Solid-Liquid Separations Pharmaceutical API Process Development and Design.

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


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


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


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


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


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



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



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


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


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



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.

Solid-Liquid Separations Pharmaceutical API Process Development and Design.

Documents

Transcript of Solid-Liquid Separations Pharmaceutical API Process Development and Design.