Porosity distribution

The relationship was based on a number of observations, firstly that the conductivity (Cq) of a water bearing formation sample is dependent primarily upon pore water conductivity (C ) and porosity distribution (as the rock matrix does not conduct electricity) such that ... 

The PDR (Porosity/Distributed Resistance) method for describing the geometry (Patankar and Spalding)... 

Although the status of many 3D codes makes it possible to carry out detailed scenario calculations, further work is needed. This is particularly so for 1) development and verification of the porosity/distributed resistance model for explosion propagation in high density obstacle fields 2) improvement of the turbulent combustion model, and 3) development of a model for deflagration to detonation transition. More data are needed to enable verification of the model in high density geometries. This is particularly needed for onshore process plant geometries. 

The washing of filter cake is carried out to remove liquid impurities from valuable solid product or to increase recovery of valuable filtrates from the cake. Wakeman (1990) has shown that the axial dispersion flow model, as developed in Sec. 4.3.6, provides a fundamental description of cake washing. It takes into account such situations as non-uniformities in the liquid flow pattern, non-uniform porosity distributions, the initial spread of washing liquid onto the topmost surface of the filter cake and the desorption of solute from the solid surfaces. 

A necessary assumption would also be that the initial porosity distribution remains constant and independent of flow rate. 

Figure Al(a) shows the constant value of porosity used in the analytic model (dashed curve), compared to the porosity distribution for a ID melt column in which the upward flux of melt is required to remain constant (see Spiegelman and Elliott 1993). The solid curves in Figure Al(b) show values of ct, calculated from equations (A12-A14) along the (dimensionless) length of the melting column for the decay chain with a constant porosity of 0.1% and solid upwelling velocity of 1 cm/yr.

Figure Al. a) Porosity distribution for a ID melt column (solid curve) assuming constant melt flux (see Spiegelman and Elliott 1993). Average porosity is shown as the dashed line, b) Emichment factors (a) calculated from the analytical solution (solid curves) and approximate analytical solution (dotted curves) for °Th and Ra. c) Emichment factors (a) calculated from the numerical solution of Spiegelman and Elliott (1993) for °Th and Ra. In these plots, depth (z) is non-dimensionalized. See text for explanation.

If the amount of fluid within a fully saturated permeable medium is known as a function of position, the spatially resolved porosity distribution can be determined. If the medium is saturated with two fluids, and the signal from one can be distinguished, the fluid saturation can be determined. In this section, we will develop a method to determine the amount of a single observed fluid using MRI, and demonstrate the determination of porosity. In Section 4.1.4.3, we will demonstrate the determination of saturation distributions for use in estimating multiphase flow functions. 

Fig. 4.1.4 Porosity distribution within a horizontal layer of the Bentheimer sample. Axis z- is parallel with the static magnetic field.

The microstructure of a catalyst layer is mainly determined by its composition and the fabrication method. Many attempts have been made to optimize pore size, pore distribution, and pore structure for better mass transport. Liu and Wang [141] found that a CL structure with a higher porosity near the GDL was beneficial for O2 transport and water removal. A CL with a stepwise porosity distribution, a higher porosity near the GDL, and a lower porosity near the membrane could perform better than one with a uniform porosity distribution. This pore structure led to better O2 distribution in the GL and extended the reaction zone toward the GDL side. The position of macropores also played an important role in proton conduction and oxygen transport within the CL, due to favorable proton and oxygen concentration conduction profiles. 

Fig. 5.16 Mercury intrusion porosimetry curves of C3S pastes showing differences in capillary porosity distribution.

Fig. 5.17 Porosity distribution curves at equal hydration with intruded volume plotted as a percentage of total intrusion (Young).

Two-fluid simulations have also been performed to predict void profiles (Kuipers et al, 1992b) and local wall-to-bed heat transfer coefficients in gas fluidized beds (Kuipers et al., 1992c). In Fig. 18 a comparison is shown between experimental (a) and theoretical (b) time-averaged porosity distributions obtained for a 2D air fluidized bed with a central jet (air injection velocity through the orifice 10.0 m/s which corresponds to 40u ). The experimental porosity distributions were obtained with the aid of a nonintrusive light transmission technique where the principles of liquid-solid fluidization and vibrofluidization were employed to perform the necessary calibration. The principal differences between theory and experiment can be attributed to the simplified solids rheology assumed in the hydrodynamic model and to asymmetries present in the experiment. 

Fig. 18. (a) Experimental and (b) theoretical time-averaged porosity distributions for a 2D air fluidized bed with a central jet. Physical properties of the particles diameter, 500 fim density, 2660 kg/m. Bed dimensions width, 0.57 m height, 1.0 m. Injection velocity through central orifice 10.0 m/s. 

Hg-injection curves give us the pore structures measurements such as mercury porosity, distribution of Hg-saturation versus pore-throat size specific surface area deduced from... 

AP-883kNm ) (b) Porosity distributions at three pressures. The curves are by Wakeman (1978). 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

---