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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. Key Points Specific interfacial area depends on dynamic conditions Interfacial velocity and production term show similar trends Further investigation of the dynamic conditions and of all interfaces is needed

Several models for two-phase flow in porous media identify trapping and connectivityof fluids as an important contribution to macroscale hysteresis. This is especially true forhysteresis in relative permeabilities. The trapping models propose trajectories from theinitial saturation to the end saturation in various ways and are often based on experiments orpore-network model results for the endpoints. However, experimental data or pore-scalemodel results are often not available for the trajectories, that is, the fate of the connectivityof the fluids while saturation changes. Here, using a quasi static pore-network model,supported by a set of pore-scale laboratory experiments, we study how the topology of thefluids changes during drainage and imbibition including first, main and scanning curves. Wefind a strong hysteretic behavior in the relationship between disconnected nonwetting fluidsaturation and the wetting fluid saturation in a water-wet medium. The coalescence of theinvading nonwetting phase with the existing disconnected nonwetting phase dependscritically on the presence (or lack thereof) of connected nonwetting phase at the beginningof the drainage process as well as on the pore geometry. This dependence involves amechanism we refer to as ‘‘reversible corner filling.’’ This mechanism can also be seen inlaboratory experiments in volcanic tuff. The impact of these pore-network model results onexisting macroscopic models is discussed.

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 5x30 mm2 was manufactured. The pore network was designed such that the REV size was around 5x7 mm2. 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.

Classical Darcy's equation for multiphase flow assumes that gravity and the gradient in fluid pressure are the only driving forces and resistance to the flow is parameterized by (relative) permeability as a function of saturation. It is conceivable that, in multiphase flow, other driving forces may also exist. This would mean that such nonequilibrium effects are lumped into a permeability coefficient. Indeed, many studies have shown that the relative permeability coefficient generally depends not only on saturation but also on dynamics of the system. Through the application of rational thermodynamics, a theory of two-phase flow had been developed in which interfacial areas were introduced as separate thermodynamic entities and their macroscale effects were explicitly included. This theory includes new driving forces whose significance needs still to be established. To study new terms in the theory, we employ a dynamic pore network model called DYPOSIT. A long pore network (several representative elementary volumes connected in series) is generated, which represents as a one-dimensional porous medium column. This model provides pore scale distribution of local phase pressures, capillary pressure, interfacial area, saturation, and flow rate, which are averaged to obtain the macroscale distributions of these variables. Our analysis shows that there are discrepancies between the simulation results and the classical equations to describe the transient behavior, especially for the nonwetting phase transient permeability. The coefficients in the extended equations are quantified and parameterized. Although under the applied Dirichlet boundary conditions, flow varies significantly, there is a clear trend illustrating dependency of coefficients on saturation, independent of dynamic conditions. Furthermore, using the new coefficients, it is possible to explain either transient or steady state flow regimes, which is a new achievement.

Current theories of two-phase flow in porous media are based on the so-called extended Darcy’s law, and an algebraic relationship between capillary pressure and saturation. Both of these equations have been challenged in recent years, primarily based on theoretical works using a thermodynamic approach, which have led to new governing equations for two-phase flow in porous media. In this research, these equations and also other physical aspects of multiphase flow in porous media are studied. To gain detailed insights into the processes and for quantitative assessment pore-network modelling has been employed. In this work, we have developed robust quasi-static and dynamic pore-network models. Several quasi-static and dynamic pore-networks have been developed to study relationships between average phase pressures, average capillary pressure, and specific interfacial area during drainage and imbibition. Other aspects of flow in porous media such as rapping mechanisms, saturation profile, non-equilibrium effects in pressure and interfacial area are investigated. In addition to the investigation of physics of multiphase flow, we have developed new approaches for better presentation of porous media, which are employed in quasi-static models. Quasi-static simulations are done in three different media; a hypothetical porous medium, a two-dimensional micro-model, and a three-dimensional glass-bead column. Capabilities of the models in simulating experiments as well as providing more detailed information about the experiments are shown. This may be impossible and time-consuming in laboratory experiments. Furthermore, a dynamic pore-network model with improved numerical features is developed. New algorithms in dynamic pore-network modelling provide very flexible formulations to simulate the two-phase flow in different capillary numbers and different viscosity ratios for drainage and imbibition.

Development of pore network models based on detailed topological data of the pore space is essential for predicting multiphase flow in porous media. In this work, an unstructured pore network model has been developed to simulate a set of drainage and imbibition laboratory experiments performed on a two-dimensional micromodel. We used a pixel-based distance transform to determine medial pixels of the void domain of micromodel. This process provides an assembly of medial pixels with assigned local widths that simulates the topology of the porous medium. Using this pore network model, the capillary pressure-saturation and capillary pressure-interfacial area curves measured in the laboratory under static conditions were simulated. On the basis of several imbibition cycles, a surface of capillary pressure, saturation and interfacial area was produced. The pore network model was able to reproduce the distribution of the fluids as observed in the micromodel experiments. We have shown the utility of this simple pore network approach for capturing the topology and geometry of the micromodel pore structure.