Scale-up of Pilot Plant Tests of a Reciprocating-Plate Extraction Column

The pilot plant data in Table P6.9 are for the extraction of an antibiotic from whole fermentation broth using the solvent chloroform in a reciprocating-plate extraction column. The concentration of the antibiotic was 1.4 g/liter in the broth. The column had a diameter of 2.54 cm, and the height of the plates was 3.05 m. The partition coefficient K for the antibiotic is known to be 2.68. For each pilot run, determine the diameter and height of the plates for the plant column that would be required for processing 50 000 liters of broth in 12 h to give an exit raffinate concentration of antibiotic of 10 mg/liter, assuming a concentration of antibiotic in the feed broth of 1.0 g/liter (a spreadsheet is convenient for these calculations). Without doing a complete economic analysis, in your judgment which scaled-up pilot run appears to be optimum? (Data from A. E. Karr, W. Gebert, and M. Wang, Can. J. Chem. Eng., vol. 58, p. 249, 1980.)

Run number	Flow rates (mL min1)		Antibiotic concentration in raffinate (mg L1)
	Broth	Chloroform
1	45	135	2
2	67.5	135	3
3	125	135	30
4	80	120	5
5	100	150	7
6	120	180	9
7	150	225	25