Pore network modelling space

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

NMR methods offer a noninvasive method of characterizing porous media. A variety of different techniques may be used to obtain useful information on the pore space. For instance, pore sizes may be measured using the freezing point depression technique for mesoporous solids or by relaxation time measurements for macroporous solids. Other pore space information comes from PFG techniques, while direct imaging of the pore space is possible for large pores. The information from studying the pore space can then be incorporated into appropriate pore network models. 

Intrinsically, a pore network contains the pore space s cormectivity data, where the term coordination number represents the number of throat comiections at each pore. In addition to this topological information, the size and shape of each element can be incorporated. A pore network model can be tuned to have the... 

The geometric and transport assumptions of pore network models built to study GDL invasion often vary. A primary distinction is in how the pore space is defined. For visual purposes, it is useful to illustrate two-phase flow behavior using a planar, 2D network however, a three-dimensional (3D) network is... 

Typically, pore network models of GDLs assume cubic or spherical pores and square or cylindrical throats. Conveniently, these pore geometries require standard calculations of volume, and these throat geometries are assumed to facilitate Poiseuille-like flow. Furthermore, the hydraulic conductance is a simple function of throat size, length and fluid viscosity. An alternative to this method, when creating a pore network from a predefined pore space, is to incorporate a shape factor for each pore and throat, which is then incorporated into the conservation and flow equations. Luo et a/. demonstrate this method by choosing a shape factor based on the surface to volume ratio of the physical elements that were converted into pore network elements. 

Pore network models, however, are not suited for the approximation of the void space of highly porous particle aggregates such as gels. The two main reasons for this are (1) the assumption of purely axial liquid flow cannot be justified in large pores and (2) the pore network would need to be continuously updated to account for the motion of the solid phase. 

The advantages of this type of system are obvious the pore space is of sufficient complexity to represent any natural or technical pore network. As the model objects are based on computer generated clusters, the pore spaces are well defined so that point-by-point data sets describing the pore space are available. Because these data sets are known, they can be fed directly into finite element or finite volume computational fluid dynamics (CFD) programs in order to simulate transport properties [7]. The percolation model objects are taken as a transport paradigm for any pore network of major complexity. 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

In this section, two examples are presented for the application of a technique of low-melting-point alloy (LMPA) impregnation that provides for a visualization of the invasion of a nonwetting fluid into the pore spaces in a typical porous article. The visualization can be linked to the modeling of mercury porosimeter curves using 3-D stochastic pore networks. This makes the quantification of pore structure more direct. Quantified structures can be visually examined against sample particle sections. The visual comparison can be made more precise by image analysis of the accessible porosity made visible by metal penetration over a series of pressures. 

Gas relative permeability, Pk, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability when the pore space is free of this second fluid. This property diminishes at the percolation threshold , at which a significant portion of the pores are still conducting but they do not form a continuous path along the flow direction. It is obvious that only the network model, can provide a satisfactory analysis of the percolation threshold problem. Nicholson et al. [3] introduced a simple network model, and applied it on gas relative permeability [4]. For the gas relative permeability, an explicit approximate analytical relation between the relative permeability and the two network parameters, namely z and the first four moments of, f(r), has been developed, based on the Effective Medium Approximation (EMA) [5]. If a porous... 

These models will be presented in order of increasing complexity in the representation of pore space geometry, from individual uniform pores to interacting nonuniform pore networks. 

We now study the morphological and topological characteristics of site-bond-site 3D cubic network model. The following additional assumptions are made about the pore space i. The pore space is a lattice of spherical cavities interconnected by cylindrical channels. The catalytic surface mainly belongs to the voids of the lattice, ii. Active sites are uniformly... 

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

In practice the active sites are not homogeneously distributed within the solid pellet. Furthermore, due to deposits (e.g. coke) within the pores the structure of the pores changes with time. This demands a local description of the pore space. At present network models are preferred for this purpose... 

Once a pore space is known, a pore network can be created through a variety of methods. Methods that reduce the pore space into a topologically equivalent skeleton involve either a thiiming algorithm or, in the case of the 2D models " -a Voronoi diagram around the material locations. An alternative method to determine the representative pore network for a pore space is the maximal ball method, which is a computationally inexpensive techniqne that has been demonstrated for GDL-like structures. ... 

Efforts of polymer scientists and fuel cell developers alike are driven by one question What specific properties of the polymeric host material determine the transport properties of a PEM, especially proton conductivity The answer depends on the evaluated regime of the water content. At water content above kc, relevant structural properties are related to the porous PEM morphology, described by volumetric composition, pore size distribution and pore network connectivity. As seen in previous sections, effective parameters of interest are lEC, pKa, and the tensile modulus of polymer walls. In this regime, approaches familiar from the theory of porous media or composites (Kirkpatrick, 1973 Stauffer and Aharony, 1994), can be applied to relate the water distribution in membranes to its transport properties. Random network models and simpler models of the porous structure were employed in Eikerling et al. (1997, 2001) to study correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake, and proton conductivity, as will be discussed in the section Random Network Model of Membrane Conductivity. ... 

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