Packing coefficient, defined

The mass transfer coefficients considered so far - namely, kQ,kj, KQ,andKj - are defined with respect to known interfacial areas. However, the interfacial areas in equipment such as the packed column and bubble column are indefinite, and vary with operating conditions such as fluid velocities. It is for this reason that the volumetric coefficients defined with respect to the unit volume of the equipment are used, or more strictly, the unit packed volume in the packed column or the unit volume of liquid containing bubbles in the bubble column. Corresponding to /cg, Kq, and we define k a, k, a, K, /i, and K a, all of which have units of (kmol h m )/(kmol m ) - that is, (h ). Although the volumetric coefficients are often regarded as single coefficients, it is more reasonable to consider a separately from the Ar-terms, because the effective interfacial area per unit packed volume or unit volume of liquid-gas mixture a (m m ) varies not only with operating conditions such as fluid velocities but also with the types of operation, such as physical absorption, chemical absorption, and vaporization. 

Avogadro s number. The ratio Tw/Tm is defined as the packing coefficient fj. The packing coefficients calculated from the Tw and Tm values of simple hydrocarbons are in the range fj = 0.5 to 0.6. The empty space between the single molecules can be attributed to the so-called void volume and expansion volume required for the thermally induced... 

The flow rate of both phases, viscosity, density, surface tension, and size and shape of the packing determine the value of a . These same factors affect the value of the mass transfer coefficients Ky and Kx. Therefore, it is expedient to include a in the mass transfer equation and define two new quantities KyU and Kxa. These quantities would then be correlated with the solution parameters as functions of various chemical systems. If A is the absorption tower cross-sectional area, and z the packing height, then Az is the tower packing volume. Defining Ai as the total interfacial area ... 

The shock wave acts as a liquid atomizer up to the point at which the momentum of the shock wave is able to disperse the liquid stream. By analogy with two-phase flow in packed columns, such hydrodynamic conditions can be construed as flooding. Hence, the region of stable atomization is mapped in terms of a flooding coefficient, defined as the mass flow ratio of undispersed liquid to the total liquid subject to the shock-wave field... 

Organic liquids only occupy a certain percentage of space. The volume of filled space by a solvent is defined as its packing coefficient (PC), and is another bulk solvent property and parameter. It is a ratio of the sum of the van der Waals volumes for a solvent (Ryv) to the given volume of space (k). 

For heat transfer in packed beds with constant wall temperature, the overall heat transfer coefficient defined by taking the difference between wall temperature and the average temperature of the flowing fluid as the driving force of heat transfer, ho, is obtained as follows. 

An exhaustive examination of overall heat transfer coefficients, defined by Eqn. (1), covering 15 combinations of packings and tube diameter, was carried out by Wellauer and co-workers [M]. 

The constant is not a tme partition coefficient because of difference, — V, includes the soflds and the fluid associated with the gel or stationary phase. By definition, IV represents only the fluid inside the stationary-phase particles and does not include the volume occupied by the soflds which make up the gel. Thus is a property of the gel, and like it defines solute behavior independently of the bed dimensions. The ratio of to should be a constant for a given gel packed in a specific column (34). 

Traditional Design Method The traditionally employed conventional procedure for designing packed-tower gas-absorption systems involving chemical reactions makes use of overall volumetric mass-transfer coefficients as defined by the equation... 

Inspection of Eqs. (14-71) and (14-78) reveals that for fast chemical reactions which are liquid-phase mass-transfer limited the only unknown quantity is the mass-transfer coefficient /cl. The problem of rigorous absorber design therefore is reduced to one of defining the influence of chemical reactions upon k. Since the physical mass-transfer coefficient /c is already known for many tower packings, it... 

Design of inorganic absorbers quite often involves a system whose major parameters are well defined such as system film control, mass transfer coefficient equations, etc. Ludwig gives design data for certain well-known systems sueh as NH3-Air-H20, CI2-H2O, COi in alkaline solutions, etc. Likewise, data for commercially available packings is well documented such as packing factors, HETP, HTU, etc. 

In fundamental SEC studies retention is often described in terms of a distribution coefficient. The theoretical distribution coefficient Kg is defined as the ratio of solute concentration inside and outside of the packing pores under size exclusion conditions. The experimental distribution coefficient as defined in Equation 1, is a measurable quantity that can be used to check the theory. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

To determine the activity coefficient at infinite dilution, packed colunms were prepared containing the IL-coated chromosorb support [12-14]. The examined mixture of probe molecules was then injected under infinite dilution conditions. The value of y can be calculated from Equation 4.4, as defined by Cruickshank and coworkers [15] ... 

With regards to handling data on industrial apparatus for gas-liquid mass transfer (such as packed columns, bubble columns, and stirred tanks), it is more practical to use volumetric mass transfer coefficients, such as KqU and K a, because the interfacial area a cannot be well defined and will vary with operating conditions. As noted in Section 6.7.2, the volumetric mass transfer coefficients for packed columns are defined with respect to the packed volume - that is, the sum of the volumes of gas, liquid, and packings. In contrast, volumetric mass transfer coefficients, which involve the specific gas-liquid interfacial area a (L L 5), for liquid-gas bubble systems (such as gassed stirred tanks and bubble columns) are defined with respect to the unit volume of gas-liquid mixture or of clear liquid volume, excluding the gas bubbles. In this book, we shall use a for the specific interfacial area with respect to the clear liquid volume, and a for the specific interfacial area with respect to the total volume of gas-liquid mixture. 

If r is defined as the mean particle radius, Eq. 25-7 also can be used for aquifers that consist of particles of different size. Then the parameter a depends on the particle size distribution. It increases with porosity ( ), which in turn is linked to the so-called sorting coefficient, So (see Fig. 25.5). Small So values indicate greater uniformity of the particles large So values indicate a greater variance of the particle size, that is, a denser packing (small particles fill the space in between the larger ones). Therefore,... 

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

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