Phenol is added to mixer $1$ and mixed with recycled phenol from distillation column $1.$ Into a pump $1$ then into mixer $2$ the product is then mixed with fresh H$2$ and recycled H$2.$ The product is sent to heat exchanger $1$ then a fixed bed reactor and reacted at $100$ degrees Celsius and $5$ bar. Cyclohexanol, Cyclohexanone, unreacted H$2$ and unreacted Phenol is then passed to heat exchanger $2$ then flash separator $1.$ h$2$ is removed and recycled back into the system through a compressor then back into mixer $2.$ The products from separator $1$ are passed through pump $2$ then heat exchanger $3$ then distillation column $1,$ phenol is separated and passed through heat exchanger $4$ and joins mixer $1$ from cyclohexanone and cyclohexanol which are removed as top product. This product is then passed through a reboiler and heat exchanger $5$ then Into Distillation column $2,$ cyclohexanol is removed as bottom product while cyclohexanone is removed as top product and stored. Cyclohexanol is passed through heat exchanger $7$ then reacted in reactor $2$ to dehydrate it into cyclohexanone. The product is passed through heat exchanger $8$ then into separator $2$ where hydrogen is removed as top product and cyclohexanone as bottom and sent into distillation column $1$ after passing through pump $3.$

Perform a MANUAL CALCULATION $($by hand$)$ energy balance to produce cyclohexanone and cyclohexanol from phenol.$($ step by step please$)$

USE specific heat capacity: Phenol$=134\mathrm{.}58$ KJ$/$molK $,$ cyclohexanone$=177\mathrm{.}20$KJ$/$molK $,$ Cyclohexanol$=214\mathrm{.}06$ KJ$/$molK$,$ H$2=28\mathrm{.}84$Kj$/$molK

Reactor $1-$ Phenol conversion rate $99\mathrm{.}9\%,$ cyclohexanone selectivity $99\mathrm{.}2\%,$ cyclohexanol selectivity $0\mathrm{.}8\%$

Reactor $2-$ temp $275$C$,$ Phenol Conversion $89\%$ Selectivity for Cyclohexanone $93\%,$Pressure $1$ atm

Mass flowrate$=$ kg$/$hr

Molar flowrate$=$kmol$/$hr

C$6$H$5$OH $+2$H$2=$C$6$H$10$O

C$6$H$10$O $+$ H$2=$ C$6$H$12$O

Reflux ratio $=0\mathrm{.}68$

Efficiency of separator $100\%$

Distillation column $1$ efficiency $90\%$

Distillation column $2$ efficiency$=80\%$

Q$1$ heat balance of mixer $1$

stream $1$ and stream $22$ are input and stream $2$ is output.

stream $1$

temp $25$ C $,$ pressure $1$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}276,$ phenol mass flowrate $=402\mathrm{.}377,$Mole fraction of phenol is $1.$ All other components are $0$

stream $2$

temp $40$C $,$ pressure $1$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $1.$ All other components are $0$

stream $22$

temp $50$C $,$ pressure $2$ bar, phenol molar flowrate in kmol$/$hr $=0\mathrm{.}0039,$ phenol mass flowrate $=0\mathrm{.}362,$Mole fraction of phenol is $1.$ All other components are $0$

Q$2$ energy balance around pump $1$

Stream $2$ in stream $3$ out

stream $2$

temp $40$C $,$ pressure $1$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $1.$ All other components are $0$

stream $3$

temp $40$C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $1.$ All other components are $0$

Q$3$ heat balance around mixer $2$

stream $3$ in $,$ stream $4$ out

stream $3$

temp $40$C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $1.$ All other components are $0$

stream $4$

temp $40$C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $0\mathrm{.}200.$ hydrogen molar flowrate in kmol$/$hr $=17\mathrm{.}118,$ hydrogen mass flowrate $=34\mathrm{.}578,$Mole fraction of hydrogen is $0\mathrm{.}800$ All other components are $0$

Q$4$ Energy balance around heat exchanger $2$

Stream $4$ in$,$ stream $5$ out

Stream $4$

temp $40$C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $0\mathrm{.}200.$ hydrogen molar flowrate in kmol$/$hr $=17\mathrm{.}118,$ hydrogen mass flowrate $=34\mathrm{.}578,$Mole fraction of hydrogen is $0\mathrm{.}800$ All other components are $0$

Stream $5$

temp $100$ C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $0\mathrm{.}200.$ hydrogen molar flowrate in kmol$/$hr $=17\mathrm{.}118,$ hydrogen mass flowrate $=34\mathrm{.}578,$Mole fraction of hydrogen is $0\mathrm{.}800$ All other components are $0$

Q$5$ Heat balance around reactor $1$

Stream $5$ in$,$ stream $6$ out

Stream $5$

temp $100$ C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=4\mathrm{.}279,$ phenol mass flowrate $=402\mathrm{.}739,$Mole fraction of phenol is $0\mathrm{.}200.$ hydrogen molar flowrate in kmol$/$hr $=17\mathrm{.}118,$ hydrogen mass flowrate $=34\mathrm{.}578,$Mole fraction of hydrogen is $0\mathrm{.}800$ All other components are $0$

stream $6$

temp $100$ C $,$ pressure $5$ bar, phenol molar flowrate in kmol$/$hr $=0\mathrm{.}004,$ phenol mass flowrate $=0\mathrm{.}403,$Mole fraction of phenol is $0\mathrm{.}000.$ Cyclohexanone molar flowrate in kmol$/$hr $=2\mathrm{.}129,$ Cyclohexanone mass flowrate $=208\mathrm{.}940,$Mole fraction of Cyclohexanone is $0\mathrm{.}199.$ Cyclohexanol molar flowrate in kmol$/$hr $=2\mathrm{.}146,$ Cyclohexanol mass flowrate $=214\mathrm{.}960,$Mole fraction of Cyclohexanol is $0\mathrm{.}201.$ hydrogen molar flowrate in kmol$/$hr $=6\mathrm{.}421,$ hydrogen mass flowrate $=12\mathrm{.}971,$Mole fraction of hydrogen is $0\mathrm{.}600$