Costing of the system: Find the capex and opex for the following:

The following data are for the Intercooler $($heat exchanger$)$System specifications:

$-$Purpose of the system is to compress natural gas through a $4$ stage compressore system.

$-$ Gas is being compressed, and we are using cooling water

$-$Mass flow rate of water$=4\mathrm{.}28$ kg$/$s

$-$Compressor efficiency at each stage is $0\mathrm{.}82$

$-$Fist pressure os $1$ bar and final pressure is $8$ bar

Intercooler details:

$-$ Shell and tube are both made of carbon steels

Compressor details:

$-$Compressor efficiency at each stage is $0\mathrm{.}82$

Operational parameters:

$-$operating for month

Costing of the system: Find the capex and opex for the following:

The following data are for the Intercooler $($heat exchanger$)$

Heat Transfer rate: $268\mathrm{.}64$ kW

Mass flow rate of water: $4\mathrm{.}28$ kg$/$s

Logarithmic temp: $51\mathrm{.}84$ C

Heat Transfer area: $8\mathrm{.}64$ m$2$

Number of tubes: $16(16$mm diameter$)$

Length of pipe $($loop$)$: $3\mathrm{.}66$ m

We have a $4$ stage compressor

Specefic Heat, cp $29\mathrm{.}2$ J$/$mol$.$K Specefic heat ratio, $1\mathrm{.}4$

Number of Stages $4$ Universal Gas Constant, R $8\mathrm{.}3$ J$/$mol$.$K

Pressure ratio $8$ Inlet Pressure P$11$ bar

Outlet Pressure P$58$ bar Inlet Temperature T$125$ degrees C

$298$ Kelvin

Efficiency $0\mathrm{.}82$

$1.$ Compression Ratio

Incremental Compression Ratio $1\mathrm{.}7$

$2.$ Compressor Stages

Stage $1$:

Suction Pressure $1\mathrm{.}0$ bar

Suction temperature $($C$)25\mathrm{.}0$ C

Suction temperature $($K$)298\mathrm{.}0$ K

Discharge Pressure $1\mathrm{.}7$ bar

Work $11386\mathrm{.}2$ Watts

Actual Work $11690\mathrm{.}5$ Watts

Discharge Temperature $($K$)355\mathrm{.}9$ K

Discharge Temperature $($C$)82\mathrm{.}9$ C

Stage $2$:

Suction Pressure $1\mathrm{.}681792831$ bar

Suction temperature $($C$)82\mathrm{.}89442378$ C

Suction temperature $($K$)355\mathrm{.}8944238$ K

Discharge Pressure $2\mathrm{.}828427125$ bar

Work $21655\mathrm{.}534971$ Watts

Actual Work $22018\mathrm{.}945086$ Watts

Discharge Temperature $($K$)425\mathrm{.}0363788$ K

Discharge Temperature $($C$)152\mathrm{.}0363788$ C

Install intercooler here

Stage $3$:

Suction Pressure $2\mathrm{.}828427125$ bar

Suction temperature $($C$)37$ C

Suction temperature $($K$)310$ K

Discharge Pressure $4\mathrm{.}75682846$ bar

Work $31442\mathrm{.}045187$ Watts

Actual Work $31758\mathrm{.}591692$ Watts

Discharge Temperature $($K$)370\mathrm{.}2257429$ K

Discharge Temperature $($C$)97\mathrm{.}22574286$ C

Stage $4$:

Suction Pressure $4\mathrm{.}75682846$ bar

Suction temperature $($C$)97\mathrm{.}22574286$ C

Suction temperature $($K$)370\mathrm{.}2257429$ K

Discharge Pressure $8$ bar

Work $41722\mathrm{.}200808$ Watts

Actual Work $42100\mathrm{.}244888$ Watts

Discharge Temperature $($K$)442\mathrm{.}1519377$ K

Discharge Temperature $($C$)169\mathrm{.}1519377$ C

Centrifugal compressor: $70$ bar, electric motor drive with gearbox, material of construction: steel

power $30-7600$ kW

$$C $=2060[$kW$]^0\mathrm{.}8$

Material factor: stainless steel $2\mathrm{.}5$

Other factors: pressure $[$P$($bar$)/70]^0\mathrm{.}18$

COSTS OF SERVICES AND RAW MATERIALS

Cooling water $0\mathrm{.}030$ per tonne

Electricity $40$ per MWh

toluene $200$ per tonne

benzoic acid $400$ per tonne

EQUIPMENT COSTS

Shell and tube heat exchangers

$1.$ carbon steel tubes and shell.

a$)$ A $=2$ to $25$ m$2$

$$C $=3800$e$^(0\mathrm{.}05$ A$)$

b$)$ A $>25$ m$2$

$$C $=7900$e$^(0\mathrm{.}01$A$)$

Shell and tube material factor, f$.$ f$=$a$+(0\mathrm{.}01$a$)^$b shell tube a b

CS SS $1\mathrm{.}750\mathrm{.}13$

SS SS $2\mathrm{.}700\mathrm{.}07$

CS monel $2\mathrm{.}10\mathrm{.}13$

monel monel $3\mathrm{.}30\mathrm{.}18$

CS Ti $5\mathrm{.}20\mathrm{.}16$

Ti Ti $9\mathrm{.}60\mathrm{.}06$

CS Admiralty $1\mathrm{.}080\mathrm{.}05$