I. PROBLEM STATEMENT

Synthetic ammonia $(N{H}_3)$ refers to ammonia that has been synthesised $($Standard Industrial Classification $2873)$ from natural gas. Natural gas molecules are reduced to carbon and hydrogen. The hydrogen is then purified and reacted with nitrogen to produce ammonia. Approximately $75$ percent of the ammonia produced is used as fertilizer, either directly as ammonia or indirectly after synthesis as urea, ammonium nitrate, and monoammonium or diammonium phosphates. The remainder is used as raw material in the manufacture of polymeric resins, explosives, nitric acid, and other products.

At Siyinqaba Petrochemicals where you are practicing as a Chemical Engineering Technologist, anhydrous ammonia is synthesised by reacting hydrogen with nitrogen at a molar ratio of $3$:$1,$ then compressing the gas and cooling it to $-33C.$ Nitrogen is obtained from air, while hydrogen is obtained from the catalytic steam reforming of natural gas, methane $(C{H}_4).$ Six process steps are required to produce synthetic ammonia using the catalytic steam reforming method: $(1)$ natural gas desulfurisation, $(2)$ catalytic steam reforming, $(3)$ carbon monoxide $(CO$ shift, $(4)$ carbon dioxide $)$ removal using monoethanolamine solution as the absorbent$,(5)$ methanation, and $(6)$ ammonia synthesis. The first, third, fourth, and fifth steps remove impurities such as sulfur, $CO,C{O}_2$ and water $(H_{2}O)$ from the feedstock i$.$e$.,$ hydrogen, and synthesis gas streams. In the second step, hydrogen is manufactured, and nitrogen $($air$)$ is introduced into this two$-$stage process. The sixth step produces anhydrous ammonia from synthetic gas. While all ammonia plants use this basic process, details such as operating pressures, temperatures, and quantities of feedstock vary from plant to plant.

It has been reported that the $C{O}_2$ removal packed absorber is experiencing some difficulties in achieving the required exit gas composition of ${1\mathrm{.}5}^{?}$mol$\%$ of $C{O}_2.$ After inspecting the packed column $($internal diameter of $1\mathrm{.}6m),$ you have concluded that the current problem can be resolved by optimising the absorbent flow rate. Note that, at column current conditions, the $K-$value of $C{O}_2$ is ${0\mathrm{.}86}^{**}$ and estimated values of $k_y$a and $k_x$a are ${256}^{***}mo\frac{l}{m^3}.hr$ and ${165}^{***}mo\frac{l}{m^3}.hr,$ respectively. As such, you have been tasked to prepare a detailed report based on your preliminary findings about the $C{O}_2$ absorber$.$ Your report should include findings on the following:

a$)$ The minimum absorbent flow rate to operate the column aimed at achieving the required $C{O}_2$ composition in the exit gas stream,