A preliminary process flow diagram for a DME process is shown in Figure B$\mathrm{.}1\mathrm{.}1,$

in which $50,000$ metric tons per year of $99\mathrm{.}5wt\%$ purity DME product is pro$-$

duced. Due to the simplicity of the process, an operating factor greater than $0\mathrm{.}95$

$(8,375\frac{h}{y}r)$ is used.

Fresh methanol, Stream $1,$ is combined with recycled reactant, Stream $14,$

and vaporized prior to being sent to a fixed$-$bed reactor operating between $250C$

and $370C.$ The single$-$pass conversion of methanol in the reactor is $80\%.$ The re$-$

actor effluent, Stream $7,$ is then cooled prior to being sent to the first of two distil$-$

lation columns: T$-201$ and T$-202.$ DME product is taken overhead from the first

column. The second column separates the water from the unused methanol. The

methanol is recycled back to the front end of the process, and the water is sent to

waste water treatment to remove trace amounts of organic compounds.

Stream summaries, utility summaries, and equipment summaries are pre$-$

sented in Tables B$\mathrm{.}1\mathrm{.}1-$B$\mathrm{.}1\mathrm{.}3.$

Table B$\mathrm{.}1\mathrm{.}1$ Flow Table for DME Unit $200$

Calculate the conderser heat duty and the reboiler heat duty of the DME distillation column showing all workings please