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Solid-Liquid Separations
Pharmaceutical API Process Development and Design 1
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Solid-Liquid Separations
Filtration Analysis Flow in packed beds Cake Filtration Centrifuges Deliquoring Washing Examples Cake compressibility Cycle time calculations 2
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Filtration Options Linear Filtration Centrifugal Filtration
Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry
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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
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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
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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
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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
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Cake Filtration suspension L, ΔP filter cake membrane
Luis Puigjaner (2007), Solid-Liquid Separations
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Flow Through Packed Beds
Darcy’s Law Permeability Carman-Kozeny Equation Pressure drop Superficial velocity Liquor viscosity Bed height Porosity Specific surface area 9
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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
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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
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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
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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
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Parabolic Data Analysis
Rearranging: Plot t/V vs V – Linear Slope – proportional to average specific cake resistance Intercept – proportional to medium resistance 14
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Cake Compressibility Filtrate Flowrate Pressure Drop Incompressible
Highly compressible Pressure Drop Incompressible solids - a is independent of pressure
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Cake Compressibility Compressible solids - a varies with pressure
t / V ΔP1, α1 ΔP2, α2 ΔP3, α3 Compressible solids - a varies with pressure 16
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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
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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
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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
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Centrifugal Separations
Constant Pressure Filtration Centrifugal Filtration R3 Rc R1 =Ro P3 Fluid Pc Cake + Fluid P1 Filter Media Po 20
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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
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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
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Filtration Flux Permeate Flux Filtration Time Filtration Flux Constant
Filtrate volume Filtration area Filtration Time
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Periodic Operation Backpressure Applied Permeate Flux Filtration Time
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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
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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
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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
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Deliquoring Time Reduced Saturation SR Dimensionless time θ 1
Dimensionless pressure difference Reduced Saturation SR 1 Dimensionless time θ
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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
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Displacement Washing c/c0 Wash Volume Perfect displacement washing 1
Actual washing 1 Wash Volume (no. of void volumes) 30
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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
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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
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Washing Analysis Combined mixing and diffusion effects
Dispersion parameter Perfect mixing Wash velocity Cake thickness Axial dispersion Wash ratio Adsorption effects 33
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Washing Analysis c/c0 Wash Ratio
Washing curves as a function of dispersion parameter 1 c/c0 1 Wash Ratio 34
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Washing Time Cake formation time Washing Time Wash Ratio Wash ratio
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Examples
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Filtration Analysis Example
Three pressures, same crystal slurry Kevin Seibert (2006), Solid-Liquid Separations in the Pharmaceutical Industry 37
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Filtration Analysis Example
Cake Filtration Cake Deliquoring Start up Effects 38
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Filtration Analysis Example
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Filtration Analysis Example
Cake Deliquoring Start up Effects 40
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Filtration Analysis Example
Slope Intercept Slope Intercept 41
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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
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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
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Filtration Analysis Compressibility
Slightly compressible Expect: Some effect of pressure on filtration flux Likely acceptable filtration in centrifuge 44
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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
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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
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Cycle Time Analysis Example
Filtration and wash times for scale-up options based on constant flux (L/M2H)
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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.
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