According to the two-film theory (Figure 3), the masstransfer of gases are liquid-phase controlled, gas-phasecontrolled, or influenced by both phases. The mass trans-fer can, according to the two-film theory, be divided intoa liquid-side resistance and a gas-side resistance to masstransfer. The mass transfer can be described usingKLavalues for the liquid phase (kl) and the gas phase (kg).9In steady state (notation as in Figure 3), the gas flux iscalculated as follows:FkgpxbpxiklxixbNklxbkgpxbklxikgpxiby substitutingkgklHxin the equationFklpxiHxxbklpxi1Hxxband rearranging,Fcan be rewritten to:F1klHxkg1pxbHxxb(9)Figure 3.Schematic of the two-film theory. The subscriptbdenotesbulk and the subscriptidenotes the interface.pxis the partialpressure of gasxin atmospheres and [x] is the concentration ofcompoundxin the liquid.Nielsen et al.158Journal of the Air & Waste Management AssociationVolume 59February 2009Downloaded by [University of California, San Diego] at 07:10 08 October 2015
The first part of eq 9:1klHxkg1KLshows that mass transfer can be divided into a resistanceacross a gas film and a resistance to mass transfer across aliquid film. The distinction between gas-side and liquid-sideresistance controlled gases, although only overallKLavaluesare used, is used to evaluate from which gasesKLavalues canbe estimated from the toluene tracer experiments.According to dimensional analysis7the gas and liquidfilmKLavalues can through the Sherwood number (Sh) bedescribed as functions of the Reynolds (Re) and Schmidt(Sc) number:ShfRe, Sc(10)withShKLLpDtolueneScDtoluene(11)ReLpwhereLpis the diameter of the leca pellets (m),KLis themass-transfer coefficient (msec1),Dtoluenethe diffusioncoefficient of toluene in the gas or liquid film (m2sec1),fluidis the viscosity of the gas or liquid (Pasec1), andfluidis the density of gas or fluid (kgm3).Although correlations of the type given by eq 10 arewell described within the field of absorption and distilla-tion, there are few if any for BFs. This might stem from thefact 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 ofwetting.10To get an estimate of the value ofKL, theKramer equation for non-wetted solids is used11:Sh21.3Sc0.150.66Sc0.31Re0.5(12)The specific surface area is required to obtain theKLavalue. The specific surface area can be estimated from howmany leca pellets can be packed per volume of BF andtheir weight. The weight of leca pellets that could bepacked in 1 cm3was 0.7 g in total and amounted to 14pellets with a diameter of 3 mm.Using eqs 11 and 12, it can be estimated that theKLaof toluene in the BF should be in the range of 0.0027–0.0106 sec1(Table 1).