Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model

Colloid Transport in Bicontinuous Nanoporous Media

Colloid transport and retention in porous media are critical processes influencing various Earth science applications, from groundwater remediation to enhanced oil recovery. These phenomena become particularly complex in the confined spaces of nanoporous media, where strong boundary layer effects and nanoconfinement significantly alter colloid behavior. In this work, we use particle dynamics models to simulate colloid transport and retention processes in bicontinuous nanoporous (BNP) media under pressure gradients. By utilizing particle-based models, we track the movement of each colloid and elucidate the underlying colloid retention mechanisms. Under unfavorable attachment conditions, the results reveal two colloid retention mechanisms: physical straining and trapping in low-flow zone. Furthermore, we investigate the effects of critical factors including colloid volume fraction, d, pressure difference, ΔP, interaction between colloids and BNP media, Ec-p, and among colloids, Ec-c, on colloid transport. Analysis of breakthrough curves and colloid displacements demonstrates that higher values of d, lower values of ΔP, and strong Ec-p attractions significantly increase colloid retention, which further lead to colloid clogging and jamming. In contrast, Ec-c has minimal impact on colloid transport due to the limited colloid-colloid interaction in nanoporous channels. This work provides critical insights into the fundamental factors governing colloid transport and retention within stochastic nanoporous materials.

Molecular Diffusion in Nanoreactors' Pore Channel System: Measurement Techniques, Structural Regulation, and Catalytic Effects

Nanoreactors, as a new class of materials with highly enriched and ordered pore channel structures, can achieve special catalytic effects by precisely identifying and controlling the molecular diffusion behavior within the ordered pore channel system. Nanoreactors-driven molecular diffusion within the ordered pore channels can be highly dependent on the local microenvironment in the nanoreactors' pore channel system. Although the diffusion process of molecules within the ordered pore channels of nanoreactors is crucial for the regulation of catalytic behaviors, it has not yet been as clearly elucidated as it deserves to be in this study. In this review, fundamental theory and measurement techniques for molecular diffusion in the pore channel system of nanoreactors are presented, structural regulation strategies of pore channel parameters for controlling molecular diffusion are discussed, and the effects of molecular diffusion in the pore channel system on catalytic reactivity and selectivity are further analyzed. This article attempts to further develop the underlying theory of molecular diffusion within the theoretical framework of nanoreactor-driven catalysis, and the proposed perspectives may contribute to the rational design of advanced catalytic materials and the precise control of complex catalytic kinetics.

Identifying the dominant transport mechanism in single nanoscale pores and 3D nanoporous media

Gas transport mechanisms can be categorized into viscous flow and mass diffusion, both of which may coexist in a porous media with multiscale pore sizes. To determine the dominant transport mechanism and its contribution to gas transport capacity, the gas viscous flow and mass diffusion processes are analyzed in single nanoscale pores via a theoretical method, and are simulated in 3D nanoporous media via pore-scale lattice Boltzmann methods. The apparent permeability from the viscous flow and apparent diffusivity from the mass diffusion are estimated. A dimensionless parameter, i.e., the diffusion-flow ratio, is proposed to evaluate the dominant transport mechanism, which is a function of the apparent permeability, apparent diffusivity, bulk dynamic viscosity, and working pressure. The results show that the apparent permeability increases by approximately two orders of magnitude when the average Knudsen number (Kn avg) of the nanoporous media or Knudsen number (Kn) of single nanoscale pores increases from 0.1 to 10. Under the same conditions, the increment in the apparent diffusivity is only approximately one order of magnitude. When Kn < 0.01, the apparent permeability has a lower bound (i.e., absolute permeability). When Kn > 10, the apparent diffusivity has an upper bound (i.e., Knudsen diffusivity). The dominant transport mechanism in single nanoscale pores is the viscous flow for 0.01 < Kn < 100, where the maximum diffusion-flow ratio is less than one. In nanoporous media, the dominant transport relies heavily on Kn avg and the structural parameters. For nanoporous media with the pore throat diameter of 3 nm, Kn avg = 0.2 is the critical point, above which the mass diffusion is dominant; otherwise, the viscous flow is dominant. As Kn avg increases to 3.4, the mass diffusion is overwhelming, with the maximum diffusion-flow ratio reaching ∼4.

Fractal analysis on CO2 hydrate-bearing sands during formation and dissociation processes with NMR

Injecting CO₂ into submarine sediments to form hydrates is one of the potential methods of CO₂ sequestration. The transition behavior of CO₂ hydrates in porous media is of great practical significance. In this work, CO₂ hydrate formation/dissociation in porous media was monitored in real time by a low-field magnetic resonance (MR) system, and a series of dynamic fractal dimensions of the pore space occupied by converted water during the hydrate formation/dissociation process were obtained based on the transverse relaxation time (T₂) distributions. In general, the dimension of the converted water space increases with hydrate formation and decreases with the hydrate dissociation progress. A smaller particle size of porous media and a lower initial water saturation can promote hydrate formation, and the corresponding fractal dimension is higher during the hydrate formation process. There is a special status of the fractal period observed during the hydrate formation/dissociation process, and it is considered the temporally and spatially uniform distribution of hydrate crystal formation/dissociation inside the porous media. These results also indicate the relationships between the hydrate transition progress and the dynamic fractal dimension, which are useful for future works on pore-scale hydrate-bearing transitions during hydrate-based CO₂ sequestration.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities (0.5≤ϕ≤0.9), Knudsen numbers (0.05≤Kn≤1.0), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number.

Pore Size Dependence of Permeability in Bicontinuous Nanoporous Media

In this work, we employ many-body dissipative particle dynamics (mDPD) simulations to investigate the fluid flow process through bicontinuous nanoporous media, which are representative models for a broad class of nanoporous materials. The mDPD formulation includes attractive and repulsive interactions describing accurately fluid-fluid and fluid-solid interactions. As a mesoscale simulation method, mDPD can bridge the length and time scale gap between continuum and atomistic simulations. The bicontinuous nanoporous models are constructed considering a defined morphology, the porosity level, and varying pore sizes in the range from 3.41 to 13.63 nm. All models have a 0.65 porosity level and the same topology. The models provide a stochastic description of the morphology and pore size distribution and allow for a direct investigation of the dependence of permeability on the average pore size. The stationary nanoporous models are filled with fluid particles, and flow is induced by the action of confining pistons. Simulation results, obtained by imposing different pressure differences on the surfaces of the nanoporous media, indicate a linear pressure drop within the nanoporous model. Regardless of the complexities and different scales of the porous media considered, the steady-state fluid flow through the nanoporous models is proportional to the pressure gradient applied, in agreement with Darcy's law. The calculated pore size dependence of permeability is well described by the Hagen-Poiseuille law, considering a single shape correction factor that accounts for the flow resistance due to the complex nanoporous morphology. This work highlights the effect of the average pore size of a complex stochastic bicontinuous nanoporous medium on fluid properties. The results indicate rather a relatively simple dependence of permeability on the average pore size. The novel method we employ to generate the stochastic bicontinuous nanoporous structure allows the control of different geometric features that can be explored in future studies.

Nanoconfinement and mass transport in metal-organic frameworks

The ubiquity of metal-organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this review, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

Nanofabrication of synthetic nanoporous geomaterials: from nanoscale-resolution 3D imaging to nano-3D-printed digital (shale) rock

Advances in imaging have made it possible to view nanometer and sub-nanometer structures that are either synthesized or that occur naturally. It is believed that fluid dynamic and thermodynamic behavior differ significantly at these scales from the bulk. From a materials perspective, it is important to be able to create complex structures at the nanometer scale, reproducibly, so that the fluid behavior may be studied. New advances in nanoscale-resolution 3D-printing offer opportunities to achieve this goal. In particular, additive manufacturing with two-photon polymerization allows creation of intricate structures. Using this technology, a creation of the first nano-3D-printed digital (shale) rock is reported. In this paper, focused ion beam-scanning electron microscopy (FIB-SEM) nano-tomography image dataset was used to reconstruct a high-resolution digital rock 3D model of a Marcellus Shale rock sample. Porosity of this 3D model has been characterized and its connected/effective pore system has been extracted and nano-3D-printed. The workflow of creating this novel nano-3D-printed digital rock 3D model is described in this paper.

Confinement Effect on Porosity and Permeability of Shales

Porosity and permeability are the key factors in assessing the hydrocarbon productivity of unconventional (shale) reservoirs, which are complex in nature due to their heterogeneous mineralogy and poorly connected nano- and micro-pore systems. Experimental efforts to measure these petrophysical properties posse many limitations, because they often take weeks to complete and are difficult to reproduce. Alternatively, numerical simulations can be conducted in digital rock 3D models reconstructed from image datasets acquired via e.g., nanoscale-resolution focused ion beam–scanning electron microscopy (FIB-SEM) nano-tomography. In this study, impact of reservoir confinement (stress) on porosity and permeability of shales was investigated using two digital rock 3D models, which represented nanoporous organic/mineral microstructure of the Marcellus Shale. Five stress scenarios were simulated for different depths (2,000–6,000 feet) within the production interval of a typical oil/gas reservoir within the Marcellus Shale play. Porosity and permeability of the pre- and post-compression digital rock 3D models were calculated and compared. A minimal effect of stress on porosity and permeability was observed in both 3D models. These results have direct implications in determining the oil-/gas-in-place and assessing the production potential of a shale reservoir under various stress conditions.

Numerical Issues for Solving Eu-type Generalized Hydrodynamic Equations to Investigate Continuum-rarefied Gas Flows

Eu-type generalized hydrodynamic equations have been derived from the Boltzmann kinetic theory and applied to investigate continuum and/or rarefied gas flows. This short communication first reports detailed and important issues in the use of the mixed discontinuous Galerkin method to solve Eu-type generalized hydrodynamic equations in multidimensions. Three major issues are reported. These include the treatment of solid boundary conditions for the nonlinear constitutive equations, a slope limiter to maintain high accuracy and avoid unphysical oscillations, and the computational efficiency compared with that of the particle method. In addition, we implement the present model to a rigid problem, which includes gas flows around the NACA0018 airfoil, a sharp wedge, a sphere and a three-dimensional Apollo configuration.

Direct Simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels

The impetus of the current research is to use the direct simulation Monte Carlo (DSMC) algorithm to investigate fluid behaviour and gas transport in porous microchannels. Here, we demonstrate DSMC’s capability to simulate porous media up to 40% porosity. In this study, the porous geometry is generated by a random distribution of circular obstacles through the microchannel with no interpenetration between the obstacles. The influence of the morphology along with rarefaction and gas type on the apparent permeability is investigated. Moreover, the effects of porosity, solid particle’s diameter and specific surface area are considered. Our results demonstrate that although decreasing porosity intensifies tortuosity in the flow field, the tortuosity reduces at higher Knudsen numbers due to slip flow at solid boundaries. In addition, our study on two different gas species showed that the gas type affects slippage and apparent gas permeability. Finally, comparing different apparent permeability models showed that Beskok and Karniadakis model is valid only up to the early transition regime and at higher Knudsen numbers, the current data matches those models that take Knudsen diffusion into account as well.

Advanced numerical investigation of the heat flux in an array of microbolometers

The investigation of the thermal properties of an array of microbolometers has been carried out by mean of two independent numerical analysis, respectively the Direct-Simulation Monte Carlo (DSMC) and the classic diffusive approach of the Fourier’s equation. In particular, the thermal dissipation of a hot membrane placed in a low-pressure cavity has been studied for different values of the temperature of the hot body and for different values of the pressure of the environment. The results for the heat flux derived from the two approaches have then been compared and discussed.

Thermal Conduction Simulation Based on Reconstructed Digital Rocks with Respect to Fractures

Effective thermal conductivity (ETC), as a necessary parameter in the thermal properties of rock, is affected by the pore structure and the thermal conduction conditions. To evaluate the effect of fractures and saturated fluids on sandstone’s thermal conductivity, we simulated thermal conduction along three orthogonal (X, Y, and Z) directions under air- and water-saturated conditions on reconstructed digital rocks with different fractures. The results show that the temperature distribution is separated by the fracture. The significant difference between the thermal conductivities of solid and fluid is the primary factor influencing the temperature distribution, and the thermal conduction mainly depends on the solid phase. A nonlinear reduction of ETC is observed with increasing fracture length and angle. Only when the values of the fracture length and angle are large, a negative effect of fracture aperture on the ETC is apparent. Based on the partial least squares (PLS) regression method, the fluid thermal conductivity shows the greatest positive influence on the ETC value. The fracture length and angle are two other factors significantly influencing the ETC, while the impact of fracture aperture may be ignored. We obtained a predictive equation of ETC which considers the related parameters of digital rocks, including the fracture length, fracture aperture, angle between the fracture and the heat flux direction, porosity, and the thermal conductivity of saturated fluid.

In-Situ Measurements in Microscale Gas Flows-Conventional Sensors or Something Else?

Within the last few decades miniaturization has a driving force in almost all areas of technology, leading to a tremendous intensification of systems and processes. Information technology provides now data density several orders of magnitude higher than a few years ago, and the smartphone technology includes, as well the simple ability to communicate with others, features like internet, video and music streaming, but also implementation of the global positioning system, environment sensors or measurement systems for individual health. So-called wearables are everywhere, from the physio-parameter sensing wrist smart watch up to the measurement of heart rates by underwear. This trend holds also for gas flow applications, where complex flow arrangements and measurement systems formerly designed for a macro scale have been transferred into miniaturized versions. Thus, those systems took advantage of the increased surface to volume ratio as well as of the improved heat and mass transfer behavior of miniaturized equipment. In accordance, disadvantages like gas flow mal-distribution on parallelized mini- or micro tubes or channels as well as increased pressure losses due to the minimized hydraulic diameters and an increased roughness-to-dimension ratio have to be taken into account. Furthermore, major problems are arising for measurement and control to be implemented for in-situ and/or in-operando measurements. Currently, correlated measurements are widely discussed to obtain a more comprehensive view to a process by using a broad variety of measurement techniques complementing each other. Techniques for correlated measurements may include commonly used techniques like thermocouples or pressure sensors as well as more complex systems like gas chromatography, mass spectrometry, infrared or ultraviolet spectroscopy and many others. Some of these techniques can be miniaturized, some of them cannot yet. Those should, nevertheless, be able to conduct measurements at the same location and the same time, preferably in-situ and in-operando. Therefore, combinations of measurement instruments might be necessary, which will provide complementary techniques for accessing local process information. A recently more intensively discussed additional possibility is the application of nuclear magnetic resonance (NMR) systems, which might be useful in combination with other, more conventional measurement techniques. NMR is currently undergoing a tremendous change from large-scale to benchtop measurement systems, and it will most likely be further miniaturized. NMR allows a multitude of different measurements, which are normally covered by several instruments. Additionally, NMR can be combined very well with other measurement equipment to perform correlative in-situ and in-operando measurements. Such combinations of several instruments would allow us to retrieve an "information cloud" of a process. This paper will present a view of some common measurement techniques and the difficulties of applying them on one hand in a miniaturized scale, and on the other hand in a correlative mode. Basic suggestions to achieve the above-mentioned objective by a combination of different methods including NMR will be given.

Modeling Gas Flow Dynamics in Metal-Organic Frameworks

Modeling fluid flow dynamics in metal organic frameworks (MOFs) is a required step toward understanding mechanisms of their activity as novel catalysts, sensors, and filtration materials. We adapted a lattice Boltzmann model, previously used for studying flow dynamics in meso- and microporous media, to the nanoscale dimensions of the MOF pores. Using this model, rapid screening of permeability of a large number of MOF structures, in different crystallographic directions, is possible. The method was illustrated here on the example of an anisotropic MOF, for which we calculated permeability values in different flow directions. This method can be generalized to a large class of MOFs and used to design MOFs with the desired gas flow permeabilities.

Quantifying the anisotropy and tortuosity of permeable pathways in clay-rich mudstones using models based on X-ray tomography

The permeability of shales is important, because it controls where oil and gas resources can migrate to and where in the Earth hydrocarbons are ultimately stored. Shales have a well-known anisotropic directional permeability that is inherited from the depositional layering of sedimentary laminations, where the highest permeability is measured parallel to laminations and the lowest permeability is perpendicular to laminations. We combine state of the art laboratory permeability experiments with high-resolution X-ray computed tomography and for the first time can quantify the three-dimensional interconnected pathways through a rock that define the anisotropic behaviour of shales. Experiments record a physical anisotropy in permeability of one to two orders of magnitude. Two- and three-dimensional analyses of micro- and nano-scale X-ray computed tomography illuminate the interconnected pathways through the porous/permeable phases in shales. The tortuosity factor quantifies the apparent decrease in diffusive transport resulting from convolutions of the flow paths through porous media and predicts that the directional anisotropy is fundamentally controlled by the bulk rock mineral geometry. Understanding the mineral-scale control on permeability will allow for better estimations of the extent of recoverable reserves in shale gas plays globally.

A Unified Framework for Modeling Continuum and Rarefied Gas Flows

The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.