Filtration scale-up — A leaf test shows a filtration rate of 100 dry lb/(ft^2·hr) for a protein product. What effective production filter area is required to obtain 100 dry lb of cake per hour?

Introduction:
Leaf test results are routinely used to size production filters in bioprocessing. The fundamental idea is simple scale-up by specific throughput: if a laboratory or pilot test provides a filtration rate per unit area, the required production area follows by proportionality.

Given Data / Assumptions:

• Measured filtration rate r = 100 dry lb/(ft^2·hr).
• Target cake production rate R = 100 dry lb/hr.
• Comparable cake properties and operating conditions between test and production.
• No significant scale-dependent limitations (e.g., channeling, extreme compressibility) beyond what the test captured.

Concept / Approach:
For constant specific throughput, required area A is determined by a direct ratio: A = R / r. When the cake and operating regime are similar, this linear scale-up is standard practice for first-pass sizing, later refined by safety factors and utility constraints.

Step-by-Step Solution:
Identify the relationship: A = R / r.Insert values: A = 100 lb/hr / 100 lb/(ft^2·hr).Compute: A = 1.00 ft^2.Interpretation: A one square foot effective filtration area will deliver the desired cake mass rate under similar conditions.

Verification / Alternative check:
If a safety factor is desired (e.g., 20 to 50 percent) to account for variability in feed solids, cake compressibility, or operator downtime, multiply A by that factor for installed area. The base computation remains A = R / r = 1.00 ft^2.

Why Other Options Are Wrong:

• 0.75 ft^2: Underestimates the needed area and would fail to reach 100 lb/hr at the stated rate.
• 1.54 and 3.08 ft^2: Excess area relative to the given rate; not required by the calculation.
• 6.50 ft^2: Significantly oversized without justification.

Common Pitfalls:
Confusing filter medium area with housing footprint; neglecting cake compressibility effects that can reduce rate; ignoring that filtrate rate and cake rate must be referenced to the same basis and steady-state conditions.

Final Answer:
1.00 ft^2