Strong Capillarity Research Articles

The Whitham equation with surface tension

The viability of the Whitham equation as a nonlocal model for capillary-gravity waves at the surface of an inviscid incompressible fluid is under study. A nonlocal Hamiltonian system of model equations is derived using the Hamiltonian structure of the free surface water wave problem and the Dirichlet-Neumann operator. The system features gravitational and capillary effects, and when restricted to one-way propagation, the system reduces to the capillary Whitham equation. It is shown numerically that in various scaling regimes the Whitham equation gives a more accurate approximation of the free-surface problem for the Euler system than other models like the KdV, and Kawahara equation. In the case of relatively strong capillarity considered here, the KdV and Kawahara equations outperform the Whitham equation with surface tension only for very long waves with negative polarity.

Numerical Simulation of Hydraulic Fracturing Water Effects on Shale Gas Permeability Alteration

Hydraulic fracturing has been recognized as the necessary well completion technique to achieve economic production from shale gas formation. However, following the fracturing, fluid–wall interactions can form a damaged zone nearby the fracture characterized by strong capillarity and osmosis effects. Here, we present a new reservoir multi-phase flow model which includes these mechanisms to predict formation damage in the aftermath of the fracturing during shut-in and production periods. In the model, the shale matrix is treated as a multi-scale porosity medium including interconnected organic, inorganic slit-shaped, and clay porosity fields. Prior to the fracturing, the matrix holds gas in the organic and the inorganic slit-shaped pores, water with dissolved salt in the inorganic slit-shaped pores and the clay pores. During and after fracturing, imbibition causes water invasion into the matrix, and then, the injected water–clay interaction may lead to clay-swelling pressure development due to osmosis. The swelling pressure gives additional stress to slit-shaped pores and cause permeability reduction in the inorganic matrix. We develop a simulator describing a system of three pores, two phases (aqueous and gaseous phases), and three components ( $$\hbox {H}_{2}\hbox {O}, \hbox {CH}_{4}$$ , and salt), including osmosis and clay-swelling effect on the permeability. The simulation of aqueous-phase transport through clay shows that high swelling pressure can occur in clays as function of salt type, salt concentration difference, and clay-membrane efficiency. The new model is used to demonstrate the damage zone characteristics. The simulation of two-phase flow through the shale formation shows that, although fracturing is a rapid process, fluid–wall interactions continue to occur after the fracturing due to imbibition mechanism, which allows water to penetrate into the inorganic pore network and displace the gas in-place near the fracture. This water invasion leads to osmosis effect in the formation, which cause clay swelling and the subsequent permeability reduction. Continuing shale–water interactions during the production period can expand the damage zone further.

Film formation from Pickering stabilized waterborne polymer dispersions

The mechanisms involved in the formation of films from high solids industrial-like – vinyl acetate – VeoVa10 (vinyl decanoate) waterborne dispersions Pickering stabilized with surface modified colloidal silica were studied using a combination of techniques including TEM, FRET, ESEM and SEM. It was found that Pickering stabilized dispersions yield films with the silica forming a honeycomb structure that partially hinders the interdiffusion of the polymers from different particles. Nevertheless, coherent films were formed only 9 °C above the Tg of the polymer, due to the strong capillarity forces developed in the compact array of particles formed during water evaporation in the film formation. These Pickering dispersions allowed achieving the remarkable effect of increasing at the same time the Young's modulus, the stress at break and the elongation at break by increasing the silica concentration. Water uptake of the films decreased with the silica concentration and with the surface modification of the silica. Films with >5 wt. % of the more hydrophobic silica absorbed less water than films stabilized with PVOH, which is the workhorse for VAc-VeoVa10 latexes.

Surface modified Fe/silica floating magnetic materials for efficient oil removal

AbstractBACKGROUNDRemediation of oil spillage accidents requires efficient and low cost floating absorbents to remove small amounts of contaminant oil. In this work, a highly hydrophobic floating magnetic macroporous structure based on silica encapsulated Fe nanoparticles was prepared and used for oil absorption from water.RESULTSThe magnetic macroporous materials were prepared by silica encapsulation of iron oxide/hydroxide nanoparticles followed by a thermal treatment with H2. Mössbauer, XRD, SEM/TEM, CHN, IR, TG/DTA and contact angle analyses showed that the Fe oxides nanoparticles are reduced by H2 to form Feo cores protected by silica which sinters to form a macroporous network. The surface reaction with octadecyltrimethoxysilane (Si(CH3O)3C18H37) was used to produce highly hydrophobic materials.CONCLUSIONSThe materials obtained showed very high oil absorption capacities for different model contaminants, i.e. petroleum, soy bean oil, diesel, gasoline and xylene removal. The results are discussed in terms of a macroporous structure with strong capillarity combined with a very hydrophobic surface. © 2015 Society of Chemical Industry

Coupled Modeling of Multiphase Flow and Fault Poromechanics During Geologic CO2 Storage

Abstract Coupling between fluid flow and mechanical deformation in porous media plays a critical role in geologic storage of CO 2 One of the key issues in simulation of CO 2 sequestration is the ability to describe the mechanical and hydraulic behavior of faults, and the influence of the stress tensor and change in pressure on fault slip. Here, we present a new computational approach to model coupled multiphase flow and geomechanics of faulted reservoirs. We represent faults as surfaces embedded in a three-dimensional medium by using zero-thickness interface elements to accurately model fault slip under dynamically evolving fluid pressure and fault strength. We incorporate the effect of fluid pressures from multiphase flow in the mechanical stability of faults by defining a fault pressure. We employ a rigorous formulation of nonlinear multiphase geomechanics based on the increment in mass of fluid phases, instead of the change in porosity. Our nonlinear formulation is required to properly model systems with high compressibility or strong capillarity, as can be the case for geologic CO 2 sequestration. To account for the effect of surface stresses along fluid-fluid interfaces, we use the equivalent pore pressure in the definition of multiphase effective stress. We develop a numerical simulation tool by coupling a multiphase flow simulator with a mechanics simulator, using the unconditionally stable fixed-stress scheme for a computationally efficient sequential solution of two-way coupling between flow and geomechanics. We validate our modeling approach using several synthetic test cases that illustrate the onset and evolution of earthquakes from fluid injection.

Rigorous Coupling of Geomechanics and Multiphase Flow with Strong Capillarity

SummaryWe study sequential formulations for coupled multiphase flow and reservoir geomechanics. First, we identify the proper definition of effective stress in multiphase-fluid systems. Although the average pore-pressure p¯ —defined as the sum of the product of saturation and pressure of all the fluid phases that occupy the pore space—is commonly used to describe multiphase-fluid flow in deformable porous media, it can be shown that the "equivalent" pore pressure pE —defined as p¯ minus the interfacial energy—is the appropriate quantity (Coussy 2004). We show, by means of a fully implicit analysis of the system, that only the equivalent pore pressure pE leads to a continuum problem that is thermodynamically stable (thus, numerical discretizations on the basis of the average pore pressure p¯ cannot render unconditionally stable and convergent schemes). We then study the convergence and stability properties of sequential-implicit coupling strategies. We show that the stability and convergence properties of sequential-implicit coupling strategies for single-phase flow carry over for multiphase systems if the equivalent pore pressure pE is used. Specifically, the undrained and fixed-stress schemes are unconditionally stable, and the fixed-stress split is superior to the undrained approach in terms of convergence rate. The findings from stability theory are verified by use of nonlinear simulations of two-phase flow in deformable reservoirs.

A drive point application of the Guelph Permeameter method for coarse-textured soils

The Guelph Permeameter (GP) is a widely used well/auger-hole method for in-situ determination of field-saturated hydraulic conductivity (Kfs) and sorptive number (α*) in the vadose or unsaturated zone. Its application can be difficult, however, in gravelly materials which are problematic to auger, and in un-cohesive sandy materials which collapse during the augering process or upon wetting of the unlined well. We circumvented these issues, by replacing the GP well with a conically tipped well screen or “drive point” which is pushed, driven, rotated or vibrated to the desired depth. We also developed a steady flow analysis to account for the fact that water discharge through the drive point screen is solely radial, rather than both radial and vertical as in the original GP method. The HYDRUS-2D numerical simulation model was used to determine appropriate shape values (CDP) for the drive point analysis; and an empirical regression equation was developed to convert the discrete CDP values into continuous shape functions for porous materials with negligible-moderate, strong and very strong capillarity. In a well-sorted medium-coarse sand, the drive point method produced Kfs and α* values which were plausible and consistent with other data from the field site. The original GP method, on the other hand, under-estimated the drive point results by factors of 2.1–3.1, which may have been caused by progressive collapse of the unlined GP well, and/or gradual sinking of the GP outflow tip into the unprotected well base. It was concluded that the drive point GP method can provide convenient and accurate estimates of Kfs and α* in materials where hydraulic properties are not substantially altered by the disturbance of drive point installation.

Modeling solute transport and transient seepage in a laboratory beach under tidal influence

This paper explored numerical techniques to simulate the movement of an applied tracer plume in a laboratory beach subjected to tide. The MARUN model ( Boufadel et al., 1999) was used. The movement of the tracer plume in the beach and the development of a transient seepage on the beach surface were modeled. By calibrating the results of the numerical model against the observed data, the laboratory beach was found to have two different zones: a top layer (thickness 9–17 cm) with a saturated hydraulic conductivity, K 0, of 0.2 cm/s and a lower layer with a K 0 of 0.12 cm/s. The simulations revealed that the plume moved seaward during falling tides and downward during rising tides, which is consistent with previous studies. It was also observed that the plume developed a tail that extended in the landward direction, and a freshwater pool became entrapped between the main plume and its extended tail. A sensitivity analysis was conducted to evaluate the effects of boundary conditions, seepage face development, capillarity, and dispersivity values. It was found that a Dirichlet boundary condition landward of the beach causes the plume of applied tracer to sink deeper into the beach in comparison with a Neumann boundary condition. The suppression of the seepage face by forcing the water table to match the tide level did not have great effects on beach hydrodynamics or on the movement of the tracer, which was probably due to the small slope of the beach (10%). However, seepage flow was around half of the seaward flow leaving the beach through the submerged face. Investigation on the capillarity through the van Genuchten parameter revealed that a decrease in the pore size of the beach greatly affects solute hydrodynamics; we noted that the effects on solute transport increase with depth. Thus, we conclude that using a saturated flow model for tidally influenced beaches should be discouraged, especially for fine textured media (i.e., small α or strong capillarity). The simulations also showed that dispersivity does not affect the travel time of the peak of solute concentration at a specific location but affects its magnitude.

Effect of water-repellent admixtures on the behaviour of aerial lime-based mortars

Two different anionic surfactants, sodium oleate and calcium stearate, commercialized as water repellents for cement-based mortars, were added to lime-based mortars in order to check whether they were improved by these admixtures. Different properties of lime-based mortars were evaluated: fresh state behaviour through water retention, air content and setting time, hardened state properties such as density, water absorption through capillarity, water vapour permeability, long-term compressive strengths, pore structure through mercury intrusion porosimetry, and durability assessed by means of freezing–thawing cycles. A clear improvement in lime-based mortars was achieved when sodium oleate was added: strong capillarity reduction and excellent durability in the face of freezing–thawing processes, without any compressive strength drop. The mechanism for this improvement was related to air void formation due to the air-entraining ability of these surfactants. Insolubility of calcium stearate turned out to be responsible for fewer air bubbles – as SEM examination revealed – and showed lower effectiveness.

Design of Inclined Covers with Capillary Barrier Effect

A design procedure is proposed to minimize water infiltration into landfills by optimizing the water diversion length of inclined covers with capillary barrier effect (CCBE). This design procedure is based on a conceptual, mathematical and numerical approach and aims at selecting materials and optimizing layer thickness. Selection among candidate materials is made based on their hydraulic conductivity functions and on a threshold infiltration rate imposed on the designer. The capillary break layer (CBL; bottom layer) is characterized by a weak capillarity, while the moisture retention layer (MRL; upper layer) is characterized by a compromise between strong capillarity and high hydraulic conductivity. The thickness of the CBL corresponds to the height where suction reaches its maximum value for a given infiltration rate. This height can be calculated using the Kisch [Géotechnique 9 (1959)] model. The optimal thickness of the MRL is determined by applying an adaptation of the Ross [Water Resources Research 26 (1990)] model. The results obtained using the proposed design procedure were compared to those obtained from numerical simulations performed using a finite element unsaturated seepage software. The procedure was applied for two cover systems; one where deinking by-products (DBP) were used as MRL and sand as CBL and another where sand was used as MRL and gravel as CBL. Using this procedure, it has been shown that an infiltration control system composed of thin layers of sand over gravel is highly efficient in terms of diversion length and that its efficiency can be enhanced by placing a hydraulic barrier – such as a layer of DBP – above the MRL.

Achieving Rapid Absorption and Extensive Liquid Uptake Capacity in Porous Structures by Decoupling Capillarity and Permeability: Nanoporous Modified Calcium Carbonate

Porous media with rapid absorption properties are greatly sought after in the fields of super absorbers and catalysts. Natural materials, such as diatomite, or synthetic zeolite feature strongly in industrial reaction processes. Most, or all, of such materials, however, are surface acidic. A novel rapidly absorbing alkaline porous structure, with a high absorption capacity, is presented here. As in the case of diatomite or zeolite, the pigment design incorporates strong capillarity within a highly permeable packed medium. A model is proposed for general use with highly absorbing media that can be proven microscopically to have separate domains of micro- or nano-capillarity embedded within a permeable matrix. The new pigment morphology, based on natural ground calcium carbonate (gcc), exhibits this property using special surface structure modifications. It is contrasted with standard gcc by using consolidated tablet blocks made from a suspension of the pigment and chosen mixtures thereof. The blocks are characterised after drying by mercury porosimetry, and the absorption dynamic of a selected liquid is studied. It is shown that using a self-assembly method of discrete pore structures provides a much faster absorption rate and a liquid capacity for up to 10 times more fluid than a conventional homogeneously distributed pore concept. In such unique discrete network systems, the mercury intrusion curve provides a separable analysis of permeability and capillarity in respect to the inflection point of the cumulative intrusion curve. The discrete decoupled properties each follow the absorption behaviour predicted by previous modelling (Ridgway and Gane, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 206(1–3), 2002). The absorption driving force is shown to be determined by the proportion of fine pores present up to a size equal to a Bosanquet inertially-defined optimum within the timescale of absorption. Combining the wetting force, from the capillarity-controlled fine pore structure, with the experimental flow resistance of the sample, consisting of the assembly of particles, it is possible to predict the trends in absorption dynamic using the pore and throat model Pore-Cor.* Use of this model allows existing materials as well as new synthetic designs to be modelled prior to manufacture. The novel alkaline material is compared with independent absorption data for diatomite and shown to be comparable.

THE CONSTANT HEAD WELL PERMEAMETER

In this paper, the constant head well per-meameter (CHWP) theory is extended analytically to account for the effects of unsaturated flow. This results in a more accurate estimate of the field-saturated hydraulic conductivity and in new methods for in situ estimation of the soil sorptivity and the α parameter of the exponential hydraulic conductivity-pressure head function. Calculations using the extended CHWP theory and “average”sand, loam, and clay soils indicate that the original CHWP theory is only slightly in error for soils exhibiting weak capillarity, but can be substantially in error for soils exhibiting strong capillarity. The extended theory successfully predicts results of previous numerical investigations of the CHWP method.

Theory of cellular solidification of binary alloys with applications to succinonitrile-salol

This paper offers a nonlocal equilibrium model for stable cell formation as an alternative to the standard but unsuccessful local equilibrium models. Recognizing from the observations that the morphology in steady state cellular solidification of alloy single crystals belongs to the family of Widmanstätten figures, a Zener-Hillert type model has been developed and applied to our experiments on succinonitrile-salol. In the inverse Widmanstätten pattern generated and observed under controlled boundary conditions the interface curvature is such that strong capillarity effects appear only at the trailing roots of the cells. Since the roots have dimensions ⪡ 1 μm the temperature-composition diagram possesses a sharp low temperature jog towards higher compositions. Thus, since neither the temperature nor liquid diffusion profiles can sustain a matching singularity, the liquid-solid interface cannot everywhere exist in local equilibrium. Concomitantly, there must exist stabilizing effects associated with crystallographic or kinetic anisotropy acting at the cell walls if these liquid-solid Widmanstätten figures are to be sustained. Manifestations of such effects are commonly observed. The liquid solute diffusion equation has accordingly been solved rigorously subject to the boundary conditions: (a) local equilibrium at the cell tip; (b) local equilibrium at the root modified by capillarity; (c) local mass balance over the entire interface, including the necessary effect of solid state diffusion behind the cell root (equivalent to diffusion in advance of a Widmanstätten tip): (d) average solid interface composition equal to the alloy composition X 0; (e) a parametric elliptic conic shape as an experimental constraint which compensates in large part for the lack of knowledge of the nonequilibrium interface states lying between the roots and tips. This solution algorithm automatically generates nonlocal equilibrium interface states lying between the roots and tips and yields a free boundary problem with two degrees of freedom which may be characterized by the cell length and cell spacing as order parameters. Alternative optimizations of the degenerate solutions via a minimum in the dissipation, a minimum in tip undercooling or a minimum in root radius yield quantitatively similar predictions. This is because all of these parameters are related in an approximately monotone fashion to the degree of liquid solute segregation from the tips to the roots of the cells. The theory together with optimization gives satisfactory predictions of experiments on two-dimensional cells including cell length, spacing and the critical supersaturation for onset of stable cells. This paper offers for the first time systematic observations on cell length and comparison with a theory which predicts this quantity.