Stochastic Pore Network Research Articles

Multiscale pore-fracture hybrid pore network modeling for drainage in tight carbonate

Tight carbonate possesses both fractures and multiscale pores. Flow through tight carbonate rocks involves several length scales and the complicated flow physics. Capturing and modeling the entire void space into a single pore network model for drainage is challenging. Here, we present a novel method for modeling of a multiscale pore-fracture hybrid pore network, which enables various void spaces at multiple length scales and the flow characteristics in them to be included. Pores and fractures in a low-resolution CT image are extracted by medial axis-maximal ball algorithm and medial surface algorithm, respectively, to generate a pore-fracture hybrid pore network. Then, a statistics-based small-scale stochastic pore network is established in the CT image solid domains to represent the micropores unresolved by the image. The two pore networks are organically integrated into a multiscale hybrid pore network by cross-scale connections. The statistics of small-scale pore network are determined by experimental permeability. We study the effects of the small-scale pore network density on connectivity, single- and two-phase flow properties of the model to obtain the robust parameter. The influence of fractures on two-phase flow properties is analyzed. Results show the significance of incorporating fractures and micropores in the model. The model is validated via comparison between simulation result and experimental data. This method can accurately, efficiently, conveniently construct multiscale pore-fracture hybrid pore network of tight carbonate rock for evaluating the drainage characteristics.

Stochastic microstructure delineation and flow simulation in asymmetric block copolymer ultrafiltration membranes

Asymmetric block copolymer ultrafiltration membranes have a wide range of applications from water purification and virus filtration all the way to drug delivery. Although optimizing flow is critical to the performance of such ultrafiltration membranes, their numerical flow characterization has remained challenging. The main problems include hierarchical pore structure delineation and lack of an efficient, image-based pore-scale modeling approach. In this study, we use 2D scanning electron microscopy (SEM) images with a variety of resolutions to delineate the hierarchical asymmetric pore structure. To simulate flow, a novel stochastic pore network model is proposed. The absolute permeabilities of two asymmetric block copolymer ultrafiltration membranes are computed and compared with experimental results showing good agreement.

The Impacts of Surface Microchannels on the Transport Properties of Porous Fibrous Media Using Stochastic Pore Network Modeling.

A stochastic pore network modeling method with tailored structures is proposed to investigate the impacts of surface microchannels on the transport properties of porous fibrous media. Firstly, we simplify the original pore network extracted from the 3D images. Secondly, a repeat sampling strategy is applied during the stochastic modeling of the porous structure at the macroscale while honoring the structural property of the original network. Thirdly, the microchannel is added as a spherical chain and replaces the overlapped elements of the original network. Finally, we verify our model via a comparison of the structure and flow properties. The results show that the microchannel increases the permeability of flow both in the directions parallel and vertical to the microchannel direction. The microchannel plays as the highway for the pass of reactants while the rest of the smaller pore size provides higher resistance for better catalyst support, and the propagation path in the network with microchannels is more even and predictable. This work indicates that our modeling framework is a promising methodology for the design optimization of cross-scale porous structures.

GPU-based Real-time Porous Medium Dynamic Network Simulation

Porous medium network simulation is to accurately describe the seepage law of multiphase fluids in porous media. Researchers have studied the relationship between various macroscopic physical properties of multiphase fluids (e.g. relative permeability, capillary pressure and fluid saturation) from theoretical, experimental, and computer simulation. This research introduces the construction method of stochastic pore network model and describes the calculation steps of pore network pressure field. In this research, the computational efficiency of the GPU-based pore network was compared with CPU. The calculation speed and simulation model scale of the pressure domain of the random pore network were improved.

Balancing Reactant Transport and PTL-CL Contact in PEM Electrolyzers by Optimizing PTL Design Parameters via Stochastic Pore Network Modeling

Optimizing the porous transport layer (PTL) structure is crucial for high current density operation of polymer electrolyte membrane (PEM) electrolyzers. Previous studies from the literature demonstrated that PTL structures, mainly porosity and titanium powder diameter, can be strategically chosen to improve the performance (1-3). However, transport mechanisms in the PTL can be further explained from the perspective of mass transport. In this work, we employed modelling approaches to investigate the effect of porosity and titanium particle size of the sintered titanium powder based PTL on mass transport. PTLs were numerically generated using a stochastic model (Figure 1) with three titanium powder diameters, 25 µm, 50 µm, and 75 µm, and three porosities, 26.5%, 40.5%, and 63.5%. Pore network modelling was used to calculate the gas saturation and the permeability of liquid water in the presence of oxygen gas. We observed that all simulated PTLs exhibited similar gas saturation profiles and relative permeabilities, yet the PTLs with higher porosities had significantly higher liquid water permeabilities. For a constant powder diameter of 25 μm, increasing the porosity from 26.5% to 63.5% led to an increase in the average surface roughness from 8.9 μm to 38.6 μm. For a constant porosity of 26.5%, increasing the powder size from 25 μm to 75 μm resulted in an increase in the average surface roughness from 8.9 μm to 18.3 μm. Larger open pore spaces were acquired for PTLs with higher surface roughness, resulting in higher liquid water permeabilities (two-phase permeability). Therefore, PTLs with higher porosities and larger particle sizes provide superior liquid water permeation and gas removal. Figure 1. The 3D reconstruction of the PTL generated with titanium powder diameter of (a) 25 µm, (b) 50 µm, and (c) 75 µm at overall porosity of 40.5%. References S. A. Grigoriev, P. Millet, S. A. Volobuev and V. N. Fateev, Int J Hydrogen Energy, 34, 11, p. 4968-4973 (2009). J. O. Majasan, F. Iacoviello, P. R. Shearing and D. J. Brett, Energy Procedia, 151 (2018). L. Zielke, A. Fallisch, N. Paust, R. Zengerle and S. Thiele, Royal Society of Chemistry Advances, 4, p. 58888-58894 (2014). Figure 1

Balancing Reactant Transport and PTL-CL Contact in PEM Electrolyzers by Optimizing PTL Design Parameters via Stochastic Pore Network Modeling

The impacts of sintered titanium powder diameter and porous transport layer (PTL) porosity on reactant transport and PTL-catalyst layer (CL) contact in the polymer electrolyte membrane (PEM) electrolyzer were studied using stochastic generation and a pore network model. Enhanced reactant transport was established with increased powder diameter and porosity, observed through increases in single- and two-phase permeabilities. Compared to increasing the powder diameter, increasing the PTL porosity dominated increases in permeabilities, especially at higher porosities (e > 40%). However, we observed a trade-off whereby increasing the powder diameter led to increased surface roughness at the PTL-CL interface. High roughnesses were observed at porosities > 40%. In conclusion, the powder diameter and porosity must be strategically selected for the desired target operating conditions of the PEM electrolyzer.

Multi-scaled pore network modeling of gas-water flow in shale formations

Abstract Multiphase flow is commonly encountered within shale reservoirs, however, the previous studies are more focused on single phase flow. Due to the extremely low permeability of shale formations, the experimental measurements are not capable to be performed. Attempts are made by applying the techniques of digital rock analysis and pore network modeling to investigate the multiphase flow mechanisms in shale reservoirs. This work follows this way. Firstly, a stochastic pore network generation algorithm and a two-phase flow simulation method are presented. This algorithm is applied and validated in Berea sandstone. By applying the proposed algorithm, the organic and inorganic pore networks are generated for shale formations, then the multi-scaled pore network is established after upscaling the organic pores to an organic path. Finally, the gas-water flow is simulated within this established multi-scaled pore network and some analysis and discussions are conducted. The results imply that the characteristics of pore systems in shale formations pose an extreme impact on the gas-water flow mechanisms, especially the proportion of organic pores and pore-throat aspect ratio.

Towards stochastic generation of 3D pore network models of building materials

Pore-scale-based prediction of the hygric properties of porous building materials is on the rise as an attractive alternative for the current experimental procedure. Pore-scale simulations do however require a complete pore network model for the building material. With the currently available characterization techniques, such complete pore network model cannot be established, instead typically fragmented direct (pores sizes, shapes, positions, connections, …) or indirect (pore size distribution, pore surface area, …) information is obtained. The aim of this paper is to present stochastic pore network generation, wherein the fragmented pore structure information is used to generate a complete pore network for the building material involved. The novelty of our approach lies in the generation of a PNM by matching the distributions of direct parameters as well as indirect parameters of the input data and the model. Additionally, the position of the pores are no longer bound to a cubic lattice. This workflow will first be tested on a single scale material with a relatively straightforward pore space such as sintered glass. Finally, the hygric properties of the generated network will be compared to the measured properties of the real material as a validation step.

Influence of limiting throat and flow regime on oxygen bubble saturation of polymer electrolyte membrane electrolyzer porous transport layers

In this work, the effect of porous transport layer (PTL) microstructure on the growth of oxygen gas bubbles was investigated using a microfluidic platform, termed PTL-on-Chip. The microfluidic chip was designed through stochastic pore network generation and height calibration, and was fabricated using soft-lithography. It was found that PTL throats have the dominating threshold capillary pressures compared to PTL pores; therefore, the size distribution of PTL throats ultimately govern the distribution of bubbles within the water saturated PTL. A unique throat is herein termed the limiting throat, whereby once it has been penetrated by the bubble, breakthrough instantly follows. This limiting throat is also the location of snap-off for subsequent bubble detachment. Within the porous media, oxygen bubble saturation increased as the distance of the limiting throat from the inlet increased. Lastly, it was observed that the heterogeneity of the PTL structure can enable the simultaneous co-existence of two flow regimes (capillary fingering and viscous fingering) at distinct regions within the bulk.

Design of Porous Banana Foam Mat to Resist Moisture Migration Using a 2-D Stochastic Pore Network and Its Textural Property

The high porosity of dried banana foam allows it to quickly adsorb moisture from the air during storage, leading to a loss of quality and textural properties. Therefore, the main purpose of this research was to design and study banana foam structure at the pore level to limit moisture migration using a 2-D stochastic pore network. A 2-D network formed by the interconnection of cylindrical pores was used to represent the voids inside the banana foam and the moisture movement inside the individual pore segments during adsorption was described by Fick's law. The pore network was divided into two layers with different banana foam densities and the top surface of the network was exposed to humid air. The upper layer was assigned with pore sizes from the banana foam density of 0.31 g/cm3, having a void area fraction of 0.22, or from a density of 0.21 g/cm3, having a void area fraction of 0.31; the lower layer was assigned specifically with the pore sizes from the banana foam density of 0.26 g/cm3, having a void area fraction of 0.26. The predictions agreed well with the experimental results, with an R2 value above 0.95. The two-layered banana foam mat with high banana foam density (characterized by mostly small pores) on the upper layer could limit the transport of moisture, with a rate relatively lower than that of a single-layered banana foam mat, and also exhibited more crispiness than the single banana foam. However, when the low banana density was in the upper layer, the two-layered sample adsorbed moisture quickly and its texture was less crispy.

Construction of Three-Dimensional Pore Network in Bulk Grain

In order to construct a 3D pore network reflecting the real pore structure of bulk grain, a series of 2D section images are obtained and used to reconstruct 3D images using MATLAB. The parameters of the 3D pore network are extracted by the maximal ball method. A stochastic 3D pore network with a random size is generated, but some throats are lost in generation. The parameter deviation between the original model and the generated model decreases with an increase in volume. There is almost no deviation when the space size is up to meter level. The image resolution of 0.5 mm is enough to extract parameters of the bulk grain.

Sensitivity of Intrinsic Permeability to Electrokinetic Coupling in Shaly and Clayey Porous Media

Classical Darcy's law assumes that the intrinsic permeability of porous media is only dependent on the micro-geometrical and structural properties of the inner geometry of the medium. There are, however, numerous experimental evidences that intrinsic permeability of shaly and clayey porous material is a function of the fluid phase used in the experiments. Several pore-scale processes have been proposed to explain the observed behavior. In this study, we conduct a detailed investigation of one such mechanism, namely the electrokinetic coupling. We have developed a numerical model to simulate this process at the pore-scale, incorporating a refined model of the electrical double layer. The model is used to conduct a detailed sensitivity analysis to elucidate the relative importance of several chemical-physical parameters on the intensity of the electrokinetic coupling. We found that permeability reduction due to this mechanism is likely to occur only if the effective pore-radius is smaller than 10-6 m. We also observed that electrokinetic coupling is strongly sensitive to electrophoretic mobility, which is normally reduced in clays compared to free-water conditions. Based on these findings, we set up a suite of stochastic pore-network simulations to quantify the extent of permeability reduction. We found that only if the effective pore-radius is ranging from 5 × 10-7 m to 5 × 10-8, electrokinetic coupling can be responsible for a 5-20% reduction of the intrinsic permeability, and, therefore, this mechanism has a minor impact on situations of practical environmental or mining interest

Modelling of moisture diffusion in pores of banana foam mat using a 2-D stochastic pore network: Determination of moisture diffusion coefficient during adsorption process

The purpose of this research was to determine the diffusion coefficient of moisture in the pores of banana foam mat using stochastic pore network. A 2-D pore network was used to represent the pore voids inside the banana foam sample and the moisture movement inside the individual pore segments was described by Fick’s law. To determine the moisture diffusion coefficient, the adsorption experiments were carried out with standard static method using saturated salt solutions. Two banana foam densities of 0.21 and 0.26 g/cm 3 were used to adsorb the water vapour. The interactions between moisture and pore structure were illustrated using a 3-D pictorial representation of network concentration gradients in spaces with colour representing the moisture content. The network model described the experimental results relatively well. The diffusion coefficient of moisture in pores was in order of 10 - 9 m 2/s which was nine times higher than the effective diffusion coefficient calculated from the continuum model. The value of moisture diffusion coefficient was dependent on the temperature and independent of the foam densities and the relative humidity, except for the diffusivity determined from the condition at higher relative humidity of 70%.

Effects of pore size distribution and pore-architecture assembly on drying characteristics of pore networks

Simulation of isothermal drying using two-dimensional networks comprised of interconnected cylindrical pores is presented. Transport of moisture inside pore segments was described by Fick’s law. The results have shown that the shielding of large pores by the smaller pores in the stochastic pore network, which is supposed to be representative of real porous medium, causes the lower drying rate and hence lower effective diffusion coefficient as compared to those predicted from the idealized network of pores with a single size. The strength of shielding is found to vary with the characteristics of pore size distribution as interpreted by the moisture concentration experienced by the pores, which is remarkably different amongst the pore size distributions. The inefficient transport of moisture through the stochastic pore network can be improved or even better with the suitable architecturally assembled structure. The minimum shielding archetype network, appearing very high porous at particle surface, is predicted to enhance greatly the drying rate. On the other hand, the maximum shielding network, which is small pores allocated onto the network exterior, exhibits the slowest drying rate.

Catalyst deactivation by coke deposition: Approaches based on interactions of coke laydown with pore structure

Catalyst deactivation by foulant deposition arises from interactions of the accumulating deposit with the geometry and void structure of particle porosity. Simple approaches involving a wedge-layering deposition in a parallel bundle of pores allow activity loss by surface coverage and pore plugging. More complex models use coking rates related to local concentration in bundles of randomly corrugated pores or in interconnected arrays of pore segments forming stochastic pore networks. Examples and illustrations are presented for cumene cracking on a supported zeolite catalyst. The optimal design of support pore structure to resist deactivation by coking is briefly discussed.

Interpretation of water isotherm hysteresis for an activated charcoal using stochastic pore networks

Water vapor adsorption equilibria on activated carbons typically exhibit hysteresis. The size and shape of the hysteresis loop which separates the adsorption and desorption branches is a strong function of the pore size and interconnectivity of the pores. Neither conventional pore filling models nor statistical thermodynamics approaches provide a means for predicting the extent of hysteresis from only adsorption measurements. This work uses the Kelvin Equation in conjunction with the structural concept of a stochastic pore network to describe measured water isotherms on BPL carbon. Using a pore segment distribution function determined from the adsorption branch, it is shown that totally random assemblies underestimate the extent of hysteresis. It is possible, however, to closely fit the measured BPL-water hysteresis loop using a patchy heterogeneity in which a proportion of the larger pores are preferentially located on the exterior, mid-range pores are concentrated in a sub-surface layer and some large pores form shielded voids behind much smaller pores.

Fluid catalytic cracking: some recent developments in catalyst particle design and unit hardware

Catalytic cracking is an old process, but is still subject to new pressures for change and improvement. In the 1990s, these pressures arise from the need to crack components drawn from deeper down the barrel as well as to reformulate fuel products which can meet more stringent environmental requirements. Recent efforts at correlating catalyst formulation and cracking performance still rely on largely empirical understanding of the role of catalyst composition and zeolite/matrix pore architecture. However, new tests measuring cracking performance at constant surface area as the zeolite/ matrix ratio varies have indicated that the pore architecture should be designed to facilitate a staged cracking. The whole range of pore sizes from micro-pores (< 20 Å) to giant macro-pores (1000 Å) are now known to be influential in determining cracking yield and activity and these pores should be assembled into an optimal architecture. Unfortunately, the configuration of pores in a typical spray dried FCC catalyst is usually far from such an optimal design. The use of stochastic pore networks to characterise macro-pore structures is described in conjunction with some experimental results employing a visualised porosimetry based on low melting point alloy impregnation. Improved designs of catalyst will impose new requirements on the fluidised bed hardware. Some recent improvements in the chemical engineering of riser reactor/regenerator units are described which centre on atomised injection, segregated feeding, closed cyclones, staged stripping and catalyst cooling.

Representation of porous catalysts using random pore networks

Stochastic pore networks are increasingly used to represent porous media and model transport processes occuring in them. Most frequently, square or cubic regular grids of pores are employed. It has been shown recently that regular and random networks give significantly different tortuosities both under conditions of diffusion-only and diffusion with simultaneous reaction. In this study the relationship between random and regular topologies is more formally investigated using percolation and finite-size scaling theories. Critical properties of the random model are determined from Monte Carlo simulations on large networks and these are compared with the results for regular lattices. Percolation thresholds are greater in the random models; it is observed that the greatest difference occurs at low pore connectivities. The critical exponents were determined by finite-size scaling and found to be independent of topology and connectivity. Further, at low connectivities the cluster size distribution is markedly different between regular and random topologies.The random model is also used to represent the bi-disperse porous structures which arise in commonly used catalyst supports. It is demonstrated that unreasonable results are obtained if macropores and micro-pores are assigned from two distributions in an uncorrelated manner. Using an appropriate random model, anomalously high tortuosities obtained by other workers are avoided. This demonstrates the importance of using a model which is a realistic representation of the porous structure.

Quantification of Random Pore Structures of Porous Adsorbents

The structure of pore spaces in typical catalyst particles could often be described as being “not so much fabricated as thrown together”. Thus whilst for certain materials, such as zeolites, the microstructures are well defined and have a precise geometry, most materials when used in typical particulate form are at least partly composed of chaotically configured pore spaces. These random pore structures can be important in determining an adsorbent's performance, so it is necessary to define them quantitatively. A heirarchy of approaches based upon developments from simple stochastic pore networks is described. A stochastic pore network is one in which simple pore segments form interconnecting networks within which pores can be either randomly or partly randomly distributed. Such stochastic networks can be characterised by mercury porosimetry and low-temperature gas adsorption. Interconnectivity and randomness affect the degree of hysteresis for both these techniques. For 3-D random pattern stochastic networks, it is possible to interpret sectioned SEM images using ‘random’ slices of particles subject to low melting point alloy visual porosimetry in order to arrive at measures of random pore structure. This ‘image analysis’ approach is being extended to 3-D image reconstruction of SEM sections using fractal surfaces in conjunction with randomly tortuous pores.

Explicit relation between relative permeability and structural parameters in stochastic pore networks

It is shown, by suitable use of the effective medium approximation, that the relative permeability of a stochastic network consisting of idealised pores of randomly varying radius, which are progressively constrited and/or blocked, can be expressed analytically as an explicit function of suitable parameters characteristic of pore and network structure as well as the physics of flow. In this manner, it is possible to: (i) gain a much deeper insight into the dependence of relative permeability on the breadth and shape of the pore radius probability distribution as well as the network connectivity, and (ii) greatly simplify the approximate evaluation of the relative permeability of given stochastic networks under suitable conditions. These points are illustrated by a detailed study of the case of (Knudsen) gas relative permeability of cylindrical pore networks, in the presence of an adsorbed and condensed foreign vapour. Results of immediate importance for experimental pore structure analysis, which emerged from this study include the capability of: (i) estimating the network connetivity, and (ii) testing the self-consistency of pore size distributions determined experimentally by conventional vapour sorption isotherm analysis.