Porous media equivalent diameter

The expressions for the hydraulic diameter and the superficial velocity can be incorporated into the definition of the friction factor to give an equivalent expression for the porous medium friction factor ... 

The simplest capillaric model is the one representing a porous medium by a bundle of straight parallel capillaries of average diameter <5, as shown in Fig. 5.14. The equivalent voidage a can be related to the averaged diameter by... 

Dq. The porosity is readily defined as the amount of space unoccupied by the objects and free to be filled with fluid, whereas the average object size is often interpreted as the equivalent spherical diameter Dq = 6js, which is determined in turn from the specific surface area s of the porous medium. If the system is described as a continuum with superficial... 

The computational domain is shown in Fig. 14.1. The domain was discretized into 300 grid points with a cluster located in regions of high-temperature gradient. The burner consists of two sections of porous media. For the reference case, the burner consisted of an upstream section of porous medium with 25.6 ppc and a downstream section with 3.9 ppc. The upstream and downstream porosities were 0.84 and 0.87, respectively. The upstream and downstream pore diameters were 0.029 and 0.152 cm, respectively. Methane and air. with an equivalence ratio of 0.65, a temperature of 298 K, and a specified velocity, flow into the domain. Hot products exit at the downstream end of the domain. Both downstream and upstream boundaries radiate to a black body at 298 K. 

The specific surface or surface per unit volume, aPy of a porous medium is defined as the ratio of the total open pore surface area to the volume of the solids. The equivalent spherical diameter, dsy is the diameter of an equivalent sphere that has the same surface area per unit volume of the solid material forming the porous medium. 

Permeability for a Rock Formation. For natural consolidated porous medium, however, the definitions of the equivalent spherical diameter and the specific surface area per unit volume are not widely used because of its difficulty in determination and relation to other measurable quantities. Just to serve as a comparison, we give the permeability equation based on the previous passage model with the tortuosity given by equation 61 and assuming that the areal porosity equation 54 still holds. The permeability can then be given by... 

In what follows we derive an empirical relation for the permeability, known as the Kozeny-Carman equation, which supposes the porous medium to be equivalent to a series of channels. The permeability is identified with the square of the characteristic diameter of the channels, which is taken to be a hydraulic diameter or equivalent diameter, d. This diameter is conventionally defined as four times the flow cross-sectional area divided by the wetted perimeter, and measures the ratio of volume to surface of the pore space. In terms of the porous medium characteristics. 

The velocity U is defined as the ratio of the liquid s volume flow rate to the net cross section of all spacings between particles in the given layer of porous medium. It is obvious that U < Ug, since also includes the volume flow rate of liquid through the pores of particles. The constant k is known as permeability (its dimensionality is m ). In order to determine k, we must choose a certain model of porous medium. A low-permeable porous medium can be conceptualized as a medium consisting of a set of microchannels of diameter de (it is called hydraulic, or equivalent, diameter). This diameter is usually defined as... 

The present model development is based on a semi-heuristic model of flow through solid matrices using the concept of hydraulic diameter, which is also known as the Carman-Kozeny theory [7]. The theory assumes the porous medium to be equivalent to a series of parallel tortuous tubules. The characteristic diameter of the tubules is taken to be a hydraulic diameter or... 

S is the ratio of the surface area of the medium to its pore volume and stands for equivalent diameter of the pores. The hydraulic (mean) radius m is defined as the ratio of the average pore cross-sectional area to the average wet perimeter, in line with the concept of the equivalent loads (as explained in Section III). All the geometrical parameters from Eq. (19) can be estimated for particulars of the porous media. For example, in the case of aligned fibers, hydraulic radius and equivalent diameter can be expressed by ... 

The derivations reported above of the viscous and inertial contributions to the Ergun equation involve the representation of a volume of a porous medium of length L by means of an equivalent cylindrical tube of diameter Dg. The effective length of this tube must clearly be greater than L because of the twisted path followed by the fluid around the solid particles. Thus, the tortuosity T for a porous medium may be defined by ... 

---