According to the two film theory Figure 3 the mass transfer of gases are liquid

According to the two film theory figure 3 the mass

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According to the two-film theory (Figure 3), the mass transfer of gases are liquid-phase controlled, gas-phase controlled, or influenced by both phases. The mass trans- fer can, according to the two-film theory, be divided into a liquid-side resistance and a gas-side resistance to mass transfer. The mass transfer can be described using K L a values for the liquid phase ( k l ) and the gas phase ( k g ). 9 In steady state (notation as in Figure 3), the gas flux is calculated as follows: F k g p xb p xi k l x i x b N k l x b k g p xb k l x i k g p xi by substituting k g k l H x in the equation F k l p xi H x x b k l p xi 1 H x x b and rearranging, F can be rewritten to: F 1 k l H x k g 1 p xb H x x b (9) Figure 3. Schematic of the two-film theory. The subscript b denotes bulk and the subscript i denotes the interface. p x is the partial pressure of gas x in atmospheres and [ x ] is the concentration of compound x in the liquid. Nielsen et al. 158 Journal of the Air & Waste Management Association Volume 59 February 2009 Downloaded by [University of California, San Diego] at 07:10 08 October 2015
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The first part of eq 9: 1 k l H x k g 1 K L shows that mass transfer can be divided into a resistance across a gas film and a resistance to mass transfer across a liquid film. The distinction between gas-side and liquid-side resistance controlled gases, although only overall K L a values are used, is used to evaluate from which gases K L a values can be estimated from the toluene tracer experiments. According to dimensional analysis 7 the gas and liquid film K L a values can through the Sherwood number ( Sh ) be described as functions of the Reynolds ( Re ) and Schmidt ( Sc ) number: Sh f Re, Sc (10) with Sh K L Lp D toluene Sc D toluene (11) Re Lp where L p is the diameter of the leca pellets (m), K L is the mass-transfer coefficient (m sec 1 ), D toluene the diffusion coefficient of toluene in the gas or liquid film (m 2 sec 1 ), fluid is the viscosity of the gas or liquid (Pa sec 1 ), and fluid is the density of gas or fluid (kg m 3 ). Although correlations of the type given by eq 10 are well described within the field of absorption and distilla- tion, there are few if any for BFs. This might stem from the fact that incomplete or partial wetting of the solid sur- faces in the BF frequently occurs and that a specific cor- relation would have to be developed for each type of wetting. 10 To get an estimate of the value of K L , the Kramer equation for non-wetted solids is used 11 : Sh 2 1.3 Sc 0.15 0.66 Sc 0.31 Re 0.5 (12) The specific surface area is required to obtain the K L a value. The specific surface area can be estimated from how many leca pellets can be packed per volume of BF and their weight. The weight of leca pellets that could be packed in 1 cm 3 was 0.7 g in total and amounted to 14 pellets with a diameter of 3 mm. Using eqs 11 and 12, it can be estimated that the K L a of toluene in the BF should be in the range of 0.0027– 0.0106 sec 1 (Table 1).
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