuniqueness of dynamic two-phase flow in porous media and, hence, dynamic effect. Simulations are conducted for quasi-static and dynamic flow of perchloroethylene (PCE) in water saturated domains. The data are then fitted to the dynamic P c relationships to obtain values of s. The effects of flow directions and, viscosity and density ratios are discussed. To consider the lumped effects of various fluid properties, s-S relationships are examined for silicone oils. The results are interpreted by examining the correlation between s and a mobility coefficient, m. We discuss a scaling relationship that shows the dependence of s on fluid and material properties.The viscosity ratio has practically no effect on quasi-static P c -S relationships and only one P c -S curve is plotted.

in Wiley Online Library (wileyonlinelibrary.com).Well-defined laboratory experiments have been conducted to determine the significance of dynamic effect in capillary pressure relationships for two-phase flow in weakly heterogeneous (layered) porous media. The heterogeneous layers are composed of a fine sand layer sandwiched between two coarse sand layers. Dynamic and quasi-static capillary pressure-saturation (P c -S) and @S/@t-t relationships are determined, which are then used to determine the dynamic effect, indicated by a dynamic coefficient (). As well known, establishes the speed at which flow equilibrium (@S/@t ¼ 0) is reached. In consistent with previous studies, is found to be a nonlinear function of saturation that depends on the medium permeability and the intensity of heterogeneity. values increase in the regions of less permeability (fine sand) in the domain. However, the -S functional dependence follows similar trends at different locations within the domain including regions of different permeability. We argue that saturation weighted average of local -S curves can be used as an effective -S curve for the whole domain which, when done, follows an exponential trend too. The effective -S curves suggest that the effective values for the porous layers lie between the values of coarse and fine sands at the same water saturation, and it is dominated by the values of coarse sand as it occupied the maximum volume of the domain.

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.