Porous media modeling

The most straightforward porous media model which can be used to describe the flow in the multichannel domain is the Darcy equation [117]. The Darcy equation represents a simple model used to relate the pressure drop and the flow velocity inside a porous medium. Applied to the geometry of Figure 2.26 it is written as... 

Fig. 5.1.9 (a) MR measured propagators and es the velocity distribution narrows due to the (b) corresponding calculated RTDs for flow in a dispersion mechanisms of the porous media model packed bed reactor composed of 241- this effect is observed in the RTDs as a pm monodisperse beads in a 5-mm id circular narrowing of the time window during which column for observation times A ranging from spins will reside relative to the mean residence 20 to 300 ms. As the observation time increas- time as the conduit length is increased. 

Profitt APB, Rose CW, Hairsine PB (1991) Rainfall detachment and deposition. Experiments with low slopes and significant water depth. Soil Sci Soc Am J 55 325-332 Rajagopalan R, Tien C (1976) Trajectory analysis of deep bed filtration with the sphere-in-ceU porous media model. AIChE J 3 523-533... 

Chuang Y.-L. Oren R. Bertozzi A.L. Phillips N. and Katul G.G. (2006). The porous media model for the hydraulic system of a conifer tree Linking sap flux data to transpiration rate. Ecological Modelling, 191(3-4), 447-468. 

The application of porous media mechanics which traditionally was mostly focussed upon geomechanics, has spread to a vast area of science. This area includes polymer science, biomechanics, biomaterials, ceramics. Many of these areas of application require the integration of many physical phenomena into one single porous media model. Electrochemistry, statistical physics, fluid mechanics, molecular biology and electromagnetism are just a few examples of these. 

The porous media model (8) is used to simulate flows through the biomass in a packed bed where biomass is the porous media. In this model, a momentum source term S, is added to the standard fluid flow equation ... 

In laminar flows through porous media, the pressure is proportional to velocity and C2 can be taken as zero. Ignoring convective acceleration and diffusion, the porous media model can be changed into Darcy s Law ... 

For turbulent flows and the cases in which the permeability term can be eliminated, the porous media model can be rewritten as follows ... 

Tang, L., Moores, K.A., Ramaswamy, C. and Joshi, Y., 1998, Characterizing the Thermal Performance of a Flow Through Electronics Module (SEM-E Format) Using a Porous Media Model, IEEE Fourteenth IEEE SEMI- THERMTM Symposium. 

Porous media models isotropic/non-isotropic pressure drop model UD Rheological models non-Newtonian fluids/UD Algorithm ... 

Rajagopalan, R., and C. Tien (1976), Trajectory Analysis of Deep-Bed Filtration with the Sphere-in-cell Porous Media Model, Am. Inst. Chem. Eng. J. 22, 523-533. 

Bicanic B (2004) Discrete element methods. In Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics Fundamentals. Wiley, New York, pp 311-337 Bowen RM (1980) Incompressible porous media models by use of the theory of mixtures. Int JEngg Sci 18(9) 1129-1148... 

The porous media model is a cubic network of unit cells. Figure 1, each one of which is a constricted segment of a sinusoidal tube. Figure 2. The dimensions of a unit cell, namely the... 

Fig. 2. Typical unit cell of the porous media model, (-h /2 z h /2). The wall profile is a sinusoidal function in z. The segment (-h/2 z h/2) is the "extended" unit cell.

Specification of proper random values for the dimensions of the unit cells of the porous media model. 

With this goal in mind, the stochastic simulation method was used to make numerical experiments, taking as basis the porous media model for a 100x200 sandpack (4). For fixed ganglion volume and random initial shape, one-thousand realizations were made with the same capillary number value = 1.5x10 ) allowing in each... 

Rajagopalan R, Tien C. Trajectory analysis of deep-bed filtration with the sphere-in-cell porous media model. AIChE J. 1976 22 523. 

Bear, J., Cheng, A.H.-D. Theory and Applications of Transport in Porous Media. Modeling Grormdwater Flow and Contaminant Transport, vol. 23. Springer (2010) Blrmt, M., King, P. Relative permeabilities from two- and three-dimensional pore-scale network modelling. Transport in Porous Media 6(4), 407-433 (1991)... 

A point of terminology is repeated here to remind the reader. The term apparent viscosity , pp, is used to describe the observed macroscopic rheology of the polymeric fluid in a porous medium. The quantity effective viscosity ,, refers in a rather similar way to the observed effective viscosity in a single capillary. Each quantity is defined phenomenologically—from Darcy s law (Equation 6.4) and rj ff from Poiseuille s law (Equation 3.75). This distinction should be kept clear, especially when considering porous media models based on networks of capillaries, as discussed later in this chapter. The overall viscosity of the non-Newtonian fluid in the network as a whole is whereas the viscosity in each of the capillaries may be different and is In this latter case, will be in some sense an average value of the in the individual capillaries. 

Approach (iii) listed above refers to the use of effective medium theory (Kirkpatrick, 1973 Koplik, 1982 Levine and Cuthiell, 1986) for calculating certain average flow properties in idealised porous media models—usually simple networks. Cannella et al (1988) have recently applied this approach to the flow of power law fluids through networks of capillaries. They use this method to derive an expression for the apparent viscosity of the polymer in the porous medium which has the same overall form as the capillary bundle expression (e.g. Equation 6.18). They then adjusted the parameters in the effective medium formula in order to match their particular form of the capillary bundle formula with C = 6 (Equation 6.18). The values of the effective medium parameters are physically interpretable, and Cannella et al (1988) deduced from these that the effective radius for the flow of a power law fluid is larger than that for the flow of a Newtonian fluid. They also... 

Johnson, P.R., N. Sun, and M. Elimelech. 1996. Colloid transport in geochemically heterogeneous porous media Modeling and measurement. Environ. Sci. Technol 30 3284-3293. 

Modeling permeation through porous media Model inputs... 

The GAMMA-F code (Lim, 2014) has been developed by KAERI for system and safety analysis of VHTR. The code has the capabilities for multidimensional analyses of the fluid flow and heat conduction as well as the chemical reactions related to the air or steam ingress event in a multicomponent mixture system. As a system thermo-fluid and network simulation code, GAMMA-F includes a nonequilibrium porous media model for pebble-bed and prismatic reactor core, thermal radiation model, point reactor kinetics, and special component models such as pump, circulator, gas turbine, valves, and more. 

They further assumed that the flow through the yam bobbins is laminar and the pressure drop is proportional to velocity. Therefore, turbulence and tnibnlent viscosity were ignored. The porous media model to describe the yam bobbins in the calculations was then reduced to Darcy s law. The pressure drop in each of the three coordinates (x, y, z) within the porous region is given by ... 

Apparently, comparing to PEM modeling, the governing equations of GDL modeling is less complex. There are abundant porous media models introduced in the literature, where the quantity of the GDL model treats these layers rigorously. 

On-site liquid velocity measurements to calibrate the coefficients in porous media model... 

In the CFD modelling of membrane filtration process, membranes are usually modelled as a porous wall while the flow within a membrane is usually solved using both Navier-Stokes and Darqr equations (Ghidossi et al, 2006). A porous media model is widely used for determining the pressure loss during flow through packed beds, filter papers, perforated plates, flow distributors and tube banks (ANSYS, 2010). A momentum source term is added to the governing momentum equations, which creates a pressure drop that is proportional to the fluid velocity ... 

---