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$\beta$-Galactosidase bound to DEAE-cellulose is used to hydrolyze lactose to glucose and galactose in a plug flow bioreactor with a packed bed of volume $100$ liters and a voidage ($\epsilon$) of $0.55$. The $K’_m$ and $V’_m$; for the immobilized enzyme are $0.72 \: gl^{-1}$ and $18 \: gl^{-1}h^{-1}$, respectively. The lactose concentration in the field stream is $20 \: gl^{-1}$, and a fractional conversion of $0.90$ is desired. Diffusional limitations may be ignored.

The residence time required for the steady state reactor operation will be

  1. $0.1 \: h$
  2. $0.4 \: h$
  3. $1.0 \: h$
  4. $1.1 \: h$ 
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