Discussion of ‘‘Gas-Liquid Mass Transfer along Small Sewer Reaches’’ by Jacek A. Koziel, Richard L. Corsi, and Desmond F. Lawler May 2001, Vol. 127, No. 5, pp. 430–437. Carlo Gualtieri 1 1 Lecturer, Hydraulic and Environmental Engineering Dept., Univ. of Napoli, Napoli, Italy. E-mail: cagualti@unina.it The writers have performed several field experiments to elucidate the roles of mass-transfer kinetics and equilibrium limitations on stripping of volatile organic compounds VOCs in small diam- eter sewers. The experiments were performed with five VOCs in a 0.2 m inside diameter sewer, where different slopes and flow rates were applied. The five compounds considered exhibit differ- ent physicochemical properties. Particularly, dimensionless Hen- ry’s law constant H c is in the range from 0.0015 to 7.167. Thus, stripping efficiencies are very different. For acetone and ethyl acetate was always 6%, while toluene, ethylbenzene, and cy- clohexane show higher volatilization rates. Also, the writers have estimated for each compound and experiment the mass-transfer coefficient K L LT -1 . This coefficient was back-calculated using the concentrations measured along the sewer reach. Then, liquid-phase mass-transfer coefficient k 1 LT -1 was obtained for cyclohexane only. In fact, mass transfer of cyclohexane is domi- nated by the liquid film because of its high H c . Thus, in Eq. 2, it results that K L k 1 . Then, the values of k 1 for cyclohexane were extrapolated for the other four compounds. The values of k 1 for cyclohexane were compared with those coming from two pre- dictive equations, derived by Parkhurst–Pomeroy PP and Owens–Edwars–Gibbs OEG. However, the application of these equations results in a poor fit with the field data. Particularly, the OEG model significantly overestimates the liquid-phase coeffi- cient, with an average relative difference equal to 182%, whereas the PP model tends toward an underestimation of k 1 , with an average difference equal to -50%. The purpose of this discussion is to test, using the field data collected by the writers, the predictive ability of a model that was originally developed to predict the reaeration rate Gualtieri and Gualtieri 2000. The starting point is the assumption that if tur- bulence is relatively low, the mass-transfer coefficient process can be depicted following the pattern of molecular diffusion. More- over, following the two-film theory Lewis and Whitman 1924, the mass transfer can be controlled by the liquid, the gas, or both films. Thus, if the mass transfer is controlled by the liquid film at the air–water interface, i.e., K L k 1 , a concentration boundary sublayer is determined in the water side by diffusive transport normal to the interface and the overall mass-transfer coefficient K L can be estimated as K L = D m w- c (1) where D m L 2 / T =molecular diffusion coefficient for the sub- stance being transferred and w- c =thickness of the concentration boundary sublayer. Otherwise, if the mass transfer is controlled by both films, Eq. 1 provides the liquid-phase mass-transfer coefficient k 1 . Now, w- c can be estimated coupling the concept of the flow boundary layer with that of the concentration bound- ary layer; this approach allows us to obtain a relationship between the rate of mass transfer and the hydrodynamic conditions at the boundary. In fact, after some simplifications, it can be shown that Weber and DiGiano 1996 w- c w- v 3 = D m = D m (2) where w- v =thickness of the velocity laminar boundary sublayer and L 2 / T =fluid kinematic viscosity. From Eq. 2 if Sc is the Schmidt number, Sc= / D m , it results that w- c = w- v Sc 1/3 (3) Now, w- v can be estimated comparing the laminar boundary su- blayer at the air–water interface with the bottom classic laminar sublayer. The latter layer lies on a solid boundary, whereas the former borders on the interface that, due to its surface tension, could be considered as a semisolid boundary. The model basic assumption is, therefore, that an analogy exists between the bot- tom and the water surface; the former has an infinite surface tension, while the latter can be assumed as a wall moving cocur- rent with a finite value of the surface tension. Thus, first, the velocity distribution in the laminar layer near the water surface can be defined starting from the velocity distribution in the lami- nar layer near the bottom, which is known. Using dimensional analysis and assuming , the density M / L 3 and the surface tension T s M / T 2 as fundamental parameters, the velocity dis- tribution at the air–water interface, where T s is accounted for, can be estimated. Moreover, the outlined analogy between the laminar layers near the air–water interface and the bottom allows us to estimate w- v as w- v = R m- t 2/3 y ¯ gi 2 g ¯ 1/3 (4) Finally, considering Eqs. 1 and 3, the overall mass-transfer coefficient K L can be obtained as K L = D m 2/3 1/3 y ¯ i 1/3 R m- t 2/3 g 2 g ¯ 1/3 (5) Table 1. Input Data for Eq. 5 T (°C) kg/m 3 m 2 /s T s (N/m) D m-cyclohexane (m 2 /s) 20 998.15 1.00310 -6 0.07276 7.9210 -10 Sc R m- t w- v-mean (mm) w- c -mean (mm) 1266.13 0.8637 0.2412 0.0223 DISCUSSIONS AND CLOSURES 1188 / JOURNAL OF ENVIRONMENTAL ENGINEERING / DECEMBER 2002 Downloaded 06 Mar 2012 to 143.225.96.41. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org