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[m.okosu]

I am doing an introductory module to bioprocess engineering and i seem to be unable to solve the given problem.

Problem:

given a chemical reaction balance is 1s --> 2p






Reactor substrate balance equation: d[S]/dz = - (1/FL )rs
Rate of enzymatic reaction: rs = rmax[S]/(Km +[S])
Maximum specific reaction rate: rmax = k[E]

Linear flow velocity: FL = F/(Ae)





where:
FL = linear flow rate (m.hr-1)
Km = Michaelis constant = 0.5 kg.m-3
k = reaction rate constant = 0.8 hr-1
[E] = enzyme concentration = 7 kg.m-3
F = volumetric flow rate (m3.hr-1)
A = reactor cross-sectional area = 0.5 m2
e = void volume fraction of reactor packing

Given F = 5 m3.hr-1 and ε = 0.4 and the following initial and final conditions: [S]o = 10 kg.m-3, zo = 0, zf = 20 metres, construct a Polymath input file to simulate conditions in the tubular enzyme reactor. Use the programme to produce plots of [S] and [P] versus reactor length. Determine the reactor length required to achieve a substrate conversion of 95% (X95).

Polymath file I constructed from given data:


d(S)/d(z) = - (1/Fl)*rs #Reactor substrate balance equation
S(0) = 10
z(0) = 0
z(f) = 20
rs = Rmax*(S)/(Km+(S)) #Rate of enzymatic reaction
Rmax = k*(E) #Maximum specific reaction rate
Fl = F/(A*e) #Linear flow velocity
m =0.5 #Michaelis constant
k=0.8 #reaction rate constant
E= 7 #enzyme concentration
A=0.5 #reactor cross sectional area
F= 5 #volumetric flowrate
e=0.4 #void volume fraction of reactor packaging
Km=0.5

The problem I now have is that i don't know how to form the equation needed to plot [p] vs reactor length from [s], although i know that the stoichiometric reaction equation s--> 2p plays an important role. I also don't know how to determine the reactor length in a 95% substrate conversion, without guessing z to achieve a close enough value of S(f)= 0.5 kg.m-3 (which would be the concentration of substrate left if 95% of initial substrate is converted to product.

Edited by m.okosu, 29 November 2012 - 07:21 AM.

[markymaark]

Computer programs are very picky remember. I see you said Fl once instead of FL (not sure how you described the variable in the program, be consistent).

I do not have my older files for polymath on me so hopefully someone else can give the line to plot.

You are correct with the S->2P imprtance.

You know P is 0 at first so P(0)=0
and from the stoichiometry you know rs=rp/2 and you already defined rs. rp=2rs
Then just write down the reaction for dp/dz in terms of rp

You can get the 95% conversion value from the plot. There is a "table" feature in the plot and then just got to where S=(1-.95)*10. (If this is for homework, i useto take a screenshot of the table)