Modeling pore-scale

Pore-scale network models (including percolation models), on the other hand, are best suited for analyzing fluid and contaminant distribution and movement within pores and clusters of pores. Such models are particularly effective for captur-... 

The dynamics of water flow therefore are a combination of those governing flow in the partially saturated zone (essentially vertical, downward flow) and flow in saturated zones (aquifers), which can be fnlly three-dimensional. In general, the modeling approaches mentioned in Sect. 9.1 are applicable here—continnnm models and pore-scale network models—althongh detailed qnantification of flow and transport in the CF has received only limited attention. 

Berkowitz B, Emmanuel S, Scher H (2008) Non-Fickian transport and multiple rate mass transfer in porous media Water Resour Res 44, D01 10.1029/2007WR005906 Bijeljic B, Blunt MJ (2006) Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 42, W01202, D01 10.1029/2005WR004578 Blunt MJ (2000) An empirical model for three-phase relative permeability. SPE Journal 5 435-445... 

Redman JA, Grant SB, Olson TM, Estes MK (2001) Pathogen filtration, heterogeneity, and the potable reuse of wastewater. Environ Sci Technol 35 1798-1805 Redman JA, Walker SL, Elimelech M (2004) Bacterial adhesion and transport in porous media Role of the secondary energy minimum. Environ Sci Technol 38 1777-1785 Reeves CP, CeUa MA (1996) A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour Res 32 2345-2358 Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1 318-333... 

S0l., So2 and SHlo refer to the respective source terms owing to the ORR, e is the electrolyte phase potential, cGl is the oxygen concentration and cHlo is the water vapor concentration, Ke is the proton conductivity duly modified w.r.t. to the actual electrolyte volume fraction, Dsa is the oxygen diffusivity and is the vapor diffusivity. The details about the DNS model for pore-scale description of species and charge transport in the CL microstructure along with its capability of discerning the compositional influence on the CL performance as well as local overpotential and reaction current distributions are furnished in our work.25 27,67... 

In order to evaluate the effect of pore volume blockage in the presence of liquid water causing hindered oxygen transport to the active reaction sites, the direct numerical simulation (DNS) model, mentioned earlier and detailed in our work,25-27 68 is deployed for the pore-scale description of species and charge transport through the reconstructed CL microstructure. 

Abstract In this paper we discuss a pore scale model for crystal precipitation and dissolution in porous media. We consider weak solutions in general domains and dissol-ution/precipitation fronts in thin strips. The latter yields an upscaled transport-reaction model. 

In this paper we consider a pore scale model for crystal dissolution and precipitation processes. We follow the ideas in [3], where the corresponding macroscopic model was introduced. Let Q C (d > 1) denote the void region. This region is occupied by a fluid in which cations (Mi) and anions (M2) are dissolved. The boundary of Q has an internal part (IV ), which is the surface between the fluid and the porous matrix (grains), and an external part, which is the outer boundary of the domain. In a precipitation reaction,... 

Haggerty R, Gorelick SM (1998) Modeling mass transfer processes in soil columns with pore-scale heterogeneity. Soil Sci Soc Am J 62 62-74... 

The Delaunay tessellation is particularly important because it provides a tool to decompose the continuum void space into discrete pores, which is essential for pore-scale modeling. An important drawback to using the Delaunay tessellation for extracting pore structure is that it leads to a fixed pore coordination number of 4, which is a geometric artifact in a real packing, not all voids conform to the tessellation s tetrahedral structure. Experimentally, the average... 

Thompson, K. E., and Eogler, H. S., Modeling flow in disordered packed beds from pore-scale fluid mechanics. AIChE J. 43,1377 (1997). 

Yin et al. (2006) qnalitatively showed this mechanism by solving relevant flow equations nnmericaUy. Xia et al. (2008) also developed a simplified pore scale model to describe polymer flow. The numerical solutions from Xia et al. have verified the proposed mechanism. Figure 6.22 shows the velocity contours of a Newtonian fluid with Weissenberg number (We) = 0 and a viscoelastic fluid with We = 0.35 in a flow channel with a dead end when the Reynolds number (Re) = 0.001. We can see that the velocity (m/day) of the viscoelastic fluid is higher than that of the Newtonian fluid at the same position of the dead end. This pulling mechanism also works in the case shown in Figure 6.20c, where the residual oil is trapped at the pore throats by capillary force. 

Common conceptual models for liquid distribution and transport in variably saturated porous media often rely on oversimplified representation of media pore space geometry as a bundle of cylindrical capillaries, and on incomplete thermodynamic account of pore scale processes. For example, liquid adsorption due to surface forces and flow in thin films are often ignored. In this study we provide a review of recent progress in modeling liquid retention and interfacial configurations in variably saturated porous media and application of pore scale hydrodynamic considerations for prediction of hydraulic conductivity of unsaturated porous media. 

The pore-scale model provides the basis for development of a statistical framework for upscaling from a single pore to a sample of variably saturated porous medium. The statistical distribution of pore sizes is modeled as a gamma distribution with the expected values of liquid configuration in pore space calculated from geometrical and chemical potential considerations within the statistical framework. Model predictions compare favorably with measured retention data, yielding similarly close fits to data as the widely used van Genuchten parametric model. Liquid-vapor interfacial area as a function of chemical potential is readily calculated from estimated retention parameters. Comparisons of calculated inter-... 

The review is organized as follows first, we discuss aspects of the unitary approach for combining adsorptive and capillary contributions, and present the new pore scale model of Tuller et al. (1999). The upscaling scheme of Or and Tuller (1999) for representing sample scale retention properties will be presented, followed by illustrative examples with measured characteristic data and a discussion of critical soil parameters. The role of liquid-vapor interfacial area will be highlighted by comparisons of model predictions with limited measurements. Finally, we introduce hydrodynamic considerations of unsaturated flow in films and comers leading to prediction of hydraulic conductivity of rough rock surfaces and unsaturated porous media. 

The upscaling scheme was applied lo Ihe pore scale model based on the SYL formulation, leading to Ihe development of closed-form expressions for sample scale... 

The results for flow on a single fracture surface are incorporated in the derivation of hydraulic properties of unsaturated fractured rock mass. Liquid retention and hydraulic conductivity in partially saturated fractured porous media are modeled in angular pores and slit-shaped spaces representing rock matrix and fractures, respectively. A bimodal distribution of pore sizes and apertures accounts for the two disparate pore scales and porosity. These considerations provide a framework for derivation of retention and hydraulic conductivity functions for fractured porous media (Or Tuller, 2001). 

The pore scale model and the associated unitary approach were upscaled to represent a sample of partially saturated porous medium. 

Celia, M.A., PC. Reeves, and L.A. Ferrand. 1995. Pore scale models for multiphase flow in porous media. Rev. Geophys. Suppl. 33 1049-1057. 

Reeves, P.C., and M.A. Celia. 1996. A functional relationships between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour. Res. 32 2345-2358. Rice, J.A. 1995. Mathematical statistics and data analysis. 2nd ed. Duxbury Press, Belmont, CA. Skopp, J. 1985. Oxygen uptake and transport in soils Analysis of the air-water interfacial area. Soil Sci. Soc. Am. J. 49 1327-1331. 

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