Nanoporous Media Research Articles

An analytical model for relative permeability in water-wet nanoporous media

A relative permeability model for gas-water two phase flow in water-wet nanoporous media is proposed based on the continuity equation with modified non-slip boundary in a single nanotube and the pore size distribution (PSD) of the media. The present model takes into account the nanoscale effects including gas slippage in the entire Knudsen range, multilayer sticking (near-wall structural water film) and the quantified thickness of water film. The flow model in single nanotube and relative permeability model in nanoporous media have been validated by comparing with the various molecular simulations, experimental data, and analytical models. The results show the nanoscale effects play an extremely significant role in determining both the gas and water phase relative permeability in nanoporous media: the gas phase relative permeability increases dramatically due to the gas slippage effect, especially at low water saturation; the multilayer sticking of the water film will reduce the water phase relative permeability as well as slightly decrease gas phase relative permeability; the flow of water film has a negative impact on both the gas and water phase relative permeability. Additionally, logarithmic normal distribution function is adopted to characterize PSD, and the sensitivity analysis of PSD on the relative permeability are examined as well.

Apparent permeability for liquid transport in nanopores of shale reservoirs: Coupling flow enhancement and near wall flow

Multiple mechanisms of oil transport in inorganic and organic nanopores of shale oil reservoirs are still unclear and possibly more complex than those of gas transport in nanoporous media, due to differences of molecules free path and fluid-solid molecular interactions. The accurate apparent permeability model considering oil transport mechanisms and different pore types is important for macroscale modeling in shale oil reservoirs development. Based on studies of molecular dynamics simulations (MDS), liquid flow through carbon nanotubes (CNTs) and theoretical analysis, a unified apparent permeability model of liquid hydrocarbon flow in the shale is derived coupling different transport mechanisms in inorganic and organic nanopores. The model of oil-wet organic nanopores considers liquid-solid adsorption, while the model of water-wet inorganic nanopores incorporates near wall flow and velocity slip. We then introduce complicated structural parameters including the tortuosity, porosity and total organic carbon (TOC) to develop models from nanotubes into porous media. After that, the proposed model is validated by MDS and experimental results, and the total apparent liquid permeability (ALP) as well as contributions of different mechanisms are studied. The results indicate that, flow enhancement should be considered in the characterization of oil transport in nanopores, and the velocity of oil in inorganic nanopores much faster than that in organic nanopores in this work. For pore radii under 10nm, the total ALP is much larger than intrinsic permeability, and adsorption effect as well as velocity slip in organic matter (OM) and inorganic matter (IM) influence the total ALP slightly when the pore radius is larger than 100nm. In addition, the greater slip length in IM results in greater contributions of oil transport in IM to the total ALP if slip length is less than 10nm. Moreover, the ratio of the total ALP to intrinsic permeability decreases as TOC increases when TOC is larger than 20%. This work focuses on enriching the theoretical research of oil transport in nanopores and provides a unified ALP model for macroscale modeling study in the shale reservoirs development.

Geometry-Dependent Drying in Dead-End Nanochannels.

Liquid drying in nanoporous media is a key process in food, textile, oil and energy industries, but the corresponding kinetics remains poorly understood due to the structural complexity of nanoporous media. Here, we directly observe the drying process and study drying kinetics in single two-dimensional (2-D) nanochannels with height ranging from 29 to 122 nm. Two different drying behaviors are discovered in such nanoconfinements: continuous meniscus receding and discontinuous meniscus receding due to liquid bridge formation ahead of the meniscus, albeit similar drying rates. The geometry dependence of the measured drying rates is studied at different humidities and compared with a theoretical model considering liquid corner flow, liquid thin film flow, and vapor diffusion as contributors to the overall drying rates. Individual contributions from vapor and liquid transport inside the nanochannels to the drying kinetics are decoupled, and the water vapor diffusivity is successfully extracted. Our results show that both corner flow and vapor diffusion play important roles on water drying in nanochannels without sharp corners. Our findings further indicate that water vapor diffusion in nanoscale confinements can still be described by the classic Knudsen diffusion theory. These results provide new insights of liquid drying in nanoporous media and have implication in optimizing drying processes in industrial applications.

Quasi-static drainage in a network of nanoslits of non-uniform depth designed by grayscale laser lithography

A method is reported to fabricate silicon-glass nanofluidic chips with non-uniform channel depths in the range 20-500 nm and micrometer resolution in width. The process is based on grayscale laser lithography to structure photoresist in 2.5 dimensions in a single step, followed by a reactive ion etching to transfer the resist depth profile into silicon. It can be easily integrated in a complete process flow chart. The method is used to fabricate a network of interconnected slits of non-uniform depth, a geometry mimicking a nanoporous medium. The network is then used to perform a pressure step controlled drainage experiment, i.e. the immiscible displacement of a wetting fluid (liquid water) by a non-wetting one (nitrogen). The drainage patterns are analyzed by comparison with simulations based on the invasion percolation algorithm. The results indicate that slow drainage in the considered nanofluidic system well corresponds to the classical capillary fingering regime.

Effect of nano-confinement on high pressure methane flow characteristics

High pressure gas flow in shale nanoporous media plays an important role in shale gas recovery. The objective of this work is to study the effect of confinement on high pressure methane flow in nanoscale pores. We used dual control volume grand canonical molecular dynamics for different temperatures and pore sizes and compared our results with conventional hydrodynamic equation. We observed that when pore size is larger than 2 nm, flux increases with pore size. But when pore size is less than 2 nm, flux shows varying behaviors depending on the pore size due to methane molecular configurations and structures under different nano-confinements. We also observed that enhancement over the prediction from Hagen-Poiseuille equation can be more than two orders of magnitude in nanopores of around 1 nm pore size. Similar to previous computer simulation and experiments on liquid flow in nanopores, the dependences of the enhancement factor ε and the calculated slip length Ls on the pore sizes show discontinuity within three distinct regions: R1) pore size less than 0.8 nm; R2) between 0.8 and 1.0 nm; and R3) larger than 1.0 nm. Within R2 and R3, ε and Ls monotonically decrease with pore size. The methane molecular flux, enhancement factor, and calculated slip length increase from 328.15 K to 368.15 K, but remain comparable for 368.15 K and 408.15 K.

Characterization of electrical properties of organic-rich shales at nano/micro scales

A new experimental protocol is explored to characterize electrical properties of hydrocarbon-bearing mudrocks at nano/micro scales. Two current flow regimes of peak force - tunneling atomic force microscopy (PF-TUNA) have been used: (1) the vertical out-of-plane current regime with hundred micrometer diameter top electrodes obtains homogenized conductivity quantitatively, (2) the horizontal in-plane current regime was shown powerful to visualize the conductive paths (related to connectivity and tortuosity) for heterogeneous and anisotropic shales. Results show that the approach works well with one to two layers of adsorbed water (25–55% relative humidity) under low frequency (0.5–20 Hz) for shale rocks. Current maps with sub-nanometer resolution emphasize the dominant role of hydrated ions associated with the hydrophilic clay minerals in driving the dielectric response of shales, while conductivity of pyrite and kerogen cannot be neglected for mature organic-rich shale conductive network. The acquired I-V curves at microscale provide a reliable mean to evaluate homogenized conductivity of such multiscale multi-component heterogeneous material under controlled environmental conditions. The procedure discussed herein serves as a complement for fine grained rocks and minerals of ionic-electronic hybrid conductive mechanism under partially water saturation. These results can be used to develop accurate electrical models, specifically for shale rocks with heterogeneous and sophisticated microstructure. The methodology can be also extended to other micro- or meso-porous geomaterials such as cementitious and bituminous nanoporous media.

Stern Layer Structure and Energetics at Mica–Water Interfaces

The screening of surface charge by dissolved ions at solid–liquid interfaces—in the region of interfacial fluid known as the electrical double layer (EDL)—plays a recurrent role in surface science, from ion adsorption to colloidal mechanics to the transport properties of nanoporous media. A persistent unknown in theories of EDL-related phenomena is the structure of the Stern layer, the near-surface portion of the EDL where water molecules and adsorbed ions form specific short-range interactions with surface atoms. Here, we describe a set of synchrotron X-ray reflectivity (XRR) experiments and molecular dynamics (MD) simulations carried out under identical conditions for a range of 0.1 M alkali chloride (Li-, Na-, K-, Rb-, or CsCl) solutions on the basal surface of muscovite mica, a mineral isostructural to phyllosilicate clay minerals and one of the most widely studied reference surfaces in interfacial science. Our XRR and MD simulation results provide a remarkably consistent view of the structure and ene...

Experimental proof of the existence of a Widom line based on peculiarities of the behavior of hydrogen in nanoporous silicate at −45°C and atmospheric pressure

We have experimentally studied the thermal and microwave properties of a nanoporous medium (silica gel) with hydrogen-filled pores. On cooling down to about −45°C at atmospheric pressure, the system exhibited chemical transformations, a first-order phase transition with heat evolution, and a sharp change in the power of microwave radiation at 34 GHz transmitted through a sample. It is concluded that this point on the phase diagram corresponds to a point on the Widom line featuring sharp increase in fluctuations of the entropy and density of supercooled water formed during hydrogen interaction with the surface of pores in silica gel. These results confirm the existence of a second critical point of water, from which the Widom line originates.

Signatures of the appearance of ice 0 in wetted nanoporous media at electromagnetic measurements

Ice 0 that is a new modification of crystalline ice, which can be formed only from supercooled water, is sought. To this end, the electric parameters of wetted nanoporous silicates SBA-15 and silica gel (Acros) for obtaining deeply supercooled water in pores are studied. Three electrical parameters of a medium are measured: the reflection coefficient of microwave radiation from the interface between the medium and air in a waveguide at a frequency of 12.4 GHz and the transmittance of radiation at a frequency of 94 GHz, the tangent of the dielectric loss angle at frequencies from 10 Hz to 100 kHz, and the characteristic electrical fluctuations in the frequency band of 1–100 Hz. Studies are performed at cyclic cooling and heating of the samples in the temperature range from + 20 °C to -150 °C. Sharp changes in all three parameters of the wetted silicates are revealed near the temperature range from -20 °C to - 24 °C. These changes can be attributed to the formation or destruction of ferroelectric ice 0.

Fractal and spinodal-decomposed turbidities of nanoporous glass: fluctuation picture in turbid and transparent Vycor.

The light propagation and scattering in monolithic transparent nanoporous materials such as Vycor glasses exhibit two optical turbidities, both of which are slightly deviated from the λ-4 Rayleigh wavelength dependence in the visible region: one is a transient white turbidity τf, characterized by the convex-upward dependence on the inverse fourth power of wavelength, and the other is turbidity τsp inherent to the structural inhomogeneity, characterized by the convex-downward dependence. The former is attributed to a fractal-like percolation network of imbibed or drained pores as a consequence of transient imbibition or drainage of wetting fluid into or from the pore space. The latter is attributed to the structural inhomogeneities inherent to the original dry porous glass, which are produced by spinodal decomposition. In this paper, we develop a general scheme to estimate the transmittance spectra of Vycor through the turbidities τf and τsp in the visible region on the basis of the theory of dielectric constant fluctuations. We show the applicability and its limitation of the turbidity analysis of the photospectroscopically measured data as a method to study the correlation functions that characterize the pore space and the structural features of isotropic transparent nanoporous media, on the presupposition that there exists no light attenuation other than the scattering.

Solid–solid phase transition of tris(hydroxymethyl)aminomethane in nanopores of silica gel and porous glass for thermal energy storage

To extend the use of phase change materials (PCMs) of those with good performance, tris(hydroxymethyl)aminomethane (THAM) is embedded in silica gels (SG) (pore diameter, d = 15–100 nm) and in controlled porous glasses (CPG) (nominal d = 12–100 nm). The THAM/SG and THAM/CPG composites are characterized by SEM and XRD. Latent heat storage performance of THAM/SG and THAM/CPG is investigated using differential scanning calorimetry, showing size dependence of phase transition temperature, enthalpy change and supercooling. THAM in the nanopores displays stable transition temperature and heat storage capacity in a short-term thermal cycling. The bulk and the nanosized THAM own the same diffraction patterns. The encapsulation of phase change material in nanoporous media is a promising way of tuning the thermal energy properties of those ideal PCMs for use in a wider range of temperature.

Some Features of Pressure Evolution in Systems “Non-Wetting Liquid – Nanoporous Medium” at Impact Intrusion

The last few decades systems consisting of nanoporous medium dispersed in a non-wetting liquid cause an increased interest from both the practical and theoretical points of view. Non-wetting liquid can infiltrate into the porous medium only with an excess pressure. Liquid infiltration tends to increase the solid-liquid interfacial energy and the absorbed energy is proportional to the specific surface area of the medium. Therefore this energy for nanoporous media can reach several orders of magnitude superior to traditional damping materials and shape-memory materials. As a consequence, the prospects of using devices based on systems consisting of a nanoporous medium immersed in a non-wetting liquid associated mainly with the absorption of mechanical energy of impact or explosion. The paper presents the results of experimental studies of impact intrusion the systems of industrially produced hydrophobic silicas Fluka 100 C8 and Fluka 100 C18 with distilled water. With increasing the impact energies nontrivial pattern of pressure changes in the system over time is observed.

Experimental and Molecular Modeling Study of Bubble Points of Hydrocarbon Mixtures in Nanoporous Media

The shale play resources have played a key role in increasing oil production in the past decade in the United States. The sizes of pores in shales storing the oil are believed to be on the order of nanometers. It is believed that the fluids present in such small nanometer-scale pores have different properties compared to properties measured in the bulk. Fluid saturation pressures at given temperatures, bubble points for oils and dew points for condensates, in the nanopores are affected by the influence of pore walls in the vicinity of the fluid molecules. An approach to bubble point or dew point influences the proportion of liquid or gas produced from a given well and, thus, impacts the economic viability. Hence, an accurate measure of saturation pressures is important. In this paper, we describe experiments in well-characterized synthesized mesoporous materials and present Gibbs ensemble Monte Carlo (GEMC) simulations for understanding the possible reason(s) for observations made in the experiments. The ...

Gas mixture flow in nanoporous media in the presence of surface forces. The dusty-gas model

The dusty-gas model has been generalized to the case of gas mixture flow in nanoporous media under the conditions of the action of surface forces. A basic set of transport equations has been derived proceeding from kinetic equations for a gas mixture and dust particles. To take into account the surface forces, the interaction between a gas and dust particles has been represented as a sum of a long-range potential, which reflects the surface forces, and a short-range potential, which describes gas molecule scattering on the surface of pore walls. The contribution of the long-range component has been taken into account in the self-consistent approximation, while the short-range component has been considered in the standard manner. The surface forces have been shown to have a substantial effect on the transfer of mixed gases through porous bodies; in particular, it becomes possible to separate mixture components due to different potentials of the interaction of their molecules with pore surface.

Asymmetric electroosmotic pumping across porous media sandwiched with perforated ion-exchange membranes

To have non-zero net flow in AC electroosmotic pumps, the electroosmosis (EO) has to be non-linear and asymmetric. This can be achieved due to ionic concentration polarization. This is known to occur close to micro-/nano-interfaces provided that the sizes of the nanopores are not too large compared to the Debye screening length. However, operation of the corresponding EO pumps can be quite sensitive to the solution concentration and, thus, unstable in practical applications. Concentration polarization of ion-exchange membranes is much more robust. However, the hydraulic permeability of the membrane is very low, which makes EO flows through them extremely small. This communication shows theoretically how this problem can be resolved via making scarce microscopic perforations in an ion-exchange membrane and putting it in series with an EO-active nano-porous medium. The problem of coupled flow, concentration and electrostatic-potential distributions is solved numerically by using finite-element methods. This analysis reveals that even quite scarce perforations of micron-scale diameters are sufficient to observe practically-interesting EO flows in the system. If the average distance between the perforations is smaller than the thickness of the EO-active layer, there is an effective homogenization of the electrolyte concentration and hydrostatic pressure in the lateral direction at some distance from the interface. The simulations show this distance to be somewhat lower than the half-distance between the perforations. On the other hand, when the surface fraction of perforations is sufficiently small (below a fraction of a percent) this "homogeneous" concentration is considerably reduced (or increased, depending on the current direction), which makes the EO strongly non-linear and asymmetric. This analysis provides initial guidance for the design of high-productivity and inexpensive AC electroosmotic pumps.

Separation of concentrated acid and salt solutions in nanoporous media as the basis for a new technology of processing of phosphorus-containing raw materials

The physical and mathematical models were used to study the method of acid retardation for separating acids from their salts in concentrated multicomponent solutions using nanoporous sorption materials. A combined mechanism of separation relies on the fact that in the sorption phase having a low dielectric permittivity, smaller-sized acid particles, namely, the molecules or strongly bound and weakly hydrated ion pairs, can penetrate the nanopores and are retained within these pores due to molecular sorption or competitive solvation forces. The dissolved salts presented by highly hydrated ions or weakly bound ion pairs can easily pass through the porous medium with a flow of concentrated solution, which is pumped through the column packed with the granulated bed of gel-type ion exchange resins or hypercrosslinked polymers. In conventional cyclic AR processes, purified acid is desorbed by water according to the mechanism of competitive solvation. However, such processes can be successfully used only when the salts separated from acids are highly soluble, as is the case with chloride and nitrate solutions free of components that may form compounds insoluble in neutral medium. At the separation in real sulfate and phosphate media, which normally contain alkaline earth metals and other components, conventional AR- based technologies proved to be unsuccessful. The new modified version of acid retardation is based on the previously discovered effect of stabilization of colloidal systems and supersaturated solutions in porous ion exchange media. A distinctive feature of the proposed technique is the use of weakly acidic aqueous solutions, instead of water, at the stages of acid displace in the cyclic AR processes. The proposed technique of WPA purification using strong-base gel-type ion exchangers in the phosphate form opens up the possibility of stable and feasible processes of acid separation and purification with simultaneous extraction of valuable components, e.g., REE concentrate.

Flow characteristics and a permeability model in nanoporous media with solid-liquid interfacial effects

Molecular dynamics simulations of water flow through nanotubes have demonstrated higher flow rates than the flow rates predicted using classical models and a significant change in flow patterns due to the thin film that forms on the solid wall of the tubes. We have developed a two-region analytical model that described the flow characteristics and permeability of fluid flow through nanoporous media and considered the solid-liquid interfacial effects. Our model considers the influence of various interfacial effects, including long-range van der Waals forces, double-layer repulsive forces, and short-range structure repulsive forces, and it establishes relationships between the permeability and the average pore diameter, porosity, surface diffusion, and contact angle by numerical calculations. Our results indicate that the permeability calculated using the present model (with interfacial effects) is more than 30 times the results that were calculated using the Kozeny-Carman equation (without interfacial effects). The thickness of the thin film significantly affects the flow characteristics. We have gained new insight and guidance regarding the development of nanoscale pore reservoirs, such as shale gas and shale oil.

Effect of Pore-Size Distribution on Phase Transition of Hydrocarbon Mixtures in Nanoporous Media

Summary Pore sizes of many shale-oil and tight gas reservoirs are in the range of nanometers. In these pores, capillary pressure and surface forces can make the phase behavior of hydrocarbon mixtures different from that characterized in pressure/volume/temperature (PVT) cells. Many existing phase-behavior models use a single pore size to describe the effect of confinement on phase behavior. To follow up with our earlier theoretical studies and experimental observations, this research investigates the effect of pore-size distribution. By use of a vapor/liquid equilibrium model that considers the effect of capillary pressure, we present a procedure to simulate the sequence of phase changes in a porous medium caused by a pore-size distribution. This procedure is used to simulate depressurizations of a light oil and a retrograde gas confined inside nanoporous media, the pore-size distributions of which are characteristic of tight reservoirs. The fluid compositions are representative of typical reservoir fluids. Predictions of the model show that phase transition in nanoporous medium with pore-size distribution is not described by a single phase boundary. The initial phase change in the large pores alters the composition of the remaining fluid, and, in turn, suppresses the next phase change. For the two cases studied, models with and without capillary pressure gave similar predictions. For light oil, capillary pressure still noticeably increased the level of supersaturation, and the critical gas saturation had a strong influence on the properties of produced fluids. For retrograde gas, the effect of capillary pressure was insignificant because of the low interfacial tension (IFT). Despite the choice of fluids, calculations indicate that the smallest pores are probably always occupied by hydrocarbon liquid during depressurization.

Nanoporous materials with a general isotropic plastic matrix: Exact limit state under isotropic loadings

In this paper, hydrostatic strength properties of nanoporous materials are investigated by addressing the limit state of a hollow sphere undergoing isotropic loading conditions. Void-size effects are modelled by treating the cavity boundary as a coherent-imperfect homogeneous interface. The hollow sphere is assumed to be comprised of a rigid-ideal-plastic material obeying to a general isotropic yield criterion. The latter is defined by considering a simplified form of the yield function proposed by Bigoni and Piccolroaz in [Int J Solids Struct; 41: 2855–2878], resulting able to account for a broad class of pressure-sensitive materials whose plastic response is also affected by the stress Lode angle. The corresponding support function is consistently derived and discussed. The exact solution of the limit-state problem is fully determined, providing a closed-form description of stress, strain-rate and velocity fields, as well as the macroscopic hydrostatic strength of nanoporous media. Proposed approach allows to consistently generalise available analytical solutions for porous and nanoporous materials, by accounting for a general plastic response of the solid matrix and for void-size effects. Finally, present exact solution, as well as the identification of the support function for the adopted general strength criterion, open towards novel kinematic limit-analysis approaches for describing macroscale strength properties of nanoporous materials under arbitrary triaxial loadings.

Capillary driven flow in nanochannels – Application to heavy oil rheology studies

Observations of capillary-driven flow of a liquid in a nanochannel can be used to study the liquid’s rheology. Capillary-driven flow of several pure liquids and bitumen diluted in Heptol (80:20) were studied using a nanofluidic chip. Filling speed of water was lower than the theoretical predictions, as expected. However, for methanol and ethanol, experimental values agreed well with theoretical predictions. 5 and 11wt.% bitumen solutions in heptol (80:20) followed the theoretical predictions quite well at the initial times but demonstrated deviation for longer penetration times. However, for 20 and 40wt.% diluted bitumen, experimental observations significantly deviated from the theoretical models. Those deviations were related to the continuous changes in the observed dynamic contact angle of the advancing meniscus. Nanochannel blockage has frequently occurred due to the presence of asphaltenes aggregates when 20wt.% diluted bitumen was used. Theoretical model for capillary filling of Bingham Plastic fluid was developed to probe the possible non-Newtonian behavior of diluted bitumen above the onset of asphaltenes precipitation. Given very small yield stress, it was difficult to precisely distinguish between Newtonian and non-Newtonian Bingham Plastic behavior. Nevertheless, our results show that Bingham Plastic model can describe the rheology of 5wt.% and 11wt.% bitumen at nanoscale more accurately than the Newtonian model. Our study shows nanochannels provide an experimental platform to analyze the flow of petroleum in the nanoporous media.