$($a$)$ MDEA solution is used to remove H$2$S and some CO$2$ from the natural gas stream. The processing system holds $50000$ gal $(189$ m$3)$ of a $50$wt$\%$ solution. The titration of the solution shows that the amine strength has increased to $57$wt$\%$ due to water evaporation. How much high purity water must be added to the system to return the concentration to $50$wt$\%?($b$)$ State the common causes of foaming in an amine contactor column. $($c$)$ For the following data calculate the terminal velocity and the diameter of the amine contactor column. Gas flow rate $=7$ MMscfd Specific gravity of gas $=0\mathrm{.}65$ Specific gravity of MDEA at $20/20\backslash$deg C $=1\mathrm{.}041$ Density of water $=62\mathrm{.}4$ lb$/$ft$3$ Temperature $=60\backslash$deg F Pressure $=500$ psig