Work index consistency across circuits: if Wi is determined in closed-circuit grinding, what is the effective work index to use for comparable open-circuit grinding conditions?

Introduction / Context:
Bond's Work Index (Wi) characterizes material grindability. While Wi is a material property, practical circuit performance differs between open and closed circuit operation due to classification efficiency and overgrinding. Empirical correction factors are therefore used to translate laboratory Wi to plant power estimates for specific flowsheets.

Given Data / Assumptions:

• Wi was measured under closed-circuit conditions.
• We seek an equivalent for open-circuit grinding to the same product size range.
• Standard Bond practice recognizes open circuit typically requires more energy for the same size reduction target.

Concept / Approach:
Open-circuit grinding lacks the classification feedback loop, so fines remain in the mill longer, reducing breakage efficiency. A widely used translation is that open-circuit power demand is about 1.34 times that of closed circuit for the same P80, which maps to an “effective” Wi_open = 1.34 * Wi_closed for preliminary estimates.

Step-by-Step Solution:
Identify circuit type difference (open vs. closed).Recall empirical relationship: P_open ≈ 1.34 * P_closed.Translate to Wi scaling: Wi_open ≈ 1.34 * Wi_closed = 1.34 Wi.

Verification / Alternative check:
Plant benchmarking often shows substantial energy savings when converting open to closed circuits, which is consistent with the factor near 1.34 used in preliminary design and feasibility studies.

Why Other Options Are Wrong:
Wi or 0.5 Wi: underestimate open-circuit energy.3.34 Wi: overstates the difference far beyond typical observations.

Common Pitfalls:
Applying the factor blindly without considering classification efficiency, circulating load limits, or drastic changes in target fineness that can alter the effective factor.

Final Answer:
1.34 Wi