$\beta$-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 feed flow rate required for the above bioconversion will be
- $50 \: lh^{-1}$
- $55 \: lh^{-1}$
- $137 \: lh^{-1}$
- $550 \: lh^{-1}$