Bimodal Rosin-Rammler Comminution
Bimodal Rosin-Rammler Comminution constructs an empirical product size distribution from two particle populations with a shared D80 and independent shape exponents. It is suited to measured comminution products that are not represented adequately by one Rosin-Rammler curve.
DPSIM model key: DPSIM.Comminution.BimodalRosinRammler
Category: Comminution
Subcategory: Product size
Display name: Bimodal Rosin-Rammler 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 bimodal parameterized PSD. |
Model description
The cumulative passing fraction is the weighted sum of two Rosin-Rammler populations:
P(d) = w[1-exp(ln(0.2)(d/D80)^nf)] + (1-w)[1-exp(ln(0.2)(d/D80)^nc)]
Both populations have the same D80, so the combined curve also has 80% passing at the specified size. The fine-population share and the two exponents control the shape of the product curve.
Mass balance and components
The model preserves feed solids, water and the total mass of every component. In global mode, the requested product mass in each size class is imposed exactly and the size-by-component matrix is balanced against the feed component totals. Feed composition by size guides the allocation, so components do not receive identical curves unless their feed distributions are already identical.
The model does not transfer solids to coarser size classes. If a requested global or component curve is coarser than the feed, it is limited to the available cumulative retained mass and the correction is reported.
In component mode, D80, population share and both shape exponents can be specified separately for each component. The global product PSD is then obtained by recombining the closed component masses.
Parameters
- Curve basis: selects a global curve or separate component curves.
- Product D80: common 80% passing size.
- Fine population mass share: weight of the fine particle population.
- Fine and coarse shape exponents: control the curvature of both populations.
- Feed size-component association retained: controls how strongly global mode retains feed grade variation by size.
At 0% association, the initial component allocation in every size uses the overall feed grade. At 100%, it follows the observed feed composition of each feed size class. Intermediate values blend both. The balancing step still closes the requested global PSD and every component total.
When To Use The Bimodal Form
Use this model when a single Rosin-Rammler curve leaves a systematic shoulder or two-slope pattern in measured cumulative passing data. The fine-population share controls the contribution of the first population, while the two exponents control their spreads. If the fitted exponents are similar or the population share approaches 0% or 100%, the response approaches a single-population curve.
Recommended Workflow And Diagnostics
- Fit or estimate D80 and the two shape exponents from measured product PSD data.
- Adjust the fine-population share to reproduce the shoulder between fine and coarse regions.
- Use Component PSDs only when component-specific size measurements support separate curves.
- After simulation, review Achieved product D80, Coarsening correction applied and both mass-closure errors.
Limitations
This is a calibrated product-curve model. It does not calculate equipment power, residence time or geometry. The target curve must be selected from process data or an appropriate engineering assumption.
Reference
Rosin, P. and Rammler, E. (1933). The laws governing the fineness of powdered coal. Journal of the Institute of Fuel, 7, 29-36.