Hydraulics in continuous reactors — A continuous bioreactor has a dilution rate D = 0.5 h^-1. What is its residence time (space time)?

Introduction:
Residence time (also called space time, tau) is a basic hydraulic parameter in continuous reactors. It relates directly to the dilution rate, which is commonly reported in bioprocessing. This question checks your ability to convert between D and tau quickly and correctly.

Given Data / Assumptions:

• Dilution rate D = F / V = 0.5 h^-1.
• Well-mixed reactor at constant volume.
• No cell recycle or volume change.

Concept / Approach:
By definition, residence time tau is the reciprocal of the dilution rate for a simple CSTR without recycle: tau = V / F = 1 / D. Natural logarithms appear in unrelated contexts (e.g., half-life in first-order decay), but not in the basic D–tau identity.

Step-by-Step Solution:
Start with tau = 1 / D.Insert D = 0.5 h^-1.Compute tau = 1 / 0.5 = 2 h.Cross-check units: h^-1 inverted gives hours.

Verification / Alternative check:
Given V and F separately, tau = V / F would yield the same value (e.g., V = 2 L and F = 1 L/h gives tau = 2 h), confirming consistency with 1/D.

Why Other Options Are Wrong:

• (a) and (b) inject ln(2), which is unrelated here.
• (c) 0.5 h corresponds to D = 2 h^-1, not 0.5 h^-1.
• (e) 1/ln(2) h is dimensionally inconsistent with D.

Common Pitfalls:
Confusing half-life t_1/2 = ln(2)/k with residence time; mixing up D with k from first-order reactions.

Final Answer:
2 h