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Wil
ey-V
CH
Ver
lag
Gm
bH
&C
o.
KG
aA,W
einhei
m10.1
002/1
4356007.b
03
06
Liq
uid
–Liq
uid
Extr
action
1
Liq
uid
–L
iqu
idE
xtr
act
ion
Eckart
Mu
ller
,F
rankfu
rta.
Mai
n,G
erm
any
(Chap
s.1
and
2)
Rosem
arie
Berger
,L
udw
igsh
afen
,G
erm
any
(Chap
s.3
and
4)
Eckh
art
Blass,T
echnis
che
Univ
ersi
tat
Munch
en,M
unch
en,G
erm
any
(Chap
s.1
–4,
Sec
tions
5.1
and
5.2
)
Dom
ien
Slu
yts,B
ayer
AG
,A
ntw
erpen
,B
elgiu
m(S
ecti
on
5.3
)
1.
Fu
nd
am
enta
lsan
dF
ield
sof
Ap
pli
-
cati
on
....................
2
2.
Th
erm
od
yn
am
icF
un
dam
enta
ls...
4
2.1
.G
rap
hic
Rep
rese
nta
tion
of
Ph
ase
Eq
uil
ibri
a.................
4
2.1
.1.
Tri
angula
rD
iagra
ms
...........
4
2.1
.2.
Oth
erG
raphic
Rep
rese
nta
tions
....
6
2.2
.M
easu
rin
gM
eth
od
sof
Ph
ase
Eq
ui-
lib
ria
....................
7
2.3
.E
mp
iric
al
Corr
elati
on
sof
Ph
ase
Eq
uil
ibri
a.................
9
2.4
.S
elec
tion
of
Solv
ent
...........
10
2.5
.C
alc
ula
tion
of
Th
eore
tica
lS
tages
.11
2.5
.1.
Sel
ecti
on
of
Cal
cula
tion
Met
hods
...
11
2.5
.2.
Spec
ific
Met
hods
.............
11
2.5
.3.
Eval
uat
ion
of
Sta
ge-
Num
ber
Cal
cula
-
tion
for
Pro
cess
Des
ign
.........
13
3.
Ap
para
tus
.................
15
3.1
.S
urv
ey...................
15
3.1
.1.
Colu
mns
wit
hout
Ener
gy
Input
....
15
3.1
.2.
Puls
edC
olu
mns
..............
17
3.1
.3.
Colu
mns
wit
hR
ota
ting
Inte
rnal
s...
20
3.1
.4.
Mix
er–
Set
tler
s..............
21
3.1
.5.
Cen
trif
ugal
Extr
acto
rs..........
23
3.2
.F
luid
-Dyn
am
icF
un
dam
enta
ls....
24
3.2
.1.
Pro
ble
ms
and
Pro
cess
Str
ateg
y....
24
3.2
.2.
Oper
atin
gC
har
acte
rist
ics
of
Puls
ed
Colu
mns
and
Colu
mns
wit
hR
ota
ting
Inte
rnal
s..................
25
3.2
.3.
Flu
idD
ynam
icC
alcu
lati
on
Met
hods
.28
3.3
.A
pp
ara
tus
Des
ign
............
30
3.3
.1.
Inte
rnal
san
dO
per
atin
gC
ondit
ions
..
30
3.3
.2.
Colu
mn
Dia
met
er.............
31
3.3
.3.
Colu
mn
Hei
ght
..............
32
3.4
.C
rite
ria
for
Eq
uip
men
tS
elec
tion
..
32
4.
Ph
ase
-Sep
ara
tion
Eq
uip
men
t....
36
4.1
.G
ravit
yS
ettl
ers
wit
hou
tIn
sert
s..
36
4.2
.S
ettl
ers
wit
hC
oale
scin
gA
ids
....
37
5.
Liq
uid
–L
iqu
idE
xtr
act
ion
Pro
-
cess
es....................
41
5.1
.G
ener
al
..................
41
5.2
.C
om
bin
edP
roce
sses
of
Extr
act
ion
an
dD
isti
llati
on
.............
43
5.3
.R
eact
ive
Extr
act
ion
...........
44
5.3
.1.
Intr
oduct
ion
................
44
5.3
.2.
Extr
acti
on
Mec
han
ism
of
Dif
fere
nt
Types
of
Solv
ent
.............
45
5.3
.3.
Use
s.....................
48
5.3
.4.
Set
ting
up
anE
xtr
acti
on
Syst
em...
49
5.3
.5.
Dil
uen
tsan
dM
odifi
ers
.........
50
6.
Ref
eren
ces
.................
51
Sy
mb
ols
2a
Pu
lsin
gam
pli
tud
e,m
Akey
com
po
nen
to
fth
ep
has
efr
om
wh
ich
the
solu
teis
extr
acte
dB
key
com
po
nen
to
fth
ep
has
ein
tow
hic
hth
eso
lute
isex
trac
ted
c ico
nst
ants
Ctr
ansf
erre
dco
mp
on
ent
di
ho
leo
rp
ack
ing
dia
m-
eter
,m
dp
par
ticl
ed
iam
eter
,m
d32
Sau
ter
mea
nd
rop
di-
amet
er,
mD
colu
mn
dia
met
er,
mD
Rro
tor
dia
met
er,
mD
dis
trib
uti
on
coef
fici
ent
E=
Km
s/m
Fex
trac
tio
nfa
cto
rf
pu
lsin
gfr
equ
ency
,s−
1
gac
cele
rati
on
du
eto
gra
vit
y,m
/s2
Gi
coef
fici
ents
inem
pir
i-ca
lco
rrel
atio
ns
of
the
dis
trib
uti
on
coef
fici
ent
2Liq
uid
–Liq
uid
Extr
action
hco
mp
artm
ent
hei
gh
t,m
Hh
eig
ht
of
colu
mn
,m
HE
TS
hei
gh
teq
uiv
alen
to
fa
theo
reti
cal
stag
e,m
k=
yc/x
cd
istr
ibu
tio
nra
tio
of
tran
sfer
red
com
po
nen
t(i
nte
rms
of
mas
sfr
ac-
tio
n)
K=
YC
/XC
dis
trib
uti
on
rati
oo
ftr
ansf
erre
dco
mp
on
ent
(in
term
so
flo
adin
g)
Kp
pla
itp
oin
tm
jk
mas
so
fco
mp
on
ent
jin
ph
ase
or
flow
k(j=
A,B
,C;k
=F,R
,S
,E),
kg
mk
=m
Ak
+m
Bk
+m
Ck
tota
lm
ass
of
ph
ase
or
flow
k(k
=F,R
,S,E
),k
gm
mas
sfl
ow
,k
g/h
ns
revo
luti
on
so
fst
irre
r,s−
1
nn
um
ber
of
stag
esN
TS
nu
mb
ero
fth
eore
tica
lst
ages
sco
lum
ncr
oss
sect
ion
,m
vsu
per
fici
alvel
oci
ty,
m3
m−
2h−
1o
rm
/sv
=m
S/m
Fex
trac
tan
tra
tio
v pin
div
idu
ald
rop
vel
oc-
ity,
m/s
v rsl
ipvel
oci
ty(E
q.
9),
m/s
xC
mas
sfr
acti
on
of
Cin
A-r
ich
ph
ase
XC
=x/(
1−
x)
load
ing
of
A-r
ich
ph
ase
wit
hco
mp
on
ent
C,
kg
/kg
yC
mas
sfr
acti
on
of
Cin
B-r
ich
ph
ase
YC
=y/(
1−
y)
load
ing
of
B-r
ich
ph
ase
wit
hC
,k
g/k
g
Gre
eksy
mb
ols
εh
old
up
,m
3/m
3
ηd
yn
amic
vis
cosi
ty,
Pa·s×
10−
3
d
ensi
ty,
kg
/m3
σin
terf
acia
lte
nsi
on
,N
/m×
10−
3
ϕfr
eear
ea
Dim
ensi
on
less
Gro
up
s
Ar
=d3 Pgc∆
/η2 c
Arc
him
edes
nu
mb
erF
r R=
N2D
R/g
Fro
ud
en
um
ber
Re p
=v p
dp/v d
Par
ticl
eR
eyn
old
sn
um
ber
KL
=2 cσ
3/
(
∆gη4 c
)
Ch
arac
teri
stic
nu
m-
ber
of
liq
uid
Su
bsc
rip
ts
Akey
com
po
nen
to
fth
ep
has
efr
om
wh
ich
the
solu
teis
extr
acte
dB
key
com
po
nen
to
fth
ep
has
ein
tow
hic
hth
eso
lute
isex
trac
ted
Ctr
ansf
erre
dsu
bst
ance
(so
lute
)c
con
tin
uo
us
ph
ase
dd
isp
erse
dp
has
eE
extr
act
ffl
oo
din
gF
feed
iin
tern
als
(ch
arac
teri
stic
size
)o
org
anic
pd
rop
(par
ticl
e)R
raffi
nat
eS
solv
ent
1p
ilo
tsc
ale
2la
rge
scal
e
1.
Fu
nd
am
enta
lsan
dF
ield
sof
Ap
pli
cati
on
Liq
uid
–li
qu
idex
trac
tio
no
rso
lven
tex
tra
ctio
n
isa
sep
arat
ion
pro
cess
wh
ich
isb
ased
on
the
dif
fere
nt
dis
trib
uti
on
of
the
com
po
nen
tsto
be
sep
arat
edb
etw
een
two
liq
uid
ph
ases
.It
dep
end
so
nth
em
ass
tran
sfer
of
the
com
po
nen
tto
be
ex-
trac
ted
fro
ma
firs
tli
qu
idp
has
eto
ase
con
do
ne.
Defi
nit
ion
s.T
he
ph
ases
form
defi
nit
eco
n-
tact
area
san
dca
nn
ot
or
can
on
lyto
ali
mit
edex
ten
tm
ixw
ith
on
ean
oth
ero
nac
cou
nt
of
thei
rp
rop
erti
es.
Th
ep
has
esar
eco
mp
ose
do
fin
di-
vid
ual
sub
stan
ces,
so-c
alle
dco
mp
on
ents
,an
dfl
ow
asli
qu
idst
ream
sth
rou
gh
the
extr
acto
r(s
eeF
ig.1
).P
has
esar
eli
qu
idst
ream
sth
atar
ein
equ
i-li
bri
um
wit
hea
cho
ther
.G
ener
ally
,m
ore
than
thre
eco
mp
on
ents
are
invo
lved
inan
extr
acti
on
.T
om
ake
the
des
crip
-ti
on
of
the
pro
ble
msi
mp
ler,
key
com
po
nen
tsar
e
Liq
uid
–Liq
uid
Extr
action
3
defi
ned
.T
he
feed
toa
liq
uid
–li
qu
idex
trac
tio
nis
the
solu
tio
nth
atco
nta
ins
the
com
po
nen
tsto
be
sep
arat
ed.
Th
ekey
com
po
nen
to
fth
isli
qu
idp
has
e(t
he
ph
ase
fro
mw
hic
hth
eso
lute
isex
-tr
acte
d)
isca
lled
A,
the
tran
sfer
red
sub
stan
ce(t
he
solu
te)
C.
Th
e(e
xtra
ctio
n)
solv
ent
isth
eli
qu
idad
ded
toth
ep
roce
ssto
extr
act
the
sub
-st
ance
Cfr
om
the
feed
.T
he
solv
ent
can
be
the
pu
reco
mp
on
ent,
B,
bu
tu
sual
lyco
nta
ins
smal
lq
uan
titi
eso
fC
and
A,b
ecau
seth
eso
lven
tis
usu
-al
lyre
cycl
edfr
om
are
cover
ysy
stem
.T
he
sol-
ven
tp
has
ele
avin
gth
eex
tra
cto
ris
the
extr
act
.
Th
eex
trac
tco
nta
ins
mai
nly
Ban
dth
eex
trac
ted
com
po
nen
tC
bu
tal
sosm
allq
uan
titi
eso
fA
.Th
era
ffin
ate
isth
eli
qu
idp
has
ele
ftfr
om
the
feed
afte
rb
ein
gco
nta
cted
by
the
extr
acti
on
solv
ent;
itis
com
po
sed
mai
nly
of
A,bu
tg
ener
ally
smal
lq
uan
titi
eso
fth
eex
trac
ted
com
po
nen
tC
and
sol-
ven
tB
.
Co
mp
ari
son
wit
hD
isti
lla
tio
n.
Liq
uid
–li
q-
uid
extr
acti
on
has
sim
ilar
itie
sw
ith
dis
till
atio
n.
Inb
oth
case
sth
esu
bst
ance
sto
be
sep
arat
edh
ave
con
cen
trat
ion
rati
os6=
1in
the
two
ph
ases
.In
the
case
of
dis
till
atio
nth
ese
con
dp
has
e(t
he
vap
or
ph
ase)
isfo
rmed
excl
usi
vel
yfr
om
the
com
po
-n
ents
ofth
ein
itia
l(li
qu
id)p
has
e,w
ith
extr
acti
on
an
ewsu
bst
ance
,th
e(e
xtr
acti
on
)so
lven
t,m
ust
be
add
edto
form
the
seco
nd
(liq
uid
)p
has
e.T
he
solv
ent
ente
rsin
toth
em
ater
ial
bal
ance
of
the
pro
cess
and
its
beh
avio
rto
war
ds
the
sub
stan
ces
tob
ese
par
ated
isd
ecis
ive
for
the
sep
arat
ion
pro
cess
.G
ener
ally
,th
eex
trac
ted
sub
stan
ceis
sep
a-ra
ted
fro
mth
eso
lven
tb
yd
isti
llat
ion
and
the
solv
entB
isre
cycl
edto
the
extr
acto
r.S
om
etim
esth
ese
lect
ive
acti
on
of
the
solv
ent
isu
sed
inth
ed
isti
llat
ion
wh
ich
gen
erat
esth
ere
flu
xfo
rth
eex
trac
tio
n,
e.g
.,ex
tra
ctiv
ed
isti
lla
tio
n(e
xtr
ac-
tio
no
far
om
atic
com
po
un
ds,
see
Sec
tio
n5
.2)
or
aze
otr
op
icd
isti
lla
tio
n(e
xtr
acti
on
of
acet
icac
id).
Inth
eex
trac
tio
no
fm
etal
salt
s(s
eeS
ec-
tio
n5
.3)
the
pu
rity
iso
ften
ach
ieved
by
adju
st-
ing
the
pH
.E
xtr
acti
on
isan
iso
ther
mal
pro
cess
,n
orm
ally
carr
ied
ou
tat
amb
ien
tte
mp
erat
ure
and
pre
ssu
re.
Co
mp
ari
son
wit
hA
bso
rpti
on
.In
bo
thab
-so
rpti
on
and
extr
acti
on
solv
ents
are
use
dw
hic
har
ere
cycl
edan
dth
ereb
yta
ke
up
the
req
uir
edco
mp
on
ents
sele
ctiv
ely
and
then
rele
ase
them
agai
n.
Sel
ecti
on
of
the
most
suit
able
solv
ents
ther
efo
rep
lay
san
imp
ort
ant
role
inth
ed
esig
no
fth
etw
ose
par
atio
np
roce
sses
.
Ap
pli
cati
on
so
fL
iqu
id–
Liq
uid
Ex
tra
c-ti
on
.L
iqu
id–
liq
uid
extr
acti
on
isp
rim
aril
yap
-p
lied
wh
ere
dir
ect
sep
arat
ion
met
ho
ds
such
asd
isti
llat
ion
and
cry
stal
liza
tio
nca
nn
otb
eu
sed
or
are
too
cost
ly.
Liq
uid
–li
qu
idex
trac
tio
nis
also
emp
loy
edw
hen
the
com
po
nen
tsto
be
sep
arat
edar
eh
eat-
sen
siti
ve
(e.g
.,an
tib
ioti
cs)
or
rela
tivel
yn
onvo
lati
le(e
.g.,
min
eral
salt
s).
Liq
uid
–li
qu
idex
trac
tio
nis
use
din
ind
ust
ryfo
rth
efo
llow
ing
pu
rpo
ses:
1)
Sep
arat
ion
of
syst
ems
wit
hsi
mil
arb
oil
ing
po
ints
(e.g
.,se
par
atio
no
far
om
atic
sfr
om
alip
hat
ichydro
carb
ons)
;2
)se
par
atio
no
fh
igh
bo
iler
san
dlo
wco
nce
n-
trat
edso
lute
sfr
om
aqu
eou
sso
luti
on
s(e
.g.,
ph
eno
l);
3)
sep
arat
ion
of
mix
ture
sw
ith
hig
hb
oil
ing
po
ints
(e.g
.,v
itam
ins)
;4
)se
par
atio
no
fte
mp
erat
ure
-sen
siti
ve
com
-p
ou
nd
s(e
.g.,
acry
late
s,b
iote
chn
olo
gy
);5
)se
par
atio
no
faz
eotr
op
icm
ixtu
res
(ex
trac
-ti
on
of
acet
ico
rfo
rmic
acid
fro
maq
ueo
us
med
iau
sin
g,
e.g
.,M
TB
Eas
solv
ent)
;6
)ex
trac
tion
of
org
anic
com
pounds
from
salt
solu
tio
ns
(e.g
.,ca
pro
lact
am);
7)
extr
acti
on
of
salt
sfr
om
po
lym
erso
luti
on
s(e
.g.,
ket
on
ere
sin
s,p
oly
ols
);8
)ex
trac
tio
no
fm
etal
salt
sfr
om
low
-gra
de
ore
s(e
.g.,
cop
per
);9
)ex
trac
tio
no
fm
etal
salt
sfr
om
was
tew
ater
(e.g
.,co
pp
er);
10
)re
cover
yo
fn
ucl
ear
fuel
s(P
ure
xp
roce
ss).
Fig
ure
1.
Pri
nci
ple
sof
extr
acti
on
–st
ream
s,phas
esan
dco
mponen
ts
Pro
cess
esap
pli
edin
the
pet
role
um
ind
ust
ry,
inm
etal
-sal
tex
trac
tio
nan
din
chem
ical
and
bio
-ch
emic
alp
roce
sses
are
des
crib
edin
Ch
apte
r5
.
4Liq
uid
–Liq
uid
Extr
action
On
lya
gen
eral
ou
tlin
eis
giv
enin
this
arti
-cl
e.F
or
furt
her
det
ails
,th
ere
ader
isre
ferr
edto
bo
ok
s[1
–7
]an
dth
eP
roce
edin
gs
of
the
Inte
r-n
atio
nal
So
lven
tE
xtr
acti
on
Co
nfe
ren
ce(I
SE
C)
[8–
17
].D
ata
of
liq
uid
–li
qu
ideq
uil
ibri
aca
nb
efo
un
din
[18
],[1
9]
and
[20
].
Fig
ure
2.
Tri
angula
rd
iag
ram
for
rep
rese
nta
tio
no
fa
thre
e-co
mponen
tsy
stem
2.
Th
erm
od
yn
am
icF
un
dam
enta
ls
Aco
mp
reh
ensi
ve
trea
tmen
to
fth
eth
erm
od
y-
nam
icfu
nd
amen
tals
of
ph
ase
equ
ilib
ria
isg
iven
else
wh
ere
(→A
bso
rpti
on
;→
Dis
till
atio
nan
dR
ecti
fica
tio
n).
2.1
.G
rap
hic
Rep
rese
nta
tio
no
fP
ha
se
Eq
uil
ibri
a
2.1
.1.
Tri
an
gu
lar
Dia
gra
ms
Tri
ang
ula
rd
iag
ram
s(F
ig.2
)ar
eu
sed
for
rep
re-
sen
tin
gth
ree-
com
po
nen
tsy
stem
s.E
ver
yp
oss
i-b
leco
mp
osi
tio
no
fth
ete
rnar
ym
ixtu
reco
rre-
spo
nd
sto
ap
oin
tin
the
dia
gra
m.
Eac
hco
rner
of
the
tria
ng
lere
pre
sen
tsa
pu
reco
mp
on
ent
and
its
des
ign
atio
nis
mar
ked
atth
isco
rner
.O
nth
esi
de
op
po
site
toth
isco
rner
the
mas
sfr
acti
on
of
this
com
po
nen
tis
zero
.T
he
sid
eso
fth
etr
ian
-g
lere
pre
sen
tth
eco
rres
po
nd
ing
two
-co
mp
on
ent
syst
ems.
Th
ep
rop
ort
ion
so
fth
ein
div
idu
alco
m-
po
nen
tsin
am
ixtu
rear
eo
bta
ined
asfo
llow
s:T
he
mas
sfr
acti
on
of
each
com
po
nen
tis
giv
enb
yli
nes
par
alle
lto
the
sid
eo
pp
osi
teto
the
cor-
ner
wh
ich
rep
rese
nts
the
pu
reco
mp
on
ent,
fro
m0
kg
/kg
atth
iso
pp
osi
tesi
de
to1
kg
/kg
atth
eco
r-n
er.
Th
en
um
ber
ing
can
be
pla
ced
atth
eed
ges
of
the
tria
ng
le,
inw
hic
hca
seit
isad
vis
able
toex
ten
dth
eli
nes
.T
he
nu
mb
ers
can
also
be
in-
sert
edin
the
mid
dle
of
the
lin
es.T
his
mak
esth
ed
iag
ram
easi
erto
use
bu
tso
me
of
the
nu
mb
ers
are
alw
ays
skew
and
inver
ted
.T
he
po
int
Ph
asth
eco
mp
osi
tio
n0
.5k
g/k
gC
,0
.2k
g/k
gA
,an
d0
.3k
g/k
gB
.T
he
foll
ow
ing
rule
sap
ply
inth
etr
ian
gu
lar
di-
agra
m:
Ifco
mp
on
ent
Cis
add
edto
am
ixtu
reo
f0
.8k
g/k
gA
and
0.2
kg
/kg
B,re
pre
sen
ted
by
the
po
int
D,
then
the
com
po
siti
on
of
the
new
mix
-tu
refo
llow
sth
ep
ath
of
the
stra
igh
tli
ne
DC
.O
nth
isst
raig
ht
lin
e,an
do
nal
lst
raig
ht
lin
esw
hic
hp
ass
thro
ug
ha
corn
er,th
era
tio
bet
wee
nth
etw
oo
ther
com
po
nen
tsw
hic
hd
on
ot
form
the
corn
eris
con
stan
t.If
am
ixtu
reo
fco
mp
osi
tio
nU
and
on
eo
fco
mp
osi
tio
nV
are
com
bin
edth
enth
ere
sult
ing
mix
ture
lies
on
the
stra
igh
tco
nn
ecti
ng
lin
eU
V.
Th
eco
mp
osi
tio
no
fth
efi
nal
mix
ture
iso
bta
ined
by
div
idin
gth
eco
nn
ecti
ng
lin
eb
etw
een
the
two
ori
gin
alm
ixtu
res
inin
ver
sera
tio
toth
eq
uan
titi
esm
ixed
(lev
erru
le).
Th
em
ixtu
reM
,fo
rex
amp
le,
com
pri
ses
thre
ep
arts
Uan
do
ne
par
tV
,an
dth
em
ixtu
reG
com
pri
ses
thre
ep
arts
Can
dtw
op
arts
D.T
he
con
cen
trat
ion
dat
ao
bta
ined
fro
mth
etr
ian
gu
lar
dia
gra
m(e
.g.,
po
int
G:
0.6
kg
/kg
C,
0.0
8k
g/k
gB
,0
.32
kg
/kg
A;
B:
A=
1:
4)
app
lyto
the
tota
lquan
tity
of
resu
ltin
gm
ixtu
rere
gar
d-
less
of
wh
eth
erit
ish
om
og
eneo
us
or
sep
arat
edin
tose
ver
alp
has
es.
As
ever
yp
oin
tin
atr
ian
gu
lar
dia
gra
mco
rre-
spo
nd
sto
aco
mp
osi
tio
nth
ere
isn
oco
ord
inat
efr
eefo
ran
oth
erre
fere
nce
var
iab
le.I
tis
on
lyp
os-
sib
leto
plo
tp
aram
eter
ssu
chas
lin
eso
feq
ual
den
sity
,boil
ing
poin
tsor
oth
erphysi
cal
dat
a,li
nes
of
equ
alac
tiv
ity
coef
fici
ents
or
lin
eso
fp
has
eb
ou
nd
arie
s.O
nly
tern
ary
syst
ems
wit
hm
isci
bil
ity
gap
sar
esu
itab
lefo
rex
trac
tio
ns,
and
the
bo
un
dar
yli
ne
bet
wee
nth
eli
qu
idsi
ng
le-p
has
ere
gio
n(s
)an
dth
etw
o-p
has
ere
gio
nis
par
ticu
larl
yim
po
r-ta
nt.
Th
isb
ou
nd
ary
lin
eis
call
edth
eb
ino
da
l
curv
e(F
ig.3
).E
ver
yp
oin
to
nth
eb
ino
dal
curv
e(e
xce
pt
the
pla
itp
oin
tin
syst
ems
wit
ha
com
-p
lete
bin
od
alcu
rve,
see
bel
ow
)is
ineq
uil
ibri
um
wit
han
oth
erb
ino
dal
po
int.
Th
eli
nes
wh
ich
con
-n
ect
po
ints
ineq
uil
ibri
um
wit
ho
ne
ano
ther
are
call
edti
eli
nes
.A
llm
ixtu
res
wh
ich
corr
esp
on
dto
ap
oin
ton
the
tie
lin
ese
par
ate
into
two
ph
ases
.T
he
com
po
siti
on
of
thes
ep
has
esis
giv
enb
yth
e
Liq
uid
–Liq
uid
Extr
action
5
Fig
ure
3.
Defi
nit
ions
of
phas
eeq
uil
ibri
aan
dm
ass
frac
tions
ina
tria
ngula
rdia
gra
mA
)P
has
eeq
uil
ibri
a;B
)M
ass
frac
tions
end
po
ints
of
the
tie
lin
esan
dth
eir
qu
anti
ties
are
giv
enb
yth
ele
ver
rule
.T
he
equ
ilib
riu
md
ata
hav
eto
be
det
erm
ined
exp
erim
enta
lly
inea
chin
-d
ivid
ual
case
.L
ines
par
alle
lto
the
tria
ng
lesi
des
CB
and
AC
resp
ecti
vel
y,d
raw
nth
rou
gh
rela
ted
po
ints
of
equ
ilib
riu
mo
nb
oth
bra
nch
eso
fth
eb
ino
dal
curv
e,p
rod
uce
anau
xil
iary
lin
e,fo
rmed
by
the
inte
rsec
tio
ns
of
the
par
alle
ls,
and
enab
leto
con
stru
ctan
yti
eli
ne
asd
emo
nst
rate
din
Fig
-u
re3
A.
Sev
eral
typ
eso
ftr
ian
gu
lar
dia
gra
ms
are
show
nin
Fig
ure
4.
Inev
ery
syst
emw
ith
aco
m-
ple
teb
ino
dal
curv
e(c
lose
dd
iag
ram
,T
yp
eII
inF
ig.4
)th
een
dp
oin
tso
fth
eti
eli
nes
dra
wcl
ose
ran
dcl
ose
rto
get
her
un
til
they
fin
ally
coin
cid
eat
the
pla
itp
oin
t.T
he
pla
itp
oin
to
nth
eb
ino
dal
curv
ere
pre
sen
tsa
sin
gle
ph
ase
wh
ich
do
esn
ot
spli
tin
totw
op
has
es.
Dia
gra
mI
isca
lled
ano
pen
dia
gra
min
wh
ich
Bis
no
tfu
lly
mis
cib
lew
ith
the
sub
stan
ceto
be
dis
solv
ed.T
he
cap
acit
yo
fsu
cha
solv
ent
isco
r-re
spo
nd
ing
lylo
wan
dit
sse
lect
ivit
yis
usu
ally
hig
h(s
eeS
ecti
on
2.4
).
Ind
iag
ram
IIth
esu
bst
ance
tob
eex
trac
ted
(C)
isto
tall
ym
isci
ble
wit
hb
oth
Aan
dB
.T
his
form
of
extr
acti
on
dia
gra
mis
oft
enfo
un
din
ex-
trac
tio
ns
wh
ere
solu
teC
and
Aar
ep
rese
ntin
ap-
pro
xim
atel
yth
esa
me
qu
anti
ties
.If
inth
isca
seth
eco
nce
ntr
atio
no
fC
inth
eA
B-m
ixtu
reis
too
hig
h(h
igh
erth
anth
eco
nce
ntr
atio
nat
the
pla
itp
oin
t)th
esy
stem
form
so
nly
on
ep
has
ean
dex
-tr
acti
on
isn
ot
po
ssib
le.
Dia
gra
mII
Ish
ow
sa
syst
emw
her
eC
has
am
isci
bil
ity
gap
wit
hA
.It
sco
nce
ntr
atio
nin
the
B-r
ich
ph
ase
isth
ensu
bst
anti
ally
hig
her
than
inth
efe
ed.
Th
ed
iag
ram
isty
pic
alfo
rw
aste
wat
erex
trac
tio
ns.
Dia
gra
mIV
isan
op
entr
ian
gu
lar
dia
gra
min
wh
ich
thre
eli
qu
idp
has
esar
efo
rmed
inth
em
id-
dle
con
cen
trat
ion
ran
ge.
Th
isb
ehav
ior
iso
ften
found
insy
stem
sco
nsi
stin
gof
inorg
anic
salt
sin
aqueo
us
solu
tions
and
org
anic
solv
ents
.T
he
app
eara
nce
ofa
thir
dli
qu
idp
has
eca
nca
use
con
-si
der
able
dif
ficu
ltie
sd
uri
ng
met
al-s
alt
extr
ac-
tio
n(s
eeS
ecti
on
5.3
).T
he
infl
uen
ceo
fp
ress
ure
on
the
bin
od
alcu
rve
and
equ
ilib
ria
isn
egli
gi-
ble
bel
ow
val
ues
of
sever
alb
ar.T
he
infl
uen
ceo
f
6Liq
uid
–Liq
uid
Extr
action
tem
per
atu
reis
stro
ng
.Th
elo
wer
the
tem
per
atu
reth
em
ore
wil
lth
etr
ian
gu
lar
dia
gra
mn
orm
ally
be
fill
edby
the
mis
cibil
ity
gap
.
Fig
ure
4.
Var
ious
typ
eso
fp
has
eeq
uil
ibri
ain
tern
ary
sys-
tem
sT
ype
I:O
pen
syst
em,m
isci
bil
ity
gap
bet
wee
nth
ekey
com
-ponen
tof
the
solv
ent
(B)
and
solu
teC
Type
II:
Clo
sed
syst
em,
Cis
com
ple
tely
mis
cib
lew
ith
the
key
com
ponen
tof
the
feed
(A)
and
the
key
com
po
nen
to
fth
eex
trac
tion
solv
ent
(B)
Type
III:
Open
syst
em,m
isci
bil
ity
gap
bet
wee
nA
and
CT
ype
IV:
Syst
emw
ith
form
atio
no
fth
ree
ph
ases
2.1
.2.
Oth
erG
rap
hic
Rep
rese
nta
tio
ns
Liq
uid
two
-ph
ase
syst
ems
com
pri
sin
gth
ree
com
po
nen
tsca
nal
sob
ep
lott
edo
nre
ctan
gu
lar
coo
rdin
ates
.In
man
yca
ses
thes
ed
iag
ram
sar
ep
refe
rred
bec
ause
the
mea
sure
dval
ues
can
be
adju
sted
bet
ter
and
the
con
fig
ura
tio
no
fth
eca
l-cu
lati
on
sis
sim
ple
r.T
he
mo
stim
po
rtan
tfo
rms
of
rep
rese
nta
tio
nar
esh
ow
nfo
rth
ree
mix
ture
sin
Fig
ure
s5
,6
,7
.A
com
pre
hen
sive
rev
iew
of
form
so
fre
pre
sen
tati
on
isg
iven
in[2
7].
Inth
eeq
uil
ibri
um
dia
gra
m(F
igs.
5,
6,
7II
)th
em
ass
frac
tio
no
fC
inth
eB
-ric
hp
has
eyC
(ord
inat
e)is
plo
tted
asa
fun
ctio
no
fth
ism
ass
frac
tio
nin
the
A-r
ich
ph
ase
xC
(ab
scis
sa).
Th
isd
iag
ram
isan
alo
go
us
toth
eM
cCab
e–
Th
iele
di-
agra
min
dis
till
atio
n(→
Dis
till
atio
nan
dR
ecti
-fi
cati
on
,C
hap
.4
.1.1
.).It
show
sth
ere
lati
on
ship
bet
wee
neq
uil
ibri
um
and
op
erat
ing
con
dit
ion
s.F
igu
re5
.Rep
rese
nta
tio
no
fp
has
ere
lati
on
ship
ofth
ete
rnar
ysy
stem
hep
tan
e(A
),d
ieth
yle
ne
gly
col
(B),
ben
zen
e(C
),at
20◦
C.
All
dat
are
fers
tom
ass
frac
tio
ns.
I)T
rian
gula
rd
iag
ram
;II
)E
qu
ilib
riu
md
iag
ram
;II
I)D
istr
i-bu
tio
nd
iag
ram
;IV
)S
elec
tiv
ity
dia
gra
m
Liq
uid
–Liq
uid
Extr
action
7
Fig
ure
6.R
epre
senta
tion
ofphas
ere
lati
onsh
ipofth
ete
rnar
ysy
stem
tric
hlo
roet
hyle
ne
(A),
wat
er(B
),ca
pro
lact
am(C
),at
20◦
C.A
lldat
are
fers
tom
ass
frac
tions.
I)T
rian
gula
rdia
gra
m;
II)
Equil
ibri
um
dia
gra
m;
III)
Dis
tri-
buti
on
dia
gra
m;
IV)
Sel
ecti
vit
ydia
gra
m
Inth
eex
amp
lesh
ow
nin
Fig
ure
s5
,6,7
III
the
dis
trib
uti
on
rati
os
of
the
extr
acte
dco
mp
on
ents
(ben
zen
e,ca
pro
lact
amo
rp
hen
ol)
are
plo
tted
asfu
nct
ion
so
fth
eir
mas
sfr
acti
on
sin
the
A-r
ich
ph
ase
(cu
rve
a)an
din
the
B-r
ich
ph
ase
(cu
rve
b).
Th
ed
istr
ibu
tio
nra
tio
kin
dic
ates
how
mu
chb
ette
ro
rw
ors
eth
eex
trac
ted
com
po
nen
tis
sol-
ub
lein
the
B-r
ich
than
inth
eA
-ric
hp
has
e;th
em
inim
also
lven
tra
tio
can
be
eval
uat
edd
irec
tly
fro
mF
igu
res
5,
6,
7II
I.T
he
dis
trib
uti
on
rati
oth
eref
ore
isan
imp
ort
ant
crit
erio
nfo
rth
ese
lec-
tio
no
fa
solv
ent.
Th
em
ass
frac
tio
nin
the
A-r
ich
ph
ase
isea
sier
tov
isu
aliz
eas
are
fere
nce
var
i-ab
le.
At
the
feed
stag
eit
corr
esp
on
ds
app
rox
i-m
atel
yto
the
init
ial
feed
con
cen
trat
ion
.It
gov
-er
ns
the
yie
ldat
the
raffi
nat
eo
utl
et.O
nth
eo
ther
han
d,s
how
ing
kas
afu
nct
ion
of
yC
(cu
rve
b)
has
the
advan
tag
eth
atit
per
mit
sco
mp
aris
on
sw
ith
resp
ectto
solv
entlo
adin
g.I
tis
alw
ays
adv
isab
leto
plo
tb
oth
curv
esb
ecau
seth
eir
suit
abil
ity
for
extr
apo
lati
on
and
inte
rpo
lati
on
var
ies
con
sid
er-
ably
inth
ed
iffe
ren
tco
nce
ntr
atio
nra
ng
es.
Inth
ese
lect
ivit
yd
iag
ram
(Fig
s.5
,6,7
IV)th
eq
uo
tien
to
ftw
od
istr
ibu
tio
nra
tio
sis
plo
tted
asa
fun
ctio
no
fth
em
ass
frac
tio
ns
of
com
po
nen
tC
inth
eA
-ric
h(c
urv
ea)
and
inth
eB
-ric
hp
has
e(c
urv
eb
).T
he
qu
oti
ent
of
the
dis
trib
uti
on
rati
os
for
the
extr
acte
dco
mp
on
ent
C(y
C/x
C)
and
for
A(y
A/x
A)
corr
esp
on
ds
toth
ere
lati
ve
vo
lati
lity
ind
isti
llat
ion
(see
Sec
tio
n5
.1).
Itis
am
easu
reo
fth
ese
lect
ivit
yo
fa
solv
ent.
2.2
.M
easu
rin
gM
eth
od
so
fP
ha
se
Eq
uil
ibri
a
Wh
enev
erp
oss
ible
ate
rnar
ysy
stem
isu
sed
asth
est
arti
ng
po
int
for
mea
sure
men
to
fli
q-
uid
–li
qu
ideq
uil
ibri
a.It
isfi
rst
nec
essa
ryto
es-
tab
lish
wh
ich
of
the
thre
ep
oss
ible
bin
ary
sys-
tem
shav
ea
mis
cibil
ity
gap
and
whic
har
eco
m-
ple
tely
mis
cib
le.F
or
this
pu
rpo
seit
issu
ffici
ent
inea
chca
seto
mix
the
two
sub
stan
ces
inra
-ti
os
of
3:
1,
1:
1an
d1
:3
.If
no
form
atio
no
ftw
oli
qu
idp
has
eso
ccu
rsin
any
of
the
case
sth
enth
esy
stem
isfu
lly
mis
cib
lean
dn
ot
suit
able
for
extr
acti
on
.
8Liq
uid
–Liq
uid
Extr
action
Fig
ure
7.R
epre
senta
tio
no
fp
has
ere
lati
on
ship
ofth
ete
rnar
ysy
stem
wat
er(A
),bu
tyl
acet
ate
(B),
ph
eno
l(C
),at
20◦
C.
All
dat
are
fers
tom
ass
frac
tio
ns.
I)T
rian
gula
rdia
gra
m;
II)
Eq
uil
ibri
um
dia
gra
m;
III)
Dis
tri-
buti
on
dia
gra
m;
IV)
Sel
ecti
vit
yd
iag
ram
If,
for
exam
ple
,A
and
Bar
en
ot
mis
cib
lew
hil
eth
eth
ird
,C
,is
com
ple
tely
mis
cib
lew
ith
the
two
oth
ers
(clo
sed
tria
ng
ula
rd
iag
ram
)th
enth
eb
ino
dal
curv
eca
nb
ed
eter
min
edas
fol-
low
s.E
qu
alam
ou
nts
of
Aan
dB
are
pla
ced
ina
con
tro
lled
-tem
per
atu
reves
sel
wh
ich
can
be
shak
en(e
.g.,
anE
rlen
mey
erfl
ask
ina
ther
mo
-st
at)
and
sub
stan
ceC
isad
ded
un
til
the
mix
ture
bec
om
escl
ear.
Intw
ofu
rth
erex
per
imen
tsp
ure
Ao
rB
isp
lace
din
the
ves
sel
and
inea
chca
seth
ese
con
dsu
bst
ance
isth
enad
ded
un
til
turb
id-
ity
occ
urs
.Th
ree
po
ints
hav
en
ow
bee
no
bta
ined
inth
etr
ian
gu
lar
dia
gra
man
dth
eap
pro
xim
ate
shap
eo
fth
eb
ino
dal
curv
eis
kn
ow
n.
Fo
rp
reci
sed
eter
min
atio
no
fth
eb
ino
dal
curv
e,m
ixtu
res
of
Aan
dC
con
tain
ing
0.9
,0
.8,
0.7
(etc
.,fo
ras
far
asap
pea
rsn
eces
sary
)k
g/k
gA
are
pre
par
edan
dti
trat
edw
ith
Bat
con
stan
tte
mp
erat
ure
.W
hen
turb
idit
yis
reac
hed
titr
atio
nis
ceas
edan
da
smal
lq
uan
tity
of
the
ori
gin
alA
Cm
ixtu
reis
added
unti
lth
eso
luti
on
iscl
ear
agai
n.
Th
ena
char
acte
rist
icvar
iab
lesu
chas
refr
ac-
tive
ind
ex,
den
sity
,d
iele
ctri
cco
nst
ant,
free
zin
gp
oin
t,b
oil
ing
po
int,
etc.
of
this
mix
ture
can
be
det
erm
ined
.In
the
sam
ew
aym
ixtu
res
of
Can
dB
are
titr
ated
wit
hA
.T
his
mea
sure
men
tg
ives
the
pre
cise
shap
eo
fth
eb
ino
dal
curv
ean
dal
lth
eco
mp
osi
tio
ns
lyin
go
nth
iscu
rve
can
be
defi
ned
by
ap
hysi
cal
par
amet
er.
To
det
erm
ine
ph
ase
equ
ilib
riu
man
dth
ere-
wit
hth
eti
eli
nes
,i.
e.,
the
po
ints
wh
ich
are
ineq
uil
ibri
um
wit
ho
ne
ano
ther
,am
ixtu
refr
om
the
two
-ph
ase
reg
ion
isp
lace
din
aco
ntr
oll
ed-t
em-
per
atu
re,s
hak
ing
cyli
nd
er.E
qu
ilib
riu
mis
esta
b-
lish
edb
ysh
akin
g.T
he
ph
ases
are
allo
wed
tose
t-tl
ean
dar
ese
par
ated
by
dra
inin
go
ffin
tod
iffe
r-en
tves
sels
.Th
enth
eir
qu
anti
ties
are
det
erm
ined
and
the
physi
calv
aria
ble
mea
sure
dduri
ng
det
er-
min
atio
no
fth
eb
ino
dal
curv
eis
then
mea
sure
dfo
rb
oth
ph
ases
.T
his
imm
edia
tely
giv
esth
etw
oti
eli
ne
po
ints
.Fu
rth
erm
ore
,bo
thp
has
esca
nal
sob
ean
aly
zed
by
wel
lk
now
nch
emic
alm
eth
od
s,su
chas
gas
or
liquid
chro
mat
ogra
phy
and
titr
a-ti
on
.Th
eco
rrec
tnes
so
fth
em
easu
rem
entca
nb
ech
ecked
by
con
nec
tin
gth
etw
oti
eli
ne
po
ints
inth
etr
ian
gu
lar
dia
gra
m.
Th
eco
nn
ecti
ng
lin
em
ust
pas
sth
rou
gh
the
po
int
of
the
ori
gin
alm
ix-
ture
,an
dth
isp
oin
tm
ust
div
ide
the
len
gth
of
the
tie
lin
ein
inver
sera
tio
toth
eq
uan
titi
eso
fth
etw
op
has
es.
Liq
uid
–Liq
uid
Extr
action
9
Ifa
syst
emo
fm
ore
than
thre
eco
mp
on
ents
has
tob
em
easu
red
then
sever
alco
mp
on
ents
are
com
bin
edin
too
ne
gro
up
ino
rder
toar
rive
ata
tern
ary
syst
emag
ain.D
eter
min
atio
nofa
bin
odal
curv
ew
ou
ldst
ill
be
po
ssib
lein
such
aca
sebu
tth
etw
op
has
esin
tow
hic
hth
ete
stm
ixtu
rese
p-
arat
esar
en
olo
ng
erid
enti
cal
wit
hth
em
ixtu
res
wh
ich
wer
eo
bta
ined
du
rin
gth
ed
eter
min
atio
no
fth
eb
ino
dal
curv
e.It
isth
eref
ore
bet
ter
toal
low
the
mix
ture
tore
ach
equ
ilib
riu
mco
nd
itio
ns
ina
con
tro
lled
-tem
per
atu
re,
shak
ing
cyli
nd
er,
sep
a-ra
teit
and
then
anal
yze
the
ph
ases
usi
ng
som
ep
rep
lan
ned
met
ho
d.
Th
eti
me
con
sum
ing
step
inth
ed
eter
min
atio
no
feq
uil
ibri
ais
the
pre
par
atio
no
fth
eex
per
imen
t,su
chas
pu
rifi
cati
on
of
the
sub
stan
ces,
sett
ing
up
the
cali
bra
tio
ncu
rves
,et
c.T
her
efo
reit
isse
nse
-le
ssto
rest
rict
the
nu
mb
ero
fm
easu
red
po
ints
and
use
inte
rpo
lati
on
met
ho
ds.
To
incr
ease
the
accu
racy
am
ater
ial
bal
ance
isse
tu
pfo
rea
chco
mp
on
enta
nd
the
mea
sure
dp
oin
tsar
ead
just
edb
yd
raw
ing
the
curv
esfr
om
Fig
ure
s5
,6
,7
.
2.3
.E
mp
iric
al
Co
rrel
ati
on
so
fP
ha
se
Eq
uil
ibri
a
Inte
rnar
ysy
stem
s,th
eu
seo
fem
pir
ical
corr
e-la
tio
ns
tore
pre
sen
tth
eb
ino
dal
curv
esan
dd
is-
trib
uti
on
equ
ilib
ria
of
com
po
nen
tC
iso
fad
van
-ta
ge
[28
].T
he
mu
tual
solu
bil
itie
so
fth
eli
qu
idp
has
esar
eu
sual
lyd
eter
min
edb
ya
lab
ora
tory
turb
idit
yti
trat
ion
.T
he
bin
od
alcu
rve
isth
end
e-te
rmin
edb
yex
trap
ola
tin
gth
em
easu
red
val
ues
(see
Sec
tio
n2
.2).
InT
yp
eI
syst
ems
wit
han
op
enm
isci
bil
ity
gap
,th
ebin
odal
curv
eca
nbe
sim
ply
des
crib
edb
yp
arab
oli
ceq
uat
ion
s:
x=
D′+
E′x′ A
+F′x′2 A
y=
D′′+
E′′x′′ B+
F′′x′′2
B
wh
ere
x′ A
isth
em
ass
frac
tio
no
fA
inth
eA
-ric
hp
has
e,x′′ B
the
mas
sfr
acti
on
of
Bin
the
B-r
ich
ph
ase
and
D′,D′′,E′,E′′,F′
and
F′′
are
coef
-fi
cien
ts.
Insy
stem
sw
ith
acl
ose
dm
isci
bil
ity
gap
(Ty
pe
II),
the
par
abo
lic
equ
atio
ns
are
on
lyval
idfo
rth
elo
wer
par
tso
fth
ecu
rve;
they
can
no
tb
eu
sed
tore
pre
sen
tth
een
tire
bin
od
alcu
rve.
Th
eb
esteq
uat
ion
for
the
clo
sed
bin
od
alcu
rve
isth
atp
rop
ose
db
yH
lavaty
[29
].T
he
corr
elat
ion
is
der
ived
fro
ma
po
lyn
om
ial
equ
atio
nan
dh
asth
ead
van
tag
eth
atth
eb
ino
dal
curv
een
ds
exac
tly
atth
eb
inar
yso
lub
ilit
yp
oin
ts.
Its
dis
advan
tag
eis
,h
ow
ever
,th
atth
elo
wer
,in
pra
ctic
ev
irtu
ally
lin
-ea
r,re
gio
ns
ofth
eb
ino
dal
curv
esar
ere
pre
sen
ted
inw
ave
form
asa
resu
lto
fth
ep
oly
no
mia
leq
ua-
tio
n.T
he
Hla
vat
yeq
uat
ion
sho
uld
,th
eref
ore
,b
eu
sed
wit
hca
uti
on
.T
he
equ
ilib
riu
md
istr
ibu
tio
no
fso
lute
Cin
the
A-an
dB
-ric
hp
has
esis
gen
eral
lyd
eter
min
edin
dep
end
entl
yfr
om
the
bin
od
alcu
rve
by
mea
ns
of
lab
ora
tory
exp
erim
ents
.Th
em
ass
frac
tio
nxC
and
yC
ofth
etw
op
has
esin
ther
mo
dy
nam
iceq
ui-
lib
riu
mar
eth
us
ob
tain
edan
dd
eter
min
eth
ep
o-
siti
on
so
fth
een
dp
oin
tso
fth
eti
eli
nes
on
the
bin
od
alcu
rves
(see
Sec
tio
n2
.2).
Eq
uat
ion
sfo
rco
rrel
atin
gan
din
terp
ola
tin
gth
een
dp
oin
to
fth
eti
eli
nes
are
des
crib
edin
the
lite
ratu
re,
they
are
pri
mar
ily
exp
on
enti
aleq
uat
ion
ssu
chas
tho
sep
rop
ose
db
yO
th
mer
and
Tobia
s,
and
Han
d
[1].
How
ever
,al
lex
po
nen
tial
equ
atio
ns
gen
er-
ally
fail
wh
enth
eco
nce
ntr
atio
no
fC
isver
ylo
w.
To
allo
wa
mo
reac
cura
tees
tim
atio
no
fd
istr
i-bu
tio
neq
uil
ibri
aan
dex
trac
tio
np
roce
sses
atth
elo
wra
ffin
ate
con
cen
trat
ion
sth
atar
eo
fin
du
stri
alim
po
rtan
ce,B
en
der
and
Block
[28
]p
rop
ose
dth
efo
llow
ing
corr
elat
ion
for
the
dis
trib
uti
on
ra-
tio
K:
K=
G1+
G2x′ C
+G
3x′2 C+
G4x′3 C
Th
eco
effi
cien
tsG
im
ust
be
fitt
edto
the
mea
-su
red
val
ues
of
the
tie
lin
esx
and
y.
Alt
ho
ug
hth
eeq
uat
ion
do
esn
ot
gen
eral
lyp
erm
itex
trap
o-
lati
on
of
the
curv
eab
ove
the
mea
sure
dval
ues
toth
ep
lait
po
int,
the
dis
trib
uti
on
coef
fici
entK
can
be
ob
tain
edac
cura
tely
up
tox
and
y→
0.
Th
eem
pir
ical
corr
elat
ion
sar
esi
mp
lean
dcl
ear.
Th
eyca
nb
eca
lcu
late
dq
uic
kly
wit
hap
-p
rop
riat
eco
mp
ute
rp
rog
ram
san
dg
ive
anac
cu-
rate
rep
rese
nta
tio
no
fth
em
easu
red
liq
uid
–li
q-
uid
equ
ilib
ria.
How
ever
,th
ese
advan
tag
esar
eac
-co
mp
anie
db
yse
ver
ald
isad
van
tag
es.T
he
corr
e-la
tio
ns
can
on
lyb
eu
sed
wit
hte
rnar
ysy
stem
san
dd
on
ot
allo
wex
trap
ola
tio
nto
hig
her
mu
lti-
com
po
nen
tsy
stem
s.E
xte
nsi
ve
lab
ora
tory
wo
rkis
req
uir
edto
det
erm
ine
the
mu
tual
solu
bil
itie
so
fco
mp
on
ents
Aan
dB
asa
fun
ctio
no
fth
eco
nce
ntr
atio
no
fC
asw
ell
asth
eeq
uil
ibri
um
dis
trib
uti
on
of
com
po
nen
tC
.S
yst
emat
icm
ea-
sure
men
ter
rors
can
no
tb
ed
etec
ted
bec
ause
the
exp
erim
enta
lval
ues
are
emp
iric
ally
corr
elat
ed.
10
Liq
uid
–Liq
uid
Extr
action
2.4
.S
elec
tio
no
fS
olv
ent
Th
ese
lect
ion
of
the
mo
stsu
itab
leso
lven
tis
on
eo
fth
eh
ard
est
pro
ble
ms
of
the
extr
acti
on
,an
dth
ed
ecis
ion
mad
eh
asa
gre
atin
flu
ence
on
the
eco
no
my
of
the
pro
cess
.Th
eso
lven
tm
ust
fulfi
lltw
ob
asic
req
uir
emen
ts:
1)
itm
ust
hav
ea
mis
cibil
ity
gap
wit
hth
eA
-ric
hp
has
e,an
d2
)it
mu
stb
ea
bet
ter
solv
ent
for
com
po
nen
tC
than
for
A.
Ag
reat
nu
mb
ero
fm
eth
od
sh
ave
bee
nre
com
-m
end
edfo
rd
isco
ver
ing
suit
able
solv
ents
[30
],[3
1].
Th
em
ore
emp
iric
alst
rate
gy
of
form
erti
mes
isb
ein
gre
pla
ced
mo
rean
dm
ore
by
asy
s-te
mat
icre
sear
chw
ith
the
aid
of
dat
ab
ank
s[2
6].
Th
eco
nce
pt
of
po
lari
tyis
use
dfo
rch
arac
teri
z-in
gsu
itab
lep
aram
eter
s[3
2].
Th
eg
reat
erth
ed
iffe
ren
cein
po
lari
tyb
etw
een
two
liq
uid
s,th
eg
reat
eris
the
pro
bab
ilit
yth
atth
eyh
ave
am
isci
bil
ity
gap
.T
he
subst
ance
tobe
extr
acte
dw
illh
ave
ah
igh
erco
nce
ntr
atio
nin
the
liq
uid
tow
hic
hit
iscl
ose
rin
po
lari
ty.
How
ever
,th
ere
lati
on
ship
sar
en
ot
sosi
mp
leth
ato
nly
asc
ale
of
po
lari
ties
has
tob
ese
tu
pan
dth
ed
iffe
ren
cein
po
lari
tyat
wh
ich
mis
ci-
bil
ity
gap
socc
ur
read
off
the
scal
e.F
or
exam
-p
le,
anil
ine,
ph
eno
l,an
dfu
rfu
ral
hav
em
isci
bil
-it
ygap
sw
ith
both
wat
eran
dhex
ane.
Ace
tone,
eth
ano
l,an
dd
iox
anw
hic
hh
ave
asi
mil
arp
ola
r-it
yar
em
isci
ble
wit
hb
oth
wat
eran
dh
exan
e.T
he
mo
lecu
lar
form
and
the
size
of
the
mo
lecu
leal
soco
ntr
ibu
teto
solv
ent
beh
avio
r.T
he
beh
avio
ro
fso
lven
tsto
war
ds
hydro
carb
ons
has
bee
nin
ves
-ti
gat
edpar
ticu
larl
yin
tensi
vel
y[3
3],
[34].
Itis
also
po
ssib
leto
ob
tain
effe
cts
fro
mm
ixin
gtw
oso
lven
tsw
hic
hco
uld
no
tb
ep
red
icte
dfr
om
the
pro
per
ties
of
the
mix
com
po
nen
ts[3
5],
[36
].T
he
mo
stim
po
rtan
tp
rop
erty
of
aso
lven
tis
its
sele
ctiv
ity.
Th
isin
dic
ates
how
mu
chb
ette
rth
eso
lute
isd
isso
lved
than
the
A-r
ich
ph
ase.
As
can
be
seen
fro
mF
igu
res
5,6
,7
III
the
sele
ctiv
ity
isst
ron
gly
dep
end
ent
on
con
cen
trat
ion
.In
add
itio
nto
sele
ctiv
ity
the
cap
aci
tyo
fa
sol-
ven
tis
also
imp
ort
ant.
Th
isis
defi
ned
by
the
dis
trib
uti
on
coef
fici
ent
of
Cb
etw
een
the
B-r
ich
and
A-r
ich
ph
ases
and
det
erm
ines
the
qu
anti
tyo
fso
lven
tw
hic
hh
asto
be
recy
cled
.W
hen
test
ing
dif
fere
nt
solv
ents
for
asp
ecifi
cex
trac
tio
nta
skit
iso
ften
fou
nd
that
solv
ents
wit
hh
igh
erse
-le
ctiv
itie
sh
ave
low
erca
pac
itie
san
dv
ice
ver
sa.
Th
eg
reat
erth
eth
rou
gh
pu
to
fa
pla
nt
the
mo
reim
po
rtan
tth
eca
pac
ity
of
the
solv
ent
isfo
rth
eec
on
om
yo
fth
ep
roce
ss.I
fth
ere
are
sever
alp
os-
sib
leso
lven
tsfo
ra
pro
cess
then
thei
rb
ehav
ior
wit
hre
spec
tto
sele
ctiv
ity
and
cap
acit
yca
nb
ete
sted
wit
ha
gas
chro
mat
og
rap
hw
ith
ou
tst
art-
ing
wit
hti
me-
con
sum
ing
equ
ilib
riu
mm
easu
re-
men
ts[3
7].
Inad
dit
ion
toth
ese
bas
icre
qu
irem
ents
ther
ear
eal
soo
ther
crit
eria
wh
ich
mu
stb
eta
ken
into
con
sid
erat
ion
wh
ense
lect
ing
aso
lven
tan
dw
hic
hsh
arp
lyre
du
ceth
en
um
ber
of
po
ssib
leco
mp
ou
nd
s.M
ost
imp
ort
anti
sth
eav
aila
bil
ity
of
the
solv
ent
inco
mm
erci
alq
uan
titi
esat
anec
o-
no
mic
ally
acce
pta
ble
pri
ce.
Itis
then
nec
essa
ryto
fin
dd
ata
con
cern
ing
bo
ilin
gp
oin
ts,
den
sity
,v
isco
sity
and
–w
her
eav
aila
ble
–in
form
atio
nab
ou
tso
lub
ilit
y[3
8],
[39
].T
he
bo
ilin
gp
oin
to
fth
eso
lven
tis
imp
ort
ant
bec
ause
the
extr
acte
dco
mp
on
entis
usu
ally
sep
-ar
ated
fro
mth
eso
lven
tb
yd
isti
llat
ion
and
the
bo
ilin
gp
oin
td
iffe
ren
ced
eter
min
esth
ere
flu
xra
tio
inth
isd
isti
llat
ion
.If
the
solv
ent
bo
ils
ata
hig
her
tem
per
atu
reth
anth
eso
lute
,th
isso
lute
isd
isti
lled
over
hea
d.If
itis
nec
essa
ryto
recy
cle
ag
reat
dea
lo
fso
lven
tth
enth
eso
lven
th
asto
be
pu
rifi
edb
yd
isti
llat
ion
ina
sub
seq
uen
tst
ep;
the
spec
ific
hea
tw
hic
his
req
uir
edfo
rh
eati
ng
the
solv
ent
toit
sb
oil
ing
tem
per
atu
rem
ust
also
be
taken
into
acco
un
t.T
oo
gre
ata
tem
per
atu
red
iffe
ren
ceis
then
ad
isad
van
tag
e.T
he
den
sity
of
the
solv
enti
sim
po
rtan
tfo
ro
b-
tain
ing
asu
ffici
entl
yla
rge
dif
fere
nce
ind
ensi
ties
bet
wee
nth
etw
oli
qu
idp
has
esfo
rth
ese
par
atio
np
roce
ss.
Ch
lori
nat
edco
mp
ou
nd
sar
esu
itab
leif
aso
lven
tw
ith
ah
igh
den
sity
isto
be
use
d,
and
par
ticu
larl
ylo
w-d
ensi
tyco
mp
ou
nd
sar
efo
un
dam
ong
the
satu
rate
dhydro
carb
ons
and
ether
s.T
he
ther
ma
lst
ab
ilit
yo
fth
eso
lven
tca
nb
eh
igh
lysi
gn
ifica
nt.
Th
ere
sear
cher
har
dly
ever
fin
ds
the
answ
erto
this
qu
esti
on
inth
eli
tera
ture
and
isd
irec
ted
toca
rry
ou
th
isow
nm
easu
re-
men
t.It
isn
eces
sary
tok
now
(1)
how
mu
chso
l-ven
tm
ake-
up
wil
lb
en
eed
edin
the
pro
cess
;(2
)w
het
her
are
gen
erat
ion
pro
cess
for
con
tin
uo
us
rem
oval
of
dec
om
po
siti
on
pro
du
cts
nee
ds
tob
ein
stal
led
.V
ery
care
ful
test
sm
ust
be
carr
ied
ou
tto
fin
do
ut
wh
eth
erd
eco
mp
osi
tio
np
rod
uct
sca
nco
nta
min
ate
the
extr
acto
rh
ave
aco
rro
sive
effe
cto
nth
eco
nst
ruct
ion
mat
eria
lso
fth
ep
lan
t.S
om
e-ti
mes
the
tox
ico
log
ical
pro
per
ties
and
bio
log
ical
Liq
uid
–Liq
uid
Extr
action
11
deg
rad
atio
no
fa
solv
ent
hav
eto
be
con
sid
ered
[40
]. Th
evi
sco
sity
sho
uld
be
aslo
was
po
ssib
leas
this
favo
rsm
ass
tran
sfer
and
ph
ase
sep
arat
ion
.H
ow
ever
,th
isp
rop
erty
isle
sssi
gn
ifica
nt
than
tho
sem
enti
on
edab
ove.
Ifth
ep
oss
ible
solv
ents
hav
eb
een
red
uce
dto
am
anag
eab
len
um
ber
afte
rte
stin
gal
lth
eas
pec
tsth
enth
ein
div
idu
alp
rop
-er
ties
can
be
eval
uat
edw
ith
ap
oin
tsy
stem
tod
isco
ver
the
bes
tso
lven
t.T
he
surf
ace
ten
sio
nis
ano
ther
imp
ort
ant
pa-
ram
eter
bec
ause
itin
flu
ence
sth
een
erg
yd
eman
dn
eces
sary
top
rod
uce
asu
itab
led
rop
dis
per
sio
n.
Hig
hsu
rfac
ete
nsi
on
giv
esri
seto
form
atio
no
fst
able
dro
ps
and
nee
ds
ah
igh
ener
gy
inp
ut.
Aso
lven
tw
ith
ah
igh
surf
ace
ten
sio
nd
ecre
ases
the
dan
ger
of
pro
du
cin
gan
emu
lsio
n.
Th
esu
rfac
ete
nsi
on
isd
epen
den
to
nth
eco
nce
ntr
atio
no
fth
etr
ansf
erco
mp
on
ent.
Fu
rth
erp
rop
erti
essu
chas
suit
abil
ity
for
reg
ener
atio
n,
dis
po
sab
ilit
y,co
sts,
com
bu
stib
ilit
y,to
xic
ity
and
corr
osi
ven
ess
also
hav
eto
be
taken
into
acco
un
tto
sele
cta
suit
able
solv
ent.
Bo
un
du
pw
ith
solv
entse
lect
ion
isth
ech
oic
eo
fth
ed
isp
erse
dan
dth
eco
nti
nu
ou
sp
has
e,re
-sp
ecti
vel
y.D
irec
tio
no
fm
ass
tran
sfer
and
ph
ase
rati
oh
ave
tob
eta
ken
into
acco
un
t.T
he
dir
ec-
tio
no
fm
ass
tran
sfer
infl
uen
ces
the
surf
ace
ten
-si
on
and
inth
isw
ayca
np
rom
ote
or
ham
per
the
coal
esce
nce
of
dro
ps.
Th
ep
has
eto
be
dis
per
sed
sho
uld
be
the
on
ew
hic
him
ped
esth
ed
rop
co-
ales
cen
ceto
pro
du
cest
able
dro
ps,
and
the
on
ew
ith
the
hig
her
flow
rate
too
bta
ina
mas
str
ansf
erar
eaas
larg
eas
po
ssib
le.
2.5
.C
alc
ula
tio
no
fT
heo
reti
cal
Sta
ges
(→A
bso
rpti
on
,C
hap
.4
.;→
Dis
till
atio
nan
d
Rec
tifi
cati
on
,C
hap
.4
.)
Tw
op
oss
ibil
itie
sex
ist
toca
lcu
late
the
mas
str
ansf
erp
erfo
rman
ceo
fex
trac
tors
.T
he
firs
to
ne
use
sth
eco
nce
pt
of
theo
reti
cal
stag
esan
dis
bas
edo
nth
eas
sum
pti
on
that
con
cen
trat
ion
equ
i-li
bri
um
ises
tab
lish
edin
ever
yse
ctio
no
fan
ex-
trac
tor.
Th
isas
sum
pti
on
can
be
fulfi
lled
on
lyin
the
mix
er–
sett
ler
wit
hlo
ng
con
tact
tim
eso
fth
ep
has
esin
vo
lved
.In
this
con
cep
tth
eto
tal
hei
gh
to
fan
extr
acti
on
colu
mn
isg
iven
by
the
pro
du
cto
fth
en
um
ber
ofth
eore
tica
lsta
ges
(NT
S)an
dth
eh
eig
ht
equ
ival
ent
of
ath
eore
tica
lst
age
(HE
TS
).
NT
Sfo
llow
sfr
om
am
ater
ial
bal
ance
inco
mb
i-n
atio
nw
ith
the
dis
trib
uti
on
equ
ilib
riu
m;
HE
TS
dep
end
so
nfl
uid
dy
nam
ics
and
mas
str
ansf
erin
the
colu
mn
san
dco
mp
rise
sal
lre
alco
nd
i-ti
on
sas
for
inst
ance
the
con
dit
ion
so
fp
has
em
ix-
ing
.T
her
efo
reth
isco
nce
pt
isp
refe
rred
on
lyfo
rro
ug
hes
tim
atio
ns
inp
ract
ice
bec
ause
itis
easy
toh
and
lean
dsu
ffici
ent
for
pre
par
atio
no
fla
bo
ra-
tory
exp
erim
ents
.In
the
foll
ow
ing
sect
ion
s,th
em
eth
od
wil
lb
ep
rese
nte
db
yai
do
feq
uil
ibri
um
dia
gra
ms.
Th
ese
con
dp
oss
ibil
ity
isa
stre
amco
nce
pt.
Th
eco
lum
nh
eig
htre
qu
ired
for
ag
iven
thro
ug
h-
pu
tan
dco
nce
ntr
atio
ng
rad
ien
to
fp
has
esal
on
gth
eco
lum
nca
nb
eca
lcu
late
dfr
om
hei
gh
tin
-te
gra
tio
no
fa
set
of
dif
fere
nti
aleq
uat
ion
s,d
e-ri
ved
fro
ma
dif
fere
nti
alm
ater
ial
bal
ance
and
the
loca
lm
ass
tran
sfer
bet
wee
nth
eb
oth
ph
ases
.T
he
stre
amco
nce
pt
sup
pli
esth
eco
urs
eo
fco
n-
cen
trat
ion
sal
on
gth
eco
lum
nan
dis
suit
able
for
anal
ysi
so
fth
ed
yn
amic
beh
avio
ro
fa
colu
mn
and
for
tak
ing
into
acco
un
tth
ed
rop
po
pu
lati
on
insi
de
the
colu
mn
.It
isp
refe
rred
un
til
now
for
scie
nti
fic
inves
tigat
ions,
e.g.,
for
stat
ionar
ily
op-
erat
edp
uls
edsi
eve
tray
colu
mn
s[4
5],
[47
–4
9],
[51
],[6
2]an
dfo
rin
stat
ion
aril
yo
per
ated
rota
tin
gex
trac
tors
[65
],[6
8].
2.5
.1.
Sel
ecti
on
of
Ca
lcu
lati
on
Met
ho
ds
Th
eco
nd
itio
ns
for
anap
pli
cab
lem
eth
od
of
cal-
cula
tio
nar
ese
tb
yth
ep
rob
lem
tob
eso
lved
,b
yw
het
her
sim
pli
fied
assu
mp
tio
ns
are
per
mis
sib
lean
db
yth
em
ain
infl
uen
cin
gvar
iab
les
of
anex
-tr
acti
on
pro
ble
m.
Th
eyar
e,th
eref
ore
,d
iffe
ren
t.T
he
foll
ow
ing
po
ints
sho
uld
be
con
sid
ered
wh
ense
lect
ing
am
eth
od
of
calc
ula
tio
n:
1)
Do
chan
ges
inm
ass
flow
sh
ave
tob
eco
nsi
d-
ered
?2
)Is
the
dis
trib
uti
on
rati
oco
nst
ant?
3)
Isth
eco
nce
ntr
atio
ng
rad
ien
tla
rge
or
smal
l?4
)D
oes
on
lyo
ne
com
po
nen
th
ave
tob
eex
-tr
acte
d,
or
are
ther
ese
ver
alw
ith
dif
fere
nt
dis
trib
uti
on
coef
fici
ents
?
2.5
.2.
Sp
ecifi
cM
eth
od
s
Met
ho
d1
.If
the
foll
ow
ing
con
dit
ion
sar
esa
tisfi
ed:
1)
the
com
po
nen
tA
and
solv
entB
are
vir
tual
lyin
solu
ble
inea
cho
ther
,
12
Liq
uid
–Liq
uid
Extr
action
Fig
ure
8.
A)
Mat
eria
lb
alan
ceo
fa
colu
mn
cro
ssse
ctio
n;
B)
Co
rres
po
nd
ing
op
erat
ing
dia
gra
m
2)
the
chan
ges
inm
ass
flow
rate
so
fth
eex
trac
tan
dra
ffin
ate
ph
ase
are
neg
lig
ible
(e.g
.,fo
ra
low
con
ten
to
fC
inth
efe
ed)
then
the
com
po
siti
on
so
fth
ep
has
esca
nb
eex
-p
ress
edas
load
s.If
am
ater
ial
bal
ance
ism
ade
assh
ow
nin
Fig
ure
8,
the
two
load
sY
can
dX
c
ina
giv
enco
lum
ncr
oss
sect
ion
can
be
rela
ted
asfo
llow
s
YC−
YC
,S=
mF
ms·(
XC−
XC
,R
)
Wh
enp
lott
edo
nth
eeq
uil
ibri
um
dia
gra
m,
this
rela
tio
ng
ives
ast
raig
ht
lin
e,th
eb
alan
ceo
ro
per
atin
gli
ne.
Th
en
um
ber
of
theo
reti
calst
ages
req
uir
edto
ob
tain
ad
esir
edd
ecre
ase
inth
eco
n-
cen
trat
ion
of
Cfr
om
XC
,F
toX
C,R
can
be
de-
term
ined
gra
ph
ical
lyb
yco
nst
ruct
ing
ase
ries
of
step
sas
show
nin
Fig
ure
9.
Th
ere
sult
of
the
use
of
the
step
so
ften
mea
ns
that
the
load
ob
tain
edfr
om
Cin
the
raffi
nat
e(X
C,R
)d
oes
no
tco
rre-
spo
nd
toth
ere
qu
ired
load
(XC
R,re
q).
Fig
ure
8al
sosh
ow
sth
ep
osi
tio
no
fth
eb
al-
ance
lin
efo
rth
em
inim
um
extr
acta
ntra
tio
Vm
in
Vm
in=
ms,
min
/m
F
Th
ed
esir
eden
rich
men
to
fth
efe
edw
ith
Cu
s-in
gth
em
inim
um
amo
un
to
fex
trac
tan
tm
s,m
in
can
on
lyb
eac
hie
ved
wit
han
infi
nit
en
um
ber
of
stag
es.
Fig
ure
9.C
on
stru
ctio
no
fst
eps
inth
eo
per
atin
gd
iag
ram
too
bta
inth
en
um
ber
of
theo
reti
cal
stag
es(N
TS
)
Met
ho
d2
.F
igu
re1
0sh
ow
sth
eeq
uil
ib-
riu
md
iag
ram
for
the
syst
emto
luen
e–
eth
yle
ne
gly
col–
wat
eras
adouble
logar
ithm
icplo
t.T
his
typ
eo
fp
lot
isu
sefu
lif
the
dis
trib
uti
on
rati
ovar
ies
con
sid
erab
ly,d
esp
ite
low
load
ing
,an
dth
eco
nce
ntr
atio
nra
ng
eco
nsi
der
ably
exce
eds
the
des
ired
raffi
nat
ep
uri
ty.I
nth
isca
seth
eo
per
atin
gli
ne
isat
anan
gle
of
45◦.
log(
YC−
YC
,S
)
=lo
g
(
mF
mS
)
+lo
g(
XC−
XC
,R
)
Liq
uid
–Liq
uid
Extr
action
13
Fig
ure
10.D
eter
min
atio
nof
the
num
ber
of
stag
esfo
ra
var
i-ab
ledis
trib
uti
on
rati
oan
da
hig
hdeg
ree
of
dep
leti
on
Th
ep
osi
tio
no
fth
est
raig
ht
lin
esis
det
er-
min
edb
yth
eex
trac
tan
tra
tio
V.
Th
en
um
ber
of
req
uir
edth
eore
tica
lst
ages
can
be
det
erm
ined
by
con
stru
ctin
ga
seri
eso
fst
eps.
Met
ho
d3
.If
the
dis
trib
uti
on
rati
oK
isa
con
-st
ant,
furt
her
sim
pli
fica
tio
nis
po
ssib
le;
inan
al-
og
yw
ith
the
Co
lbu
rneq
uat
ion
(→A
bso
rpti
on
,C
hap
.4
.2.)
,th
en
um
ber
of
theo
reti
cal
stag
esN
TS
can
be
calc
ula
ted
:
NT
S=
log[
1+
(E−
1)(
XC
,F
XC
,R
+YC
,S
XC
,R
)]
logE
−1
wh
ere
the
extr
acti
on
fact
or
Eis
giv
enb
y
E=
K·m
s/m
F
IfN
TS
isk
now
nan
dth
ed
egre
eo
fd
eple
tio
nX
C,R
/XC
,F
isd
esir
ed,t
he
foll
ow
ing
equ
atio
nis
ob
tain
ed:
XC
,R
XC
,F=
(E−
1)(
1+
YC
,S
XC
,F
)
E(N
TS+
1)−
1
Th
iseq
uat
ion
can
on
lyb
eso
lved
iter
ativ
ely
;a
gra
ph
ical
solu
tio
nis
show
nin
Fig
ure
11
.
Met
ho
d4
.If
no
ne
of
the
above-
men
tio
ned
con
dit
ion
sis
sati
sfied
,an
dth
eex
trac
tio
np
rob
-le
mca
nb
eli
mit
edto
con
sid
erat
ion
of
the
thre
ekey
com
po
nen
ts,
the
calc
ula
tio
nca
nb
eca
rrie
do
ut
wit
hth
eai
do
fth
etr
ian
gu
lar
mas
sfr
acti
on
dia
gra
m.
Th
ism
eth
od
isb
ased
on
the
mix
ing
rule
sd
escr
ibed
inS
ecti
on
2.1
.1.
Th
esp
ecifi
edco
mp
osi
tio
ns
of
the
feed
Fan
dso
lven
tS
stre
ams
are
plo
tted
on
the
ph
ase
equ
ilib
riu
md
iag
ram
for
the
tern
ary
mix
ture
(Fig
.12
).F
or
mat
eria
lb
alan
ceo
fth
efe
edan
dp
rod
uct
stre
ams,
the
colu
mn
can
be
assu
med
tob
ea
sim
ple
mix
ing
ves
sel.
Th
eco
mp
osi
tio
nM
of
the
mix
ture
lies
on
the
tie
lin
eF
S;
the
po
si-
tio
no
fM
on
the
tie
lin
eis
det
erm
ined
by
the
rati
om
S:
mF
=M
F:
MS
.T
he
com
po
siti
on
so
fth
era
ffin
ate
Ran
dex
trac
tE
stre
ams
leav
ing
the
colu
mn
are
ob
tain
edfr
om
the
inte
rcep
tso
fth
eti
eli
ne
wit
hth
eb
ino
dal
curv
e.T
he
raffi
nat
eco
mp
o-
siti
on
isd
eter
min
edb
yth
ed
esir
edm
ass
frac
tio
no
fC
inth
era
ffin
ate
(xC
,R
).T
he
com
po
siti
on
of
the
extr
act
Eis
giv
enb
yth
ep
oin
tat
wh
ich
the
exte
nd
edli
ne
RM
inte
rsec
tsth
eb
ino
dal
curv
e.T
he
rati
om
R:
mE
iso
bta
ined
by
app
lyin
gth
ele
ver
rule
.T
he
qu
anti
ties
and
the
com
po
siti
on
so
fth
ein
com
ing
and
ou
tflow
ing
stre
ams
are
thu
sd
eter
min
ed.
Th
ere
qu
ired
nu
mb
ero
fst
ages
ina
cou
nte
r-cu
rren
tco
lum
nar
eo
bta
ined
by
usi
ng
the
po
le
po
intp
roce
du
re.T
he
pro
ced
ure
can
be
exp
lain
edb
yim
agin
ga
stre
amP
tom
ain
tain
the
mat
eria
lb
alan
ce.M
ixin
go
fth
isst
ream
wit
hth
era
ffin
ate
stre
amR
giv
esth
eco
mp
osi
tio
no
fth
eso
lven
tst
ream
S.
To
mai
nta
inth
em
ater
ial
bal
ance
the
extr
act
on
the
oth
erh
and
mu
stb
eco
mp
ose
do
fth
efe
edst
ream
Fan
dth
eim
agin
ary
stre
amP.
The
imag
inar
yst
ream
Pca
nth
us
be
regar
ded
asa
com
mo
nm
ixin
gp
artn
erfo
rF
and
Rto
mai
nta
inth
eco
mp
osi
tio
ns
of
Ean
dS
.Th
eco
mp
osi
tio
no
fth
eim
agin
ary
stre
amP
isre
pre
sen
ted
by
ap
oin
to
uts
ide
the
tria
ng
ula
rd
iag
ram
,th
ep
ole
po
int.
Th
eim
agin
ary
mas
sfr
acti
on
so
fth
eth
ree
com
-p
on
ents
inth
ep
ole
po
intc
anb
e>
1o
rn
egat
iv.I
fth
em
ater
ial
bal
ance
bo
un
dar
ies
for
the
ind
ivid
-u
alst
ages
are
taken
assh
ow
nin
Fig
ure
13
,th
eab
ove
pro
ced
ure
giv
esth
est
age
extr
acts
E2,E
3,
etc.
fro
mth
em
ixtu
reo
fth
eim
agin
ary
stre
amP
and
the
ind
ivid
ual
stag
era
ffin
ates
inth
ep
ro-
ceed
ing
stag
esR
1,
R2,
etc.
Th
eco
mp
osi
tio
no
fth
era
ffin
ates
R1,R
2,e
tc.a
reli
nked
toth
eco
rre-
spo
nd
ing
extr
acts
E1,E
2,e
tc.v
iath
ed
istr
ibu
tio
nra
tio
s(t
ieli
nes
).
2.5
.3.
Eva
lua
tio
no
fS
tag
e-N
um
ber
Ca
lcu
lati
on
for
Pro
cess
Des
ign
Ino
rder
tod
eter
min
eth
eo
per
atin
gco
nd
itio
ns
and
the
dim
ensi
on
so
fth
eeq
uip
men
tu
sed
for
14
Liq
uid
–Liq
uid
Extr
action
Fig
ure
11.
Dep
enden
ceo
fth
eth
eore
tica
ln
um
ber
of
stag
es,th
ed
egre
eo
fdep
leti
on
,an
dth
ey
ield
on
the
extr
acti
on
fact
or
E
Fig
ure
12.
Pole
poin
tco
nst
ruct
ion
–b
alan
ced
iag
ram
Liq
uid
–Liq
uid
Extr
action
15
Fig
ure
13.
Pole
poin
tco
nst
ruct
ion
–oper
atin
gdia
gra
m
extr
acti
on
,th
ere
sult
so
fse
ver
alst
age-
nu
mb
erca
lcu
lati
on
sm
ust
be
plo
tted
ina
dia
gra
msh
ow
-in
gth
ere
lati
on
ship
bet
wee
nth
eso
lven
tci
rcu
la-
tio
n,th
en
um
ber
of
stag
es,an
dth
ere
sid
ual
con
-te
nt
of
solu
tein
the
raffi
nat
e.S
uch
ad
iag
ram
issh
ow
nin
Fig
ure
14
for
mix
ture
II(s
eeal
soF
ig.6
).It
rep
rese
nts
the
extr
acti
on
of
a1
0%
so-
luti
on
of
cap
rola
ctam
intr
ich
loro
eth
yle
ne
wit
hw
ater
asth
eex
trac
tio
nso
lven
t.T
he
favo
rab
leo
per
atin
gre
gio
nis
usu
ally
loca
ted
inth
ere
gio
nw
hic
hsh
ow
sth
em
ost
pro
no
un
ced
curv
atu
re.
Oth
ervar
iab
les
(e.g
.,th
eef
fect
of
tem
per
atu
rean
dth
ere
sid
ual
load
ing
of
the
solv
ent
wit
hso
-lu
te)
may
hav
eto
be
taken
into
con
sid
erat
ion
.
3.
Ap
para
tus
3.1
.S
urv
ey
Ex
trac
tio
nap
par
atu
sca
nb
ecl
assi
fied
into
cou
n-
terc
urr
ent
colu
mns,
centr
ifugal
extr
acto
rs,
and
mix
er–
sett
lers
.A
llin
du
stri
aleq
uip
men
td
e-si
gn
su
seth
ep
rin
cip
leto
dis
per
seo
ne
of
the
two
liq
uid
sin
toth
eo
ther
ino
rder
toen
larg
eth
eco
nta
ctar
eafo
rm
ass
tran
sfer
and
toin
flu
ence
the
dro
pg
ener
atio
nb
yen
erg
yin
pu
tsu
chas
mix
-in
go
rp
uls
ing
.A
fter
the
resu
ltin
gd
rop
lets
hav
eb
een
con
tact
edw
ith
the
con
tin
uo
us
ph
ase
lon
gen
ou
gh
toal
low
the
extr
acta
ble
com
po
nen
t(s)
tom
igra
teto
the
dis
per
sed
ph
ase,
bo
thli
qu
ids
hav
eto
be
separ
ated
agai
n.
Den
siti
esw
ill
defi
ne
the
flow
dir
ecti
on
so
fth
ep
has
es:T
he
hea
vie
rli
qu
idfl
ow
sfr
om
top
tob
ott
om
,th
eli
gh
ter
on
efr
om
bo
tto
mto
top
.A
cco
rdin
gly
,th
efl
uid
sh
ave
tob
etr
ansp
ort
edto
the
app
arat
us
and
rem
oved
by
pu
mp
s.In
the
foll
ow
ing
chap
ter,
afe
wty
pic
ald
e-si
gn
sh
ave
bee
nse
lect
edfr
om
the
larg
en
um
ber
of
equ
ipm
ent
des
ign
sac
tual
lyu
sed
inin
du
stry
.A
mo
red
etai
led
trea
tmen
tca
nb
efo
un
din
lite
r-at
ure
,es
pec
iall
yin
[5]
and
[6].
3.1
.1.
Co
lum
ns
wit
ho
ut
En
erg
yIn
pu
t
Th
esi
mp
lest
extr
acto
ris
the
spra
yco
lum
n
(Fig
.15
A).
Th
esp
ray
colu
mn
ach
ieves
on
lyver
ysm
all
nu
mb
ers
of
sep
arat
ion
stag
esan
dis
rare
lyu
sed
now
aday
s.If
the
colu
mn
of
Fig
-u
re1
5A
isfi
lled
mai
nly
wit
hth
eh
eav
ier
liq
uid
,th
eli
gh
ter
liq
uid
bre
aks
atth
efe
edin
gp
oin
tin
tod
rop
sth
atri
sein
the
con
tin
uo
us
liq
uid
.D
rop
sre
ach
ing
the
inte
rfac
ear
ekep
tat
this
po
siti
on
by
con
tro
llin
gth
eb
ott
om
dis
char
ge
(LIC
).T
her
e,th
eyw
illt
hen
gra
du
ally
coal
esce
and
form
aco
n-
tin
uo
us
lay
erfl
oat
ing
on
top
of
the
con
tin
uo
us
liq
uid
.T
he
rever
sep
roce
du
reis
po
ssib
leas
wel
l,as
show
nin
Fig
ure
15
B.H
ere,
the
dis
trib
uto
ris
lo-
cate
dat
the
top
and
the
wat
erin
terf
ace,
call
edth
ep
rin
cip
lein
terf
ace,
isco
ntr
oll
edat
the
bo
t-to
mo
fth
eco
lum
nb
yfi
llin
git
mai
nly
wit
hth
eli
gh
ter
liq
uid
.In
this
case
,th
eh
eav
ier
liq
uid
isth
ed
isp
erse
do
ne,
bro
ken
into
dro
ple
tsd
esce
nd
-in
gin
the
lig
hte
rli
qu
id.
Th
ep
rin
cip
lein
terf
ace
can
be
adju
sted
atan
yh
eig
ht
(bet
wee
nto
pan
d
16
Liq
uid
–Liq
uid
Extr
action
Fig
ure
14.
Extr
acti
on
of
cap
rola
ctam
fro
ma
10
wt%
solu
tio
nin
tric
hlo
roet
hy
len
ew
ith
wat
eras
solv
ent
Fig
ure
15.
Colu
mns
wit
ho
ut
ener
gy
inp
ut
(LIC
=le
vel
ind
icat
ing
con
tro
ller
)A
)S
pra
yco
lum
n(l
igh
tp
has
ed
isp
erse
d);
B)
Pac
ked
colu
mn
(hea
vy
ph
ase
dis
per
sed
);C
)S
ieve
pla
teco
lum
n(l
igh
tp
has
edis
per
sed)
Liq
uid
–Liq
uid
Extr
action
17
bo
tto
m)
of
the
colu
mn
asn
eed
ed,th
us
the
hea
v-
ier
liq
uid
bei
ng
dis
per
sed
above
and
the
lig
hte
rli
qu
idb
elow
the
pri
nci
ple
inte
rfac
e.C
ou
nte
rcu
rren
tco
lum
ns
are
equ
ipp
edw
ith
sett
lin
gzo
nes
atth
eto
pan
dth
eb
ott
om
,w
ith
coal
esci
ng
aid
sp
rov
ided
ifn
eces
sary
.T
he
liq
-u
ids
sho
uld
nev
erb
efe
din
toth
eco
lum
nin
thes
ese
ttli
ng
zones
bec
ause
this
would
cause
hydro
-d
yn
amic
inst
abil
ity
of
the
colu
mn
thu
sre
du
c-in
gth
eo
per
atio
nal
per
form
ance
.T
he
dis
per
sed
liq
uid
oft
enca
nn
ot
be
sele
cted
fro
mth
eore
tica
lco
nsi
der
atio
ns,
bu
to
nly
by
aid
of
exp
erim
ents
ina
pil
otco
lum
nu
sin
gth
ere
alm
ater
ialsy
stem
.P
ack
edco
lum
ns
(str
uct
ure
dan
du
nst
ruc-
ture
d)
and
siev
ep
late
colu
mn
sh
ave
bee
nad
op
ted
fro
md
isti
llat
ion
tech
no
log
y(→
Dis
till
atio
nan
dR
ecti
fica
tio
n,
Ch
ap.
8.)
.In
pa
cked
colu
mn
sd
rop
form
atio
no
ccu
rso
nen
try
of
the
dis
per
sed
ph
ase
inth
ep
acked
bed
(Fig
.15
B).
Th
ed
rop
sri
seth
rou
gh
the
pac
ked
bed
wit
ho
utsi
gn
ifica
ntfu
rth
erd
isp
ersi
on
.How
-ev
er,
mas
str
ansf
erta
kes
pla
cem
ain
lyd
uri
ng
the
form
atio
no
fa
new
inte
rfac
ial
area
.T
his
exp
lain
sth
elo
wef
fici
ency
of
pac
ked
colu
mn
s[6
,C
hap
.8].
Ina
siev
ep
late
colu
mn
wit
hd
ow
nco
mer
s,as
show
nin
Fig
ure
15
C,t
he
lig
hte
rd
isp
erse
dp
has
eco
ales
ces
ben
eath
each
pla
teto
giv
ea
con
tin
uo
us
lay
er.I
tsbu
oy
ancy
pre
sses
the
liq
uid
thro
ug
hth
eh
ole
so
fth
esi
eve
pla
tes,
pro
du
cin
gje
tsw
hic
hd
isin
teg
rate
into
dro
ps.
Th
eco
nti
nu
ou
sli
qu
idfl
ow
sth
rou
gh
the
dow
nco
mer
sfr
om
stag
eto
stag
ean
dth
enac
ross
the
pla
tes.
Inth
eca
seo
flo
win
terf
acia
lte
nsi
on
the
lay
ers
of
coal
esce
dp
has
ear
eto
osm
all
for
asy
mm
etri
cal
op
erat
ion
of
the
pla
tes.
Th
enit
isad
van
tag
eou
sto
use
du
alfl
ow
pla
tes
wit
ho
ut
dow
nco
mer
s[5
7].
Sie
ve
pla
teco
lum
ns
hav
eth
ead
van
tag
eover
pac
ked
colu
mn
sth
atn
ewd
rop
sar
efo
rmed
atea
chtr
ay.
How
ever
,th
ed
rop
load
of
the
pla
teis
oft
enir
reg
ula
rly
dis
trib
ute
d,
esp
ecia
lly
ifth
eco
lum
nd
iam
eter
isla
rge
(mo
reth
an1
m).
Th
isis
the
reas
on
why
siev
epla
teco
lum
ns
can
reac
hef
-fi
cien
cies
of1
0–
15
%o
nly
inra
refa
vo
red
case
s.M
ore
over
,sin
ceco
lum
ns
are
gen
eral
lybu
iltw
ith
ap
late
spac
ing
of
0.3
m,e
ven
sim
ple
sep
arat
ion
sre
qu
ire
con
sid
erab
leover
all
hei
gh
ts.
Mas
str
ansf
erb
etw
een
the
two
liq
uid
sca
nb
esu
bst
anti
ally
imp
roved
by
app
lica
tio
no
fad
di-
tio
nal
mec
han
ical
ener
gy
info
rmo
fsu
per
im-
po
sed
agit
atio
no
rp
uls
atio
n,
resu
ltin
gin
hig
her
turb
ule
nce
nea
rth
ed
rop
san
den
larg
edm
ass
tran
sfer
area
du
eto
smal
ler
dro
psi
zes.
3.1
.2.
Pu
lsed
Co
lum
ns
Th
esi
mp
lest
des
ign
of
pu
lsed
colu
mn
isth
ep
uls
edsi
eve
pla
teco
lum
n(F
ig.1
6A
).A
pis
ton
pu
mp
wit
han
elec
tric
alo
ran
air-
pre
ssu
red
rive
cau
ses
the
enti
reli
qu
idco
nte
nt
of
the
colu
mn
tov
ibra
te.
Bo
thp
has
esar
eal
tern
atel
yfo
rced
thro
ugh
the
hole
sin
the
rhyth
mof
the
puls
a-ti
on
.T
he
dow
nco
mer
su
sed
inth
eco
nven
tio
nal
siev
ep
late
colu
mn
are
thu
ssu
per
flu
ou
s.T
he
dis
-p
erse
dp
has
ed
oes
no
tco
ales
ceab
ove
or
bel
ow
the
pla
tes
tog
ive
aco
nti
nu
ou
sla
yer
.T
he
pu
l-sa
tio
nsh
ock
flin
gs
the
dro
ps
off
the
pla
tefa
ster
than
wo
uld
be
po
ssib
leas
are
sult
ofo
nly
the
den
-si
tyd
iffe
ren
ce.T
his
lead
sto
afi
ne,
un
ifo
rmd
rop
dis
trib
uti
on
and
hen
ceen
larg
esth
em
ass
tran
s-fe
rar
ea.
Appli
cati
ons
are
lim
ited
by
the
physi
-ca
lp
rop
erti
eso
fth
esu
bst
ance
sco
nce
rned
and
hig
hth
rou
gh
pu
ts.
Sy
stem
sw
hic
hem
uls
ify
eas-
ily
can
no
tbe
pro
cess
edin
pu
lsed
colu
mn
sju
stas
stic
ky
and
gre
asy
liq
uid
s.F
orver
yla
rge
thro
ug
h-
pu
ts(c
olu
mn
dia
met
er>
0.6
m),
the
pu
lsed
vo
l-u
me
and
pu
lsin
gp
ow
erb
eco
me
ver
yh
igh
;h
ow
-ev
er,
pu
lsin
gu
nit
sfo
rla
rge
colu
mn
dia
met
ers
hav
eb
een
dev
elo
ped
.T
he
sep
arat
ion
effe
cto
fth
eco
lum
nd
e-cr
ease
sw
ith
incr
easi
ng
dia
met
er,
this
has
no
tyet
bee
nfu
lly
inves
tigat
ed.T
he
pla
tesp
acin
gis
50
–1
00
mm
.L
arg
erp
late
spac
ing
sfa
vo
rb
ack
-m
ixin
gan
dh
ence
red
uce
the
effi
cien
cyo
fth
eco
lum
n.
Sm
alle
rp
late
spac
ing
sle
adto
ast
ron
gd
ecre
ase
of
the
thro
ug
hp
ut.
Sie
ve
pla
tes
hav
ecy
lin
dri
cal
ho
les
and
atr
ian
gu
lar
pit
ch.
Th
ere
-la
tio
nsh
ipb
etw
een
the
frac
tio
nal
free
area
ϕ,t
he
ho
led
iam
eter
di
and
the
pit
chp
isg
iven
by
ϕ=
πd2 i/√
12p2
Fo
ru
sual
liq
uid
–li
qu
idsy
stem
ssi
eve
pla
tes
wit
hh
ole
dia
met
ers
fro
m2
to4
mm
resu
ltin
gin
free
area
so
f2
3to
40
%ar
ere
com
men
ded
[6,
Ch
ap.1
0],
the
low
erval
ue
of
23
%is
use
dfo
rh
igh
and
the
hig
her
val
ue
of
40
%fo
rlo
win
-te
rfac
ial
ten
sio
ns.
Fre
ear
eas
less
than
20
%ar
eu
sed
for
liq
uid
sw
ith
hig
her
vis
cosi
ties
[58
].T
he
pla
tem
ater
ial
has
ap
ron
ou
nce
din
flu
-en
ceo
nd
rop
form
atio
nan
dh
ence
on
the
sep
-ar
atio
nef
fici
ency
.T
he
pla
tem
ater
ial
and
ph
ase
sele
ctio
nm
ust
be
mat
ched
insu
cha
way
that
the
18
Liq
uid
–Liq
uid
Extr
action
Fig
ure
16.
Puls
edan
dre
cip
roca
tin
g-p
late
colu
mn
s(L
igh
tp
has
ed
isp
erse
d)
A)
Puls
edsi
eve-
pla
teco
lum
n;
B)
Rec
ipro
cati
ng
-pla
teco
lum
n(K
arr)
pla
tes
are
wet
ted
by
the
con
tin
uo
us
ph
ase
bu
tno
tb
yth
ed
isp
erse
dp
has
e,b
ecau
seth
isw
ou
ldle
adto
stro
ng
coal
esce
nce
effe
cts.
If,
for
exam
ple
,an
aqu
eou
sp
has
eis
tob
ed
isp
erse
din
tod
rop
s,m
etal
tray
sar
eu
nsu
itab
le,
bu
tp
last
icp
late
sar
esa
tisf
acto
ry.
Th
esh
arp
edg
edsi
de
of
the
siev
ep
late
,w
hic
his
du
eto
man
ufa
ctu
rin
g,sh
ou
ldex
-ac
tly
face
the
flow
dir
ecti
on
of
the
dis
per
sed
liq
-u
idso
that
dro
ps
wil
lsh
ear
atth
eed
ges
of
the
ho
les.
Gap
sb
etw
een
the
siev
ep
late
edg
ean
dth
eco
lum
nw
all
sho
uld
be
avo
ided
by
pre
cise
con
-st
ruct
ion
or
by
app
lyin
ged
ge-
seal
ing
elem
ents
mad
eo
fm
ater
ials
wh
ich
are
wet
ted
by
the
con
-ti
nu
ou
sli
qu
id.
Inm
ost
case
s,p
isto
np
um
ps
or
dia
ph
rag
mp
um
ps
are
use
das
the
pu
lsat
ors
.T
he
pu
lsin
gfr
equ
enci
esar
eb
etw
een
30
and
15
0m
in−
1,w
ith
pu
lsin
gam
pli
tud
esfr
om
5–
15
mm
(rel
ativ
eto
the
colu
mn
cro
ssse
ctio
n).
(Pu
lsin
gam
pli
tud
eis
defi
ned
asth
ed
ista
nce
bet
wee
nu
pp
eran
dlo
wer
cen
ter
of
the
pu
lsin
gm
oti
on
inth
eac
-ti
ve
par
to
fth
eco
lum
n.)
Th
ed
isp
erse
dp
has
eh
asto
be
fed
into
the
colu
mn
via
ad
istr
ibu
-to
r.T
he
mea
nd
rop
dia
met
ero
fth
ep
red
isp
erse
dsw
arm
sho
uld
be
larg
erth
anth
em
ean
dro
psi
zein
the
acti
ve
par
to
fth
eco
lum
n,
oth
erw
ise
the
hydro
dynam
ics
of
the
colu
mn
would
mai
nly
be
affe
cted
by
the
dis
trib
uto
r.T
he
ho
les
inth
ed
is-
trib
uto
rsh
ou
ldb
ever
ysh
arp
-ed
ged
toav
oid
ver
y
fin
ed
rop
s.E
ven
inp
acked
colu
mn
s,th
ese
pa-
rati
on
effe
ctca
nb
esu
bst
anti
ally
imp
roved
by
pu
lsin
go
fth
eco
nti
nu
ou
sp
has
e,at
the
exp
ense
of
are
du
ced
thro
ug
hp
ut.
Th
ein
crea
sed
per
for-
man
cere
sult
sfr
om
gre
ater
shea
rfo
rces
cau
s-in
ga
red
uct
ion
ind
rop
size
and
anin
crea
sein
inte
rfac
ial
area
[6,
Ch
ap.8
].A
sin
dis
till
atio
nco
lum
ns,
the
ph
eno
men
on
of
mal
dis
trib
uti
on
inra
nd
om
lyp
acked
colu
mn
so
fla
rger
dia
met
erca
nb
eover
com
eb
yu
seo
fst
ruct
ure
dp
ack
ing
s.T
hes
ep
ack
ing
sle
adto
ag
oo
dcr
oss
-sec
tio
nal
mix
ing
and
hav
ea
hig
her
cap
acit
y,ty
pic
ally
ato
tal
flow
rate
of
bo
thp
has
eso
fap
pro
xim
atel
y1
00
m3m−
2h−
1co
mp
ared
to3
0m
3m−
2h−
1fo
ra
ran
do
mly
pac
ked
colu
mn
.Str
uct
ure
dp
ack
ing
sar
ep
arti
cula
rly
suit
able
for
low
inte
rfac
ial
ten
-si
on
syst
ems
or
for
smal
ld
ensi
tyd
iffe
ren
ces;
sep
arat
ion
effi
cien
cyis
nea
rly
ind
epen
den
to
fsc
ale-
up
.Hy
dro
dy
nam
ics
and
mas
str
ansf
erp
er-
form
ance
are
wel
linves
tigat
ed[6
,Chap
.8],
[59].
Pu
lsin
gU
nit
s.T
he
use
of
pu
lsed
colu
mn
sis
curr
entl
yli
mit
edto
smal
lan
dm
ediu
mth
rou
gh
-p
uts
.Th
eco
lum
nd
iam
eter
isli
mit
edb
yth
ep
uls
-in
gu
nit
.F
or
ver
yla
rge
thro
ug
hp
uts
,th
ep
uls
edvo
lum
eb
eco
mes
sola
rge
that
the
use
of
ap
isto
np
um
pas
the
pu
lsin
gu
nit
cau
ses
dif
ficu
ltie
s.C
on
-se
qu
entl
y,p
uls
ing
un
its
hav
eb
een
dev
elo
ped
wh
ich
op
erat
ew
ith
ou
ta
pis
ton
pu
mp
.T
he
pu
l-sa
tor
dev
elo
ped
by
Mis
ek
(Fig
.17
)is
bas
edo
n
Liq
uid
–Liq
uid
Extr
action
19
ace
ntr
ifugal
pum
p.
The
pum
p(e
)is
connec
ted
on
bo
thth
esu
ctio
nsi
de
and
the
del
iver
ysi
de
top
ress
ure
ves
sels
wh
ich
are
alte
rnat
ely
con
nec
ted
toth
eco
lum
nb
ym
ean
so
fa
rota
tin
gval
ve
(c).
Wit
hth
eval
ve
sett
ing
show
nin
Fig
ure
17
A,
the
pu
mp
del
iver
sth
eli
qu
idin
toth
eco
lum
nv
iath
ed
isch
arg
ed
rum
(b),
tak
ing
the
rate
del
iver
edfr
om
the
suct
ion
dru
m(a
).A
fter
chan
geo
ver
of
the
val
ve
(Fig
.17
B),
the
pu
mp
del
iver
sfr
om
the
colu
mn
via
ves
sel
(a)
into
dru
m(b
).T
he
pu
mp
thu
sal
way
sd
eliv
ers
con
tin
uo
usl
yin
on
ed
irec
-ti
on
.Rev
ersa
lofth
ed
irec
tio
no
ffl
ow
inth
ep
uls
eli
ne
isef
fect
edb
yth
ech
ang
e-over
val
ve
(c)
inac
cord
ance
wit
hth
ep
uls
efr
equ
ency
.A
pu
lsat
or
bas
edo
nth
isp
rin
cip
leh
asb
een
dev
elo
ped
by
Bro
nsw
erk
/DS
M(F
ig.1
7C
),an
dis
now
ino
p-
erat
ion
for
colu
mn
sw
ith
am
axim
um
dia
met
ero
f2
.7m
.F
or
larg
epuls
edvolu
mes
,th
ehydra
uli
cpul-
sato
rfr
om
Wep
uko
[60
]is
also
suit
able
(Fig
.18
).It
isfl
ang
edd
irec
tly
toth
elo
wer
bo
tto
mo
fth
eco
lum
nen
dan
dac
tsin
the
dir
ecti
on
of
the
col-
um
nax
is.T
he
pu
lsin
gp
isto
nis
con
nec
ted
via
aco
mm
on
pis
ton
rod
toa
work
ing
pis
ton,th
ehy-
dra
uli
cd
rive
of
the
pis
ton
isa
rap
idly
rever
sib
lera
dia
lp
isto
np
um
p.
Rec
ipro
cati
ng
-Pla
teC
olu
mn
s.In
ano
ther
app
roac
hfo
rso
lvin
gth
ep
rob
lem
of
larg
eth
rou
gh
pu
ts,
the
pla
tes,
and
no
tth
eli
qu
id,
are
mad
eto
reci
pro
cate
,so
that
the
pu
lsin
gp
um
pis
elim
inat
ed.
Th
isp
rin
cip
lele
dto
the
dev
elo
p-
men
to
fth
ere
cip
roca
tin
g-p
late
colu
mn
wh
ich
can
be
regar
ded
asth
eco
nver
seof
the
puls
edsi
eve
pla
teco
lum
n.I
nth
ep
uls
edsi
eve
pla
teco
l-u
mn
,th
etr
ays
are
fixed
and
the
enti
reli
qu
idco
nte
nt
of
the
colu
mn
isca
use
dto
vib
rate
;in
the
reci
pro
cati
ng
-pla
teco
lum
n,
the
pla
tes
are
moved
.In
bo
thca
ses,
the
liq
uid
un
der
go
esan
osc
illa
tin
gm
oti
on
rela
tive
toth
ep
late
.In
the
Ka
rrco
lum
n(F
ig.1
6B
),si
eve
pla
tes
wit
ha
free
area
of
abo
ut
60
%,
a1
0–
15
mm
ho
led
iam
eter
,an
da
25
–5
0m
mp
late
spac
ing
,ar
em
ou
nte
do
na
cen
tral
shaf
t.T
he
com
ple
tep
ack
ism
oved
up
and
dow
n,
dri
ven
by
anec
-ce
nte
r.
Fig
ure
17.
Puls
ator
wit
hro
tati
ng
val
ve
A)P
rinci
ple
dia
gra
mofco
mpre
ssio
nst
roke;
B)P
rinci
ple
di-
agra
mof
suct
ion
stro
ke;
C)
Tec
hnic
aldes
ign
(Bro
nsw
erk)
a)S
uct
ion
dru
m;
b)
Dis
char
ge
dru
m;
c)R
ota
ting
val
ve;
d)
Colu
mn;
e)C
entr
ifugal
pum
p
Th
ere
lati
vel
yla
rge
free
area
of
reci
pro
cat-
ing
pla
teco
lum
ns
allo
ws
mu
chg
reat
erth
rou
gh
-p
uts
than
conven
tio
nal
pu
lsed
colu
mn
s.H
ow
-ev
er,
rece
nt
inves
tigat
ions
show
edth
atpuls
edsi
eve
pla
teco
lum
ns
can
be
equ
ipp
edw
ith
larg
erfr
eear
eas,
too
.B
oth
typ
eso
fp
uls
edco
lum
ns
show
ver
ysi
mil
arp
erfo
rman
ces
and
op
erat
ion
alb
ehav
ior
ifth
eyar
eeq
uip
ped
wit
hth
esa
me
free
area
s[6
1].
Res
earc
ho
nth
ees
tab
lish
edty
pes
of
pu
lsed
colu
mn
sh
asb
een
ver
yin
ten
sive
sin
ceth
e1
97
0s.
20
Liq
uid
–Liq
uid
Extr
action
Fig
ure
18.
Hydra
uli
cp
uls
ato
ra)
Puls
ing
pis
ton;
b)
Wo
rkin
gp
isto
n;
c)R
insi
ng
;d
)H
y-
dra
uli
cag
gre
gat
ew
ith
radia
lpis
ton
pum
p
Fig
ure
19.
Rota
ting
dis
kco
nta
cto
r(R
DC
)a)
Rota
ting
dis
k;
b)
Sta
tor
rin
g
3.1
.3.
Co
lum
ns
wit
hR
ota
tin
gIn
tern
als
Ro
tati
ng
Dis
kC
on
tact
or
(RD
C).
Inth
eR
DC
(Fig
.19
A),
stat
or
rin
gs
are
mo
un
ted
atcl
ose
inte
rval
s.D
isk
sar
efi
tted
bet
wee
nth
eri
ng
sto
aro
tati
ng
shaf
t.T
he
rota
tin
gd
isk
sfl
ing
the
dro
ps
of
the
dis
per
sed
phas
eoff
centr
ifugal
ly,
on
toth
est
ato
rri
ng
sw
her
eth
eyar
eb
raked
and
defl
ecte
d.T
he
dro
pd
istr
ibu
tio
nis
exce
llen
tan
dca
nre
ach
the
emu
lsifi
cati
on
lim
itas
the
rota
-ti
on
alsp
eed
incr
ease
s.T
he
RD
Ch
asa
rela
tivel
ysi
mp
leco
nst
ruct
ion
wit
ha
larg
efr
eecr
oss
-sec
tio
nal
area
.On
the
on
eh
and
,it
reac
hes
larg
eth
rou
gh
pu
ts,
on
the
oth
erh
and
itfa
vo
rsb
ack
mix
ing
of
ph
ases
cau
sin
ga
dec
reas
eo
fef
fici
ency
.Ala
rge
ran
ge
of
thro
ug
h-
pu
tsis
po
ssib
lew
ith
ou
tre
mar
kab
led
ecre
ase
of
effi
cien
cy.
Th
elo
adin
gli
mit
isg
ener
ally
low
erth
anin
pu
lsed
colu
mn
s.T
he
RD
Cis
un
suit
able
for
mix
ture
sw
hic
hte
nd
tofo
rmem
uls
ion
san
dfo
rp
rod
uct
sco
nta
inin
gd
irt.
Th
ese
par
atio
nef
-fi
cien
cyd
ecre
ases
shar
ply
wit
hin
crea
sin
gd
i-am
eter
.N
ever
thel
ess,
succ
essf
ul
RD
Cs
of
up
to3
50
0m
min
dia
met
erh
ave
bee
nco
nst
ruct
ed.
Th
eyar
eth
us
suit
able
for
gre
ater
thro
ug
hp
uts
than
pu
lsed
colu
mn
san
dar
ep
refe
rab
lyu
sed
too
per
ate
wit
hla
rge
pro
du
ctfl
ow
sw
hen
the
de-
man
ds
on
sep
arat
ion
per
form
ance
are
on
lylo
was
for
inst
ance
inth
eo
ilin
du
stry
or
inw
aste
wa-
ter
trea
tmen
t[4
2].
As
inp
uls
edco
lum
ns,
the
wet
tin
gb
ehav
ior
also
infl
uen
ces
dro
pfo
rmat
ion
inth
eR
DC
,an
dsh
ou
ldth
eref
ore
be
taken
into
acco
un
tw
hen
se-
lect
ing
am
ater
ial
for
the
colu
mn
inte
rnal
s.
Ku
hn
iE
xtr
act
or.
Th
eK
uh
ni
extr
acto
r(F
ig.2
0A
)u
ses
atu
rbin
eas
the
mix
ing
ele-
men
t.P
erfo
rate
dp
arti
tio
nd
isk
sse
par
ate
the
extr
acti
on
stag
esan
dre
du
ceb
ack
mix
ing
.T
his
app
arat
us
isal
sou
sed
for
per
form
ing
reac
tio
ns
bet
wee
ntw
oli
qu
idp
has
es;
the
resi
-d
ence
tim
eca
nb
ead
just
edv
iath
efr
eear
eao
fth
ep
erfo
rate
dd
isk
.
QV
F-E
xtr
act
or.
Th
eQ
VF
extr
acto
rR
ZE
(Fig
.20
B)u
ses
bla
de
stir
reras
mix
ing
elem
ents
.T
he
par
titi
on
dis
ks
hav
em
ean
der
-fo
rmed
met
alst
rip
esat
the
inn
erci
rcu
mfe
ren
ceto
red
uce
the
ph
ase
dis
per
sio
nb
ych
ann
elin
go
fb
oth
ph
ases
.T
he
op
erat
ion
alb
ehav
ior
issi
mil
arto
that
of
the
Ku
hn
iex
trac
tor
(see
Fig
.20
A).
Liq
uid
–Liq
uid
Extr
action
21
Fig
ure
20.
Colu
mns
wit
hro
tati
ng
inte
rnal
sA
)K
uhni
extr
acto
r;B
)Q
VF
extr
acto
r
Gra
esse
rC
on
tact
or.
Th
eG
raes
ser
con
tac-
tor
(Fig
.21
)is
ano
ther
typ
eo
fro
tati
ng
equ
ip-
men
t.H
ere,
no
to
nly
the
inte
rnal
sbu
tth
een
tire
app
arat
us
rota
te.In
tern
alh
alf-
tub
esar
efi
tted
assc
oo
pin
gel
emen
tsin
ah
ori
zon
talro
tati
ng
cyli
n-
der
.D
ue
toth
ero
tati
on
,th
eh
alf-
tub
estr
ansp
ort
par
to
fth
eh
eav
yp
has
ein
toth
eover
lyin
gli
gh
tp
has
e,an
dv
ice
ver
sa.
To
red
uce
bac
km
ixin
g,
the
extr
acto
rle
ng
this
div
ided
into
cham
ber
sb
yp
arti
tio
nd
isk
s.B
ecau
seo
fit
slo
wd
isp
ersi
ng
ef-
fect
,th
iseq
uip
men
tis
par
ticu
larl
ysu
itab
lefo
rsy
stem
sw
hic
hte
nd
toem
uls
ify.
Th
eth
rou
gh
pu
tis
low
com
par
edw
ith
oth
erex
trac
tors
.
Fig
ure
21.
Gra
esse
rco
nta
ctor
3.1
.4.
Mix
er–
Set
tler
s
Mix
er–
sett
lers
con
sist
of
sin
gle
or
sever
alst
ages
inse
ries
(Fig
.22
A),
each
stag
eco
nsi
st-
ing
of
ast
irre
dves
sel
and
ase
ttli
ng
ves
sel
(Fig
.22
B).
Var
iou
sar
ran
gem
ents
are
po
ssib
lesu
chas
cocu
rren
t,co
un
terc
urr
ent,
or
cro
ssw
ise
flow
of
ph
ases
.Th
em
ixer
–se
ttle
ris
the
on
lyex
-tr
acto
rth
atre
ach
esst
age
effi
cien
cies
of
nea
rly
10
0%
and
isal
mo
stin
sen
siti
ve
for
load
flu
ctu
-at
ion
s.T
his
extr
acto
rh
asth
ead
van
tag
eth
atb
ack
-m
ixin
gca
nb
eco
mp
lete
lyp
recl
ud
edd
ue
toth
eco
mp
lete
ph
ase
sep
arat
ion
inea
chst
age.
As
are
-su
lt,
ther
ear
en
otr
ansf
erp
rob
lem
sin
scal
e-u
p.
Th
efa
vo
rab
leef
fici
ency
isal
mo
stco
mp
lete
lyre
-ta
ined
even
for
larg
eth
rou
gh
pu
ts.
Any
nu
mb
ero
fse
par
atio
nst
ages
can
be
bu
ilt,
and
,m
ore
over
,th
rou
gh
pu
td
oes
no
tap
pea
rto
be
lim
ited
.T
hes
ead
van
tag
esac
cou
nt
for
the
wid
esp
read
use
of
mix
er–
sett
lers
inin
du
stri
alp
roce
sses
for
man
yd
ecad
es.
How
ever
,ea
rly
mix
er–
sett
ler
equ
ip-
men
tw
asver
yco
mp
lex
.E
ach
sep
arat
ion
stag
eco
nsi
sted
of
ast
irre
dves
selan
da
sett
lin
gves
sel.
Th
etw
op
has
esh
adto
be
pu
mp
edb
etw
een
the
ind
ivid
ual
stag
es.
Eac
hse
ttle
rn
eed
edan
inte
r-fa
cele
vel
con
tro
l.T
he
ho
rizo
nta
lar
ran
gem
ent
resu
lted
ina
larg
ear
eare
qu
irem
ent.
Inan
effo
rtto
over
com
eth
ese
dis
advan
tag
eso
fth
em
ixer
–se
ttle
rb
atte
ries
wit
ho
utfo
reg
oin
gan
yo
fth
eirad
van
tag
es,a
nu
mb
ero
fd
iffe
ren
tde-
sig
ns
wer
ed
evel
op
ed.
Mix
er–
sett
lers
are
use
d
22
Liq
uid
–Liq
uid
Extr
action
Fig
ure
22.
Pri
nci
ple
of
am
ixer
–se
ttle
rA
)F
low
Shee
t;B
)A
rran
gem
ent
intw
od
iffe
ren
tar
eas.
Ind
ust
rial
-sca
leeq
uip
-m
ent
isu
sed
too
bta
inex
trem
ely
hig
hth
rou
gh
-p
uts
wh
ena
smal
ln
um
ber
of
stag
esis
nee
ded
,e.
g.,
inth
eex
trac
tio
no
fm
etal
salt
s.L
abo
rato
ry-
scal
ed
evic
esar
eem
plo
yed
inp
roce
ssd
evel
op
-m
ent
toch
eck
the
nu
mb
ero
fca
lcu
late
dst
ages
asa
fun
ctio
no
fth
era
tio
solv
ent.
Lar
ge-
scal
em
ixer
–se
ttle
rsw
ere
ori
gin
ally
dev
elo
ped
toex
trac
tco
pp
erfr
om
dil
ute
aqu
e-o
us
solu
tio
ns.
Th
eb
asic
des
ign
isa
bo
x-ty
pe
mix
er–
sett
ler
acco
rdin
gto
Den
ver
(Fig
.23
).T
he
mix
ing
and
sep
arat
ing
zon
esar
eco
mb
ined
ina
sin
gle
un
itan
dar
ese
par
ated
by
anover
-fl
ow
wei
rfo
rth
eli
gh
tp
has
ean
dan
un
der
flow
slit
for
the
hea
vy
ph
ase.
Th
ein
div
idu
alst
ages
are
arra
ng
edso
that
the
ou
tlet
of
the
sett
ler
also
acts
asth
ein
let
of
the
mix
er.
Th
eag
itat
or
has
two
fun
ctio
ns,
itd
isp
erse
san
dco
nvey
sth
eli
q-
uid
ph
ases
.T
hes
efu
nct
ion
sm
ayco
nfl
ict
wit
ho
ne
ano
ther
.T
he
rate
of
rota
tio
nn
eces
sary
toover
com
eth
eco
nvey
ing
hei
gh
tm
ayb
eto
oh
igh
wh
enu
nst
able
syst
ems
mu
stb
ed
isp
erse
d,ca
us-
ing
pro
ble
ms
inp
has
ese
par
atio
n,
e.g
.,a
hig
hd
egre
eo
fen
trai
nm
ent.
Mix
ing
pu
mp
sw
ith
low
shea
rin
gfo
rces
,an
dth
us
alo
wm
ixin
gin
ten
sity
,h
ave
bee
nd
evel
op
edto
avo
idth
ese
dif
ficu
ltie
s.E
xam
ple
sar
eth
eP
um
pm
ixim
pel
ler
use
dw
ith
the
Da
vyM
cKee
mix
er–
sett
ler
(Fig
.24
A)
and
the
IMI
turb
ine
pu
mp
-mix
un
it(F
ig.2
4B
).
Fig
ure
23.
Bo
x-t
yp
em
ixer
–se
ttle
r(D
enver
)A
)S
ide
vie
w;
B)
Gro
un
dp
lain
Afu
rth
erd
evel
op
men
to
fth
eD
avy
McK
eem
ixer
–se
ttle
rh
asb
een
des
crib
ed[4
3].
Eac
hst
age
con
sist
sso
lely
of
aves
selin
wh
ich
mix
ing
and
sep
arat
ion
occ
ur.
Th
ep
rod
uct
inle
tan
dth
eag
itat
or
are
loca
ted
inth
em
idd
lean
dcr
eate
ad
isp
ersi
on
zon
e.T
he
lig
htp
has
ese
par
ates
ou
tat
the
top
and
the
hea
vy
ph
ase
atth
eb
ott
om
.In
the
Lu
rgi
tow
erex
tra
cto
r,th
eb
atte
ryo
fad
jace
nt
sett
lers
isre
pla
ced
by
asp
ace-
sav
ing
Liq
uid
–Liq
uid
Extr
action
23
Fig
ure
24.
Indust
rial
mix
er–
sett
lers
A)
Dav
yM
cKee
mix
er–
sett
ler;
B)
IMI
turb
ine
pum
p-m
ixunit
(cro
ssse
ctio
nA
–B
–C
–D
show
nin
the
low
erpar
t);C
)L
urg
ito
wer
extr
acto
r
tow
erd
esig
nin
wh
ich
the
sett
lers
are
arra
ng
edon
top
of
each
oth
er.E
xte
rnal
centr
ifugal
pum
ps
are
use
dfo
rm
ixin
g(F
ig.2
4C
).L
ike
all
mix
er–
sett
lers
,th
isd
evic
eis
suit
able
for
ver
yla
rge
thro
ug
hp
uts
pro
vid
edth
atth
eli
qu
idsy
stem
can
wit
hst
and
the
hig
hen
erg
yin
pu
to
fth
em
ixin
gp
um
p.
Bac
km
ixin
gto
ace
rtai
nd
egre
eis
un
-av
oid
able
since
the
stag
eshav
ehydro
dynam
icco
nn
ecti
on
s.M
ult
ista
ge
mix
er–
sett
lers
are
aval
uab
leai
din
pro
cess
dev
elo
pm
ent
on
ala
bo
rato
rysc
ale.
Th
eyca
nb
ein
teg
rate
din
“min
ip
lan
ts”;
atth
isst
age
of
dev
elo
pm
ent
no
dec
isio
nsh
ou
ldb
em
ade
wh
ich
typ
eo
feq
uip
men
tis
suit
able
for
the
larg
e-sc
ale
pla
nt.
Sev
eral
exam
ple
so
fla
b-
ora
tory
mix
er–
sett
lers
are
show
nin
Fig
ure
25
.
3.1
.5.
Cen
trif
ug
al
Ex
tra
cto
rs
Cen
trif
ugal
extr
acto
rsar
euse
dw
hen
the
den
sity
dif
fere
nce
bet
wee
nth
etw
op
has
esis
insu
ffici
ent
top
rod
uce
aco
un
terc
urr
ent
un
der
gra
vit
y.T
he
bes
tk
now
no
fth
ese
dev
ices
isth
eP
od
bie
lnia
k
cen
trif
ug
ale
xtra
cto
r(F
ig.2
6A
),in
wh
ich
cyli
n-
dri
cal
per
fora
ted
shee
tsar
eco
nce
ntr
ical
lyar
-
ran
ged
asa
com
pac
tro
tor
on
ah
igh
-sp
eed
shaf
t.T
he
hea
vy
ph
ase
isfe
din
via
the
shaf
tan
dm
oves
outw
ards
due
toth
ece
ntr
ifugal
forc
e.T
he
light
ph
ase
moves
inth
eo
pp
osi
ted
irec
tio
n.
Sim
ilar
toco
lum
ns,
eith
erth
eli
gh
tp
has
eo
rth
eh
eav
yp
has
eca
nb
ed
isp
erse
din
tod
rop
s,as
des
ired
.If
the
lig
htp
has
eis
tob
ed
isp
erse
d,th
em
ain
inte
r-fa
cem
ust
be
loca
ted
nea
rth
esh
aft.
Dep
end
ing
on
the
syst
emth
en
um
ber
of
stag
esw
hic
hca
nb
eco
mb
ined
ino
ne
un
itis
lim
ited
to3
to4
the-
ore
tica
lst
ages
.T
he
Ro
ba
telce
ntr
ifu
ga
lex
tra
cto
ris
bas
edo
na
tota
lly
dif
fere
nt
pri
nci
ple
and
allo
ws
gre
ater
nu
mb
ers
of
stag
es(F
ig.2
6B
).D
isk
sse
rvin
gas
the
mix
ing
elem
enta
rece
nte
red
on
aver
tica
lsta
-to
r.T
he
ho
usi
ng
isd
ivid
edb
yan
nu
lar
dis
ks
into
an
um
ber
of
stag
esan
dro
tate
sar
ou
nd
the
cen
tral
shaf
t.E
ach
stag
eco
nsi
sts
of
am
ixin
gch
amb
eran
da
sett
lin
gch
amb
er.
Th
ed
isk
sea
chd
ipin
toth
em
ixin
gch
amb
er.A
nex
ten
sive
rev
iew
on
op
-er
atio
nan
dca
lcula
tion
of
centr
ifugal
extr
acto
rsis
giv
enin
[6,
Ch
ap.1
4].
Cen
trif
ug
esar
em
ore
com
ple
xth
anco
lum
ns,
thei
rin
ves
tmen
tan
dm
ain
ten
ance
cost
sar
eco
r-re
spo
nd
ing
lyh
igh
.T
hey
can
ther
efo
reo
nly
stan
dco
mp
aris
on
wit
hco
lum
ns
inca
ses
wh
ere
24
Liq
uid
–Liq
uid
Extr
action
Fig
ure
25.
Lab
ora
tory
mix
er–
sett
lers
A)
Norm
agm
ixer
–se
ttle
r;B
)S
cho
tt/Q
VF
mix
er–
sett
ler
they
hav
ead
van
tag
esw
hic
hn
oco
lum
nca
np
rov
ide.
Ph
ase
sep
arat
ion
isp
oss
ible
even
insy
stem
sh
avin
ga
den
sity
dif
fere
nce
aslo
was
15
kg
/m3.S
yst
ems
wit
hla
rge
dif
fere
nce
sin
vis
-co
sity
can
be
pro
cess
ed,
sin
ceth
eh
igh
shea
rfo
rces
effe
ctin
ten
sive
mix
ing
.A
sa
resu
lto
fit
sco
mp
actd
esig
n,t
he
cen
trif
u-
gal
extr
acto
ris
asp
ace-
savin
gap
par
atus
wit
han
extr
emel
ysm
all
op
erat
ing
vo
lum
ean
da
sho
rtre
sid
ence
tim
e.T
hes
ead
van
tag
esca
nb
ed
esir
-ab
leif
exp
ensi
ve
solv
ents
or
sub
stan
ces
of
lim
-it
edst
abil
ity
are
use
d.T
he
stea
dy
stat
eis
reac
hed
soo
naf
ter
star
tin
g.
Th
isex
trac
tor
isth
eref
ore
suit
able
for
bat
chw
ise
op
erat
ion
and
freq
uen
tch
ang
eso
fp
rod
uct
s.E
xtr
acti
on
un
der
pre
ssu
res
of
up
to5
MP
ais
po
ssib
le.
3.2
.F
luid
-Dy
na
mic
Fu
nd
am
enta
ls
Aco
mp
reh
ensi
ve
trea
tmen
to
ffl
uid
-dy
nam
icfu
nd
amen
tals
isg
iven
else
wh
ere
(→F
luid
Me-
chan
ics)
.
3.2
.1.
Pro
ble
ms
an
dP
roce
ssS
tra
teg
y
InS
ecti
on
2.5
,it
was
show
nh
ow
the
nu
mb
ero
fth
eore
tica
lst
ages
and
the
flow
dia
gra
mo
fth
eu
nit
op
erat
ion
“ex
trac
tio
n”
are
calc
ula
ted
on
the
bas
iso
feq
uil
ibri
a.T
he
sele
ctio
nan
dd
esig
no
f
app
arat
us
are
bas
edo
nfl
uid
dy
nam
ics
and
are
no
tca
rrie
do
ut
un
til
the
ther
mo
dy
nam
icd
esig
nis
com
ple
ted
.Atp
rese
nt,
mo
del
exp
erim
ents
are
stil
ln
eces
sary
for
the
des
ign
of
extr
acti
on
app
a-ra
tus.
Fo
rth
isre
aso
n,
ak
now
led
ge
of
the
op
-er
atin
gch
arac
teri
stic
so
fth
evar
iou
sty
pes
of
app
arat
us
iso
fg
reat
inte
rest
soth
atth
en
um
-b
ero
fex
per
imen
tsca
nb
esu
bst
anti
ally
red
uce
d,
and
pre
sele
ctio
nan
dp
reli
min
ary
sizi
ng
can
be
carr
ied
ou
tat
are
lati
vel
yea
rly
stag
eo
fp
roce
ssd
evel
op
men
t.T
he
flu
id-d
yn
amic
des
ign
of
anap
par
atu
sis
div
ided
into
the
foll
ow
ing
area
s:
1)
Sel
ecti
on
of
suit
able
inte
rnal
sw
ith
resp
ectt
om
ater
ial
of
con
stru
ctio
n,
shap
e,an
dsi
ze.
2)
Det
erm
inat
ion
of
the
op
erat
ing
con
dit
ion
sw
ith
resp
ect
top
has
ese
lect
ion
,p
uls
ing
,an
dlo
adin
g.
3)
Siz
ing
of
the
colu
mn
dia
met
erin
acco
rdan
cew
ith
the
req
uir
edth
rou
gh
pu
tso
ffe
edan
dso
lven
t.4
)S
izin
go
fth
eco
lum
nh
eig
ht
inac
cord
ance
wit
hth
eac
tual
sep
arat
ion
pro
ble
m.
How
ever
,th
ese
fou
rp
rob
lem
sca
nn
otb
eco
n-
sid
ered
inis
ola
tio
n.T
hu
s,b
oth
the
inte
rnal
san
dth
eo
per
atin
gco
nd
itio
ns
affe
ct(1
)th
elo
adin
gli
mit
and
hen
ceth
eco
lum
nd
iam
eter
and
(2)
the
sep
arat
ion
effi
cien
cyan
dth
us
the
colu
mn
hei
gh
t.M
easu
res
for
incr
easi
ng
the
load
ing
lim
ith
ave
Liq
uid
–Liq
uid
Extr
action
25
anad
ver
seef
fect
on
the
sep
arat
ion
effi
cien
cy,
and
vic
ever
sa.
Fig
ure
26.
Cen
trif
ugal
extr
acto
rsA
)P
odbie
lnia
kex
trac
tor;
B)
Robat
elfo
ur-
stag
eco
unte
rcur-
rent
extr
acto
r
Th
esi
zin
go
fth
eco
lum
nd
iam
eter
dep
end
so
nth
efl
oo
din
gp
oin
t,i.
e.,
the
max
imu
mlo
ad-
ing
lim
itat
wh
ich
aco
lum
nca
nb
eo
per
ated
.O
nfl
oo
din
g,
accu
mu
lati
on
of
the
dis
per
sed
ph
ase
occ
urs
atin
div
idu
alp
oin
tsw
ith
inth
eco
lum
nan
db
lock
sco
un
terc
urr
ent
flow
.C
on
seq
uen
tly,
the
lig
ht
ph
ase
app
ears
inth
ed
isch
arg
eo
fth
eh
eav
yp
has
e,an
dv
ice
ver
sa.
Th
isp
hen
om
eno
nis
det
ecta
ble
by
ho
ldu
pm
easu
rem
ents
.On
flo
od
-in
g,th
eh
old
up
incr
ease
sco
nti
nu
ou
sly
and
ind
i-ca
tes
anu
nst
able
op
erat
ing
stat
e.
Th
efl
oo
din
gli
mit
dep
end
so
nth
ed
rop
size
.S
mal
ld
rop
sri
sele
ssra
pid
lyth
anla
rge
dro
ps
and
ther
efo
reca
use
ag
reat
erh
old
up
.T
he
mo
reen
erg
yis
sup
pli
edto
the
syst
em–
eith
erb
yp
uls
-in
go
rb
yro
tati
ng
inte
rnal
s–
the
smal
ler
are
the
dro
ps,
soth
atth
efl
oo
din
gli
mit
dec
reas
es.
Inte
rna
lsal
soef
fect
dis
per
sin
g.
Th
esm
alle
rth
eir
op
enar
ea,
the
mo
reth
efl
oo
din
gli
mit
de-
crea
ses.
Th
esi
zin
go
fth
eco
lum
nh
eig
hti
sd
eter
min
edb
yth
em
ass
tran
sfer
,w
hic
his
des
crib
edb
yth
ew
ell-
kn
ow
nm
ass-
tran
sfer
equ
atio
n:
the
rate
of
mas
str
ansf
erre
dis
equ
alto
the
pro
du
cto
fth
em
ass-
tran
sfer
coef
fici
ent,
the
mas
s-tr
ansf
erar
eaan
dth
eco
nce
ntr
atio
nd
iffe
ren
ceb
etw
een
the
two
ph
ases
.A
gre
atp
rog
ress
insc
ien
tifi
cre
-se
arch
has
bee
nac
hie
ved
asre
gar
ds
mea
sure
-m
ent
and
calc
ula
tio
no
fth
eq
uan
titi
eso
fin
flu
-en
ceo
nm
ass
tran
sfer
(see
for
inst
ance
[6],
[45
–4
9],
[51
],[6
2–
65
],[6
8].
Bu
tin
pra
ctic
e,th
evar
-io
us
infl
uen
ces
on
mas
str
ansf
erar
eb
est
sum
-m
ariz
edin
the
exp
ress
ion
“h
eig
ht
equ
ival
ent
of
ath
eore
tica
lst
age”
(HE
TS
),as
am
easu
refo
rth
ese
par
atio
nef
fici
ency
of
the
colu
mn
,as
men
-ti
on
edin
Sec
tio
n2
.5.
Mea
sure
men
tsin
pil
ot-
pla
ntco
lum
ns
wil
lb
eu
sed
bel
ow
tod
emo
nst
rate
the
way
inw
hic
hvar
-io
us
par
amet
ers
affe
ctth
elo
adin
gli
mit
and
sep
a-ra
tio
nef
fici
ency
.Th
ete
stsy
stem
sre
com
men
ded
by
the
Eu
rop
ean
Fed
erat
ion
of
Ch
emic
alE
ng
i-n
eeri
ng
(EF
CE
)ar
eu
sed
for
this
dem
on
stra
tio
n[4
4].
3.2
.2.
Op
era
tin
gC
ha
ract
eris
tics
of
Pu
lsed
Co
lum
ns
an
dC
olu
mn
sw
ith
Ro
tati
ng
Inte
rna
ls
Lo
ad
ing
Lim
it.
Fig
ure
27
show
sth
elo
ad-
ing
lim
itvC
+v D
asa
fun
ctio
no
fth
ep
uls
ing
freq
uen
cyfo
rp
late
so
fsm
all
free
area
ϕfo
rth
eto
luen
e–
wat
ersy
stem
,i.
e.,
for
hig
hin
ter-
faci
alte
nsi
on
.v c
and
vd
are
the
vo
lum
efl
ow
so
fco
nti
nu
ou
s(c
)an
dd
isp
erse
d(d
)p
has
ere
late
dto
the
tota
lcr
oss
-sec
tio
nal
area
of
the
colu
mn
,th
eso
-cal
led
sup
erfi
cial
vel
oci
ties
.T
his
flo
od
-in
gp
oin
tcu
rve
star
tsat
the
ori
gin
of
the
co-
ord
inat
es;
ino
ther
wo
rds,
wit
ho
ut
pu
lsin
g,
no
thro
ug
hp
utis
po
ssib
le.W
ith
incr
easi
ng
pu
lsin
g,
the
thro
ug
hp
utal
sori
ses
up
toa
max
imu
m.T
his
par
to
fth
ecu
rve
isca
lled
the
low
erfl
oo
din
gli
mit
;h
ere,
pu
lsin
gh
asm
ain
lya
tran
spo
rtfu
nc-
26
Liq
uid
–Liq
uid
Extr
action
tio
n.
Wit
hin
crea
sin
gfr
equ
ency
,h
ow
ever
,th
ed
isp
ersi
ng
fun
ctio
np
red
om
inat
es,th
ed
rop
sb
e-co
me
smal
ler
and
the
load
ing
lim
itfa
lls.
Th
ein
tere
stin
gre
gio
nin
pra
ctic
eis
that
inw
hic
hd
isp
ersi
ng
pre
do
min
ates
.
Fig
ure
27.
Load
ing
lim
itas
afu
nct
ion
of
the
pu
lsin
gfr
e-quen
cyat
dif
fere
nt
free
area
for
tolu
ene
–w
ater
[50
]a
=6
mm
;vd
/vc=
1△
ϕ=
0.6
0;
d=
6.5
mm
2ϕ
=0.4
0;
d=
4.0
mm
◦ϕ
=0.2
3;
d=
2.5
mm
As
isto
be
exp
ecte
d,
the
load
ing
lim
itri
ses
wit
hin
crea
sin
gfr
eear
eaover
the
enti
rep
uls
ing
ran
ge,
bu
tth
ep
osi
tio
no
fth
em
axim
um
rem
ain
su
nch
ang
ed.
At
the
larg
est
free
area
of
ϕ=
0.6
,a
mo
des
tth
rou
gh
pu
tis
po
ssib
leev
enw
ith
ou
tp
uls
ing
.
Fig
ure
28.
Load
ing
lim
itas
afu
nct
ion
of
pu
lsat
ion
freq
uen
cyat
dif
fere
nt
inte
rfac
ial
ten
sio
n[5
0]:
ϕ=
0.2
3;
vd
/vc=
1a)
Buta
nol–
wat
er:σ
=1
.8m
N/m
;b
)B
uty
lac
etat
e–
wat
er:
σ=
13.5
mN
/m;
c)T
olu
ene
–w
ater
:σ
=3
6.1
mN
/m
Th
eef
fect
ofth
eg
eom
etry
ofth
ein
tern
als
can
also
be
show
nfo
rp
uls
edp
acked
colu
mn
s.T
her
eis
no
low
erlo
adin
gli
mit
.Atf
req
uen
cyf
=0
,i.e
.,th
eu
np
uls
edco
lum
n,
the
load
ing
lim
ith
asit
sm
axim
um
val
ue,
and
dec
reas
esw
ith
incr
easi
ng
freq
uen
cy[5
3].
Of
all
the
physi
cal
pro
per
ties
,th
ein
terf
aci
al
ten
sio
nh
asth
eg
reat
est
effe
cto
nth
efl
uid
dy
-n
amic
so
fan
extr
acti
on
colu
mn
.Fig
ure
28
show
sa
com
par
iso
no
fth
ree
test
syst
ems
wit
hd
iffe
ren
tin
terf
acia
lte
nsi
on
s.A
sca
nb
ese
en,t
he
thro
ug
h-
pu
top
tim
um
issh
ifte
dto
hig
her
pu
lsin
gfr
equ
en-
cies
wit
hin
crea
sed
surf
ace
ten
sio
n,i
.e.,
hig
hsu
r-fa
cete
nsi
on
sn
eed
ah
igh
ener
gy
sup
ply
.In
addit
ion
toth
ephysi
cal
pro
per
ties
,th
ep
has
era
tio
isan
oth
erp
aram
eter
det
erm
ined
by
the
pro
cess
.D
ecis
ion
sca
no
nly
be
mad
eas
tow
hic
ho
fth
etw
op
has
esis
tob
ed
isp
erse
d(t
he
org
anic
or
the
aqueo
us
phas
e)an
dw
het
her
inth
eg
reat
ero
rsm
alle
rq
uan
tity
.F
igu
re2
9sh
ow
sth
eef
fect
of
the
par
amet
erv d
/vc
[52
].A
sth
ep
has
era
tio
incr
ease
s,th
eth
rou
gh
pu
td
ecre
ases
.
Fig
ure
29.
Rel
ativ
elo
adin
go
fa
pu
lsed
siev
ep
late
colu
mn
asa
fun
ctio
no
ffl
ow
rati
o[5
2]
◦T
olu
ene
–w
ater
;2
MIB
K–
wat
er;△
Bu
tyl
acet
ate
–w
ater
;�
n-B
uta
no
l–w
ater
Afu
rth
erp
aram
eter
affe
ctin
gth
elo
adin
gli
mit
and
sep
arat
ion
effi
cien
cyis
the
dir
ecti
on
of
the
mas
str
ansf
er.
Cu
rve
bin
Fig
ure
30
Ash
ow
sth
efl
oo
din
gp
oin
tcu
rve
of
the
pu
retw
o-
com
po
nen
tm
ixtu
reto
luen
e–
wat
er,
wh
ere
no
mas
str
ansf
erta
kes
pla
ce[5
4].
Cu
rve
afo
rm
ass
tran
sfer
from
the
dis
per
sed
org
anic
phas
eto
the
con
tin
uo
us
aqu
eou
sp
has
eli
essu
bst
anti
ally
hig
her
by
com
par
iso
n.
Th
ere
aso
nfo
rth
isis
anin
crea
sed
ten
den
cyto
coal
esce
nce
and
hen
cefo
rmat
ion
of
larg
erd
rop
s.In
the
conver
seca
se(m
ass
tran
sfer
fro
mth
eco
nti
nu
ou
sto
the
dis
-p
erse
dp
has
e),
the
inte
rfac
ial
ten
sio
nan
dh
ence
the
dro
psi
zear
ere
du
ced
by
the
com
po
nen
t
Liq
uid
–Liq
uid
Extr
action
27
bei
ng
tran
sfer
red
,le
adin
gto
alo
wer
ing
of
the
flo
od
ing
po
int
[53
],[5
5].
Th
eef
fect
of
the
di-
rect
ion
of
mas
str
ansf
ero
nth
ed
rop
size
also
cau
ses
dif
fere
nce
sin
the
sep
arat
ion
effi
cien
cy.
Inth
eca
seo
fm
ass
tran
sfer
fro
mth
eco
nti
nu
-o
us
ph
ase
toth
ed
isp
erse
dp
has
e(i
nto
the
dro
p),
smal
ler
HE
TS
val
ues
resu
lt,
i.e.
,b
ette
rse
par
a-ti
on
effi
cien
cyis
ob
tain
ed(F
ig.3
0B
).
Fig
ure
30.
Infl
uen
ceof
mas
str
ansf
eron
load
ing
lim
itan
dse
par
atio
nef
fici
ency
for
the
tolu
ene
–ac
etone
–w
ater
sys-
tem
(ϕ=
0.6
0)
△M
ass
tran
sfer
from
the
dis
per
seto
the
conti
nuous
phas
e;2
Syst
emw
ithout
mas
str
ansf
er;◦
Mas
str
ansf
erfr
om
the
conti
nuous
toth
edis
per
sephas
e
Pil
hofer
[56
]h
assh
ow
nth
atth
elo
adin
gli
mit
of
extr
acti
on
colu
mn
sd
epen
ds
on
lyo
nth
ed
rop
size
.A
cco
rdin
gly
,h
igh
load
ing
lim
its
can
be
ob
tain
edo
nly
wit
hre
lati
vel
yla
rge
dro
ps.
Sep
ara
tio
nE
ffici
ency
.H
ow
ever
too
bta
ina
hig
hse
par
atio
nef
fici
ency
ala
rge
mas
str
ansf
erar
ea,
i.e.
,th
eg
reat
est
po
ssib
leh
old
up
of
dis
-p
erse
dp
has
e,is
req
uir
ed.T
he
ho
ldu
pri
ses
wit
hd
ecre
asin
gd
rop
size
.Any
inp
uto
fen
erg
yh
asth
ep
urp
ose
of
pro
du
cin
gth
eo
pti
mal
dro
pd
isp
er-
sio
n.
Th
ein
terr
elat
ion
of
sep
arat
ion
effi
cien
cyan
dp
uls
ing
can
be
dem
on
stra
ted
by
mea
sure
-
men
tso
nth
eto
luen
e–
wat
er–
acet
on
esy
stem
,w
hic
hh
asa
hig
hin
terf
acia
lte
nsi
on
[41
].F
ig-
ure
31
show
sth
em
easu
red
hei
gh
to
fa
theo
ret-
ical
stag
e(H
ET
S)
for
this
syst
emas
afu
nct
ion
of
the
pu
lsat
ion
freq
uen
cy,f
or
the
thre
ed
iffe
ren
tp
late
typ
es(c
urv
esa
–c)
.In
allca
ses,
the
HE
TS
dec
reas
esas
exp
ecte
dw
ith
incr
easi
ng
pu
lsin
gin
ten
sity
,i.
e.,
pu
lsin
gen
han
ces
the
sep
arat
ion
effi
cien
cy.
Th
ecu
rves
show
anim
po
rtan
tin
flu
-en
ceo
fth
ep
late
geo
met
ry:
wit
hin
crea
sin
gfr
eear
ea,t
he
sep
arat
ion
effi
cien
cyd
ecre
ases
shar
ply
.
Fig
ure
31.S
epar
atio
nef
fici
ency
mea
sure
das
afu
nct
ion
of
inte
rfac
ial
tensi
on
[41]
a)–
c)T
olu
ene
–w
ater
–ac
etone;
d)
Buta
nol–
wat
er–
succ
inic
acid
+ϕ
=0.6
0;◦
ϕ=
0.4
0;▽
ϕ=
0.2
3
Th
ebu
tan
ol–
succ
inic
acid
–w
ater
syst
emsh
ow
sver
yfa
vo
rab
leH
ET
Sval
ues
bec
ause
ofit
sex
trem
ely
low
inte
rfac
ial
ten
sio
n(c
urv
ed
).T
he
effe
cto
ffr
eear
eais
neg
lig
ible
.T
his
mea
ns
that
,fo
rsy
stem
so
flo
win
terf
acia
lte
nsi
on
,th
efr
eear
eaca
nb
ein
crea
sed
infa
vo
ro
fh
igh
erth
rou
gh
-p
uts
,w
ith
ou
ta
sig
nifi
can
tlo
ssin
sep
arat
ion
ef-
fici
ency
.A
com
par
iso
no
fth
ese
two
syst
ems
clea
rly
show
sth
ep
ron
ou
nce
din
flu
ence
of
the
inte
rfa-
cial
ten
sio
no
nse
par
atio
nef
fici
ency
.T
his
flu
id-
dy
nam
icas
pec
tsh
ou
ldal
sob
eta
ken
into
ac-
cou
ntw
hen
sele
ctin
gso
lven
tsfo
rex
trac
tio
np
ro-
cess
es.H
ith
erto
,th
isse
lect
ion
has
bee
nm
ade
al-
mo
stex
clu
sivel
yu
nd
erth
erm
od
yn
amic
crit
eria
.
28
Liq
uid
–Liq
uid
Extr
action
Th
ere
lati
on
ship
bet
wee
np
late
geo
met
ry,in
-te
rfac
ial
ten
sio
n,
and
sep
arat
ion
effi
cien
cy,
asd
escr
ibed
her
efo
ra
pu
lsed
siev
ep
late
colu
mn
,q
ual
itat
ivel
yap
pli
esal
soto
reci
pro
cati
ng
-pla
teco
lum
ns
and
pu
lsed
pac
ked
colu
mn
s.G
ener
ally
spea
kin
g,in
syst
ems
wit
ha
hig
hin
terf
acia
lte
n-
sio
n,
par
ticu
lar
atte
nti
on
mu
stb
ep
aid
toth
ech
oic
eo
fth
ein
tern
als,
ah
igh
eren
erg
yin
pu
tis
also
nec
essa
ry.
3.2
.3.
Flu
idD
yn
am
icC
alc
ula
tio
nM
eth
od
s
Th
eca
lcu
lati
on
met
ho
ds
for
det
erm
inin
gth
elo
adin
gli
mit
can
be
clas
sifi
edin
two
cate
go
ries
.T
he
firs
tca
teg
ory
con
sist
so
fem
pir
ical
corr
ela-
tions
whic
har
ebas
edon
physi
calan
dgeo
met
ri-
cal
dat
a,an
den
erg
yin
pu
t.T
he
seco
nd
cate
go
ryis
bas
edo
nfl
uid
-dy
nam
icm
od
els
and
pre
sup
-p
ose
sk
now
led
ge
of
the
dro
psi
ze.B
oth
met
ho
dcl
asse
sar
eap
pli
cab
leo
nly
totw
o-c
om
po
nen
tsy
stem
san
dth
us
neg
lect
the
effe
cto
fm
ass
tran
s-fe
r,as
show
nin
Fig
ure
30
.T
he
effe
cts
of
wet
-ti
ng
and
of
dro
pco
ales
cen
cear
eli
kew
ise
dis
-re
gar
ded
.M
ore
over
,th
eem
pir
ical
corr
elat
ions
inp
arti
cula
rar
efr
equ
entl
yre
stri
cted
toce
rtai
ng
eom
etri
esan
dca
nn
ot
be
extr
apo
late
dto
oth
erd
esig
ns,
they
can
ther
efo
reo
nly
be
use
dto
ob
-ta
inan
app
rox
imat
ees
tim
ate.
Fo
rfi
nal
equ
ip-
men
tsi
zin
g,
anex
per
imen
tal
det
erm
inat
ion
of
the
load
ing
lim
itin
the
par
ticu
lar
typ
eo
feq
uip
-m
ent
wit
hth
eo
rig
inal
pro
cess
stre
ams
isab
so-
lute
lyn
eces
sary
.
Pa
cked
Co
lum
n.
Un
pu
lsed
pac
ked
colu
mn
sh
ave
no
ind
ust
rial
sig
nifi
can
cean
ylo
ng
er.A
re-
vie
wo
nem
pir
ical
equ
atio
ns
toca
lcu
late
ho
ldu
p,
dro
psi
ze,fl
oo
din
g,m
ass
tran
sfer
,an
dax
ial
dis
-p
ersi
on
isg
iven
in[6
,C
hap
.8].
Per
form
ance
can
be
imp
roved
by
mec
han
ical
pu
lsat
ion
of
the
con
tin
uo
us
ph
ase
atth
eex
pen
seo
fa
red
uce
dth
rou
gh
pu
t.F
or
aro
ug
hes
tim
ate,
pu
lsin
gw
ith
inre
aso
nab
lera
ng
esm
ayb
eas
sum
edto
cau
seth
elo
adli
mit
sto
fall
by
20
–3
0%
asco
mp
ared
wit
hth
eu
np
uls
edco
lum
n.S
till
,n
oeq
uat
ion
sfo
rca
l-cu
lati
on
are
kn
ow
n.
Sie
ve
Pla
teC
olu
mn
.T
he
conven
tio
nal
siev
epla
teco
lum
nhas
bee
nin
ves
tigat
edby
Pil
hofer
[66
]fo
rto
luen
e–
wat
ersy
stem
s.H
irsch
man
n[6
9]
expan
ded
the
inves
tigat
ions
of
Pil
hofer
toli
qu
idsy
stem
sw
ith
low
er
surf
ace
ten
sio
ns
and
den
sity
dif
fere
nce
sth
anto
luen
e–
wat
eran
dto
du
alfl
ow
pla
tes.
Fo
rca
l-cu
lati
on
see
[69
].
Sie
ve
Pla
tea
nd
Ro
tati
ng
Co
lum
ns.
Sp
e-ci
alem
pir
ical
equ
atio
ns
are
giv
enin
the
lit-
erat
ure
for
each
typ
eo
fex
trac
tio
nco
lum
ns
ino
rder
toca
lcu
late
the
flo
od
ing
con
dit
ion
,so
,e.
g.,
for
siev
ep
late
colu
mn
sin
[66
]an
d[6
7],
for
pu
lsed
siev
ep
late
colu
mn
sin
var
iou
sch
apte
rso
f[6
],fo
rro
tati
ng
colu
mn
sin
[6]
and
[5].
How
-ev
er,
since
import
ant
effe
cts
are
dis
regar
ded
asm
enti
on
edb
efo
re,
her
eit
wil
lb
esu
ffici
ent
toin
tro
du
cea
rou
gh
met
ho
db
ased
on
afl
uid
dy
nam
icm
od
el[6
6].
Th
em
od
el,
ori
gin
ally
de-
vel
op
edfo
ru
np
uls
edsi
eve
tray
colu
mn
s,p
roved
tob
eap
pli
cab
leto
all
typ
eso
fco
lum
ns.
Itis
as-
sum
edth
atth
eli
qu
ids
occ
upy
ash
are
of
the
cro
ss-s
ecti
on
acco
rdin
gto
thei
rh
old
up
εan
dfl
ow
tow
ard
each
oth
eras
lay
ers.
Ifth
eir
sup
er-
fici
alvel
oci
tyv
,i.
e.th
eir
vo
lum
etri
cfl
ow
rate
V
rela
ted
toth
eco
mp
lete
colu
mn
cro
ssse
ctio
nS
,is vc
=Vc S
;vd
=Vd S
(1)
they
hav
ean
effe
ctiv
evel
oci
tyv c
/(1−
ε d)
or
vd/ε
d.
Th
aty
ield
sth
ere
lati
ve
vel
oci
tyv r
,al
soca
lled
slip
velo
city
,b
etw
een
the
two
liq
uid
s
vr
=vd
ε d+
vc
1−
ε d(2
)
Eit
her
v ro
rε d
can
be
calc
ula
ted
fro
mE
qu
a-ti
on
(2)
ifo
ne
or
mo
rere
lati
on
ship
sb
etw
een
the
two
term
sar
ek
now
n.In
[45
]a
sim
ple
emp
iric
aleq
uat
ion
isg
iven
toca
lcu
late
v r
vr
vp
=(1−
ε d)k
(3a)
k=
4.6−
0.1
3ln
Ar
(3b
)
wh
en1
<A
r<
107
and
2.5
<k<
4.6
v Pis
the
ind
ivid
ual
dro
pvel
oci
tyg
iven
by
[66
]fo
rci
rcu
lati
ng
dro
ps
Re p
=K
0.1
5L
(
Ar0.5
23K−
0.1
435
L−
0.7
5)
(4a)
if 1.8
3K
0.2
75
L<
Ar<
3.9
4K
0.2
75
L
for
osc
illa
tin
gd
rop
s
Liq
uid
–Liq
uid
Extr
action
29
Re p
=K
0.1
5L
(
4.1
8A
r0.2
18K−
0.0
0773
L−
0.7
5)
(4b)
if Ar
>372.9
K0.2
75
L(4
c)
Th
ed
imen
sio
nle
ssn
um
ber
sar
ed
efin
edas
fol-
low
s:p
arti
cle
Rey
no
lds
nu
mb
er
Re p
=vpdp
νd
(5)
Arc
him
edes
nu
mb
er
Ar
=d3 pgc∆
η2 c
(6)
char
acte
rist
icn
um
ber
of
liq
uid
KL
=2 cσ
3
∆gη4 c
(7)
den
sity
dif
fere
nce
∆
=|
c−
d|
(8)
Mat
hem
atic
alfo
rmu
lati
on
imp
lies
the
fact
that
anin
crea
seo
fth
efl
ow
rate
atfl
oo
din
gca
nn
ot
incr
ease
the
dro
ph
old
up
:
dvd
dε d
=0
(9a)
wh
env c
=co
nst
ant,
dvc
dε d
=0
(9b)
wh
env d
=co
nst
ant.
Wit
hE
qu
atio
n(2
)fo
rth
esl
ipvel
oci
tyv r
the
equ
atio
ns
for
calc
ula
tin
gth
esu
per
fici
alvel
oci
-ti
esvc,v d
atth
efl
oo
din
gp
oin
tar
eo
bta
ined
ina
dim
ensi
on
less
form
:
vc
(
c
∆vcg
)
1/3
=A
r−
1/3
(1−
ε d)2
(Re r
+
ε ddR
e r
dε d
)
(10a)
vd
(
c
∆vcg
)
1/3
=A
r−
1/3ε2 d
(Re r−
(1−
ε d)
dR
e r
dε d
)
(10b)
Eq
uat
ion
s(1
0a)
and
(10
b)
tog
eth
erw
ith
Eq
ua-
tio
n(3
)fo
rvr
and
Eq
uat
ion
(4)
are
the
bas
is
for
flo
od
ing
po
int
dia
gra
ms
acco
rdin
gto
Fig
-u
re3
2.
Ord
inat
ean
dab
scis
saco
nta
inth
esu
-p
erfi
cial
vel
oci
ties
vd
and
v c,
i.e.
,th
ep
has
efl
ow
rate
s,m
odifi
edby
physi
cal
dat
agro
ups
toa
dim
ensi
on
less
form
.T
he
dia
gra
msh
ow
sth
eca
lcu
late
dfl
oo
din
gcu
rves
of
circ
ula
tin
gd
rop
sas
soli
dli
nes
wit
hth
ep
aram
eter
Ar.
Das
hed
lin
eso
fco
nst
ant
ph
ase
rati
ov d
/vc
and
the
to-
tal
thro
ug
hp
ut
asth
esu
mo
fvd
and
v car
eal
sosh
ow
n.
Fig
ure
32.
Gen
eral
load
ing
dia
gra
m[5
2],
[56]
Itca
nb
ese
enfr
om
Eq
uat
ion
(4b
)th
atR
e Pis
app
rox
imat
ely
pro
po
rtio
nal
toA
r0.3
and
ther
e-fo
reto
dP
.T
hat
mea
ns
that
the
dro
pvel
oci
tyv P
isn
earl
yin
dep
end
ento
fd
rop
dia
met
erd
Pin
the
reg
ion
of
osc
illa
tin
gd
rop
s.T
her
efo
reF
igu
re3
2ca
nb
eu
sed
also
for
osc
illa
tin
gd
rop
sif
Ar
isre
pla
ced
by
KL
usi
ng
Eq
uat
ion
4c.
Oth
erw
ise
the
dia
gra
mis
val
idfo
ra
cert
ain
KL
val
ue
inth
ere
gio
no
fci
rcu
lati
ng
dro
ps,
inca
seo
fF
igu
re3
2,
KL
=1
011.
Th
ed
epen
den
ceo
fd
rop
dia
met
erd
Pu
po
np
aram
eter
so
fin
flu
ence
mu
stb
ek
now
nin
or-
der
tou
seF
igu
re3
2an
dto
calc
ula
tefl
oo
din
gcu
rves
.M
any
scie
nti
fic
inves
tigat
ions
on
dro
pd
isin
teg
rati
on
invar
iou
sex
trac
tors
are
fou
nd
inth
eli
tera
ture
,bu
to
ften
wit
ho
ut
con
sid
erin
gth
ein
flu
ence
of
mas
str
ansf
eran
dth
ein
tera
ctio
no
fd
isp
ersi
ng
and
coal
esce
nce
.F
urt
her
mo
re,
par
-ti
cula
rly
for
hig
her
inte
rfac
ial
ten
sio
nsy
stem
sa
con
sid
erab
leh
eig
ht
of
colu
mn
isre
qu
ired
tore
ach
ast
ead
y-s
tate
dro
psi
ze,
and
this
hei
gh
tvar
ies
wit
hli
qu
idsy
stem
and
inle
tar
ran
gem
ent
for
the
dis
per
sed
ph
ase.
Sin
cep
op
ula
tio
nb
al-
ance
sar
en
ot
use
din
this
intr
od
uct
ory
arti
cle,
30
Liq
uid
–Liq
uid
Extr
action
the
con
cep
to
fm
ean
dro
psi
zes
isap
pli
ed–
no
r-m
ally
rep
ort
edas
the
Sau
ter
mea
no
rsu
rfac
ep
erce
nta
ge
mea
nd
rop
size
–d
efin
edb
y
d32
=
∑
in
pid3 p
i
∑
in
pid2 p
i
(11
)
wh
ere
np
ire
pre
sen
tth
en
um
ber
so
fd
rop
so
fth
ecl
ass
io
fd
iam
eter
dp
i.
Fin
ally
,d
iscu
ssio
nw
ill
be
rest
rict
edto
em-
pir
ical
equ
atio
ns
by
Ku
mar
and
Hartlan
d[6
,C
hap
.17
]w
hic
hg
ive
the
bes
tfi
tto
exp
erim
enta
ld
ata
and
hav
eth
eb
road
est
ran
ge
of
val
idit
y:
Pu
lsed
siev
etr
ay
an
dre
cip
roca
tin
gex
tra
cto
r
d32
√
σ∆
g
=C
1e0
.74
(
h
0.0
5m
)
0.1
0
·
·[
exp
(
−3.0
0af∆
1/4
gσ
1/41/4
)
+
exp
(
−28.6
5af∆
1/4
gσ
1/41/4
)]
(12
)
Th
eb
est
val
ues
of
the
par
amet
erC
1ar
e1
.51
,1
.36
,an
d2
.01
for
no
mas
str
ansf
er,
c→
d,
and
d→
cd
irec
tio
no
ftr
ansf
er,
resp
ecti
vel
y.T
he
pro
du
cta·f
isco
nsi
der
edas
the
agit
atio
nvar
i-ab
lein
the
equ
atio
n,
sin
ceth
efi
tco
uld
no
tb
eim
pro
ved
ifa
and
fw
ere
trea
ted
sep
arat
ely.
Th
eav
erag
eab
solu
teval
ue
of
the
rela
tive
dev
iati
on
inth
ep
red
icte
dval
ues
of
d32
fro
mth
eex
per
i-m
enta
lp
oin
tsis
16
.3%
.R
ota
tin
gd
isk
extr
act
ors
d32
DR
=
(
C1
0.0
7+√
Fr R
)(
ηc
√σcD
R
)
−0.1
2
(
d c
)
0.1
6
·(
D2 R
cg
σ
)
−0.5
9
(
h DC
)
0.2
5(
D DR
)
0.4
6
(13
)
Th
eo
pti
miz
edval
ues
of
C1
are
0.6
3,0
.53
,an
d0
.74
for
no
mas
str
ansf
er,
c→
dan
dd→
cd
i-re
ctio
ns
of
tran
sfer
,re
spec
tivel
y.T
he
effe
cto
fh
old
up
isig
no
red
du
eto
lack
of
dat
a.E
qu
atio
n(1
3)
pre
dic
tsth
ed
rop
size
wit
han
aver
age
ab-
solu
teval
ue
of
the
rela
tive
dev
iati
on
of
23
%.
Ku
hn
ico
lum
ns
d32
DR
=C
1e0
.37n−
0.1
1S
[0.1
4+
exp
(−18.7
3F
r R)]·
·(
ηc
√σcD
R
)
−0.2
0(
D2 R
cg
σ
)
−0.2
4
(14
)
Th
eval
ues
of
the
con
stan
tC
1ar
e9
.81×
10−
2
for
no
mas
str
ansf
eran
dc→
dtr
ansf
eran
d0
.31
for
d→
ctr
ansf
er.
Th
est
age
nu
mb
ernS,
wh
ich
var
ies
fro
m2
to1
7in
the
pre
sen
tse
to
fd
ata,
show
sa
rath
erw
eak
effe
cto
nd
rop
size
.E
qu
a-ti
on
(14
)p
red
icts
the
dro
pd
iam
eter
wit
han
av-
erag
eab
solu
teval
ue
and
rela
tive
dev
iati
on
of
17
.6%
.
3.3
.A
pp
ara
tus
Des
ign
Ex
trac
tio
nap
par
atu
sca
nb
eap
pro
xim
ativ
ely
des
ign
edp
ure
lyb
yca
lcu
lati
on
usi
ng
flu
id-
dy
nam
icm
od
els
[49
],[7
0].
Fo
rre
liab
led
esig
n,
how
ever
,p
ilo
t-sc
ale
test
sar
ein
dis
pen
sab
le.
Ifp
oss
ible
,th
ete
stsh
ou
ldb
eca
rrie
do
ut
wit
hth
eo
rig
inal
op
erat
ing
mix
ture
inth
ety
pe
of
app
ara-
tus
wh
ich
isal
soen
vis
aged
for
the
larg
e-sc
ale
un
it.
Des
irab
ly,
the
geo
met
ryo
fth
ein
tern
als
sho
uld
be
the
sam
ein
the
pil
ot-
scal
ean
din
du
s-tr
ial
app
arat
us.
How
ever
,th
isco
nd
itio
nca
nn
ot
alw
ays
be
sati
sfied
.G
ener
ally
,a
colu
mn
dia
me-
ter
of
atle
ast6
0–
80
mm
isn
eces
sary
for
des
ign
test
s.T
ests
insm
alle
rco
lum
ns
can
no
tb
eu
sed
asth
eb
asis
for
equ
ipm
ent
sizi
ng
(fo
rcr
iter
iao
neq
uip
men
tse
lect
ion
,se
eS
ecti
on
3.4
).T
he
nu
mb
ero
fte
sts
can
,h
ow
ever
,b
esu
bst
anti
ally
red
uce
dif
kn
ow
led
ge
of
the
op
erat
ing
char
ac-
teri
stic
sis
uti
lize
d.
The
physi
cal
dat
aan
dth
ephas
era
tio
are
de-
term
ined
by
the
pro
cess
use
d,th
efo
llow
ing
pa-
ram
eter
sar
eav
aila
ble
for
op
tim
izat
ion
:p
uls
ing
or
rota
tio
n,
geo
met
ryo
fth
ein
tern
als,
mat
eria
lo
fth
ein
tern
als,
and
ph
ase
sele
ctio
n,i.
e.,th
ed
i-re
ctio
no
fm
ass
tran
sfer
.E
ner
gy
inp
ut
and
the
geo
met
ryo
fth
ein
tern
als
are
sele
cted
on
the
ba-
sis
of
the
physi
cal
dat
a.
3.3
.1.
Inte
rna
lsa
nd
Op
era
tin
gC
on
dit
ion
s
Th
efo
llow
ing
gu
idel
ines
app
lyfo
rth
ese
lect
ion
of
the
free
area
inp
uls
edco
lum
ns.
An
incr
ease
inth
efr
eear
eais
reco
mm
end
edin
syst
ems
wit
ha
low
inte
rfac
ialte
nsi
on
wh
ere
itle
ads
toa
gre
atre
du
ctio
nin
the
colu
mn
vo
lum
e.A
tm
od
erat
ein
terf
acia
lte
nsi
on
,th
eco
lum
nd
iam
eter
can
be
red
uce
db
ya
gre
ater
free
area
,bu
tat
the
exp
ense
of
the
colu
mn
hei
gh
t.In
the
case
of
extr
emel
y
Liq
uid
–Liq
uid
Extr
action
31
Fig
ure
33.
Sel
ecti
on
of
phas
esan
dpla
tem
ater
ials
hig
hin
terf
acia
lte
nsi
on
,th
ere
isn
op
oin
tin
in-
crea
sin
gth
efr
eear
ea.
Th
em
ater
ial
of
the
inte
rnal
ssh
ou
ldb
ese
-le
cted
soth
atth
eco
nti
nu
ou
sp
has
e,bu
tn
ot
the
dis
per
sed
ph
ase,
wet
sth
ep
late
s.A
sa
rule
of
thu
mb
,m
etal
pla
tes
can
be
use
dw
hen
the
or-
gan
icphas
eis
dis
per
sed;
ifth
eaq
ueo
us
phas
eis
dis
per
sed
,th
ein
tern
als
sho
uld
be
of
pla
stic
,b
oth
inp
uls
edco
lum
ns
and
inro
tary
-ag
itat
edco
lum
ns.
Ind
ecid
ing
wh
ich
ph
ase
sho
uld
be
dis
per
sed
,th
ed
irec
tio
no
fm
ass
tran
sfer
mu
stb
eta
ken
into
acco
un
t.In
acco
rdan
cew
ith
Fig
ure
30
,m
ass
tran
sfer
sho
uld
be
fro
mth
eco
nti
nu
ou
sp
has
eto
the
dis
per
sed
ph
ase,
ifp
oss
ible
.In
the
fin
alp
has
ese
lect
ion
,how
ever
,flu
id-d
yn
amic
con
sid
-er
atio
ns
freq
uen
tly
con
flic
tw
ith
op
erat
ing
and
safe
tyre
qu
irem
ents
.T
he
po
siti
on
of
the
inte
r-fa
cein
the
colu
mn
det
erm
ines
the
ph
ase
wh
ich
isd
isp
erse
d.F
igu
re3
3su
mm
ariz
esth
ep
oss
ible
com
bin
atio
ns.
Th
ese
par
atio
nef
fici
ency
det
erm
ines
the
col-
um
nh
eig
hta
nd
the
load
lim
itd
eter
min
esth
eco
l-u
mn
dia
met
er.F
or
op
tim
izat
ion
,th
etw
op
aram
-et
ers
are
rela
ted
by
the
rati
oθ
=H
ET
S/(vc+
v d)
wh
ich
can
be
use
dto
op
tim
ize
the
colu
mn
in-
tern
als
and
ener
gy
inp
ut.
Am
inim
um
val
ue
of
this
exp
ress
ion
iseq
uiv
alen
tto
am
inim
um
col-
um
nvo
lum
e.F
igu
re3
4sh
ow
sth
ato
pti
mu
mp
uls
ing
iso
bta
ined
bet
wee
nth
em
axim
um
of
the
flo
od
ing
po
int
curv
ean
dth
em
inim
um
of
the
HE
TS
curv
e.A
nan
alo
go
us
pro
ced
ure
isu
sed
for
rota
ryag
itat
edco
lum
ns.
Th
ed
esig
np
oin
tfo
rin
du
stri
al-s
cale
colu
mn
sis
cho
sen
tob
e7
5–
80
%o
fth
elo
adli
mit
.T
he
op
erat
ing
po
int
wit
hre
spec
tto
load
and
pu
lsin
g(r
ota
tio
n)
isfi
xed
by
this
pro
ced
ure
.
3.3
.2.
Co
lum
nD
iam
eter
Ass
um
ing
the
sam
eco
lum
ng
eom
etry
,th
esp
e-ci
fic
thro
ug
hp
uto
fth
ete
stco
lum
nis
ado
pte
dfo
rth
ela
rge-
scal
eco
lum
n.
(vc
+vd) 2
=(v
c+
vd) 1
wit
h
(vc
+vd) 1
=0.7
5·(
vc
+vd) 1
max
Ind
ex1
=p
ilo
tsc
ale
Ind
ex2
=la
rge
scal
e
Th
isg
ives
the
colu
mn
dia
met
er:
D2=
√ √ √ √
4(
mF
F
+m
S
S
)
2
π·(
vc
+vd) 2
32
Liq
uid
–Liq
uid
Extr
action
Fig
ure
34.
Opti
miz
atio
no
fp
uls
atio
n
3.3
.3.
Co
lum
nH
eig
ht
Th
ese
par
atio
nef
fici
ency
of
all
colu
mn
sd
e-cr
ease
sw
ith
incr
easi
ng
colu
mn
dia
met
er,
be-
cau
seth
ere
sid
ence
tim
ed
istr
ibu
tio
ns
of
the
ph
ases
incr
ease
.T
her
efo
reval
ues
of
the
hei
gh
to
fa
theo
reti
cal
stag
e,m
easu
red
for
ala
bo
rato
ryco
lum
n,n
eed
tob
eco
rrec
ted
by
emp
iric
alsc
ale-
up
equ
atio
ns
tob
eap
pli
cab
lefo
rin
du
stri
al-s
cale
colu
mns.
How
ever
,sc
ienti
fic
inves
tigat
ions
of
this
pro
ble
mar
era
ther
po
or
and
mai
nly
emp
iri-
calk
now
led
ge
ofin
du
stri
alen
gin
eers
exis
ts.T
he
dif
fere
nt
chap
ters
of
[5]
list
form
ula
efr
om
ex-
per
ien
cew
ith
cou
nte
rcu
rren
tex
trac
tors
asd
e-sc
rib
edh
ere,
incl
ud
ing
Pu
lsed
siev
etr
ay
colu
mn
s[7
1]
HE
TS2
HE
TS1
=ex
p[1
.64
(D2−
D1)]
(15
)
(in
Eq
uat
ion
15
the
fact
or1
.64
,giv
enb
yT
horn
-
ton
,is
on
lyval
idfo
rsm
all
colu
mn
s.F
igu
re3
5sh
ow
san
emp
iric
ald
epen
den
ceo
fth
eT
ho
rnto
nfa
cto
rfr
om
the
colu
mn
dia
met
erp
ub
lish
edb
yR
eis
sin
ger
[49
])R
ecip
roca
tin
gco
lum
ns
[72
]
HE
TS2
HE
TS1
=
(
D2
D1
)
0.3
8
(16
)
Wh
enth
ep
late
geo
met
ryan
dam
pli
tud
eo
fth
ev
ibra
tio
nar
ele
ftu
nch
ang
edin
the
larg
e-sc
ale
colu
mn
,th
efr
equ
ency
sho
uld
be
red
uce
d,
acco
rdin
gto
:
f2
f1
=
(
D1
D2
)
0.1
4
Th
efo
llow
ing
app
lies
tost
irre
dco
lum
ns
[73
]:
HE
TS2
HE
TS1
=
(
D2
D1
)
0.3
3
Fig
ure
35.
Dep
end
ence
of
Th
orn
ton
fact
or
on
colu
mn
di-
amet
er
3.4
.C
rite
ria
for
Eq
uip
men
tS
elec
tio
n
Fo
ra
giv
ense
par
atio
np
rob
lem
,eq
uip
men
tis
sele
cted
esse
nti
ally
acco
rdin
gto
thre
ecr
iter
ia:
physi
cal
pro
per
ties
,re
quir
ednum
ber
of
separ
a-ti
on
stag
es,
and
thro
ug
hp
ut.
Fu
rth
ero
per
atin
gas
pec
tsar
efr
equ
entl
yim
po
rtan
t,fo
rex
amp
le,
flex
ibil
ity
regar
din
glo
advar
iati
ons
or
pro
duct
qu
alit
y,se
nsi
tiv
ity
tosm
all
amo
un
tso
fso
lid
s,su
itab
ilit
yfo
rb
atch
op
erat
ion
.T
he
physi
cal
pro
per
ties
of
inte
rest
inex
trac
-ti
on
are
the
den
sity
dif
fere
nce
bet
wee
nth
etw
o
Liq
uid
–Liq
uid
Extr
action
33
Fig
ure
36.C
om
par
ison
of
the
num
ber
of
theo
reti
cal
stag
esN
TS
indep
enden
ceof
tota
llo
adfo
rK
uhni,
QV
F,K
arr
and
puls
edsi
eve
pla
teex
trac
tors
(PS
E)
[64]
(syst
embuty
lac
etat
e–
wat
er–
acet
one,
phas
era
tio
vd
/vc≈
1.1
2,
mea
sure
men
tsof
var
ious
auth
ors
cite
din
[64])
ph
ases
,th
eir
vis
cosi
ty,
and
inte
rfac
ial
ten
sio
n.
Th
ese
thre
ep
aram
eter
saf
fect
dis
per
sib
ilit
yan
dp
has
ese
par
atio
nb
ehav
ior.
Hig
hd
ensi
tyd
iffe
ren
ce,
vis
cosi
ty,
and
inte
r-fa
cial
ten
sio
nm
ake
dis
per
sin
gm
ore
dif
ficu
lt;
syst
ems
wit
hsu
chphysi
cal
pro
per
ties
requir
ea
hig
her
dis
sip
atio
no
fen
erg
yth
anin
the
conver
seca
se.P
has
ese
par
atio
nis
favo
red
by
ah
igh
den
-si
tyd
iffe
ren
cean
din
terf
acia
lte
nsi
on
,w
her
eas
ah
igh
vis
cosi
tym
akes
ph
ase
sep
arat
ion
mo
red
iffi
cult
.
Th
elo
wer
lim
itfo
rth
ed
ensi
tyd
iffe
ren
ceca
nb
eta
ken
tob
e5
0k
g/m
3.
Mix
ture
sw
ith
hig
her
den
sity
dif
fere
nce
sca
ng
ener
ally
be
pro
cess
edin
colu
mn
san
dm
ixer
–se
ttle
rs.
Ifth
ed
ensi
tyd
if-
fere
nce
issm
alle
r,a
centr
ifugal
extr
acto
rm
ust
be
use
d.
Alo
win
terf
acia
lte
nsi
on
lead
sto
ph
ase
sep
-ar
atio
np
rob
lem
s.In
ind
ust
rial
un
its,
app
rox
i-m
atel
yσ
=1
–2
mN
/mca
nb
eta
ken
asth
elo
wer
lim
it.
Th
eref
ore
,m
ixer
–se
ttle
rsca
nce
rtai
nly
no
tbe
use
dfo
rm
ixtu
res
ofre
lati
vel
ylo
win
terf
a-ci
alte
nsi
on
;bec
ause
ofth
esh
earfi
eld
gen
erat
ed,
centr
ifugal
extr
acto
rsal
sohav
ea
dis
per
sing
ef-
fect
wh
ich
sho
uld
no
tbe
un
der
esti
mat
ed.I
nsu
chca
ses,
the
ener
gy
inp
ut
mu
stb
ever
yca
refu
lly
con
tro
lled
.R
ota
ry-a
git
ated
colu
mn
san
dp
uls
edco
lum
ns
can
be
use
d,in
wh
ich
the
ener
gy
inp
ut
can
be
adap
ted
toth
ephysi
cal
pro
per
ties
by
the
spee
do
fro
tati
on
or
the
pu
lse
freq
uen
cy.
Th
ese
lect
ion
ofeq
uip
men
tis
also
affe
cted
by
the
nu
mb
ero
fth
eore
tica
lst
ages
(NT
S)
req
uir
edfo
ra
giv
ense
par
atio
np
rob
lem
.On
lysm
alln
um
-b
ers
of
theo
reti
cal
stag
esca
nb
eac
hie
ved
inco
lum
ns
wit
ho
ut
ener
gy
inp
ut,
bec
ause
of
thei
rp
oo
rse
par
atio
nef
fici
ency
.P
uls
edco
lum
ns
and
rota
ryag
itat
edco
lum
ns
giv
eh
igh
ern
um
ber
so
fse
par
atio
nst
ages
.T
hey
are
lim
ited
by
the
pu
lsin
gu
nit
so
rb
yth
ele
ng
ths
of
the
con
tin
-uous
shaf
t.In
centr
ifugal
extr
acto
rs,
the
Ro-
bat
eld
esig
np
rov
ides
mo
rese
par
atio
nst
ages
than
,fo
rex
amp
le,
the
Po
db
ieln
iak
extr
acto
r.M
ixer
–se
ttle
rsar
eco
nst
ruct
edin
mo
du
les
soth
atth
ere
isv
irtu
ally
no
lim
itto
the
nu
mb
ero
fse
par
atio
nst
ages
.
Afi
rst
esti
mat
eo
fth
em
axim
um
po
ssib
leth
rou
gh
pu
tsin
the
ind
ivid
ual
extr
acto
rty
pes
can
be
ob
tain
edb
yco
nsi
der
ing
the
larg
estd
iam
eter
s(D
max)
wh
ich
hav
eh
ith
erto
bee
nin
stal
led
:
Dm
ax
,m
Rec
ipro
cati
ng
-pla
teco
lum
n1
.5
Pu
lsed
colu
mn
2.7
Ku
hn
iex
trac
tor
2.5
QV
Fex
trac
tor
2.8
Ro
tati
ng
Dis
kE
xtr
acto
r3
.0
Mix
er–
sett
ler
tow
er8
.0
34
Liq
uid
–Liq
uid
Extr
action
Fig
ure
37.C
om
par
iso
no
fef
fici
ency
ver
sus
load
of
pac
ked
colu
mn
sw
ith
and
wit
ho
ut
pu
lsin
gan
dp
uls
edsi
eve
tray
extr
acto
rsa·f
=puls
atio
nin
ten
sity
,Bf
=fl
oo
din
glo
ad,ϕ
=re
lati
ve
free
area
Acc
ord
ing
ly,
the
hig
hes
tth
rou
gh
pu
tsca
ncl
earl
yb
eac
hie
ved
wit
hth
em
ixer
–se
ttle
r.In
pu
lsed
colu
mn
s,th
ed
iam
eter
isli
mit
edb
yth
ep
uls
ing
un
it.In
rota
tio
nco
lum
ns,
the
sep
arat
ion
effi
cien
cyat
larg
ed
iam
eter
sis
no
lon
ger
sati
s-fa
cto
ry.
How
ever
,in
form
atio
ns
abo
ut
max
imal
cro
ss-s
ecti
on
allo
ads
wh
ich
are
nec
essa
ryto
ob
-ta
ind
efin
itiv
eth
rou
gh
pu
td
ata
of
aty
pe
of
ex-
trac
tor
are
no
tg
iven
inth
eli
st.
Th
eli
tera
ture
con
tain
sso
me
pu
bli
cati
on
sw
hic
hre
com
men
dcr
iter
iafo
rth
ese
lect
ion
of
the
bes
tap
par
atu
s.H
ow
ever
,m
ost
of
thes
ere
c-o
mm
end
atio
ns
are
on
lyq
ual
itat
ive,
and
som
ear
eev
enco
ntr
adic
tory
;n
ost
ud
ies
of
app
arat
us
hav
eso
faral
low
edan
ob
ject
ive
com
par
iso
n.O
nly
the
stan
dar
diz
atio
no
fte
stsy
stem
sfo
rex
trac
tio
nh
asal
low
edfl
uid
-dy
nam
icst
ud
ies
tob
eca
rrie
do
ut
un
der
com
par
able
con
dit
ion
s[4
4].
Th
efo
llow
-in
gsy
stem
sh
ave
bee
nre
com
men
ded
:
To
luen
e–
wat
er–
acet
on
eB
uty
lac
etat
e–
wat
er–
acet
on
eB
uta
no
l–w
ater
–su
ccin
icac
id
Th
ese
syst
ems
pro
vid
ean
ob
ject
ive
bas
isfo
rco
mp
aris
on
ofeq
uip
men
t.N
ever
thel
ess,
inves
ti-
gat
ions
by
dif
fere
nt
auth
ors
are
not
alw
ays
mu-
tual
lyco
mp
arab
lew
ith
resp
ect
toth
eab
solu
teH
ET
Sval
ues
.E
vid
entl
y,th
eco
lum
nle
ng
than
dth
ep
has
era
tio
hav
ean
un
exp
ecte
dly
larg
eef
fect
.F
or
the
tolu
ene
syst
em,Pil
hofer
com
par
edth
ed
iffe
ren
to
per
atin
gch
arac
teri
stic
so
fvar
i-o
us
gro
up
so
feq
uip
men
t.A
nal
og
ou
sst
ud
ies
on
the
liq
uid
syst
embu
tylac
etat
e–
wat
er–
acet
on
ew
ere
carr
ied
ou
tb
yG
oldm
an
n[6
4].
Fig
ure
36
show
sa
dia
gra
mo
fG
oldm
an
nw
ith
the
nu
mb
ero
fth
eore
tica
lst
ages
NT
Sp
erm
eter
of
colu
mn
hei
gh
t,as
afu
nct
ion
of
the
load
.T
he
fig
ure
con
-ta
ins
dat
afo
rQ
VF
and
Ku
hn
ico
lum
ns
–th
ela
t-te
rw
ith
five
dif
fere
ntfr
eear
eas
of
the
per
fora
ted
par
titi
on
dis
ks
–an
dfo
rp
uls
edsi
eve
pla
teex
-tr
acto
rs(P
SE
)w
ith
five
dif
fere
ntf
ree
area
sϕ
and
on
ere
cip
roca
tin
gco
lum
n(K
arr)
.Th
ero
tary
agi-
tate
dco
lum
ns
ofQ
VC
and
Ku
hn
iwit
hth
esm
all-
est
free
area
sϕ
clea
rly
ach
ieve
the
hig
hes
tN
TS
val
ues
,bu
tal
low
on
lylo
wlo
ads.
Als
o,th
eo
ther
Ku
hn
ico
lum
ns
show
hig
her
NT
Sval
ues
than
the
Liq
uid
–Liq
uid
Extr
action
35
pu
lsed
colu
mn
sbu
tsm
alle
rra
ng
eso
flo
ad.G
en-
eral
lysp
eak
ing
,all
mea
sure
sw
hic
him
pro
ve
the
sep
arat
ion
effi
cien
cyre
du
ceth
elo
adca
pac
ity.
Aco
mp
aris
on
bet
wee
np
uls
edsi
eve
tray
san
dst
ruct
ure
dp
ack
ing
sw
ith
the
test
syst
emto
luen
e–
wat
er–
acet
on
ew
asp
ub
lish
ed[7
4].
Fig
ure
37
show
sth
ed
iag
ram
wit
hth
eex
trac
tor
effi
cien
cyin
dep
end
ence
on
the
load
.It
iso
bv
i-o
us
that
stru
ctu
red
pac
kin
gs
hav
eth
eb
road
est
ran
ge
of
load
cap
acit
yan
dre
ach
the
sam
eo
rh
igh
eref
fici
enci
esas
pu
lsed
siev
etr
ays.
Fro
mth
ere
sult
sfo
rtw
ost
ruct
ure
dp
ack
ing
sw
ith
ou
tp
uls
atio
nth
ep
osi
tive
infl
uen
ceo
fp
uls
ing
can
clea
rly
be
seen
:T
he
pu
lsed
un
stru
ctu
red
pac
k-
ing
,Pal
lri
ng
s1
5×
15
mm
,has
acl
earl
ysm
alle
rlo
adra
ng
e.In
Fig
ure
38
,th
era
ng
eo
flo
ads
isco
mp
ared
for
siev
etr
ays
and
stru
ctu
red
pac
kin
gs
wit
hp
ul-
sati
on
[75
].A
cco
rdin
gto
that
,p
acked
colu
mn
sh
ave
sig
nifi
can
tad
van
tag
es.
As
show
nin
[75
],th
ein
ves
tmen
tco
sts
of
pu
lsed
stru
ctu
red
pac
ked
colu
mn
sar
e3
0%
low
erth
anth
eo
nes
of
pu
lsed
siev
etr
ayco
lum
ns
and
40
to5
0%
low
erth
anp
uls
edu
nst
ruct
ure
dp
acked
colu
mn
s.
Fig
ure
38.
Ran
ge
of
load
of
puls
edst
ruct
ure
dpac
ked
colu
mns
inco
mpar
ison
topuls
edsi
eve
tray
colu
mns
inde-
pen
den
ceofth
em
ass
den
sity
dif
fere
nce
foraq
ueo
us
syst
ems
and
syst
ems
sim
ilar
tow
ater
In[7
6]
asy
stem
atic
stu
dy
on
extr
acto
rse
lec-
tio
nis
giv
en.
Ad
ap
tati
on
of
the
Co
lum
nG
eom
etry
toth
eS
epa
rati
on
Pro
ble
m.
Inth
eea
rly
day
so
fex
trac
tio
n,
var
iou
sty
pes
of
app
arat
us
wer
ere
-st
rict
edto
clea
rly
defi
ned
geo
met
ries
and
wer
eth
us
shar
ply
dis
tin
gu
ish
edfr
om
on
ean
oth
er.R
e-ce
nt
app
arat
us
dev
elo
pm
ents
allo
wad
apta
tio
n
of
the
colu
mn
geo
met
ryto
physi
cal
dat
a,both
forp
uls
edco
lum
ns
and
rota
ry-a
git
ated
colu
mn
s.T
he
bo
un
dar
ies
are
thu
sn
olo
ng
erd
isti
nct
and
ag
ener
alfl
uid
-dy
nam
icd
escr
ipti
on
of
rela
ted
typ
eso
fap
par
atu
sis
feas
ible
.T
he
op
tim
izat
ion
of
op
erat
ing
con
dit
ion
san
dth
eg
eom
etry
of
the
inte
rnal
sis
aseq
ual
lyim
po
rtan
tas
the
sele
ctio
no
fa
suit
able
typ
eo
fap
par
atu
s.In
pra
ctic
eth
efi
nal
sele
ctio
no
feq
uip
men
tis
oft
enb
ased
on
pro
du
ct-s
pec
ific
con
dit
ion
so
rp
lan
tre
qu
irem
ents
wh
ich
incl
ud
ese
nsi
tiv
ity
toso
lid
s,te
nd
ency
of
the
pro
du
ctto
po
lym
eriz
e,an
dsa
fety
aspec
ts,
for
exam
ple
wit
hre
gar
dto
solv
ent
ho
ldu
p.
Un
typ
ica
lO
per
ati
ng
Co
nd
itio
ns.
Usu
ally
extr
acto
rso
per
ate
wit
hn
earl
yth
esa
me
vo
l-u
me
flow
for
bo
thli
qu
ids
and
for
liq
uid
sw
ith
vis
cosi
ties
sim
ilar
toth
ato
fw
ater
.T
her
efo
re,
the
equ
atio
ns
giv
enb
efo
rear
eo
nly
val
idfo
rsu
chco
nd
itio
ns.
So
me
app
roac
hes
for
un
typ
ical
op
erat
ing
con
dit
ion
sar
eg
iven
bel
ow
.R
au
sch
er
[62]in
ves
tigat
edpuls
edsi
eve
tray
extr
acto
rsw
ith
ph
ase
rati
os
bet
wee
n0
.06
and
10
and
the
liq
uid
syst
emn
-bu
tylac
etat
e(o
)–
wat
er(d
)–
met
hyl
isopro
pyl
ket
one
(MIP
K),
whic
hen
rich
esM
IPK
ineq
uil
ibri
um
pre
fera
ble
inth
eorg
anic
phas
e.H
eco
nfi
rmed
the
exper
ience
that
the
sep
arat
ion
effi
cien
cyd
ecli
nes
for
ph
ase
ra-
tio
su
neq
ual
1an
dfo
un
dth
efo
llow
ing
cau
ses:
By
dis
per
sio
no
fth
esm
alle
rvo
lum
efl
ow
(ph
ase
rati
o≪
1),
stro
ng
erb
ack
mix
ing
of
dro
ple
tsb
yth
eco
nti
nu
ou
sp
has
ew
ill
occ
ur,
lead
ing
toa
bro
ader
dro
psi
zed
istr
ibu
tio
n.
By
dis
per
sio
no
fth
ela
rger
vo
lum
efl
ow
(ph
ase
rati
o≫
1),
the
wak
eb
ehin
dth
ed
rop
sca
use
sre
mar
kab
leb
ack
-m
ixin
go
fco
nti
nu
ou
sp
has
e.T
hes
ep
hen
om
ena
hav
eto
be
taken
into
acco
un
tb
yan
adeq
uat
eca
lcu
lati
on
via
dro
pp
op
ula
tio
nb
alan
ces.
G.
Wagn
er
[58]
inves
tigat
edth
efl
uid
dy-
nam
ics
of
pu
lsed
siev
etr
ayan
dK
uh
ni
rota
tin
gex
trac
tors
usi
ng
liq
uid
syst
ems
wit
hv
isco
siti
esu
pto
50
mP
a·s
,m
ixed
fro
mp
araf
fin
oil
and
n-h
exan
eas
org
anic
phas
ean
dof
gly
cero
lan
dw
ater
asaq
ueo
us
ph
ase.
I.W
agn
er
[77
]co
n-
tinued
the
work
wit
hm
ass
tran
sfer
inves
tiga-
tio
ns
usi
ng
the
syst
emtr
idec
ano
las
dro
pp
has
e(η
=4
2m
Pa·s
),w
ater
,an
dp
rop
ano
l.T
he
exp
er-
imen
tssh
ow
edth
atth
em
ean
Sau
ter
dro
pd
i-am
eter
incr
ease
sw
ith
incr
easi
ng
dro
pv
isco
sity
;h
old
up
isd
ecre
ased
,w
hil
eth
efl
oo
din
gcu
rve
issh
ifte
dto
hig
her
thro
ug
hp
uts
.In
case
the
36
Liq
uid
–Liq
uid
Extr
action
con
tin
uo
us
ph
ase
isth
em
ore
vis
cou
so
ne,
the
dro
psw
arm
con
tain
sa
larg
erfr
acti
on
of
smal
ld
rop
lets
cau
sin
gin
crea
sed
dro
ple
ten
trai
nm
ent
by
the
con
tin
uo
us
ph
ase.
Inst
irre
dco
lum
ns,
the
dro
psi
zeca
nb
ein
flu
ence
din
ab
road
erra
ng
eth
anin
pu
lsed
colu
mn
s;y
et,m
ore
ener
gy
wil
lb
ere
qu
ired
for
ace
rtai
nd
rop
dis
per
sio
n.In
ten
sive
stir
rers
asin
Ku
hn
ian
dQ
VF
extr
acto
rssh
ou
ldb
ep
refe
rred
tost
irre
rsin
RD
Cex
trac
tors
.In
the
case
of
am
ore
vis
cou
sco
nti
nu
ou
sp
has
e,th
ed
rop
dis
per
sio
nis
nea
rly
ind
epen
den
to
fd
rop
vis
cosi
tyan
dis
har
dly
infl
uen
ced
by
the
rota
tin
go
rp
uls
atin
gin
tern
als.
Her
e,lo
wer
in-
ten
sity
dis
per
sers
are
pre
fera
ble
,su
chas
RD
Cex
trac
tors
.T
he
mas
str
ansf
erto
dro
ps
isd
isti
nct
lyd
e-cr
ease
db
yin
crea
sin
gd
rop
vis
cosi
ty,d
evel
op
ing
tow
ard
sth
est
ate
of
tran
sfer
tori
gid
sph
eres
,an
dd
epen
ds
on
the
con
tact
tim
e.It
can
be
imp
roved
by
suit
able
inte
rnal
san
db
ysu
pp
lyo
fen
erg
y.
4.
Ph
ase
-Sep
ara
tion
Eq
uip
men
t
4.1
.G
rav
ity
Set
tler
sw
ith
ou
tIn
sert
s
Eac
hex
trac
tio
nst
age
con
sist
so
ftw
ost
eps:
(1)
dis
per
sin
gan
d(2
)p
has
ese
par
atio
nb
yco
ales
-ce
nce
of
dro
ps,
thu
sg
ener
atin
ga
ho
mo
gen
eou
sla
yer
of
dro
pp
has
e.F
igu
re3
9A
show
sa
ver
tica
lse
ttle
rat
the
top
of
aco
lum
nfo
rth
eca
seth
atth
ed
rop
ph
ase
has
alo
wer
den
sity
than
the
con
tin
-uous
phas
e.T
he
dro
ps
rise
agai
nst
the
sinkin
gco
nti
nu
ou
sli
qu
idan
dar
eb
lock
edb
yth
eu
pp
erle
vel
of
the
con
tin
uo
us
ph
ase,
wh
ich
isth
ep
rin
-ci
pal
inte
rfac
e.T
her
e,co
ales
cen
ceo
fth
ed
is-
per
sed
ph
ase
wil
lo
ccu
rb
oth
bet
wee
nad
jace
nt
dro
ps
and
atth
ep
rin
cip
alin
terf
ace.
Th
eco
a-le
sced
dro
pp
has
ele
aves
the
extr
acto
rat
the
top
of
the
colu
mn
.In
ah
ori
zon
tal
sett
ler,
assh
ow
nin
Fig
-u
re3
9B
,bo
thp
has
esfl
ow
inth
esa
me
dir
ecti
on
.D
rop
so
fli
gh
ter
dis
per
sed
ph
ase
rise
toth
ein
ter-
face
wh
ere
they
coal
esce
tofo
rma
ho
mo
gen
eou
sla
yer
.In
the
low
erp
art
of
the
sett
ler
ala
yer
of
the
con
tin
uo
us
ph
ase
rem
ain
s,g
row
ing
infl
ow
dir
ecti
on
du
eto
dec
reas
ing
dro
pn
um
ber
s.T
he
wed
ge-
shap
edzo
ne
of
dis
per
sio
nsh
ou
lden
db
e-fo
reth
ep
lace
men
to
fp
has
eo
utl
ets.
As
the
accu
mu
lati
on
of
imp
uri
ties
inte
ch-
nic
alli
qu
idsy
stem
sch
ang
esim
po
rtan
tp
rop
er-
ties
such
asv
isco
sity
and
surf
ace
ten
sio
n,an
ex-
clu
sivel
yth
eore
tica
lm
od
elin
g,as
dev
elo
ped
by
man
yau
tho
rs(s
eefo
rin
stan
ce[8
0])
,is
insu
ffi-
cien
t.H
ow
ever
,th
ele
ng
tho
fa
ho
rizo
nta
lse
ttle
rca
nb
ees
tim
ated
by
aco
mb
ined
pro
ced
ure
of
calc
ula
tio
ns
and
sim
ple
and
chea
pb
atch
sett
lin
gex
per
imen
ts[7
9].
Th
eca
lcu
lati
on
isb
ased
on
am
odel
of
the
physi
cal
pro
cess
esin
ase
ttle
r,w
hil
eex
per
imen
tssu
pp
lyo
ne
emp
iric
alp
aram
-et
erto
incl
ud
esu
rfac
ep
hen
om
ena
that
cou
ldn
ot
be
mo
del
edso
far
(see
Fig
s.4
0an
d4
1).
Ag
lass
cyli
nd
eras
show
nin
Fig
ure
40
A,
fill
edw
ith
abo
ut
1L
of
the
ori
gin
alli
qu
id–
liq
-u
idsy
stem
,is
vig
oro
usl
ysh
aken
for
1/2
to1
min
.Aft
erp
laci
ng
itin
anu
pri
gh
tp
osi
tio
n,t
he
hei
gh
tso
fse
dim
enta
tio
nan
dco
ales
cen
cefr
on
tsar
em
easu
red
ind
epen
den
ceo
fti
me
assh
ow
nin
Fig
ure
40
Bfo
rd
rop
sb
ein
gli
gh
ter
than
the
con
tin
uo
us
ph
ase.
Th
ed
rop
sar
eb
anked
up
ina
den
sela
yer
ifse
dim
enta
tio
nis
fast
erth
anth
ed
rop
coal
esce
nce
.T
he
curv
eso
fse
dim
enta
tio
nan
dco
ales
cen
cem
eetea
cho
ther
atti
me
t ew
hen
all
dro
ps
are
coal
esce
d.
Fo
ra
suffi
cien
tre
pro
-d
uci
bil
ity
of
mea
sure
men
tsit
sho
uld
be
mad
esu
reth
atth
eg
lass
flas
kis
was
hed
wit
hd
eio
n-
ized
wat
er,
that
the
dis
trib
uti
on
of
dro
psi
zes
isn
arro
wan
dth
ete
mp
erat
ure
so
fth
eli
qu
id–
liq
-u
idsy
stem
inth
eg
lass
cyli
nd
eran
dth
eco
nti
nu
-o
us
sett
ler
are
equ
al[7
8].
Fig
ure
37
Csh
ow
sth
eh
eig
htH
of
the
wed
ge-
shap
edzo
ne
bet
wee
nth
ecu
rves
of
sed
imen
tati
on
and
coal
esce
nce
.T
he
con
cep
to
fse
ttle
rd
imen
sio
nin
gis
show
nin
Fig
ure
41
.A
lleq
uat
ion
sm
enti
on
edin
the
fol-
low
ing
are
giv
enin
[79
].S
ettl
erd
imen
sio
nin
gst
arts
wit
hev
alu
atio
no
fse
ttli
ng
exp
erim
ents
ac-
cord
ing
toF
igu
re4
1A
.T
he
lin
ear
curv
eo
fse
d-
imen
tati
on
sup
pli
esth
evel
oci
tyo
fse
dim
enta
-ti
on
;a
mo
del
of
dro
psw
arm
sed
imen
tati
on
sup
-p
lies
the
dia
met
ero
fth
est
arti
ng
dro
psw
arm
[66
].T
he
thic
kn
ess
of
the
den
sela
yer
of
dro
ps
foll
ow
sfr
om
ab
alan
ceo
fse
dim
enti
ng
and
co-
ales
cin
gd
rop
sin
tim
est
eps.
Th
en
ext
stag
eis
calc
ula
tio
no
fd
rop
def
orm
atio
nin
ver
tica
lst
eps
[80
].T
his
serv
esto
calc
ula
teco
ales
cen
ceti
mes
bet
wee
nd
rop
san
db
etw
een
dro
ps
and
thei
rh
om
op
has
e,th
efo
rmer
tod
eter
min
eth
ed
rop
gro
wth
,th
ela
tter
toca
lcu
late
the
dro
ph
o-
mo
ph
ase
form
edb
yco
ales
cen
ce[8
0].
Th
eco
a-le
scen
cem
od
elco
nta
ins
afi
ttin
gp
aram
eter
Fp
tofi
tth
eca
lcu
late
dan
dm
easu
red
coal
esce
nce
curv
ein
Fig
ure
41
B.
Th
isp
aram
eter
isth
eli
nk
bet
wee
nth
ese
ttli
ng
exp
erim
ent
and
the
sett
ler
Liq
uid
–Liq
uid
Extr
action
37
Fig
ure
39.
Ver
tica
l(A
)an
dhori
zonta
l(B
)gra
vit
yse
ttle
rsfo
rdro
pse
par
atio
nfr
om
aco
nti
nuous
liquid
Fig
ure
40.
Exper
imen
tson
bat
chse
ttli
ng
dim
ensi
on
ing
;F
pca
nb
eu
sed
for
the
sett
ler
cal-
cula
tio
n,
giv
enin
Fig
ure
41
B.
Th
ese
ttle
rn
eed
san
inle
tle
ng
thL
inw
hic
hca
nb
eca
lcu
late
db
ya
mo
del
equ
atio
nin
dep
en-
den
ceo
nse
ttle
rd
iam
eter
,o
per
atio
np
aram
eter
s,an
dth
em
ean
dro
psi
zeat
the
sett
lerin
let,
com
ing
fro
mth
eex
trac
tor
ou
tlet
.Fo
rca
lcu
lati
on
of
coa-
lesc
ence
inth
ed
ense
dro
pla
yer
the
sam
eeq
ua-
tio
ns
that
wer
em
od
eled
for
the
sett
lin
gex
per
i-m
ent
can
be
app
lied
usi
ng
the
fitt
ing
par
amet
erF
pd
eriv
edfr
om
thes
eex
per
imen
ts.
Th
ere
sult
isth
eg
eom
etry
of
the
wed
ge
of
dis
per
sio
n,i.
e.,
its
hei
gh
tan
dle
ng
th,w
hic
hh
asto
be
taken
into
acco
un
tfo
rd
imen
sio
nin
gth
ese
ttle
r.T
his
com
bin
edex
per
imen
tal
and
theo
reti
cal
pro
ced
ure
yie
lds
go
od
resu
lts
alth
ou
gh
the
dro
pd
istr
ibu
tio
ns
inth
ese
ttli
ng
exp
erim
ent
and
the
real
sett
ler
are
no
tth
esa
me.
Th
eex
ten
sive
equ
a-ti
on
syst
emn
eed
sco
mp
ute
rai
ded
solv
ing
.A
com
pu
ter
pro
gra
mis
off
ered
by
[81
].A
sim
pli
-fi
edm
eth
od
isg
iven
in[7
9].
4.2
.S
ettl
ers
wit
hC
oa
lesc
ing
Aid
s
Gra
vit
yse
ttle
rsar
eo
ften
equ
ipp
edw
ith
coal
esc-
ing
aid
sto
fita
sett
ler
tosp
ecia
lco
nd
itio
ns
of
the
liq
uid
syst
emo
ro
fth
eo
per
atio
nal
beh
avio
r.In
-d
ust
rial
lyp
roven
coal
esci
ng
aid
sar
ein
clin
edo
rco
rrugat
edpla
tes,
fixed
bed
sof
smal
lpac
kin
gs,
fib
erb
eds,
po
rou
ssi
nte
red
mat
eria
ls,an
dm
em-
bra
nes
.In
som
eca
ses,
wh
enth
ed
rop
size
sto
be
sett
led
are
smal
ler
than
1µ
mo
rif
surf
acta
nts
ren
der
the
sett
lin
gm
ore
dif
ficu
lt,ce
ntr
ifu
ges
[6,
Ch
ap.8
]o
rel
ectr
ical
fiel
ds
mu
stb
eap
pli
ed[8
2].
Th
em
ost
imp
ort
antco
ales
cin
gai
ds
are
incl
ined
pac
kag
esof
pla
inor
corr
ugat
edpla
tes
and
fiber
bed
filt
ers.
38
Liq
uid
–Liq
uid
Extr
action
Fig
ure
41.
Dim
ensi
on
ing
aco
nti
nu
ou
sse
ttle
r[7
9]
A)
Eval
uat
ion
of
sett
lin
gex
per
imen
ts;
B)
Fit
tin
go
fm
easu
red
and
calc
ula
ted
curv
e
Incl
ined
Pla
tes.
Fig
ure
42
show
so
ne
po
ssi-
ble
arra
ng
emen
to
fin
clin
edp
late
sin
ah
ori
zon
-ta
lse
ttle
r.O
ther
pla
teco
nfi
gu
rati
on
sar
ep
oss
i-b
le.
Inan
yca
se,
the
feed
has
tob
ed
istr
ibu
ted
by
asi
eve
pla
teat
the
sett
ler
entr
yover
the
cro
ss-s
ecti
on
alar
ea,
fill
edw
ith
incl
ined
pla
tes.
Th
ep
late
ssh
ort
enth
ese
dim
enta
tio
nd
ista
nce
of
dro
ps
and
pro
vid
ea
larg
erin
terf
acia
lare
afo
rth
eco
ales
cen
ce.
Th
ed
rop
sco
ales
cin
gat
the
pla
tes
form
tric
kli
ng
film
sw
hic
hfl
ow
off
toth
eh
or-
izo
nta
l,p
rin
cip
lein
terf
ace
du
eto
ahy
dro
stat
icp
ress
ure
dif
fere
nce
.Ap
late
mat
eria
lwet
tab
leb
yth
ed
rop
ph
ase
isa
pre
req
uis
ite.
Sev
eral
scie
n-
tifi
cin
ves
tigat
ions
and
exper
imen
tsw
ith
liquid
syst
ems
of
aw
ide
ran
ge
of
pro
per
ties
wer
em
ade
duri
ng
the
1970s
and
1980s
on
the
hydro
dynam
-ic
so
fin
clin
edfi
lms
and
the
coal
esce
nce
ofd
rop
s
atth
efi
lmsu
rfac
e,th
ese
are
sum
mar
ized
in[8
3–
86
].T
he
mai
nre
sult
sar
e:
1)
Th
inla
min
arfi
lms
sho
uld
flow
on
the
pla
tes,
bec
ause
the
coal
esce
nce
of
dro
ps
isp
rom
ote
db
yth
esh
ear
stre
sso
ffi
lmfl
ow
nea
rth
ep
late
;th
ela
rger
the
vo
lum
efl
ow
of
cocu
rren
tco
nti
nu
ou
sp
has
e,th
esm
alle
rth
efi
lmth
ick
nes
san
dth
eb
ette
rth
eco
ales
-ce
nce
.2
)T
he
pla
tesh
ou
ldb
ew
etta
ble
by
the
dro
pp
has
e(a
dvan
cin
gco
nta
ctan
gle
<7
0◦,
re-
ced
ing
con
tact
ang
le>
15◦).
3)
Th
ed
rop
swar
mh
asto
be
dis
trib
ute
deq
ual
lyover
the
wid
tho
fp
late
s.4
)C
on
stru
ctio
ns
that
can
thin
the
tric
kli
ng
film
incr
ease
the
sett
ler
per
form
ance
.
Liq
uid
–Liq
uid
Extr
action
39
5)
Sh
ort
len
gth
so
fp
late
so
fab
ou
t4
00
mm
are
suffi
cien
tfo
rco
ales
cen
ceo
fd
rop
sri
din
go
nth
efi
lm.
6)
Th
ew
idth
bp
of
ap
late
can
be
calc
ula
ted
by
the
emp
iric
aleq
uat
ion
of
the
Rey
no
lds
nu
mb
ero
ftr
ick
lin
gfi
lm
Re f≤
80K
0.1
9L
,d
b p=
0.0
3Vd
(Re f
kvd)3
/2
[
∆gsi
nα
ηd
]
wit
hth
eli
qu
idn
um
ber
of
tric
kli
ng
film
KL
,d=
σ3d
gη4 d
d
∆
wh
ereα
isth
ep
late
incl
inat
ion
,Vd,1
=V
d/n
the
vo
lum
efl
ow
of
dis
per
sed
ph
ase
on
ap
late
,an
dn
the
nu
mb
ero
fp
late
s.7
)T
he
op
tim
um
of
pla
tein
clin
atio
nis
wit
hin
the
ran
ge
10◦<
α<
15◦.
8)
Th
ed
ista
nce
of
adja
cen
tp
late
ssh
ou
ldn
ot
be
smal
ler
than
30
to4
0m
min
ord
ern
otto
dis
turb
film
flow
and
dro
pco
ales
cen
ce.
9)
Th
etr
ick
lin
gfi
lmco
nti
nu
ou
sly
carr
ies
sur-
fact
ants
toth
eo
utfl
ow
of
ap
late
and
thu
sp
reven
tsth
eirac
cum
ula
tio
n.T
her
efo
resu
r-fa
ctan
tsh
ard
lyin
flu
ence
coal
esce
nce
and
sett
lin
gp
erfo
rman
ceu
pto
med
ium
flow
rate
so
fd
rop
ph
ase.
10
)U
nd
erce
rtai
nco
nd
itio
ns,
the
dro
pco
a-le
scen
cele
aves
ver
ysm
all
dro
ple
ts,
so-
call
edse
con
dar
yd
rop
s,d
ue
top
arti
alco
a-le
scen
ce,w
hic
hg
ener
ate
ad
rop
leten
trai
n-
men
tatt
he
sett
ler
exit
.Its
occ
urr
ence
isp
ri-
mar
ily
aq
ues
tio
no
fli
qu
ids
invo
lved
,i.
e.,
thei
rv
isco
sity
rati
o[8
6].
Th
eco
ales
cen
ceti
me
of
seco
nd
ary
dro
ps
issi
gn
ifica
ntl
yh
igh
erth
anth
ato
fp
rim
ary
dro
ps,
du
eto
inte
rfac
ial
effe
cts.
Set
tlin
go
fse
con
dar
yd
rop
sre
qu
ires
oth
erco
ales
cers
,fo
rin
stan
cem
emb
ran
eco
ales
cers
or
cen
trif
ug
es.
Fib
erb
edfi
lter
sar
ebu
ilt
fro
msh
ort
fib
ers
stu
ffed
tore
ctan
gu
lar
mat
so
rto
dis
ks
of
15
to2
5m
mth
ick
nes
s,h
eld
ina
suit
able
sup
po
rt,
or
fro
mfi
ber
flee
ces
assh
ow
nin
Fig
ure
43
.T
hey
hav
ea
defi
nit
e,la
rge
vo
idag
eo
fab
ou
t9
5%
,nev
erth
eles
sth
eyar
ese
nsi
tive
toso
lid
dir
tp
arti
cles
inth
eli
qu
id.T
he
dro
ple
tsco
up
leto
the
fib
ers
wh
ile
flow
ing
thro
ug
hth
efi
ber
bed
,su
c-ce
edin
gd
rop
sco
ales
cew
ith
them
and
enla
rge
the
size
of
adh
erin
gd
rop
su
nti
lth
eli
qu
idfl
ow
pu
lls
them
ou
to
fth
eb
edd
ue
toin
crea
sin
gfl
ow
resi
stan
ce.A
fib
erb
edis
able
toen
larg
eth
esi
zes
of
inco
min
gd
rop
sat
leas
tb
yo
ne
ord
ero
fm
ag-
nit
ud
eso
that
they
can
coal
esce
ina
sub
seq
uen
tse
ttle
rw
ith
thei
rh
om
op
has
e.F
iber
bed
filt
ers
are
rest
rict
edto
dro
pco
nce
ntr
atio
ns<
10
vo
l%to
avo
idre
dis
per
sio
n.
Rebelein
[87
],[8
8]
and
Magie
ra
[89
],[9
0]
defi
ned
heu
rist
icru
les
forth
ed
esig
no
ffi
ber
bed
so
nth
eb
asis
of
care
fulex
per
imen
tsw
ith
ab
road
var
iati
on
of
par
amet
ers
of
infl
uen
ce:
1)
Fib
erm
ater
ials
asg
lass
or
stai
nle
ssst
eel
wit
hh
igh
ener
get
icsu
rfac
esp
rov
ide
dif
fer-
ent
inte
ract
ion
site
s(e
.g.,
hydro
gen
bonds
and
ion
–d
ipo
lein
tera
ctio
n)
for
the
liq
uid
and
imp
rove
the
fib
erb
edp
erfo
rman
ceco
m-
par
edto
mat
eria
lsw
ith
low
ener
get
icsu
r-fa
ces
asfo
rin
stan
cete
flo
n.
Hig
hen
erg
etic
surf
aces
imp
rove
the
wet
tin
gp
rop
erti
eso
fth
efi
ber
s.2
)T
he
dro
pen
larg
emen
tin
afi
ber
bed
de-
crea
ses
wit
hin
crea
sin
gfl
ow
rate
,i.
e.,
wit
hsu
per
fici
alvel
oci
ties
>1
cm/s
.3
)S
mal
lfi
ber
dia
met
ers
of
abo
ut
15
µm
are
fa-
vo
rab
le.
4)
Th
eb
edd
epth
req
uir
edfo
rco
ales
cen
cein
-cr
ease
sw
ith
the
fib
erd
iam
eter
.5
)T
he
con
cen
trat
ion
of
dro
ple
tsin
the
inco
m-
ing
liq
uid
har
dly
infl
uen
ces
the
bed
per
for-
man
ce.
6)
Bes
tef
fici
ency
mea
ns
ase
par
atio
no
fab
ou
t9
5%
of
inco
min
gd
rop
s.7
)T
he
larg
erth
esu
rfac
ete
nsi
on
of
the
liq
-u
idsy
stem
,th
eb
ette
rth
ese
par
atio
np
erfo
r-m
ance
.8
)S
mal
lest
dro
psi
zes
that
can
be
sep
arat
edar
eab
ou
t1
0µ
m.
9)
Pre
sen
ceo
fsu
rfac
tan
tsan
dm
ud
and
ah
igh
erv
isco
sity
of
the
con
tin
uo
us
ph
ase
red
uce
the
sep
arat
ion
per
form
ance
,th
ev
isco
sity
of
the
dro
pp
has
eh
asn
oin
flu
ence
wit
hin
50
and
50
00
mP
a·s
.
All
atte
mp
tsto
calc
ula
teth
eb
edp
erfo
rman
cein
advan
cev
iafi
lter
coef
fici
ents
wer
efr
uit
less
[87
–9
0].
Magie
ra
dev
elo
ped
am
ath
emat
ical
model
of
physi
calm
echan
ism
sin
side
afi
ber
bed
and
was
able
tosi
mu
late
the
bed
beh
avio
ran
dd
rop
enla
rgem
ent
by
intr
od
uct
ion
of
two
exp
er-
imen
tal
fitt
ing
par
amet
ers.
Th
eref
ore
,a
reli
able
dim
ensi
on
ing
of
fib
erb
eds
nee
ds
exp
erim
ents
40
Liq
uid
–Liq
uid
Extr
action
Fig
ure
42.
Hori
zonta
lg
rav
ity
sett
ler
wit
htw
oin
clin
edp
ack
ages
of
pla
ne,
par
alle
lp
late
s.T
he
hei
gh
to
fp
rin
cip
alin
terf
ace
isbes
tsi
tuat
ed,w
hen
bo
thp
has
esh
ave
the
sam
eex
itvel
oci
ty
Fig
ure
43.
Com
bin
edfi
ber
bed
coal
esce
ran
dg
rav
ity
sett
ler
wit
hth
eli
qu
idd
isp
ersi
on
wh
ich
isto
be
sep
a-ra
ted
.
Fig
ure
44.
Mem
bra
ne
coal
esce
r[9
1]
Mem
bra
ne
Co
ale
scen
ce.
An
ewan
dver
yp
rom
isin
gm
eth
od
tose
par
ate
fin
ed
rop
lets
dow
nto
1µ
mfr
om
emu
lsio
ns,
stab
iliz
edb
ysu
rfac
-ta
nts
,w
asdis
cover
edan
din
ves
tigat
edby
Hoff-
man
n[9
1]
(Fig
.44
).M
emb
ran
eco
ales
cers
are
app
lica
ble
ina
bro
adra
ng
eo
fvo
lum
eco
nce
ntr
atio
ns
dow
nto
alo
wer
conce
ntr
atio
nli
mit
of
the
org
anic
phas
e(0
.1vo
l%).
Ath
in,
hydro
phobic
,st
retc
hed
mem
bra
ne,
for
inst
ance
po
lyte
trafl
uo
roet
hy
len
e(P
TF
E),
hel
din
pla
ceb
ya
sup
po
rt,
isp
erm
e-at
edb
ytw
o-p
has
efl
ow
of
emu
lsio
n.
Th
eem
ul-
sio
nle
aves
the
mem
bra
ne
asa
liq
uid
foam
wit
hla
rge
oil
do
mai
ns
wh
ich
wil
lim
med
iate
lyco
-al
esce
atth
ep
rin
cip
lein
terf
ace
ina
succ
eed
-in
gse
ttle
r.A
sup
erfi
cial
vel
oci
tyth
rou
gh
the
mem
bra
ne
isp
oss
ible
wit
hin
the
ran
ge
of
0.1
to1
9cm
/s,t
he
pre
ssu
red
rop
isco
mp
arab
lew
ith
that
infi
ber
bed
s.T
he
mai
nad
van
tag
esar
eh
ug
ese
par
atio
np
erfo
rman
ces
of
abo
ut9
8%
,in
com
-b
inat
ion
wit
ha
larg
era
ng
ein
thro
ug
hp
ut;
the
Liq
uid
–Liq
uid
Extr
action
41
abil
ity
tose
par
ate
dro
ple
tso
ne
ord
ero
fm
ag-
nit
ud
esm
alle
rth
anin
fib
erb
eds;
and
the
in-
sensi
tivit
yag
ainst
hydro
phobic
surf
acta
nts
.H
y-
dro
ph
ilic
surf
acta
nts
are
wit
ho
ut
infl
uen
ce,
too
,if
thei
ram
ou
nt
iscl
earl
ylo
wer
than
the
crit
ical
mic
elle
con
cen
trat
ion
.
Sel
ecti
on
of
Ap
pro
pri
ate
Set
tler
.M
ost
im-
po
rtan
tan
dth
efi
rst
step
inse
lect
ion
of
ase
ttle
ris
aca
refu
lan
aly
sis
of
sep
arat
ion
pro
ble
ms
[78
],[9
2].
Th
efl
ow
shee
to
fth
eco
mp
lete
pro
cess
can
giv
eh
ints
on
ori
gin
and
kin
do
fth
ed
isp
ersi
on
tob
ese
par
ated
.S
om
etim
esth
ep
rece
din
gst
eps
cou
ldb
eal
tere
din
ord
erto
sim
pli
fyth
ep
has
ese
par
atio
np
rob
lem
.Mea
sure
men
tso
fp
rop
erti
eso
fth
eli
qu
idsy
stem
and
sett
lin
gex
per
imen
tsin
agla
sscy
linder
show
,if
and
why
aphas
ese
par
a-ti
on
can
be
pro
ble
mat
ic.D
rop
size
ssm
alle
rth
an1
00
µm
nee
dsu
itab
leco
ales
cin
gai
ds
wh
ich
are
sup
po
sed
tob
ew
ell
wet
tab
leb
yth
ed
rop
ph
ase.
Wh
enth
ed
rop
sett
lin
gin
ag
lass
cyli
nd
eris
fast
,bu
tth
eli
qu
ids
app
ear
clo
ud
y,th
isin
dic
ates
par
-ti
alco
ales
cen
ce,
resu
ltin
gin
ver
yfi
ne
dro
ps,
soth
ata
fib
erb
edo
ra
mem
bra
ne
coal
esce
rw
ill
be
nec
essa
ry.
Th
ep
rese
nce
of
soli
dp
arti
cles
and
mu
dre
-q
uir
esfi
lter
sb
efo
reth
ese
ttle
r.T
he
wet
tin
gb
ehav
ior
of
coal
esci
ng
aid
sca
nsi
gn
ifica
ntl
ych
ang
eth
eo
per
atio
no
fth
ep
roce
ss.T
his
sho
uld
be
acco
un
ted
for
inth
ep
rocc
es.
Th
ep
has
era
-ti
oca
nb
ech
ang
edb
yre
cycl
ing
of
on
ep
has
eto
the
sett
ler.
By
this
,th
ety
pe
of
dis
per
sio
nca
nb
ein
ver
ted.
Inca
seth
eorg
anic
phas
ehas
ahig
her
vis
cosi
tyth
anth
ew
ater
ph
ase,
ano
/wd
isp
ersi
on
sep
arat
esm
uch
bet
ter
than
aw
/od
isp
ersi
on
,an
dv
ice
ver
sa.
5.
Liq
uid
–L
iqu
idE
xtr
act
ion
Pro
cess
es
5.1
.G
ener
al
Th
eq
ual
ity
of
the
raffi
na
tein
liq
uid
–li
qu
idex
-tr
acti
on
can
be
con
tro
lled
easi
lyb
ych
ang
ing
the
rati
oo
fso
lven
tto
feed
and
the
extr
acti
on
tem
-p
erat
ure
.T
he
qu
alit
yo
fth
eex
tra
ctis
gover
ned
on
lyb
yth
eco
nd
itio
ns
of
feed
loca
tio
nan
dn
od
irec
tco
ntr
ol
isp
oss
ible
.T
his
ises
pec
iall
ytr
ue
bec
ause
mo
stex
trac
-ti
on
sar
eca
rrie
do
ut
ina
clo
sed
syst
emto
min
-im
ize
solv
ent
req
uir
emen
ts.
Insu
cha
syst
em,
a
max
imu
mex
trac
tp
uri
tyis
ob
tain
able
and
som
eco
mp
on
ents
that
sho
uld
end
up
inth
era
ffin
ate
leav
ew
ith
the
extr
act.
Ad
dit
ion
alst
eps
are,
ther
efo
re,
req
uir
edto
enh
ance
extr
act
pu
rity
and
thu
sra
ffin
ate
yie
ld.
Ifth
eex
trac
tis
the
pro
du
ctd
esir
ed,
imp
rov
ing
extr
act
pu
rity
isth
em
ost
imp
ort
ant
–in
fact
,th
eo
nly
–o
bje
ctiv
e.D
iffe
ren
tso
luti
on
sto
this
pro
ble
mar
eap
pli
edin
com
mer
cial
op
erat
ion
.
Ch
an
ge
inT
emp
era
ture
.E
xtr
actp
uri
tyca
nb
ein
crea
sed
by
coo
lin
gth
eex
trac
tfr
om
the
mai
nsy
stem
and
add
ing
on
em
ore
stag
e(s
eeF
ig.4
5A
).In
the
tria
ng
ula
rd
iag
ram
,th
ism
ean
sth
atth
eb
ino
dal
curv
eis
chan
ged
fro
ma
tob
(Fig
.45
B).
Bec
ause
the
com
po
siti
on
of
the
firs
tex
trac
tis
now
insi
de
bin
od
alcu
rve
b,
itse
par
ates
ina
sett
ler
bin
ap
ure
rfi
nal
extr
actp
has
ean
da
smal
lam
ou
nt
of
inte
rmed
iate
raffi
nat
ep
has
e.T
he
lat-
ter
isre
turn
edto
the
mai
nex
trac
tio
nsy
stem
.T
he
sele
ctiv
ity
of
sep
arat
ion
inth
ead
dit
ion
alst
age
isn
ot
ver
yg
reat
bec
ause
the
load
ing
of
the
firs
tex
trac
tp
has
eis
rath
erh
igh
and
sep
ara-
tio
nta
kes
pla
cen
ear
the
pla
itp
oin
t.T
his
syst
emca
nb
eu
sed
wh
enth
em
ain
syst
emis
op
erat
edat
hig
hte
mp
erat
ure
for
oth
erre
aso
ns
or
wh
enan
incr
ease
inex
trac
tp
uri
tyan
dth
ere
sult
ant
incr
ease
inra
ffin
ate
yie
ldar
ed
esir
able
.
Ad
dit
ion
of
Wa
ter.
Th
ead
dit
ion
of
wat
erat
or
bel
ow
the
feed
po
int
gen
eral
lych
ang
esth
esy
stem
fro
ma
clo
sed
toan
op
eno
ne
(see
Sec
-ti
on
2.1
.1.)
.In
this
way
,ex
trac
tp
uri
tyca
nb
ein
crea
sed
toth
ere
qu
ired
level
.W
ater
isso
lub
le,
atle
ast
toso
me
exte
nt,
inm
ost
po
lar
solv
ents
and
ther
efo
rele
aves
the
syst
emw
ith
the
fin
alex
trac
tp
has
e.In
this
way
,n
ou
nw
ante
din
flu
-en
ceis
exer
ted
on
the
mai
nex
trac
tio
nsy
stem
.H
ow
ever
,b
ecau
sew
ater
mu
stb
ese
par
ated
fro
mth
eso
lven
tb
yd
isti
llat
ion
bef
ore
its
rein
-tr
od
uct
ion
inth
em
ain
extr
acto
r,th
eh
eatr
equ
ire-
men
tsar
eh
igh
.A
dd
itio
no
fw
ater
is,
ther
efo
re,
not
regar
ded
asa
gen
eral
lyat
trac
tive
solu
tion.
Als
o,
wat
erca
no
nly
be
add
edw
hen
its
bo
ilin
gp
oin
tis
mu
chlo
wer
than
tho
seo
fth
eso
lven
tan
dth
efe
edst
ock
.
Use
of
aC
ou
nte
rso
lven
t.A
ssh
ow
nin
Fig
-u
re4
6,a
seco
nd
solv
entca
nb
efe
din
too
ne
end
of
the
extr
acti
on
syst
em,o
nth
eo
pp
osi
tesi
de
of
42
Liq
uid
–Liq
uid
Extr
action
Fig
ure
45.
Use
of
coo
lin
gst
age
A)
Pro
cess
flow
schem
e:a)
Ex
trac
tor;
b)
Set
tler
B)
Tri
angula
rdia
gra
m:
a)B
ino
dal
curv
eat
hig
her
tem
per
atu
re;
b)
Bin
od
alcu
rve
atlo
wer
tem
per
atu
re
the
solv
ent
entr
yp
oin
t.T
he
feed
inth
isca
seis
intr
od
uce
dso
mew
her
ein
the
mid
dle
of
the
sys-
tem
.
Fig
ure
46.
Extr
acto
rfo
rse
par
atio
nu
sin
ga
cou
nte
rso
lven
t(a
)E
xtr
acto
r
Th
eco
un
ters
olv
ent
sho
uld
be
on
lysl
igh
tly
solu
ble
inth
eso
lven
tan
d,th
eref
ore
isg
ener
ally
sim
ilar
inch
emic
alst
ruct
ure
toth
ekey
com
-p
on
ent
of
the
raffi
nat
ep
has
e.T
he
bo
ilin
gp
oin
to
fth
eco
un
ters
olv
ent
sho
uld
be
such
that
itca
nea
sily
be
sep
arat
edb
yd
isti
llat
ion
fro
mth
eso
l-ven
tas
wel
las
fro
mth
era
ffin
ate
and
the
extr
act
(i.e
.,ei
ther
am
uch
low
ero
ra
mu
chh
igh
erb
oil
-in
gp
oin
t).B
ecau
seth
eco
un
ters
olv
ent
do
esn
ot
con
tain
any
raffi
nat
eco
mp
on
ents
wh
enit
ente
rs,
itca
nw
ash
ou
tth
era
ffin
ate
com
po
nen
tsin
the
solv
ent
atth
efe
edp
oin
t.A
dd
itio
nal
ly,
som
eex
trac
tco
mp
on
ents
are
was
hed
bac
kb
yth
eco
un
ters
olv
ent,
thu
sin
crea
s-in
gth
elo
adin
the
top
sect
ion
.In
this
way
,aver
yp
ure
fin
alex
trac
tcan
be
pro
du
ced
,dep
end
ing
on
the
rati
oo
fco
un
ters
olv
ent
tofe
edu
sed
.A
dis
advan
tag
eo
fth
issy
stem
isth
atth
eco
un
-te
rso
lven
ten
ters
the
top
sect
ion
.C
on
seq
uen
tly,
the
ph
ase
rati
oo
fB
-ric
hto
A-r
ich
ph
ase
isre
-d
uce
d,r
esu
ltin
gin
ale
ssp
ure
raffi
nat
e(t
his
also
mea
ns
alo
wer
yie
ldo
fex
trac
t).T
ore
sto
rera
ffi-
nat
ep
uri
ty,m
ore
B-r
ich
ph
ase
mu
stb
eap
pli
ed.
Su
cha
syst
emis
thu
sco
stly
and
sen
siti
ve
toch
ang
esin
feed
com
po
siti
on
,so
lven
t-to
-fee
dra
-ti
o,
and
rati
oo
fco
un
ters
olv
ent
tofe
ed.
So
me
imp
rovem
ent
can
be
ob
tain
edb
yca
r-ry
ing
ou
tth
eex
trac
tio
nin
two
par
ts(F
ig.4
7).
Inth
efi
rst
extr
acto
r(a
),th
efe
edis
extr
acte
dw
ith
the
pri
mar
yso
lven
t.T
he
inte
rmed
iate
ex-
trac
tp
has
eis
fed
toa
seco
nd
extr
acto
r(c
)an
d
Liq
uid
–Liq
uid
Extr
action
43
bro
ug
ht
inco
nta
ctw
ith
the
cou
nte
rso
lven
t.T
he
mix
ture
of
cou
nte
rso
lven
tan
din
term
edia
tera
f-fi
nat
eis
fed
toa
colu
mn
(b)
inw
hic
hth
ein
-te
rmed
iate
raffi
nat
ean
dth
eco
un
ters
olv
ent
are
sep
arat
edb
yd
isti
llat
ion
.T
he
pu
rein
term
edia
tera
ffin
ate
isth
enfe
dto
the
firs
tex
trac
tor,
wh
ile
the
cou
nte
rso
lven
tis
char
ged
toth
ese
con
dex
-tr
acto
r.In
this
way
,so
me
of
the
dis
advan
tag
esca
nb
eover
com
e.
Fig
ure
47.
Use
of
counte
rsolv
ent
wit
hin
term
edia
tere
cov-
ery
a)F
irst
extr
acto
r;b)
Dis
till
atio
nco
lum
n;
c)S
econd
extr
ac-
tor
5.2
.C
om
bin
edP
roce
sses
of
Ex
tra
ctio
n
an
dD
isti
lla
tio
n
Aze
otr
op
icD
isti
lla
tio
n.
Usu
ally
itis
nec
es-
sary
toco
mb
ine
extr
acti
on
and
dis
till
atio
np
ro-
cess
esfo
rre
cover
ing
the
solv
ent
fro
mth
eex
-tr
act
ph
ase
and
also
fro
mth
era
ffin
ate
ph
ase,
ifth
eso
lven
tis
solu
ble
inth
era
ffin
ate.
Fig
ure
48
show
sas
anex
amp
leth
ere
cover
yo
fac
etic
acid
fro
man
aqu
eou
sso
luti
on
wit
hm
ethyl
tert
-bu
tyl
eth
er(M
TB
E)
asso
lven
t.T
he
syst
emo
fw
ater
and
acet
icac
idis
ah
igh
lyn
on
-id
ealaz
eotr
op
icm
ixtu
reth
atco
uld
be
sep
arat
edb
ysi
mp
led
isti
llat
ion
.H
ow
ever
,fo
rd
ilu
tefe
edco
mp
osi
tio
ns
solv
ent
extr
acti
on
ism
ore
advan
-ta
geo
us
bec
ause
of
the
ver
yh
igh
ener
gy
dem
and
of
aw
ater
-ric
hfe
edd
isti
llat
ion
.T
he
tria
ng
ula
rd
iag
ram
of
Fig
ure
48
show
sth
atth
eb
inar
ysy
s-
tem
of
solv
entM
TB
Ean
dw
ater
has
ah
eter
og
e-n
eou
saz
eotr
op
e.A
sa
con
seq
uen
ce,
extr
acti
on
has
tob
eco
mb
ined
wit
haz
eotr
op
icd
isti
llat
ion
assh
ow
nin
the
flow
shee
to
fF
igu
re4
8B
.B
yex
trac
tio
nin
the
extr
acto
rE
extr
acti
on
feed
Fis
chan
ged
tora
ffin
ate
Ran
dth
eso
lven
tL
1to
extr
act
ph
ase
F1
,w
hic
ho
nth
eo
ther
han
dis
the
feed
of
dis
till
atio
nco
lum
nC
-1.
InC
-1th
eex
-tr
act
issp
lit
into
the
bo
tto
ms
acet
icac
idB
1an
dan
acet
icac
id-f
ree
dis
till
ate
D1
con
nec
ted
by
the
mai
nb
alan
celi
ne
of
dis
till
atio
nin
the
tria
n-
gle
dia
gra
m.
Th
eac
etic
acid
-fre
era
ffin
ate
Ris
fed
into
colu
mn
C-2
wh
ere
itis
sep
arat
edin
toth
eb
ott
om
s,p
ure
wat
erB
2an
dw
ater
–M
TB
Eaz
eotr
op
eD
2.
Bo
thd
isti
llat
esD
1an
dD
2li
ein
the
imm
isci
ble
reg
ion
bet
wee
nM
TB
Ean
dw
ater
.T
his
mak
essi
mp
led
ecan
tati
on
(S)
of
the
con
den
sed
ph
ases
po
ssib
le.T
he
solv
ent-
rich
frac
tio
nL
1is
no
tfu
rth
erp
uri
fied
sin
ceM
TB
Eas
solv
ent
nee
ds
no
tto
be
pu
re.
So
L1
can
be
recy
cled
dir
ectl
yto
the
extr
acto
rE
,a
par
to
fit
isu
sed
asre
flu
xfo
rC
-1.
Inco
lum
nC
-2a
mix
ture
of
wat
eran
dM
TB
Eh
asb
een
sep
arat
edin
top
ure
wat
eran
dM
TB
E–
wat
eraz
eotr
op
e.T
her
efo
re,
L2
,th
ew
ater
-ric
hp
has
efr
om
the
sett
ler,
can
also
be
fed
into
colu
mn
C-2
.T
he
econom
yof
the
hybri
dpro
cess
dep
ends
on
aca
refu
lo
pti
miz
atio
no
fo
per
atio
nal
and
con
stru
ctio
nal
par
amet
ers,
bes
ides
the
care
ful
sele
ctio
no
fth
eso
lven
t.R
ecen
tly,
mix
edin
te-
ger
no
nli
nea
rp
rog
ram
min
g(M
INL
P)
has
bee
nsu
cces
sfu
lly
intr
od
uce
din
op
tim
izat
ion
of
such
pro
cess
es[9
3],
[94
].M
INL
Pca
nb
eu
sed
asa
pro
cess
syn
thes
isto
ol.
Itis
nec
essa
ryto
gen
-er
ate
aso
-cal
led
super
stru
cture
of
the
hybri
dp
roce
ssw
hic
hco
nta
ins
avar
iety
of
alte
rnat
ive
flow
shee
ts.
Th
enM
INL
Pis
able
toch
oo
seth
eb
estso
luti
on
for
giv
enp
aram
eter
san
dal
sofr
om
com
pet
itiv
eu
nit
op
erat
ion
sli
ke
extr
acti
ve
dis
til-
lati
on
,p
roce
sses
wit
hm
ore
than
on
eso
lven
to
rp
roce
sses
wit
hre
extr
acti
on
for
solv
entre
cover
y.
Ex
tra
ctiv
eD
isti
lla
tio
n.
An
oth
erp
oss
ibil
ity
tose
par
ate
azeo
tro
pic
mix
ture
sis
extr
acti
ve
dis
-ti
llat
ion
.A
solv
ent
wit
ha
mu
chh
igh
erb
oil
-in
gp
oin
tth
anth
efe
edis
fed
atth
eto
po
fa
dis
till
atio
nco
lum
nto
entr
ain
on
eco
mp
on
ent
of
the
dis
till
atio
nfe
edth
aten
ters
the
colu
mn
atth
eb
ott
om
(→D
isti
llat
ion
and
Rec
tifi
cati
on
,C
hap
.6.5
.).T
he
com
bin
edsy
stem
ofli
qu
id–
liq
-u
idex
trac
tio
nan
dex
trac
tive
dis
till
atio
nis
ap-
pli
edin
nea
rly
allp
roce
sses
use
dto
man
ufa
ctu
re
44
Liq
uid
–Liq
uid
Extr
action
ver
yp
ure
lig
htar
om
atic
s.N
-Fo
rmy
lmo
rph
oli
ne
isa
suit
able
solv
ent
tose
par
ate
the
lig
ht
aro
-m
atic
sb
enze
ne
and
tolu
ene
use
das
feed
sto
ckfo
rth
ep
etro
chem
ical
ind
ust
ry[9
5–
10
0].
Du
eto
the
sele
ctiv
ity
of
N-f
orm
ylm
orp
ho
lin
e(N
FM
),ex
trem
ely
hig
hy
ield
so
fver
yp
ure
pro
du
cts
are
ob
tain
ed.
Fig
ure
48.
Tri
angula
rd
iag
ram
(A)
and
flow
shee
t(B
)o
fa
hybri
dex
trac
tion
–d
isti
llat
ion
pro
cess
for
sep
arat
ion
of
wat
eran
dac
etic
acid
wit
hM
TB
Eas
solv
ent
[93
]E
=ex
trac
tion;
C-1
,C
-2=
dis
till
atio
n;
S=
sett
lin
g;
H=
conden
ser
Asi
mp
lifi
edp
roce
ssfl
ow
sch
eme
for
N-
form
ylm
orp
ho
lin
eex
trac
tio
nis
giv
enin
Fig
-u
re4
9.
Fee
den
ters
the
extr
acto
rat
anap
pro
-p
riat
ep
oin
tin
the
bo
tto
mh
alf
of
the
colu
mn
.T
he
exac
tlo
cati
on
dep
end
so
nth
eco
mp
osi
tio
no
fth
efe
edan
dca
nb
eo
pti
miz
edfo
rea
chfe
ed-
sto
ck.
So
lven
ten
ters
atth
eto
po
fth
eex
trac
-to
rat
the
sele
cted
tem
per
atu
re.
Bec
ause
NF
Mh
asa
hig
hso
lven
tp
ow
er,
this
mu
sto
ften
be
re-
du
ced
by
add
itio
no
fw
ater
.In
gen
eral
,4
–1
0%
wat
eris
suffi
cien
tto
ensu
rea
low
solu
bil
ity
of
satu
rate
dhydro
carb
ons
whil
est
illm
ainta
inin
ga
hig
hso
lub
ilit
yo
far
om
atic
s.T
he
raffi
nat
ep
has
ele
avin
gth
eto
po
fth
eex
trac
tor
issa
tura
ted
wit
hso
lven
t.W
ash
ing
wit
hw
ater
has
pro
ved
tob
ea
sim
ple
and
effe
ctiv
em
ean
so
fre
cover
ing
dis
-so
lved
solv
ent.
Th
ew
ater
–so
lven
tmix
ture
fro
mth
isw
ash
ing
op
erat
ion
isch
arg
edto
the
bo
tto
mo
fth
em
ain
extr
acto
rto
incr
ease
the
wat
erco
n-
ten
to
fth
eso
lven
tp
has
eas
dis
cuss
edab
ove.
Th
eso
lven
t–ar
om
atic
sm
ixtu
refr
om
the
bo
t-to
mo
fth
eex
trac
tor
stil
lco
nta
ins
som
eal
kan
es.
Th
isst
ream
isro
ute
dto
anex
trac
tive
dis
till
atio
nco
lum
n.
Inth
elo
wer
par
to
fth
isco
lum
n,
satu
-ra
ted
hydro
carb
ons
are
stri
pped
off
,w
hic
hre
-su
lts
inh
igh
-pu
rity
aro
mat
ics
atth
eb
ott
om
.B
e-ca
use
the
vo
lati
lity
of
alk
anes
inth
ep
rese
nce
of
NF
Mis
mu
chh
igh
erth
anth
ato
far
om
atic
s,th
en
eed
for
shar
pse
par
atio
nis
no
tver
yh
igh
.Atth
eto
po
fth
eex
trac
tive
dis
till
atio
nco
lum
n,
som
eso
lven
tis
add
ed.
Th
isso
lven
tst
ream
serv
esto
was
hb
ack
any
aro
mat
ics
evap
ora
ted
atth
efe
edp
oin
t.T
he
resu
ltin
gto
pp
rod
uct
,th
eref
ore
,has
aver
ylo
war
om
atic
con
ten
tan
dis
ver
yef
fect
ive
asa
refl
ux
inth
eb
ott
om
par
to
fth
eex
trac
tor,
was
hin
go
ut
the
hea
vie
ral
kan
es.
Th
eb
ott
om
pro
du
cto
fth
eex
trac
tive
dis
till
a-ti
on
colu
mn
,co
nsi
stin
go
fso
lven
tan
dver
yp
ure
aro
mat
ics,
isfe
dto
ad
isti
llat
ion
colu
mn
wh
ere
the
aro
mat
ics
are
evap
ora
ted
alo
ng
wit
hw
ater
.T
he
top
pro
du
cto
fth
isco
lum
nis
con
den
sed
and
fed
toa
sett
ler.
Th
eex
trac
ted
aro
mat
ics
are
avai
l-ab
leas
pro
du
cto
rca
nb
ero
ute
dto
ad
isti
lla-
tio
ntr
ain
tose
par
ate
the
ind
ivid
ual
com
po
un
ds.
So
me
of
the
aro
mat
ics
are
retu
rned
toth
eto
po
fth
ed
isti
llat
ion
colu
mn
asre
flu
x.I
nth
isw
ay,a
ny
asce
nd
ing
solv
entv
apo
ris
con
den
sed
and
the
top
pro
du
cts
are
solv
ent-
free
.T
he
wat
erla
yer
fro
mth
ese
ttle
ris
use
dfo
rra
ffin
ate
was
hin
g.
So
me-
tim
es,p
art
of
the
wat
eris
use
das
refl
ux
inst
ead
of
extr
act.
Inth
isco
mb
inat
ion
,u
ltim
ate
use
ism
ade
of
the
solv
ent
char
acte
rist
ics
inb
oth
the
extr
acti
on
and
the
extr
acti
ve
dis
till
atio
nst
eps.
5.3
.R
eact
ive
Ex
tra
ctio
n
5.3
.1.
Intr
od
uct
ion
Ifth
eso
lven
tre
acts
wit
hth
eex
trac
ted
sub
stan
ced
uri
ng
the
extr
acti
on
,th
ew
ho
lep
roce
ssis
call
edre
acti
ve
extr
acti
on
.T
his
reac
tio
nis
no
rmal
ly
Liq
uid
–Liq
uid
Extr
action
45
Fig
ure
49.
Morp
holi
ne
solv
ent
pro
cess
a)E
xtr
acto
r;b)
Was
hin
g;
c)E
xtr
acti
ve
dis
till
atio
nco
lum
n;
d)
Dis
till
atio
nco
lum
n;
e)S
ettl
er
use
dto
alte
rth
epro
per
ties
of
inorg
anic
cati
ons
that
are
tob
eex
trac
ted
fro
man
aqu
eou
sso
lu-
tio
nto
mak
eth
emso
lub
lein
the
no
np
ola
ro
r-gan
icso
lven
t.T
he
reac
tion
mec
han
ism
can
bes
tb
eco
mp
ared
wit
ha
cati
on
exch
an
ge
pro
cess
.T
he
solv
entac
tsli
ke
ali
qu
idio
nex
chan
gin
gth
eio
nto
be
extr
acte
dfo
rp
roto
ns.
Ta
ble
1.
Co
mm
erci
alch
elat
ing
extr
acti
on
reag
ents
Nam
eP
rod
uce
rC
hem
ical
com
po
siti
on
LIX
63
Hen
kel
5,8
-die
thyl-
7-h
ydro
xy-6
-dodec
anone
ox
ime
LIX
64
Hen
kel
2-h
ydro
xy-5
-dodec
ylb
enzo
phen
one
oxim
e
LIX
64
NH
enkel
LIX
65
Nw
ith
add
edL
IX6
3(p
rom
ote
r)
LIX
65N
Hen
kel
2-h
ydro
xy-5
-nonylb
enzo
phen
one
oxim
e
LIX
70
Hen
kel
chlo
rin
ated
LIX
65
Nw
ith
add
edL
IX6
3
(pro
mo
ter)
LIX
71
Hen
kel
mix
ture
of
LIX
64
Nan
dL
IX7
0
LIX
73
Hen
kel
mix
ture
of
LIX
64
Nan
dL
IX7
0
LIX
34
Hen
kel
8-(
p-d
od
ecy
lph
eny
lsu
lfo
nam
ido
)qu
ino
lin
e
LIX
54
Hen
kel
acet
yl-
p-d
od
ecy
lac
eto
ph
eno
ne
LIX
62
2H
enkel
LIX
60
22
Hen
kel
SM
E529
Shel
l2-h
ydro
xy-5
-nonyla
ceto
phen
one
oxim
e
SM
E5
30
Sh
ell
SM
E5
29
wit
hk
inet
icm
od
ifier
P1
7A
corg
aphen
yl
ben
zyl
ket
one
oxim
e
P50
Aco
rga
subst
itute
dsa
licy
lal
doxim
e
P5100
Aco
rga
one
par
tP
50
wit
heq
ual
par
tnonylp
hen
ol
P5200
Aco
rga
one
par
tP
50
wit
htw
opar
tsnonylp
hen
ol
P5300
Aco
rga
one
par
tP
50
wit
hth
ree
par
tsnonylp
hen
ol
P5050
Aco
rga
two
par
tsP
50
wit
hone
par
ttr
idec
anol
Kel
ex100
Sher
exsu
bst
itute
d8-h
ydro
xyquin
oli
ne
wit
h10
%
iso
dec
ano
l
Kel
ex1
20
Sh
erex
sim
ilar
toK
elex
10
0bu
tw
ith
20
%
iso
dec
ano
l
Th
eu
seo
fth
isp
roce
ssfo
rex
trac
tio
no
fan
-io
ns
isfa
rle
ssk
now
nbu
tis
of
the
sam
eim
po
r-
tan
ce.
Th
em
ech
anis
mo
fth
isty
pe
of
reac
tio
np
roce
eds
mo
sto
fth
eti
me
thro
ug
hio
np
air
for-
mat
ion
and
can
bes
tb
eco
mp
ared
wit
han
an
ion
exch
an
ge
pro
cess
.A
thir
dp
oss
ible
mec
han
ism
isth
eso
lva
tin
g
an
d/o
rch
ela
tin
gre
act
ion
.In
are
acti
on
of
this
type,
one
or
more
mole
cule
sof
wat
erin
the
hy-
dra
tela
yer
of
the
ion
sar
ere
pla
ced
by
the
acti
ve
solv
ent.
Th
en
ewco
mp
lex
wil
lb
ein
solu
ble
inw
ater
bu
tso
lub
lein
the
solv
ent.
Gen
eral
ly,
the
form
atio
no
fa
com
ple
xis
asl
ow
reac
tio
n.
Th
eref
ore
,in
man
yca
ses,
itis
no
tp
oss
ible
tou
seco
lum
ns
for
this
typ
eo
fex
-tr
acti
on
.In
man
yap
pli
cati
on
sm
ixer
–se
ttle
rar
eu
sed
tom
ake
the
extr
acti
on
po
ssib
le.
Are
acti
ve
extr
acti
on
wil
lnee
da
re-e
xtr
acti
on
tois
ola
teth
eex
trac
ted
sub
stan
cefr
om
the
sol-
ven
t.T
he
acti
ve
solv
ents
use
din
reac
tive
extr
ac-
tio
ns
are
wat
erin
solu
ble
com
po
un
ds.
Th
eyar
eu
sed
un
dil
ute
do
rin
solu
tio
nin
anin
ert
solv
ent.
5.3
.2.
Ex
tra
ctio
nM
ech
an
ism
of
Dif
fere
nt
Ty
pes
of
So
lven
t
Cla
ssic
al
Co
mp
lex
ing
an
d/o
rC
hel
ati
ng
Ag
ents
.T
he
acti
ve
solv
ents
are
usu
ally
larg
e,p
oly
fun
ctio
nal
mo
lecu
les.
Mo
sto
fth
emar
ed
e-si
gned
toex
trac
tsp
ecifi
cca
tions.
Dio
xim
es,hy-
dro
xy
ox
imes
,q
uin
oli
nes
,β
-dik
eto
nes
,et
c.,
are
rath
erex
pen
sive
bu
tw
idel
yu
sed
solv
ents
toex
-tr
act
met
alio
ns
such
asco
pp
eran
dn
ickel
fro
mth
eaq
ueo
us
ph
ase.
46
Liq
uid
–Liq
uid
Extr
action
Met
alco
mp
lexes
are
form
edin
the
wat
erp
has
ein
asu
bst
ance
-sp
ecifi
cp
Hra
ng
ean
dex
-tr
acte
din
toan
iner
tso
lven
t.A
fter
extr
acti
on
the
met
alio
nis
lib
erat
edfr
om
the
com
ple
xb
ych
ang
ing
the
pH
,an
dre
-ex
trac
ted
into
the
wat
erp
has
e.T
he
com
ple
xin
g/c
hel
atin
gag
ents
are
de-
sig
ned
such
that
they
are
chem
ical
lyst
able
,no
n-
tox
ic,a
nd
inso
lub
lein
wat
erto
min
imiz
elo
sses
.T
he
liq
uid
ion
exch
ang
e(L
IX)
[5]
agen
tsu
sed
inth
ep
rod
uct
ion
of
cop
per
are
typ
ical
for
this
cate
go
ry.
Hen
kel
,H
oec
hst
,S
hel
l,S
her
ex,
and
Aco
rga
are
the
larg
est
pro
duce
rsof
com
ple
x-
ing
/ch
elat
ing
extr
acta
nts
(see
Tab
le1
).
Ph
osp
ho
ric,
Su
lfo
nic
,a
nd
Ca
rbo
xy
lic
Aci
ds.
Th
iscl
ass
of
pro
du
cts
acts
typ
ical
lyas
cati
on
exch
ang
ers
inso
luti
on
.Th
ep
rod
uct
sh
ave
on
eo
rm
ore
pro
ton
sth
atca
nb
eex
chan
ged
for
met
alio
ns.
Nap
hth
enic
acid
sV
ersa
tic
acid
s
Su
lfo
nic
acid
sP
ho
sph
ori
cac
ids
Th
iop
ho
sph
ori
cac
ids
Ph
osp
ho
nic
acid
s
Th
em
etal
salt
so
fth
ese
acid
sar
eso
lub
lein
mo
stn
on
po
lar
solv
ents
and
,d
epen
din
go
nth
ep
Ho
fth
eex
trac
tio
nan
dth
ep
Ka
of
the
acid
,th
eca
tion
wil
lm
igra
teto
the
org
anic
phas
eor
stay
inth
ew
ater
ph
ase.
Th
ed
epen
den
ceo
fth
ed
istr
ibu
tio
ns
coef
fici
ents
on
pH
issh
ow
nin
Fig
-u
re5
0.
Th
ed
iffe
ren
tcu
rves
giv
eth
evar
iati
on
of
the
dis
trib
uti
on
coef
fici
ent
Din
dep
end
ence
of
pH
for
dif
fere
ntca
tio
ns.
Th
ese
solv
ents
are
no
tsp
e-ci
fic
for
cert
ain
cati
on
s,bu
tar
ever
ysu
itab
leto
con
cen
trat
ean
dre
cup
erat
etr
ace
elem
ents
fro
mef
flu
ent
stre
ams
[10
9],
[11
0].
Th
em
ajo
rp
rod
uce
rso
fth
isty
pe
of
com
-p
ou
nd
sar
eB
ayer
,Ho
ech
st,D
aih
ach
i,S
hel
l,an
dA
lbri
gh
t&W
ilso
n.
Eth
ers
an
dT
hio
eth
ers.
R2
O+
HX
⇋R
2O
H+
+X−
R2
S+
HX
⇋R
2S
H+
+X−
wh
ere
HX
stan
ds
for
ast
ron
gac
id,e.
g.,
H2S
O4
or
HC
l,an
dX
isth
ean
ion
icre
sto
fth
eac
id.
Mo
stm
etal
ion
sth
atar
eca
pab
leo
ffo
rmin
gan
-io
nic
com
ple
xes
are
extr
acta
ble
wit
het
her
san
dth
ioet
her
s.F
e,A
u,
In,
Ga,
etc.
can
be
extr
acte
dw
ith
thes
eso
lven
tsfr
om
anaq
ueo
us
HC
lso
lu-
tio
n(H
Clco
nce
ntr
atio
n>
6M
)an
dre
-ex
trac
ted
from
the
org
anic
phas
ew
ith
wat
er.M
ost
of
thes
ean
ion
icco
mp
lexes
form
stro
ng
acid
sw
hic
hp
ro-
ton
ate
wit
hth
eet
her
gro
up
tofo
rmo
xo
niu
m(t
hio
niu
m)
salt
s.T
hes
esa
lts,
how
ever
,ar
eso
l-u
ble
inet
her
or
thio
eth
er.
Itis
also
po
ssib
leto
extr
act
Cl−
fro
mw
ater
wit
h(R
2O
) 2·
H2S
O4,
the
sulf
ate
ion
bei
ng
rep
lace
db
yth
ech
lori
de.
Th
isty
pe
of
solv
ent
isn
orm
ally
use
din
un
di-
lute
dfo
rm[1
06
].
Ket
on
esex
trac
tth
esa
me
anio
nic
com
ple
xes
aset
her
s,bu
tin
mo
stca
ses
atlo
wer
acid
con
cen
trat
ion
.C
om
ple
xes
wit
hw
eaker
acid
sca
nal
sobe
extr
acte
d.
Met
hyl
isobuty
lke-
ton
ean
dcy
clo
hex
ano
ne
are
ind
ust
rial
lyu
sed
inth
ese
par
atio
no
fN
b–
Ta
asF−
com
ple
xes
[11
2]
(→N
iob
ium
and
Nio
biu
mC
om
po
un
ds,
Ch
ap.4
.3.1
.)an
din
the
sep
arat
ion
of
Zr–
Hf
asC
NS−
com
ple
xes
(→Z
irco
niu
man
dZ
irco
niu
mC
om
po
un
ds,
Ch
ap.
1.4
.2.)
[11
6].
Th
eso
lven
tsar
eu
sed
inu
nd
ilu
ted
form
.A
gre
atd
isad
van
-ta
ge
of
this
and
of
the
form
erty
pe
of
solv
ents
isth
atth
eyar
en
ot
com
ple
tely
inso
lub
lein
wat
er.
Ad
isti
llat
ion
isn
eed
edto
rem
ove
the
dis
solv
edso
lven
tfr
om
the
wat
erp
has
e.
Tri
alk
ylp
ho
sph
ine
ox
ides
,T
ria
lky
lph
os-
ph
ina
tes,
-ph
osp
ho
na
tes,
an
d-p
ho
sph
ate
s.
R3
PO
+H
X⇋
R3
PO
H+
+X−
RO
R2
PO
+H
X⇋
RO
R2
PO
H+
+X−
(RO
) 2R
PO
+H
X⇋
(RO
) 2R
PO
H+
+X−
(RO
) 3P
O+
HX
⇋(R
O) 3
PO
H+
+X−
Liq
uid
–Liq
uid
Extr
action
47
Fig
ure
50.
Plo
tsof
log
Dvs.
pH
for
extr
acti
on
of
met
als
Wit
hth
isty
pe
of
extr
acta
nts
mo
stm
etal
sfr
om
gro
up
3to
gro
up
8ca
nb
eex
trac
ted
,ev
enif
on
lyw
eak
com
ple
xes
are
form
edw
ith
the
solv
ent.
Itis
for
exam
ple
po
ssib
leto
extr
act
TiO
SO
4
[11
4]
fro
ma
sulf
uri
cac
idso
luti
on
wit
hd
ibu
tyl
bu
tylp
ho
sph
on
ate
(DB
BP
)as
the
solv
ated
com
-p
lex
2D
BB
P·T
iOS
O4·
H2S
O4·
5H
2O
.T
hes
eorg
anophosp
horu
sso
lven
tsar
e,due
toth
eir
out-
stan
din
gch
emic
alst
abil
ity
and
good
physi
cal
pro
per
ties
,m
ost
wid
ely
use
din
reac
tive
extr
ac-
tio
n[1
07
],[1
08
].F
ree
acid
sca
nal
sob
eex
trac
ted
,th
eb
asic
-it
yo
fth
eso
lven
tsd
ecre
ases
fro
mp
ho
sph
ine
ox
ide
totr
ialk
ylp
ho
sph
ate.
Th
ed
istr
ibu
tio
nco
-ef
fici
ents
are
rath
ersm
all
soth
atla
rge
vo
lum
eso
fso
lven
tar
en
eed
edin
anex
trac
tio
np
roce
ss[1
04
],[1
05
],[1
11
].T
hes
eex
trac
tan
tsar
eu
sed
assu
cho
rd
ilu
ted
inan
iner
tso
lven
t(p
etro
leu
mfr
acti
on
)w
ith
or
wit
ho
ut
mo
difi
er.T
he
dis
trib
u-
tio
nco
effi
cien
tsin
met
alex
trac
tio
nar
eu
sual
lyver
yh
igh
and
dep
end
on
the
acid
con
cen
trat
ion
.T
he
pro
du
cts
are
rath
erex
pen
sive.
Bay
er,
Ho
ech
st,
Dai
hac
hi,
Sh
ell,
and
Al-
bri
gh
t&W
ilso
nar
eth
em
ajo
rp
rod
uce
rs.
Tri
alk
yls
ulf
on
ium
(Sel
eniu
m,
Tel
luri
um
),T
etra
alk
yla
mm
on
ium
,a
nd
Tet
raa
lky
lph
os-
ph
on
ium
(Ars
on
ium
,S
tib
on
ium
)S
alt
s.
[R4
N+
A−
] Solv
ent
+[B−
] Raffi
nate
⇋
[R4
N+
B−
] Solv
ent
+[A−
] Raffi
nate
Th
ese
on
ium
com
po
un
ds
form
ion
sb
oth
inac
idic
and
bas
icm
ediu
m.
Th
em
ech
anis
mo
fex
trac
tio
nis
pra
ctic
ally
alw
ays
anio
nex
chan
ge
[10
6].
Th
eo
niu
mco
mp
ou
nd
sar
ere
gen
erat
edin
the
sam
ew
ayas
anio
nex
chan
ger
resi
ns
by
re-
extr
acti
on
wit
ha
bas
e.T
hes
eso
lven
tsar
eu
sed
inth
ep
rod
uct
ion
of
Cr,
V,
Re,
Tc,
Mo
,an
dW
asa
solu
tio
nin
ap
etro
leu
mfr
acti
on
.
Pro
du
cers
are
Hen
kel
,S
her
ex,
Ho
ech
st,
and
BA
SF.
Am
ine
an
dP
ho
sph
ine
Sa
lts.
R3
N+
HX−→
R3
NH
++
X−
R3
P+
HX−→
R3
PH
++
X−
Pri
mar
y,se
con
dar
y,an
dte
rtia
ryam
ines
mu
stb
ep
roto
nat
ed,
thu
sco
nver
ted
toth
eio
nic
form
bef
ore
they
can
be
use
das
anio
nex
chan
ger
.T
hu
sac
ids
can
be
extr
acte
dw
ith
free
amin
es,
met
als
hav
eto
be
tran
sfo
rmed
toth
eco
rre-
spo
nd
ing
acid
s:van
adiu
mca
nb
eex
trac
ted
asH
VO
3,
chro
miu
mas
H2C
r 2O
7,
and
man
gan
ese
asH
Mn
O4.M
ost
use
dar
eth
ete
rtia
ryam
ines
be-
cau
seth
eyar
ech
emic
ally
iner
tto
mo
stre
agen
ts.
Inth
esy
stem
tril
aury
lam
ine
–ci
tric
acid
are
ver
sib
leex
trac
tio
nca
nb
ese
tu
p,
du
eto
the
dif
fere
nce
ind
istr
ibu
tio
nco
effi
cien
tat
dif
fer-
ent
tem
per
atu
res.
At
low
tem
per
atu
re(2
0◦C
),th
ed
istr
ibu
tio
nco
effi
cien
tso
lven
t/ra
ffin
ate
is>
10
.A
th
igh
tem
per
atu
re(1
30◦C
),th
eco
effi
-ci
ent
for
the
sam
esy
stem
is<
1.
Th
us,
the
acid
can
be
extr
acte
dfr
om
wat
erat
low
tem
per
atu
rean
dre
-ex
trac
ted
wit
hw
ater
ath
igh
tem
per
atu
re.
Mu
chle
ssac
cou
nte
dfo
ris
the
fact
that
thes
eam
ines
hav
ever
yd
iffe
ren
td
istr
ibu
tio
nco
effi
-ci
ents
for
dif
fere
nt
anio
ns.
[R3
NH
+A−
] Solv
ent
+[B−
] Raffi
nate
⇋
[R3
NH
+B−
] Solv
ent
+[A−
] Raffi
nate
Fo
rtr
ioct
yla
min
ein
anar
om
atic
solv
ent
the
or-
der
of
extr
acta
bil
ity
is
I−≫
Br−
>N
O− 3
>C
l−
≫F−
>S2
O2−
3>
PO
3−
4>
SO
2−
4
48
Liq
uid
–Liq
uid
Extr
action
Th
isse
ries
isd
epen
den
to
nth
ety
pe
of
amin
e,th
ed
ilu
ent,
and
the
tem
per
atu
rean
dm
ust
be
de-
term
ined
for
any
giv
ensy
stem
[5].
Th
isse
ries
can
be
enla
rged
for
org
anic
com
pounds,
capa-
ble
of
form
ing
ion
pai
rsw
ith
the
amin
e.P
hen
ols
and
sub
stit
ute
dp
hen
ols
can
be
extr
acte
dw
ith
bet
ter
dis
trib
uti
on
coef
fici
ents
than
chlo
rid
es.In
this
seri
esth
iop
hen
ols
and
som
em
erca
pta
ns
are
situ
ated
bet
wee
nb
rom
ide
and
nit
rate
and
allsu
l-fo
nic
acid
sar
eb
ette
rex
trac
ted
than
ph
osp
hat
e.T
his
mak
esth
esu
lfat
esa
lts
of
amin
esa
ver
yg
oo
dch
oic
efo
rn
ewex
trac
tio
nsy
stem
s.(R
3N
) 2·
H2S
O4
(R=
oct
yl)
isca
pab
leo
fex
-tr
acti
ng
Cl−
and
/or
NO− 3
[11
3]
fro
ma
mix
ture
of
bo
than
ion
sw
ith
SO
2−
4.T
he
val
ue
of
the
dis
-tr
ibu
tio
nco
effi
cien
to
fth
ean
ion
sis
surp
risi
ng
lyh
igh
.
DC
l/D
SO
4≈
100
DN
O3/D
SO
4≈
400
Ad
isad
van
tag
eo
fth
ese
solv
ents
isth
efa
ctth
atp
erm
ole
amin
eo
ne
mo
leo
fsa
ltis
form
edaf
-te
rre
gen
erat
ion
.H
ow
ever
,m
ost
of
the
tim
e,th
ean
ion
sto
be
rem
oved
are
pre
sen
tin
the
solu
-ti
on
on
lyas
trac
eim
pu
riti
es,
soth
atth
isd
raw
-b
ack
isn
ot
sig
nifi
can
t.A
no
ther
dis
advan
tag
eo
fam
ines
isth
ep
oo
rso
lub
ilit
yo
fam
mo
niu
msa
lts
inal
iphat
ichydro
carb
ons.
To
avoid
thir
dp
has
efo
rmat
ion
,th
eu
seo
far
om
atic
solv
ents
(sm
ell)
or
alip
hat
ics
wit
hm
od
ifier
sis
nec
essa
ry.
Am
ines
can
also
act
asso
lvat
ing
agen
tsin
anac
idm
ediu
m.
Iro
n,
zin
c,an
du
ran
ium
salt
sca
nb
eex
trac
ted
inth
isw
ay[1
06
].
5.3
.3.
Use
s
1)
Ab
leed
fro
ma
(NH
4) 2
SO
4cr
yst
alli
zati
on
un
itin
aca
pro
lact
amp
lan
tco
nta
ins
40
%(N
H4) 2
SO
4,
10
%N
O− 3
,5
0p
pm
Cl−
and
3–
4%
org
anic
sulf
on
icac
ids.
Th
eso
lu-
tio
nis
extr
acte
db
ytr
ioct
yla
mm
on
ium
sul-
fate
,th
ead
ded
amo
un
tis
sto
ich
iom
etri
cto
[NO− 3
]+
[Cl−
]+
[su
lfo
nic
acid
].In
thre
est
ages
>9
9%
of
the
nit
rate
,9
0%
of
the
chlo
rid
e,an
d8
5%
of
the
sulf
on
icac
ids
are
extr
acte
db
yth
etr
ioct
yla
min
ein
solu
tio
n(4
0%
)in
Shel
lsol
AB
(aro
mat
ichydro
car-
bo
n).
Th
era
ffin
ate
isre
turn
edto
the
cry
stal
-li
zati
on
pla
nt
for
(NH
4) 2
SO
4re
cover
y.T
he
re-e
xtr
act
con
tain
s3
5%
of
nit
rate
,0
.01
6%
of
chlo
rid
e,th
esu
lfo
nic
acid
s,an
do
nly
0.1
%o
fsu
lfat
ean
dis
trea
ted
sep
arat
ely.
Co
mp
ared
wit
ha
conven
tio
nal
stri
pp
ing
,th
eu
seo
fch
emic
als
inth
issy
stem
isst
ron
gly
red
uce
d.
80
%le
ssN
aOH
isco
nsu
med
be-
cau
seth
eb
ase
iso
nly
use
dto
lib
erat
eth
eam
ine
and
no
tto
neu
tral
ize
the
NH
3fr
om
(NH
4) 2
SO
4[1
13
].2
)T
race
so
fp
hen
ol(2
0–
20
0p
pm
)an
db
isp
he-
no
l(2
0–
10
0p
pm
)ca
nb
eex
trac
ted
fro
mth
ew
aste
wat
ero
fa
po
lyca
rbo
nat
ep
lan
tto
val
ues
<1
pp
m,
thu
sav
oid
ing
bio
log
ical
trea
tmen
to
fth
ew
ater
.T
he
re-e
xtr
act
con
-ta
inin
gso
diu
mp
hen
ola
tean
db
isp
hen
ola
te(3
00
–5
00
tim
esm
ore
con
cen
trat
ed)
can
be
retu
rned
toth
ep
oly
carb
on
ate
pla
nt.
Th
eso
l-ven
tuse
dis
5%
trio
cty
lam
ine
inS
hel
lso
lAB
[11
7].
3)
Fro
ma
pla
nt
for
the
pro
du
ctio
no
fv
ulc
an-
izat
ion
acce
lera
tors
2-m
erca
pto
ben
zoth
iazo
l(1
00
–3
00
pp
m)
and
its
ox
idat
ion
pro
du
cts
are
com
ple
tely
extr
acte
din
two
stag
esan
dre
-ex
trac
ted
asa
20
–3
0%
solu
tio
n.
Th
isco
nce
ntr
ated
was
teca
nb
eea
sily
rem
oved
.T
he
solv
ent
is2
0%
trio
cty
lam
ine
inS
hel
l-so
lA
B[1
13
].4
)B
rom
ide
ion
sca
nb
eex
trac
ted
sele
ctiv
ely
fro
mse
aw
ater
(co
nce
ntr
atio
nin
the
Dea
dS
ea≈
4%
)w
ith
amin
ehydro
chlo
rides
and
con
cen
trat
edin
are
-ex
trac
tio
nst
ep,
thu
sav
oid
ing
the
ener
get
ical
lyu
nfa
vo
rab
lest
rip
-p
ing
of
sea
wat
er.T
he
extr
acti
on
can
be
car-
ried
ou
tw
ith
var
iou
sty
pes
of
amin
esas
HC
lo
rH
2S
O4
salt
[10
6].
5)
Mg2+
can
be
rem
oved
fro
ma
satu
rate
dso
-lu
tio
no
f(N
H4) 2
SO
4b
yex
trac
tio
nw
ith
the
amm
oniu
msa
ltof
die
thylh
exyl
phosp
honic
acid
(DE
HPA
)at
pH
>5
.It
can
be
reco
ver
edb
ylo
wer
ing
the
pH
to<
3[1
15
].6
)T
race
so
fu
ran
ium
are
extr
acte
dfr
om
ph
os-
ph
ate
ore
s.T
he
ura
niu
mco
nte
nti
nth
ese
ore
sis
on
ly3
0–
30
0p
pm
.T
he
rese
rves
of
tho
seo
res
are
soh
ug
eth
atth
eq
uan
tity
of
ura
niu
mfr
om
ph
osp
hat
esm
any
tim
esex
ceed
sth
ato
fu
ran
ium
fou
nd
ino
ther
ura
niu
mo
res.
7)
Lan
than
ides
and
acti
nid
esh
ave
on
lyre
cen
tly
bec
om
eav
aila
ble
inh
igh
erq
uan
tity
and
hig
hp
uri
ty.T
his
was
enab
led
by
the
dev
elo
pm
ent
of
the
extr
acti
on
tech
no
log
y(→
Rar
eE
arth
Ele
men
ts).
Liq
uid
–Liq
uid
Extr
action
49
8)
Wo
rld
wid
eab
ou
t4
0%
of
the
cop
per
isp
ro-
du
ced
by
reac
tive
extr
acti
on
.T
he
pla
nts
are
ano
rder
of
mag
nit
ud
ela
rger
then
any
oth
erty
pe
of
solv
ent
extr
acti
on
pre
sen
tly
ino
per
-at
ion
(→C
op
per
,C
hap
.5
.8.)
.W
ith
anaq
ue-
ou
sfe
edo
f2
00
–3
00
0m
3/h
aw
ho
len
ewte
chn
olo
gy
had
tob
ed
evel
op
ed.C
op
per
can
be
extr
acte
daf
ter
acid
or
amm
on
iaca
lle
ach
-in
g.T
he
aqu
eou
sst
rip
pin
gp
has
eis
use
dd
i-re
ctly
inth
eel
ectr
ow
inn
ing
of
cop
per
.T
oav
oid
the
bu
ild
-up
of
imp
uri
ties
inth
eel
ec-
tro
lysi
so
fco
pp
er,
Fe,
Zn
,an
do
ther
met
als
are
rem
oved
fro
mth
isp
has
eb
yex
trac
tio
nw
ith
oth
erso
lven
ts[5
],[1
02
],[1
11
].9
)M
ore
than
90
%o
fth
ew
orl
dp
rod
uct
ion
of
cob
alt
isp
erfo
rmed
by
reac
tive
extr
acti
on
.S
epar
atio
no
fC
oan
dN
ica
nb
eac
hie
ved
fro
mal
kal
ine,
neu
tral
,o
rfr
om
acid
icm
edia
.M
ost
of
the
imp
uri
ties
(Sn
,B
i,F
e,P
b,
Cu
,C
d,a
nd
Zn
)h
ave
tob
ere
moved
fro
mth
eso
-lu
tio
nb
yp
reci
pit
atio
no
rex
trac
tio
n.F
rom
am
ediu
mco
nce
ntr
ated
aqu
eou
sch
lori
de
solu
-ti
on
(10
0–
20
0g
/L),
Co
can
be
extr
acte
db
yam
ines
tog
eth
erw
ith
on
lytr
aces
of
Ni.
Aft
ersc
rub
bin
gw
ith
4–
5M
HC
l,m
ost
of
the
Ni
isre
moved
fro
mth
eso
lven
t.T
he
cob
alt
isst
rip
ped
by
wat
er.
Fro
mn
eutr
alo
rw
eak
lyac
idic
med
ia(p
H4
.8–
5.5
)C
oca
nb
eex
trac
ted
by
the
Na+
or
NH
+ 4sa
ltof
di-
2-e
thylh
exylp
hosp
hori
cac
id(D
2E
HPA
)(t
oav
oid
acid
ifica
tio
no
fth
eaq
ueo
us
solu
tio
n).
So
me
Ni
isco
-ex
trac
ted
and
isre
moved
by
scru
bb
ing
wit
ha
Co
solu
-ti
on
thu
sre
pla
cin
gan
yex
trac
ted
Ni
by
Co
.C
ois
fin
ally
stri
pp
edb
yH
Cl,
H2S
O4,
or
HN
O3
dep
end
ing
on
the
use
.T
he
use
of
mo
no
oct
yl
oct
ylp
ho
sph
on
icac
id(M
OO
P)
tore
pla
ceD
2E
HPA
[10
1]
per
mit
sth
esa
me
sep
arat
ion
,bu
tatl
ow
erp
Han
dw
ith
enh
ance
dd
istr
ibu
tio
nco
nst
ants
for
Co
.In
alk
alin
eso
luti
on
Co
and
Ni
can
be
ex-
trac
ted
by
LIX
agen
tsfr
om
amm
on
iaca
lso
-lu
tio
n.
Pri
or
toth
eex
trac
tio
n,
cob
alt
iso
x-
idiz
edto
the
Co3+
stat
e.N
ickel
isst
rip
ped
firs
tw
ith
dil
ute
acid
,C
ore
mai
nin
gin
the
solv
ent.
Co
bal
tis
then
red
uce
dto
the
Co2+
stat
ean
dst
rip
ped
wit
hd
ilu
ted
acid
[5],
[10
2],
[10
4],
[10
5].
All
thes
eex
amp
les
are
use
din
ind
ust
ryo
rin
pil
ot
pla
nts
.E
lab
ora
tep
roce
ssan
dfl
ow
con
tro
l
are
esse
nti
alto
use
this
tech
no
log
yin
aec
on
om
-ic
alan
dm
ean
ing
ful
way
.
5.3
.4.
Set
tin
gu
pa
nE
xtr
act
ion
Sy
stem
Aso
luti
on
Rco
nta
ins
thre
eco
mp
on
ents
:ac
id,
met
alA
and
met
alB
.B
oth
met
als
and
the
acid
are
extr
acta
ble
wit
ha
solv
ent
San
dm
etal
Ais
the
des
ired
com
po
nen
tth
atis
tob
eo
bta
ined
inac
idso
luti
on
.T
he
pro
ced
ure
tose
tu
pa
new
ex-
trac
tio
nsy
stem
wit
hth
ese
dat
ais
typ
ical
for
any
reac
tive
extr
acti
on
syst
em[1
14
],[1
18
].T
he
dis
trib
uti
on
coef
fici
ents
are
tob
em
ea-
sure
dat
dif
fere
nt
acid
con
cen
trat
ion
sat
ate
m-
per
atu
resu
itab
lefo
rth
eex
trac
tio
n.
Aty
pic
alm
easu
rem
ent
curv
eis
show
nin
Fig
ure
51
.
Fig
ure
51.
Dis
trib
uti
on
coef
fici
ent
indep
enden
ceon
acid
conce
ntr
atio
n
Th
ed
iag
ram
show
sa
po
or,
pra
ctic
ally
con
-st
ant
dis
trib
uti
on
coef
fici
ent
Dfo
rth
eac
idan
dan
incr
easi
ng
on
efo
rb
oth
met
als
Aan
dB
atin
crea
sin
gac
idco
nce
ntr
atio
n.
Th
ism
ean
sth
atth
eac
idex
trac
tio
nis
infa
cta
norm
alphysi
cal
extr
acti
on
and
that
both
met
als
form
solv
atio
nco
mp
lexes
.A
tan
yac
idco
nce
n-
trat
ion
,al
lth
ree
com
po
nen
tsar
eex
trac
ted
to-
get
her
.T
he
extr
acti
on
coef
fici
ents
Ear
ere
late
din
the
sam
ew
ayas
are
the
dis
trib
uti
on
coef
fi-
cien
ts,
E=
D·S
/R
.
To
extr
act
met
alA
com
ple
tely
and
ina
reas
on
-ab
len
um
ber
of
step
sex
trac
tio
nh
asto
be
carr
ied
ou
tin
zon
e4
of
Fig
ure
51
,th
eex
tra
ctio
nzo
ne.
At
the
sam
eti
me,
met
alB
and
the
acid
are
on
lyp
arti
ally
extr
acte
din
toth
eso
lven
t.T
he
nu
m-
ber
of
step
sca
nb
eca
lcu
late
dw
ith
the
Kre
mse
rfo
rmu
la.T
he
Kre
mse
rfo
rmu
laca
lcu
late
sth
eef
-fi
cien
cyZ
inth
eex
trac
tio
n
Z=
(
En
+1−
E)
/(
En
+1−
1)
50
Liq
uid
–Liq
uid
Extr
action
over
nst
ages
.F
or
this
equ
atio
nth
en
um
ber
of
stag
esca
nea
sily
be
calc
ula
ted
n=
log{[
1/
(1−
Z)·(
1−
1/E
)]+
1/E}
/lo
gE
To
rem
ove
met
alB
fro
mth
eso
lven
tth
eso
lven
th
asto
be
was
hed
wit
hw
ater
orac
idin
such
aw
ayth
atm
ost
of
met
alA
stay
sin
the
solv
ent,
wh
ile
met
alB
isw
ash
edo
utas
com
ple
tely
asp
oss
ible
.T
his
isd
on
ein
zon
e3
ofF
igu
re5
1,t
he
scru
bb
ing
zon
e.T
he
amo
un
to
fw
ater
tob
eu
sed
isg
iven
agai
nby
the
dis
trib
uti
on
coef
fici
ents
ofboth
acid
and
met
alB
.If
too
mu
chac
idis
rem
oved
,m
etal
Aw
ill
also
be
was
hed
ou
t.T
her
efo
reit
ism
ore
adeq
uat
eto
use
anac
idso
luti
on
.T
he
con
cen
-tr
atio
no
fth
ed
ilu
teac
idsh
ou
ldb
esu
chth
atth
eac
idso
luti
on
can
on
lyta
ke
up
the
amo
un
to
fac
idto
be
rem
oved
fro
mth
eso
lven
t.B
ysc
rub
-b
ing
wit
hp
ure
wat
ero
nly
ali
mit
edam
ou
nt
of
scru
bb
ing
flu
idca
nb
eu
sed
bec
ause
of
the
low
dis
trib
uti
on
coef
fici
ent
of
the
acid
.B
yad
din
ga
calc
ula
ted
amo
un
to
fac
idth
eam
ou
nt
of
scru
b-
bin
gfl
uid
can
be
incr
ease
dan
dm
ore
com
po
nen
tB
can
be
rem
oved
wit
ho
utre
mov
ing
com
po
nen
tA
.Th
era
ffin
ate,
leav
ing
the
scru
bb
ing
zon
eco
n-
tain
sto
om
uch
of
met
alA
tob
ed
isca
rded
and
isse
nt
bac
kto
on
eo
fth
est
eps
inth
eex
trac
tio
n.
The
num
ber
ofst
eps
can
agai
nbe
calc
ula
ted
wit
hth
eK
rem
ser
form
ula
.In
zon
e2
of
Fig
ure
51
,th
est
rip
pin
gzo
ne,
met
alA
isw
ash
edo
ut
of
the
solv
ent
wit
hw
ater
or
ad
ilu
teac
idso
luti
on
.T
he
amo
un
to
fw
ater
isch
ose
nsu
chas
too
bta
inth
ed
esir
edco
nce
ntr
a-ti
on
of
met
alA
inth
ere
-ex
trac
t.W
ith
the
giv
end
istr
ibu
tio
nco
effi
cien
t,it
isn
ot
po
ssib
leto
re-
move
met
alA
com
ple
tely
form
the
solv
ent.
At
any
acid
con
cen
trat
ion
,tr
aces
of
met
alA
wil
lre
mai
nin
the
solv
ent.
Inzo
ne
1o
fF
igu
re5
1,th
ew
ash
ing
zon
e,th
eac
idan
dth
ere
sto
fm
etal
Aar
ew
ash
edo
uto
fth
eso
lven
t.A
fter
this
step
,th
eso
lven
tis
com
ple
tely
reg
ener
ated
and
can
be
reu
sed
.
Gen
era
lF
low
Sh
eet.
Fig
ure
52
show
sa
gen
eral
flow
shee
to
fa
reac
tive
extr
acti
on
sys-
tem
. So
lven
tM
ake
-Up
.D
ue
toth
ep
oo
rd
istr
ibu
-ti
on
coef
fici
ent
of
the
acid
sever
alex
trac
tio
nst
eps
are
nee
ded
tolo
adth
eso
lven
tw
ith
suffi
-ci
ent
acid
tom
ake
extr
acti
on
of
the
met
als
po
s-si
ble
.In
the
giv
enex
amp
leth
eac
idco
mes
fro
mth
ein
itia
lso
luti
on
.T
oav
oid
loss
eso
fm
etal
A,
the
solv
ent
mu
stb
eco
mp
lete
lyfr
eeo
fA
.A
tth
elo
wac
idco
nce
ntr
atio
nin
the
firs
tst
eps
of
the
solv
ent
mak
e-u
pan
ym
etal
Ap
rese
nt
inth
eso
lven
tw
ill
be
re-e
xtr
acte
din
the
raffi
nat
e.R
eact
ive
Ext
ract
ion
.If
suffi
cien
tac
idis
pre
sen
tin
the
solv
ent,
bo
thm
etal
sw
ill
be
ex-
trac
ted
fro
mth
efe
edso
luti
on
.To
lim
itth
en
um
-b
ero
fst
eps
inth
eex
trac
tio
n,
con
cen
trat
edac
idis
add
ed.T
he
hig
hco
nce
ntr
atio
nis
nec
essa
ryfo
rth
em
etal
extr
acti
on
and
inth
eso
lven
tm
ake-
up
.S
olv
ent
Scr
ub
bin
g.
To
mak
esu
reth
atm
ost
of
met
alB
isw
ash
edo
utfr
om
the
solv
ent,
the
acid
solu
tio
nco
nta
inin
gm
etal
Aan
dac
idfr
om
the
solv
ent
was
hin
gst
epis
use
d,
soth
atw
est
ayin
the
extr
acti
on
zon
efo
rm
etal
A.T
he
seco
nd
com
-p
on
ent,
wit
ha
low
erd
istr
ibu
tio
nco
effi
cien
t,is
alre
ady
init
sst
rip
pin
gzo
ne
and
wil
lb
ew
ash
edo
uto
fth
eso
lven
t.T
oav
oid
loss
es,th
isst
ream
isse
nt
bac
kto
on
eo
fth
est
eps
inth
eex
trac
tio
n.
So
lven
tS
trip
pin
g.
Aft
ersc
rub
bin
g,
the
sol-
ven
tco
nta
ins
on
lym
etal
Aan
dac
id.U
sin
gw
ater
or
ad
ilu
teac
idso
luti
on
,th
ep
uri
fied
met
alA
can
now
be
re-e
xtr
acte
din
toa
wat
erp
has
e.S
olv
ent
Wa
shin
g.
Th
eso
lven
tm
ust
be
com
-p
lete
lyre
gen
erat
edb
efo
reit
can
be
recy
cled
toth
eso
lven
tm
ake-
up
.T
his
isd
on
eb
yad
din
gso
me
sup
ple
men
tary
was
hin
gst
eps
toth
esy
s-te
m.
Th
eam
ou
nt
of
wat
eris
cho
sen
acco
rdin
gto
the
req
uir
emen
tsin
the
scru
bb
eran
dth
en
um
-b
ero
fst
eps
isca
lcu
late
das
afu
nct
ion
of
that
amo
un
t.
5.3
.5.
Dil
uen
tsa
nd
Mo
difi
ers
Dil
uen
tsar
eu
sed
tore
du
ceth
eso
lven
tvis
cosi
ty,
imp
rove
ph
ase
sep
arat
ion
,an
dm
ost
of
all,
wh
enp
rop
erly
cho
sen
,to
red
uce
the
loss
of
solv
ent.
Th
eso
lub
ilit
yo
ftr
i-n
-bu
tylp
ho
sph
ate
(TB
P,o
ne
of
the
mo
stfr
equ
entl
yu
sed
extr
acta
nts
)in
pu
rew
ater
is4
20
mg
/Lat
roo
mte
mp
erat
ure
;a
50
%d
ilu
tio
no
fT
BP
inn
-hex
ane
low
ers
this
solu
bil
-it
yto
17
5m
g/L
.T
he
cho
ice
of
dil
uen
tis
ver
yim
po
rtan
t.H
igh
eram
ines
are
com
ple
tely
solu
-b
lein
alip
hat
icd
ilu
ents
.T
hei
rsa
lts,
how
ever
,ar
eo
nly
slig
htl
yso
lub
lein
the
sam
eso
lven
ts.
Th
eref
ore
itis
esse
nti
alto
test
the
solu
tio
ns
inal
lst
eps
of
the
pro
cess
.If
thir
d-p
has
efo
rma-
tio
no
ccu
rsin
on
eo
fth
est
eps,
the
dil
uen
tm
ust
be
chan
ged
or
am
od
ifier
isto
be
add
ed.
Th
ese
mo
difi
ers
are
no
rmal
lylo
ng
chai
nal
coh
ols
,mo
-noes
ters
of
poly
hydri
cal
cohols
,or
phosp
hat
e
Liq
uid
–Liq
uid
Extr
action
51
Fig
ure
52.
Gen
eral
flow
shee
tof
are
acti
ve
extr
acti
on
syst
em
este
rs.
Th
ese
mo
difi
ers
may
con
sid
erab
lyin
flu
-en
ceth
ek
inet
ics
of
the
extr
acti
on
.E
spec
iall
yin
the
extr
acti
on
of
cop
per
the
cho
ice
of
mo
difi
eris
ver
yim
po
rtan
t.T
he
dif
fere
nt
typ
eso
fso
lven
tar
eso
ldm
ixed
wit
ha
suit
able
mo
difi
erw
hic
hg
reat
lyen
han
ces
the
extr
acti
on
per
form
ance
of
the
solv
ent.
6.
Ref
eren
ces
1.
R.E
.T
reybal
:L
iquid
Ext
ract
ion,
McG
raw
-Hil
l,N
ewY
ork
–T
oro
nto
–L
ondon
1963.
2.
S.H
artl
and:
Counte
rC
urr
ent
Ext
ract
ion,
Per
gam
on
Pre
ss,O
xfo
rd1970.
3.
J.R
ydber
g,C
.M
usi
kas
,G
.R.C
hoppin
(eds.
):
Pri
nci
ple
sand
Pra
ctis
esof
Solv
ent
Ext
ract
ion,
M.D
ekker
,In
c.,N
ewY
ork
1992.
4.
C.H
anso
n:
Rec
ent
Adva
nce
sin
Liq
uid
–L
iquid
Ext
ract
ion,
Per
gam
on
Pre
ss,O
xfo
rd1971.
5.
T.C
.L
o,M
.H.I
.B
aird
,C
.H
anso
n(e
ds.
):
Handbook
of
Solv
ent
Ext
ract
ion,
Wil
ey-I
nte
rsci
ence
,N
ewY
ork
1983.
6.
J.D
.G
odfr
ey,M
.J.S
late
r(e
ds.
):
Liq
uid
–L
iquid
Ext
ract
ion
Equip
men
t,J.
Wil
ey&
Sons,
New
York
1994.
7.
J.W
isnia
k,A
.T
amir
:L
iquid
–L
iquid
Equil
ibri
um
and
Ext
ract
ion.A
Lit
eratu
re
sourc
eB
ook.
Physi
cal
Sci
ence
sD
ata,
7,P
artA
1980,P
artB
1981,P
hysi
cal
Sci
ence
sD
ata,
23,
Supple
men
t1
1985,E
lsev
ier,
Am
ster
dam
.
8.
Pro
ceed
ings
ISE
C’8
8,V
ernad
sky
Inst
itute
of
Geo
chem
istr
yan
dA
nal
yti
cal
Chem
istr
yof
the
US
SR
Aca
dem
yof
Sci
ence
s,4
vols
.,N
AU
KA
,
Mosc
ow
,1988.
9.
Pro
ceed
ings
ISE
C’9
0,C
hem
ical
Soci
ety
of
Japan
,E
lsev
ier,
New
York
1992.
10.
Pro
ceed
ings
ISE
C71,T
he
Hag
ue,
2vols
.,
Soci
ety
of
Chem
ical
Indust
ry,L
ondon
1971.
11.
Pro
ceed
ings
ISE
C74,L
yon,3
vols
.,S
oci
ety
of
Chem
ical
Indust
ry,L
ondon
1974.
12.
Pro
ceed
ings
ISE
C77,T
oro
nto
,2
vols
.,C
IMM
Spec
ial
Publi
cati
on,no.2
1,C
an.In
st.M
in.
Met
.,1979.
13.
Pro
ceed
ings
ISE
C80,L
iege,
3vols
.,A
ssocn
.
des
Ingen
ieurs
sort
isde
l’U
niv
ersi
tede
Lie
ge,
Lie
ge
1980.
14.
Pro
ceed
ings
ISE
C83,D
enver
AIC
hE
1983.
15.
Pro
ceed
ings
ISE
C86,M
unch
en,3
vols
.,
DE
CH
EM
A,F
rankfu
rt1986.
16.
Pro
ceed
ings
ISE
C’9
3,S
olv
ent
Extr
acti
on
in
the
Pro
cess
Indust
ries
,2
vols
.,E
lsev
ier,
New
York
1993.
17.
Pro
ceed
ings
ISE
C’9
6,V
alue
Addin
gT
hro
ugh
Solv
ent
Extr
acti
on,2
vols
.,T
he
Univ
ersi
tyof
Mel
bourn
e,P
arkvil
le,V
icto
ria,
Aust
rali
a1996.
18.
J.M
.S
ore
nse
n,W
.A
rlt:
“Liq
uid
–L
iquid
Equil
ibri
um
Dat
aC
oll
ecti
on,”
vol.
V,par
t
1–
3,D
EC
HE
MA
Chem
istr
yD
ata
Ser
.,
Fra
nkfu
rt1979.
19.
Lan
dolt
-Born
stei
n:
II2
c,S
pri
nger
Ver
lag,
Ber
lin
1980.
20.
O.M
adel
ung:
Landolt
-Born
stei
ndir
ecto
ry
dis
k1.1
,S
pri
nger
-Ver
lag,B
erli
n1994.
21.
A.S
eidel
,F.W
.L
inke:
“Solu
bil
itie
sof
Inorg
anic
and
Org
anic
Com
pounds,
”in
A.W
.
Fra
nci
s(e
d.)
:Ter
nary
Sys
tem
sSep
ara
ting
into
Tw
oL
iquid
Laye
rs,
van
Nors
tran
d,L
ondon
1952.
22.
A.W
.F
ranci
s:L
iquid
–L
iquid
Equil
ibri
a,
Wil
ey,N
ewY
ork
1963.
52
Liq
uid
–Liq
uid
Extr
action
23.
H.S
tephen
,T
.S
tephen
:Solu
bil
itie
sof
Inorg
anic
and
Org
anic
Com
pounds,
4vols
.,
Per
gam
on
Pre
ss,O
xfo
rd1964.
24.
F.R
uiz
,D
.P
rats
,A
.F.M
arci
lla:
“Liq
uid
–L
iquid
Extr
acti
on:
aG
raphic
al
Met
hod
for
Equil
ibri
um
Sta
ge
Cal
cula
tions
for
Quat
ernar
yS
yst
ems,
”F
luid
Phase
Equil
ib.
15
(1984)
no.3
,257
–265.
25.
W.R
uck
l,R
.M
arr:
“Mult
icom
ponen
t
Liq
uid
–L
iquid
Extr
acti
on,”
Ger
.C
hem
.E
ng.
(Engl.
Tra
nsl
.)8
(1985)
no.1
,27
–31.
26.
M.J
.H
ampe:
“Sel
ecti
on
of
Solv
ents
in
Liq
uid
–L
iquid
Extr
acti
on
Acc
ord
ing
to
Physi
co-C
hem
ical
Asp
ects
,”G
er.C
hem
.E
ng.
(Engl.
Tra
nsl
.)9
(1986)
no.4
,251
–263.
27.
Ull
mann,
4th
.,vol.
2,
550
–551.
28.
E.B
ender
,U
.B
lock
,“T
her
modynam
isch
e
Ber
echnung
der
Flu
ssig
-Flu
ssig
-Extr
akti
on,”
Ver
fahre
nst
echnik
(Mai
nz)
9(1
975)
no.3
,
106
–111.
29.
K.H
lavat
y:
“Corr
elat
ion
of
the
Bin
odal
Curv
e
ina
Ter
nar
yL
iquid
Mix
ture
wit
hO
ne
Pai
rof
Imm
isci
ble
Liq
uid
s,”
Coll
ect.
Czc
h.C
hem
.
Com
mun.
37
(1972)
4005
–4007.
30.
E.H
ecker
:“A
usw
ahl
von
Losu
ngsm
itte
lsyst
emen
zur
mult
ipli
kat
iven
Ver
teil
ung,”
Chim
ia8
(1954)
229
–236.
31.
C.M
.H
anso
n:
“The
Univ
ersa
lity
of
Solu
bil
ity
Par
amet
er,”
Ind.E
ng.C
hem
.P
rod.R
es.D
ev.
8
(1969)
no.1
,2
–11.
32.
C.R
eich
ardt,
K.D
imro
th:
“Losu
ngsm
itte
lund
empir
isch
eP
aram
eter
zur
Char
akte
risi
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