Packed volumetric coefficients

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. 

Thus, the required packed height Z can be calculated using Equation 6.38 with the given values of r and the volumetric coefficient Kq a oi a. 

The packed density of the bed, the void fraction of the particle bed, and the density ofthe feed solution are 386 kg m , 0.5, and 1000 kg m , respectively. The averaged overall volumetric coefficient of mass transfer is 9.2 h , and a constant pattern of the adsorption zone can be assumed in this case. 

In most types of separation equipment such as packed or spray towers, the interfacial area that is effective for mass transfer cannot be accurately determined. For this reason it is customary to report experimentally observed rates of transfer in terms of transfer coefficients based on a unit volume of the apparatus rather than on a unit of interfacial area. Such volumetric coefficients are designated as Kca, kLa, etc., where a represents the interfacial area per unit volume of the apparatus. Experimentally observed variations in the values of these volumetric coefficients with variations in flow rates, type of packing, etc., may be due as much to changes in the effective value of a as to changes in k. Calculation of the overall coefficients from the individual volumetric coefficients is made by means of the equations... 

Packing volumetric heat transfer coefficient, = 3 kW/m3 °C superficial gas velocity =... 

The interfacial area (a) is not the geometric surface area of the packing, but it is the mass transfer area between the gas and liquid phases. Thus, the product of a and AZ represents the total interfacial area within the entire packed bed. As stated in Chapter 3, the value of this interfacial area can be influenced by gas and liquid flow rates as well as the type and size of tower packing employed therefore, overall terms have been used. The interfacial area is combined with the liquid-phase mass transfer coefficient to produce an overall volumetric coefficient (Kj a). 

The individual fluid mass-transfer coefficients ky, F ) and the interfacial area a which make up these overall volumetric coefficients are differently dependent upon fluid properties, flow rates, and type of packing. The overall volumetric coefficients are therefore useful only in the design of towers filled with the same packing and handling the same chemical system at the same flow rates and concentrations as existed during the measurements. For general design purposes, the individual coefficients and the interfacial area are necessary. 

The mass transfer characteristics obtained on packings are reported in several different ways. At the more fundamental level, we extract volumetric mass transfer coefficients from the experimental performance data. These coefficients, which we encountered in Illustrations 2.2 and 2.3, consist of the product of a film coefficient and the nominal specific surface area a (in w /m ) of the packing, expressed in units of square meter (m ) per cubic meter (m ) of packing. If we use the molar concentration-based coefficient or /cl that has units of meter per second (m/s), then the volumetric coefficient given by the product k a or ki a will have units of reciprocal seconds, which is the same as that of a first-order reaction rate constant. Specific surface areas of packings span the range of 100 to 1000 m /m. ... 

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... 

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. 

The influence of pressure on the mass transfer in a countercurrent packed column has been scarcely investigated to date. The only systematic experimental work has been made by the Research Group of the INSA Lyon (F) with Professor M. Otterbein el al. These authors [8, 9] studied the influence of the total pressure (up to 15 bar) on the gas-liquid interfacial area, a, and on the volumetric mass-transfer coefficient in the liquid phase, kia, in a countercurrent packed column. The method of gas-liquid absorption with chemical reaction was applied with different chemical systems. The results showed the increase of the interfacial area with increasing pressure, at constant gas-and liquid velocities. The same trend was observed for the variation of the volumetric liquid mass-transfer coefficient. The effect of pressure on kia was probably due to the influence of pressure on the interfacial area, a. In fact, by observing the ratio, kia/a, it can be seen that the liquid-side mass-transfer coefficient, kL, is independent of pressure. 

Spray columns are used with slurries or when the reaction product is a solid. The coefficient kL in spray columns is about the same as in packed columns, but the spray interfacial area is much lower. Considerable backmixing of the gas also takes place, which makes the spray volumetrically inefficient. An entrainment control device (e.g., mist eliminator) usually is needed at the outlet. In the treatment of phosphate rock with sulfuric acid, off-gases contain HF and SiF4. In a spray column with water, solid particles of fluorosilic acid are formed but do not harm the spray operation. 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

Abstract—Gas-liquid interfacial areas a and volumetric liquid-side mass-transfer coefficients kLa are experimentally determined in a high pressure trickle-bed reactor up to 3.2 MPa. Fast and slow absorption of carbon dioxide in aqueous and organic diethanolamine solutions are employed as model reactions for the evaluation of a and kLa at high pressure, and various liquid viscosities and packing characteristics. A simple model to estimate a and kLa for the low interaction regime in high pressure trickle-bed reactors is proposed. 

The reported study on gas-liquid interphase mass transfer for upward cocurrent gas-liquid flow is fairly extensive. Mashelkar and Sharma19 examined the gas-liquid mass-transfer coefficient (both gas side and liquid side) and effective interfacial area for cocurrent upflow through 6.6-, 10-, and 20-cm columns packed with a variety of packings. The absorption of carbon dioxide in a variety of electrolytic and ronelectrolytic solutions was measured. The results showed that the introduction of gas at high nozzle velocities (>20,000 cm s ) resulted in a substantial increase in the overall mass-transfer coefficient. Packed bubble-columns gave some improvement in the mass-transfer characteristics over those in an unpacked bubble-column, particularly at lower superficial gas velocities. The value of the effective interfacial area decreased very significantly when there was a substantial decrease in the superficial gas velocity as the gas traversed the column. The volumetric gas-liquid mass-transfer coefficient increased with the superficial gas velocity. 

The overall volumetric heat transfer coefficient is obtained by combining a gas and liquid coefficient. Woods provides a value of 3 kW/m °C for a typical volumetric overall heat transfer coefficient for a packed tower under the above conditions (see Table 3-18). For greater accuracy values for the individual gas and liquid volumetric heat transfer coefficient may be obtained using the relations... 

Overall volumetric mass-transfer coefficient more than five times larger than that of the packed bed device [19]... 

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