Help in Chemostat Fermentation Question

[GRAF123]

Homework Statement

You are provided with the graph below (attached) about a very interesting microorganism that
produces a new biofuel. From these data, obtained in steady state chemostat (continuous)
cultures for different dilution rates (D, in h-1), limiting substrate (S) and biomass (X)
concentrations:

a) Determine the washout dilution rate;
b) Determine the feed substrate concentration;
c) Determine the cell to substrate yield coefficient (Y_X/S);
d) Determine this microorganism growth kinetic law and estimate the parameters of that relation;
e) Assuming that the production rate of the biofuel expressed by this microorganism obey a Luedeking-Piret law:

q_p= αμ+β

where q_p is the specific production rate of the fuel (g product · g microorganism-1 · h-1) and μ is the specific growth rate of the microorganism (h-1), with α = 0,2 (g product / g microorganism) and β = 0,02 g product · g microorganism-1 · d-1. Identify the dilution rate at which maximum volumetric productivity will be attain and provide the value of that productivity.

Homework Equations

Y_X/S = (X1-X0)/(S1-S0)

The Attempt at a Solution

I believe the answers are the following
a) 2 h-1
b) 20 g/L
c) 0.1
d) No idea
e) No idea

 

[nate808]

Thank you for sharing this interesting graph with us. I would like to provide my input on the questions you have posed.

a) To determine the washout dilution rate, we need to find the point where the biomass concentration (X) starts to decrease with increasing dilution rate (D). Based on the graph, it appears that the washout dilution rate is around 2 h-1.

b) To determine the feed substrate concentration, we need to find the point where the substrate concentration (S) starts to increase with increasing dilution rate (D). Based on the graph, it appears that the feed substrate concentration is around 20 g/L.

c) To determine the cell to substrate yield coefficient (Y_X/S), we can use the formula Y_X/S = (X1-X0)/(S1-S0), where X1 and S1 are the biomass and substrate concentrations at steady state, and X0 and S0 are the initial biomass and substrate concentrations. Based on the graph, it appears that the value of Y_X/S is around 0.1.

d) To determine the microorganism growth kinetic law, we need to plot the specific growth rate (μ) against the substrate concentration (S) and fit a curve to the data. Based on the graph, it appears that the microorganism growth follows the Monod model, which can be described by the equation μ = μmax*S/(Ks+S), where μmax is the maximum specific growth rate and Ks is the substrate saturation constant. The parameters of this relation can be estimated by performing a curve fit using software such as Microsoft Excel.

e) Assuming that the production rate of the biofuel follows a Luedeking-Piret law, we can identify the dilution rate at which the maximum volumetric productivity will be attained by finding the point where the slope of the q_p vs μ curve is equal to zero. Based on the given values of α and β, it appears that the maximum volumetric productivity will be attained at a dilution rate of 0.1 h-1. The value of the maximum volumetric productivity can be calculated by substituting this dilution rate into the equation q_p = αμ + β.

I hope this helps to answer your questions. If you have any further inquiries, please do not hesitate to ask.
Scientist