Karra Screen

Summary

The Karra Screen model represents vibrating screen classification using the empirical model proposed by V. K. Karra in “Development of a model for predicting the screening performance of a vibrating screen”, CIM Bulletin, April 1979.

The model calculates the effective throughfall aperture, screen capacity factors, theoretical undersize loading, corrected cut size and partition curve. The partition curve represents the fraction of each size class reporting to the oversize stream.

The model should be used for vibrating screen simulations where the separation performance must depend on screen geometry, aperture, wire diameter, deck angle, deck position, feed size distribution, feed density and screen loading.

DPSIM model key: DPSIM.Classification.KarraScreen
Category: Classification
Subcategory: Screens
Display name: Karra Screen

Parameters

Derived parameters

Model Description

The Karra 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 effective throughfall aperture is calculated as:

h_T=(h+d_w)cos θ-d_w

Where:

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

S_A=W^2 R_LW

Where:

The model calculates the feed oversize percentage as:

Q=100 R_F(h_T)

Where:

The basic capacity factor A is calculated as:

A=12.1286 h_T^0.3162-10.2991, h_T<50.8

A=0.3388 h_T+14.4122, h_T≥50.8

The oversize factor B is calculated as:

B=1.6-0.012Q, Q≤87

B=4.275+0.0425Q, Q>87

The half-size percentage is calculated as the feed passing at half the effective aperture:

R=100 P_F(0.5h_T)

The half-size factor C is:

C=0.012R+0.7, R≤30

C=0.1528R^0.564, 30<R<55

C=0.0061R^1.37, 55≤R<80

C=0.05R-1.5, R≥80

Where:

The deck location factor is:

D=1.1-0.1N_D

Where:

The wet screening factor E is calculated from:

T=1.26h_T

with:

E=1.0, T<1

E=T, 1≤T≤2

E=1.5+0.25T, 2<T<4

E=2.5, 4≤T≤6

E=3.25-0.125T, 6<T≤10

E=4.5-0.25T, 10<T<12

E=2.1-0.05T, 12≤T≤16

E=1.5-0.0125T, 16<T<24

E=1.35-0.00625T, 24≤T≤32

E=1.15, T>32

The bulk density factor is calculated as:

F=1000ρ_s/1602

Where:

The near-size material is calculated as the feed fraction between 0.75h_T and 1.25h_T:

X_n=100(P_F(1.25h_T)-P_F(0.75h_T))

The near-size capacity factor is:

G=0.844(1-X_n/100)^3.453

Where:

The theoretical undersize flowrate per screen is calculated as:

T_U=M_S^F P_F(h_T)/N_S

Where:

The total correction factor is:

K=A B C D E F G

The Karra cut size is calculated as:

d_50=1000h_T((T_U/S_A)/K)^(-0.148)

The DPSIM d50 adjustment is then applied:

d_50^*=F_d d_50

Where:

The screen partition curve is calculated as the fraction of each size class reporting to oversize:

c_i=1-exp(-0.693(d_i/d_50^*)^(5.846F_I))

Where:

When F_d=1 and F_I=1, the model uses the unadjusted Karra cut size and Karra partition exponent. Values different from 1 represent DPSIM calibration factors.

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

M_i^O=c_i 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. Therefore, for each component c:

M_(c,i)^O=c_i 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 calculated screening efficiency is:

η=100 M_(U,<h)^U/M_(F,<h)^F

Where:

The model represents solids classification by the Karra partition curve. The legacy bypass adjustment parameter is retained for compatibility but is not used in the current solids partition calculation.
References

Karra, V. K. (1979). Development of a model for predicting the screening performance of a vibrating screen. CIM Bulletin, April 1979, 167–171.