Experimental measurement of dynamic effect in capillary pressure relationship for two‐phase flow in weakly layered porous media

Abstract

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.

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

“…In particular, it has been shown that the heterogeneity in porous media affects the dynamic coefficient significantly by altering the rate to flow equilibrium (Manthey et al 2005;Mirzaei and Das 2007;Sakaki et al 2010;Das and Mirzaei 2013). Das et al (2007) and Das and Mirzaei (2013) show that the dynamic coefficient in heterogeneous domain is higher than in homogeneous domain implying that the two-phase flow system reaches equilibrium earlier in the homogeneous domain at a given water saturation.…”

“…In the last decade, a number of studies have determined the significance of τ in different circumstances Dahle et al 2005;Manthey et al 2005;Das et al 2007Das et al , 2014Das 2007, 2013;Peszynska and Yi 2008;Juanes 2009;Sakaki et al 2010;Bottero et al 2011;Mumford and O'Carroll 2011;Hanspal and Das 2012;Mirzaei 2012, 2013;Hanspal et al 2013;Hou et al 2014;Zhang et al 2014). In particular, it has been shown that the heterogeneity in porous media affects the dynamic coefficient significantly by altering the rate to flow equilibrium (Manthey et al 2005;Mirzaei and Das 2007;Sakaki et al 2010;Das and Mirzaei 2013). Das et al (2007) and Das and Mirzaei (2013) show that the dynamic coefficient in heterogeneous domain is higher than in homogeneous domain implying that the two-phase flow system reaches equilibrium earlier in the homogeneous domain at a given water saturation.…”

“…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.…”

“…However, it is known that even at the sub-sample scale some heterogeneities (e.g., micro-scale heterogeneity) may exist. 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).…”

“…Mathematical models of two-phase (e.g., oil-water) flow in porous medium require equations for conservation of fluids' mass and momentum in conjunction with appropriate constitutive equations for capillary pressure (P c )-saturation (S w )-relative permeability (K r ) relationships (Ataie-Ashtiani et al 2003;Das and Mirzaei 2013). In these models, the capillary pressure is commonly described by formulation such as the Brooks-Corey (Brooks and Corey 1964) or van Genuchten (van Genuchten 1980) relationship where the capillary pressure is defined as an empirical function of water saturation as shown in Eq.…”