Nanoporous Media Research Articles

Estimation of shale pore-size-distribution from N2 adsorption characteristics employing modified BJH algorithm

Accurate pore-size-distribution (PSD) is the key to comprehending porous media and shale rock characteristics. There are multiple methods for calculating the PSD of porous media. The Barrett–Joyner–Halenda (BJH) method is the most widely used and simplest calculation, and therefore, this study focus on the BJH algorithm to discuss the accurate shale PSD based on N2 adsorption characteristics. Despite conducting more than a hundred experiments there are certain phenomena for which the calculated pore volume is smaller than the actual pore volume. Therefore, we combined the Brunauer–Emmet–Teller (BET) multilayer adsorption theory and Halsey adsorption equation to analyze the capillary evaporation and desorption demarcation points in the desorption isotherm of each shale sample, and a modified PSD calculation model was established. In addition, we applied the modified BJH algorithm to a homogeneous silicon material with the pore radius known, for calculating the theoretical pore radius and subsequently the pore radii; this allowed determining the correctness of the modified algorithm. The calculation error was approximately 5% that indicated the accuracy of this algorithm. Therefore, this study could provide meaningful insights into the accurate PSD calculation and gas-in-place estimation in shale nanoporous media.

Nanoconfined Water in Shales and Its Impact on Real Gas Flow

The presence of water, i.e., connate or hydraulic fracturing water, along with the gaseous hydrocarbons in shale nanopores is largely overlooked by previous studies. In this work, a new unified real gas-transport model has been developed for both organic and inorganic porous media accounting for the nanoconfined water film flow. More specifically, a gas core flows in the center of the organic/inorganic pore surrounded by a water film which can be further divided into an interfacial region (near-wall water) and bulk region (bulk water). We differentiate the varying water viscosity between the two regions and consider disparate slip boundaries; that is, the near-wall water can slip along the hydrophobic organic pore surface while it is negligible in hydrophilic inorganic pores. Incorporating modified boundary conditions into the Navier-Stokes equations, gas transport model through single organic/inorganic pore is derived. The model is also comprehensively scaled up to the porous media scale considering the porosity, tortuosity, and total organic carbon (TOC) contents. Results indicate that the gas flow capacity decreases in moist conditions with mobile or nonmobile water film. A mobile water film, however, compensates its negative effect up to 50% by enhancing gas flow compared with static water molecules. The real gas flow is dominated by the gas slippage and water film mobility which are dependent upon pore-scale parameters such as pore sizes, topology, pressure, and surface wettability. Compared with inorganic pores, gas transport in organic pores is greatly enhanced by the water film flow due to the strong water slip. Moreover, the contribution of water film mobility is remarkable in small pores with large contact angles, especially at high pressures. At moist conditions, the real gas effect enhances gas flow by improving both gas slippage and water film mobility, which is more prominent in smaller pores at high pressures. The presented model and its results will further advance our understanding of the mechanisms responsible for the water and gas transport in nanoporous media, and consequently, the hydrocarbon exploration of shale reservoirs.

New Model of Relative Permeability for Two-Phase Flow in Mixed-Wet Nanoporous Media of Shale

New Model of Relative Permeability for Two-Phase Flow in Mixed-Wet Nanoporous Media of Shale

Fast Spontaneous Transport of a Non-wetting Fluid in a Disordered Nanoporous Medium

Fast Spontaneous Transport of a Non-wetting Fluid in a Disordered Nanoporous Medium

Oil–Water Relative Permeability in Shale Considering the Effect of Kerogen: Modeling and Analysis

Abstract Nontrivial initial water and the indispensable hydraulic fracturing technique for enhanced recovery result in the prevalence of oil–water two-phase flow in shale oil reservoirs. However, limited research has focused on their presumably unique flow characteristics so far. In this paper, based on assumptions about the two-phase distribution pattern, the relative permeability models for organic/inorganic pores are established. Then, the two models are combined by an upscaling model to arrive at the expression for the relative permeability of shale rocks. Effects of total organic carbon (TOC), pore size, and slip length are considered. Sensitivity analysis demonstrates their impacts on the relative permeability of inorganic/organic media and the shale rock. This is the very first work that provides an analytical relative permeability model for the oil/water two-phase flow in shale matrix considering the effect of kerogen, and it is important for understanding the performance of shale oil reservoirs and other kinds of nanoporous media.

Diffusion‐to‐Imbibition Transition in Water Sorption in Nanoporous Media: Theoretical Studies

AbstractThe ability to predict multiphase fluid transport in nanoporous rocks such as shales is critical for many geoscience applications, for example unconventional hydrocarbon production, geologic carbon sequestration, and nuclear waste disposal. When the pore sizes approach nanoscales, the impact of the molecular interaction forces between fluids and solids becomes increasingly important. These forces can alter macroscopic fluid phase behavior and control transport. Recent experimental studies have shown that capillary condensation and subsequent imbibition of liquid water can occur in hydrophilic nanoporous media even if the vapor phase is at a critical relative humidity (rhcrit) well below vapor saturation. This study presents a theoretical investigation of the processes controlling adsorption, capillary condensation and imbibition in nanoporous media, using the square‐gradient classical density functional theory. The proposed theoretical model explicitly includes the relevant interaction forces among fluids and solids in macroscopic porous media. Application of the model to a relative‐humidity‐controlled water adsorption experiment is presented to demonstrate the impact of water‐pore wall attractive forces on multiphase water behavior in a hydrophilic silicon nanoporous medium. The model represents well the measured time‐dependent evolution of the water imbibition front inside the nanoporous medium and also explains the diffusion‐like water transport regimes observed at rh < rhcrit and the imbibition‐like flow regimes observed at rh > rhcrit. The study furthermore gives an insight on hysteresis phenomenon in adsorption and desorption isotherms.

Growth of carbon nanotubes inside porous anodic alumina membranes: Simulation and experiment

Porous anodic alumina (PAA) membranes represent a widely used and extensively studied template for production of carbon nanotubes (CNT). The PAA–CNT membranes possess a number of unique properties, such as controllable nanotube geometry, size– and chemically–based selectivity as well as high water permeability. In this work, we first propose a combination of gas phase and surface reaction models to quantitatively describe the growth of carbon nanotubes in PAA membranes in a commercial CVD reactor. A complimentary experimental study of CNT formation from ethanol precursor with argon as a carrier gas is performed. A new method for characterizing carbon nanotubes geometry by SEM and TEM image processing of membrane cross–sections is proposed. The simulations show that the carbon growth rate (in nm/min) averaged over the membrane remains constant during the deposition process until the pore diameter becomes relatively small, and rapidly falls to zero after that. The carbon nanotube thickness near the membrane surface is slightly higher than that in the membrane center. The carbon growth rate increases with synthesis temperature and pressure, while it decreases with the argon flow rate. The dependence of carbon growth rate on the ethanol/water flow rate reaches maximum at some intermediate value. These results are supported by the experimental data obtained from SEM/TEM image processing. It is found that the SEM data provide overestimated values of nanotube diameter and thickness in comparison with the TEM data. The obtained results provide new insights into the CNT growth kinetics in nanoporous media, and develop quantitative guidelines for synthesis of CNT–PAA membranes with precisely controlled nanopore geometry. It also validates the combined homogenous / heterogeneous reaction model by comparison with carbon deposition kinetics on a nanometer scale.

Elastic properties of confined fluids from molecular modeling to ultrasonic experiments on porous solids

Fluids confined in nanopores are ubiquitous in nature and technology. In recent years, the interest in confined fluids has grown, driven by research on unconventional hydrocarbon resources—shale gas and shale oil, much of which are confined in nanopores. When fluids are confined in nanopores, many of their properties differ from those of the same fluid in the bulk. These properties include density, freezing point, transport coefficients, thermal expansion coefficient, and elastic properties. The elastic moduli of a fluid confined in the pores contribute to the overall elasticity of the fluid-saturated porous medium and determine the speed at which elastic waves traverse through the medium. Wave propagation in fluid-saturated porous media is pivotal for geophysics, as elastic waves are used for characterization of formations and rock samples. In this paper, we present a comprehensive review of experimental works on wave propagation in fluid-saturated nanoporous media, as well as theoretical works focused on calculation of compressibility of fluids in confinement. We discuss models that bridge the gap between experiments and theory, revealing a number of open questions that are both fundamental and applied in nature. While some results were demonstrated both experimentally and theoretically (e.g., the pressure dependence of compressibility of fluids), others were theoretically predicted, but not verified in experiments (e.g., linear scaling of modulus with the pore size). Therefore, there is a demand for the combined experimental-modeling studies on porous samples with various characteristic pore sizes. The extension of molecular simulation studies from simple model fluids to the more complex molecular fluids is another open area of practical interest.

Pore-Surface Modification as a Method of Controlling the Relaxation of a Nonwetting Liquid Dispersed in a Nanoporous Medium

Pore-Surface Modification as a Method of Controlling the Relaxation of a Nonwetting Liquid Dispersed in a Nanoporous Medium

Comprehensive Review about Methane Adsorption in Shale Nanoporous Media

Shale/tight gas plays an increasingly important role to meet the growing global energy demand and reduce carbon emissions. Unlike conventional reservoirs, shale formations are subject to rock heter...

Lattice Boltzmann simulation of phase equilibrium of methane in nanopores under effects of adsorption

Owing to the strong interaction between fluid molecules and solid surface, thermodynamic phase behavior of fluids in nanopores deviates from that at bulk condition. In this work, a pseudopotential lattice Boltzmann method is employed to directly model phase equilibrium of methane in nanopores. The effects of adsorption and fluid–solid force on confined phase behavior are studied. In the absence of solid walls, our simulation of nanoscale droplets is consistent with prediction from thermodynamic model coupling Peng-Robinson equation of state and capillary pressure. The shifted phase equilibrium is compared with Kelvin equation. When the pore space is confined by solid walls, heterogeneous density distributions in nanopores are developed by adsorption. It is observed that the apparent critical temperature and critical pressure decrease whereas critical density increases in nanopores from the simulated co-existence curves. In addition, it is found that a larger fluid–solid force leads to a more heterogeneous density distribution in nanopores. However, the average liquid/vapor density and apparent critical temperature in confined space are not significantly affected by the strength of fluid–solid force. Density of gas in equilibrium with condensed liquid, on the other hand, is significantly decreased with increasing fluid–solid force. We propose that the phase equilibrium in nanopores under different fluid–solid forces can be characterized by using contact angle. In the end, we extend this method to model the phase equilibrium in a nanoporous medium with chemical heterogeneity.

Spontaneous Imbibition Dynamics of Liquids in Partially-Wet Nanoporous Media: Experiment and Theory

Nanoscale spontaneous imbibition is a common process in nanoporous soil and unconventional reservoirs. Due to the complexity of these natural nanoporous media, the relevant spontaneous imbibition dynamics are still unclear. Thus, this paper studies spontaneous imbibition dynamics of liquids into a nanoporous carbon scaffold (NCS, with controllable wettability and pore geometry). The effects of evaporation and surfactant on spontaneous imbibition are also examined. For low-volatility liquids, a linear relationship between spontaneous imbibition height ( $$H$$ ) and square root of time ( $$\sqrt{t}$$ ) is observed. A modified Lucas–Washburn (L–W) equation is developed to describe the corresponding dynamics and to predict the NCS effective radius and the advancing water contact angle. A dimensionless time function is presented, which includes the properties of solid and liquid and their interactions, and can be used for upscaling spontaneous imbibition data in nanoporous media from laboratory to reservoir scales. Both a larger NCS pore diameter and pore throat diameter cause faster imbibition. The addition of surfactant into an aqueous solution increases the imbibition rate, although this influence is suppressed with pore size decrease. In contrast, for high-volatility liquids, a significant deviation from the linear relationship between $$H$$ and $$\sqrt{t}$$ is found at late times. The modified L–W equation is further developed to include evaporation effect. This study thus provides fundamental understanding of spontaneous imbibition dynamics at nanoscales. The developed theoretical models are expected to be applicable to important problems such as water infiltration into soil, fracturing fluid loss in unconventional reservoirs, and electrolyte migration in electrochemical devices.

Evidence for 4D XY Quantum Criticality in 4He Confined in Nanoporous Media at Finite Temperatures

$^4$He confined in nanoporous media is a model Bose system that exhibits quantum phase transition (QPT) by varying pressure. We have precisely determined the critical exponent of the superfluid density of $^4$He in porous Gelsil glasses with pore size of 3.0 nm using the Helmholtz resonator technique. The critical exponent $\zeta$ of the superfluid density was found to be 1.0 $\pm$ 0.1 for the pressure range 0.1 < P < 2.4 MPa. This value provides decisive evidence that the finite-temperature superfluid transition belongs to the four-dimensional (4D) XY universality class, in contrast to the classical 3D XY one in bulk liquid 4He, in which $\zeta$ = 0.67. The quantum critical behavior at a finite temperature is understood by strong phase fluctuation in local Bose-Einstein condensates above the superfluid transition temperature. $^4$He in nanoporous media is a unique example in which quantum criticality emerges not only at 0 K but at finite temperatures.

Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion

Owing to their complex morphology and surface, disordered nanoporous media possess a rich diffusion landscape leading to specific transport phenomena. The unique diffusion mechanisms in such solids stem from restricted pore relocation and ill-defined surface boundaries. While diffusion fundamentals in simple geometries are well-established, fluids in complex materials challenge existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered media. Our hierarchical strategy allows bridging microscopic/mesoscopic dynamics with parameters obtained from simple laws. The residence and relocation times – tA, tB – are shown to derive from pore size d and temperature-rescaled surface interaction ε/kBT. tA obeys a transition state theory with a barrier ~ε/kBT and a prefactor ~10−12 s corrected for pore diameter d. tB scales with d which is rationalized through a cutoff in the relocation first passage distribution. This approach provides a formalism to predict any fluid diffusion in complex media using parameters available to simple experiments.

Effect of Pore Size Distribution on Capillary Condensation in Nanoporous Media

The occurrence of capillary condensation is often ignored in many naturally occurring nanoporous media, such as shale rock, simply because their isotherms do not adhere to the prescribed shapes presented in the literature. In particular, it is apparent from the literature that most shale isotherms do not display a clear capillary condensation step, which is commonly observed for much simpler adsorbents, such as MCM-41. We contend that the absence of this step from the isotherms for natural adsorbents is not due to the absence of nanoconfinement-induced phase behavior. Rather, it is due to the broad pore size distribution characteristic of such materials. By mechanically mixing different sizes of MCM-41 together and measuring isotherms for propane and n-butane in them at a variety of temperatures, we show that phase behavior in different pore sizes is additive and suppresses the commonly observed appearance of capillary condensation. By comparing the isotherms in the mixtures of MCM-41 to those measured in single pore sizes of MCM-41, we develop correlations, using the Lorentzian function, that make the determinations of porosity and fluid density from the mixture isotherms straightforward.

Pore-Scale Perspective of Gas/Water Two-Phase Flow in Shale

SummaryThe transport behaviors of both single-phase gas and single-phase water at nanoscale deviate from the predictions of continuum flow theory. The deviation is greater and more complex when both gas and liquid flow simultaneously in a pore or network of pores. We developed a pseudopotential-based lattice Boltzmann (LB) method (LBM) to simulate gas/water two-phase flow at pore scale. A key element of this LBM is the incorporation of fluid/fluid and fluid/solid interactions that successfully capture the microscopic interactions among phases. To calibrate the model, we simulated a series of simple and static nanoscale two-phase systems, including phase separation, a Laplace bubble, contact angle, and a static nanoconfined bubble. In this work, we demonstrate the use of our proposed LBM to model gas/water two-phase flow in systems like a single nanopore, two parallel nanopores, and nanoporous media. Our LBM simulations of static water-film and gas-film scenarios in nanopores agree well with the theory of disjoining pressure and serve as critical steps toward validating this approach. This work highlights the importance of interfacial forces in determining static and dynamic fluid behaviors at the nanoscale. In the Applications section, we determine the water-film thickness and disjoining pressure in a hydrophilic nanopore under the drainage process. Next, we model water imbibition into gas-filled parallel nanopores with different wettability, and simulate gas/water two-phase flow in dual-wettability nanoporous media. The results showed that isolated patches of organic matters (OMs) impede water flow, and the water relative permeability curve cuts off at water saturation [= 1–volumetric total organic carbon (TOC)]. The residual gas saturation is also controlled by the volumetric TOC, ascribed to the isolation of organic patches by the saturating water; therefore, the gas relative permeability curve cuts off at water saturation (= 1–volumetric TOC).

On the solution of a parabolic PDE involving a gas flow through a semi-infinite porous medium

Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, forming a porous matrix/pipe. The modeling of the gas flow through a porous media is quite valuable because of its importance in investigating the gas-solid processes.The present study is a valid contribution to the existing literature, by developing a nonstandard line method for the partial differential equation, in order to obtain a numerical solution of unsteady flow of gas through nano porous medium. Hence, the physical problem is modeled by a highly nonlinear ordinary differential equation detailed on a semi-finite domain and represents a guidance for several questions originating in the gas flow theory.The findings of this study offered a facile approach to improve an attractive issue related to materials science/chemistry, like synthesis of ZnO or TiO2 nanoparticles forming an ideal nano porous pipe with efficiency in industrial waste waters decontamination.

Hydrocarbon mixture phase behavior in multi-scale systems in relation to shale oil recovery: The effect of pore size distributions

Shale media contains a large amount of nano-scale pores, with their total pore volume comparable to that of the connected macropores and natural/hydraulic fractures (bulk). Previous work largely neglected the interplay between nanopores and bulk region as well as the effect of pore size distribution (PSD), where fluids can freely exchange between nanopores and bulk region. To accurately predict production and ultimate oil recovery, PSD effect should be taken into consideration. In this work, engineering density functional theory (DFT) is used to study phase behaviors of hydrocarbon mixtures in multi-scale nanoporous media with PSD effect during constant composition expansion (CCE) and constant volume depletion (CVD) processes. We found that under the PSD effect, due to the chemical equilibrium between various nanopores and connected bulk as well as competitive adsorption in nanopores, the interplay between nanopores and bulk region influences phase behaviors and properties of fluids in the multi-scale system. Phase transitions first occur in the bulk region, then the larger pores followed by the smaller pores. The bulk bubble point pressure increases as the volume ratio of the smaller pores in the system increases, while the bulk dew point decreases. When fluids in one specific pore begin to vaporize, in other pores, the heavier component would be adsorbed, while the lighter component would be released, which suppresses the phase transitions in the smaller pores because of the heavier component accumulation. The higher volume ratio of the smaller pores suppresses the heavier component production, when pressure is below the bulk dew point.

Investigations on Water Imbibing into Oil-Saturated Nanoporous Media: Coupling Molecular Interactions, the Dynamic Contact Angle, and the Entrance Effect

Spontaneous imbibition of hydraulic fracturing fluids into the water-wet inorganic media is a ubiquitous phenomenon, which has an important influence on tight/shale oil recovery and groundwater contamination. However, in nanoscale space, the fluid–solid (water–wall and oil-wall) molecular interactions, which can result in the nanoscale effects of the slip boundary and the varying interfacial fluid viscosity, will make the fluid flow behaviors be more complex and difficult to characterize. In this work, a new generalized imbibition model in inorganic nanopores and porous media is established by the theoretical analysis and a nanoscale Shan–Chen lattice Boltzmann method (LBM). The effects of pore dimensions and shapes in porous media, the nanoscale effects, the dynamic contact angle, and the entrance effect are considered and discussed. The results show that the proposed model can accurately characterize the oil/water imbibition mechanisms and be adapted to different nanoscale effects. Based on discussions, this study can provide microscopic basics of water imbibing into nanopores and provide guiding information and theoretical model for the oil recovery from tight/shale reservoirs by hydraulic fracturing, the groundwater remediation by restricting imbibition rate, and other relevant applications.

Pore network extraction for shale gas flow in nanoporous media

Most of pore network models were originally designed for conventional porous media (e.g. sandstone), where pore size is at micron-scale and the dominant flow is Darcy-flow. However, those models could be inapplicable for shale (a typical unconventional porous media), since plenty of nanopores exist therein and therefore the non-Darcy effects can no longer be ignored. In this contribution, the details of shale gas flow were analyzed, and it was found that flow resistance could be misestimated by previous models. For this reason, we propose a pore network model that takes into account the influences of non-Darcy effects on pore structure. In the model, pore/throat radius and throat length are not constant but change with pressure, which is distinguishable from previous models where parameters are independent of pressure. The proposed model and previous models are defined as apparent pore network (APN) and intrinsic pore network (IPN), respectively. A shale sample, imaged by focused ion beam-scanning electron microscope, was used to extract APN and IPN, and then, their network structures were compared in the terms of throat length and throat radius. Under different pressure conditions (ranging from 0.1 MPa to 48 MPa) and image resolutions (5 nm, 10 nm, 20 nm, 50 nm, and 100 nm), shale gas flow was simulated through APN and IPN, respectively. Numerical results show that apparent permeability is likely to be erroneously predicted by IPN, while APN provides a relatively reasonable solution.