Influence Of Capillarity Research Articles

Influence of Capillarity on Relative Permeability in Fractional Flows

AbstractThe effect of capillary pressure on multiphase flow is described by the capillary pressure gradient term in the fractional flow equation. This term is typically neglected during core‐flooding experiments, as it is not easily accessible. However, the capillary pressure is not constant during core flooding owing to a capillary pressure discontinuity at the core outlet. By imaging spatial fluid distributions under two‐phase steady‐state flow, we determine in situ phase saturations and capillary pressures from interfacial curvature measurements along an entire core, thus achieving the assessment of the capillary pressure gradient and its influence on multiphase flow. We demonstrate how the pore‐scale capillary pressure gradient affects multiphase flow and, in turn, the core‐scale relative permeability measurements. Further, an alternative approach to determining relative permeability from a single fractional flow experiment is proposed. The approach provides a range of relative permeabilities for a single fractional flow experiment and does not require capillary‐end correction, as the formulation directly accounts for the effect of capillary pressure on the flow.

Influence of capillarity and gravity on confined Faraday waves

Experiments characterizing the influence of gravity and interfacial tension on Faraday instability in immiscible, confined fluid layers are presented. The variation in interfacial tension was obtained by controlling the temperature of a suitable binary fluid pair while the influence of gravity was analyzed through a series of terrestrial and microgravity (parabolic flight) experiments. These experiments confirm the existence of a crossover frequency, on either side of which gravity plays opposing roles. The current experiments also reveal that the neutral stability curves under Earth's gravity drift toward lower frequencies as the temperature of the liquid pair approaches its upper consolutal value, i.e., the temperature of complete miscibility. Such drifts in the low frequency range are shown to occur primarily due to the reduction in density difference between the layers, whereas at very high frequencies they are controlled by the lowering of interfacial tension. In the absence of gravity, the Faraday waves are characterized by larger wave numbers, and, as in terrestrial conditions, the instability thresholds at high frequencies increase with an increase of temperature, i.e., reduction in interfacial tension value. This surprising stabilization originates from the lowering of the critical wavelength that leads to increased viscous dissipation.

New ν‐type relative permeability curves for two‐phase flows through subsurface fractures

AbstractAppropriate relative permeability curves for two‐phase flows through subsurface fractures remain unclear. We have conducted decane‐water and nitrogen‐water two‐phase flow experiments and simulations on real variable‐aperture fractures in rocks under confining stress. Experiments have been conducted on fractures for different combinations of rock type (granite or limestone), wettability (contact angle of water: 0° or 90°), and intrinsic fracture permeability (10−11 m2 or 10−10 m2) using different combinations of shear displacement (0 or 1 mm) and effective confining stress (1 or 40 MPa). It has been demonstrated that nonwetting phase relative permeability depends on capillary pressure, except at either a higher contact angle or higher intrinsic permeability (i.e., bigger aperture), where no influence of capillarity is expected from the Young‐Laplace equation. In the absence of an influence of capillarity, relations between wetting and nonwetting phase relative permeabilities agree with that of the X‐type relative permeability curves. In order to determine the relative permeability curves under the influence of capillarity, the experimental results have been analyzed by two‐phase flow simulations of the aperture distributions of the fractures. It has been revealed that nonwetting phase relative permeability becomes zero, even at a small wetting phase saturation of approximately 0.3, while wetting phase relative permeability exhibits Corey‐type behavior, resulting in ν‐shaped relative permeability curves. Similar curves have been reported in the literature, but have not been demonstrated for real fractures. It has been revealed that the new ν‐type and traditional X‐type relative permeability curves are appropriate for describing two‐phase flows through subsurface fractures.

Origin of the patchy emission pattern at the ZERT CO2 release test

A numerical experiment was carried out to test whether the patchy CO2 emission patterns observed at the Zero Emissions Research and Technology release facility are caused by the presence of packers that divide the horizontal injection well into six CO2-injection zones. A three-dimensional model of the horizontal well and cobble–soil system was developed and simulations using TOUGH2/EOS7CA were carried out. Simulation results show patchy emissions for the seven-packer (six-injection-zone) configuration of the field test. Numerical experiments were then conducted for the cases of 24 packers (23 injection zones) and an effectively infinite number of packers. The time to surface breakthrough and the number of patches increased as the number of packers increased suggesting that packers and associated along-pipe flow are the origin of the patchy emissions. In addition, it was observed that early breakthrough occurs at locations where the horizontal well pipe is shallow and installed mostly in soil rather than the deeper cobble. In the cases where the pipe is installed at shallow depths and directly in the soil, higher pipe gas saturations occur than where the pipe is installed slightly deeper in the cobble. It is believed this is an effect mostly relevant to the model rather than the field system and arises through the influence of capillarity, permeability, and pipe elevation of the soil compared to the cobble adjacent to the pipe.

Influence of capillarity on nano-liter flowrate measuremet with displacemet method

Nano-liter flowrate measurements in micro-tubes with displacement method were performed and the effect of capillarity force on the accuracy was investigated through lab experiments and theoretical analysis in this article. The experiments were conducted under the pressure drops ranging from 1 kPa to 10 kPa in a circular pipe with a diameter of 50 μm, to give the pressure-flowrate ( P-Q) relation and verify the applicability of the classical Hagen-Poiseuille (HP) formula. The experimental results showed that there existed a discrepancy between the experimental data and the theoretical values predicted by the HP formula if the capillary effect was not considered, which exceeded obviously the limit of the system error. And hence a modified formula for the relation, taking the capillary effect into account, was presented through theoretical deduction, and after the HP formula had been modified the error was proved to be less than 3%, which was permitted in comparison with the system error. It was also concluded that only by eliminating the effect of the capillary force in experiments could the original HP formula be employed to predict the pressure-flowrate relation in the Hagen-Poiseuille flow in the micro-tube.

Reply to comment by A. G. J. Hilberts and P. A. Troch on “Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling”

We thank Hilberts and Troch [2006] for their comment on our paper [Cartwright et al, 2005]. Before proceeding with our specific replies to the comments we would first like to clarify the definitions and meanings of equations (1)-(3) as presented by Hilberts and Troch [2006]. First, equation (1) is the fundamental definition of the (complex) effective porosity as derived by Nielsen and Perrochet [2000]. Equations (2) and (3), however, represent the linear frequency response function of the water table in the sand column responding to simple harmonic forcing. This function, which was validated by Nielsen and Perrochet [2000], provides an alternative method for estimating the complex effective porosity from the experimental sand column data in the absence of direct measurements of h_(tot) (which are required if equation (1) is to be used).

Comment on “Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling” by Nick Cartwright et al.

[1] Cartwright et al. [2005] and, in a preceding paper, Nielsen and Perrochet [2000] conducted an investigation to assess the effects of an oscillating water table on the effective porosity. Both studies present results from a thorough laboratory experiment and numerical simulations. We wish to comment on some of the findings and conclusions of Cartwright et al. [2005] with regard to the effect of capillarity and the response at very high and very low oscillation frequencies. We also present some results from a simple numerical solution to a nonhysteretic one-dimensional Richards equation model and compare these to the original data and the modeling results presented by Cartwright et al. [2005].

Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling

Comprehensive measurements of the water table response to simple harmonic forcing at the base of a sand column are presented and discussed. In similar experiments, Nielsen and Perrochet (2000) observed that fluctuations in the total moisture were both damped and lagged relative to the water table fluctuations. As a result, the concept of a complex effective porosity was proposed as a convenient means to account for the damping and phase lag through its magnitude and argument, respectively. The complex effective porosity then enables simple analytical solutions for the water table (and total moisture) dynamics including hysteresis. In this paper, these previous experiments are extended to cover a wider range of oscillation frequencies and are conducted for three well‐sorted materials with median grain diameters of 0.082, 0.2, and 0.78 mm, respectively. In agreement with existing theory, the influence of the capillary fringe is shown to increase with the oscillation frequency. However, the complex effective porosity model corresponding to the classical Green and Ampt (1911) capillary tube approximations is shown to be inadequate when compared to the data. These limitations are overcome by the provision of an empirical, frequency‐dependent complex effective porosity model fit to the data. Using measured moisture retention parameters, numerical simulation of the data solving a nonhysteretic van Genuchten–Richards' equation type model is unable to replicate the observations. Existing results of a hysteretic numerical model are shown to be in good agreement with the extended database.

Edge capillary-gravity waves on a sloping beach

It is shown how the solution for velocity potential may be determined when the effect of surface tension is included in the linearized theory of Ursell-type edge waves over a plane-sloping beach. The problem is examined without making a hydrostatic assumption. Explicit solutions for edge capillary-gravity waves are given and the dispersion equation is obtained. The influence of capillarity on gravity waves is discussed.

The influence of capillarity on multiphase flow within porous media: a new model for interpreting fluid levels in groundwater monitoring wells in dynamic aquifers

A new approach is presented to calculate the volume of oil in the underground at an oil spill site from fluid levels in monitoring wells. The approach includes the effects of hysteresis due to irregular pore geometry and to phase entrapment. It is possible to explain the drastic changes in the oil thickness in a monitoring well due to the decrease and increase in the groundwater table. A correct evaluation of the oil volume infiltrated underground from an oil spill and the effective control of remediation works can only be done by using the newly developed approach with a consideration of the dynamic changes in the groundwater table.

The Capillarity Influence On Shape Of Small Liquid Inclusions Enclosed In A Solid Under Non-Stationary Thermal Conditions

AbstractAn analytical model taking into account the influence of capillarity on the process of changing the cross-sectional shape of a cylindrical liquid inclusion enclosed in an anisotropic crystal under non-stationary thermal conditions is suggested. It is shown that the capillary effect confines the possibilities for controlling the inclusion shape under non-stationary thermal conditions. The capillarity influence becomes stronger with decreasing cross-sectional area and increasing interfacial energy. The results of calculations of the limit inclusion shape under different thermal conditions are presented and discussed.

Influence of capillarity on chemical stability and of electric field on surface tension near the critical point

In the present paper, we show that the stability of a chemical reaction occuring in a capillary layer depends on surface properties. A chemical reaction unstable in a bulk phase may be stabilized i...

The influence of capillarity in numerical modeling of organic liquid redistribution in two-phase systems

Numerical experiments are performed to explore the influence of model assumptions and parameters on the prediction of two-phase flow during long-term NAPL redistribution. Sensitivity of numerical solutions to grid resolution and the use of alternative fitting functions for capillary retention data are examined. Due to the inclusion of capillary entrapment, numerical solutions in one- and two-dimensions are strongly dependent on grid resolution. Solution convergence tests based upon spreading behavior reveal that nodal spacings as small as one-fifth to one-tenth of the displacement pressure head may be required to obtain reasonable convergence in some simulations. Solutions employing the Brooks and Corey and van Genuchten functional forms are found to yield different solution behavior. These differences are attributed to the representation of capillary pressure below the entry pressure. Brooks and Corey solutions exhibited greater spreading, less inclination to penetrate semi-permeable layers, and poorer spatial convergence behavior.

The influence of capillarity on the location of liquid soils on textile fabrics

The influence of capillarity on the location of liquid soils on textile fabrics

Analysis of steady-state shallow cell solidification in metal matrix composites

The influence of capillarity on the near-plane front solidification of metal matrix composites is examined by analysis of the one-sided solidification of a binary alloy in a planar interstice of constant width in the limit of low Peclet number. We assume that in this limit, solute isoconcentrates in the liquid are everywhere orthogonal to the growth direction. Capillarity causes the alloy to solidify in a cellular mode, even in the absence of constitutional supercooling. Two solution branches are derived for this solidification mode, one for shallow symmetric cells, the other for asymmetric cells. Restricting attention to the former solution branch, as the growth velocity increases, or the temperature gradient decreases, the cell amplitude increases gradually, to reach a critical point which depends strongly on the contact angle along the reinforcement/solidification front triple line.

Diffusion-controlled dissolution of a spherical precipitate in an infinite binary alloy

An exact numerical solution of the dissolution kinetics of spherical precipitates was obtained from the Green's function method and compared with previous approximate solutions. The same equation can be used to simulate the growth of precipitates having a non-zero initial radius. The Green's function method is useful to predict the kinetics of dissolution or growth in case the solubility is not very small or the solvus curve extends into the interior of the phase diagram. The influence of capillarity on the dissolution kinetics can be incorporated in the present formalism. The results will be presented elsewhere.

Multiphase Flow In Porous Media

The field of two-phase flow through porous media is currently undergoing intense development following many years of relatively sluggish activity. This makes it difficult to present a definitive account at this time. Even classical concepts such as relative permeabilities [the cornerstones of which were laid down by M. Muskat and coworkers long ago (cf. Section 3)] are now seriously questioned. Owing to this provisional state, we adopt a conservative attitude in organizing this review by adhering closely to chronological developments in the field. Historically, global macro scale conservation laws and consti­ tutive equations were developed merely by analogy with comparable enti­ ties already existing for single-phase flow in porous media. As such, these relations may be regarded as semiempirical in nature. For example, per­ tinent quantities such as relative permeabilities were invariably measured experimentally rather than calculated or estimated from basic physical principles. This reflected the generally poor predictive power of such governing laws. This strictly phenomenological focus endured from roughly the early 1930s until the 1960s, when attention shifted to local, micro scale phenom­ ena. These proved difficult to analyze owing to both the tortuous geometry of porous media and the influence of capillarity. Since pore dimensions

Dynamic phase transitions: Existence of “cavitation” waves

SynopsisIn this paper we examine the influence of capillarity on existence and uniqueness of travelling wave solutions in an isothermal system of van der Waals fluids. Existence and non-uniqueness theorems are proved using phase-space analysis and topological methods.

Effects of capillarity and coherency on δ' (Al 3Li) precipitation in dilute AlLi alloys at low undercoolings

The influence of capillarity and coherency on the δ' (Al 3Li) solvus line in dilute AlLi alloys are described. Capillarity effects are small but detectable in very dilute alloys (~ 8 at.% Li) at temperatures near the solvus line. The effect of coherency strain on the position of the solvus line is calculated to be extremely small and was not measurable experimentally. However, evidence for coherency effects on δ' stability are observed when particle sizes are very small. The heterogeneous precipitate distributions observed on aging a 7.9 at.% Li alloy at small undercoolings are interpreted in terms of a combination of excess vacancy effects on particle growth at low temperature and capillarity effects on particle stability at elevated temperatures. This interpretation contrasts with earlier reports of a coherent δ' solvus in dilute AlLi alloys.

Coalescence of Two Equal Cylinders: Exact Results for Creeping Viscous Plane Flow Driven by Capillarity

The coalescence of two equal viscous cylinders under the influence of capillarity is of interest in the theory of sintering. Although the flow in typical cylinder coalescence experiments is not planar, the plane‐flow case is of general interest and is a good approximation in the early stage. An essentially exact analytic solution giving the shape as a function of time for slow plane flow is presented in simple closed form.