Target Product P80 Partition
Summary
Target Product P80 Partition determines a smooth two-product partition curve from the requested P80 of either the coarse or fines product. The user can target the global particle-size distribution or solve an independent curve for each component.
DPSIM model key: DPSIM.Classification.TargetProductP80Partition
Category: Classification
Subcategory: Partition curves
Display name: Target Product P80 Partition
Streams
| Port | Role |
|---|---|
| Feed | Feed solids, water, global PSD and component distributions. |
| Coarse | Coarse product calculated from the resolved partition. |
| Fines | Complementary fines product calculated by difference. |
Curve And P80 Solution
For a coarse-product target, the corrected size term is Y(d) = 1 - exp[-ln(2)(d/d50)n]. For a fines-product target, the complementary term Y(d) = exp[-ln(2)(d/d50)n] is used.
The recovery to the selected product is E(d) = B + (1 - B)Y(d), where B is the lower plateau and n controls sharpness. DPSIM resolves the curve midpoint that minimizes the difference between requested and calculated product P80. Logarithmic sampling is followed by bounded refinement because a nonzero plateau can make the inverse relationship non-monotonic.
The other product is always the exact complement of the selected partition for every component and size class.
Choosing The Target
Select Coarse when the specified P80 belongs to the coarse product and Fines when it belongs to the fines product. This selection changes the direction of the partition curve; it does not merely rename the outlets.
Global PSD mode resolves one partition curve from the total feed PSD and applies it to all component-size masses. Component PSD mode resolves an independent curve for each component and recombines the resulting component masses into the global products. Use component mode only when component-specific product sizes are known or intentionally assumed.
The lower plateau represents material reporting to the selected product at the size extreme where ideal separation would send little material there. For a coarse-product target it behaves like fines bypass to coarse; for a fines-product target it represents coarse misplaced material reporting to fines.
Parameters
| Parameter | Description |
|---|---|
| P80 target product | Select fines or coarse as the parameterized product. |
| P80 target basis | Use one global PSD target or independent component PSD targets. |
| Target product P80 | Requested P80 in micrometers. |
| Partition sharpness | Controls the slope around the solved midpoint. |
| Selected-product lower plateau | Minimum recovery to the selected product at the opposite size extreme. |
| Water recovery to coarse | Fraction of feed water reporting to coarse; remaining water reports to fines. |
Recommended Workflow
- Select the product for which P80 is known.
- Begin with Global PSD unless component-specific product analyses support separate targets.
- Enter the target P80, then adjust sharpness and lower plateau from measured separation behavior when available.
- Run the simulation and review achieved P80, solved midpoint, P80 error and solution status.
Diagnostics And Safeguards
| Status | Meaning |
|---|---|
| 0 | Target achieved within tolerance. |
| 1 | Target is not attainable; nearest bounded solution used. |
| 2 | Selected product has no solids. |
| 3 | Component has no feed mass. |
| 4 | Invalid input or size mesh; safe bounded behavior used. |
Curve recoveries are limited to zero through one. Solids, water and component masses are closed, and an unattainable target does not stop the simulation.
A target may be unattainable when the selected product receives too little solids, the requested P80 lies outside the feed mesh or the lower plateau prevents the requested cumulative passing value. In these cases DPSIM uses the nearest bounded solution and exposes the remaining P80 error instead of violating mass closure.
Application And Limitations
This is an empirical inverse partition model, not a mechanistic representation of a particular classifier. Product P80 alone does not uniquely identify the physical separation response, especially when a lower plateau is present. Calibrate sharpness and plateau against measured partition or product-size data when predictive use is intended.
References
King, R. P. (2001). Modeling and Simulation of Mineral Processing Systems. Butterworth-Heinemann.
Wills, B. A., and Finch, J. A. (2016). Wills' Mineral Processing Technology, 8th ed. Butterworth-Heinemann.
The inverse numerical solution from product P80 is a DPSIM implementation based on standard partition-curve concepts.