A system for recovering methanol from a solid product wet with methanol involves evaporation of the alcohol into a stream of inert gas, essentially nitrogen. In order to recover the methanol from the nitrogen, an absorption scheme involving washing the gas countercurrently with water in a packed tower is being considered. The resulting water-methanol solution is then to be distilled to recover the methanol.

The absorption tower will be filled with \(50-\mathrm{mm}\) ceramic Pall rings. Design for a gas-pressure drop not to exceed \(400 \mathrm{~Pa} / \mathrm{m}\) of packed depth. Assume cooling coils will allow isothermal operation at \(300 \mathrm{~K}\). The gas will enter the column at the rate of \(1.0 \mathrm{~m}^{3} / \mathrm{s}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). The partial pressure of methanol in the inlet gas is \(200 \mathrm{~mm} \mathrm{Hg}\left(\mathrm{Sc}_{G}=0.783\right)\). The partial pressure of methanol in the outlet gas should not exceed \(15 \mathrm{~mm} \mathrm{Hg}\). Pure water enters the tower at the rate of \(0.50 \mathrm{~kg} / \mathrm{s}\) at \(300 \mathrm{~K}\). Neglecting evaporation of water, calculate the diameter and packed depth of the absorber.

Solutions of methanol and water follow Wilson equation. The corresponding parameters can be found in Smith et al. (1996).