## Introduction

To characterize a variety of industrial problems (e.g., remediation of contaminated subsurface), one needs to quantify two-phase flow in porous media. Various authors have developed numerical schemes to quantify such flow behavior in which the relationships between capillary pressure (P^{c}) and water saturation (*S*_{w}) are needed. The P^{c}-*S*_{w} relationships are largely determined by well defined experiments in the laboratories using porous samples of 10–12 cm height. In these experiments, P^{c} is calculated by measuring the difference in average nonwetting (*P*_{nw}) and wetting (*P*_{w}) fluid phase pressures, expressed as a function of wetting phase saturation (*S*_{w})

In Eq. 1, P^{c,equ} is the capillary pressures at equilibrium saturation condition (∂*S*_{w}/∂t = 0). Traditionally, the capillary pressure relationship in Eq. 1 is defined to include a combined effect of all the factors that influence the equilibrium saturation distribution in the porous sample, namely, fluid properties (e.g., surface tension, viscosity, and density ratios), medium properties (e.g., pore size distribution, permeability and porosity) and so on. However, the determination of the equilibrium P^{c}-*S*_{w}relationships is a time consuming process and the fluids do not necessarily flow under the equilibrium condition, particularly at smaller time durations when *S*_{w} changes with time is fast implying that the time derivative of saturation (∂*S*_{w}/∂t) may be high. Under these circumstances, P^{c}-*S*_{w}relationships strongly depend on both *S*_{w} and ∂*S*_{w}/∂t. This dependence is known as the dynamic effect.^{1–4} There are a number of authors who suggest that the conventional quasi-steady capillary pressure relationship as given in Eq. 1 may not describe the two-phase flow behavior under the dynamic conditions.1–19 It was suggested that Eq. 1 should be generalized to include a capillary damping or dynamic coefficient (*τ*) as below6

where, and *P*^{c,equ} are the capillary pressures at dynamic and equilibrium conditions, all measured at the same *S*_{w}. As evident, the equation has the general form of a straight line and, in theory, should pass through the origin on a plot of vs. ∂*S*_{w}/∂t. The slope of this linear relationship is the dynamic coefficient (τ). These are discussed in detail by Mirzaei and Das2 and Das et al.3 and the references therein where the values of *t* are reported to range from 1.93 × 10^{6} to 9.95 × 10^{9} Pa s. Recently, more studies on determination of τ and its physical interpretation have been reported4, 18–20 which suggest the importance of obtaining the values of the dynamic coefficient. Other recent work21, 22 in the area have focused on developing numerical codes for simulating two-phase flow in porous media based on the dynamic capillary pressure relationship (Eq. 2).

Despite the knowledge that has accumulated so far, there is still ambiguity concerning the magnitude of the dynamic coefficient and consequently dynamic P^{c}-*S*_{w}relationships for quantifying the dynamic two-phase flow behavior in porous media. In this regard, a number of fundamental questions need to be addressed carefully, e.g., can the functional dependence of the dynamic coefficient on porous medium properties such as the permeability be measured experimentally and the interpretation of these relationships. This article aims to resolve these issues through well-defined laboratory experiments. In particular, the experimental characterization of dynamic coefficient in two different types of porous media is attempted. The experimental results of silicone oil-water flow in homogeneous porous domains are presented to explore the effect of porous medium properties by considering samples with different grain size, e.g., bulk permeability, porosity and pore size distribution index.

To achieve the aims of this article, we have designed in-house experiments for determining local and effective (average) P^{c}-*S*_{w}relationships for two-phase flow in homogeneous porous media. The experiments are specifically aimed at (1) understanding the behavior of P^{c}-*S*_{w}relationship caused by applied boundary conditions and types of porous sample and (2) quantifying dynamic effect for silicone oil-water flow in homogeneous porous media at different locations within the domain. The methodology of our experiments and, the results of drainage experiments conducted on two different porous media are presented and discussed. Transient and quasi-static experimental results are used to calculate dynamic coefficient and quantify dynamic effect locally and at the scale of the whole domain. This point is of particular interest since *τ*-*S*_{w}curves are determined locally and then averaged to find an effective *τ*-*S*_{w}curve for the full domain. The experiments are also simulated using already developed computer models1–4 by these authors.