King Flotation Cell

Summary

The King Flotation Cell model represents mechanical flotation using a simplified first-order kinetic formulation based on the flotation modelling approach described by R. P. King. The model calculates a size-dependent flotation rate for each component and size class, applies the kinetic response through a series of perfectly mixed cells, and separates the feed into floated and bottom streams.

The model should be used for flotation simulations where the recovery of each component depends on particle size, maximum floatable particle size, particle size of maximum flotation rate, kinetic rate scale factor, residence time and number of cells.

In this DPSIM implementation, each flotation bank is represented as a sequence of perfectly mixed cells in series. Multiple banks may operate in parallel. The floated stream is the concentrate stream, and the bottom stream is the non-floated product.

DPSIM model key: DPSIM.Concentration.KingFlotationCell
Category: Concentration
Subcategory: Flotation
Display name: King Flotation Cell

Parameters

Derived parameters

Model Description

The King Flotation Cell model receives one feed stream and generates two product streams. In DPSIM, the tail port represents the floated stream and the product port represents the bottom stream.

The feed solids and water are divided equally among the flotation banks:

M_(F,b,c,i)=M_(F,c,i)/N_B

W_(F,b)=W_F/N_B

Where:

For each component c and size class i, the model calculates a size-dependent flotation rate:

k_(c,i)=a_c/sqrt(d_i) (1-(d_i/d_(max,c))^1.5) exp(-(d_(opt,c)/(2d_i))^2)

If the calculated rate is negative, it is set to zero.

Where:

For each cell, the pulp volumetric flowrate is calculated from the component solids volumes and the water flowrate:

Q_p=sum_c sum_i M_(cell,c,i)/ρ_c + W_cell

Where:

The residence time in each cell is:

τ=V_cell f_V/Q_p

with:

f_V=V_eff/100

Where:

The mass floated from each component and size class in one cell is calculated from a first-order perfectly mixed cell expression:

M_(float,c,i)=M_(cell,c,i)(1-1/(1+k_(c,i)τ))

Where:

The bottom stream from one cell becomes the feed to the next cell in the same bank:

M_(next,c,i)=M_(cell,c,i)-M_(float,c,i)

The model repeats this calculation for all cells in series. The total floated mass from one bank is the sum of the floated masses from each cell. The final bank products are then multiplied by the number of parallel banks.

The total floated and bottom retained masses are:

M_i^Flt=sum_c M_(Flt,c,i)

M_i^Bot=sum_c M_(Bot,c,i)

The retained size distributions are normalized as:

p_i^Flt=M_i^Flt/sum_i M_i^Flt

p_i^Bot=M_i^Bot/sum_i M_i^Bot

The component fractions in each size interval are:

z_(Flt,c,i)=M_(Flt,c,i)/M_i^Flt

z_(Bot,c,i)=M_(Bot,c,i)/M_i^Bot

Where:

The water split is calculated from the water split basis parameter.

If the selected stream is the floated stream, the floated water is calculated as:

W_Flt=M_S^Flt X_W/(1-X_W)

and:

W_Bot=W_F-W_Flt

If the selected stream is the bottom stream, the bottom water is calculated as:

W_Bot=M_S^Bot X_W/(1-X_W)

and:

W_Flt=W_F-W_Bot

with:

X_W=W_sel/100

Where:

The calculated water assigned to the selected stream is limited by the water available in the feed. The complementary stream receives the remaining water.

The overall solids recovery to concentrate is:

R_M=100 M_S^Flt/M_S^F

For each component c, the metallurgical recovery to concentrate is:

R_c=100 M_c^Flt/M_c^F

Where:

The model is a simplified kinetic flotation model. It represents the pulp phase as a sequence of perfectly mixed cells and uses a component- and size-dependent flotation rate. It does not explicitly calculate bubble surface area, froth transmission, air rate, froth recovery, entrainment, non-floatable fractions, reagent chemistry or pulp hydrodynamics.

References

King, R. P. (2001). Modeling and Simulation of Mineral Processing Systems. Butterworth-Heinemann.