An immobilized enzyme reactor must have the enzyme...

An immobilized enzyme reactor must have the enzyme regenerated periodically because of the decay in the activity of the enzyme. The enzyme will convert $87 \%$ of the substrate to product within the first day of operation, and this conversion changes to $0.87 /(t)^{0.82}$ after the first day. If the feed rate is $150 \mathrm{lb}$ of substrate per day, the amount of product formed after $\mathrm{t}$ days of operation

Key Concepts

Immobilized Enzyme Reactor

An immobilized enzyme reactor is a system where enzymes are attached to a solid support, allowing the substrate to flow through and react. This type of reactor benefits from enhanced enzyme stability, ease of separation, and continuous operational schemes, but it also faces challenges such as enzyme decay or deactivation over time which necessitates periodic regeneration.

Enzyme Activity Decay

Enzyme activity decay refers to the loss of catalytic efficiency as the enzyme ages or becomes deactivated during operation. In this context, the enzyme’s ability to convert the substrate into product decreases over time, following a specified decay function after the initial period. Understanding this decay is crucial for modeling reactor performance and scheduling enzyme regeneration.

Reaction Conversion Rate

The reaction conversion rate represents the fraction of substrate that is transformed into product. Initially, a high conversion rate is observed, which then decreases over time according to a mathematical decay relationship. This rate is central to comparing the instantaneous and cumulative production over the reactor's operational period.

Feed Rate

The feed rate is the amount of substrate introduced into the reactor per unit time. It directly influences the overall production capacity of the reactor by determining the quantity of substrate available for conversion. In continuous processes, the constant feed rate must be integrated over time while accounting for enzyme activity decay to predict total product yield.

Integration Over Time

Integration over time is a mathematical process used to accumulate the total amount of product formed in the reactor over a given period. By integrating the product of the feed rate and the time-dependent conversion function, engineers can quantify the cumulative yield, which is essential for reactor design and performance evaluation.

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