Ideal Size Partition
Summary
The Ideal Size Partition model is a deterministic classification model that splits each component by a component-specific cut size. For each component, size classes coarser than the cut size report completely to the coarse stream, while size classes equal to or finer than the cut size report to the fines stream.
The model should be used when an ideal separation is required, such as for simplified flowsheet logic, limiting cases, preliminary studies, or testing the effect of a perfect size cut.
DPSIM model key:
DPSIM.Classification.IdealPartition
Category: Classification
Subcategory: Partition curves
Display name: Ideal Size Partition
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 ideal cut size. Size classes with representative size greater than this value report to the coarse stream. Size classes equal to or finer than this value report to the fines stream. |
Model Description
The Ideal Size Partition model 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 to the coarse stream is calculated as an ideal step function:
E_(c,i)=1, d_i>d_(50,c)
E_(c,i)=0, d_i≤d_(50,c)
Where:
| Symbol | Description | Unit |
|---|---|---|
| E_(c,i) | Partition of component c in size class i to the coarse stream. | fraction |
| d_i | Representative particle size of size class i. | µm |
| d_(50,c) | Ideal cut size of component c. | µm |
The first and last size intervals are treated explicitly:
E_(c,0)=1
E_(c,N-1)=0
Where:
| Symbol | Description | Unit |
|---|---|---|
| E_(c,0) | Partition of the DPSIM top-size class to the coarse stream. | fraction |
| E_(c,N-1) | Partition of the pan class to the coarse stream. | fraction |
| N | Number of DPSIM size intervals. | dimensionless |
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 represents an ideal cut and does not include imperfection, bypass, near-size misplacement, capacity effects, feed-rate effects or equipment geometry. It should therefore be interpreted as a limiting-case separator rather than a predictive equipment model.