Technical note: A rapid method for measurement of fineness of grind

Minerals Engineering, Vol. 1, No. I, pp. 81-84, 1988

0892-6875/88 $3.00 + 0.00 Pergamon Press plc

Printed in Great Britain

T E C H N I C A L NOTE: A RAPID M E T H O D FOR M E A S U R E M E N T OF FINENESS OF GRIND

B.A.WILLS Camborne School of Mines, Redruth,

Cornwall,

England

(Received 7 May 1987)

ABSTRACT A rapid method of estimating fineness of grind is presented. The method involves no drying of screened products, and results can be obtained within a few minutes. Although the rapid method is less accurate than the conventional method of drying screened products, in certain cases this lack of accuracy may be of less importance than the increased speed of assessment. The accuracy of assessment can be reliably forecast from a simple expression providing measurement errors can be estimated. Ke~words Grind; grinding; screening; sizing; size analysis

INTRODUCTION The m o s t i m p o r t a n t u n i t o p e r a t i o n in m i n e r a l p r o c e s s i n g is u n d o u b t e d l y grinding. Control of g r i n d i n g circuit product p a r t i c l e size distribution, or 'mesh of grind' is vital, as u n d e r g r i n d i n g produces i n a d e q u a t e l i b e r a t i o n , while overgrinding is w a s t e f u l of e n e r g y a n d can lead to poor d o w n s t r e a m p e r f o r m a n c e due to the p r o d u c t i o n of 'slimes' particles. Control of p r o d u c t size d i s t r i b u t i o n to a p r e - d e t e r m i n e d o p t i m u m is a c h i e v e d in a v a r i e t y of ways. Continuous on-line p a r t i c l e monitoring, by devices such as the A u t o m e t r i c s P S M - 4 0 0 a n d the B e s t o b e l l C y c l o m e t r i c sizer, a l t h o u g h expensive, is used on m a n y plants, p a r t i c u l a r y where the g r i n d i n g circuit is c o n t r o l l e d by computer. Some o p e r a t i o n s infer mesh of grind by m o n i t o r i n g the o p e r a t i n g p a r a m e t e r s of h y d r o c y c l o n e s in the g r i n d i n g circuit and feeding this data into m a t h e m a t i c a l models. Many operations, particularly modular pilot plants, may not have these facilities, and r e c o u r s e may h a v e to be m a d e to r o u t i n e a n a l y s i s of m i l l products. If t h i s i n f o r m a t i o n is u s e d for c o n t r o l , the c o n t r o l w i l l be r e t r o s p e c t i v e and may be m e a n i n g l e s s in a very small pilot o p e r a t i o n w h e r e small input changes rapidly affect output. As mesh of grind is usually related to one point on the c u m u l a t i v e size d i s t r i b u t i o n curve, e.g. % p a s s i n g 150 microns, a n a l y s i s can be speeded up by screening a sample on one sieve only, and w e i g h t i n g o v e r s i z e d and u n d e r s i z e d products. As t h e s e p r o d u c t s r e q u i r e drying, this method is a l s o r a t h e r slow, and control s t e p s m a y be r e t r o s p e c t i v e by times in the order of one hour. A rapid m e t h o d for routine measurement of m e s h of g r i n d , w h i c h r e q u i r e s no d r y i n g of p r o d u c t s , is presented. Results are o b t a i n e d w i t h i n a b o u t 2 m i n u t e s of c o l l e c t i n g the sample. A l t h o u g h the results are less accurate than those obtained by product drying, this may be of less importance than the increased speed of assessment, p a r t i c u l a r y w h e n the i n f o r m a t i o n is used for the control of f a s t - r e s p o n s e pilot circuits.

M E A S U R E M E N T OF M E S H OF GRIND BY DRYING PRODUCTS In this method a sample of mill product is w e t - s c r e e n e d on a standard sieve of m e s h s i z e P m i c r o n s . T h e u n d e r s i z e a n d o v e r s i z e p r o d u c t s are d r i e d a n d 81

~;2

I c'chnic~d Nole~

weighed,

from which

%-P

(Q

can

be

found

from:

Q : 100u U+0 where U = weight and 0 = weight

of u n d e r s i z e p r o d u c t of o v e r s i z e p r o d u c t

RAPID

MESH

OF GRIND

METHOD

In t h i s m e t h o d , a s a m p l e of m i l l p r o d u c t is t a k e n in a g r a d u a t e d m e a s u r l n g c y l i n d e r . T h e v o l u m e of s l u r r y t a k e n , Lf (mls) a n d w e i g h t of s l u r r y , Wf (g) are recorded. The slurry is w e t s c r e e n e d as before, the undersize being c o l l e c t e d in a n o t h e r m e a s u r i n g c y l i n d e r . A f t e r s c r e e n i n g , t h e u n d e r s i z e s l u r r y is w e i g h e d (Wu) a n d its v o l u m e r e c o r d e d (Lu). T h e s e o p e r a t i o n s t a k e n o m o r e than a few minutes. The :

proportion

where

~_ddf

in t h e

feed

(df

since

F = df

of f e e d s l u r r y (kg/l) of s o l i d s in f e e d s l u r r y of w a t e r (kg/l)

dry weight (Df

Df

sample

[I!

of

solids

in f e e d

(kg/l)

sample,

F

(g)

- awl _ - dw)

Df

= Wf/Lf,

(Wf - d w L f ! (df - dw)

Similarly, =

by w e i g h t

2~

Df = d e n s i t y df = d e n s i t y d w = density

Therefore

and

solids

(Df - dwi (df - d w)

d__f

Df

=

of

dry

weight

of

solids

in u n d e r s i z e

fraction,

U

(g) 5)

d_u (W u - L u d w ) (d u - d w)

where

d u = density

of

solids

in u n d e r s i z e

fraction

(kg/l)

Therefore: 6)

Q : 100 d u (W u - L u d w ) ( d f -- d w ~ (d u - d w) df (Wf - d w Lf) Equation 6 is r e l a t i v e l y that, a s s u m i n g df = du:

insensitive

to

small

differences

The variance experimental =

du,

so

OF ACCURACY

OF DRY AND WET METHODS

in t h e c a l c u l a t i o n of Q c a n be c a l c u l a t e d from the estimated v a r i a n c e s in t h e i n d e p e n d e n t d e r i v a t i v e s , i.e. f r o m Eq.I:

(aQ/gU) 2 V U +

where

and

d w = I kg/])

ESTIMATION

VQ

df

7)

Q = ]00 (W u Lu) (Wf - Lf)

(assuming

in

V U and V O are

(9Q/80) 2 V O the v a r i a n c e s

(8) in m e a s u r e m e n t

of U a n d O

Hence: VQ

=

(100/[U+O]Z) 2 {U2Vo+O2Vu }

(9)

Technical Notes

83

From Eq.7: VQ = VWu

(aQ/aWu)2 + VLu

(aQ/aLu)2 + Vwf

(aQ/aWf) 2 + VLf

w h e r e Vwu , VLu , VWf and VLf are the variances respectively.

(10)

(aQ/aLf) 2

in m e a s u r e m e n t of Wu, Wf and Lf

Therefore: VQ =

1002 (Wf-Lf) 2

[VWu + VLu + {(Wu-Lu)/(Wf-Lf)} 2 + {(Wu-Lu)/(Wf-Lf)} 2 VLf]

(11)

For a typical value of Q of about 33%, and assuming Wf = 400g, Lf = 250mls, W u = 150g, and L u = 1000mls, then from Eq.11: VQ = 0.44

(12)

(Vwu + VLu ÷ 0.11Vwf + 0.11VLf)

E q u a t i o n 12 shows that the a c c u r a c y of the result using the wet method is most s e n s i t i v e to the e r r o r s in m e a s u r e m e n t of W u and Lu, and p a r t i c u l a r care should therefore be taken to e n s u r e h i g h p r e c i s i o n in the m e a s u r e m e n t of u n d e r s i z e data.

C O M P A R I S O N OF WET AND DRY METHODS The d i s c h a r g e from an o p e r a t i n g p i l o t - s c a l e rod mill was sampled every hour, a n d the m e s h of g r i n d at 300 m i c r o n s d e t e r m i n e d by b o t h the wet and dry techniques, Results from the dry method were o b t a i n e d roughly an hour a f t e r taking the sample, whereas the wet method p r o d u c e d a result w i t h i n 2 minutes. A total of 82 samples was taken, and the results are compared in Figure I. The root m e a n square error between the two sets of data was ±4.4%.

x/

80 70

x x

60 I

E

x

o ro

x;~,xy~ ,~x

~ 30

I0

x

Xx

× L~x x

' 40 i

20

S

/Xx x

/ I

I0

Figure I

I 20

I

I

i

I

30 40 50 60 Dry % - 300/.Lrn

I

70

I

80

I

90

C o m p a r i s o n of wet and dry methods

A n a l y s i s of v a r i a n c e was p e r f o r m e d on typical results; at values of Wf, Wu, and L u of 400g, 250mls, I050g and 1000mls respectively, from Eq.7: Q = 100

(1050-1000) (400-250)

Lf,

= 33.3%

and from Eq. 12: VQ = 0.44

(Vwu ÷ VLu + 0.11Vwf + 0.11VLf )

It was e s t i m a t e d that the w e i g h t s ±2mls (±Is.d) and L u to ±5mls.

could be m e a s u r e d

to ±0.2g

(±Is.d.),

Lf to

84

Hence, ±3.3%

Technical Notes

VQ

=

11.2,

and

estimated

standard

deviation

in m e a s u r e m e n t

of

Q

is

A f t e r d r y i n g the o v e r s i z e and u n d e r s i z e slurries, values of U and O of 80g and 150g r e s p e c t i v e l y were obtained, from w h i c h (Eq.1), Q = 34.8% It was e s t i m a t e d that the dry p r e p a r a t i o n , could be m e a s u r e d VQ = 3.6 x 10 -6 The e s t i m a t e d

weights, a l l o w i n g for losses in f i l t r a t i o n to ±2g (±Is.d.), hence from Eq.9:

(6400V 0 + 22500Vu)

standard

deviation

and

= 0.4

in m e a s u r e m e n t

of Q is thus

±0.6%

The c o m b i n e d e r r o r in c o m p a r i n g the two methods is thus e s t i m a t e d to be ±(11.2 + 0.4) I/2 = ±3.4%, w h i c h c o m p a r e s f a v o r a b l y with the root mean square error of ±4.4% obtained.

CONCLUSIONS A rapid m e t h o d of e s t i m a t i n g mesh of grind is presented. The m e t h o d involves no d r y i n g of s c r e e n e d products, a n d r e s u l t s can be o b t a i n e d w i t h i n a few minutes. A n a l y s i s of v a r i a n c e shows that very a c c u r a t e results can be a c h i e v e d by drying the screened products, whereas the rapid method is far l e s s accurate. In c e r t a i n cases, however, particularly where information is required for t h e c o n t r o l of f a s t r e s p o n s e pilot circuits, t h i s l a c k of a c c u r a c y may be of less i m p o r t a n c e than the i n c r e a s e d speed of assessment. The a c c u r a c y of a s s e s s m e n t can be r e l i a b l y f o r e c a s t from a simple e x p r e s s i o n p r o v i d i n g m e a s u r e m e n t errors can be estimated.

REFERENCES I. W i l l s B.A. Mineral Ltd, O x f o r d (1988)

Processing Technology,

4th

Edn,

p.95.

Pergamon

Press