Component Partition Separator
Summary
The Component Partition Separator model is an empirical classification model that splits a feed stream into coarse and fines products using component-specific partition curves. Each component has its own cut size, sharpness and bypass parameter.
The model should be used when the classification performance is known or calibrated by component and can be represented by a smooth size-dependent partition curve. It is suitable for simplified screens, classifiers, separators, or any unit where the user wants direct control of the recovery of each size class to the coarse stream.
DPSIM model key:
DPSIM.Classification.PartitionPerComponent
Category: Classification
Subcategory: Partition curves
Display name: Component Partition Separator
Parameters
| # | Parameter | Description |
|---|---|---|
| 1 | Coarse stream solids (%) | Target solids percentage of the coarse product stream. The model calculates the water assigned to the coarse stream from this value, limited by the water available in the feed. |
| 2 | [Component] d50 (µm) | Component-specific cut size. At this size, the corrected classification term is equal to 0.5 before bypass is applied. |
| 3 | [Component] sharpness | Component-specific sharpness exponent of the partition curve. Higher values produce a steeper transition around the cut size. |
| 4 | [Component] bypass (%) | Component-specific non-selective bypass to the coarse stream. This value defines the minimum partition to coarse before the size-dependent classification term is applied. |
Model Description
The Component Partition Separator receives one feed stream and generates two product streams. In DPSIM, the product port represents the coarse stream and the tail port represents the fines stream.
For each component c and size class i, the model calculates the representative particle size d_i from the size mesh. The partition curve gives the fraction of the component-size mass reporting to the coarse stream.
The corrected size-dependent classification term is:
Y_(c,i)=1-exp(-ln(2)(d_i/d_(50,c))^(n_c))
The final partition to coarse is:
E_(c,i)=B_c+(1-B_c)Y_(c,i)
Where:
| Symbol | Description | Unit |
|---|---|---|
| E_(c,i) | Final partition of component c in size class i to the coarse stream. | fraction |
| Y_(c,i) | Size-dependent classification term before bypass. | fraction |
| B_c | Component bypass to coarse. | fraction |
| d_i | Representative particle size of size class i. | µm |
| d_(50,c) | Cut size of component c. | µm |
| n_c | Sharpness exponent of component c. | dimensionless |
The final partition is limited internally between 0 and 1. The first size interval, corresponding to the DPSIM top-size class, is forced to report to the coarse stream:
E_(c,0)=1
For each component and size class, the feed component retained mass is calculated as:
M_(F,c,i)=z_(F,c,i) M_(F,i)
The coarse and fines component retained masses are then:
M_(C,c,i)=E_(c,i) M_(F,c,i)
M_(U,c,i)=(1-E_(c,i))M_(F,c,i)
Where:
| Symbol | Description | Unit |
|---|---|---|
| M_(F,c,i) | Feed mass flowrate of component c in size class i. | tph |
| M_(C,c,i) | Coarse product mass flowrate of component c in size class i. | tph |
| M_(U,c,i) | Fines product mass flowrate of component c in size class i. | tph |
| z_(F,c,i) | Fraction of component c in feed size class i. | fraction |
| M_(F,i) | Feed retained mass flowrate in size class i. | tph |
The total retained mass in each product size interval is calculated by summing over components:
M_(C,i)=sum_c M_(C,c,i)
M_(U,i)=sum_c M_(U,c,i)
The product retained size distributions are then:
p_(C,i)=M_(C,i)/sum_i M_(C,i)
p_(U,i)=M_(U,i)/sum_i M_(U,i)
The component fractions in each product size interval are:
z_(C,c,i)=M_(C,c,i)/M_(C,i)
z_(U,c,i)=M_(U,c,i)/M_(U,i)
Where:
| Symbol | Description | Unit |
|---|---|---|
| M_(C,i) | Total coarse product mass flowrate in size class i. | tph |
| M_(U,i) | Total fines product mass flowrate in size class i. | tph |
| p_(C,i) | Coarse product retained fraction in size class i. | fraction |
| p_(U,i) | Fines product retained fraction in size class i. | fraction |
| z_(C,c,i) | Fraction of component c in coarse product size class i. | fraction |
| z_(U,c,i) | Fraction of component c in fines product size class i. | fraction |
The model calculates the water assigned to the coarse stream from the requested coarse stream solids percentage:
W_C=M_S^C(1-X_C)/X_C
with:
X_C=S_C/100
Where:
| Symbol | Description | Unit |
|---|---|---|
| W_C | Water flowrate assigned to the coarse stream. | tph |
| M_S^C | Coarse stream solids flowrate. | tph |
| X_C | Target coarse stream solids fraction. | fraction |
| S_C | Target coarse stream solids percentage. | % |
If the calculated coarse water is greater than the feed water, all feed water is assigned to the coarse stream and the fines stream receives no water. If the target solids percentage is zero, the model also assigns all feed water to the coarse stream.
The model preserves the total feed solids and water by splitting them between the coarse and fines streams. The detailed separation response is empirical and should be calibrated against measured partition data when used for design or reconciliation.