Model Reference / Vendor Known Product Crusher

Vendor Known Product Crusher

Summary

The Vendor Known Product Crusher model is an empirical crusher model that imposes a user-defined product size distribution on the crusher product stream. The model should be used when the crusher product PSD is known from vendor data, plant survey data, laboratory testwork, or a previously calibrated product curve.

The model does not predict breakage from crusher geometry or operating conditions. Instead, it normalizes the user-defined retained percentages and applies the resulting retained size distribution directly to the product stream.

DPSIM model key: DPSIM.Comminution.VendorKnownProductCrusher
Category: Comminution
Subcategory: Crushers
Display name: Vendor Known Product Crusher

Parameters

#	Parameter	Description
1	Product retained at [size] µm (%)	User-defined retained mass percentage assigned to each DPSIM size interval. One parameter is created for each size interval in the project size mesh. The values are normalized internally, so they do not need to sum exactly 100%. Negative values are treated as zero.

Derived parameters

#	Derived parameter	Description
1	Product P80 (µm)	Calculated P80 of the product stream after applying the normalized product size distribution.

Model Description

The model receives one feed stream and generates one product stream. The feed solids flowrate and water flowrate are preserved. The product size distribution is imposed from the user-defined retained percentages.

For each size interval $i$ , the user-defined retained percentage is first limited to non-negative values:

$r_{i}^{*} = \max\left( 0,R_{i} \right)$

The sum of the retained values is calculated as:

$R_{T} = sum_{i = 1}^{n}r_{i}^{*}$

If $R_{T}$ is greater than zero, the normalized retained fraction in each size interval is:

$p_{i} = \frac{r_{i}^{*}}{R_{T}}$

If $R_{T}$ is zero or negative, the model assigns all retained mass to the last size interval:

$p_{i} = 0,\ i < n$

$p_{n} = 1$

The product retained mass in each size interval is then calculated as:

$m_{i}^{P} = p_{i}M_{S}^{F}$

Where:

Symbol	Description	Unit
$R_{i}$	User-defined retained percentage for size interval i.	%
$r_{i}^{*}$	Non-negative retained value used internally by the model.	%
$R_{T}$	Sum of all non-negative retained values.	%
$p_{i}$	Normalized retained fraction in size interval i.	fraction
$m_{i}^{P}$	Product solids mass flowrate retained in size interval i.	tph
$M_{S}^{F}$	Feed dry solids flowrate.	tph
$n$	Number of size intervals.	dimensionless

The product solids and water flowrates are preserved from the feed:

$M_{S}^{P} = M_{S}^{F}$

$M_{W}^{P} = M_{W}^{F}$

Where:

Symbol	Description	Unit
$M_{S}^{P}$	Product dry solids flowrate.	tph
$M_{S}^{F}$	Feed dry solids flowrate.	tph
$M_{W}^{P}$	Product water flowrate.	tph
$M_{W}^{F}$	Feed water flowrate.	tph

The component distribution is calculated from the global component mass fractions in the feed. For each component c:

$g_{c} = \frac{M_{c}^{F}}{M_{S}^{F}}$

The same component fraction is assigned to every product size interval:

$z_{c,i}^{P} = g_{c}$

Where:

Symbol	Description	Unit
$g_{c}$	Global mass fraction of component c in the feed solids.	fraction
$M_{c}^{F}$	Feed solids mass flowrate of component c.	tph
$z_{c,i}^{P}$	Fraction of component c in product size interval i.	fraction

If the feed solids flowrate is zero, the model assigns component 1 as the default component and sets the other component fractions to zero.

The model copies the feed stream properties to the product stream, then overwrites the product retained size distribution with the normalized user-defined retained fractions. The model preserves the feed solids flowrate and water flowrate.

The component-by-size matrix is rebuilt using the global feed component fractions. This means that the model preserves the overall component masses but does not preserve any size-dependent component distribution present in the feed.

The imposed product PSD is independent of the feed PSD. The model can therefore generate a product distribution that is not physically achievable for a real crusher if the entered product curve is inconsistent with the feed.