Porous media hydraulic 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 ... 

Equation 71 is the basic equation that relates permeability of a porous medium to its other properties. However, equation 71 contains the hydraulic diameter of the passage (pore), tortuosity, and areal porosity of the medium, which may not be easily accessible. For example, sandstones or rock formations have irregular pore structure and often have inconsistent pore size measurement values (see previous section). It is rather difficult to measure the average hydraulic pore diameter. On the other... 

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... 

Since the fluid in a porous medium follows a tortuous path through channels of varying size, one method of describing the flow behaviour in the pores is to consider the flow path as a non-circular conduit . This requires an appropriate definition of the hydraulic diameter as shown in Eq. 3.15 ... 

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 ... 

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 ... 

---