An aeration tank treats180000 m³/day water, lowering VOC from 33 to 12 µg/L. Equilibrium saturation concentration5 µg/L and gas-transfer constant.40/s at 25°C. Find required tank volume in m³,to two decimals.
Using the plug-flow/contact-time first-order transfer interpretation,$C-C^*=(C_0-C^*)e^{-kt}$. Thus $t=\ln[(33-5)/(12-5)]/.40=\ln4/.40=3.465736$ s. Flow is 180000/86400=2.083333 m³/s, and $V=Qt=\mathbf{7.22}$ m³. The keyed answer assumes plug flow; an ideal continuously mixed tank would require a different balance and volume.
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