The transfer of oxygen from air bubbles to water is very important for many biochemical processes....

 

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The transfer of oxygen from air bubbles to water is very important for many biochemical processes. Bubbles that are approximately spherical and 2 cm in diameter are slowly and individually sparged into the bottom of a tank of water that is 1.5 m in diameter and 1 m deep. The bubbles rise through the tank of water at a velocity of 30 cm/s. The entire system is at a pressure of 1 atm and a temperature of 12C. Air can be assumed to be 21 mole % O2 and 79 mole% Nz. The equilibrium relationship of oxygen in the gas phase and dissolved oxygen in the liquid phase is: y = 410 x where y and x are the mole fractions of the oxygen in the gas and liquid phases, respectively. (19%) (a) Determine the overall mass transfer coefficients, Kx' and Ky'. (6%) (b) Estimate the amount of oxygen transferred to the liquid from one bubble as it rises through the tank. Clearly state any assumptions. Gas properties Molecular weight of air = 29 g/mole Molecular weight of oxygen = 32 g/mole Molecular weight of nitrogen = 28 g/mole PG = 1.24 kg/m MG 1.75 x 105 kg/(ms) 8G = 0.0001 m Surface area of a sphere: Volume of a sphere: (diameter) Liquid properties Molecular weight of water = 18 g/mole PL = 999.5 kg/m L = 1.3 x 103 kg/(ms) DAB,L 1.5 x 109 m/s /6 (diameter) The transfer of oxygen from air bubbles to water is very important for many biochemical processes. Bubbles that are approximately spherical and 2 cm in diameter are slowly and individually sparged into the bottom of a tank of water that is 1.5 m in diameter and 1 m deep. The bubbles rise through the tank of water at a velocity of 30 cm/s. The entire system is at a pressure of 1 atm and a temperature of 12C. Air can be assumed to be 21 mole % O2 and 79 mole% Nz. The equilibrium relationship of oxygen in the gas phase and dissolved oxygen in the liquid phase is: y = 410 x where y and x are the mole fractions of the oxygen in the gas and liquid phases, respectively. (19%) (a) Determine the overall mass transfer coefficients, Kx' and Ky'. (6%) (b) Estimate the amount of oxygen transferred to the liquid from one bubble as it rises through the tank. Clearly state any assumptions. Gas properties Molecular weight of air = 29 g/mole Molecular weight of oxygen = 32 g/mole Molecular weight of nitrogen = 28 g/mole PG = 1.24 kg/m MG 1.75 x 105 kg/(ms) 8G = 0.0001 m Surface area of a sphere: Volume of a sphere: (diameter) Liquid properties Molecular weight of water = 18 g/mole PL = 999.5 kg/m L = 1.3 x 103 kg/(ms) DAB,L 1.5 x 109 m/s /6 (diameter)