Capillary-driven flow in corner geometries

Wetting of corner-containing geometries is ubiquitous, since the man-made surfaces and natural surfaces are usually not atomically smooth and contain pores, grooves, and cracks. In spite of the very long history of the research of capillary phenomena, the most attention was paid to capillary rise in cylindrical capillaries leaving the rich physics of the capillary transport of the liquids in the corner geometries unravelled. The present work aims to review the progress in studying of wetting of corner-containing geometries: isolated corners, rectangular channels, and confined angular geometries. The review is believed to be of interest for readers from fields such as oil and gas industry, space science, biophysics, and microfluidics.     

Experimental displacement patterns in a 2 × 2 quadrant block with permeability and wettability heterogeneities—problems for numerical modelling

The effect of heterogeneities on miscible and immiscible flood displacements in 2D bead packs in quadrant form, 2 × 2 block heterogeneity, with either a permeability or a wettability contrast is the subject of this paper. The physical processes occurring during miscible and immiscible flow and displacement within permeability and wettability quadrant bead pack models have been studied experimentally. This geometry occurs in a number of situations relevant to hydrocarbon production: particularly faults where adjacent rocks have large permeability contrasts with rapid changes, in the laboratory with core butting, in reservoir simulation where grid blocks have different permeability and in reservoirs having near-wellbore damage problems. The model quadrants 1–4, had 1 and 4 and 2 and 3 with identical properties, either in permeability or wettability. Reported are complete unit mobility miscible displacements, then the effects of viscosity differences (mobility modifiers) and finally immiscible displacements on displacement patterns for initial linear injection. The experiments demonstrate that nodal flow occurs for both miscible and immiscible flow, but for immiscible flow there are boundary effects due to capillary pressure differences created by water saturation changes or wettability contrasts which can leave patches of isolated fluid within a quadrant. The displacement patterns for the different models and fluids change significantly with the viscosity and wettability changes, particularly for the immiscible displacements. This is due to the changing capillary pressure between the quadrant blocks as the water saturation change. These are difficult to address in numerical modelling but should be accounted for. Other effects include coupling of all physical processes governing the flow through the node and creations of microzones of trapped residual oil. Our displacement patterns can therefore be a valuable verification benchmark tool for numerical modelling and a calibration data source for those wishing to simulate the effects of capillary pressure under differing wettability conditions and for those investigating upscaling modelling procedures. However, the possible loss of physical reality when averaging must always be considered.     

Gas/Solid Reactions with Acetone

Gas/solid reactions of acetone vapor with neutral organic compounds, salts, or host crystals with strict exclusion of solvents are reported. This gas/solid technique largely avoids waste formation and saves resources. Starting hydrochlorides or hydrobromides are also synthesized by gas/solid techniques. Dihydrohalides of o-phenylenediamines give 1,5-benzodiazepines 3 , aromatic and aliphatic 1,2-aminothiols (o-aminothiophenol, penicillamines, cysteine) yield five-membered thiazolines and thiazolidines 7, 9, 11, 13. Virtually all carbonyl reagents of the primary amino type 14 give quantitatively the imino derivatives 15 and water. Salt formation may be helpful for increasing melting points and sometimes reactivity as in 8, 10 , and 12 if surface passivation has to be overcome. In the case of solid 14 the free bases react equally well. Acetone ( 2 ) may be quantitatively removed from exhaust gases by using hydroxylaminium phosphate with formation of free acetone oxime at high flow rates. Inclusion of acetone into various hosts ( 17-20 , but not 16 ) is more efficient by imbibition from the gas phase than by crystallization from acetone as the solvent. This advantage may be utilized for gas separations. Some further gases (vapors) coexist in imbibed clathrates whereas others do not. The mechanisms of the gas/solid reactions are elucidated using atomic force microscopy (AFM). Phase rebuildings involve anisotropic movements of molecules over large distances and the formation of characteristic features. In some cases surface hydrates catalyze the gas/solid reaction. Solid-state mechanisms for imbibition from the gas phase into host crystals with formation of clathrates are similar in nature to those of the covalent reactions. These results are correlated with known X-ray crystal structures where available.     

Spreading and sorption of droplets on layered porous substrates

In this paper spreading and sorption of a droplet on an anisotropic, layered porous substrate are investigated numerically. Flow in the saturated part of the porous material is governed by Darcy's law, assuming a sharp wetting front separating the saturated regions from the dry regions. Numerical results are presented for spreading and sorption of droplets in their dependence on the material and process parameters for axisymmetric configurations. Limiting cases of sorption into infinitely thick and very thin porous layers are considered. For an analytical sorption model for thin substrates fed by an infinite reservoir a correction term taking into account the flow resistance in the inlet region is derived and the consistence of the modified model with numerical and experimental results is shown. For two-layer substrates, numerical results on the influence of the layer permeabilities on the sorption kinetics are presented.     

Theoretical and experimental aspects of vacuum impregnation of porous media using transparent etched networks

Vacuum impregnation is a process method in which air and native solution are removed from the porous space of a given porous material and replaced by an external solution. Vacuum impregnation is divided into two steps: Firstly, the porous material is immersed in a liquid solution and exposed to subatmospheric pressure for a given time to ensure that air trapped in the porous materials will be removed; secondly, atmospheric pressure is re-established and the external solution penetrates the pore structure of the porous material. The objective of this study was to describe the hydrodynamic mechanisms involved in vacuum impregnation of porous materials as a function of capillary number and viscosity ratio. To achieve the objectives proposed in the present study, a transparent glass micromodel 7.7 cm × 7.4 cm was first constructed using the photolithographic technique. In addition, a stainless steel vacuum tank was built. The tank top was covered with a transparent reinforced glass plate. The whole system was connected to a vacuum pump, and a conventional video camera was adapted to record the experiments. Liquid saturation was determined through the image analysis process. Capillary number and viscosity ratio were determined for the drainage and imbibition processes. For the systems studied, we conclude that transport mechanisms ranged between stable displacement and capillary fingering during the vacuum step (drainage) while transport mechanisms ranged between continuous capillary and discontinuous capillary domains during the atmospheric step (imbibition). Earlier work indicated that our proposed process should be even more efficient for realistically large systems.     

Some generic capillary-driven flows

This paper deals with numerical simulations of some capillary-driven flows. The focus is on the wetting phenomenon in sintering-like flows and in the imbibition of liquids into a porous medium. The wetting phenomenon is modeled using the coupled Cahn–Hilliard/Navier–Stokes system. The Cahn–Hilliard equation is treated as a system where the chemical potential is solved first followed by the composition. The equations are discretised in space using piecewise linear functions. Adaptive finite element method is implemented with an ad hoc error criterion that ensures mesh resolution along the vicinity of the interface. In the 3D case we use parallel adaptive finite element method. First, a basic wetting of a liquid drop on a solid surface is shown and is established the independence of the dynamic contact angle on the interface width. In addition, the dependence of the dynamic contact angle on the Capillary number is matched with experimental data. Next, some generic sintering-like flows with a fixed matrix is presented. Different geometries in 2D and 3D are considered. We observed rapid wetting, precursor films, coalescence, breakup of melt drops as well as pore migration and elimination that are all microstructural characteristics of a liquid phase sintering. Finally, the effect of equilibrium contact angles on imbibition of liquid into a porous medium is studied.     

Hydrocarbons imbibition for geometrical characterization of porous media through the effective radius approach

Surface energetic characterization of porous solids usually requires the determination of the contact angle. This quantity is deduced by imbibition experiments carried out in such media with high surface tension liquids. Now then, this methodology needs the geometrical characterization of the porous medium by means of the deduction of its effective radius. Normally, this is made by imbibition experiments with n-alkanes, liquids whose surface tension is low enough as to suppose their contact angles with the solid surface are null. However, this last procedure is not free from some criticisms. Among them, the possible influence of the imbibition velocity on the contact angle, the effect of the precursor liquid film ahead the advancing liquid front on the driving force that gives rise to the movement, or the dependence of the effective radius on the length of the hydrocarbon chain of the n-alkanes. In an attempt of going deeply in these questions, imbibition experiments with n-alkanes have been carried out in porous columns of powdered calcium fluoride. These experiments have consisted of the measurement of the increase in the weight of the columns caused by the migration of the liquids through their interstices. The analysis of their results has been carried out by means of a new procedure based on the study of the velocity profile associated to the weight increase. This analysis has permitted us to conclude that, at least in the calcium fluoride columns, the contact angle of the n-alkane is not influenced by the capillary rise velocity, it taking in fact a null value during the process. On the other hand, it has been also proved that the driving force of the movement is caused by the replacement of the solid-vapour interface by the solid-liquid interface that happens during the imbibition, which means that only the Laplace's pressure, and not the precursor liquid film, contributes to the development of the phenomenon. Finally, it has been compared the values of the effective radius associated to each n-alkane, similar values being found independently from the particular liquid employed in the experiments, fact that indicates that the porous solid can be considered as a bunch of cylindrical and parallel capillaries of the same radius.     

Dimensionless scaling methods for capillary rise

In this article the different dimensionless scaling methods for capillary rise of liquids in a tube or a porous medium are discussed. A systematic approach is taken, and the possible options are derived by means of the Buckingham π theorem. It is found that three forces (inertial, viscous and hydrostatic forces) can be used to obtain three different scaling sets, each consisting of two dimensionless variables and one dimensionless basic parameter. From a general point of view the three scaling options are all equivalent and valid for describing the problem of capillary rise. Contrary to this we find that for certain cases (depending on the time scale and the dominant forces) one of the options can be favorable. Individually the different scalings have been discussed and used in literature previously, however, we intend to discuss the three different sets systematically in a single paper and try to evaluate when which scaling is most useful. Furthermore we investigate previous analytic solutions and determine their ranges of applicability when compared to numerical solutions of the differential equation of motion (momentum balance).     

Effect of network topology on two-phase imbibition relative permeability

In a previous study Arns et al. (2004, Transport Porous Media 55, 21–46) we considered the role of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition displacements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore–throat and longer range spatial correlations.