percolation behaviour of a cane diffuser -...
TRANSCRIPT
PERCOLATION BEHAVIOUR OF A CANE DI F FUSER
By
D.J. Love and P.W. Rein Huletts Sugar Limited Mount Edgecombe, South Africa
7015 1 •
ABSTRACT
The percolation behaviour of a c ane d i ffu s e r h a s b e e n i nve s t i
gat ed in both pilot p l an t and full sca le di ffu ser s . A wide r ang e
of fa ctors wa s i nve s ti g at e d and cor r e l a t ion s hav e b e e n d ev elop e d
from the p i lot p l an t exper ime nts which relate t h e percolation rate
at which f l ood i ng o c c u r s to t h e bed height, speci f ic s ur fac e , mean
particle s i z e and fibre con t en t of the c ane. The di s pers e d p l ug
f low mod e l was found to fit t h e re s u l t s of t rac e r t es t s on both the
pi lot p l ant and fu l l s c a l e diffuser s , prov id ing m e a su res of the
percolation v e loc i ty an d t h e d i spe r s i o n coeff i cients .
7015 2 .
INTRODUCTION
Flooding is probably the most serious operating problem en-
countered i n mov i ng bed diffusers. Flooding occu rs when more
liquid is sprayed onto the top surface of the bed than is able
to percolate downwards through the bed, and i ts occurrence cau ses
a noticeable drop in extraction a s the countercurrent extraction
process is destroyed.
9 However it has been shown that high l i quid flow
rate s through the cane bed a re highly desirable, as these condi-
tions promote high rates of mas s transfer. Idea lly then the
diffuser should be operated at all timcs with liquid flow rates
at a maximum but just slightly below levels at which flooding
occu rs. The maximum percolation rate i s therefore a very impor-
tant operating parameter.
A considerable amount of work ha s been done on bagasse diffu-
sion, and maximum percolation rates were shown to be dependent on
degree of preparation and bed den s ity. 9
However,
Payne7
has stated that higher percolation rates should be obtainable
in cane di ff users, due to the les s dense beds with a more fibrous
type of p reparation . Experience with running a bagasse diffuser
at Empangcni as a ca�c diffuser for a limited period t�n�ea to rein-
force these ideas.
However, operation of a cane diffu ser at Amatikulu has re-
suIted in fibre packing densities � 20% higher than originally
anticipated, and percolation rates well below expected valu es,
lower even than obtained in bagasse diffusers.
A program was therefore initia ted to investigate the nature
of flooding in a cane diffuser.
3 .
Work was concentrated in two areas :
1 ) Pilot plant plant experiments aimed at establishing the factors
affectin g maximum percolation rates and
2) Measurements of percolation behaviour in a full s cale diffuser
via tracer testin g.
THE NATURE OF PERCOLATION IN A CANE
DIFFUSER
Flooding i n a packed bed
Most wo rk on flow through packed beds is in relation to either
single phase fluid flow through packed beds (filters, catalyst
beds, fluidised beds) or countercurrent ga S-liquid flow through
packed beds (absorption or distillation columns).
ReinS
developed a correlation for predicting the maximum per
colation rate attainable without flooding, U, in a ba gasse diffuser
from the results of pilot plant experiments, as a function of bUlk
fibre density D, and specific surface (or fineness) of prepar e d
cane S :
U = K 50,664 D Z,64
(1 )
The form of this corre lation is bas ed on the work of Lavin4
who
considered s ingle phase flooding as a special case of flooding in
countercurrent gas-liqu id flow (i.e. no gas flow).
An alternative approach is to consider flooding as a special
case of single phase flow through a packed bed. By drawing an
analogy between viscous flow in packed beds and viscou s flow in
pipes, the well known Kozeny Carman Equation can be derived.
Appendix 1 details the modification of this equation £or the
c a s e o f f l o od ing pe rc o l atio n r a te thro ugh a p a cked b e d v i z .
u = 2
S D
3 E: 2
Nomenc l a t u r e u s e d is list ed a t the end o f the p ap e r .
4 .
(2)
This equation is not d i r e c tly ap p l ic able t o fib r o u s b e ds due
to the p r e senc e of sta t i c liquid h o l d-up and, in t h e cas e o f p e r c ola
t ion , t r appe d a i rS
. The v o i d a g e o f a c an e b e d c anno t t h u s b e
simply c o n s ider ed as t h e vo l ume fr a c t ion of the bed un o c cup i e d by
fibre .
F ig. 1 o ut l ine s the f a c t o r s which a f f e ct flo o ding i n a cane
d iffu s e r and the m e c h anism by whic h t h i s t akes p lac e, ba s ed on
the Kozeny Carman equa t i on .
In s e r t Fi g. ,
Fl ow pa tt e rn s in a p i l o t p l an t d i ffu s e r
Th e re sidence time distr ibution o f liqu i d f l owing th rough a
packed bed (as m e a su r e d b y t ra c e r t e s t s ) ha s be e n s uc c e s s ful l y
modelled by t he a x i ally dis p e r s ed p lug flow model'O
.
The dif f e r ent i a l e qua t i on d e s cribing tra c e r dispersion in an
axially disp e r s e d plug flow sys t em is :
2 c C
- v =
6Z
cC
6t
whe r e EZ i s a d i sp e r sion c o e f f i cient in t h e d i r e c tion o f f low . F o r
plug f l ow EZ = 0, and higher value s ind ica te a great e r s p re a d in
r e sid e n ce time s . v i s the p e rco l a t i on ve l o c it y wh i c h is dif-
fe r ent fr om th e perco l a tion r a t e (sup e r fic i a l ve l o c i t y ) due t o t h e
reduce d open are a fo r f l ow i n the bed .
Th I · h· . 1 0 f h .
f e s o u tlo n t o t 15 e qua tIon o r t e concentratIon 0 t ra c er
in t he l i q u i d l e av i n g a packed b e d o f lengt h � when a p u l s e o f
5 .
is app l i ed a t th e i n l e t t o t h e bed a t t ime t = 0 i s
:I C = g exp ( - (t - vt) )
4 EZ t Z/ lT EZ
t
The f l ow mo d e l use d by Re i nS in wo r k o n a p i l ot p lan t bag a s s e
d i f fuse r w a s tha t o f p l ug f low w i t h e x c h a n g e w i th s t agnant reg ion s .
T he d ifferen t i a l equ a t i o ns d es c rib i ng t rac e r d i s p e r s io n un d e r
the s e c o nd i t i ons a r e :
H 6Cb -K (C
b- C) ---rt =
and - p,U 6C K(C b-C) H tiC 6Z + = ""Tt
where K r epre s en ts t he r a t e of i n t erchange be tw e e n f l ow i ng l i qu i d
(co nce nt r a tion C) and s ta gnan t l i qu i d of c on c entra t i o n Cb .
The solu tio n t o t h ese equa t i o ns11 f o r t h e con c en t rat ion o f
tracer i n t he l i qu i d l e av ing a bed o f length t whe n a p u lse of t r a c e r
is applied to t h e su rfa c e of th e b e d a t t im e t = 0 i s
C ( t ) = e xp ( a ) 0 (t + b) + e x p ( a) / - a \ v' d-C t-+-;-b--=:" )-
x exp ( - (t+b) ) -er
x 11 ( �� � ( t+b) )
x H ( t+b)
whe r e a = eK �
b = ew pU
d = H K
6 .
Flo w p a t t e rn s in a mov i ng b ed diffu s e r
It h a s b e e n s hown 8 t h a t i n a mov i ng b e d type dif fu s e r e x t rac-
t i on may be inc r e a s e d by inc re a s ing the amount o f juic e r e circu-
l a t ion . The i n c r eas e d j u i c e r e c i rcu lat i o n g iv e s highe r flow
r a t e s t h rough the bed inc r e a s i ng th e l i quid s o l i d c o n t act e ff i
c i enc y a nd t h u s a l l ow i ng mo r e o f t he s uc r o s e t o b e ex t ract e d by
wa shing and l e s s by d i ffu s i on. Ju i c e r eci r c u l a ti o n mu s t how-
eve r n o t b e inc r e ased t o t he p o i n t whe r e f l o o ding occ u r s a s thi s
d ra s t i cal l y r educ es e x t r act i o n .
The u s e o f t r a c e r s i s a w el l known me t ho d o f de t e rmin i ng f l ow
pa t t e rn s in p roce s s equ i pme n t and ha s a l r ea dy b e e n u se d to i n
ve s tigate flow pat t e rns in mov i ng b e d t y p e d i f fu s e r s .6 I t wa s
felt howev e r , t h a t t h e va lue o f t he s e t e s t s would be g r ea t l y
enhan c e d i f (1) a rap i d me tho d of p e r f o rming t r a c e r t e s t s w i t h
continuou s t r a c e r moni t o r in g c ou l d b e dev i s ed and ( 2 ) a ma the -
ma t i c a l mode l c ou l d b e de rive d t o ana l y s e t he r e s u l t s .
The ax ial ly d is p e r s e d p l ug flo w mo de l whic h wa s inv e s tig a t e d
in t he p ilo t p l ant wa s ex t ended to a mo d e l po s t u lat ing b o t h
a xia l and l a t e ra l di s p e r s i on s u p e rimp o s ed o n plug f l ow . F i g . 2
repre sents t h e phys i c a l s i t uation and t he d i f fe r e n t i a l equ a t i on fo r
th i s mo del i n r e c t a ngu l a r c o-o rd i nat e s i s'
E Y
2 o c Oy"l _v QC
or =
EZ and Ey represent dispersion coefficients i n the Z direc tion
( ve r t i cally downwa r d s t hr o ugh t h e b e d) a n d i n t he y dir e c tion
(d i r ec t i on of t rav e l of t h e bed)
In s e r t F ig . 2
( 3 )
App end ix 2 s hows how t he e quat i on is s olve d and how the
co ncen t rat i o n s of t ra c e r f r om the va r iou s diffu s e r t ra y s a r e
calcu l ated.
EXPERIMENTAL DETAILS
Pil ot plan t di f fu s e r t e s t s
7 .
A p ilo t plant d i f fu s e r wa s c o n s t ruc t ed i n which p e rco lgtion
rate s c ou l d be m e a s u r e d under con t ro l l ed c ond i t ions.
diagram of t he p ilo t plant i s given in F i g . 3 .
In s e r t F i g. 3
A s ch ematic
The samp l e o f shredded c an e i s held in t h e c olumn wh i ch i s
0,32 m in diame t e r and 2 , 42 m h igh. The column i s p r ov i d e d w i t h
plast ic windows down one s i d e so tha t p e rco l a t i o n and t hus t h e
occu r r e nce of flooding could b e o b s erve d.
Ju ice f low to t h e p i lo t p l an t d i f fu s e r is controll e d by a
pneuma t ic va lve ope r a t e d from a manua l loading s t a t i on. The flow
is measured by an o r ifice p l ate and dip c ell. A ju i c e dis t r i
bu t or i s prov ided a t t h e t op of the c o l umn t o e n su r e eve n d i s t r i
bution of juice over the s u r fa c e of t h e b e d. T o main t a i n a c o n
stan t flow fo r any v a lve s e t t i n g , a co n s tant h e ad t a nk i s pro
v i ded, w i th exce s s juice ove r f low i ng back t o the s t ora g e t ank.
The t emperat ure of ju i c e i n t he s to rage t a n k i s regula t e d by
the rmo static a lly co n t ro l l ed direct s t e am injec t i on.
The co lumn i s hung f rom a beam wh i ch i s c o un t e rb alance d by
t he dial mech an i sm o f a pl atform scale. This a llows the ma s s of
liq u i d h eld up i n the co l umn dur i n g ope r a t i o n t o b e me a su r e d .
To p e r f o rm a t e s t , a consignmen t of c an e w a s select ed and
a sample of sllredded cane was t a ken from the cane sampling hatch.
The dir e c t can e a n aly s i s figur e s we r e u t il ised fo r t h e co r r e sponding
con signmen t.
8 .
The pilo t plan t diffu s e r column wa s fille d with t his cane to
a level s e l e c t ed t o g ive t h e de sired bed height after c ompa c t ion .
The ma s s o f cane was r eco rded.
Pe r c o l at i o n was st a rte d and the b ed allowed t o compact a s
a r e su l t of the we i gh t o f the ju ice holdup in t he bed and
so ften i n g o f t he fibres with increased temperature. The f low t o
the co lumn was manually a d j us ted t o g ive t h e max imum flow without
f l o od i n g o c cur r in g o n th e s u r fa c e o f the bed . Th i s maximum flow
rate decre a s ed wi t h t ime a s t h e b e d c ompa c t e d . When the bed had
s tabili s e d , this flow r a te wa s r e c orde d a s t he max imum per co lat io n
rate, and the bed he igh t w a s me a sured.
To pe rform a t r a cer t e st on the p ilo t plant d i ffu se r , 100 gms
of NaCI was add e d as a 10% s olut i on to t h e d i s t ributo r a t t h e t op
of the column. The c onduct ivi ty of the ju i c e le avi ng t h e bottom
of the column was reco rded o n a ch a r t r e c o r d e r fo r 20 m i ns . Du ring
this time, the juice leaving the c o l Umn wa s run t o d ra i n t o pre
ven t a ny interference f r om r e cycle d salt.
Cane p rep a r a t i on was varied by a lter i ng the s p e ed a nd / o r
c l ear ances in th e s h r edd e r. Samples we r e taken fo r part i c l e s i z e
analysis.
Tracer tests i n full s c ale d if fuse r
Some i ni t ial exp e riments s h owed that NaC l could be used fo r
t r ac e r experimen t s in a full scal e di ffus e r w i t h c onduc tivi t y being us ed as the mea s u r emen t t echnique for monitoring the tracer.
Co nduct ivit y probes (Beckman type 414) we re p l a c e d i n the d i s
c h a r g e l i n e s o f t h r e e c o n s ecut ive stage pump s. The probes were
conne c t e d t o conductivity t r a n sm i t t e r s (Bekcman Mod el SM 222) and
r eco rd e r s to g ive a pe rm an ent r e c o rd of t h e t race r peaks appe a rin g
i n e ach t r ay dur i ng a t r ace r tes t .
9.
To pe r f o rm a t e s t , t he c onduc t iv i ty m e t e r s and r eco rders we r e
sw it ched on a b ou t 15 m i nute s b e fo r e s a l t a d d i tion, t o mon i tor the
n a t ural v a r i a t i ons in b a c k g r ound conductivity . Approx imat ely
70 kg o f NaCI wa s d i s s o lv e d in 180 l i tre s o f hot w a t e r . To s ta r t
t h e t e s t , the s a l t solu t i on wa s added rapidly to t he l a s t o f t h e
three mon i t o r e d ju i c e t rays ( t r ay R i n F i g. 2). T h e c oncen t r a-
t i o n o f t r a c e r appe a r i ng in e a c h o f t he t h r ee t r a y s w a s t hus aut o-
m a t i c a l l y rec o rd e d .
The bed he i gh t wa s meas u r e d a t t h e windows a t t h e s i de o f
the d i f fuse r . Be d s pee d wa s rec o r ded . In t e s t s a t Ama t ikulu
the f e e d r a t e of c a n e t o the d i f fuse r c ould be m e a sured by a
be l t weigh e r .
PI LOT PLANT D I FFUSER TESTS
Due t o the l a rge numb e r of f a c t o r s wh i c h can a f fect perc o l a -
tio n r a t e s a n d t h e c o mp l e x i ty of their e ff e c t s , o n ly some of t hem
c ould b e inv e s tigat e d quant i t a t i v ely . On e of the f a c t o r s whi c h
was anticipated t o have a subs tant i a l effe c t wa s c ane qualit y.
Although an analy s is o f t h e c an e a n d m e asureme n t o f t ops and
tra s h wa s unde r t a k en, th e s e measu rab l e fa c t o r s do not characterise
c ane qu a l ity a d equ a t e l y . The r e fore al l t e s t s w e r e und e rtake n o n
burn t c ane cons ignments, o f v a r i e t y NCo 3 7 6 . Apa r t f r om cane an aly-
sis , the me a sur a ble f ac t o r s wh i c h w e r e v a r ied i n a t e s t p ro gram to
d e v elop c o r r elat i on s for use in opt i m i s i ng d i f fus e r p e r f ormanc e
were bed heigh t and l e v e l o f c ane p r epa r a tio n .
Temp e r a t ur e s w e r e not v a r ie d i n t his s e r i e s of expe r iment s,
as t h e e f fe c t o f temp erat u r e h a s be en i nve s tig a t e d e l s ewhe r e fo r b ag-
a s se dif fusion8
. A ll m e a s u r ement s h e r e we re und e r t a ken a t n o rmal
d i f fu s e r o p e r a t ing t empe r a tu r e s o f + 75°C. Pe rco l a t ion ra t es a r e 3 2
e xp r e s s e d i n unit s o f m l iqu id pe r m bed a r e a p e r minut e i . e . 3 :l
m /m m in, o r mo r e simply, m/ m in .
10.
Init i al t e s ts w e r e und e r t aken t o c h e ck r eproduc ibi l i ty of
the meas u reme n t s. Suf f i c i en t cane wa s samp l ed f rom a s ingl e
consignm e n t o f c an e t o a l l o w a t e s t t o b e dupl ica t ed . Fo r t h e
rep l i c a t e t e s t, t h e c olumn w a s fil l e d to t h e s ame l ev e l, k e e p i ng
the method of pac k in g a s c o n s i s t en t a s p o s s i b l e . Tab l e 1 s hows
good agr eemen t of pack i ng d e n s i ty and pe rc o l a tion rat e for the f ive
dup l i c a t e t e s t s p e r f o rmed .
In s e r t Tab le 1.
The s e t e s t s do n o t i n clude t h e e ff e c t s o f any e rr o r i n t he
ana l y s i s o f the cane a s only one s ample o f c an e wa s ana lys e d for
e a c h s e t of dup l i c a t e t e s t s .
I t w a s n o t ant i c i p a t e d t ha t wall e f f e c t s d u e t o t h e s ize o f
t he column wou ld be s ign i f i c an t , s in c e t h e c o l umn d i am e t e r /
pa r t i c l e s ize r a t i o wa s we l l ove r t h e minimum va l u e of 1 2 q uo t e d
b y Gunn 3 T o che c k whe t h e r t h e r e wa s a n e f fe c t o n eit her p a c king
dens i t y o r p e r c ol a t i on r a t e , a c olumn 0,61 m i n diame t er wa s c o n
s truct ed fo r c ompa r a t ive t est s u sing dupl i ca t e s ampl e s o f t h e s ame
prepa red c ane. No evide n ce o f a ny wall e ffe c t c o u l d b e e s t ab l i s h e d .
A number of o t h e r e f f e c t s were check e d qual i t a t i v ely t o d e t er
m i n e whe t he r t hey hav e a s ign i f i c an t effe c t on p e r c o lat ion r a t e .
Qua l i t a t i v e i nves t i g a t i on s .
Pack ing method
Two v a r i a t ions i n th e met hod o f pack ing the p i l o t p l an t c o l umn
we r e comp a r e d w i th t h e no rma l met h o d in dupl i c a t e t e s t s .
Comp a c t i o n o f t h e c an e b e d u s i n g h i gh in i t i a l f l ows (app ro x i
mately 3 t o 4 t imes t h e p e rco l a tion r a t e ac h i ev e d a f t e r c omp a c t i o n
o f t h e b e d) had no n o t i c e ab l e e f f ect o n the p e r c o l a t i o n rate
a c h i ev e d aft e r comp a c t ion .
In i t ial t e s t s o n f i lli ng t he column w i th wat er f rom t he
bo t t om befo r e s t a r t i n g per c ola tion (to remove all a i r f rom the
b ed) in d ica t e d t h a t t h i s r e s u l t e d in an inc r e a s ed p e r c o l a t i on
11.
r ate aft e r c ompa c t ion of t he bed.
by the re s ults of s ub s e qu ent t e s t s .
Th i s wa s howe v e r not conf i rm e d
Su rface ten s i on of ju ice
T e epol , a d e t e r g e n t , and Suc r ap ol, a l ow fo am i n g s urf a c e
ten s i on r e duc e r , were t est e d for t h e i r ab ility to i n c r e a s e p e r c o-
la t i on ra t e by lowe r i ng s u rface t en s ion o f the ju i c e (thu s r e du cing
t h e quantity o f s t agnant liqu i d and a i r i n t h e bed).
Ne i t he r o f the s e p ro du c t s h ad a n y e f f e c t on perc ola t i o n r a t e
wh en added to the pe rco l a t in g ju i c e a f t er the be d h a d comp a ct e d and
the p e r co l a t i on r a t e s t a b ilis ed . Sucrapo l wa s t e s t e d i n the re-
commended concentration range of 9 t o 20 p . p . m. wh ils t T e epol wa s
tes t ed t o t h e l eve l wh e r e fo amin g b ecame exc e s s ive .
Ag i t a t i on o f b e d
I n an a t t empt t o r e duc e th e b e d densit y a t t h e b o t tom o f the
bed and thereby i ncr eas e p e rc o l at i o n r a t e, a i r , wa t e r and s t eam
were in ject ed i n t o th e bo t t om o f t h e b e d through t h e pe rfo r a t ed
p l a t e . No e f f e c t on p e rc o l a t i on r a t e was m e a s u r e d .
Bagac i llo add i tion t o s u r f a c e of b e d
Bagac illo was ad ded t o t he s u r face o f t h e c a n e b e d i n t he
p ilot p l ant d iffus e r to s i mu l ate c o nd i t i ons i n the fu l l s c a l e
dif fus e r .
In a movi n g b e d d i ffu s e r pith p art i cl e s wa s h ed out of the
bo t t om of the c ane bed a re r e-d epos ited on t he sur f a c e o f t h e bed.
From meas u r ements of p i t h co n t e n t in s t a g e juice i n t h e Amat iku lu
d i ffus e r , the qu ant i t y o f p i th depo s i t e d on the su rfa c e o f t he
b e d ( exclud i n g that added with p r e s s wa t e r) wa s e s t ima t ed to be z 1,8 kg/m .
1 2 .
The addit i on of b agac i l lo t o t he p i l ot plant equ iva l ent t o 2,�
k g /m2
cau s ed a r e d uct i on in percbla t ion r a t e o f 15%.
pH o f jui c e
The e f f e c t o f p H o n pe rcol a t ion rate i n t he pilot p l ant wa s
invest i g at e d both b y add i n g l im e a fte r t he b e d h ad comp a c ted and
the p e r c o lat i o n r a te s t a b i l i s e d t o che ck fo r any dec rea s e i n p e r
col a t i o n rat e, and by d o i ng dupl i c a t e t e st s a t d iff e r e n t pH's .
Tab l e 2 g i v e s the res ult s of two tes t s whe r e l ime wa s added
aft e r t h e p e r c o l a tion r a te h ad s t a bilis ed.
I n sert T ab l e 2.
In dup l icate t e s t s pe r fo rmed o n s u b -samp les o f the s am e c a n e
s amp l e, l i m e was a dded t o the wa t e r b efore s t a rt i ng pe rco l a t i on .
The fol l ow i ng r e s u l t s w e r e o b ta ined
In ser t Tab l e 3 .
I n t he te s t s we r e l ime wa s added t o t he s u rface of the bed
aft e r th e p e rcolat ion rat e h a d s t a b i l i s ed, some c ompac t ion o f t h e
bed o c c u r r e d . I t appe a r e d, h oweve r, t h a t only t h e s u r fa c e
o f t he bed mig h t be c o mp a c t ing, r e s u l t i ng in a s mall r egio n of
high density on the s u rface of th e b ed . Th i s would cause t he r e
du ct i o n i n perc o lat i o n r a t e without a sign ifi c ant drop i n t h e over
a l l b ed d e n s ity .
When l ime wa s u s ed i n the dup l i c a t e te s t s , (Ta b l e 3) i t wa s
add e d to the wate r, b e fo re s ta r t ing pe rco l a tio n . The c a n e b e d
t hus c ompa cted ev e n l y w i thou t t h e s u rfa c e o f t h e bed exp e rien c ing
high l ime con cen t rat ions, as in t he o t he r t e s ts . I n this t e s t
wh e r e l ime was u s e d , the bed d en s i ty wa s o n ly 2� h ighe r t han i n
the dup l i c a t e w i t hou t l ime, wh ils t as c an b e seen from T a ble 3 ,
t h e pe rcol a t i on r a t e w as 33� l owe r . The e f f e c t of l ime (pH)
o n p e rco l a t ion ra t e c anno t t hu s be e xp l a i n ed b y i t s e ffe c t on f i bre
p a ck i ng den s i ty a l on e .
13 .
Me a s urement of c ane qua l i t y and can e p repara t i o n
T o deve l o p n ume r ica l c or r e l at i o n s fo r perco l at i o n r a t e i t wa s
necess a ry t o quant i fy bo t h c an e qua l i t y and can e p repa r a t i on.
1) Can e qua l i ty
Cane qua l i ty , p art icu l a r l y in t e rm s of i t s e ffec t on perco l a
t i o n r a t e i n a d i ffuser , i s d i f f i cu l t t o qu an t i fy. No rma l l y
cane qua l i ty is m e a su r e d i n t e rm s o f t ops and tra s h but s i n c e
bur n t c an e of a s i ngl e v a r i e t y wa s us e d in t h e te s t s, t op s
and t ras h were found t o b e very l ow and d i d not va ry much
b e t we en s amples . The p e r c en t a ge of f i b r e i n the c a n e wa s found
to co r r elate we l l w i th d e n s i t i e s o b t a ined i n t h e c ane bed.
F i bre % cane h a s t hus b e e n s ele cted a s an a rb i t r a ry m e a sure o f
cane qu al i ty f o r t h ese t e s t s .
2) Can e p r e p a r a tio n
Alt hough t he leve l of p r epar a t i o n of c ane is u s u a l l y mea sur e d in
te rms o f P.I., t h i s applies t o the e x t ractab i l i t y o f t he can e
and n o t t o i t s pe r c o l a t ion b ehaviour . Part i cle s ize d i s t ri-
but i on, me a sur e d by s i eve ana l y s i s, i s a mo r e d i rect m e a su r e
o f c ane p r e p a r a t i o n and i s a l s o more d i rect l y app l i c a b l e t o
the p e rcolat i o n b e hav i ou r o f t h e c ane .
S i nce t he r e s ult s o f the s i ev i ng an a l y s is c o n s i s t o f f i v e p o i n t s
o n a cumu l a t i v e s ize d i s tribut i on curve, they c anno t b e u s ed
d irec t ly fo r co r r e l a t i ng w i t h p e rcola tio n ra t e. By nume rica l ly
f itt ing a smo o t h curve t o t h is cumu l a t i v e s ize d i s t r i but i o n,
t h e mome n �of t he d i s t r i but i on (me an , va r i a n ce and s kewn e s s )
and the s p e c i f i c surface o f t h e s hr e dded c a n e w e re c a l cu l a t e d
(Se e App endix 3).
Co r re l ation of p e rcola t i o n t e s t i ng res u l t s
A s p r e v i o u sly de sc r i b e d t h e e qu a t i on 3
1 4 •
(2)
has b e e n u s ed a s a b a s i s fo r c o r re l a t i n g t h e r e s ul t s o f t he pe r c o -
l a t ion t e s t s .
Of t he v a r i a bl e s i n t he above equa t i on , bo t h the voidage , E
and the ef f e c t i ve b e d he i g ht, ee, c anno t be m e asu red.
Rearr ang i ng e qu a t i o n (2) i n t o t he f o rm
Z 2 U S D =
3
( 3)
al l o w s t he unknown qu anti t y Kl £ (! ).2 to be c a l c u l a t e d from the
mea s u r e d va l ue s o f U , S and D. e e
Since both the v o idage , £ , and the r a tio of bed heigh t t o
e ffective bed he ight , e/€e s hould be d e p endent on t he par t i c le 3
size distribution o f t he c a n e , t h e c alcu la t ed values o f Kl £ (t )z 'le
we re i nve s t i ga t e d fo r cor re l a tio n s w i th mea s u r e s o f the par tic l e
si ze di s t r ibut i o ns . ( e.g . me a n , s p e c i f i c s u r fac e) . T h e best
co r r ela t i on s were obt a i ne d w i t h sp ec i f ic s ur f a c e , w i th a r e l a t i o n -
sh ip of the fo l lowing fo rm being sugg e s ted :
A l i ne a r r egres s i on o n t h e d a t a g ives n = 0,94.
T a k i ng nas unity an d s ub s tit u t i ng i n t o equ a t i o n (2) g i ve s
( 4) .2
SD
8 Th i s is s im i l a r to t he e q u a t ion (1 ) dev e l oped for flood ing
in a bag a s s e d i f fuser.
Fig . 4 shows p e rco l a t ion r a t e (U ) pl otte d agains t 1 •
SD2
In s e r t Fig . 4
A linear regression on t he dat a gives
1 U = 4,98 x 10
15.
:I SD (5)
which is s i gn i f i ca n t at the 0,1� l evel. Th i s is s hown a s t he
sol i d line in Fi g . 4.
To complet e the cor r e lat i o n o f perco lation rate w i th the
fac t ors varied in the t e sts , the dependence o f bulk f ib re
den s ity (D) on f ibre in cane , bed h e i gh t a n d level of p repa ra
tion must b e o b tained.
Unfortunately the t e s t s f o r whi c h partic l e size anal yse s
are ava ilable , o nly hav e a sma ll v a ria t i on in bed h e i ght and the
dep endence of density on bed hei ght mus t be corr e lated s ep a ra t e ly
by inc lud i ng o t he r r e s u lts ove r a wid e r range of b ed h e i ght.
From a line a r r e g r e s s i on, the c o r r e l at ion
D = F (a � + b) (6)
wa s found to be s i gn ifican t at t h e 0 , 1 � l evel, wit h a = 0 , 58 and
b = 4,3, despite the fact tha t t he s e t est s inc lud e d a w i d e range of
l evels o f c ane p rep a r a t i on.
In lin e a r co r re l a tions of b e d dens i ty w i th me a s ures of the
par t ic l e size distributions, t h e b est c o r re l a t i o n s we re o b t a ine d
with the inver s e o f t he mean par t i c l e s i ze.
I f i t is assumed tha t bed density i s i nver s e l y r e l a t e d t o
m e a n partic l e size, w i th a finit e max imum d e n s i t y for infinitely
16 .
small p a r tic l e s i z e s , the fo l l ow ing r e l a t i ons h i p f o r dens i t y c an
b e ex p e c t ed
D c - M+""g F (a t + b) (7)
whe re M is t he m e an pa r t ic le size (mm ) .
Us i ng the p revi ou s ly d e t e rm i n ed v a l u e s o f a and b in a
non- l i n ear r egre s s i o n o n the res u l t s fo r which p a r t i c l e s ize
ana lyse s a r e av a ilable y i e lds
c
g
=
=
26 , 5
2 1 ,2
w i t h a c o r r ela t i o n c o e f f i c i ent o f 0 , 9 98 .
T r ace r tes ting i n the p i lo t p lan t d i f fu s e r
To ana lyse t he se results, a smo o t h c u rve wa s d r awn t h rough the
conductivity t r ace o n t h e r e c o r d e r cha r t and d a t a po i n t s read o f f
t his curve, rela t ive t o the ba s e - l ine conduc t iv i ty .
These data p oint s were use d fo r p e rfo rming computerised non
l i nea r regressions to fit the flow mo de ls t o t h e ex p e r iment a l
results.
Fig . 5 shows t he f i t of the two f l ow mode l s v i z . axially d isp e rse d
plug flow and plug f l ow w i t h e x c h ange w i th s t a gnan t r e gion s,t o a
set of exper iment a l data.
Ins e r t F ig . 5
Sinc e a b e t t e r f i t was ob t a i n e d w i t h t h e a x i a l ly d i s pe r s e d p l ug
flow mo de l , t h i s m o d e l w a s u s e d in pref e r enc e to the p l ug f l ow
with e x c h ange mo d el .
The results of t race r tests ( dete rmined by fit t ing the mo d e l
to the e x pe r imen t a l d at a ) , a r e g i v en i n Tab l e 4 .
In ser t Tab l e 4 .
17.
The perco l at i o n ve l o c i t i es de t erm i n e d from the tracer t e s t s are
l a r g er t h an t he perco l at i o n r at e s (s up e rf i ci a l v e l o c i t i e s) due t o
the re duc t i on i n flow area in th e b ed . The ratio of p e rco l atio n
r a t e (U) to pe r colat i on v e l o c i t y CV) is thu s a m e a s u re o f t he voi
d age o f t he b e d i . e . t h e vo l ume f r ac t i o n o f t h e bed ava i lab l e t o
t h e f l o w i ng l iqu i d .
No co r r e l a t i o n i s ev i d en t b e twe en t h i s e s t imat e o f bed vo ida g e
and e i t h e r b e d d e n s i t y or me an pa rti c l e s i z e . However t he ave r ag e
va lue of t he v o i da g e o f 0,70 i s of i n t e r e s t be c au s e t h e po sition i ng
of s p ray s i n a mov i ng b e d t yp e d i ffuser depends on the p erco l at i o n
veloc i ty and n o t t he perco l at i on r a t e.
The ax i a l d i s p er s i on coe f f i c i en t (EZ) i s a meas u r e of t h e
amount o f m i x i ng i n t h e b e d i n the d i r e c tion o f fl u i d f low . F i g . 6
s hows how t h e d i s p e r s i on c o e f f i c i en t i n c re a s e s w i t h i nc rea s i ng pe r -
co l at ion ve l o c i ty .
I ns e r t F i g . 6
Fo r compar i s o n w i t h oth e r work on d i s p e r s ion i n p ac k e d b e ds,
the r e s u l ts mu s t b e compar e d i n t e rm s o f P e c l e t and Reyno lds numbers .
Fo r ave rage value s f r om Tab l e 4, t h e Pec l e t numb e r (Pe = vM/EZ)
i s 0,06 an d the Reyno lds number (Re = UpM/p) i s 19,9. C omp aris o n
w i th e s t ab l i s hed cor r e 1a t ion sS
s how th i s Pec l et numbe r to b e con-
s i d erab l y l owe r by a fa c t o r of roug h t l y 30. Th i s i nd icat e s t hat
d i s per s i on in a c ane bed i s far gre at e r t han tha t no rma l l y foun d i n
a g r an u l a r b e d .
Liquid ho 1 d up i n bed
The tot a l l iquid ho l dup i n t he b e d du r ing p e rc o l at ion exp ress e d
as mas s of l i qu i d per u n i t ma s s o f f i b r e was found to d e c re as e
w i t h incre a s ing bed den sity (Fig . 7). This is p robably due t o
t he d ecre as e d vo i d s p a c e s a t h i gher b ed d e n s i t i e s a lthough the r e
I nse r t F i g . 7
1 8 .
m i g h t b e s ome e f fe c t r e s u l t i ng f r om t he l owe r p e rc o l a t i o n r a t e s
a t h i gh e r b e d d e ns i t i e s .
The ave r a g e v a l ue o f 1 1 , 5 kg/ kg f i b r e i s s i gn i f i c a nt l y h i gh e r
t h an t h a t p r e v i o u s l y me a s u r e d i n a b a g a s s e d i f f u s e r8 ( l O kg/kg f i b re ) .
FUL L S CAL E D I F FUS E R T RAC ER TESTS
A t yp i c a l conduc t iv i t y r e c o r d i n g d u r i n g a t rac e r t e s t o n t h e
fu l l s c a l e d i f fu s e r a t Ama t i ku l u i s s hown in Fig . B .
I n s e r t F i g . S
To an a l y s e t he s e r e s u l t s , smo o t h c u rv e s we r e d rawn t hr ou g h
t h e c onduc t i v i t y t r a c e o n t h e r e c o rd e r c ha r t , and d a t a p o in t s r e a d
o f f t h i s curve r e l at i v e to t h e b a s e l i n e conduc t iv i ty .
The e qu a t i o n s p re v i ou s l y deve l o p e d f rom t h e mo de l o f p l u g f l ow
w i t h d i s p e r s i on ( s e e Ap p end i x 2 ) were f i t t e d t o t h e s e d a t a p o i n t s
u s i n g a c omput e r i s e d non- l i n e a r r e g r e s s i on t e c hn i qu e .
The f i t o f t h e mo de l t o t he e xp e r iment a l r e s u l t s i s s hown in
F i g . 9 .
I n s e rt F i g . 9
T h e r e s u l t s o b t a in e d by f i t t i n g t he mode l t o t h e da t a f r om
t r a c e r t e s t s o n t h e Ama t i ku l u d i f fu s e r a r e s hown i n T ab l e 5 . The
t e s t s we r e a l l p e r f o r m e d o n s t a g e s 5 , 6 and 7 o f t h e d i f fus e r wh i c h
c o n t a i n s 1 3 s t a g e s .
I n s e r t Tab l e 5 .
Al t hough s ome o f t he s e t ra c e r t e s t s we r e und e r t aken when f l o o d
i n g w a s no t o c c u r r i ng t o a n y g r e a t e x t e n t , t h e p e rc o l at i o n r a t e s
a r e s t i l l c o n s i d e r ab l y l owe r t h a n t h o s e o b t a i n e d i n t h e p i l o t p l ant ,
and l owe r t han t h e v a l ue o f 0 , 2 6 m / m i n r e p o r t e d by Payne 7 i n Hawa i i .
The r e a s on fo r t h i s l a r g e d i s c r e p a n c y h a s n o t y e t b e en adequ a t e -
l y e xp l a i n e d . Howev e r t h e e f f e c t s o f b a g a c i l lo add i t ion and l ime
add i t i o n a r e l a r g e enough to exp l a i n t he s e d i f fe r e nc e s .
19.
The ax i a l d i spe r s ion c o e f f i c i en t s c a l cu l a t e d fo r t he s e t e s t s a r e
s i gn i f i c an t l y h i gh e r t h an t ho s e me a s u r e d i n t h e p i l o t p l an t d i f fu s e r .
The r e s u l t s s ho w a n i nc r e a s e i n d i s p e r s i on w i t h i n c r e a s i n g p e rc o l a
t i o n ve l o c i t y wh i c h i s g r e a t e r t ha n t h a t foun d w i t h t he p i l o t p l an t
r e s u l t s a s s hown i n F i g . 1 0 b e l ow . Th i s can b e e xp l a ine d by a mo re
t o r tuou s bed or a b e d wh ic h i s n o t un i fo rm a c ro s s i t s who l e w i d t h .
S i nc e b e d d e n s i t i e s o f c omp a r ab l e va l u e h av e b e e n o b t a i n ed i n t h e
p i l o t p l an t an d t he d i f fu s e r o n t h e s am e c an e , t h e f o rm e r i s un l ik e l y .
Be c a u s e o f th e g r e a t w i dth of t h e Ama t i ku l u d i f fu s e r ( 1 1 m ) , i t i s
d i f f i c u l t t o en su r e a n ev e n b e d ac r o s s thi s len g t h , and t h i s c o u l d
we l l ac c oun t f o r t he i n c r e a s e d s p r e a d i n r e s i de nc e t ime s wh i c h t h e
h i g h e r d i s p e r s ion c o e f f i c i en t imp l i e s .
I n s e r t F i g . 1 0
The d ev i a t i on from s t a g ew i s e pe r c o l a t i on i s in a l l b u t o n e o f
t h e t e s t s , in t h e f o rm o f byp a s s i n g ra t he r t h an r e c yc l e . Th i s
in d i c a t e s t h a t t h e d i f fu s er s p r a y s h a v e b e e n a dv a n c e d t oo f a r t o
wa rd s t h e h e a d end o f t he d i f fu s e r i n an a t t emp t t o r e du c e f l o o d ing .
T r a c e r t e s t s w e r e a l s o p e r fo rm e d o n t he Ton g a a t c ane d i f fu s e r
fo r c ompa r i s o n purp o s e s , o n s t a g e s 4, 5 and 6 .
S in c e in the T onga at d i f fu s e r , j u ic e i s a d d e d t o t h e t op o f
t he b ed from we i r s ( and n o t from s p r a y s wh i c h e f fe c t ive l y c o v e r t h e
who l e s u r f a c e o f t h e b e d ) t h e re mu s t b e s ome ho r izon t a l p e r co l a t i on
o f j u i ce to c omp en s a t e fo r t h e ove r load i n g o f t h e b e d d i r e c t l y b e l ow
t h e w e i r s . I t i s mo s t l i ke l y t h a t t he d i re c t ion o f t h e ho r i z ont a l
p e r c o l a t io n o f t he j u i c e from t h e po i n t whe r e t h e j u i c e i s added
w i l l b e t owards t he f e e d end o f t h e d i ffus e r s i n c e t h e b e d on t h e
d i s ch a rge s i d e o f t h i s p o i n t h a s j u s t p a s s ed unde r t he w e i r and
s hou l d t h u s b e s a tu r a t ed w i th j u ic e .
2 0 .
The e ff e c t o f t h i s h o r i z on t a l p e r c o l a t i o n wa s c omp e n s a t e d fo r
by a s s um i n g , i n t h e m a t hemat i c a l mode l u s e d fo r ana l y s i n g t h e r e
s u l t s , t h at t h e j u i c e i s a d d e d o v e r 2 , 0 m o f b e d l en g t h f rom b e l ow
t he we i r t owa rd s t h e f e e d end of the d i f fu s e r . F r om v i su a l o b
s e rv a t i o n s , t he a c t ua l l en g t h o f b ed o v e r wh i c h t he j u i c e i s
add e d f r o m t he we i r i s o n l y a b o u t 0 , 6 m .
The f i t s of t h e mod e l t o t h e exp e r ime n t a l da t a , e v e n w i t h t h i s
emp i r i c a l c o r r e c t i o n , a r e n o t a s g o o d a s t h o s e a c h i e v e d w h e n a n a
l y s i n g t h e Ama t i ku l u d a t a . T h e r e s u l t s a r e t abu l at e d b e l o w
I n s e r t T a b l e 6 .
The p e r c o l a t i on v e l o c i t i e s m e a s u r e d a r e o n ave r a g e s im i l ar t o
t ho s e me a su r e d a t Ama t i ku l u a l t ho u g h s i gn i f i c an t l y l owe r v a l u e s h a v e
b e e n m e a s u r e d a t Ama t i ku l u ( S e e T a b l e 5 )
A s i n g l e s amp l e o f s h r e d d e d c ane f rom Ton g a a t wa s a n a l y s e d
fo r pa r t i c l e s i z e by t h e s am e g r a d i n g me t ho d u s e d fo r a l l t e s t s
a t Ama t i ku l u . T h e s hr e d d e d c a n e wa s found to b e c o a r s e r t han any
u s e d i n t he p i l o t p l an t p e r c o l a t i o n t e s t s .
CONC LUS I ON S
A c o r r e l a t i o n ha s b e e n d ev e l op e d f rom t h e Ko z eny C a rman e qua
t i o n fo r f l ow t h r ough p a c k e d b e d s , wh i c h c o r re l a t e s p e r c o l a t i o n
r a t e s w i th d e g r e e o f p r ep a r a t i o n and b u l k f i b r e d e n s i ty . L o w b u l k
den s i t i e s and c o a r s e p r e p a r a t i o n l ea d t o h i g h e r max imum p e r c o l a t i o n
r a t e s . P r e p a ra t i o n h a s a f u r t h e r e f f e c t i n t ha t i t a f fe c t s b u l k
f i b r e d en s i t y ; a c o r re l a t i on fo r d e n s i ty i n t e rm s o f p re p a r a t i o n ,
b e d he i g h t and t he f i b r e c o n t e n t of the c an e has b e en p roduc e d .
De g r e e o f c an e p r ep a ra t i o n w a s v a r i e d b y c hang i n g t h e s hr e dd e r
s p e e d and the c l e a ranc e b e tween haIllffie r s and. a nv i l s . I t wa s no t
p o s s i b l e t o e s t ab l i s h how t he s h redd e r s h o u l d b e op e r a t e d t o g iv e
t he o p t imum t yp e o f p re p a r a t i o n f o r d i f fu s i o n , t o a c h i ev e b o t h a
h i g h d e g r e e o f f i n e n e s s and an o p e n b e d p romo t i n g h i gh p e r c o l a t i on
2 1.
r a t e s . The va r i an c e and t h e s kewn e s s o f t h e p a r t i c l e s i z e d i s
t r i b u t ion d id no t app e a r t o a f fd c t b e d d en s i t y i n a c o n s i s t e n t way .
Othe r fac t o r s wh i c h we re i nve s t i g a t ed i nc l ud e d t h e e ff ec t s o f
me t hod o f pac k ing t he p i l o t p l ant c o l umn , s u r face t e ns ion and
ag i t a t i o n o f the b e d , none of wh ich had a s i gn i f i c an t e f f e c t . The
quan t i ty o f b a g a c i l l o depo s i te d o n t h e t o p s u r face of a d i ffu s e r
s hou l d not hav e a subs t an t i a l e f fe c t on t h e max imum percol a t i o n
r a t e , b u t t h e p H o f t h e p e r c o l a t i n g l i qu i d d o e s h av e a v e r y s i gn i
f i c an t e f fe c t .
U s e h a s b e e n m a d e o f t h e d i s p e r s i on mode l t o ana l y s e t r a c e r
t e s t s i n t he p i l o t p l an t c o l umn . Th i s y i e l d s i n fo rma t io n o n t h e
a c t u a l l i qu i d v e l o c i t i e s t h rough t h e b e d . Rat i o s o f app l i e d
li quid p e r co l a t i on rat e s t o a c t u a l p e rc o l a t i o n ve l o c i t i e s we r e
found t o av e ra g e 0 , 7 0 .
o b t a i ne d from t h e mode l .
I n a dd i t i on d i s p e r s i o n co e f f i c i e n t s a r e
The s e i nd i c a t e t ha t t h e d e g r e e o f d i s -
p e rs i o n o c cu r r i ng i s v e ry much l ar g e r t h an t h a t found i n b e d s o f
m o r e c onv ent i on a l p a c k i n g mat e r i a l s .
T r ac e r t e s t s have b e e n und e r t a k e n i n fu l l s c a l e d i f fu s e r s .
O f int e r e s t i s t h e l ar g e d e g r e e o f f l ow byp a s s i n g n ec e s s a ry t o
r edu c e f l ow r a t e s t o a p oin t whe r e f l o o d ing i s n o t a p r ob l em .
The d i s p e r s i o n mo d e l h a s b e en app l i e d t o the s e t e s t s a s we l l , and
appe a r s to ad equa t e ly de s c r i b e the f l ow p ro c e s s . Pe rco l at i o n
ve l o cit i e s a r e o n av e ra g e s i gn i f i c an t l y l o w e r i n t h e fu l l s c a l e
d i ffu s e r s t h an t ho s e m e a s u r e d i n t h e p i l o t p l ant . I n add i t i o n a
g r e a t e r d e g r e e o f d i sp e r s ion i s p r e s e n t , wh i ch may b e c a u s ed by
un ev enne s s i n t h e d i ffus e r b ed .
Th i s inve s t i g a t i on h a s p rov i d e d s i gn i f i c a n t in s i gh t ' int o t he
fl ow p ro c e s s e s , and t h e exp e r imen t a l t echn i qu e s h av e b e en u s e d t o
op t im i s e d i f fus e r s p ray po s i t i o n s .
NOMENC LATURE
A D imen s i o n o f mov ing b e d d i f fu s e r ( m )
C C o n c e n t r a t i o n o f t ra c e r i n p e r c o l a t ing j u i c e
Conc e n t r a t i o n o f t ra c e r i n st a gn a n t j u i c e
Conc ent r a t i o n o f t ra c e r i n d i f fu s e r t ray B
C o n c e n t r a t i o n o f t ra c e r i n d i f fu s e r t ray D
C o nc en t ra t i o n o f t ra c e r i n d i f fu s e r t r ay R :5
Bu l k f i b re dens i t y o f c a n e b e d ( kg /m )
2 2 .
:5 ( kg /m )
:5 ( kg / m )
:5 ( kg /m )
:5 ( k g /m )
:5 ( kg / m )
D i sp e r s i o n c o e f f i c i ent In d i re c t i o n p e rpend i cu l a r t o p e rc o l a t i o n (mz /m i n )
Z D i s p e r s i o n c o e f f i c i e n t i n d i r e c t i o n o f p e r c o l a t i o n (m /m i n )
F ib r e i n c an e ( \ )
f ( x ) F requ ency d i s t r i bu t i o n o f p a r t i c l e s i z e s Z
g G r av i t a t i o n a l c on s t an t (m/ s e c ) 3
H S t a t i c l i qu i d ho l dup i n c a n e b e d ( kg /m )
H ( x ) H e av i s i d e s un i t func t i on
h He i g h t ( m )
I , Mod i f i e d B e s s e l func t i o n o f t h e f i r s t o r d e r
K # ) )
Ko ) P r o po r t i o na l i t y c o n s t an t s . )
K 1 ) ) K 2 )
K M a s s t r an s fe r c o e f f i c i en t b e tween s t agnan t and dynam i c l i qu i d ho l du p s .
L T r ay l eng t h i n mov i n g b e d d i f f u s e r ( m )
€ B e d h e i g h t ( m )
e e E f f e c t i v e b e d he i gh t ( m )
M M e an p a r t i c l e s i z e ( mm )
Pe P e c l e t numb e r
P C omb i n e d e f f e c t o f s t a t i c p r e s s u r e a n d g rav i t a t i on a l fo r c e e N /mZ )
Q
t
u
v
v
w
y
Z
et
Cl
S
V
Qu ant i t y o f t ra c e r added p e r u n i t a r e a o f b ed su r fa c e ( k g /m2 )
Re yno l d s,
numb e r z
Spe c i f i c su r fac e o f s h r edded c a n e (m / k g )
2 3 S p e c i f i c s u r f a c e o f c ane b e d ( m /m )
L e n g t h o f b e d o v e r wh i ch t ra c e r i s a dded (m )
T ime (m i n )
Pe rco l a t i on r a t e ( m /m i n )
B e d v e l o c i t y o f mov ing b e d d i f fu s e r (m/m i n )
Pe r c o l a t i o n v e l o c i t y ( m/m i n ) 3
Dy n am i c l iqu i d ho l du p i n c ane b e d ( k g /m )
Co - o rd in a t e i n d i re c t i on o f mo v em en t o f c an e b e d
D i s t a n c e f r om t o p of c an e b e d
S u r f a c e s h a p e f a c t o r
Vo lume s h a p e f a c t o r
o ( x ) D i ra c impu l s e func t i on
£; Vo i d a g e o f c an e b e d 3
p D e n s i ty o f j u i c e i n b e d ( kg /m )
)l V i s c o s i t y o f j u i c e i n b e d ( kg /m m i n )
° 1 M e a n of p a r t i c l e s i z e d i s t r i b u t i o n
° 2 V a r i a n c e o f p a r t i c l e s i z e d i s t r i bu t i o n a 3 S k ewne s s o f p a r t i c l e s i z e d i s t r i bu t i o n
2 3 .
1 •
RE F E RENC E S
B i r d , R . B . , W . E . S t ewa r t and E . N .
phe nomen a John W i l e y New Y o r k .
2 4 .
L i g ht fo o t ( 1 9 6 0 ) . Trans p o rt
7 8 0 p
2 . C a r s l aw H . S . and J . C . J a g e r ( 1 9 5 9 ) . C o nduc t i o n o f he a t i n
s o l i d s Ox f o r d Un i ve r s i ty P r e s s Ox f o r d .
3 . Gunn, D . J . ( 1 9 6 8 ) . M i x in g i n p ac ke d and f l u i d i s e d b e d s Chem .
En g r ( London ) 2 1 9 1 5 3 .
4 . Lav i � R. E . ( 1 9 6 4 ) . M . S . Th e s i s Po l y t e c hn i c I n s t . o f B ro o k l yn
5 . Leve n s p i e l , O . ( 1 9 6 2 ) . Chem i c a l R e a c t i o n Eng i n e e r i n g John W i l ey
N ew Yo r k . 5 0 1 p
6 . Ma t t h e s iu s , G . ( 1 9 7 7 ) . An i n v e s t i g a t i o n o f j u i c e f l ow b e hav i o ur
i n c an e a n d b a g a s s e d i f fu s e r s . P r o c . I S S C T 1 6 : 2 1 8 7 - 2 1 9 7
8 . Re in , P . W . ( 1 9 7 2 ) . A s t udy o f t h e c a n e s u g a r d i f fu s i o n p r o c e s s
PhD t h e s i s . Un i v . o f N a t a l 3 3 0 p .
9 . Re i n, P . W . ( 1 9 7 4 ) . P r e d i c t ion o f t h e e x t r a c t i o n p e r fo rmanc e o f
a d i f f u s e r u s i ng a mat hema t i c a l mod e l . P r o c . I S S CT 1 5 : 1 5 2 3 -
1 5 3 7 .
1 0 . Van Swa a i j , W . P . M . , J . C . C h a r p e n t i e r and J . V i l l e rmaux ( 1 9 6 9 ) .
Re s i d e n c e t ime d i s t r i bu t i o n i n t h e l i qu i d p h a s e o f 't r i c k l e f l ow
i n p a c ked c o l umn s . C hem . Eng . S c i . 2 4 : 1 083 .
1 1 . V i l 1 e rmaux, J . and W . P . M . Van Swa a i j ( 1 9 6 9 ) . Mo d e l e r ep r e s en
t a t i f d e l a d i s t r i b u t i on d e s t emp s d e s e j o u r d a n s un r e a c t e u r
s em i - i n f i n i a d i s p e r s i o n ax i a l e av e c z one s s t a gn an t e s . Ap
p l i c a t i o n a l ' ecou l ement ru i s s e l a n t d a n s d e s c o l onn e s d ' anneaux
Ra s c h i g . Chem . Eng . S c i . 2 4 : 1 0 9 7 .
APPEND I X 1 . 2 5 .
The Ko z eny C a rman equa t i on
The Ko z eny C a rman equat i o n i s g iv e n b y . . :z
liP = K Sb (f e }l U f
0 :z
-3 - ) E -f-
whe r e P r ep r e s en t s t h e c omb i ne d e f f e c t o f s t a t i c p r e s s u r e and
g r av i t a t i o n a l fo r c e i . e .
P = p + p g h
Fo r t he s i t u a t i o n whe r e f l o o d i n g j u s t b e g i n s t o o c cu r o n t h e s u r fac e
o f t he b e d ,
u
liP = p gf
=
The s p e c i f i c s urf a c e o f t h e b e d i s r e l a t e d t o t h e s p e c i f i c s u r f a c e
of t he p a r t i c l e s b y :
T h u s for c o n s t an t l i qu i d d e n s i t y and v i s c o s i ty ,
3 e:
:z :z S D
APPEND I X 2 .
So l u t i o n o f t w o d imen s i on a l d i sp e r s ion
- v oC 52
c C 6t
2 6 .
( 3 )
whe r e C i s t he c o n c e n t r a t i on o f t r ac e r a t po int y Z a n d
t ime t
y , Z a r e the r e c t an gu l a r c o - o rd in a t e s
t i s t he t ime
Ey ' EZ are t he d i sp e r s ion c o e f f i c i ent s i n y a nd Z co - o rd i n at e
d i re c t i ons r e s p e c t i v e l y .
V i s t he f l u i d v e l o c i t y i n t h e Z d i r e c t i on .
The i n i t i a l cond i t i on s fo r t h i s e qua t i o n a r e o b t a i n ed b y c o n s i d e r i n g
t he cond i t i o n s d u r ing a t r a c e r t e s t .
At t ime t = 0, a p u l s e o f t ra c e r i s a d d e d t o t h e s u r f a c e o f t he
bed ove r a l en g t h o f b e d , T , a c ro s s t h e fu l l w i d t h o f t he b e d . The
c o - o rd in a t e s are f i xed r e l a t i v e to t h i s p o i n t o f t ra c e r a dd i t i o n a s
s hown in F i g . 2 . Unde r t h e s e c on d i t i o n s , t h e s o l u t i o n t o t h e d i f f e r e n t i a l
equa t i o n i s
C ( y , Z , t ) = _Q�_ 4 ( lT t E Z ) !
z ex p { - ( Z · vt ) } [ e r f y - e r f 4 t E Z ( VfE ) y
y - T ] ( 2rt£: ) y
At a ny t ime t t h e po s i t i on of t he j u i c e t r ay s B , D and R r e
l a t i v e t o t he c ane b e d are g i v e n by :
Tra y B
T r ay n
Tray R
f rom
f rom
f rom
y = A - V t
y = A + L - V t
y = A + 2 L - V t
t o
t o
t o
y = A + L - V t
y = A + 2 L - Vt
y = A + 3 L - Vt
2 7 .
The c on c en t r a t i o n o f t ra c e r l eav i n g a t r ay a t t ime t may be
e qu a t e d t o t he ave r ag e c on c en t r a t i o n o f t ra c e r l e av ing t h e c ane b e d
d i re c t l y a b o v e t h e t ray
Cn ( t ) :::
and
CR ( t ) =
A+ L -Vt _1_ r
C ( y , e , t ) dy
L A- V t
A+ 2 L -Vt 1 f C C y , € , t ) dy -r
A+ L - V t
A+ 3 L - V t
1 ! C ( y , .e , t ) dy -r
A+ 2 L - Vt
B y f i t t i ng t h i s equa t i on t o t h e re su l t s o f t h e t r ac e r t e s t s , e s
t im a t e s o f t h e p e rc o l a t ion v e l o c i t y v and t h e d i s p e r s i o n c o e f f i c i en t s
Ey ' E Z c an b e o b t a i n e d .
I t c an b e s e en f r om F i g . 2 t h a t t o a c h i e v e s t a g ew i s e p e r c o l a -
t i o n w i t h o u t r e c y c l e o r byp a s s i n g , t h e b e d mu s t have t r av e l l e d a
d i s t an c e A + 1 , 5 L - O , ST . For 1 0 0 % r e c y c l e t h e b e d w i l l hav e
t r av e l l e d A + 2 , S L - O , S T and fo r 1 0 0 � byp a s s i ng t h e b e d w i l l have
t rav e l l e d A + 0 , 5 L - O , S T .
. ' . t he p e rc e nt a g e o f r e c y c l e o r byp a s s i n g i s g i v e n b y
Re cy c l e / b yp a s s i n g = 1 0 0 ( V� _ CA + 1 , S L - O , S T ) ) % L v
whe r e + v e v a l u e i n d i c a t e s r e c y c l e
- v e v a l u e i nd i ca t e s byp a s s i ng .
2 8 .
APPEND I X 3
P a r t i c l e s i z e d i s t r i b u t i o n c a l c u l a t i o n s
The r e s u l t s o f a g r a d i n g t e s t a r e ava i l a b l e a s t h e m a s s
f r a c t i o n o f pa r t i c l e s l e s s t han f i v e g i ven s i z e s . I t h a s b e e n
found t h a t t h e s e r e s u l t s c an b e f i t t e d by a c u rv e of t he fo rm : 3 :: - 1 y = exp ( a x + b x + c x )
whe r e y i s t he ma s s f ra c t i o n o f p a r t i c l e s l e s s t h an a g iven
s i z e x .
The f re qu e n c y d i s t r i b u t i o n o f p ar t i c l e s i z e s i s t h u s g iv e n by
f e x ) = * :: 3 2 - 1 3 2
= ( 3 ax + 2 b x + c ) exp ( a x + b x + c x ) tn ( ax + b x + c x )
The momen t s o f t h e d i s t r i b u t i o n may be c a l c u l a t e d f rom : 00
(J = [ x f ( x ) dx 1 0
(J [00 :: = ( x - � ) f ( x ) dx 2 0
(J [rtl 3 = ( x- � ) f ( x ) dx 3 0
I t c an b e s hown t h a t t he s p e c i f i c s u r f a c e o f t he s h r e dded c ane i s
g i v e n by
/OOf e x ) d x x
S i n c e i t i s d i f f i c u l t t o e s t ima t e t h e a c tu a l vo l ume and s u r f a c e
s hap e f ac t o r s , a r e l a t ive va l u e fo r s p e c i f i c s u r f a c e may b e
o b t a i n e d by a rb i t r a r i l y s e t t i ng
= 6 P
t he n S = d x
A compu t e r p r o g r am i s ava i l a b l e t o eva l ua t e t he moment s and t he
s p e c i f i c s u r fa c e when g iv e n t h e p o i n t s o n t h e cumu l a t iv e s i z e
d i s t r i bu t i o n c u rve f rom t he g rad ing ana l y s i s .
L i s t o f Tab l e s
1 . Reproduc i b i l i t y t e s t r e su l t s
2 . E f fec t o f l ime a dd i t i o n on p e r c o l a t i o n r a t e
3 . E f f e c t o f l ir.le on pe r.c'o l a t i o n r a t e
4 . Re s u l t s o f p i l o t p l a n t t ra c e r t e s t s
5 . Re su l t s o f t r a c e r t e s t s o n Ama t i ku l u d i f fu s e r .
6 . Re s u l t s o f t ra c e r t e s t s on Tonga a t d i f fu s e r
2 9 .
Tab l e 1 Rep r oduc i b i l i t y t e s t r e s u l t s
Bed he i ght B e d dens i tr P e r c o l a t i o n r a t e (m ) ( kg f i b r e /m ) (rn/m i n )
A B A B A B
0 , 9 6 0 , 8 5 6 3 , 4 6 5 , 6 0 , 2 3 0 , 2 4
0 , 8 1 0 , 7 5 6 9 , 8 7 2 , 9 0 , 2 5 0 , 2 4
0 , 8 4 0 , 7 5 7 5 , 7 7 5 , 1 0 , 1 8 0 , 1 8
1 , 7 6 1 , 7 1 7 5 , 4 7 5 , 6 0 , 1 8 0 , 1 8
I 1 J 5 4 1 , 5 4 6 2 , 3 6 1 , 6 0 , 3 3 0 , 3 3 I
3 0 .
T a b l e 2 E f fe c t o f l ime a dd i t i o n o n p e r c o l a t i on r a t e
I n i t i a l p H a f t e r P e r c o l a t i o n Pe rco l a t i o n p H l ime ra t e b e f o r e r a t e a ft e r
add i t i o n l im e ( m /m in ) l im e ( m /m i n )
5 , 3 7 , 8 0 , 3 3 5 0 , 1 4 7
5 , 1 8 , 6 0 , 2 4 8 0 , 0 8 4 '----
3 1.
T a b l e 3 E f fe c t o f l im e o n p e r c o l a t i on r a t e
...---' P e r c o l a t l on pH ra t e
(m/m i n )
W i t hout l ime a dd i t i o n 5 , 2 0 , 2 0 0
W i t h l ime a d d i t i o n 7 , 6 0 , 1 3 4
Tab l e 4 Re s u l t s o f p i l o t p l an t t ra c e r t e s t s
B e d Me an Va r i an c e F i b r e P a c k ing h e i gh t tpa:- t i cl e o f p a r t i - i n c an e d e n s i t y
S 1 z e c l e s i z e
2 ( m ) (mm ) (mm ) (% ) ( kg f i b /
3 m )
1 , 3 9 6 , 4 4 6 2 , 7 1 6 , 4 3 8 3 , 1 1 , 5 0 - - 1 4 , 2 0 7 9 , 0 1 , 7 0 5 , 1 7 6 3 , 3 1 5 , 8 6 8 2 , 7 1 , 5 8 - - 1 2 , 8 5 6 8 , 0 1 , 5 3 4 , 2 2 4 5 , 6 1 4 , 7 0 7 8 , 4 1 , 52 5 , 0 2 6 2 , 6 1 2 , 9 0 7 2 , S 1 , 5 2 4 , 7 9 4 9 , 8 1 5 , 1 4 8 0 , 7 1 , 4 5 6 , 4 2 6 S, 3 1 0 , 2 6 4 9 , 9 1 , 3 6 - - 1 4 , 7 6 6 3 , 9 1 , 4 7 - - 1 7 , 3 9 8 7 , 6 1 , 1 3 5 , 4 5 5 5 , 4 1 4 , 6 2 7 5 , 8
!Me an 1 , 4 7 5 , 3 6 5 8 , 4 1 4 , 5 7 4 , 7
Pe r c o l a - P e r c o l a -t i on ra t e t i on v e -
l o c i ty
(m/m in ) (m/m in)
0 , 2 3 0 , 3 1 0 , 1 7 0 , 2 4 0 , 1 5 0 , 2 1 0 , 2 1 0 , 2 9 0 , 2 1 0 , 3 0 0 , 24 0 , 38 0 , 2 8 0 , 4 0 0 , 3 2 0 , 4 5 0 , 2 1 0 , 3 1 0 , 1 9 0 , 2 9 0 , 2 5 0 , 3 4
0 , 2 2 0 , 3 2
D i s p e r s i m c o e f f i - -c i ent
2 (m / m i n )
0 , 0 3 7 0 , 0 1 8 0 , 0 1 5 0 , 0 2 4 0 , 0 3 1 0 , 0 3 7 0 , 0 4 5 0 , 0 4 1 0 , 0 2 2 0 , 0 3 1 0 , 0 2 1
0 , 0 2 9
Ra t i o o f p e r-c o l a t i o n v e -l o c i t y t o p e r -c o l a t i o n r a t e
0 , 7 4 0 , 7 1 0 , 7 1 0 , 7 2 0 , 7 0 0 , 6 3 0 , 7 0 0 , 7 1 0 , 6 8 0 , 6 6 0 , 7 4
0 , 7 0
� N
Ta b l e 5 Re s u l t s o f t r a c e r t e � t s o n Amat i ku l u d i f fus e r
B e d B e d Cane Pe rc o l a -h e i g ht s p e e d th r ou g h - t i on Ve -
put l o c i t y (m ) (m/m i n ) ( t o n s /hr ) Cm/m i n )
t , 7 0 , 7 0 - 0 , t 7 1 , 7 0 , 6 3 - 0 , 1 4 1 , 7 0 , 7 5 - 0 , 2 0 1 , 7 0 , 62 - 0 , 2 8 1 , 6 0 , 8 0 - 0 , 2 1
.. . - - - - - - - - - - - - - - - - - - - _ . - - - - - - - - - - - - - - - - - -
t , 6 0 1 , 6 0 1 , 7 0 1 , 5 5 1 , 7 0 1 , 6 0
M e an 1 , 6 S
f *
0 , 6 5 3 5 0 0 , 1 4 0 , 6 3 3 6 4 0 , 1 7 0 , 6 6 3 7 3 0 , 2 3 0 , 6 6 4 0 0 0 , 1 4 0 , 7 0 3 6 6 0 , 2 0 0 , 7 0 4 6 8 0 , 1 8
0 , 1 9
A s s um i n g 7 0 � v o i d a g e
- v e v a l u e i n d i c a t e s bypa s s i n g + v e va l ue in d i c a t e s r e c y c l i n g
Recyc l e B e d o r den s i t y
b yp a s s ( � ) ( kg / f i b /
* 3 m )
- 2 0 -
3 -
- 3 3 -
- 1 0 0 -
- 4 8 -
- - - - - - - - - - - - - - - - - - -
- 5 7 2 , 9 - 5 2 7 8 , 2 - 8 5 7 2 , 1 - 1 7 8 4 , 7 - 5 2 6 6 , 6 - 4 2 8 9 , 9
7 7 , 4
3 3 .
P e rc o l a -
t i on rate
( m /m i n )
-/-
0 , 1 2 0 , 1 0 0 , 1 4 0 , 2 0 0 , 1 5
- - - - - - - - - - -
0 , 1 0 0 , 1 2 0 , 1 6 0 , 1 0 0 , 1 4 0 , 1 3
0 , 1 3
.3 4 .
Tab l e 6 Re su l t s o f t rac e r t e s t s o n Tongaat d i ffu s e r
Bed Bed Pe r c o l a t ion Recyc l e *
he i gh t s p e e d ve l oc i t y o r (m ) (m/m i n ) (m/m in ) bypa s s ing
1 , 2 5 1 � 0 0 0 , 2 2 - 4 5 t 1 , 2 5 1 , 0 1 0 , 2 2 - 4 3 % 1 , 2 0 1 , 0 0 0 , 1 8 - 1 2 %
1 , 2 5 1 , 0 3 0 , 1 8 - 1 t
* -ve va l ue s ind i ca t e b y p a s s in g
L i s t o f F igu r e s
F i g . 1 . M e c h an i sm o f f l o o d i ng i n a c a n e d i f fu s e r .
F i g . 2 . S ch e m a t i c d i a g ram o f a mov i n g b e d c an e d i f fu s e r .
F i g . 3 . P i l o t p l an t d i f fu s e r .
F i g . 4 . D e p e n d e n c e o f p e r c o l a t i o n r a t e o n s pe c i f i c s u r fac e and bU l k d e n s i t y .
F i g . 5 . F i t o f mo d e l s t o exp e r iment a l r e s u l t s o f a t r a c e r t e s t o n t h e p i l o t p l an t d i f fu s e r . B e d h e i gh t 1 , 4 6 m , p e r c o l a t i o n r a t e 0 , 2 0 6 rn /m i n .
F i g . 6 . Ax i a l d i s p e r s i o n c o e f f i c i en t s me a s u r e d i n a p i l o t p l an t c an e d i f fu s e r .
F i g . 7 . The e f f e c t o f b u l k f i b r e d e n s i t y o n t o t a l l iqu i d ho l du p in a p i l o t p l ant c a n e d i f f u s e r . S o l i d l i n e r e p r e s en t s max i mum l i q u i d ho l dup b a s e d on a f i b re d e n s i ty o f 1 5 2 0 k g / m l
F i g . 8 . Typ i c a l c o n d u c t i v i t y r e c o rd f o r a t r ac e r t e s t o n t h e Ama t i ku l u d i f f u s e r .
F i g . 9 . F i t o f mo d e l t o r e su l t s o f a t r a c e r t e s t o n t he Ama t i ku l u d i ffus e r . B e d h e i g h t 1 , 5 5 m. B e d s p e e d 0 , 6 6 rn / m i n .
F i g . 1 0 . Ax i a l d i s p e r s i on c o e f f i c i e n t s m e a su r e d i n fu l l s c a l e d i f f u s e r s .
[ ,
F i g u r e 1 Page 3 5 . -
I ____ =��4 ql
-I
- � '1' � O& �
-I L
L..
� '--
I r= .... Cl) � -� '--
- -I I � I -
I I
.J lQ� � ()
�
� � r� ---�- I
r -, - �� �
�
- � l � I 1"1- <I) � .!-I'--JU � �
o 8 � __ ---11 _
r lIE � �
;> '-� t;i <l _
- I I -� ) a
'--... ...
_ I -
'!C
1__ I ---=�I � i � r-----.I � I � . ca;.
I l- _ -
C 1t ::J' r------J t r- -( � ') ( III
---�--� ---. ---========-�-::�-=-
� '""\ � ) � ----...1- �
. � ...
_ _ � '---- J L--{�
-----I..! �I )
I
-
F i gu r e 2
/'" ,/
Pa g e 3 6 .
FICURE 3
...-- CONSTIlNT HEll/) TIINK
. OR.IF ICE ___ --"'"'-""
: PL I1 TE
COL UMN CONTIlINING CRNE BEt
FX - FLOW TI?IlNSMIT1£R . . FP. - F/..1)W I<£COR.DEP. lAX - MI1NUI1L L ORDING STlfT/ON re - T£MPERFlrURE.
.CON T/?O l- L £R.
S T£!lM
...... ______ � STo� IIGE TRNK.
Page 3 7 .
t D IRL
MEC J.lI1}./ISM OF PL. RTFORM SCRL E
o
, -4'
w >
o o
L I
! !
lrt l • I () L._. __ _
o -w
F i g u r e 4 . ;
<:)
o
L _ _ . __ .
Pa g e 3 8 . ' I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
t::J 0 I I I
\ \ ,
8 (.)
.""
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
Pa g e
F i gu r e 5 .
� � .... � r-I'
", '< . , '\) � < •
\I'
� � rt,
'1 '" 1. \f\
' > , I
V r� .. "" '" ... :� !t l> � � <;- "" (r. "-
I\:) 1 � \) l '" I;) rr, \i r - '"
"
Figur e 6 .
\ \
>- 0
I-
I-
'8 cS
l / ;1" 7(/ .: ! (/ )
r I
� \
\ \
0 \ \
\ \
0 \ 0 0
I t cS' r/) C',. '2>
,:),"
" / " " ) " . . . . , _ . � j ,; .. .1. .:;! j j v )
\
r
0
0
0
\ \
\ 0
\ \ 0
\ \
\ \
J r--< c c)
, • t • • i" 5 ;:>of ] d 5 I (f
Pa g e 4 0 .
''') I �� �
----� -'"
� �
- '-....-
>-.. i...... f.-, '-l
'>- \:; - .... "-.l
Q ..... 1 �
> --- . CJ
i-.. I ""
"'-. ..... --.'I � '"
M '" - , .....
() \...i... . Q.
-
N - a
-
\ -\ a
\ \
-
\ \
t \ 0 (�) cs-
0 Cl c)" <S 7 i./ [ X (i
1 4
1 2.
1 /
1 0
F i gu r e 7 .
( 0
o o
o
o
7 0
o 0 o 0 o 0 o
o 0�
f3�t L K )) t=" IV 5 I T Y O F
Pa g e 4 1 .
o
o o
C IINt
..
u r e 8 . I � I I . . .. -.. - -- . --
I _t
2 I
'PM 99� .. - � - -- --
I ! -
I I .- . _ - - ---- - - - - - --- - . . . ---
--�-. - - - -- -- -- -- -_ ... _ _ . . - .
!
I. I !
I I I 1 · · · ·- �· i -.-. _ . . . .•. . . . . . , . -�J
I . - -- - I . _- - �
I- . _ - .
--:---! --.-:. '--- - - " ...-.�.---- --- -. ' ; . I ; i I ' I i , I I . I I ' I I I I
_I _ _ � _ _ ' ' _ ! . I I
· : i · · ---- --- ---·- · · · --
· ----r-- ·--·-·-- - ---- - -I I --. _ - -_ . . . . _.- . . - - - - - -
, I
I .
I I
_ . . .. . _ _ ..1
- -· · - - -·-- -r--�--I
- - - - - - - - - ,-_. _ - -
I , --- --. ----;;---,----_ .
• 1 I
Page 4 2 .
Fi gur e 9 . Pa g e 4 3 .
iD A �
"- )0- "-Q: ':t � X � I'( f- f-. .....
G IJ 11(
o "< o
{ :; J fNI1 J. 2'1 {-I L I9 "(;t f.:I ) ;/(; F L J .;I ;: N 3 ? NO) 'i!J.3 1 fI�.1.
� I'i
C, '"
o