You have 30;000 liters of a fermentation beer containing 66 mg/liter of an enzyme used to control coatings in the paper industry. You plan to extract this enzyme with an isoosmotic polyethylene glycol solution which does not dissolve significantly in the beer. The equilibrium for this extraction at the operating level of pH 6.6 is
y = 103x
where y and x are the concentrations in polyethylene glycol and beer, respectively. You plan to extract 99% of this enzyme with staged cross flow (not countercurrent) extraction. In such an extraction, you use pure enzyme-free extractant in each stage. How much extractant should you use to achieve your goal in four stages?