Models of porous media

Fig. 11.1 Schematic representation of NAPL movement from land surface to the water table region, (a) LNAPL movement, and (b) DNAPL movement (after Abriola and Pinder 1985). Reproduced by permission of American Geophysical Union. Abriola LM, Pinder GF (1985) A multiphase approach to the modelling of porous media contamination by organic compounds. Water Resour Res 21 11-18. Copyright 1985 American Geophysical Union...

Abriola LM, Pinder GF (1985) A multiphase approach to the modeling of porous media contamination by organic compounds. 1. Equation development. Water Resour Res 21 11-18... 

A similar model has been applied to the modeling of porous media with condensation in the pores. Capillary condensation in the pores of the catalyst in hydroprocessing reactors operated close to the dew point leads to a decrease of conversion at the particle center owing to the loss of surface area available for vapor-phase reaction, and to the liquid-filled pores that contribute less to the flux of reactants (Wood et al., 2002b). Significant changes in catalyst performance thus occur when reactions are accompanied by capillary condensation. A pore-network model incorporates reaction-diffusion processes and the pore filling by capillary condensation. The multicomponent bulk and Knudsen diffusion of vapors in each pore is represented by the Maxwell-Stefan model. 

Sbaiti, B., 1985, "Modelling of porous media using 3-D stochastic pore networks", Ph D. Thesis, UMIST... 

Cfossiey, P. A., Schwartz, L. M., Banavar, J. R. (1991) Image-based models of porous media Application to Vyoor glass and carbonate rocks. Appl. Phys. Leu, 59 (27), 3553 3555. 

Fatt, I. (1956). The network model of porous media I capillary pressure characteristics. Petrol. Trans. A.I.M.E., 207, 144—59. 

Chatzis and Dullien (1977) were the first to use tubular bonds and spherical sites to simulate pore throats and bodies respectively, in network models of porous media. Previously, intersections (sites) were assumed not to have any volume. In their model, individual elements are represented as cylindrical tubes with spherical indentations in the middle (Fig. 3-17C). Bond lengths and bond and site radii can be drawn from independent distribution functions, or as is more common, correlated with each other so that only one distribution function is required (Ioanni-dis Chatzis, 1993). 

Researchers have used physical models of porous media to study flow problems for many years. For example, the Hele-Shaw cell appeared in the late 1800s (Sahimi, 1993). The first reported use of such models for two-phase systems is attributed to Chatenever and Calhoun (1952), who used Lucite and glass bead packs to view immiscible displacement of brine and crude oil (Buckley, 1991). Subsequently, etched and photo-etched glass were used to construct physical models. The use of molded resins for model construction was introduced in the 1970s (Buck-ley, 1991). 

Sukop, M.C., G.-J. van Dijk, E. Perfect, and W.K.P. van Loon. 2001. Percolation thresholds in 2-dimensional prefractal models of porous media. Transp. Por. Media. (In press.)... 

The structure of a tissue influences its resistance to the diffusional spread of molecules, as discussed previously (see Figure 4.18). Similarly, the structure of a tissue will influence its resistance to the flow of fluid. If Darcy s law is assumed, then the hydraulic conductivity, k, depends on tissue structure. Models of porous media are available in the simplest model, the medium is modeled as a network of cylindrical pores of constant length, but variable diameter. This model produces a relationship between conductivity and geometry ... 

Chuanliang Li, Xiangyan Kong Zhimin Du, et al. 2003. A study on the rheological model of porous media. Act Mechanic Science, 35(2) 230-234. 

The disturbance effect produced by expansion pressure above can be analyzed further by the circular tube model of porous media. 

The use of complementary experimental techniques as a numerical and visual basis in the formulation of more realistic and applicable pore structure characterisation models has become widespread. Examples of the use of these techniques include mercury porosimetry [9] in the study of entrapment hysteresis in porous media, and in the characterisation of permeable solids [7], the use of NMR (nuclear magnetic resonance) in the heterogeneous and hierarchical stractural modelling of porous media [8,10], and flie use of SEM imaging techniques [7,11]. 

R. Showalter, Distributed microstructure models of porous media, pages 155-164 in Douglas, J. Jr. and Hornung, U., editors. Flow in Porous Media, ISNM Series, Vol. 114, Birkhauser, Basel, 1993... 

Horak Z, Schneider P (1971) Comparison of some models of porous media for gas diffusion. Chem Eng J 2 26-36... 

The subject of this paper is acoustic investigation of porous media, using sintered copper as an example. The method of investigation is described and results of measurements of moduli of elasticity versus porosity and temperature are given. The comparison was than carried out of the data obtained with theoretical relationships according to Mackenzie and Rossi models of porous media. 

Li, K., 2004. Theoretical development of the Brooks-Corey capillary pressure modeling of porous media. SPE 89429, In Paper Presented at the 2004 SPE 14-th Symposium on Improved Oil Recovery, Tulsa/OK. 

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