Average superficial

The spin-displacement density function, c (z, Z), and the normalized displacement distribution function, P(z, Z), can be converted readily into the joint spin-velocity density function, q(z, vn), and the normalized velocity distribution function, P(z, vn), respectively, with the net velocity vn defined as vn = Z/A. Once the velocity density function is determined for each of the volume elements, the superficial average velocity, v, is calculated by [23] ... 

Fig. 4.1.7 Superficial average velocity data for the flow experiment with the thin Bentheimer sandstone sample. Each arrow represents the direction and relative magnitude of the superficial average velocity at the corresponding voxel. The velocities are measured for 58 x 20 voxels.

In this notation for the volume averages, a Greek subscript is used to identify the particular phase under consideration, while a Greek superscript is used to identify an intrinsic average. Since the intrinsic and superficial averages differ by a factor of Sy, it is essential to make use of a notation that clearly distinguishes between the two averages. 

Even though equation 1.69 is considered to be the preferred form of the species continuity equation, it is best to begin the averaging procedure with equation 1.35, and we express the superficial average of that form as... 

Here we have used the intrinsic average concentration since this is most closely related to the concentration in the fluid phase, and we have used the superficial average velocity since this is the quantity that normally appears in Darcy s law (Whitaker, 1999) or the Forchheimer equation (Whitaker, 1996). Use of equation 1.87 in equation 1.84 leads to... 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

Flue particles ia a fluidized bed are analogous to volatile molecules ia a Foiling solution. Therefore, the concentration of particles ia the gas above a fluidized bed is a function of the saturation capacity of the gas. To calculate the entrainment rate, it is first necessary to determine what particle sizes ia the bed can be entrained. These particles are the ones which have a terminal velocity less than the superficial gas velocity, assuming that iaterparticle forces ia a dilute zone of the freeboard are negligible. An average particle size of the entrainable particles is then calculated. If all particles ia the bed are entrainable, the entrained material has the same size distribution as the bed material. 

For estimating purposes for direct-heat drying applications, it can be assumed that the average exit-gas temperature leaving the sohds bed wih approach the final solids discharge temperature on an ordi-naiy unit carrying a 5- to 15-cm-deep bed. Calculation of the heat load and selec tion of an inlet-air temperature and superficial velocity (Table 12-32) will then permit approximate sizing, provided an approximation of the minimum required retention time can be made. 

In a first approximation the average size of pore diameter has no effect on porosity, even though a superficial view leads to other conclusions. A mental experiment may be of assistance imagine a pore and its outside wall, decrease both to identical scale, then the ratio of void to outside volume remains constant. Of course the re-... 

The catalyst was prepared by impregnating porous alumina particles with a solution of nickel and lanthanum nitrates. The metal loading was 20 w1% for nickel and 10 wt% for lanthanum oxide. The catalyst particles were A group particles [8], whereas they were not classified as the AA oup [9]. The average particle diameter was 120 pm, and the bed density was 1.09 kg m . The minimum fluidization velocity was 9.6 mm s. The settled bed height was around 400 mm. The superficial gas velocity was 40-60 mm s. The reaction rate was controlled by changing the reaction temperature. 

Fig. 19. Time-average rate of S02 oxidation under periodic liquid flow interruption as a function of cycle period, cycle split, and the time-average superficial liquid velocity at 26°C, 1 bar using a BPL activated carbon. (Figure from Haure et al., 1990, with permission, 1990 Elsevier Science Publishers.)...

CSS steady state at the time-average liquid superficial velocity... 

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