Capillary ascension in porous media: A scaling law

A relationship between the microstructure of a porous medium and the height of ascension of a fluid in the material is proposed. The porous medium is modelled by means of a square lattice randomly filled with matter. A scaling law is derived from a numerical simulation. An analytical solution is also obtained and compared with the numerical results.     

Percolation Thresholds in 2-Dimensional Prefractal Models of Porous Media*

Considerable effort has been directed towards the application of percolation theory and fractal modeling to porous media. We combine these areas of research to investigate percolation in prefractal porous media. We estimated percolation thresholds in the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. The percolation thresholds for these simulations were found to increase beyond the 0.5927l... porosity expected in Bernoulli (uncorrelated) percolation networks. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media and can be used to bound modeling efforts. More fundamental applications are also possible. Only a limited range of parameters has been explored empirically but extrapolations allow the critical fractal dimension to be estimated for a large combination of b and i values. Extrapolation to infinite iterations suggests that there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 – the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks.     

Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media

We review and discuss diffusion and hydrodynamic dispersion in a heterogeneous porous medium. Two types of heterogeneities are considered. One is percolation disorder in which a fraction of the pores do not allow transport to take place at all. In the other type, the permeabilities of various regions of the pore space are fractally distributed with long-range correlations. Both systems give rise to unusual transport in which the mean square displacement <r ²(t)> of a particle grows nonlinearly with time. Depending on the heterogeneities and the mechanism of diffusion and disperison, we may havefractal transport in which <r ²> growsslower than linearly with time, orsuperdiffusive transport in which <r ²> growsfaster than linearly with time. We show that percolation models can give rise to both types of transport with scale-dependent transport coefficients such as diffusivity and dispersion coefficients, which are consistent with many experimental observations.     

Strain-thickening transition in ferric-oxide suspensions under oscillatory shear

Shear-strain-thickening transition under oscillatory flow was observed in flocculated ferric-oxide suspensions in mineral oil. The value of the dynamic modulus of the suspensions that was measured at small strain amplitude after cessation of shear also became higher when the strain amplitude of the applied shear had been within or above the transition region.The ferric-oxide powders used were an acicular submicron maghemite (magnetic) and the hematite (non-magnetic) that was converted from the maghemite by heat treatment. The powders were treated with a dispersing agent and the suspensions were prepared in 33% by particle weight. The strain-thickening transition was observed in both the magnetic and the non-magnetic suspensions. However, the onset of the strain-thickening in the magnetic suspension was found at about one decade larger strain amplitude than that in the non-magnetic analog suspension, indicating particle interactions affect to the appearance of the phenomenon.A qualitative interpretation was made in view of site percolation for the enhancement of modulus at rest after the application of the large-amplitude oscillatory shear, where the process of the strain-thickening transition under shear and the development of the modulus after stopping the shear was described with a floc model in which the flocculation phase dilates as a result of the reduction of the particle linkages under higher shear.     

Displacement of trapped oil from water-wet reservoir rock

Displacement of oil trapped in water-wet reservoirs was analyzed using percolation theory. The critical capillary number of the CDC (Capillary Desaturation Curve) was be predicted based on the pore structure of the medium. The mobilization and stability theories proposed by Stegemeier were used to correlate oil cluster length to the capillary number needed to mobilize the trapped oil. Under the assumption that all pore chambers have the same size, a procedure was developed using the drainage capillary pressure curve and effective accessibility function to predict the CDC curve for a given medium. The prediction of critical capillary numbers was compared with the experimental data from 32 sandstone samples by Chatzis and Morrow. Also, the CDC curve of one sandstone sample was calculated using the procedure developed in this work and compared with the measured data. Very good agreements were obtained.Nomenclature a average radius of a liquid filament [m] - c constant - D pore throat diameter [m] - D _a advancing diameter of an oil cluster [m] - D _af average flowing diameter of the medium [m] - D _da controlling diameter of the medium [m] - D _r receding diameter of an oil cluster [m] - D _X difficulty index - f ratio of length to average radius of an oil cluster - F _i interfacial forces [N] - F _p force from pressure gradient [N] - g wettability function - k absolute permeability [m²] - l length of an oil cluster [m] - l _m mobile oil cluster length [m] - l _s stable oil cluster length [m] - l _w wavelength [m] - n* relative length of an oil cluster - N _c 1 capillary number defined by Equation (1) - N _c 2 capillary number defined by Equation (2) - P _b probability of oil filling a pore - P _c percolation threshold value - p _c capillary pressure [N/m²] - r radius of a pore [m] - r _e average pore radius [m] - S _n the nonwetting phase saturation - S _or residual oil saturation - S _orn normalized oil saturation - v Darcy flow rate [m/s] - X _t total fraction of pores - X _t ^a accessibility - X _e ^a effective accessibility - (D) pore throat size distribution function - _a advancing contact angle - _r receding contact angle - porosity - density of the liquid [kg/m³] - constant in Equation (4) - dynamic length of an oil cluster [m] - interfacial tension [N/m] - viscosity [N/(m s)] - p pressure gradient [N/m³]     

Fabrication of b‐Oriented MFI Zeolite Films under Neutral Conditions without the Use of Hydrogen Fluoride

The fabrication of MFI zeolite films with particular b‐axis orientation is especially fascinating. Unlike the conventional alkaline or hydrofluoric acid (HF) assisted neutral synthesis route, here we develop a novel neutral synthesis solution system of TPABr/fumed silica/H₂O without the use of HF and successfully synthesize highly b‐oriented MFI zeolite films on glass‐plate substrates by secondary growth. The localized weak alkaline environment created by the dissolved Na₂O species from the substrate is identified as the key factor for the depolymerization of fumed silica and subsequently the in‐plane growth of zeolite seed layers. Continuous b‐oriented MFI films can also be synthesized on other substrates in the presence of a glass plate or a trace amount of NaOH, which making our neutral synthesis route promising for the direct synthesis of MFI zeolite films and membranes on various substrates.     

Technical Note: Percolation Thresholds and Conductivities of a Uniaxial Anisotropic Simple-Cubic Lattice

We have investigated the percolation and transport behavior of uniaxial anisotropic networks, in which the bond occupation probability in one, perpendicular, direction is different from that in the other two, parallel, directions. The percolation threshold in the perpendicular direction depends on the bond occupation probability in the parallel directions, and vice versa. We report simulation results for these thresholds, and for the conductivity of finite-sized lattices, and some extrapolated estimates of percolation thresholds of infinite anisotropic lattices.     

Damage percolation during stretch flange forming of aluminum alloy sheet

A multi-scale finite element (FE)-damage percolation model was employed to simulate stretch flange forming of aluminum alloys AA5182 and AA5754. Material softening and strain gradients were captured using a Gurson-based FE model. FE results were then fed into the so-called damage percolation code, from which the damage development was modelled within measured microstructures. The formability of the stretch flange samples was predicted based upon the onset of catastrophic failure triggered by profuse void coalescence within the measured second-phase particle field. Damage development is quantified in terms of crack and void areal fractions, and compared to metallographic results obtained from interrupted stretch flange specimens. Parametric study is conducted on the effect of void nucleation strain in the prediction of formability of stretch flanges to “calibrate” proper nucleation strains for both alloys.     

A linked FEM-damage percolation model of aluminum alloy sheet forming

A so-called damage percolation model is linked with a finite element model of a sheet forming process to offer a comprehensive study of ductile damage evolution. In the current study, a damage percolation code is linked with LS-DYNA, an explicit dynamic FEM code used to introduce local strain gradients and compliance effects due to damage-induced softening. The linked model utilizes a Gurson-based yield surface to account for the softening effects of void damage, while the local damage development and void linkage events are modeled using the damage percolation code. The percolation code accepts detailed second phase particle fields from image analysis of a 2.0×1.6 mm optical micrograph of AA5182 aluminum alloy sheet. The model is applied to a stretch-flange stamping process which is known to be a damage-sensitive operation. The critical conditions for fracture are predicted for various initial stretch flange hole sizes.     

Optical and electrical properties of carbon nanotube-containing Se85Te10Ag5 glassy composites

The infrared optical transmission spectra of 3 and 5 wt.% of carbon nanotube (CNT)-containing Se₈₅Te₁₀Ag₅ glassy composites were recorded in the mid-IR region from 4000 to 400 cm^?1 using Fourier transform infrared spectroscopy (FTIR). The FTIR spectra manifested functional groups interacting the CNT surface and the Se₈₅Te₁₀Ag₅ glassy matrix. Photoluminescence (PL) spectra of the CNT-containing Se₈₅Te₁₀Ag₅ glassy composites exhibited PL emission peaks centred within the range 715–725 nm. The optical absorption spectra differed between pure Se₈₅Te₁₀Ag₅ glass and the CNT-containing Se₈₅Te₁₀Ag₅ glassy composites. The electrical conductivity of CNT-containing Se₈₅Te₁₀Ag₅ glassy composites was enhanced by four orders of magnitude with the CNT additive. This can be attributed to the formation of many conductive paths through the CNT–CNT internanotube percolation network.