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Mobilisation Phase 1971 To 1990

Understanding the mobilisation of trapped globules of non-wetting phase during two-phase flow has been the aim of numerous studies. However, the driving forces for the mobilisation of the trapped phases are still not well understood. Also, there is little information about what happens within a globule before, at the onset and during mobilization. In this work, we used micro-particle tracking velocimetry in a micro-fluidic model in order to visualise the velocity distributions inside the trapped phase globules prior and during mobilisation. Therefore, time-averaged and instantaneous velocity vectors have been determined using fluorescent microscopy. As a porous medium, we used a polydimethylsiloxane (PDMS) micro-model with a well-defined pore structure, where drainage and imbibition experiments were conducted. Three different geometries of trapped non-wetting globules, namely droplets, blobs and ganglia were investigated. We observed internal circulations inside the trapped phase globules, leading to the formation of vortices. The direction of circulating flow within a globule is dictated by the drag force exerted on it by the flowing wetting phase. This is illustrated by calculating and analyzing the drag force (per unit area) along fluid-fluid interfaces. In the case of droplets and blobs, only one vortex is formed. The flow field within a ganglion is much more complex and more vortices can be formed. The circulation velocities are largest at the fluid-fluid interfaces, along which the wetting phase flows and decreases towards the middle of the globule. The circulation velocities increased proportionally with the increase of wetting phase average velocity (or capillary number). The vortices remain stable as long as the globules are trapped, start to change at the onset of mobilization and disappear during the movement of globules. They reappear when the globules get stranded. Droplets are less prone to mobilization; blobs get mobilised in whole; while ganglia may get ruptured and get mobilised only partially.

Mobilisation Phase 1971 To 1990

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Trapping and mobilisation of trapped non-wetting phase has been the subject of numerous studies. In these studies, the behaviour of trapped phase has been linked to a variety of parameters, such as capillary number, viscosity ratio and fluid topology. Here, we define the capillary number as the ratio of product of average wetting phase flow velocity and its viscosity to the fluid-fluid interfacial tension. It is observed that the mobilisation or complete removal of ganglia from the host porous medium is possible only if the wetting phase flows at high capillary numbers2,3,4,5,6,7,8. The effect of capillary number, Ca (usually defined in terms of the wetting phase), on trapping and mobilization of ganglia has been extensively studied1,4,5,9. Experiments have shown that the increase of Ca leads to a bigger chance of ganglia mobilisation, regardless of other physical and flow parameters10. It is reported that for the mobilization of the trapped non-wetting phase to occur, the imposed capillary number must be 25 times larger than the capillary number at which trapping occurred4. In the case of sandstone, in order to maximize recovery of the trapped non-wetting phase, the applied Ca number should be 100 times larger than the capillary number required for trapping5. Figure 1 shows the internal circulation in the form of counter-rotating vortices within a stationary droplet surrounded by another flowing fluid, marked by a red circle, as adopted and modified from Dong & Sau11.

Despite the wealth of literature focused on the entrapment and mobilisation of ganglia, there is no experimental study of the momentum exchange between two fluid phases and its effect on the remobilisation and movement of the non-wetting phase. There are some two-phase systems, albeit not in porous media, where such studies have been carried out. One example is the flow around droplets inside another fluid27,28,29,30,31. In case of spherical droplets, an internal circulation in the form of counter-rotating vortices, shown in Fig. 1, has been observed11,32,33. This is due to the momentum transfer between the two immiscible fluids, which depends strongly on their viscosity ratio34,35. Similar recirculations have been observed within falling droplets, with their intensity influenced by the resulted drag coefficient36. Another situation analogous to the ganglia in porous media is the movement of microfluidic droplets in micro-channels37,38,39,40,41. Experimental and numerical works on liquid-liquid slug flows in capillary channels have shown internal recirculations within both phases, which were affected by capillary forces42, the viscosity ratio between the fluids43,44, the channel flow velocity and the slug size45,46. Low capillary numbers resulted in slower channel flows and large slugs caused the attenuation of recirculation zones inside the mobilised slugs. There are two fundamental differences between such two-phase flow systems and the case of entrapped non-wetting phases in porous media. One is the presence of capillary forces that can cause the trapping of ganglia and the other is the blocking of droplets or ganglia by the solid phase. The geometry of the porous medium is of course much more complex than a micro-channel and large local variations in wetting phase velocity field may exist. Stagnant areas may exist where the wetting phase velocity could be close to zero. In such areas, the viscous drag exerted on the fluid-fluid interface would be negligible and thus there would no momentum exchange between the two fluid phases. These are passive interfaces. In areas that the wetting phase velocity is nonzero, we have active interfaces, where momentum exchange occurs, resulting in circulations within the ganglia.

The mobilization of non-wetting phase globules is controlled by the following four forces: drag forces exerted by the flowing wetting phase, friction exerted by the solid phase, capillary forces and the pressure differences in the wetting phase across a globule. As explained above, the drag force is believed to cause flow circulation within the globule. In fact, in order to quantify the drag force, one needs to measure detailed velocity field in the vicinity of the fluid-fluid interface within either the wetting phase or the non-wetting phase. In other words, knowledge of induced flow inside trapped non-wetting globules is important for the overall understanding of their fate. An effective technique for obtaining such information is microscopic particle velocimetry, where florescent tracers within the fluids are imaged in order to obtain the fluid velocity field. There are two major approaches: Particle Tracking Velocimetry (PTV) and Particle Imaging Velocimetry (PIV). PTV is a Lagrangian-based approach and provides trajectories and velocity magnitudes of flowing fluid, where PIV is Eulerian based and gives the velocity contour lines. Reviews of these techniques can be found in the work of Lindken et al.47. These techniques have been widely used in microfluidic devices33,36,38,39. x In this study, we have developed a micromodel setup and employed microscopic particle tracking velocimetry (μPTV) in order to visualise and quantify the flow inside trapped non-wetting phase. Our aim is to follow the development of velocity field within individual droplets, blobs and ganglia as the wetting phase capillary number increases, until the mobilisation of trapped phase occurs. We quantify the drag force exerted along the fluid-fluid interfaces and discuss its role in determining the direction of circulating flow within a globule. We discuss the reasons behind the fact that some non-wetting phase globules mobilise and some do not. Our highly-controlled experiment and detailed information about the velocity field within the trapped phase elements and mobilization of some of them will be also valuable for the testing and validation of direct pore-scale simulation methods such as Lattice-Boltzmann models.

Our goal is to quantify and analyse the velocity distributions in trapped non-wetting phase prior and during mobilisation. For a better understanding of the process, three different types of trapped bodies are identified and investigated separately: droplets, blobs and ganglia. The trapped fluid bodies smaller than a single pore are known as droplets. Blobs are larger than a droplet and fully occupy a single pore. So, they have more contact surfaces with the solid phase. The effect of capillary forces is therefore more pronounced compared to droplets, adding complexity to the momentum transfer and mobilisation processes. Larger trapped non-wetting phase bodies, which occupy more than one pore, are referred to as ganglia. As explained above, the capillary number was increased stepwise until mobilisation of some trapped elements took place. In the cases of droplets and blobs, this covered a range of about two orders of magnitude. We focus on two key features of the process: the evolution of induced internal flow due to viscous drag and the mobilisation of the trapped phase.

Breakup of a ganglion is a common occurrence that leads to a partial mobilisation of ganglia. The breakup, as described by Lenormand & Sarr12, is commonly characterised by the deformation of the ganglion and the formation of a non-wetting phase filament. The increase of wetting phase flow local velocity and pressure causes the filament to get thinner and eventually to rupture. Due to the rapture, two daughter ganglia are formed. This happened in the case of the ganglion shown in Figs 9 and 10.

We performed two-phase flow experiments with focus on observing the evolution of flow within trapped non-wetting phase globules prior, during and after their mobilisation. Flow visualisation and quantitative velocity measurements were obtained using Particle Tracking Velocimetry (PTV).

The trapped globules can become mobilised due to the momentum transfer from the wetting phase; this occurs in the form of viscous drag as well as a difference in the local wetting phase pressure between upstream and downstream liquid-liquid interfaces of the globules. Droplets are trapped at a relatively low capillary number and do not mobilise even at high capillary numbers. This is because they can adopt their shape in order to minimise the drag force. Also, the pressure difference in the wetting phase along the droplet is not large enough to dislodge it. Blobs can get mobilised once the momentum transfer is large enough to dislodge them. In concordance with the literature, Blob-1 was mobilised at a Ca 20 times larger than the trapping Ca5. However, Blob-2 was mobilised at Ca 8 times larger than the trapping Ca. This concludes that the local flow conditions are the main controlling factors for their mobilisation. A blob trapped near the side walls of the micro-model was less prone to mobilisation than those trapped more towards the middle of the micro-model.


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