Rosin-Rammler Product Comminution
Rosin-Rammler Product Comminution constructs an empirical comminution product size distribution from product D80, a Rosin-Rammler shape exponent and a fine-size passing plateau.
DPSIM model key: DPSIM.Comminution.RosinRammlerProduct
Category: Comminution
Subcategory: Product size
Display name: Rosin-Rammler Product Comminution
Streams
| Port | Role |
|---|---|
| Feed | Feed solids, water, PSD and component-by-size composition. |
| Product | Product with unchanged total solids, water and component masses and a parameterized PSD. |
Model formulation
The cumulative passing fraction is calculated as:
P(d) = L + (1-L)[1-exp(-k(d/D80)^n)], with k = ln((1-L)/0.2).
This normalization ensures that 80% passes at the specified D80 even when the fine-size passing plateau is nonzero.
Curve parameters
| Parameter | Meaning |
|---|---|
| Product D80 | Size at which 80% of the product passes. |
| Rosin-Rammler shape exponent | Controls the slope and spread of the product size distribution. |
| Fine-size passing plateau | Lower asymptote representing a persistent ultrafine population. |
Components and mass balance
Global PSD mode applies one curve to the total product. DPSIM balances the size-component matrix so that every size total follows the requested PSD while every component retains its feed mass.
Component PSDs mode uses an individual D80, exponent and plateau for every component. The global product PSD is obtained by recombining the closed component masses.
In global mode, Feed size-component association retained controls the initial allocation used by the balancing calculation. At 0%, each size starts from the overall feed grade; at 100%, it starts from the observed feed composition in that size class. Intermediate values blend both descriptions. This parameter influences the component PSDs but never changes the requested global PSD or component totals.
As a comminution model, it does not permit material to move to coarser size classes. Requests that are coarser than the feed are limited to the physically available feed mass and identified in the calculated diagnostics.
Feed solids and water are preserved. The model does not calculate energy demand or equipment capacity.
Recommended Workflow And Diagnostics
- Use Global PSD when only the total product PSD is known; use Component PSDs only when component-specific size data are available.
- Enter D80, exponent and plateau and run the static simulation.
- Compare Achieved product D80 with the requested value.
- Check Coarsening correction applied. A value of 1 means the target required material to become coarser and DPSIM limited it to a valid comminution product.
- Confirm that solids and maximum component closure errors remain negligible.
Reference
Rosin, P. and Rammler, E. (1933). The laws governing the fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36.