Model Reference / Available Power Comminution

Available Power Comminution

Summary

The Available Power Comminution model is a comminution model that estimates product size distribution from the total available power applied to the feed stream. It calculates the specific energy from available power and feed solids flowrate, estimates a product P80 for each component using a generalized energy-size relationship, and then reconstructs the product PSD with a Rosin-Rammler-like distribution. It should be used when the comminution product size must be calculated from available installed or operating power rather than from a fixed product P80 or a fixed specific energy. The model belongs to the Comminution category and the Energy subcategory.

DPSIM model key: DPSIM.Comminution.AvailablePower
Category: Comminution
Subcategory: Energy
Display name: Available Power

Parameters

#	Parameter	Description
1	Available power(kW)	Total available comminution power. The model divides this value by the feed dry solids flowrate to calculate the specific energy applied to the feed.
2	Model exponent (1.5: Bond, 2.0:Rittinger)	Exponent used in the energy-size relationship. A value of 1.5 represents Bond-type behavior, while 2.0 represents Rittinger-type behavior.
3	[Component] WI(kWh/short ton)	Component-specific Work Index used to calculate the product P80 for each component. One parameter is created for each component in the feed stream.

Model Description

The model represents a comminution unit where the product size is controlled by the available energy. The model preserves the feed solids flowrate and water flowrate in the product stream, while recalculating the product PSD and the component-by-size matrix.

The overall specific energy is calculated from available power and feed solids flowrate:

$E_{g} = \frac{P_{avail}}{S_{f}}$

The mass fraction of each component in the feed is calculated as:

$g_{c} = \frac{M_{c}}{S_{f}}$

The available power assigned to each component is calculated as:

$P_{c} = g_{c}*P_{avail}$

The component specific energy is calculated as:

$E_{g,c} = \frac{P_{c}}{M_{c}}$

The implementation calculates the component energy-size constant as:

$C_{c} = \left( \frac{WI_{c}}{1.102} \right)*10$

The product P80 for each component is calculated using the generalized energy-size relationship:

$d_{80,c} = \left( \frac{C_{c}*F_{80c}^{1 - n} + E_{g,c}}{C_{c}} \right)^{\frac{1}{1 - n}}$

After calculating the component product P80, the model generates a Rosin-Rammler-like passing curve for each component:

$P_{c,i} = B_{c} + \left( 1 - B_{c} \right)\left( 1 - \exp\left( \ln(0.2)\left( \frac{d_{i}}{d_{80,c}} \right)^{s_{c}} \right) \right)$

Where:

Symbol	Description	Unit
$E_{g}$	Overall specific energy calculated by the model	kWh/t
$P_{avail}$	Available comminution power	kW
$S_{f}$	Feed dry solids flowrate	tph
$g_{c}$	Mass fraction of component c in the feed solids	dimensionless
$M_{c}$	Feed mass flowrate of component c	tph
$P_{c}$	Available power assigned to component c	kW
$E_{g,c}$	Specific energy assigned to component c	kWh/t component
$C_{c}$	Component energy-size constant used by the implementation	model unit
$WI_{c}$	Work Index of component c	kWh/short ton
$F_{80}c$	Feed component P80 used by the model	same unit as size mesh
$n$	Energy-size model exponent	dimensionless
$d_{80,c}$	Calculated product P80 for component c	same unit as size mesh
$d_{i}$	Size opening for interval i	same unit as size mesh
$s_{c}$	Rosin-Rammler sharpness parameter for component c	dimensionless
$B_{c}$	Fines or bypass fraction used in the Rosin-Rammler-like curve	fraction
$P_{c,i}$	Cumulative passing fraction of component c at size i	fraction

Derived parameters:

#	Derived parameter	Description
1	Specific energy(kWh/t)	Calculated as available power divided by feed dry solids flowrate.