Two-dimensional Pore Network Research Articles

Influence of sedimentary structure and pore-size distribution on upscaling permeability and flow enhancement due to liquid boundary slip: A pore-scale computational study

Low-permeability sedimentary formations, such as tight sandstones, exhibit fluid flow and transport phenomena distinct from those in conventional porous systems due to the dominance of micro- to nanometer-sized pores and variable amounts of boundary slip. The widely used traditional no-slip boundary condition often fails to accurately describe fluid behavior in these formations. A knowledge gap exists in understanding how liquid slip influences fluid dynamics in complex, heterogeneous sedimentary structures, as previous studies have primarily focused on simplified, homogeneous pore geometries. In this study, we investigated the impact of boundary slip on low-Reynolds number fluid dynamics within synthetically designed two-dimensional graded and random pore networks with varying pore-size distributions to account for heterogeneity. Our results showed that velocity variance increased with increasing heterogeneity, following a power-law relationship. The power-law exponents decreased with boundary slip, quantifying how boundary slip mitigated the impact of heterogeneity on velocity variance. We developed a theoretical model to predict asymptotic flow enhancement and derived constitutive relations to estimate the coefficient C and maximum flow enhancement (ΔE) based on the pore-to-grain size ratio and porosity. Energy dissipation increased with both heterogeneity and boundary slip, which we identified as the primary mechanism contributing to asymptotic flow enhancement. This relationship was illustrated by a 1:1 linear correlation between maximum energy dissipation and maximum flow enhancement, regardless of heterogeneity, indicating that energy dissipation due to boundary slip entirely controls the emerging fluid dynamics. The presented theoretical model and constitutive equations offer practical applications for optimizing fluid dynamics in heterogeneous formations.

Pore-scale flooding experiments reveal the thermally regulated flow fields of the curdlan solution

Polymers can enhance oil recovery depending on viscoelasticity. In a field, during polymer flow through porous strata, continuous shear forces result in severe viscosity loss. However, polymers with great shear resistance result in limited migration distance. One solution to the above dilemma is to regulate viscosity, which enables a polymer to migrate long distances through pores with low viscosity and subsequently maintain high viscosity in deep reservoirs. The viscosity of curdlan can be regulated by changing temperature. By curdlan, we mean a biopolymer that shows applications in food industry. However, regarding oil reservoirs, it is unclear whether curdlan viscosity can be effectively regulated in pores. To reveal the feasibility of curdlan viscosity regulation to enhance oil recovery, flooding experiments combined with micro-particle image velocimetry were conducted in a two-dimensional pore network to investigate flow fields of curdlan solutions (0.25%, 0.5%, 1%, and 2%, w/v) at different temperatures (40, 65, and 85 °C). As a result, at 40 °C, curdlan solution (0.25%) easily migrated with low viscosity loss and low adsorption [88.3% original throat diameter (OTD)], and the mobility of curdlan was higher than hydrolyzed polyacrylamide. After heating (65 °C), the viscoelasticity, adsorption (55.1% OTD), and flow resistance (injection pressure, 2.2–8.8 kPa) of curdlan increased, and the greater adsorption capacity of curdlan than xanthan gum led to a more homogeneous flow field [average velocity ratio (Rm), from 2.6 to 1.1]. Since a homogeneous flow field indicated better sweep efficiency, curdlan regulated by temperature could achieve both long-distance migration and improved sweep efficiency in deep strata. These results suggested that viscosity regulation by curdlan could potentially improve oil recovery in water-flooded reservoirs.

Study of the Flow Field and Permeability Characteristics in the Goaf using the OpenPNM Package

The roof-caving step scale goaf behind the working face is sensitive to the region’s spontaneous combustion and gas concentration distribution, including many rock block cracks and holes. A severe deviation from the dynamics of fluids in porous media by representative element volume (REV), leading to the results of Computational Fluid Dynamics (CFD) simulation, has a significant error. A heterogeneous two-dimensional pore network model was established to simulate the goaf flow accurately. The network was first created using the simple cubic lattice in the OpenPNM package, and the spatial distribution of the “O-ring” bulking factor was mapped to the network. The bulking factor and Weibull distribution were combined to produce the size distribution of the pore and throat in the network. The constructed pore network model was performed with single-phase flow simulations. The study determined the pore structure parameters of the pore network through the goaf’s risked falling characteristics and described the flow field’s distribution characteristics in the goaf. The permeability coefficient increases as pore diameter, throat diameter, pore volume and throat volume increase and increases as throat length decreases. The correlation between throat volume and permeability coefficient is the highest, which indicates that the whole throat is the main control factor governing the air transport capacity in the goaf. These results may provide some guidelines for controlling thermodynamic disasters in the goaf.

Stoichiometry-Directed Two-Level Hierarchical Growth of Lanthanide-Based Supramolecular Nanoarchitectures.

The design of a well-ordered arrangement of atoms on a solid surface has long been sought due to the envisioned applications in many different fields. On-surface synthesis of metal-organic networks is one of the most promising fabrication techniques. Hierarchical growth, which involves coordinative schemes with weaker interactions, favours the formation of extended areas with the desired complex structure. However, the control of such hierarchical growth is in its infancy, particularly for lanthanide-based architectures. Here the hierarchical growth of a Dy-based supramolecular nanoarchitecture on Au(111) is described. Such an assembly is based on a first hierarchical level of metallo-supramolecular motifs, which in a second level of hierarchy self-assemble through directional hydrogen bonds, giving rise to a periodic two-dimensional supramolecular porous network. Notably, the size of the metal-organic based tecton of the first level of hierarchy can be tailored by modifying the metal-ligand stoichiometric ratio.

Comparative study of the imbibition patterns of two types of surfactants and their residual oil morphology in low-permeability reservoirs

Forward imbibition and reverse imbibition are common imbibition modes in reservoir development. In order to understand the characteristics of recovery efficiency, sweep mode and residual oil morphology of Surfactin (reverse imbibition) and an anionic gemini surfactant (AG, forward imbibition) systems, multiscale imbibition experiments were carried out. The core and microtube experiments showed that the capillary force was dominant in the Surfactin solution and the Marangoni force was dominant in the AG solution, when the model was horizontal. In the two-dimensional pore network imbibition experiment, the recovery rate of reverse imbibition was higher than that of forward imbibition, which was consistent with the core experiment. In Surfactin solution, the dominant imbibition channel formed and swept in a fan-like pattern, however, in AG solution it failed to form a dominant imbibition channel and swept in a finger-in pattern. In the initial stage, the imbibition rate in Surfactin solution was significantly higher than that of AG solution, and its sweep efficiency was 1.5 times higher than that of AG solution. In terms of the morphology of residual oil, less oil remains on the wall during reverse imbibition, and columnar and cluster residual oil was easy to form in the channel. After long-term molecular diffusion, the Marangoni effect can effectively improve mixing between the oil and water phases, thus improving the sweep efficiency. In the case of forward imbibition, there were more residual oil films on the solid wall and punctiform residual oil was easily formed in the channel. These discoveries provide a basis for the selection of imbibition fluids or the optimization of oil recovery processes in reservoir development.

Experimental evidence of the effect of solute concentration on the collective evolution of bubbles in a regular pore-network

The dissolution of bubbles confined in porous media is relevant to applications such as carbon sequestration and soil remediation. Recent numerical work indicates that a rich variety of collective dissolution behaviors can be obtained depending on the initial solute concentration, the size distribution of bubbles and the structure of the porous network. However, there is only sparse experimental evidence that supports these findings. Here, we present an experimental study that uses optical microscopy to track the dissolution of CO2 bubbles in a two-dimensional porous network etched on a microfluidic chip filled with CO2–saturated water. We consider two distinct level of initial liquid supersaturation for situations involving a single isolated bubble and small bubble clusters, and observe dissolution, growth or a combination of these processes. A pore-network model is used to complement the experimental observations with information on local concentration development. The model captures qualitatively the evolution of the bubble size in each case tested experimentally and enables shedding light on the interplay between the inter- and intra-pore diffusive fluxes in driving the dissolution process.

One-pot hydrothermal synthesis of MgV2O5-NC porous composite for hybrid supercapacitors with enhanced storage properties

A facile and scalable method is reported for MgV 2 O 5 (MVO) interconnected with a porous nitrogen-doped carbon (NC) sphere network using a hydrothermal technique. The synthesized MgV 2 O 5 -N-doped Carbon (MVO-NC) nanocomposite has an orthorhombic crystal plane and a sheet-like MVO with a porous NC network based on structural and morphological analyses. In an aqueous electrolyte, the hydrothermally produced MVO-NC electrode demonstrates good charge–discharge performance, with an exceptional cycling retention of 97.05% over 5000 cycles. At 2 A g −1 , the MVO-NC has a higher specific capacitance of 358 F g −1 than other MVO electrode compositions (272 F g −1 ) and V 2 O 5 (146 F g −1 ). Owing to the highly redox-active MVO-NC composite and exceptionally porous activated carbon components, the hybrid supercapacitors achieve a maximum energy density of 38 W h kg −1 and maximum power density of 8000 W kg −1 . The two-dimensional porous network structure of the MVO, along with the porous NC, creates sufficient interstitial space for electrolyte accommodation, thereby allowing a rapid and reversible electrochemical process. • A simple and scalable synthesis of MVO-NC composite has been prepared by hydrothermal technique. • The MVO-NC composite provides the higher conductivity than the MVO and VO materials. • At 2 A g −1 , the MVO-NC has a higher specific capacitance of 358 F g −1 than MVO and VO. • The MVO-NC composite shows the high energy and power density in hybrid supercapacitors.

Nonuniform Collective Dissolution of Bubbles in Regular Pore Networks

Understanding the evolution of solute concentration gradients underpins the prediction of porous media processes limited by mass transfer. Here, we present the development of a mathematical model that describes the dissolution of spherical bubbles in two-dimensional regular pore networks. The model is solved numerically for lattices with up to 169 bubbles by evaluating the role of pore network connectivity, vacant lattice sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the average dissolution time of the lattice, and the strength of the phenomenon depends on the network connectivity. The extension of the final dissolution time relative to the unbounded (bulk) case follows the power-law function, {B^k/ell }, where the constant ell is the inter-bubble spacing, B is the number of bubbles, and the exponent k depends on the network connectivity. The solute concentration field is both the consequence and a factor affecting bubble dissolution or growth. The geometry of the pore network perturbs the inward propagation of the dissolution front and can generate vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly nonuniform solute concentration fields. Sparse bubble lattices experience decreased collective effects, but they feature a more complex evolution, because the solute concentration field is nonuniform from the outset.

Facile synthesis of hemin-based Fe-N-C catalyst by MgAl-LDH confinement effect for oxygen reduction reaction

Because oxygen reduction reaction (ORR) is vital in high-capacity energy conversion and storage systems such as metal–air batteries and fuel cells, developing high-performance, low-cost ORR catalysts is crucial. Hemin containing Fe–N4 macrocycle is an inexpensive and readily available natural material widely present in animal blood. Herein, an efficient and environment-friendly method for preparing hemin-based carbon material is proposed based on the characteristic of the flexible interlayer space of layered double hydroxides (LDH). Hemin (Hm) was initially intercalated into the interlayer region of LDH. Subsequently, high-temperature carbonization was used to prepare Hm-LDH-700, a material with a graphene-like 2D lamellar structure with high ORR catalytic activity. Characterization results showed that the material has a two-dimensional porous network structure and a large specific surface area (1065.79 m2 g−1), which provides numerous active sites in the ORR reaction. Electrochemical tests revealed that Hm-LDH-700 exhibits greater ORR catalysis than Pt/C, with a higher half-wave potential (0.86 V vs. reversible hydrogen electrode (RHE)), a higher limiting current density (6.21 mA cm−2), and a lower Tafel slope (74 mV dec−1). This study presents a simple and effective strategy for preparing high-performance ORR hemin-based catalysts, which is crucial in the practical applications of sustainable clean energy.

Patterning Porous Networks through Self-Assembly of Programmed Biomacromolecules.

Two-dimensional (2D) porous networks are of great interest for the fabrication of complex organized functional materials for potential applications in nanotechnologies and nanoelectronics. This review aims at providing an overview of bottom-up approaches towards the engineering of 2D porous networks by using biomacromolecules, with a particular focus on nucleic acids and proteins. The first part illustrates how the advancements in DNA nanotechnology allowed for the attainment of complex ordered porous two-dimensional DNA nanostructures, thanks to a biomimetic approach based on DNA molecules self-assembly through specific hydrogen-bond base pairing. The second part focuses the attention on how polypeptides and proteins structural properties could be used to engineer organized networks templating the formation of multifunctional materials. The structural organization of all examples is discussed as revealed by scanning probe microscopy or transmission electron microscopy imaging techniques.

Thermal-Driven Formation of 2D Nanoporous Networks on Metal Surfaces

Controlling the quantum confinement of (spin-dependent) electronic states by material design opens a unique avenue to accelerate the implementation of quantum technology in next generation photonic and spintronic applications. In the nanoworld, two-dimensional porous molecular networks have emerged as highly tunable material platform for the realization of exotic quantum phases for which the nanopores can be tuned by chemical functionalization of the size and shape of the molecules. Here, we demonstrate a new approach to control the periodicity, size, and barrier width in 2D porous molecular networks on surface by tuning the balance between intermolecular and molecule–surface interactions using temperature. At 106 K, the prototypical TPT molecules form nanoporous networks with different periodicity and barrier width depending on the surface reactivity. The network structures continuously transform into a close-packed molecular structure at room temperature. This reversible structural phase transition can ...

Low-Dimensional Metal-Organic Coordination Structures on Graphene.

We report the formation of one- and two-dimensional metal–organic coordination structures from para-hexaphenyl-dicarbonitrile (NC–Ph6–CN) molecules and Cu atoms on graphene epitaxially grown on Ir(111). By varying the stoichiometry between the NC–Ph6–CN molecules and Cu atoms, the dimensionality of the metal–organic coordination structures could be tuned: for a 3:2 ratio, a two-dimensional hexagonal porous network based on threefold Cu coordination was observed, while for a 1:1 ratio, one-dimensional chains based on twofold Cu coordination were formed. The formation of metal–ligand bonds was supported by imaging the Cu atoms within the metal–organic coordination structures with scanning tunneling microscopy. Scanning tunneling spectroscopy measurements demonstrated that the electronic properties of NC–Ph6–CN molecules and Cu atoms were different between the two-dimensional porous network and one-dimensional molecular chains.

Pore Network Simulation and Experimental Investigation on Water-Heat Transport Process of Soil Porous Media

The research on water-heat transport of soil porous media has important theoretical and practical significance for the problem of agricultural production and environmental governance. In this work, the water-heat transport characteristics of sandy soil porous media are analyzed. The two-dimensional continuum physical model is constructed by continuum method, and the two-dimensional pore network physical model is constructed directly at pore scale by taking into account the complicated pore and skeleton structures of soil. Mathematical models of water-heat transport process of sandy soil are constructed based on heat-mass transfer mechanism. Mathematical models of the continuum method and pore network method are solved by ANSYS and self-designed solving algorithm, respectively. The numerical simulation results of soil temperature distributions and moisture distributions are in good agreement with the experimental results. The pore network simulation results are in good agreement with the measured data and are superior to the existing continuous scale method. The pore network simulation results can directly present the characteristics of the preferential flow and wetting front during the water-heat transport process of soil.

Steering Two-Dimensional Porous Networks with σ-Hole Interactions of Br···S and Br···Br

The self-assembly of 3,10-dibromo-perylo[1,12-b,c,d]thiophene on Ag(111) leads to three types of ordered porous networks: honeycomb PN1, Kagome PN2, and hybrid PN3. Detailed experimental and theore...

Sherwood correlation for dissolution of pooled NAPL in porous media

The rate of interphase mass transfer from non-aqueous phase liquids (NAPLs) entrapped in the subsurface into the surrounding mobile aqueous phase is commonly expressed in terms of Sherwood (Sh) correlations that are expressed as a function of flow and porous media properties. Because of the lack of precise methods for the estimation of the interfacial area separating the NAPL and aqueous phases, most studies have opted to use modified Sherwood expressions that lump the interfacial area into the interphase mass transfer coefficient. To date, there are only two studies in the literature that have developed non-lumped Sherwood correlations; however, these correlations have undergone limited validation. In this paper controlled dissolution experiments from pooled NAPL were conducted. The immobile NAPL mass is placed at the bottom of a flow cell filled with porous media with water flowing horizontally on top. Effluent aqueous phase concentrations were measured for a wide range of aqueous phase velocities and for two different porous media. To interpret the experimental results, a two-dimensional pore network model of the NAPL dissolution kinetics and aqueous phase transport was developed. The observed effluent concentrations were then used to compute best-fit mass transfer coefficients. Comparison of the effluent concentrations computed with the two-dimensional pore network model to those estimated with one-dimensional analytical solutions indicates that the analytical model which ignores the transport in the lateral direction can lead to under-estimation of the mass transfer coefficient. Based on system parameters and the estimated mass transfer coefficients, non-lumped Sherwood correlations were developed and compared to previously published data. The developed correlations, which are a significant improvement over currently available correlations that are associated with large uncertainties, can be incorporated into future modeling studies requiring non-lumped Sh expressions.

Discrete pore network modeling of superheated steam drying

ABSTRACTA nonisothermal two-dimensional pore network model is developed to describe the superheated steam drying of a capillary porous medium. The complex void space is approximated by a network of spherical pores interconnected by cylindrical throats. In this model, the condensation of water vapor at the network surface as well as the network drying are taken into account. During the network drying period, the liquid transport is driven by capillary action, whereas vapor transport occurs because of convection. The condensation of water vapor within the pores is modeled based on newly formulated liquid invasion rules. The simulation results, presented as temperature and moisture content profiles over time, indicate qualitative agreement with available experimental observations. The inclusion of the liquid invasion rules is shown to accommodate more of the condensed water mass compared to earlier models, in which condensation is only partly treated. Due to the viscous vapor flow, the vapor overpressure within the network, which is the driving force of vapor transport, is reproduced in these simulations. The influence of vapor overpressure on the disintegration of the liquid phase is also discussed.

Nitrogen-rich two-dimensional porous polybenzimidazole network as a durable metal-free electrocatalyst for a cobalt reduction reaction in organic dye-sensitized solar cells

Nitrogen-enriched two-dimensional (2D) porous polybenzimidazole (2D-HPBI) network was synthesized from the reaction between 1,2,4,5-tetraaminobenzene (TAB) and benzene-1,3,5-tricarboxylic acid (BTA) in polyphosphoric acid (PPA) medium. Interestingly, the remnant terminal groups such as amine and carboxyl groups at the periphery of 2D-HPBI were selectively stripped off by heat-treatment at 470°C. The resultant heat-treated 2D-HPBI (HT-HPBI) displayed substantially improved electrical conductivity and thus outstanding performance as the counter electrode (CE) for the cobalt reduction reaction (CRR) in dye-sensitized solar cells (DSSCs). The charge-transfer resistance (Rct=0.51Ωcm2) at the HT-HPBI-CE/electrolyte interface was even lower than that of Pt-CE (1.09Ωcm2). More importantly, HT-HPBI-based CE showed near “zero” loss of electrochemical stability (1/Rct) even after 1000 potential cycles, while the 1/Rct of Pt decreased to <10% that of a fresh cell.

ChemInform Abstract: Host—Guest Chemistry in Two‐Dimensional Supramolecular Networks

AbstractReview: 119 refs.

Adsorption Kinetics Emulation With Lattice Gas Cellular Automata

ABSTRACTLattice gas cellular automata (LGCA), as a fluid dynamic simulation method, are conceptually simple and can be applied to deal with thermal interface effects to a wide array of boundary conditions. Based on LGCA, the lattice Boltzmann method has been successfully used to model a number of typical continuous fluid dynamic problems. In this research, however, we extend the general Frisch, Hasslacher, and Pomeau method from LGCA to the microscopic scale to emulate the surface adsorption process. Specifically, hexagonal grids topology and geometry are applied in two dimensions with 6-bit digits to represent different states of each grid node. The rule space is then determined as 66. A two-dimensional porous network is constructed for simulating a practical adsorbent material structure. The lattice gas collision and movement are implemented within periodic space boundary conditions. Local rules of lattice gas interaction with network surface are defined and examined. The adsorption probabilities on each adsorptive site, corresponding to adsorption potential with relationship to temperature, are taken into account. As a result, an intuitive visualization of physical surface adsorption kinetics is achieved.

A new approach to study deposition of heavy organic compounds in porous media

A two-dimensional pore network model is presented to validate the deposition of heavy organic compounds (HOC) formed out of an oleic phase in a porous medium. The thickness of the deposition covering the pore surface and the associated pressure drop across each channel of the pore network as well as the overall pressure drop across the entire network model were simulated using the Wang-Civan deposition model. The results were then compared to the measured total pressure drop for each experimental run. Heptane and decane were the two types of precipitator (solvent) used in the experiments with carbon numbers of 7 and 10, respectively. Additionally, three crude oil/solvent volumetric ratios of 10:5, 10:6, and 10:7, as well as three different total flow rates of 4, 8, and 12ml/h were examined to investigate their impacts on the deposition of HOC. The deposition was evaluated through release and deposition coefficients for each experiment. Results indicated that as the solvent carbon number, crude oil/solvent ratio, and total flow rate of crude oil and solvent increases, the deposited layer and the corresponding total pressure drop decreases, the deposition continues until the complete blockage of the entire network because of deposition.