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Deck 16: Mixed Cultures
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Question
Organism A grows on substrate S and produces product P, which is the only substrate that or-
ganism B can utilize. The batch kinetics are
Assume the following parameter values: 
Determine the behavior of these two organisms in a chemostat. Plot S, P, 
versus
dilution rate. Discuss what happens to organism B as the dilution rate approaches the washout
dilution rate for organism A. (Courtesy of L. Erickson, from "Collected Coursework Prob-
lems in Biochemical Engineering," compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ.
Summer School.)
ganism B can utilize. The batch kinetics are
Assume the following parameter values: Determine the behavior of these two organisms in a chemostat. Plot S, P, versusdilution rate. Discuss what happens to organism B as the dilution rate approaches the washout
dilution rate for organism A. (Courtesy of L. Erickson, from "Collected Coursework Prob-
lems in Biochemical Engineering," compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ.
Summer School.)
Question
The 
value of a waste-water feed stream to an activated-sludge unit is 
and the effluent is desired to be S = 30 mg/l. The feed flow rate is 
l/day. For the
recycle ratio of
and a steady-state biomass concentration of X = 5 g/l, calculate the
following:
a. Required reactor volume (V).
b. Biomass concentration in recycle
c. Solids (cells) residence time
d. Hydraulic residence time
e. Determine the daily oxygen requirement.
Use the following kinetic parameters:
value of a waste-water feed stream to an activated-sludge unit is and the effluent is desired to be S = 30 mg/l. The feed flow rate is l/day. For therecycle ratio of
and a steady-state biomass concentration of X = 5 g/l, calculate thefollowing:
a. Required reactor volume (V).
b. Biomass concentration in recycle
c. Solids (cells) residence time
d. Hydraulic residence time
e. Determine the daily oxygen requirement.
Use the following kinetic parameters:
Question
For the activated-sludge unit shown in Fig. 16.7, the specific growth rate of cells is given by 
The following parameter values are known: F = 500 1/h, 
substrate.
a. Calculate the substrate concentration (S) in the reactor at steady state.
b. Calculate the cell concentration(s) in the reactor.
c. Calculate Xr and Sr in the recycle stream.
Figure 16.7
The following parameter values are known: F = 500 1/h, substrate. a. Calculate the substrate concentration (S) in the reactor at steady state.
b. Calculate the cell concentration(s) in the reactor.
c. Calculate Xr and Sr in the recycle stream.
Figure 16.7
Question
In a trickling biological filter, the BOD value of the feed stream is 
with a feed
flow of F =
The effluent BOD value is desired to be 
= 10 mg/l. The following ki-
netic parameters for the biocatalysts are known:
S/l. The
biofilm thickness is L = 0.1 mm. The cross-sectional area of the filter is A = 2
and the biofilm surface area per unit volume of the bed is 
Assume that dis-
solved oxygen is the rate-limiting substrate and the diffusion coefficient of oxygen is
Determine the required height of the bed. You can assume first-order
bioreaction kinetics.
with a feedflow of F =
The effluent BOD value is desired to be = 10 mg/l. The following ki-netic parameters for the biocatalysts are known:
S/l. Thebiofilm thickness is L = 0.1 mm. The cross-sectional area of the filter is A = 2
and the biofilm surface area per unit volume of the bed is Assume that dis-solved oxygen is the rate-limiting substrate and the diffusion coefficient of oxygen is
Determine the required height of the bed. You can assume first-orderbioreaction kinetics.
Question
An activated-sludge waste treatment system is required to reduce the amount of 
from
1000 mg/l to 20 mg/l at the exit. The sedimentation unit concentrates biomass by a factor of
3. Kinetic parameters are
MLVSS/g 
The flow of waste water is 10000 l/h and the size of the treatment basin is 50,000 l.
a. What is the value of the solids residence time
b. What value of the recycle ratio must be used?
from1000 mg/l to 20 mg/l at the exit. The sedimentation unit concentrates biomass by a factor of
3. Kinetic parameters are
MLVSS/g The flow of waste water is 10000 l/h and the size of the treatment basin is 50,000 l. a. What is the value of the solids residence time
b. What value of the recycle ratio must be used?
Question
Consider a well-mixed waste treatment system for a small-scale system. The system is oper-
ated with a reactor of 1000 l and flow rate of 100 l/h. The separator concentrates biomass by
a factor of 2. The recycle ratio is 0.7. The kinetic parameters are
What is the exit substrate concentration?
ated with a reactor of 1000 l and flow rate of 100 l/h. The separator concentrates biomass by
a factor of 2. The recycle ratio is 0.7. The kinetic parameters are
What is the exit substrate concentration? Question
Redo Example 16.4 if the Contois equation for growth applies. In this case 
The values of 
are the same as for Example 16.4, but 
no longer applies. Assume 
MLVSS.
Example 16.4.
An industrial waste with an inlet
of 800 mg/l must be treated to reduce the exit 
level to 20 mg/l. The inlet flow rate is 400 m ³/h. Kinetic parameters have been estimated for waste as 
A waste treatment unit of 3200 m ³is available. Assume a recycle ratio of 0.40 and 
If you operate at a value of c 120 h, find S and determine if sufficient 
removal is attained in a well-mixed activated-sludge process to meet specifications. What will
be X and the sludge production rate from this process?
The values of are the same as for Example 16.4, but no longer applies. Assume MLVSS.Example 16.4.
An industrial waste with an inlet
of 800 mg/l must be treated to reduce the exit level to 20 mg/l. The inlet flow rate is 400 m ³/h. Kinetic parameters have been estimated for waste as A waste treatment unit of 3200 m ³is available. Assume a recycle ratio of 0.40 and If you operate at a value of c 120 h, find S and determine if sufficient removal is attained in a well-mixed activated-sludge process to meet specifications. What willbe X and the sludge production rate from this process?
Question
A batch fermenter receives 1 l of medium with 5 g/l of glucose, which is the growth-rate-
limiting nutrient for a mixed population of two bacteria (a strain of E. coli and Azotobacter
vinelandii). A. vinelandii is five times larger than E. coli. The replication rates for the two or-
ganisms are:
The yield coefficients are: 
The inoculum for the fermenter is 0.03 g dw/l of E. coli 
and 0.15 g dw/l of
A. vinelandii
cells/ml).
What will be the ratio of A. vinelandii to E. coli at the time when all of the glucose is
consumed?
Example 16.1.
Competition of two species for the same growth-rate-limiting substrate is common. Deter- mine when the two organisms may stably coexist if both A and B follow Monod kinetics.
limiting nutrient for a mixed population of two bacteria (a strain of E. coli and Azotobacter
vinelandii). A. vinelandii is five times larger than E. coli. The replication rates for the two or-
ganisms are:
The yield coefficients are: The inoculum for the fermenter is 0.03 g dw/l of E. coli and 0.15 g dw/l ofA. vinelandii
cells/ml).What will be the ratio of A. vinelandii to E. coli at the time when all of the glucose is
consumed?
Example 16.1.
Competition of two species for the same growth-rate-limiting substrate is common. Deter- mine when the two organisms may stably coexist if both A and B follow Monod kinetics.
Question
Consider Example 16.1, where we demonstrated that two bacteria competing for a single nu-
trient in a chemostat (well-mixed) could not coexist. Consider the situation where B can ad-
here to a surface but A cannot. Redo the balance equations, where
is the surface area
available per unit reactor volume and the rate of attachment is first order in
with a rate
constant
The sites available for attachment will be 
The attached cells can
detach with a first-order dependence on the attached cell concentration
with a rate con-
stant of
Attached cells grow with the same kinetics as suspended cells.
a. Without mathematical proofs, do you think coexistence may be possible? Why or
why not?
b. Consider the specific case below and solve the appropriate balance equations for
trient in a chemostat (well-mixed) could not coexist. Consider the situation where B can ad-
here to a surface but A cannot. Redo the balance equations, where
is the surface areaavailable per unit reactor volume and the rate of attachment is first order in
with a rateconstant
The sites available for attachment will be The attached cells candetach with a first-order dependence on the attached cell concentration
with a rate con-stant of
Attached cells grow with the same kinetics as suspended cells. a. Without mathematical proofs, do you think coexistence may be possible? Why or
why not?
b. Consider the specific case below and solve the appropriate balance equations for
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Deck 16: Mixed Cultures
1
Organism A grows on substrate S and produces product P, which is the only substrate that or-
ganism B can utilize. The batch kinetics are Assume the following parameter values: Determine the behavior of these two organisms in a chemostat. Plot S, P, versus
dilution rate. Discuss what happens to organism B as the dilution rate approaches the washout
dilution rate for organism A. (Courtesy of L. Erickson, from "Collected Coursework Prob-
lems in Biochemical Engineering," compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ.
Summer School.)
ganism B can utilize. The batch kinetics are
Assume the following parameter values: Determine the behavior of these two organisms in a chemostat. Plot S, P, versusdilution rate. Discuss what happens to organism B as the dilution rate approaches the washout
dilution rate for organism A. (Courtesy of L. Erickson, from "Collected Coursework Prob-
lems in Biochemical Engineering," compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ.
Summer School.)
Steady state material balances for a Chemostat with 2 Organisms and Commensalism 
……(1) 
…… (2) 
……(3) 
…… (4)
Solving equation (1) for D ( F/V ) as a function of S
…… (5)
Solving equation (2) for P as a function of S and D
…… (6) 
…… (7)
Solving equation (3) for
as a function of S , D and P 
…… (8)
Solving equation (4) for
as a function of S , D , P and 
…… (9)
Choose S and use equation (5) to compute D , equation (7) to compute P , equation (8) to compute
, and equation (9) to compute 
Since organism B relies on organism A to produce its substrate, P, washout of organism A, and thus the cessation of P production, results in washout of organism B as well. In examining equation (8) notice the direct dependence of 
on 
……(1) …… (2) ……(3) …… (4)Solving equation (1) for D ( F/V ) as a function of S
…… (5)Solving equation (2) for P as a function of S and D
…… (6) …… (7)Solving equation (3) for
as a function of S , D and P …… (8)Solving equation (4) for
as a function of S , D , P and …… (9) Choose S and use equation (5) to compute D , equation (7) to compute P , equation (8) to compute
, and equation (9) to compute Since organism B relies on organism A to produce its substrate, P, washout of organism A, and thus the cessation of P production, results in washout of organism B as well. In examining equation (8) notice the direct dependence of on 2
The value of a waste-water feed stream to an activated-sludge unit is and the effluent is desired to be S = 30 mg/l. The feed flow rate is l/day. For the
recycle ratio of and a steady-state biomass concentration of X = 5 g/l, calculate the
following:
a. Required reactor volume (V).
b. Biomass concentration in recycle
c. Solids (cells) residence time
d. Hydraulic residence time
e. Determine the daily oxygen requirement.
Use the following kinetic parameters:
value of a waste-water feed stream to an activated-sludge unit is and the effluent is desired to be S = 30 mg/l. The feed flow rate is l/day. For therecycle ratio of
and a steady-state biomass concentration of X = 5 g/l, calculate thefollowing:
a. Required reactor volume (V).
b. Biomass concentration in recycle
c. Solids (cells) residence time
d. Hydraulic residence time
e. Determine the daily oxygen requirement.
Use the following kinetic parameters:
a) Required reactor volume ( V ) 
b) Biomass concentration in recycle ( X r ) 
14.9 g/l
c) Solids (cells) residence time
d) Hydraulic residence time 
e) Determine the daily oxygen requirement. 
b) Biomass concentration in recycle ( X r ) 14.9 g/lc) Solids (cells) residence time
d) Hydraulic residence time e) Determine the daily oxygen requirement. 3
For the activated-sludge unit shown in Fig. 16.7, the specific growth rate of cells is given by The following parameter values are known: F = 500 1/h, substrate.
a. Calculate the substrate concentration (S) in the reactor at steady state.
b. Calculate the cell concentration(s) in the reactor.
c. Calculate Xr and Sr in the recycle stream.
Figure 16.7
The following parameter values are known: F = 500 1/h, substrate. a. Calculate the substrate concentration (S) in the reactor at steady state.
b. Calculate the cell concentration(s) in the reactor.
c. Calculate Xr and Sr in the recycle stream.
Figure 16.7
(a)The value of 
is zero therefore the above expression of biomass material balance equation becomes, 
Substitute tha values and solve, 
Rarrange the ratio and solve, 
Reduced biomass material balance equation (from equation16.35 provided in text book) is expressed as follows, 
The value of the 
is zero, therefore the above expression becomes, 
Rearrange the expression for 
, 
Substitute the value and solve, 
From the question provided in text book, 
Substitute the value and solve for 
, 
Further solve, 
Therefore, substrate concentration 
is 
(b)The expression of the Cell concentartion in the reactor is, 
Now, the is calculated as follow, 
Substitude the values from part (a) and solve, 
Substitute tha values and solve, 
Hence the value of the cell concentration in the reactor is 
(c)
The value of the X r and S r in the recycle stream is calculated as follows,
The ratio
is calculated in part (a) therefore rearrange this to find the value of 
, 
Rearrange for 
and then substitute the value of 
from above and solve, 
Hence the value of 
is 
The value of 
is same as 
, therefore, 
Hence the value of 
is 
is zero therefore the above expression of biomass material balance equation becomes, Substitute tha values and solve, Rarrange the ratio and solve, Reduced biomass material balance equation (from equation16.35 provided in text book) is expressed as follows, The value of the is zero, therefore the above expression becomes, Rearrange the expression for , Substitute the value and solve, From the question provided in text book, Substitute the value and solve for , Further solve, Therefore, substrate concentration is (b)The expression of the Cell concentartion in the reactor is, Now, the is calculated as follow, Substitude the values from part (a) and solve, Substitute tha values and solve, Hence the value of the cell concentration in the reactor is (c)The value of the X r and S r in the recycle stream is calculated as follows,
The ratio
is calculated in part (a) therefore rearrange this to find the value of , Rearrange for and then substitute the value of from above and solve, Hence the value of is The value of is same as , therefore, Hence the value of is 4
In a trickling biological filter, the BOD value of the feed stream is with a feed
flow of F = The effluent BOD value is desired to be = 10 mg/l. The following ki-
netic parameters for the biocatalysts are known: S/l. The
biofilm thickness is L = 0.1 mm. The cross-sectional area of the filter is A = 2 and the biofilm surface area per unit volume of the bed is Assume that dis-
solved oxygen is the rate-limiting substrate and the diffusion coefficient of oxygen is Determine the required height of the bed. You can assume first-order
bioreaction kinetics.
with a feedflow of F =
The effluent BOD value is desired to be = 10 mg/l. The following ki-netic parameters for the biocatalysts are known:
S/l. Thebiofilm thickness is L = 0.1 mm. The cross-sectional area of the filter is A = 2
and the biofilm surface area per unit volume of the bed is Assume that dis-solved oxygen is the rate-limiting substrate and the diffusion coefficient of oxygen is
Determine the required height of the bed. You can assume first-orderbioreaction kinetics.
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An activated-sludge waste treatment system is required to reduce the amount of from
1000 mg/l to 20 mg/l at the exit. The sedimentation unit concentrates biomass by a factor of
3. Kinetic parameters are MLVSS/g The flow of waste water is 10000 l/h and the size of the treatment basin is 50,000 l.
a. What is the value of the solids residence time
b. What value of the recycle ratio must be used?
from1000 mg/l to 20 mg/l at the exit. The sedimentation unit concentrates biomass by a factor of
3. Kinetic parameters are
MLVSS/g The flow of waste water is 10000 l/h and the size of the treatment basin is 50,000 l. a. What is the value of the solids residence time
b. What value of the recycle ratio must be used?
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Consider a well-mixed waste treatment system for a small-scale system. The system is oper-
ated with a reactor of 1000 l and flow rate of 100 l/h. The separator concentrates biomass by
a factor of 2. The recycle ratio is 0.7. The kinetic parameters are What is the exit substrate concentration?
ated with a reactor of 1000 l and flow rate of 100 l/h. The separator concentrates biomass by
a factor of 2. The recycle ratio is 0.7. The kinetic parameters are
What is the exit substrate concentration? Unlock Deck
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Redo Example 16.4 if the Contois equation for growth applies. In this case The values of are the same as for Example 16.4, but no longer applies. Assume MLVSS.
Example 16.4.
An industrial waste with an inlet of 800 mg/l must be treated to reduce the exit level to 20 mg/l. The inlet flow rate is 400 m ³/h. Kinetic parameters have been estimated for waste as A waste treatment unit of 3200 m ³is available. Assume a recycle ratio of 0.40 and If you operate at a value of c 120 h, find S and determine if sufficient removal is attained in a well-mixed activated-sludge process to meet specifications. What will
be X and the sludge production rate from this process?
The values of are the same as for Example 16.4, but no longer applies. Assume MLVSS.Example 16.4.
An industrial waste with an inlet
of 800 mg/l must be treated to reduce the exit level to 20 mg/l. The inlet flow rate is 400 m ³/h. Kinetic parameters have been estimated for waste as A waste treatment unit of 3200 m ³is available. Assume a recycle ratio of 0.40 and If you operate at a value of c 120 h, find S and determine if sufficient removal is attained in a well-mixed activated-sludge process to meet specifications. What willbe X and the sludge production rate from this process?
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A batch fermenter receives 1 l of medium with 5 g/l of glucose, which is the growth-rate-
limiting nutrient for a mixed population of two bacteria (a strain of E. coli and Azotobacter
vinelandii). A. vinelandii is five times larger than E. coli. The replication rates for the two or-
ganisms are: The yield coefficients are: The inoculum for the fermenter is 0.03 g dw/l of E. coli and 0.15 g dw/l of
A. vinelandii cells/ml).
What will be the ratio of A. vinelandii to E. coli at the time when all of the glucose is
consumed?
Example 16.1.
Competition of two species for the same growth-rate-limiting substrate is common. Deter- mine when the two organisms may stably coexist if both A and B follow Monod kinetics.
limiting nutrient for a mixed population of two bacteria (a strain of E. coli and Azotobacter
vinelandii). A. vinelandii is five times larger than E. coli. The replication rates for the two or-
ganisms are:
The yield coefficients are: The inoculum for the fermenter is 0.03 g dw/l of E. coli and 0.15 g dw/l ofA. vinelandii
cells/ml).What will be the ratio of A. vinelandii to E. coli at the time when all of the glucose is
consumed?
Example 16.1.
Competition of two species for the same growth-rate-limiting substrate is common. Deter- mine when the two organisms may stably coexist if both A and B follow Monod kinetics.
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9
Consider Example 16.1, where we demonstrated that two bacteria competing for a single nu-
trient in a chemostat (well-mixed) could not coexist. Consider the situation where B can ad-
here to a surface but A cannot. Redo the balance equations, where is the surface area
available per unit reactor volume and the rate of attachment is first order in with a rate
constant The sites available for attachment will be The attached cells can
detach with a first-order dependence on the attached cell concentration with a rate con-
stant of Attached cells grow with the same kinetics as suspended cells.
a. Without mathematical proofs, do you think coexistence may be possible? Why or
why not?
b. Consider the specific case below and solve the appropriate balance equations for
trient in a chemostat (well-mixed) could not coexist. Consider the situation where B can ad-
here to a surface but A cannot. Redo the balance equations, where
is the surface areaavailable per unit reactor volume and the rate of attachment is first order in
with a rateconstant
The sites available for attachment will be The attached cells candetach with a first-order dependence on the attached cell concentration
with a rate con-stant of
Attached cells grow with the same kinetics as suspended cells. a. Without mathematical proofs, do you think coexistence may be possible? Why or
why not?
b. Consider the specific case below and solve the appropriate balance equations for
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