**Yield calculations.**

You are trying to decide between using a bacterium and a yeast for your fermentation, so you decide to use your bioprocess engineering know-how to make some estimates. Assuming the following overall biomass reactions and an equal respiratory quotient (RQ) of 0.5 for both organisms, which organism will most efficiently use its substrate to create biomass? Calculate yield coefficients (in terms of ** mass**) to justify your answer. Assume MW

_{substrate}= 180.

Bacterium (MW_{biomass} = 25.5):

Yeast (MW_{biomass} = 24)

**Fed-batch**

Penicillin is produced by P. chrysogenum in a fed-batch culture with the intermittent addition of glucose solution to the culture medium. The intial culture violume at quasi-steady state is Vo=500 L and glucose containing nutrient solution is added with a flow rate of F=50 L/h. Glucose concentration is the feed solution and initial cell concentrations are So=300 g/L and Xo=20g/L, respectively. The kinetic and yield coefficients of the organism are *u _{m }*= 0.2 h

^{-1}, Ks=0.5g/L, and Y

_{x/s}=0.3g dw/g glucose.

- Determine the culture volume at t=10 h.
- Determine the concentration of glucose at t=10 h at quasi-steady state.
- Determine the concentration and total amount of cells at quasi-steady state when t = 10h.
- If q
_{P}= 0.05 g product /g cells h and Po=0.1g/L, determine the product concentration in the vessel at t= 10 h. **Sterilization of Liquids**

An autoclave malfunctions, and the temperature reaches only 119.5°C. The sterilization time at the maximum temperature was 20 min. The jar contains 10 l of complex medium that has 10^{5} spores/l. At 121°C *k _{d }*= 1.0 min

^{-1}and

*E*= 90 kcal/g-mol. What is the probability that the medium was sterile?

_{0d}**Centrifuge**

Yeast cells are recovered from a fermentation broth by using a tubular centrifuge. Sixty percent (60%) of the cells are recovered at a flow rate of 12 l/min with a rotational speed of 4000 rpm. Recovery is inversely proportional to flow rate.

- To increase the recovery of cells to 95% at the same flow rate, what should be the rpm of the centrifuge?

- At a constant rpm of 4000 rpm, what should be the flow rate to result in 95% cell recovery?
**Chromatography**

Consider the use of gel chromatography to separate two proteins A and B. The partition coefficient (*K _{D}*) for A is 0.5 and for B is 0.15.

*V*, the void volume in the column, is 20 cm

_{o}^{3}.

*V*, the void volume within the gel particles, is 30 cm

_{i}^{3}. The total volume of the column is 60 cm

^{3}. The flow rate of elutant is 100 cm

^{3}/h. Ignoring dispersion and other effects, how long will it take for A to exit the column? How long for B?

**Scale-down**

A stirred-tank reactor is to be scaled down from 10 m^{3} to 0.1 m^{3}. The dimensions of the large tank are: D_{t} = 2 m; D_{i }= 0.5 m; N= 100 rpm.

- Determine the dimensions of the small tank (D
_{t}, D_{i}, H) by using geometric similarity - What would be the required rotational speed of the impeller in the small tank if the following criteria were used?

- Constant tip speed
- Constant impeller Re number

- 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
*coli*and*Azotobacter vinelandii*).*A. vinelandii*is five times larger than E. coli. The replication rates for the two organisms are:

The inoculum for the fermenter is 0.03 g dw/l of E. coli (1e8 cells/ml) and 0.15 g dw/l of *A. vinelandii* (1e8 cells/ml). What will be the ratio of *A. vinelandii* to *E. coli* at the time when all of the glucose isconsumed?

- Please discuss the Weaknesses and potential challenges in the following proposal (true case study from a DoE funded project):

Dr. ABC proposes the development of a process enabling sustainable production of biodiesel fuel from a one carbon CH_{4} (methane) feedstock using an engineered microbial catalyst. The process is enabled by a novel microbial host (Methylotroph) for biological C1 utilization. Dr. ABC has shown in his preliminary studies, via synthetic biology and protein engineering tools, the host pathways (methane uptake and fatty acid synthesis) can be enhanced and the cell can accumulate lipid >50% of total biomass under Nitrogen limited condition. Based on the preliminary results in his laboratory, Dr. ABC wants to commercialize this technology so that natural gas (shale gas/biogas) can be directly convert into transport fuels using the engineered microbes. He claims his technology offers a new mode of chemical production based on small-scale, low capital intensity, distributed biological processes, which can significantly reduce greenhouse gas emissions and gasoline prices. He said his work has the potential to disrupt the conventional chemical industry paradigm of high capital expense, large-scale, centralized processes.