Question $4[28$ points$]$

An industrial facility has an old boiler that consumes $20MW$ with $8\%$ excess $m,$ and the stack temperature rise $($STR$)$ is $360C.$ The boiler consumes natural gas whose heating value is $54M\frac{J}{k}g.$ The cost of natural gas is $SR\frac{1\mathrm{.}1}{k}g.$

The facility also has a compressed air system that provides air at a pressure of $8$ bar and consumes $1,500kW$ continuously throughout the year. The facility needs hot water and it is provided by electric water heaters that consume $250kW$ continuously throughout the year.

The facility owner would like to reduce energy consumption by hiring an ESCO on a $10-$year shared savings contract, where the ESCO receives annual payments equal to $50\%$ of the annual savings.

The ESCO is considering taking the following actions:

$O_2$

Install a new boiler that delivers the same amount of steam, but with only $2\%$ excess $$ and with an STR of $310C.$

Fix compressed air system leaks. The number of leaks that were detected was ${10}_{?},$ and each of them has a $9-$mm diameter

Install a heat recovery unit that recovers $250kW$ of energy which is used to replace the electric water heaters no Electric heaters used

The capital cost of the project is SR $3,000,000.$

Calculate the following:

a$.$ Rate of thermal energy delivery to the steam by the old boiler. $[2$ points$]$

b$.$ Rate of natural gas consumption by the old boiler $($in $k\frac{g}{s}).[3$ points$]$

c$.$ Cost of natural gas consumption $($in Saudi Riyals$)$ per year by the old boiler. $[3$ points$]$

d$.$ Cost of electricity consumption of the compressed air system and water heaters $($in Saudi Riyals$)$ per year. Assume the tariff is SR points$]$

e$.$ Cost of natural gas consumption $($in Saudi Riyals$)$ per year by the new boiler. $[4$ points$]$

f$.$ Cost of electricity consumption of the compressed air system $($in Saudi Riyals$)$ per year after project implementation. $[4$ points$]$ withaut heaters

g$.$ Annual financial savings $($in Saudi Riyals$).[4$ points$]$

h$.$ The net present value $($from the ESCO's point of view$)$ based on an $8\%$ discount rate. $[3_{?}$ points$]$

i$.$ Based on your answer in Part $($h$),$ should the ESCO agree to implement this project? $[1$ points$]$