Experimental mass transfer data, which were obtained for the $CO_2$-water slug flows in vertical tubes with 2, 5, and 8mm diameters, were analyzed in comparison with the penetration theory. It was found that a penetration model with molecular diffusion coefficient cannot predict the experimental data accurately. An effective diffusion coefficient, which considers enhancement effect of interfacial waves, was suggested to improve prediction. Another empirical factor was also suggested to consider the effect of non-uniform interface velocity. A modified penetration model was found to be capable of predicting the experimental data reasonably well.