Post on 17-Dec-2015
Solid-Liquid Separations
Pharmaceutical API Process Development and Design
Solid-Liquid Separations
• Filtration Analysis– Flow in packed beds– Cake Filtration– Centrifuges– Deliquoring– Washing
• Examples– Cake compressibility– Cycle time calculations
Linear Filtration Centrifugal Filtration
Filtration Options
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry
Backpressure AppliedRetentate Stream
Permeate Stream
Filtration Options
Cross Flow Filtration
Feed Tank
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry
Mechanisms in Filtration
• Depth filtration– Particles captured within pore spaces– Slurries with less than 0.1% solids
• Cake filtration– Particles bridge pores in medium– Cake formed on surface of medium
• Cross flow filtration– Porous tube with cross flow
Driving Forces• Gravity
– Hydrostatic pressure
– Free filtering materials
• Vacuum– Downstream pressure below atmospheric
– Rotary drum, moving belt, disc filters
• Pressure– Pumps or compressed gas
– Plate and frame, leaf
• Centrifugal Force– Perforated bowl centrifuge, peeler centrifuge
Operating Mode
• Constant pressure filtration– Vacuum pumps, compressed gas
• Constant rate filtration– Positive displacement pumps
• Variable pressure, variable rate filtration– Centrifugal pumps
Cake Filtration
suspension
filter cake
membrane
L, ΔP
Luis Puigjaner (2007), Solid-Liquid Separations
Carman-Kozeny Equation 3
221 1
oSk
L
P
Darcy’s Law
Flow Through Packed Beds
221
3
)1( oSkk
vkL
P
Permeability
Pressure drop
Superficial velocity
Liquor viscosity
Bed height
Porosity
Specific surface area
P
v
L
oS
Mass Balance
filtrateofmasscakeofmassslurryofmass
A
Vc
A
V
ms
sw
1
Filter area
Filtrate volume
Dry solids/unit area
Dry solids/unit volume filtrate
Mass of wet cake/Mass of dry cake
Mass fraction of solids in slurry
AV
w
c
m
s
Filtrate density
Solid density
Thickness of cake
Porosity
Ls
Lw s 1
Cake filtration equationRewrite Darcy’s law in terms of specific cake resistance, filtrate volume, solids concentration
With medium resistance
sk
)1(
1
dt
dV
Av
kw
P
s
c 1
1
mm R
AcVPA
Rw
PA
dt
dV
AVc
AP
w
AP
dt
dV cc
Cake pressure drop
Total pressure drop
Specific cake resistance
Filtrate volume
Dry solids/unit area
Dry solids/unit volume filtrate
Medium Resistance
V
w
c
cP
P
mR
: Characteristic parameter of a specific solid/liquid system
W Leu (1986), Principles of Compressible Cake Filtration
Ease of Separation
Ease of Separation Average Specific Cake Resistance (, m/kg
Very Easy 1x109
Easy 1x1010
Moderate 1x1011
Difficult 1x1012
Very Difficult 1x1013
mave RAcV
AP
dt
dVQ
Q = Flow Rate of Eluentt = time of filtrationP = pressure dropA = effective area of filtrationμ = viscosity of filtrateave = average specific cake resistancec = kg of dry cake per volume of filtrateV = volume of filtrateRm = medium resistance
Assumptions:Constant pressureConstant area Ignore gravity
Filtration Analysis
VPA
RVPA
ct
drivingm
drivingave
222
drivingm
drivingave PA
RVPA
c
V
t 22
Rearranging:
Plot t/V vs V – LinearSlope – proportional to average specific cake resistanceIntercept – proportional to medium resistance
Parabolic Data Analysis
Cake Compressibility
Pressure Drop
Filt
rate
Flo
wra
te Incompressible
Highly compressible
Incompressible solids - is independent of pressure
Cake Compressibility
V
t /
V
ΔP1, α1
ΔP2, α2
ΔP3, α3
Compressible solids - varies with pressure
so P Where usually, 0.1 < s < 0.8
s
oo P
P
1
Sometimes expressed as:
Where o, Po, and s are empirical constants
Cake Compressibility
ln ΔP
ln
Medium Resistance
• Typically a linear contributor to overall cake pressure drop
• May foul if size chosen inappropriately
V
t /
V Increase in medium resistance due to blinding
Run 1
Run 2
Run 3
Laboratory Pressure Filtration
Parabolic Data Analysis
Factory or Pilot Plant Filtration
Scale Up Calculations
Representative SlurryVolume vs Time DataCake Size and dry weightThree-Four Runs at various P’sVarious Medium Types
Ave. Specific Cake ResistanceMedium ResistancePorosity (bulk density)Liquor viscosity and densityCompute ave, Rm
Sample slurry for laboratoryVolume vs Time dataCake size and dry weightDifferent pressures (if possible)Different medium types (if possible)
Understand geometric considerationsDevelop a working modelUnderstand equipment specific issuesOptimize operational strategy
Experimental Method and Analysis
Constant Pressure Filtration
o
m
oo
ave
AR
AAcV
P
dt
dVQ
o
m
mlm
ave
driving
AR
AAcV
P
dt
dVQ
areacloth oA
c
o
colm
r
r
rrhA
ln
2
Filter Media
Cake + Fluid
FluidP3
Pc
P1
Po
2
2 com
rrhA
R3 Rc R1 =Ro
Centrifugal SeparationsCentrifugal Filtration
o
m
oo
ave
driving
AR
AAcV
P
dt
dVQ
o
m
mlm
ave
driving
A
R
AA
cV
P
dt
dVQ
pressure applied drivingP 2
2
123
2 RRP fluiddriving
VPA
RVPA
ct
drivingm
drivingave
222
Driving force and surface area are functions of time, feed profile
Filtration equation can be integrated numerically
Centrifugal SeparationsConstant Pressure Filtration Centrifugal Filtration
Cross-Flow Filtration
Retentate Stream
Permeate Stream
Feed Tank
Backpressure Applied
Concentrate a dilute two phase (liquid solid) stream
Wash out a soluble impurity(diafiltration)
Switch solvents for further processing
Scales very easily on filter surface area
Filtration Flux
Filtration Time
Per
mea
te F
lux
21 ktkV
t
221
211
ktk
k
Adt
dV
AJ
Filtration Flux
Constant
Constant
Filtrate volume
Filtration area
2k
V
J
1k
A
Periodic Operation
Filtration Time
Per
mea
te F
lux
Backpressure Applied
Cycle Time Analysis
• Cake formation
• Operation times that depend on cake thickness– Washing, deliquoring
• Operation times independent of cake thickness– Loading, cake discharge, cleaning
Deliquoring
• Application of vacuum• Blowing with compressed gas• Centrifugation• Compression of the cake• Complete drainage is not usually achieved
– Final drying with hot gas flow through cake is used
• Kinetics and equilibrium of deliquoring– Threshold pressure: minimum pressure to achieve reduction in
saturation– Irreducible saturation: limiting value of saturation beyond which
no reduction in liquid content is possible S
bP
Deliquoring Time
)1(
SL
tkPb
Cake permeability
Liquid viscosity
Cake thickness
Porosity
Gas pressure
Mean particle size
Surface tension
L
k
aP
Dimensionless Time
Dimensionless Pressure Differenceoutletb
a
inletb
aa P
P
P
PP
Reduced Saturation
S
SSSR 1
49.0031.01155.0 cNS
L
PgLxNc 2
23
1
Capillary Number
x
x
Pb
16.4
Irreducible Saturation
Threshold Pressure
Deliquoring Time
aP
Red
uced
Sat
urat
ion
SR
1
1
Dimensionless time θ
Dimensionless pressuredifference
Washing• Remove contaminants in retained liquor• Methods
– Displacement washing– Reslurrying followed by refiltering
• “Perfect” displacement washing– Wash volume=void volume– Solute concentration=initial concentration
• Actual washing– Wash liquor tends to proceed through preferential pathways or
cracks in cake– Concentration of solute in wash liquid depends on mixing and
mass transport
Displacement Washing
Wash Volume
c/c 0
Perfect displacement washing
(no. of void volumes)
1
1
Actual washing
0cc
0cc
Washing Curves
Wash Ratio
c/c 0
Saturated cake: displacementfollowed by mixing and diffusion
1
1
Drained cake:No displacement stage
Washing curve for partially drained cakes will be in between curves for saturated and drained cake
Washing Analysis• “Perfectly Mixed” washing
L
kFt
eccConcentration at end of displacement washing
Wash flowrate/area
Cake thickness
Time from end of displacement washing
FL
c
Time
ln c
t
• Combined mixing and diffusion effects• Dispersion parameter
• Perfect mixing
Washing Analysis
Wash velocity
Cake thickness
Axial dispersion
Wash ratio
Adsorption effects
u
L
D
nD
uLf
c
c
o
s ,,
n
n
o
s ec
c
0
D
uL
D
uL
Washing Analysis
5001.0
D
uL
c/c 0
1
1
Wash Ratio
Washing curves as a function of dispersion parameter
Washing Time
Wash Ratio
Was
hin
g T
ime
Cake formation time
fw ntt Wash ratio
Washing time
Cake formation time
n
wt
ft
Examples
5 PSI delta P
0
20
40
60
80
100
120
140
0 10 20 30 40 50
Time (s)
Wei
gh
t o
f F
iltra
te (
g)
15 PSI filtration data
0
20
40
60
80
100
120
140
0 5 10 15 20
Time (s)
25 PSI data
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100 120
time (s)w
eigh
t (g)
Three pressures, same crystalslurry
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry
Filtration Analysis Example
5 PSI delta P
0
20
40
60
80
100
120
140
0 10 20 30 40 50
Time (s)
Wei
gh
t o
f F
iltra
te (
g)
Start up Effects
Cake Filtration
Cake Deliquoring
Filtration Analysis Example
dt/dw vs w for 5 PSI
y = 0.0031x + 0.0473
R2 = 0.8251
0
0.1
0.2
0.3
0.4
0.5
0 20 40 60 80 100 120
Weight (g)
dt/
dw
(s/
g)
dt/dw vs w for 15 PSI data
y = 0.0014x + 0.0362R2 = 0.9334
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100 120
weight (g)
dt/
dw
(s/
g)
dt/dw vs w for 25 psi data
y = 0.0011x + 0.0468
R2 = 0.7117
0.15
0.2
0.25
0.3
0.35
0.4
0.45
100 150 200 250 300
w (g)
dt/
dw
(s/g
)
PA
RV
PA
c
dV
dt mave2
PA
RV
PA
c
Vd
dt mave
22
filtrateofweightV
Filtration Analysis Example
dt/dw vs w for 5 PSI
y = 0.006x - 0.127
R2 = 0.4515
-0.5
0
0.5
1
1.5
2
0 50 100 150
Weight (g)
dt/
dw
(s/
g)
Start up Effects
Cake Deliquoring
Filtration Analysis Example
dt/dw vs w for 5 PSI
y = 0.0031x + 0.0473
R2 = 0.8251
0
0.1
0.2
0.3
0.4
0.5
0 20 40 60 80 100 120
Weight (g)
dt/
dw
(s/
g)
Intercept
Slope
InterceptSlope
Filtration Analysis Example
PA
RV
PA
c
Vd
dt mave
22
Slope 0.0031 s/g2
Viscosity 8.94E-04 kg/m-s
c 61.12 kg/m3
A 0.002 m2
ΔP 34474 N/m2 (5 psi)
Density 1.0 g/cm3 Alpha = 0.782E+10
22 PA
cslope ave
Filtration Analysis Example
so P
P alpha ln(p) ln()
5 0.785E+10 1.609438 22.78378
15 1.06E+10 2.70805 23.08412
25 1.39E+10 3.218876 23.35515
Pso lnlnln
Filtration Analysis Compressibility
ln ΔP
ln
Pso lnlnln
0.00E+00
2.00E+09
4.00E+09
6.00E+09
8.00E+09
1.00E+10
1.20E+10
1.40E+10
1.60E+10
0 10 20 30
Series1
ln (alpha) vs ln (dp)
y = 0.342x + 22.215R2 = 0.9686
22.722.822.9
2323.123.223.323.4
1.5 2 2.5 3 3.5
ln (dp)
ln (
alp
ha)
342.0s
Slightly compressible
Expect:Some effect ofpressure onfiltration flux
Likely acceptablefiltration in centrifuge
Filtration Analysis Compressibility
Filtrate volume as a function of time at several pressures
Understand the relationship between specific cake resistance and pressure (compressibility)
Fully characterized liquid / solid system(physical properties etc.).
How do we scale up to understandplant time cycles?
Filtration Analysis Scale Up
VPA
RVPA
ct
drivingm
drivingave
222
Parameters: Rm, - known from scaled down experimentsAll else known
Assuming: Same slurry composition, same filter medium, 25 psi
Kg Product 50 100 200 300 400 500 750 1000
2 m2 Filter 6 m 25 m 1.6 h 3.7 h 6.5h 10 h 23 h 41 h
4 m2 Filter 1.5m 6 m 25 m 55m 1.6 h 2.6 h 5.8 h 10 h
Filtration Time
Filtration Analysis Scale Up
Cycle Time Analysis Example
Filtration and wash times for scale-up options based on constant flux (L/M2H)
BaseA (2x) B C D E F G
Batch Size (kg) 11.0 50.0 100.0 100.0 100.0 200.0 200.0 200.0FD Area (m2) 0.2 0.6 0.6 2.0 4.0 0.6 2.0 4.0
Mother Liquor Volume (L) 86.0 390.9 781.8 781.8 781.8 1563.6 1563.6 1563.6Mother Liquor Filtration Time (Hr) 3.3 5.0 10.0 3.0 1.5 20.0 6.0 3.0
Wash 1 Volume (L) 50.0 227.3 454.5 454.5 454.5 909.1 909.1 909.1Wash 1 Filtration Time (hr) 7.3 11.0 22.0 6.6 3.3 43.9 13.2 6.6
Wash 2 Volume (L) 50.0 227.3 454.5 454.5 454.5 909.1 909.1 909.1Wash 2 Filtration Time (hr) 20.0 30.3 60.6 18.2 9.1 121.2 36.4 18.2
Wash 3 Volume (L) 50.0 227.3 454.5 454.5 454.5 909.1 909.1 909.1Wash 3 Filtration Time (hr) 5.7 8.6 17.2 5.1 2.6 34.3 10.3 5.1
Cake Depth (ratio to base) 1.5 3.0 0.9 0.5 6.1 1.8 0.9
Filtration Cycle Time 36.21 110 109.7 32.9 16.5 219.5 65.8 32.9Milling Time per slurry mill (hr) 3.0 27.3 27.3 27.3 27.3 54.5 54.5 54.5
Total Time Cycle (hr) 39.2 137.0 137.0 60.2 43.7 274.0 120.4 87.5
Scale-Up Options
References
• W. Leu, Principles of Compressible Cake Filtration, in Encyclopedia of Fluid Mechanics (N.P. Cheremisinoff, ed), Gulf, 1986.
• A. Rushton, A. S. Ward, R. G. Holdich, Solid-Liquid Filtration and Separation Technology, VCH, 1996.
• A. Rushton, Batch filtration of solid-liquid suspensions, in Handbook of Batch Process Design (P.N. Sharatt, ed), 153-192, Springer, 1997.