1. The
1. The Zymomonas mobilis Zymomonas mobilis cells are used for chemostat culture in a cells are used for chemostat culture in a 60 m60 m33 fermenter. The feed fermenter. The feed contains 12 g l
contains 12 g l-1-1 glucose; K glucose; K ss for the organism is 0.2 g l for the organism is 0.2 g l-1-1. µ. µmm= 0.3 h= 0.3 h-1-1 and Y and Yx/sx/s= 0.06 gdw/g.= 0.06 gdw/g. a.
a. What flow rate is required for a steady-state substrate concentration of 1.5 g lWhat flow rate is required for a steady-state substrate concentration of 1.5 g l -1-1 ? ? b.
b. What is the corresponding steady state cell density and volumetric cell production rate?What is the corresponding steady state cell density and volumetric cell production rate? 1. Consider a continuous, aerobic bacterial
1. Consider a continuous, aerobic bacterial culture in a chemostat with culture in a chemostat with sterile feed. sterile feed. ThreeThree different dilution rates
different dilution rates D D are tested for a glucose are tested for a glucose feed concentrationfeed concentration S S f f = 10 mM, and the biomass = 10 mM, and the biomass concentration
concentration x x and glucose concentration and glucose concentration S S in the exit stream in the exit stream are measured. are measured. The results are The results are asas follows: follows: D D (h (h-- )) x x (g/L) (g/L) S S (mM) (mM) 0.05 0.248 0.067 0.05 0.248 0.067 0.5 0.5 0.208 0.208 1.6671.667 5 5 0 0 1010
a. Estimate the glucose yield coefficient
a. Estimate the glucose yield coefficient Y Y X/S X/S (g biomass/mole glucose). (g biomass/mole glucose).
b. Assuming Monod growth kinetics, estimate the maximum specific growth rat
b. Assuming Monod growth kinetics, estimate the maximum specific growth rate μe μmaxmax (h (h-1-1) and) and the Monod constant
the Monod constant K K S S (mM). (mM). Ans.
Ans. i.
i. Between Between time time t t = = 0.05 0.05 to to 0.050.05
11..66 00..020255 04 04 .. 0 0 06 0677 .. 0 0 66 6677 .. 1 1 24 2488 .. 0 0 20 2088 .. 0 0 //
S S X X S S X X C C C C Y Y Between time t = 0.5 to 5 Between time t = 0.5 to 5
88..333333 00..020255 20 2088 .. 0 0 66 6677 .. 1 1 10 10 20 2088 .. 0 0 0 0 .. 0 0 //
S S X X S S X X C C C C Y Y ii.ii. Monod chemostat Monod chemostat model model equationequation
0
0
ma ma xx
f f s sDx
Dx
x
x
D
D
s
s
K
K
s
s
For sterile feed
D
DK
s
Y
x
s f S X m ax / feed sterile andD
DK
s
s
m ax feed sterile (any of this two equation could be use to solve the problem) D = At 0.05 h-1 05 . 0 K 0.05 0.067 ma x s (1) At 0.5 h-1 5 . 0 μ K 0.5 1.667 MAX S
(2)Solve equation (1) and (2) to get MAX (= 0.802) and K S (=1.007)
3. Consider a culture of bacteria making a valuable product in a chemostat operated at steady state. The liquid feed is sterile and contains 50 mM glucose (the limiting growth substrate S ). In a series of steady state runs, the dilution rate D is increased incrementally, and the cell density exiting the chemostat is measured for each:
D (h-1) x (g/L) 0.05 1.58 0.10 2.17 0.15 2.47 0.20 2.65 0.25 2.76 0.30 2.83 0.35 2.86 0.40 2.84 0.45 2.74 0.50 2.25 0.52 1.32 0.53 0
a. Explain why the cell density can increase as the flow rate is increased, as shown here with D < 0.35 h-1.
b. At what dilution rate should you operate the chemostat to optimize productivity of a strictly growth-associated product? Explain the basis for your answer.
c. At what dilution rate should you operate the chemostat to optimize productivity of a strictly non-growth-associated product? Explain the basis for your answer.
4. Consider cell growth in a chemostat at steady state, with sterile feed. In bench-scale
experiments, it is found that the specific growth rate is inhibited at high glucose concentrations S , modeled according to the phenomenological expression
μ (h-1) = 0.6S /(0.2 + S + 0.1S 2), with S in g/L.
a. If the glucose concentration in the feed is 10 g/L, estimate the minimum dilution rate at which cell washout would occur.
b. Is the dilution rate estimated in part a the highest that will support cell growth in the bioreactor? Justify and briefly explain your answer.
5. A new strain of yeast is being considered for biomass production. The following data were obtained using a chemostat. An influent substrate concentration of 800 mg/l and an excess of oxygen were used at a pH of 5.5 and T = 350C. Using the following data, calculate µm, K s, YX/SM, k d and ms assuming µnet=µmS/(K s + S)- k d.
Dilution rate (h-1) Carbon substrate concentration (mg/l) Cell concentration (mg/l) 0.1 16.7 366 0.2 33.5 407 0.3 59.4 408 0.4 101 404 0.5 169 371 0.6 298 299 0.7 702 59
6. The specific growth rate for unlimited growth in a chemostat is given by the following equation:
where S0 = 10 g/l K s= 1 g/l I= 0.05 g/l YX/SM= 0.1 g cells/g subs X0=0 K I=0.01 g/l µm= 0.5 h-1 k d=0
a. Determine X and S as a function of D when I=0.
b. With inhibitor added to a chemostat, determine the effluent substrate concentration and X as a function of D.
c. Determine the cell productivity, DX, as a function of dilution rate.
7. Pseudomonas sp. has a mass doubling time of 2.4 h when grown on acetate. The saturation
constant using this substrate is 1.3 g /l (which is unusually high), and cell yield on acetate is g
gcell / 46
.
0 acetate. If we operate a chemostat on a feed stream containing 38 g/l acetate, find the following:
a. Cell concentration when the dilution rate is one-half of the maximum b. Substrate concentration when the dilution rate is 0 D.8 max
c. Maximum dilution rate
d. Cell productivity at 0.8 Dmax
8. Under substrate-limited conditions, a microorganism exhibits the following net specific growth rate, μnet, and yield coefficient, Y X/S :
μnet (h-1) = 0.70 S /(0.1 + S ), with S in g/L; Y X/S (g DCW/g) = 0.40
The available growth medium contains 10 g/L substrate.
a. When a batch bioreactor containing 100 L of the growth medium is inoculated with 1.0 g DCW of biomass, estimate the maximum cell density achieved, and the approximate time required to achieve it, after exponential growth is initiated.
b. You decide instead to culture the microorganism in a chemostat, using the same growth
medium as the (sterile) feed. Estimate the dilution rate (h-1) at which the chemostat will achieve maximum steady-state productivity of biomass.
c. Calculate and compare the overall biomass productivities (g DCW/L/h) of the two scenarios in parts a & b. What other consideration will make the batch process even less productive
8. The following data are obtained in oxidation of pesticides present in wastewater by a mixed culture of microorganisms in a continuously operating aeration tank .
S.No. ( 1) h D S ( Pesticides),mg /l X (mg /l ) 1. 0.05 15 162 2. 0.11 25 210 3. 0.24 50 250 4. 0.39 100 235 5. 0.52 140 220 6. 0.7 180 205 7. 0.82 240 170
Assuming the pesticide concentration in the feed wastewater stream as S 0 500 mg/L, determine Y X M /S ,k d , m,and K s.
