Stagnant fraction

Liquid holdup is made up of a dynamic fraction, 0.03 to 0.25, and a stagnant fraction, 0.01 to 0.05. The high end of the stagnant fraction includes the hquid that partially fills the pores of the catalyst. The effective gas/liquid interface is 20 to 50 percent of the geometric surface of the particles, but it can approach 100 percent at high hquid loads with a consequent increase of reaction rate as the amount of wetted surface changes. 

The results depicted in Fig. 7, which concern the stagnant fraction of the dispersed phase in downflow trickle and upflow bubble operation, show the dependence on physical properties and the decrease of the stagnant holdup with increasing flow rate of the respective phase [68,25]. 

T] Use with log mean mole fraction differences based on ends of column, t = rise time. No continuous phase resistance. Stagnant drops are likely if drop is very viscous, quite small, or is coated with surface active agent. A.y uiean dispersed liquid M.T. coefficient. 

A stirred tank sometimes can be modeled as having a fraction Ot in bypass and a fraction of the reactor volume stagnant. The material balance then is made up of... 

At a particular location in a distillation column, where the temperature is 350 K and the pressure 500 m Hg, the tnol fraction of the more volatile component in the vapour is 0.7 at the interface with the liquid and 0.5 in the bulk of the vapour. The molar latent heat of the more volatile component is 1.5 times that of the less volatile. Calculate the mass transferrates (kmol m s-11 of the two components. The resistance to mass transfer in the vapour may be considered to lie in a stagnant film of thickness 0.5 mm at the interface. The diffusivity in the vapour mixture is 2 x )() ° mV. ... 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

Fig. 3.3.6 Comparison of the relative fractions of stagnant and moving fluid obtained from the propagators for catalyst and glass beads.

Fig. 4.5.16 Schematic drawing of a boundary layer mixing mechanism. It is proposed that a thin layer with thickness 8 has a linear velocity profile with average velocity V/2. Material with bulk droplet volume fraction ( >in is drawn into the creamed layer (area Ac) and material with average creamed layer volume fraction (j)ou, is swept out. The remainder of the emulsion (inside the dashed circle) is stagnant.

The Wilson bubble rise model (a void fraction of steam bubbling through stagnant water)... 

Equation (9.41) constitutes a fundamental solution for purely convective mass burning flux in a stagnant layer. Sorting through the S-Z transformation will allow us to obtain specific stagnant layer solutions for T and Yr However, the introduction of a new variable - the mixture fraction - will allow us to express these profiles in mixture fraction space where they are universal. They only require a spatial and temporal determination of the mixture fraction/. The mixture fraction is defined as the mass fraction of original fuel atoms. It is as if the fuel atoms are all painted red in their evolved state, and as they are transported and chemically recombined, we track their mass relative to the gas phase mixture mass. Since these fuel atoms cannot be destroyed, the governing equation for their mass conservation must be... 

Flow to a vessel is bypassed with a fraction a and a fraction l-p 0f the volume is stagnant. Find the transfer function and the response to step input, Cfu(t-a). 

From the measured pulse tracer response curves (see figure), find the fraction of gas, of flowing liquid, and of stagnant liquid in the gas-liquid contactor shown in Fig. E12.1. 

Thus, two mass balance equations are written in the lumped pore diffusion model for the two different fractions of the mobile phase, the one that percolates through the network of macropores between the particles of the packing material and the one that is stagnant inside the pores of the particles ... 

If the fluids are stagnant (i.e., Pe = Pep == 0), the concentration profiles display angular symmetry and the fractional approach to equilibrium is a function only of H, p/, and x or Xp. The corresponding solution for F (K3, PI) is shown in Figs. 3.12-3.14, for a wide range of values of these parameters. Fluid motion always increases F for given Xp, so that these solutions give a lower limit for the fractional approach to equilibrium. 

Fig. 3.12 Variation of fractional approach to equilibrium F with dimensionless time, ip = for a sphere in stagnant surroundings with H =. ...

Fig. 3.21 Variation of fractional approach to equilibrium with time for stagnant spheres (Pe = 0) with constant external resistance.

Relative viscosities are calculated from viscosities for the individual components at 0° (II7), weighting them on a mole fraction basis. The change in diffusivities and viscosities with temperature and pressure is assumed to be independent of gas mixture. If desired, more accurate calculations of diffusivities and viscosities of gas mixtures can be made using the approaches of Wilke (IIS) and Bromley and Wilke (II0), respectively. Table V presents relative values for Dfree, m, and p across the stagnant film for the gas-carbon reactions. Substituting these values in Equation (42), the relative reaction rates in Zone III for the gas-carbon reactions are calculated and also presented in Table V. Qualitatively, the rates of the carbon-oxygen and carbon-steam reactions are predicted to be about twice the rate... 

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