You are planning to run a fermenter to produce antibiotics from fungi, using a f

Question

You are planning to run a fermenter to produce antibiotics from fungi, using a fermentation broth that contains 15 wt% glucose, 6 wt% phosphate, 6 wt% nitrate, various trace nutrients, and water. At 8 a.m. the fermentor is filed with 6000mL broth and some antibiotic-producing fungi. Over the course of the fermentation, additional broth is pumped into the fermentor at 200 mL/h. The cells consume glucose at a rate of 35 g/h, phosphates at a rate of 13 g/h, and nitrate at a rate of 12 g/h. The fermentation is stopped when the concentration of one of these three nutrients goes to zero ( because the cells can no longer grow). Which nutrient-glucose, phosphate, or nitrate-will be depleted first? When is the fermentation stopped? What is the concentration (g/L) of the other two nutrients in the fermenter at the end of the run? Assume broth density is 1 g/mL.

Explanation / Answer

6000mL of broth

15% glucose w/v , therefore , 90 g

6% phosphate w/v, therefore, 36 g

6% nitrate w/v, therefore, 36 g

glucose at a rate of 35 g/h, phosphates at a rate of 13 g/h, and nitrate at a rate of 12 g/h Is getting consumed .

Broth is being pumped at the rate of 200mL/hr. Therefore nutrients are being pumped at the rate of

Glucose - 3 g/hr

Phosphate - 1.2 g/hr

Nitrate - 1.2 g/hr

Glucose - 35 g/hr consumption and 3.0 g/hr refilling

This implies - a loss of 32 g/hr of glucose

By this rate , glucose would be depleted in 2.81 hours , consumed at the rate of 32 g/hr.

Nitrates consumption rate - 12 g/hr and filling rate - 1.2 g/hr

Depletion rate - 10.8 g/hr

At this rate , phosphates would be depleted after 3.33 hr at the rate of 10.8 g/hr . 3 hours and 20 minutes.

Phosphates consumption rate - 13 g/hr and filling rate - 1.2 g/hr

Depletion rate - 11.8 g/hr

At this rate , phosphates would be depleted after 3.05 hr at the rate of 11.8 g/hr. 3 hours and 3 minutes.

Glucose will be consumed fastest in 2 hours and 48 minutes. The fermentation stops at 2 hours and 48 minutes as glucose completely gets depleted and becomes zero.

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