1. Solid-Liquid Separations
Pharmaceutical API Process Development and Design 1

2. Solid-Liquid Separations
Filtration Analysis
Flow in packed beds
Cake Filtration
Centrifuges
Deliquoring
Washing
Examples
Cake compressibility
Cycle time calculations 2

3. Filtration Options Linear Filtration Centrifugal Filtration
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry

4. Filtration Options Cross Flow Filtration Retentate Stream
Backpressure Applied
Feed Tank
Permeate Stream
Cross Flow Filtration
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry

5. 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

6. Driving Forces Gravity Vacuum Pressure Centrifugal Force
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

7. Operating Mode Constant pressure filtration Constant rate filtration
Vacuum pumps, compressed gas
Constant rate filtration
Positive displacement pumps
Variable pressure, variable rate filtration
Centrifugal pumps

8. Cake Filtration suspension L, ΔP filter cake membrane
Luis Puigjaner (2007), Solid-Liquid Separations

9. Flow Through Packed Beds
Darcy’s Law
Permeability
Carman-Kozeny Equation
Pressure drop
Superficial velocity
Liquor viscosity
Bed height
Porosity
Specific surface area 9

10. Mass Balance 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
Filtrate density
Solid density
Thickness of cake
Porosity

11. Cake filtration equation
Rewrite Darcy’s law in terms of specific cake resistance, filtrate volume, solids concentration
With medium resistance
Cake pressure drop
Total pressure drop
Specific cake resistance
Filtrate volume
Dry solids/unit area
Dry solids/unit volume filtrate
Medium Resistance
a : Characteristic parameter of a specific solid/liquid system

12. Average Specific Cake Resistance (a), m/kg
Ease of Separation
Ease of Separation
Average Specific Cake Resistance (a), m/kg
Very Easy
1x109
Easy
1x1010
Moderate
1x1011
Difficult
1x1012
Very Difficult
1x1013
W Leu (1986), Principles of Compressible Cake Filtration 12

13. Filtration Analysis Q = Flow Rate of Eluent t = time of filtration
DP = pressure drop
A = effective area of filtration
μ = viscosity of filtrate
aave = average specific cake resistance
c = kg of dry cake per volume of filtrate
V = volume of filtrate
Rm = medium resistance
Assumptions:
Constant pressure
Constant area
Ignore gravity 13

14. Parabolic Data Analysis
Rearranging:
Plot t/V vs V – Linear
Slope – proportional to average specific cake resistance
Intercept – proportional to medium resistance 14

15. Cake Compressibility Filtrate Flowrate Pressure Drop Incompressible
Highly compressible
Pressure Drop
Incompressible solids - a is independent of pressure

16. Cake Compressibility Compressible solids - a varies with pressure
t / V
ΔP1, α1
ΔP2, α2
ΔP3, α3
Compressible solids - a varies with pressure 16

17. Cake Compressibility ln a ln ΔP Where usually, 0.1 < s < 0.8
Sometimes expressed as:
Where ao, Po, and s are empirical constants 17

18. 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 18

19. Experimental Method and Analysis
Laboratory Pressure Filtration
Factory or Pilot Plant Filtration
Representative Slurry
Volume vs Time Data
Cake Size and dry weight
Three-Four Runs at various P’s
Various Medium Types
Sample slurry for laboratory
Volume vs Time data
Cake size and dry weight
Different pressures (if possible)
Different medium types (if possible)
Parabolic Data Analysis
Scale Up Calculations
Understand geometric
considerations
Develop a working model
Understand equipment specific
issues
Optimize operational strategy
Ave. Specific Cake Resistance
Medium Resistance
Porosity (bulk density)
Liquor viscosity and density
Compute aave, Rm 19

20. Centrifugal Separations
Constant Pressure Filtration
Centrifugal Filtration R3 Rc
R1 =Ro P3
Fluid Pc
Cake + Fluid P1
Filter Media Po 20

21. Centrifugal Separations
Constant Pressure Filtration
Centrifugal Filtration
Driving force and surface area are functions of time, feed profile
Filtration equation can be integrated numerically 21

22. Cross-Flow Filtration
Backpressure Applied
Retentate Stream
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
Feed Tank
Permeate Stream

23. Filtration Flux Permeate Flux Filtration Time Filtration Flux Constant
Filtrate volume
Filtration area
Filtration Time

24. Periodic Operation
Backpressure Applied
Permeate Flux
Filtration Time

25. Cycle Time Analysis Cake formation
Operation times that depend on cake thickness
Washing, deliquoring
Operation times independent of cake thickness
Loading, cake discharge, cleaning 25

26. 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 26

27. Deliquoring Time Capillary Number Cake permeability Liquid viscosity
Cake thickness
Porosity
Gas pressure
Mean particle size
Surface tension
Irreducible Saturation
Threshold Pressure
Dimensionless Time
Dimensionless Pressure Difference
Reduced Saturation

28. Deliquoring Time Reduced Saturation SR Dimensionless time θ 1
Dimensionless pressure
difference
Reduced Saturation SR 1
Dimensionless time θ

29. 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 29

30. Displacement Washing c/c0 Wash Volume Perfect displacement washing 1
Actual washing 1
Wash Volume
(no. of void volumes) 30

31. Washing Curves c/c0 Wash Ratio Saturated cake: displacement
followed by mixing and diffusion 1
c/c0
Drained cake:
No displacement stage 1
Wash Ratio
Washing curve for partially drained cakes will be in between curves for saturated and drained cake 31

32. Washing Analysis “Perfectly Mixed” washing
Concentration at end of displacement washing
Wash flowrate/area
Cake thickness
Time from end of displacement washing
ln c
Time 32

33. Washing Analysis Combined mixing and diffusion effects
Dispersion parameter
Perfect mixing
Wash velocity
Cake thickness
Axial dispersion
Wash ratio
Adsorption effects 33

34. Washing Analysis c/c0 Wash Ratio
Washing curves as a function of dispersion parameter 1
c/c0 1
Wash Ratio 34

35. Washing Time Cake formation time Washing Time Wash Ratio Wash ratio

36. Examples

37. Filtration Analysis Example
Three pressures, same crystal
slurry
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry 37

38. Filtration Analysis Example
Cake Filtration
Cake Deliquoring
Start up Effects 38

39. Filtration Analysis Example39

40. Filtration Analysis Example
Cake Deliquoring
Start up Effects 40

41. Filtration Analysis Example
Slope
Intercept
Slope
Intercept 41

42. Filtration Analysis Example
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 42

43. Filtration Analysis Compressibility
ln ΔP
ln a DP
alpha
ln(p)
ln(a) 5
0.785E+10 15
1.06E+10 25
1.39E+10 43

44. Filtration Analysis Compressibility
Slightly compressible
Expect:
Some effect of
pressure on
filtration flux
Likely acceptable
filtration in
centrifuge 44

45. Filtration Analysis Scale Up
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 understand
plant time cycles? 45

46. Filtration Analysis Scale Up
Parameters: Rm, a - known from scaled down experiments
All else known
Assuming: Same slurry composition, same filter medium, 25 psi
Filtration Time 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
55m
2.6 h
5.8 h 46

47. Cycle Time Analysis Example
Filtration and wash times for scale-up options based on constant flux (L/M2H)

48. 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), , Springer, 1997.