King Screen

Summary

The King Screen model represents vibrating screen classification using the screen capacity and transmission efficiency model described by R. P. King in Modeling and Simulation of Mineral Processing Systems.

The model estimates the rated screen capacity from the screen aperture, screen area and capacity correction factors. It then compares the actual feedrate with the rated capacity to calculate the transmission efficiency of undersize material through the screen.

The model should be used for vibrating screen simulations where the objective is to estimate the split between undersize and oversize from screen loading, screen geometry, open area, feed size distribution, material bulk density, deck position, inclination, aperture shape, particle shape and moisture condition.

DPSIM model key: DPSIM.Classification.KingScreen
Category: Classification
Subcategory: Screens
Display name: King Screen

Parameters

Derived parameters

Model Description

The King Screen model receives one feed stream and generates two product streams. In DPSIM, the product port represents the undersize stream and the tail port represents the oversize stream.

The screen area is calculated from screen width and length/width ratio:

A_S=W^2 R_LW

Where:

The feed solids flowrate per screen is:

M_(S,screen)^F=M_S^F/N_S

Where:

The basic unit capacity is calculated from the screen opening h:

I_u=0.783h+37, h≥25

I_u=20h^0.33-1.28, h<25

Where:

The open area factor is:

K_1=OA/OA_std

with:

OA_std=50, B≥0.8

OA_std=60, B<0.8

Where:

The half-size factor is:

K_2=2P_F(0.5h)+0.2

Where:

The oversize factor is:

K_3=0.914 exp(exp(4.22R_F(h)-3.5))

Where:

The bulk-density factor is:

K_4=B/1.6

Where:

The deck-position factor is:

K_5=1.1-0.1S_D

Where:

The screen-angle factor is:

K_6=1-0.01(θ-15)

Where:

The wet-screening factor is:

K_7=1+2.4×10^(-4)(25-h)^2.5, h≤25 and wet screening enabled

K_7=1, h>25 or wet screening disabled

Where:

The remaining correction factors are entered directly by the user:

K_8=F_A

K_9=F_P

K_10=F_M

Where:

The total capacity correction factor is:

K_T=K_1 K_2 K_3 K_4 K_5 K_6 K_7 K_8 K_9 K_10

The rated feed capacity of one screen is:

M_(rated)=I_u K_T A_S

The rating ratio is:

RR=M_(S,screen)^F/M_(rated)

Where:

The undersize transmission efficiency is calculated from the rating ratio:

e=0.95-0.25(RR-0.8)-0.05(RR-0.8)^2, RR≥0.8

e=0.95-1.67(0.8-RR)^2, RR<0.8

The calculated efficiency is limited between 0 and 1.

Where:

The model then applies a discrete partition rule to the feed size classes. Size classes coarser than the screen opening report completely to the oversize stream:

E_i^O=1, d_i≥h

Size classes finer than the screen opening report to the oversize stream according to the screen inefficiency:

E_i^O=1-e, d_i<h

Where:

The oversize and undersize retained masses are calculated size by size:

M_i^O=E_i^O M_i^F

M_i^U=M_i^F-M_i^O

Where:

The retained size distributions are normalized as:

p_i^O=M_i^O/sum_i M_i^O

p_i^U=M_i^U/sum_i M_i^U

The same partition curve is applied to the component-by-size matrix. For each component c:

M_(c,i)^O=E_i^O M_(c,i)^F

M_(c,i)^U=M_(c,i)^F-M_(c,i)^O

Where:

The model calculates the water assigned to the oversize stream from the requested coarse stream solids percentage:

W_O=M_S^O(1-X_O)/X_O

with:

X_O=S_O/100

Where:

If the calculated oversize water is greater than the feed water, all feed water is assigned to the oversize stream and the undersize stream receives no water. If the target oversize solids percentage is zero, the model also assigns all feed water to the oversize stream.

The model preserves total solids and water by splitting the feed into undersize and oversize streams. The model represents a capacity-based screen calculation and applies one common undersize transmission efficiency to all size classes finer than the screen opening. It does not calculate a gradual partition curve around the aperture.

References

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