Green hydrogen production unit with electrolysis produces $100$ mol$/$s of hydrogen through renewable electricity sources, yielding $10$ mol H$2/$kWh$.$ Hydrogen is produced at a pressure of $10$ bar and a temperature of $60$ oC$.$ The produced hydrogen will be stored at an intermediate pressure of $100$ bar in horizontal cylindrical containers with a maximum volume of $100$ m$3$ with a ratio of height to diameter equal to $5.$ The containers are emptied by compressing the hydrogen to $700$ bar and "loading" them into containers suitable for marketing. Due to problems in the $100$ bar $->700$ bar compression system, the intermediate vessels should have the capacity to store the produced hydrogen for a period of $3$ hours. Design the hydrogen initial compression $(10$ bar $->100$ bar$),$ storage and final compression $(100$ bar $->700$ bar$)$ unit. More specifically:

a$)$ What is the state of the hydrogen at the outlet of the electrolysis unit $(60$ oC$,10$ bar$),$ in the intermediate storage tank $(25$ oC$,100$ bar$)$ and in the final tank $(60$ oC$,700$ bar$).$

b$)$ What is the structure of the compression system $10$ bar $->100$ bar.

c$)$ What is the energy consumption of the $10$ bar $->100$ bar compression system.

d$)$ What is the heat exchange surface of the heat exchangers used in the $10$ bar $->100$ bar compression system. These exchangers use slightly chilled water with an inlet temperature of $15$ oC and an outlet temperature of $<35$ oC$.$

e$)$ What are the number and dimensions of intermediate storage containers.

f$)$ What is the total equipment purchase cost in $@$2024$ for the $10$ bar $->100$ bar system and the storage system?

Given:

$1)$ The temperature of the intermediate storage containers is maintained at $25$ oC$.$

$2)$ Coefficient of compressibility of hydrogen at $25$ oC: Z$=1+0\mathrm{.}0108*($P $/19\mathrm{.}065),$ P in bar.

$3)$ Supply cost of horizontal cylindrical tanks Ctank$($$@$2020)=5000*$V$^0\mathrm{.}6,[$V$]=$m$^3$

$4)$ Electricity cost: $$0\mathrm{.}07/$kWh$.$

$5)$ The temperature of the hydrogen at the outlet of the compressors, which have an efficiency of $75\%,$ must in no case exceed $180$ oC$.$

$6)$ The hydrogen output from the compression system is cooled to $-40$ oC$.$

$7)$ CEPSI @$2024=800.$

$8)$ For hydrogen it can be assumed that the specific heat capacity of the ideal gas $($Cp$=3\mathrm{.}5$R$)$

$9)$Critical properties of hydrogen: Pc$=13\mathrm{.}16$ bar, Tc$=33\mathrm{.}45$ K$=-239\mathrm{.}7$ oC$,\backslash$omega $=-0\mathrm{.}1201$