During the last 25 to 30 yr , micromodels have been increasingly used to study the behavior of fl uids inside microstructures in various research areas. Studies have included chemical, biological, and physical applica ons. Micromodels have proven to be a valuable tool by enabling us to observe the fl ow of fl uids and transport of solutes within the pore space. They have helped to increase our insight into fl ow and transport phenomena on both micro-and macro-scales. In this review, we have considered only the applica on of micromodels in the study of two-phase fl ow in porous media. Various methods exist for genera ng pa erns used in micromodels. These include perfectly regular pa erns, par ally regular pa erns, fractal pa erns, and irregular pa erns. Various fabrica on methods and materials are used in making micromodels, each with its own advantages and disadvantages. The major fabrica on methods include: Hele-Shaw; glass beads; op cal lithography; wet, dry, and laser or plasma etching; stereo lithography, and so lithography. The distribu on of phases in micromodels can be visualized using (confocal) microscopes, digital cameras, or their combina on. Micromodels have been applied to the study of twophase displacement processes, measurements of fl uid-fl uid interfacial area and phase satura on, measurements of rela ve permeability, and the study of enhanced oil recovery.
Using a visualization setup, we characterized the solute transport in a micromodel filled with two fluid phases using direct, real-time imaging. By processing the time series of images of solute transport (dispersion) in a two fluid-phase filled micromodel, we directly delineated the change of transport hydrodynamics as a result of fluid-phase occupancy. We found that, in the water saturation range of 0.6-0.8, the macroscopic dispersion coefficient reaches its maximum value and the coefficient was 1 order of magnitude larger than that in single fluid-phase flow in the same micromodel. The experimental results indicate that this non-monotonic, non-Fickian transport is saturation- and flow-rate-dependent. Using real-time visualization of the resident concentration (averaged concentration over a representative elementary volume of the pore network), we directly estimated the hydrodynamically stagnant (immobile) zones and the mass transfer between mobile and immobile zones. We identified (a) the nonlinear contribution of the immobile zones to the non-Fickian transport under transient transport conditions and (b) the non-monotonic fate of immobile zones with respect to saturation under single and two fluid-phase conditions in a micromodel. These two findings highlight the serious flaws in the assumptions of the conventional mobile-immobile model (MIM), which is commonly used to characterize the transport under two fluid-phase conditions.
[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.
In two-phase flow through porous media, the percolating pathways can be hydrodynamically split into the flowing and stagnant regions. The highly variable velocity field in the pore space filled by the carrier fluid leads to significant differences in the transport time scales in the two regions that cannot be explained by the Fickian (Gaussian) advection-dispersion equation. In contrast with the Darcy-scale studies, up to now, relatively limited pore-scale studies have been devoted to the characterization of transport properties in two-phase flow. In this paper, we report on the results of computer simulation of advection-dispersion transport in steady state two-phase flow through porous media using a pore network model, employed as an upscaling tool. The simulation results are upscaled to directly estimate the Darcy-scale transport coefficients and properties, namely, stagnant saturation, the mass transfer coefficient between the flowing and stagnant regions, and the longitudinal dispersion in the flowing regions. The mobile-immobile model, one of the most commonly used models for simulating non-Fickian transport in porous media, is used to estimate the transport properties using the inverse modeling of effluent concentration profiles. The disagreement between the directly estimated parameters and those obtained by the mobile-immobile-based inverse modeling implies fundamental shortcomings of the latter for describing transport in two-phase flow. The simulation results indicate that the relative permeabilities may be used to obtain accurate estimates of the stagnant saturation, which link two-phase Darcy's law and transport.Plain Language Summary Solute transport in two-phase flow through porous media is an important topic for many industrial and natural processes such as nutrient transport in partially saturated soils in agriculture, transport of chemicals in oil reservoirs for enhanced oil recovery, or in soil remediation. Modeling multiphase flow and transport in different applications is essential to improve the design and operational condition. Hence, the predictive capabilities of such models need to be improved. To evaluate the assumptions embedded in one of the most commonly used theories, referred to as the mobile-immobile theory, we have performed pore-scale simulations of these physical processes. By upscaling the simulation results, we directly estimated the transport properties and compared them with the inverse modeling results using the mobile-immobile theory. There is a significant discrepancy between the directly and indirectly estimated results that imply the potential shortcomings in the mobile-immobile theory. Moreover, it has been discussed that potentially the two-phase relative permeability data can be used as a proxy to estimate the stagnant (immobile) saturation that will link two-phase Darcy theory with the transport models. Key Points:• The steady state simulation resultsshow that the stagnant saturation strongly depends on the fluids topology rather than Peclet number • The preliminar...
Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.
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.
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