CBEN460Fall2017 ‐1‐ October18,2017

Homework #6 Fromtheprimarytextbook(Shuler,et.al.3rded.),problems10.2,10.5,10.8.

 

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GARCIA-OCHEA, F., AND E. GoMEZ, " Bioreactor Scale Up and Oxygen Transfer Rate in Microbial Processes: An Overview," Biotechnology Advances 27: 153- 176, 2009.

JosT, J. , "Selected Bioengineering Problems in Stirred-Tank Fermenters," in S. L. Sandler and B. A. Finlayson, eds., Chemical Engineering Education in a Changing En vironment, Engineering Foundation, New York, 1988.

JUNKER, B. H ., M . STANIK, C. BARNA, P. SALMON, E . PAUL, AND B. C. Bu cKLAND, "Influence of Impeller Type on Power Input in Fermentation Vessels," Bioprocess Eng. 18: 401-412, 1998.

KARGI, F., AND M . Moo-YouNG, "Transport Phenomena in Bioprocesses," in Comprehen­sive Biotechnology, Vol. 2, M . Moo-Young, ed ., Pergamon Press, Oxford, UK, 1985, pp. 5- 55.

KIM, B. J ., J . DIAO, AND M . L. SHULER, "Mini-scale Bioprocessing Systems for Highly Parallel Animal Cell Cultures," Biotechnol. Progr. 28: 595- 607, 2012.

KLUTZ, S., J. MAGNUS, M . LOBEDANN, P. SCHAWN, B. MAISER, J . NIKLAS, M . TEMMING, AND G . SCHEMBECKER, "Developing the Biofacility of the F uture Based on Continuous Processing and Single-Use Technology," J. Biotechnol. 213: 120-130, 2015.

KOMIVES, C. , AND R. S. PARKER, "Bioreactor State Estimation and Control," Curr. Opin. Biotechnol. 14: 468-474, 2003 .

LoFFELHOLZ, C. , S. C. KAISER, M. KRAUME, R. EIBL, AND D . EIBL, "Dynamic Single-use Bioreactors Used in Modern Liter and m3-scale Biotechnological Processes: Engineering Characteristics and Scaling Up," Adv. Biochem. Eng./Biotechnol. 138: 1-44, 2014.

POHLSCHEIDT, M. , S. CHARANIYA, C. BORK, M . JENZSCH, T. NOETZEL, AND A. LUEBBERT, "Bioprocess and Fermentation Monitoring," Chapter 69, pp. 1471- 1491, in Upstream Industrial Biotechnology: Equipment, Process Design, Sensing, Control, and cGMP Opera­tions, Vol. 2, M. C. Flickenger, ed ., 2013.

RAMEEZ, S. , S. S. MosTAFA, C. MILLER, AND A. SHUKLA, " High-Throughput Miniaturized Bioreactors for Cell Culture Process Development; Reproducibility, Scalability and Con­trol," Biotechnol. Progr. 30: 718- 727, 2014.

PR OBLEM S

10.1. The air supply to a fermenter was turned off for a short period of time and then restarted. A value for C* of 7.3 mg/1 has been determined for the operating conditions. Use the tabulated measurements of dissolved oxygen (DO) values in the following table to estimate the oxygen uptake rate and kLa in this system.

Selection, Scale-Up, Operation, and Control of Bioreactors Chap. 10

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Time (min) DO (mg/1)

- I 3.3 Air off 0 3.3

2.4 2 1.3 3 0.3 4 0.1 5 0.0

Air on 6 0.0 7 0.3 8 1.0 9 1.6 10 2.0 II 2.4 12 2.7 13 2.9 14 3.0 15 3.1 16 3.2 17 3.2

10.2. A value of kLa = 30 h-1 has been determined for a fermenter at its maximum practical agitator rotational speed and with air being sparged at 0.5 I gas/1 reactor volume-min. E. coli with a q0 , of I 0 mmol 0 2/g-dry wt-h are to be cultured. The critical dissolved oxygen concentration is 0.2 mg/1. The solubility of oxygen from air in the fermentation broth is 7.3 mg/1 at 30°C. a. What maximum concentration of E. coli can be sustained in this fermenter under

aerobic conditions? b. What concentration could be maintained if pure oxygen was used to sparge the

reactor?

10.3. You are asked to design the temperature control system for a large fermenter. a. Estimate the required cooling-water flow rate for a 100,000 I fermenter with an 80,000

1 working volume when the rate of oxygen consumption is 100 mmol 0 2 /1 -h. The desired operating temperature is 35°C. A cooling coil is to be used. The minimum allowable temperature differential between the cooling water and the broth is soc. Cooling water is available at l5°C. The heat capacities of the broth and the cooling water are roughly equal.

b. Estimate the required length of cooling coil if the coil has a 2.5-cm diameter and the overall heat transfer coefficient is 1420 J/s-m2

-0 C.

10.4. A lethal agent (KCN) was added to the fermentation medium in the presence of aeration using diffusors. Dissolved oxygen (DO) concentration increased with time as follows when N = 100 rev/min:

t (min) DO(mg/L)

0 I 1.93

2 2.7

3 3.36

5 4.4

7 5.1

8 10 5.4 5.9

Saturation DO concentration in the fermentation medium is 7.0 mg/L. a. Determine oxygen transfer coefficient kLa. b. Determine k La when Ni is increased to 200 rev/min .

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10.5. A laboratory-scale stirred-tank fermenter of volume 5 I (Do/H = 112) is to be scaled up to 500 I by using the following criteria: DilDo = 1/3, N = 100 rev/min. Determine the size of the fermenter, impeller diameter and speed for each case: a. Constant oxygen transfer rate b. Constant power/volume c. Constant impeller tip speed d. Constant mixing time

10.6. Consider Example 10.4. What would be the substrate concentrations in each com­partment in the 10 I and 10,000 I tanks if the probe were placed in the bottom compartment?

10.7. Consider the 10 I and 10,000 I tanks described in Example 10.4. Suppose that fully continuous operation is to be used, Fwas fixed at 5 mg/1-s for both tanks, and D = 0.2 h-1

for each tank with fluid removal from the top. What fraction of the inlet substrate would be consumed in each tank? If the biomass yield coefficient were 0.5 g cells/g substrate and YPtx = 0.1 g product/g cells, what would be the effect on volumetric productivity upon scale-up?

10.8. A continuous culture system is being constructed. The fermentation tank is to be 50,000 I in size, and the residence time is to be 2 h. A continuous sterilizer is to be used. The unsterilized medium contains l04 spores/l. The value of k" has been determined to be I min-1 at 121°C and 61 min-1 at 140°C. For each temperature (121°C and 140°C), deter­mine the required residence time in the holding section so as to ensure that 99% of the time 4 weeks of continuous operation can be obtained without contamination (due to contaminants in the liquid medium).

10.9. Discuss the effects of mixing on sterilization in a batch fermenter.

10.10. A medium containing a vitamin is to be sterilized. Assume that the number of spores ini­tially present is 105 /1. The values of the pre-Arrhenius constant and £ 0" for the spores are

E0" = 65 kcal/g-mol

For the inactivation of the vitamin, the values of E0" and a are

E0" = 10 kcal/g-mol

The initial concentration of the vitamin is 30 mg/1. Compare the amount of active vita­min in the sterilized medium for 10 I and 10,000 I fermenters when both are sterilized at 121°C when we require in both cases that the probability of an unsuccessful fermenta­tion be 0.001. Ignore the effects of the heat-up and cool-down periods.

10.11. Consider the data given in the following table on the temperature changes in a 10,000 I fermenter, which includes the heat-up and cool-down periods. Use the values for the Arrhenius parameters given in Problem 10.8 and assume an initial spore concentration of 105 II and a vitamin concentration of 30 mg/1.

Selection, Scale-Up, Operation, and Control of Bioreactors Chap. 10

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Time(min) Temperature (0 C)

0 30 10 40 20 54 30 70 40 95 50 121 55 121 60 121 65 106 70 98 90 75

100 64 120 46 140 32

a. What is the probability of a successful sterilization? b. What fraction of the vitamin remains undegraded? c. What fraction of the vitamin is degraded in the sterilization period? d. What fraction of the vitamin is degraded in the heat-up and cool-down periods? e: What is the fraction of spores deactivated in the heat-up and cool-down cycles?

10.12. E. coli has a maximum respiration rate, qo,max, of about 240 mg Oi g-dry wt-h . It is desired to achieve a cell mass of 20 g dry wt/1. The kLa is 120 h-1 in a 1000 I reactor (800 I working volume). A gas stream enriched in oxygen is used (i.e., 80% 0 2 ), which gives a value of C* = 28 mg/L. If oxygen becomes limiting, growth and respiration slow; following is an example:

qo, = 0.2 mg/1 +CL max

Here CL is the dissolved oxygen concentration in the fermenter. What is CL when the cell mass is at 20 g/1?

10.13. The temperature history of the heating and cooling of a 40,000 I tank during ster­ilization of medium follows: 0 to 15 min, T = 85°C; 15 to 40 min, T = 12!°C; 40 to 50 min, T = 85°C; 50 to 60 min, T = 55°C; > 60 min, T = 30°C. The medium contains vitamins, the most fragile of the vitamins has an activation energy for destruction of 10 kcal/g-mol, and the value of a (see equation 10.18) is 1 · 104 min-' . Assume vitamin destruction is first order and the initial concentration is 50 mg/1. R is 1.99 cal/g-mol-K. The medium contains 2.5 ·103 spores/l. The spores have an £ 0" = 65 kcal/g-mol, and k" at

10.14.

10.15.

Problems

121°C is 1.02 min-'. Estimate the probability of a successful sterilization. What fraction of the vitamin remains active?

Estimate kLa from Figure 10.5 if C* is 35 mg/1 due to the use of nearly pure oxygen rather than air.

In cultivation of baker's yeast in a stirred and aerated tank, lethal agents are added to the fermentation medium to kill the organisms immediately. Increase in dissolved oxy­gen (DO) concentration upon addition of lethal agents is followed with the aid of a DO analyzer and a recorder. Using the following data, determine the oxygen transfer coef-ficient (kLa) for the reactor. Saturation DO concentration is C* = 9 mg/1.

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Time (min) DO (mg/1)

2 3 2.5 4 3 5 4 6.5 5 7.2

10.16. A stirred-tank reactor is to be scaled down from I 0 m3 to 0.1 m3. The dimensions of the

large tank are D1 =2m; D,. = 0.5 m; N = 100 rpm. a. Determine the dimensions of the small tank (D1, D,., H) by using geometric similarity. b. What would be the required rotational speed of the impeller in the small tank if the

following criteria were used? bl. Constant tip speed b2. Constant impeller Re number

10.17. An autoclave malfunctions, and the temperature reaches only 119.5°C. The sterilization time at the maximum temperature was 20 min. The jar contains I 0 I of complex medium that has 105 spores/!. At 12l°C, kd = 1.0 min- 1 and Eod = 90 kcal/g-mol. What is the probability that the medium was sterile?

10.18. You are asked to design a continuous sterilizer to produce 330,000 Lid of sterile media. The system must operate for 30 days with the probability of failure to be 0.001. The initial concentration of spores in the medium is 104/1. The value of kd is 1 min- 1 at 121 °C and 60 min- 1 at 140°C. a. Estimate the residence time in the sterilizer at 121 °C necessary to achieve the desired

probability of success. b. Estimate the residence time required at 140°C. c. What is the ratio of residence times for high-temperature, short-time sterilization to

operation at 121 oc?

10.19. One hundred tubes are to be sterilized. Each tube contains 10 mL of fluid. The value of kd = 0.6 min- 1• The tubes are sterilized for 20 min. Ten of the tubes showed growth of contaminants. What was the concentration of spores in the tubes?

Selection, Scale-Up, Operation, and Control of Bioreactors Chap. 10