[1] A series of primary drainage experiments was carried out in order to investigate nonequilibrium capillarity effects in two-phase flow through porous media. Experiments were performed with tetrachloroethylene (PCE) and water as immiscible fluids in a sand column 21 cm long. Four drainage experiments were performed by applying large pressures on the nonwetting phase at the inlet boundary: 20, 30, 35, 38 kPa. Our results showed that the nonequilibrium local fluids pressure difference-saturation curves are above the capillary pressure saturation curve. Moreover, the nonequilibrium pressure difference showed a nonmonotonic behavior with an overshoot that was more pronounced at higher injection pressures. The dynamic capillarity coefficient was calculated from measured local pressures and saturations (the scale of sensor devices, 0.7 cm). Its value was found to vary between 1.3 Â 10 5 to 2 Â 10 5 Pa s. Within the saturation range of 0.50 > S w > 0.85, no clear dependency of the dynamic coefficient on the wetting saturation was observed. Also, no dependency of the dynamic capillarity coefficient on the applied boundary pressure was found. Averaged values of ½ at the length scales of 11 and 18 cm were also estimated from averaged pressures and saturations. The upscaled dynamic coefficient was found to vary between 0.5 Â 10 6 and 1.2 Â 10 6 Pa s at the average window size of 11 cm. This is one order of magnitude larger than the local-scale coefficient. Larger values were found for the length scale of 18 cm: 1.5 Â 10 6 and 2.5 Â 10 6 Pa s. This suggests that the value of dynamic coefficient increases with the scale of observation.

[1] Micromodels have been increasingly employed in various ways in porous media research, to study the pore-scale behavior of fluids. Micromodels have proven to be a valuable tool by allowing the observation of flow and transport at the micron scale in chemical, biological, and physical applications. They have helped to improve our insight of flow and transport phenomena at both microscale and macroscale. Up to now, most micromodels that have been used to study the role of interfaces in two-phase flow were small, square, or nearly square domains. In this work, an elongated PDMS micromodel, bearing a flow network with dimensions 5Â30 mm 2 was manufactured. The pore network was designed such that the REV size was around 5Â7 mm 2 . So, our flow network was considered to be nearly four times the REV size. Using such micromodels, we established that the inclusion of interfacial area between the wetting and the nonwetting fluids models the hysteretic relationship between capillary pressure and saturation in porous media. In this paper, we first present the procedure for manufacturing PDMS micromodels with the use of soft lithography. Then, we describe an innovative and novel optical setup that allows the real-time visualization of elongated samples. Finally, we present the results obtained by quasi-static, two-phase flow experiments.

Recent computational studies of two-phase flow suggest that the role of fluid-fluid interfaces should be explicitly included in the capillarity equation as well as equations of motion of phases. The aim of this study has been to perform experiments where transient movement of interfaces can be monitored and to determine interfacial variables and quantities under transient conditions. We have performed two-phase flow experiments in a transparent micromodel. Specific interfacial area is defined, and calculated from experimental data, as the ratio of the total area of interfaces between two phases per unit volume of the porous medium. Recent studies have shown that all drainage and imbibition data points for capillary pressure, saturation, and specific interfacial area fall on a unique surface. But, up to now, almost all micromodel studies of two-phase flow have dealt with quasi-static or steady state flow conditions. Thus, only equilibrium properties have been studied. We present the first study of two-phase flow in an elongated PDMS micromodel under transient conditions with high temporal and spatial resolutions. We have established that different relationships between capillary pressure, saturation, and specific interfacial area are obtained under steady state and transient conditions. The difference between the surfaces depends on the capillary number. Furthermore, we use our experimental results to obtain average (macroscale) velocity of fluid-fluid interfaces and the rate of change of specific interfacial area as a function of time and space. Both terms depend on saturation nonlinearly but show a linear dependence on the rate of change of saturation. We also determine macroscale material coefficients that appear in the equation of motion of fluid-fluid interfaces. This is the first time that these parameters are determined experimentally.

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In the last few decades, micro-models have become popular experimental tools for two-phase flow studies. In this work, the design and fabrication of an innovative, elongated, glass-etched micromodel with dimensions of 5 6 35 mm 2 and constant depth of 43 microns is described. This is the first time that a micro-model with such depth and dimensions has been etched in glass by using a dry etching technique. The micro-model was visualized by a novel setup that allowed us to monitor and record the distribution of fluids throughout the length of the micro-model continuously. Quasi-static drainage experiments were conducted in order to obtain equilibrium data points that relate capillary pressure to phase saturation. By measuring the flow rate of water through the flow network for known pressure gradients, the intrinsic permeability of the micro-model's flow network was also calculated. The experimental results were used to calibrate a pore-network model and test its validity. Finally, we show that glass-etched micro-models can be valuable tools in single and/or multi-phase flow studies and their applications.