Liquid phase controlled mass transfer to bubbles in cocurrent turbulent pipeline flow

Abstract

Liquid-phase controlled turbulent-flow mass-transfer coefficients for bubbles flowing cocurrently with liquids in a pipeline were determined using transient response experiments. Five different mixtures of glycerol and water were used in which dissolved oxygen was transferred to small helium bubbles flowing with the liquids in both vertical and horizontal directions. Two general types of behavior were observed: 1. (1) Above pipe Reynolds numbers for which turbulent inertial forces dominated over gravitational forces, horizontal and vertical flow mass-transfer coefficients were essentially equal with a recommended correlation of Sh/Sc 1/2=0·34 Re 0·94( d vs / D) 1·0. The observed Reynolds number exponent agreed generally with other data from the literature for cocurrent pipeline flow but did not agree with expectation based on equivalent power dissipation comparisons with agitated vessel data. 2. (2) At values of Reynolds number below that marking the equivalence of horizontal and vertical flow coefficients, the horizontal-flow coefficients continued to vary according to Eq. (1) until, at low flows, severe stratification of the bubbles made operation impractical. The vertical-flow coefficients, however, passed through a minimum with decreasing Reynolds numbers and underwent transitions to approach constant asymptotes characteristic of bubbles rising through the quiescent liquid. An expression was developed for the relative importance of turbulent inertial forces compared with gravitational forces, F i / F g . This expression introduced a “turbulence” Froude number which served as a good criterion for establishing the pipe Reynolds numbers above which horizontal and vertical flow mass-transfer coefficients were equivalent. In addition, it proved to be a useful linear scaling factor for calculating the vertical-flow coefficients in the above mentioned transition region. The turbulent inertial forces were equated with drag forces to obtain bubble-mean Reynolds numbers which were substituted into Frössing-type equations to determine the mass-transfer Sherwood numbers. The resulting pipe Reynolds numbers exponent agreed well with the observed data.