NEED HELP ASAP PLEASE! Please show all steps to calculations.

Model a two$-$stage fermentation system for conversion of syngas into ethanol.

Write a general set of differential equations describing the production of ethanol $($E$)$ from syngas using a microbe $($X$).$ The system consists of three vessels:

Seed reactor $$ This reactor has volume V$1.$ The substrate, syngas, which is a mixture of CO$,$ CO$2,$ and H$2$ gases, enters in the stream FSG$,1.$ In addition, ammonia $($N$)$ is added as the nitrogen source along with the microbe $($X$)$ which consumes the gaseous substrates following Simple Monod Kinetics. The microbe produces acetic acid $($A$)$ which is fed to the production reactor $($the bubble column$).$ All excess gas leaves the reactor in the exhaust to be recycled $($not shown$).$

Bubble column $$ This vessel with volume V$2$ is the reactor where acetic acid is converted to ethanol $($E$)$ by the cells $($X$).$ The syngas mixture is introduced $($FSG$,2)$ and the outgoing stream passes through a hollow fibre module that separates the cells, which are then recycled back into the column.

Hollow fibre module $$ This module with volume V$3$ is where the cells are separated from the media. The cells are recycled back to the bubble column and the media containing ethanol is collected in stream F$5.$

Summary of variables to be used:

X $$ g dry X$-$cells$/$ L A $$ g Acetic acid$/$L E $$ g Ethanol$/$L

N $$ g NH$3/$L F $$ volumetric flow rate in L$/$hr V $$ volume of reactor in L

SG $$ g syngas$/$L FSG $$ volumetric flow rate of syngas in L$/$hr

Note: Use subscripts appropriately to denote stream and vessel numbers. Include any necessary yields, growth kinetics etc.

You can assume the following:

$$ All vessels are perfectly mixed

$$ The densities in all streams and vessels are constant

$$ Model the syngas mixture, not the individual components

$$ Perfect separation occurs in the hollow fibre module

$$ All acetic acid is consumed and converted to ethanol in the bubble column

a$)$ Write the Mathematical Model for the Seed reactor $(10$ marks$)$

b$)$ Write the Mathematical Model for the Bubble column $(15$ marks$)$

c$)$ Write the Mathematical Model for the Hollow fibre module $(5$ marks$)$