Preparative Chromatography E-Book
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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Sprache: Englisch
Completely revised and substantially extended to reflect the developments in this fast-changing field. It retains the interdisciplinary approach
that elegantly combines the chemistry and engineering involved to describe the conception and improvement of chromatographic processes.
It also covers recent advances in preparative chromatographic processes for the separation of "smaller" molecules using standard
laboratory equipment as well as the detailed conception of industrial chemical plants. The increase in biopharmaceutical substances is
reflected by new and revised chapters on different modifications of continuous chromatography as well as ion-exchange chromatography and
other separation principles widely used in biochromatography.
Following an introductory section on the history of chromatography, the current state of research and the design of chromatographic processes, the book goes on to define the general terminology. There then follow sections on stationary phases, selection of chromatographic
systems and process concepts. A completely new chapter deals with engineering and operation of chromatographic equipment. Final chapters on modeling and determination of model parameters as well as model based design, optimization and control of preparative chromatographic processes allow for optimal selection of chromatographic processes.
Essential for chemists and chemical engineers in the chemical, pharmaceutical, and food industries.
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Seitenzahl: 855
Veröffentlichungsjahr: 2012
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Contents
Cover
Related Titles
Title Page
Copyright
Preface
About the Editors
List of Contributors
List of Abbreviations
Notation
Symbols
Greek Symbols
Subscripts
Definition of Dimensionless Parameters
Chapter 1: Introduction
1.1 Development of Chromatography
1.2 Focus of the Book
1.3 Recommendation to Read this Book
References
Chapter 2: Fundamentals and General Terminology
2.1 Principles of Adsorption Chromatography
2.2 Basic Effects and Chromatographic Definitions
2.3 Fluid Dynamics
2.4 Mass Transfer Phenomena
2.5 Equilibrium Thermodynamics
2.6 Thermodynamic Effects on Mass Separation
References
Chapter 3: Stationary Phases and Chromatographic Systems
3.1 Column Packings
3.2 Selection of Chromatographic Systems
References
Chapter 4: Chromatography Equipment: Engineering and Operation
4.1 Introduction
4.2 Engineering and Operational Challenges
4.3 Chromatography Columns Market
4.4 Chromatography Systems Market
4.5 Process Control
4.6 Packing Methods
4.7 Process Troubleshooting
4.8 Disposable Technology for Bioseparations
References
Chapter 5: Process Concepts
5.1 Discontinuous Processes
5.2 Continuous Processes
5.3 Choice of Process Concepts
References
Chapter 6: Modeling and Model Parameters
6.1 Introduction
6.2 Models for Single Chromatographic Columns
6.3 Modeling HPLC Plants
6.4 Calculation Methods
6.5 Parameter Determination
6.6 Experimental Validation of Column Models
References
Chapter 7: Model-Based Design, Optimization, and Control
7.1 Basic Principles and Definitions
7.2 Batch Chromatography
7.3 Recycling Chromatography
7.4 Conventional Isocratic SMB Chromatography
7.5 Isocratic SMB Chromatography under Variable Operating Conditions
7.6 Gradient SMB Chromatography
7.7 Multicolumn Systems for Bioseparations
7.8 Advanced Process Control
References
Appendix A: Data of Test Systems
A.1 EMD53986
A.2 Tröger's Base
A.3 Glucose and Fructose
A.4 β-Phenethyl Acetate
A.5 ß-Lactoglobulin A and B
References
Index
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Preface
Over 7 years have passed since the 1st edition of this book was published, and practical application as well as theoretical research on preparative chromatography has since then progressed rapidly. This motivated us to revise the content of the 1st edition.
We decided to rearrange the structure in this 2nd edition. Our intention was to present the aspects of practical equipment design and operation together in a separate chapter, to merge the discussion on stationary phases and the selection of chromatographic systems in one chapter, and to reduce the content concerning chromatographic reactors because of their specific features and the still limited practical relevance. These changes provided room for important new sections on ion exchange, bioseparation, and new process concepts and calculation methods.
What else is new in this revised second edition? First of all, the team did change significantly. Besides the additional editors, there are several new authors from industry and academia. The former crew from Dortmund University went to industries and is now active in other fields of chemical engineering. Their names as well as the names of other authors of the first edition are marked by asterisk in the byline of the corresponding chapters.
We are grateful to Klaus Unger, Jules Dingenen, and Reinhard Ditz that they agreed to join us as senior authors. The most challenging task to tackle is presented in Chapter 4 that has been efficiently handled by Abdelaziz Toumi, Joel Genolet, Andre Kiesewetter, Martin Krahe, Michele Morelli, Olivier Ludemann- Hombourger, Andreas Stein, and Eric Valery. It is in the nature of practical design and plant operation that the experience and interests are sometimes different. Additionally, the limited volume further constrains the content. But we hope to meet most of the practical aspects related to design and operation of chromatographic plants.
In Chapter 3, Matthias Jöhnck and Romas Skudas with the team of Michael Schulte combined the formerly separated topics on stationary phases and chromatographic systems to a unique and completely revised chapter and also extended it to ion exchange. We are especially indebted to Malte Kaspereit for his valuable contributions to Chapters 5 and 7. Sebastian Engell provided in Chapter 7 an overview of the latest research results on advanced process control. We hope that this will motivate practitioners to have a closer look at these promising methods.
Finally, we want to acknowledge the assistance of Fabian Thygs, who produced the new drawings and was patient enough to handle all our revisions.
As in the 1st edition, we have summarized the recently published results. In addition, we have made efforts to address preparative and process chromatographic issues from both the chemist and the process engineer viewpoints in order to improve the mutual understanding and to transfer knowledge between both disciplines.
With this book we want to reach colleagues from industries as well as universities interested in chromatographic separation with preparative purpose. Students and other newcomers looking for detailed information about design and operation of preparative chromatography are hopefully other users. Our message to all of them is that chromatography is nowadays rather well understood and not that difficult and expensive as it is often said and perceived. On the other hand, it is of course not the solution for all separation problems.
We would like to thank all authors for their contributions. We apologize for sometimes getting on their nerves pressing them to meet time limits. Last but not least, we thank our families and friends for their patience and cooperation in bringing out this book.
August 2012
Henner Schmidt-Traub
Michael Schulte
Andreas Seidel-Morgenstern
About the Editors
Henner Schmidt-Traub was Professor of Plant and Process Design at the Department of Biochemical and Chemical Engineering, TU Dortmund University, Germany, until his retirement in 2005. He is still active in the research community and his main areas of research focus on preparative chromatography, downstream processing, integrated processes, and plant design. Prior to his academic appointment, Prof. Schmidt-Traub gained 15 years of industrial experience in plant engineering.
Michael Schulte is Senior Director, Emerging Businesses Energy, at Merck KGaA Performance Materials, Darmstadt, Germany. In his PhD thesis at the University of Münster, Germany, he developed new chiral stationary phases for chromatographic enantioseparations. In 1995 he joined Merck and since then he has been responsible for research and development in the area of preparative chromatography, including the development of new stationary phases, new separation processes, and the implementation of Simulated Moving Bed technology at Merck. In his current position, one of the areas of his research is the use of ionic liquids for separation processes.
Andreas Seidel-Morgenstern is Director at the Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, and holds the Chair in Chemical Process Engineering at the Otto-von-Guericke-University, Magdeburg, Germany. He received his PhD in 1987 at the Institute of Physical Chemistry of the Academy of Sciences in Berlin. From there he went on to work as postdoctoral fellow at the University of Tennessee, Knoxville, TN. In 1994 he finished his habilitation at the Technical University in Berlin. His research is focused on new reactor concepts, chromatographic reactors, membrane reactors, selective crystallization, adsorption and preparative chromatography, and separation of enantiomers among others.
List of Contributors
Jules Dingenen
Horststraat 51
2370 Arendonk
Belgium
Reinhard Ditz
Merck KGaA
Technology Office Chemicals (TO-I)
Frankfurter Str. 250
64291 Darmstadt
Germany
Sebastian Engell
TU Dortmund
Fakultät Bio- und Chemieingenieurwesen
Lehrstuhl für Systemdynamik und Prozessführung
Emil-Figge-Str. 70
44227 Dortmund
Germany
Joel Genolet
Merck Serono S.A.
Corsier sur Vevey
Zone Industrielle B
1809 Fenil sur Corsier
Switzerland
Matthias Jöhnck
Merck KGaA
R&D Performance & Life Science Chemicals
Frankfurter Str. 250
64291 Darmstadt
Germany
Malte Kaspereit
Friedrich-Alexander-Universität Erlangen-Nürnberg
Lehrstuhl für Thermische Verfahrenstechnik
Egerlandstr. 3
91058 Erlangen
Germany
Andre Kiesewetter
Merck KGaA
PC-SRG-Bioprocess Chromatography
Frankfurter Str. 250
64293 Darmstadt
Germany
Martin Krahe
Bideco AG
Bankstr. 13
8610 Uster
Switzerland
Olivier Ludemann-Hombourger
Polypeptide laboratories France
7 rue de Boulogne
67100 Strasbourg
France
Michele Morelli
Merck-Millipore SAS
39 Route Industrielle de la Hardt – Bldg E
67120 Molsheim
France
Henner Schmidt-Traub
TU Dortmund
Fakultät für Bio- und
Chemieingenieurwesen
Lehrstuhl für Anlagen- und Prozesstechnik
Emil-Figge-Str. 70
44227 Dortmund
Germany
Michael Schulte
Merck KGaA
R&D Performance & Life Science Chemicals
Frankfurter Str. 250
64291 Darmstadt
Germany
Andreas Seidel-Morgenstern
Otto-von-Guericke-Universität
Lehrstuhl für Chemische Verfahrenstechnik
Universitätsplatz 2
and
Max-Planck-Institut für Dynamik komplexer technischer Systeme
Sandtorstraße 1
39106 Magdeburg
Germany
Romas Skudas
Merck KGaA
R&D Performance & Life Science Chemicals
Frankfurter Str. 250
64291 Darmstadt
Germany
Andreas Stein
Merck KGaA
Chromatography Global Applied Technology
Frankfurter Str. 250
64291 Darmstadt
Germany
Abdelaziz Toumi
Merck Serono S.A.
Corsier sur Vevey
Zone Industrielle B
1809 Fenil sur Corsier
Switzerland
Klaus K. Unger
Am alten Berg 40
64342 Seeheim
Germany
Eric Valery
Novasep Process
Boulevard de la Moselle
BP 50
54340 Pompey
France
List of Abbreviations
ACD:At-column dilutionAIEX:Anion exchangerARX:Autoregressive exogenousATEX:Explosion proof (French: ATmospheres EXplosibles)BET:Brunauer–Emmet–TellerBJH:Barrett–Joyner–HalendaBR:Chromatographic batch reactorBV:Bed volumeCACR:Continuous annular chromatographic reactorCD:Circular dichroism (detectors)CEC:Capillary electrochromatographyCFD:Computational fluid dynamicscGMP:Current good manufacturing practiceCIEX:Cation exchangerCIP:Cleaning in placeCLP:Column liquid chromatographyCLRC:Closed-loop recycling chromatographyCOGS:Cost of goods soldCPG:Controlled pore glassCSEP®:Chromatographic separationCSF:Circle suspension flowCSP:Chiral stationary phaseCTA:Cellulose triacetateCTB:Cellulose tribenzoateDAC:Dynamic axial compressionDAD:Diode array detectorDMF:Dimethyl formamideDMSO:Dimethyl sulfoxideDTA:Differential thermal analysisDVB:DivinylbenzeneEC:Elution consumptionECP:Elution by characteristic pointsEDM:Equilibrium dispersive modelEMG:Exponential modified Gauss (function)FACP:Frontal analysis by characteristic pointsFDM:Finite difference methodsFFT:Forward flow testFT:Flow throughGC:Gas chromatographyGMP:Good manufacturing practiceGRM:General rate modelHCP:Health care providerHETP:Height of an equivalent theoretical plateHFCS:High fructose corn syrupHIC:Hydrophobic interaction chromatographyH-NMR:Hydrogen nuclear magnetic resonance (spectroscopy)HPLC:High-performance liquid chromatographyHPW:Highly purified waterIAST:Ideal adsorbed solution theoryICH:International Guidelines for HarmonizationIEX:Ion exchangeIMAC:Immobilized metal affinity chromatographyIR:InfraredISEC:Inverse size exclusion chromatographyISEP®:Ion exchange separationISMB:Improved/intermittent simulated moving bedLC:Liquid chromatographyLGE:Linear gradient elutionLHS:Liquid-handling stationLOD:Limit of detectionLOQ:Limit of quantificationLPLC:Low-pressure liquid chromatographyLSB:Large Scale Biotech projectMaB:Monoclonal antibodymAbs:monoclonal antibodiesMD:Molecular dynamicsMPC:Model predictive controlMS:Mass spectroscopyMW:Molecular weightNMPC:Nonlinear model predictive controlNMR:Nuclear magnetic resonance (spectroscopy)NN:Neural networkNP:Normal phaseNPLC:Normal-phase liquid chromatographyNSGA:Non-dominating sorting generic algorithmOC:Orthogonal collocationOCFE:Orthogonal collocation on finite elementsODE:Ordinary differential equationPAT:Process analytical technologyPDE:Partial differential equationPDT:Pressure decay testPEEK:Poly(ether ether ketone)PES:Poly(ethoxy)siloxanePLC:Programmable logic controllerPMP:PolymethylpentenePSD:Particle size distributionQC:Quality controlR&D:Research and DevelopmentRI:Refractive indexRMPC:Repetitive model predictive controlRP:Reversed phaseS/N:Signal-to-noise ratioSEC:Size exclusion chromatographySEM:Scanning electron microscopySFC:Supercritical fluid chromatographySIP:Sanitization in placeSIP:Steaming in placeSMB:Simulated moving bedSMBR:Simulated moving bed reactorSOP:Standard operation procedureSQP:Sequential quadratic programmingSSRC:Steady-state recycling chromatographySt-DVB:Styrene-divinylbenzeneTDM:Transport dispersive modelTEM:Transmission electron microscopyTEOS:TetraethoxysilaneTFA:Trifluoroacetic acidTG/DTA:Thermogravimetric/differential thermal analysisTHF:TetrahydrofuranTLC:Thin-layer chromatographyTMB:True moving bed processTMBR:True moving bed reactorTPX™:Transparent polymethylpenteneUPLC:Ultrahigh-performance liquid chromatographyUSP:United States pharmacopoeiaUV:UltravioletVSP:Volume-specific productivityWFI:Water for injectionWIT:Water intrusion testNotation
Symbols
SymbolDescriptionUnitsaiCoefficient of the Langmuir isothermcm3 g−1asSpecific surface areacm2 g−1AAreacm2AcCross section of the columncm2AiCoefficient in the Van Deemter equationcmAsSurface area of the adsorbentcm2ASPCross section-specific productivityg cm−2 s−1biCoefficient of the Langmuir isothermcm3 g−1BColumn permeabilitym2BiCoefficient in the Van Deemter equationcm2 s−1ciConcentration in the mobile phaseg cm−3cp,iConcentration of the solute inside the particle poresg cm−3CAnnual costs€CiCoefficient in the Van Deemter equationsCDL,iDimensionless concentration in the liquid phase—Cp,DL,iDimensionless concentration of the solute inside the particle pores—CspecSpecific costs€ g−1dcDiameter of the columncmdpAverage diameter of the particlecmdporeAverage diameter of the porescmDanAngular dispersion coefficientcm2 s−1Dapp,iApparent dispersion coefficientcm2 s−1Dapp,poreApparent dispersion coefficient inside the porescm2 s−1DaxAxial dispersion coefficientcm2 s−1DmMolecular diffusion coefficientcm2 s−1Dpore,iDiffusion coefficient inside the porescm2 s−1Dsolid,iDiffusion coefficient on the particle surfacecm2 s−1DaDamkoehler number—ECEluent consumptioncm3 g−1FPrices€ l−1, € g−1fiFugacity—hReduced plate height—hRfRetardation factor—ΔhvapHeat of vaporizationkJ mol−1HiHenry coefficient—HpPrediction horizon—HrControl horizon—HETPHeight of an equivalent theoretical platecmkads,iAdsorption rate constantcm3 g−1 s−1kdes,iDesorption rate constantcm3 g−1 s−1keff,iEffective mass transfer coefficientcm2 s−1KeqEquilibrium constantMiscellaneousKEQDimensionless equilibrium coefficient—kfilm,iBoundary or film mass transfer coefficientcm s−1Retention factor—Modified retention factor—k0Pressure drop coefficient—kreacRate constantMiscellaneousLFLoading factor—LcLength of the columncmMass flowg s−1miMassgmjDimensionless mass flow rate in section j—msTotal massgniMolar cross section of component i—nTPore connectivity—NColumn efficiency, number of plates—NcolNumber of columns—NcompNumber of components—NpNumber of particles per volume element—ΔpPressure dropPaPePéclet number—PriProductivityg cm3 h−1PsSelectivity point—PuiPurity%qiSolid loadg cm−3qi∗Total loadg cm−3Averaged particle loadg cm−3qsat,iSaturation capacity of the stationary phaseg cm−3QDL,iDimensionless concentration in the stationary phase—rRadial coordinatecmriReaction rateMiscellaneousrpParticle radiuscmRfRetardation factor—RiRegulation term—RsResolution—ReReynolds number—SBETSpecific surface aream2 g−1ScSchmidt number—ShSherwood number—StStanton number—tTimest0Dead time of the column (for total liquid holdup)st0,intDead time of the column (for interstitial liquid holdup)stcycleCycle timestgGradient timestinjInjection timestlifeLifetime of adsorbenthtplantDead time of the plant without columnstR,iRetention timestR,i,netNet retention timestshiftSwitching time of the SMB plantsttotalTotal dead timesTTemperatureKTDegree of peak asymmetry—u0Velocity in the empty columncm s−1uintInterstitial velocity in the packed columncm s−1umEffective velocity (total mobile phase)cm s−1vspSpecific pore volumecm3 g−1VVolumecm3Volume flowcm3 s−1VadsVolume of the stationary phase within a columncm3VcTotal volume of a packed columncm3ViMolar volumecm3 mol−1VintInterstitial volumecm3VmOverall fluid volumecm3VporeVolume of the pore systemcm3VsolidVolume of the solid materialcm3VSPVolume-specific productivityg cm3 s−1wiVelocity of propagationcm s−1xCoordinatecmxiState of the plant—XiMole fraction—XConversion%XcatFraction of catalyst of the fixed bed—YiYield%ZDimensionless distance—Greek Symbols
SymbolDescriptionUnitsαSelectivity—αexpLigand densityµmol m−2βModified dimensionless mass flow rate—γObstruction factor for diffusion or external tortuosity—ΓObjective function—εVoid fraction—ε0Solvent strength parameter—εpPorosity of the solid phase—εtTotal column porosity—ηDynamic viscositymPa sΘAngle of rotation°Total ion exchange capacitymMλIrregularity in the packing—µiChemical potentialJ mol−1µtFirst absolute moment—νKinematic viscositycm2 sνiStoichiometric coefficient—πSpreading pressurePaρDensityg cm−3σtStandard deviation—σiSteric shielding parameter—τDimensionless time—ϕBed voidage—ϕRunning variableψFriction number—ψreacNet adsorption rateg cm−3 s−1ωjCoefficient in the triangle theory—ωRotation velocity°s−1Subscripts
SymbolDescription1, 2Component 1/component 2I, II, III, IVSection of the SMB or TMB processaccAccumulationadsAdsorbentcColumncatCatalystconvConvectioncrudeCrude lossdesDesorbentdiffDiffusiondispDispersionDLDimensionlesseffEffectiveelEluentexpExperimentalextExtractfeedFeedhetHeterogeneoushomHomogeneousiComponent iinInletinjInjectionjSection j of the TMB or SMB processlLiquidlinLinearmaxMaximumminMinimummobMobile phasemtMass transferoptOptimaloutOutletpParticleporePorepipePipe within HPLC plantplantPlant without columnprodProductrafRaffinatereacReactionrecRecyclesatSaturationsecSectionshockShock frontSMBSimulated moving bed processsolidSolid adsorbentspecSpecificstatStationary phasetankTank within HPLC planttheoTheoreticalTMBTrue moving bed processDefinition of Dimensionless Parameters
Péclet numberConvection to dispersion (column)Péclet number of the particleConvection to dispersion (particle)Péclet number of the plantConvection to dispersion (plant without column)Reynolds numberInertial force to viscous forceSchmidt numberKinetic viscosity to diffusivitySherwood numberMass diffusivity to molecular diffusivityStanton number (modified)Mass transfer to convectionChapter 1
Introduction
Henner Schmidt-Traub and Reinhard Ditz
1.1 Development of Chromatography
Adsorptive separations have been in use well before the twentieth century. Tswett (1906, 2010), however, was the first who coined the term “Chromatography” in 1903 for the isolation of chlorophyll constituents. Kuhn and Brockmann, in the course of their research recognized the need for more reproducible and also more selective adsorbents, specially tuned for specific separation problems. This recognized demand for reproducible stationary phases led to the development of first materials standardized for adsorption strength and describes the first attempt toward reproducible separations (Unger et al., 2010).
Liquid Chromatography (LC) was first applied as a purification tool and has thereby been used as a preparative method. It is the only technique that enables to separate and identify both femtomoles of compounds out of complex matrices in life sciences, and also allows the purification and isolation of synthetic industrial products in the ton range. The development of modern LC methodology and the corresponding technologies are based on three main pillars, which have developed over different time scales (Figure 1.1).
Figure 1.1 Development of chromatography (reproduced from Unger et al., 2010).
In the field of preparative and process chromatography the “restart” after the dormant period between the 1930s and the 1960s was not induced by the parallel emergence of analytical HPLC, but from engineering in search of more effective purification technologies. High selectivity of HPLC in combination with the principle to enhance mass transfer by counter current flow significantly increased the performance of preparative chromatography in terms of productivity, eluent consumption, yield, and concentration. The first process of this kind was the Simulated Moving Bed (SMB) chromatography for large-scale separation in the petrochemical area and in food processing. The development of new processes was accompanied by theoretical modeling and process simulation which are a prerequisite for better understanding of transport phenomena and process optimization.
In the 1980s, highly selective adsorbents were developed for the resolution of racemates into enantiomers. These adsorbents were mainly employed in analytical HPLC (Allenmark, 1992). However, the availability of enantioselective packings in bulk quantities also enabled the production of pure enantiomers by the SMB technology in the multi ton range. Productivities larger than 10 kg of pure product per kilogram of packing per day were achieved in the following years. In the 1990s the SMB concept was adapted and down-sized for the production of pharmaceuticals.
While preparative as well as analytical liquid chromatography were heavily relying on equipment and engineering and on the physical aspects of their tools for advancement in their fields, the domain Bioseparation was built around a different key aspect, namely, selective materials that allowed the processing of biopolymers, for example, recombinant proteins under nondegrading conditions, thus maintaining bioactivity. Much less focus in this area was on process engineering aspects, leading to the interesting phenomenon, that large-scale production concepts for proteins were designed around the mechanical instability of soft gels (Janson and Jönsson, 1905). The separation of proteins and other biopolymers has some distinctly different features compared with the separation of low molecular weight molecules from synthetic routes or from natural sources. Biopolymers have a molecular weight (MW) ranging from several thousand to several million. They are charged and characterized by their isoelectric point. More importantly, they have a dynamic tertiary structure that can undergo conformational changes. These changes can influence or even destroy the bio-activity in case of a protein denaturation. Biopolymers are separated in aqueous buffered eluents under conditions that maintain their bioactivity. Moreover, these large molecules exhibit approximately 100 times lower diffusion coefficients and consequently slower mass transfer than small molecules (Unger et al., 2010). Due to these conditions, processes for biochromatography differ substantially from the separation of low-weight molecules. For instance, process pressure which is in many cases much lower for bio-processes than for HPLC requires a different plant design. Selectivity makes another difference; due to the very different retention times of bio-solutes an effective separation is only possible with solvent gradients.
Taking a peek into the future reveals a technology trend toward the use of continuous process operations and also downstream processing. Costs and production capacities will have to be addressed, asking for more integrated and efficient approaches. Adapting counter current solvent gradient concepts for the isolation of antibodies from complex fermentation broths will probably allow for more cost effective downstream processing of biopharmaceuticals within the next couple of years. A similar path might be useful to consider for dealing with the “glyco”-issue. Knowing that glycosylation plays a significant role in therapeutic drug efficacy, the analytical approaches developed around mixed-mode separation methods might be transferred to the process scale within a short time.
Validation of methods and assays will become a key issue. This fits directly with the Process Analytical Technology (PAT) initiative launched already years ago by the Food and Drug Administration (FDA), calling for a better process understanding. Among other things, this requires a much deeper insight into the underlying interactions using model-based approaches, which should finally allow “predictable” process design and monitoring strategies in the future to enhance process robustness and safety.
1.2 Focus of the Book
The general objective of preparative chromatography is to isolate and purify products independent of the amount of material to be separated. During this process, the products have to be recovered in the exact condition that they were in before undergoing the separation. In contrast to this analytical chromatography, which is beyond the content of this book, focuses on the qualitative and quantitative determination of a compound, that is, the sample can be processed, handled, and modified in any way suitable to generate the required information, including degradation, labeling, or otherwise changing the nature of the compounds.
The book describes and develops access to chromatographic purification concepts through the eyes of both engineers and chemists. This includes on one side the fundamentals of natural science and the design of matter and functionalities and on the other side mathematical modeling, simulation and plant design, as well as joined intersections in characterizing matter, process design, and plant operation. Such a joint view is necessary as the earliest possible interaction and cooperation between chemists and engineers is important to achieve time and cost-effective solutions and develop consistent methods that can be scaled up to a process environment.
With the second edition of this book the focus on fine chemicals and small pharmaceutical molecules is expanded to ion-exchange chromatography and the separation of biopolymers such as proteins. In accordance with the first edition these topics are restricted to those applications that can be modeled and simulated by current methods and procedures.
1.3 Recommendation to Read this Book
For most readers it is not necessary to read all chapters in sequence. For some readers the book may be a reference to answer specific questions depending on actual tasks, for others it may be a guide to acquire new fields of work in research or industrial applications. The different chapters are complementary to each other; therefore, it is recommended to be familiar with basic definitions explained in Chapter 2. The book may not provide answers to all questions. In which case, the reader can obtain further information from the cited literature.
Chapter 2 presents the basic principles of chromatography and defines the most important parameters such as retention, retention factor, selectivity, and resolution. It also explains the main model parameters as well as different kinds of isotherm equations including the IAS theory, and the determination of pressure drop. Other passages are devoted to plate numbers, HETP values as well as their determination based on first and second moments. The experienced reader may pass quickly through this chapter to become familiar with definitions used. For beginners this chapter is recommended in order to learn the general terminology and acquire a basic understanding. A further goal of this chapter is the harmonization of general chromatographic terms between engineers and chemists.
Chapter 3 focuses on stationary phases and the selection of chromatographic systems. The first part explains the structure and specifies the properties of stationary phases such as generic and designed phases, reversed-phase silicas, cross-linked organic polymers, and chiral phases, and gives instructions for their maintenance and regeneration. This part may be used as reference for special questions and will help those looking for an overview of attributes of different stationary phases. The second part deals with the selection of chromatographic systems, that is, the optimal combination of stationary phases and eluent or mobile phases for a given separation task. Criteria for choosing NP-, RP-, and CSP-systems are explained and are completed by practical recommendations. Other topics discussed are the processing of monoclonal antibodies and size exclusion. Finally, practical aspects of the overall optimization of chromatographic systems are discussed.
The selection of chromatographic systems is the most critical for process productivity and thus process economy. On one hand, the selection of the chromatographic system offers the biggest potential for optimization but, on the other hand, it is a potential source of severe errors in developing separation processes.
Chapter 4 focuses on practical aspects concerning equipment and operation of chromatographic plants for the production and purification of fine chemicals and small pharmaceutical molecules as well as proteins and comparable bio-molecules. It starts with the market of chromatographic columns followed by chromatography systems, that is, all equipment required for production. This includes high performance as well as low-pressure batch systems and SFC plants as well as continuous SMB systems, supplemented by remarks on auxiliary equipment. Further topics are standard process control and detailed procedures for different methods of column packing. The section on trouble shooting might be an interesting source for practitioners. Especially for the manufacturing of bio-therapeutics special disposable technologies such as prepacked columns and single-use membrane chromatography are exemplified.
Chapter 5 gives an overview of process concepts available for preparative chromatography. Depending on the operating mode, several features distinguish chromatographic process concepts: batch-wise or continuous feed introduction, operation in single- or multicolumn mode, integration of reaction and separation in one process step, elution under isocratic or gradient conditions, recycling of process streams, withdrawal of two or a multitude of fractions, and SMB processes under variable conditions. It finishes with guidelines for the choice of a process concept.
In Chapter 6, modeling and determination of model parameters are key aspects. “Virtual experiments” by numerical simulations can considerably reduce the time and amount of sample needed for process analysis and optimization. To reach this aim, accurate models and precise model parameters for chromatographic columns are needed. Validated models can be used predictively for optimal plant design. Other possible fields of application for process simulation include process understanding for research purposes as well as training of personnel. This includes the discussion of different models for the column and plant peripherals. Besides modeling, a major part of this chapter is devoted to the consistent determination of the model parameters, especially those for equilibrium isotherms. Methods of different complexity and experimental effort are presented which allow a variation of the desired accuracy, on the one hand, and the time needed on the other hand. Chapter 6 ends with a selection of different examples showing that an appropriate model combined with consistent parameters can simulate experimental data within high accuracy.
After general criteria and parameters for process optimization are defined, Chapter 7 focuses first on single-column processes. Design and scaling procedures for batch as well as recycle processes are described and a step-by-step optimization procedure is exemplified. In case of isocratic and gradient SMB processes, rigorous process simulations combined with short-cut calculations based on the TMB-model are useful tools for process optimization, which is illustrated by different example cases. Further sections discuss the improvements of SMB chromatography by variable operating conditions as given by Varicol, PowerFeed, or ModiCon processes. Finally, the latest scientific results on model-based advanced control of SMB processes are presented which are thought to be of increasing importance for practical applications.
References
Allenmark, S. (1992) Chromatographic Enantioseparation: Methods and Applications, Wiley, New York.
Janson, J. and Jönsson, J.-A. (2010) Protein Purification (ed. J.C. Janson), VCH, Weinheim.
Tswett, M.S. (1905) O novoy kategorii adsorbtsionnykh yavleny i o primenenii ikh k biokkhimicheskomu analizu (On a new category of adsorption phenomena and on its application to biochemical analysis), Trudy Varhavskago Obshchestva Estestvoispytatelei, Otdelenie Biologii (Proceedings of the Warsaw Society of Naturalists [i.e., natural scientists], Biology Section), 14, no. 6, 20–39.
Tswett, M.S. (1906) Physical chemical studies on chlorophyll adsorption. Berichte der Deutschen botanischen Gesellschaft, 24, 316–323 (as translated and excerpted in H.M. Leicester, Source Book in Chemistry 1900–1950, Cambridge, MA: Harvard, 1968).
Unger, K., Ditz, R., Machtejevas, E., and Skudas, R. (2010) Liquid chromatography – its development and key role in life sciences applications. Angew. Chemie, 49, 2300–2312.
Chapter 2
Fundamentals and General Terminology
Andreas Seidel-Morgenstern, Michael Schulte1, and Achim Epping1
This chapter introduces fundamental aspects and basic equations for the characterization of chromatographic separations. Starting from the simple description of an analytical separation of different compounds, the influences of fluid dynamics, mass transfer, and thermodynamics are explained. The important separation characteristics for preparative and process chromatography, for example, the optimization of resolution and productivity as well as the differences compared with chromatography for analytical purposes, are described. The importance of understanding the behavior of substances in the nonlinear range of the adsorption isotherm is highlighted.
One further goal of this chapter is to contribute to the harmonization of general chromatographic terms between engineers and chemists.
2.1 Principles of Adsorption Chromatography
Chromatography belongs to the thermal separation processes used to separate homogeneous molecular dispersive mixtures. The separations can be divided in general into three steps (Sattler, 1995):
Regarding chromatographic separation, the homogeneous mixture phase is a fluid. The additional second phase is a solid or a second immiscible fluid. The driving force for transport between the phases is the deviation of the compositions from the equilibrium state. The mixture introduced is separated by selective relative movements of the components between the two phases. Usually, the solid phase is fixed and designated accordingly as stationary phase. The fluid phase moves and is therefore called mobile phase. Chromatographic behavior is determined by the specific interactions of all single components present in the system with the mobile and stationary phases. The mixture of substances to be separated, the carrier (solvent), which is used for dissolution and transport, and the adsorbent (stationary phase) are summarized as the chromatographic system (Figure 2.1). In laboratory practice a chromatographic system suitable to solve a given separation problem is selected by a process typically called method development.
Figure 2.1 Definitions of adsorption and the chromatographic system.
According to the state of aggregation of the fluid phase, chromatographic systems can be divided into several categories. If the fluid phase is gaseous, the process is called gas chromatography (GC). If the fluid phase is a liquid, the process is called liquid chromatography (LC). For a liquid kept at temperature and pressure conditions above its critical point the process is called supercritical fluid chromatography (SFC). Liquid chromatography can be further divided according to the geometrical orientation of the phases. A widely used process for analytical purposes as well as rapid method development and, in some cases, even a preparative separation process is thin-layer chromatography (TLC). The adsorbent is fixed onto a support (glass, plastic, or aluminum foil) in a thin layer. The solute is placed onto the adsorbent in small circles or lines. In a closed chamber one end of the thin-layer plate is dipped into the mobile phase, which then progresses along the plate due to capillary forces. Individual substances can be visualized either by fluorescence quenching or after chemical reaction with detection reagents. The advantages of TLC are the visualization of all substances, even those sticking heavily to the adsorbent, as well as the easiness of parallel development.
In GC and LC the adsorbent is fixed into a cylinder (column) that is usually made of glass, polymer, or stainless steel (column). In this column the adsorbent is present as a porous or nonporous randomly arranged packing or as a monolithic block. If the columns are well packed with small particles and liquid mobile phases are used, a successful technique, designated as high-performance liquid chromatography (HPLC), is frequently applied.
2.1.1 Adsorption Process
Depending on the kind of interface between mobile and stationary phases, the following types of chromatographic systems can be distinguished:
gaseous mobile phases/solid stationary phase;liquid mobile phases/solid stationary phase;gaseous mobile phases/liquid stationary phase;liquid mobile phases/liquid stationary phase.Most chromatographic processes exploit the principle of adsorption and the separation process is based on the deposition and accumulation of molecules on solid surfaces.
Examples of industrial relevance for the first two phase combinations are the adsorption of pollutants from waste air or water onto activated carbon. Combinations three and four are relevant, for example, related to foam formation and stabilization in the presence of surfactants on water/air interfaces or at the interface of two immiscible liquids (e.g., oil and water). This book deals mainly with the case most typical for preparative chromatographic separations, that is, the exploitation of solid surfaces, liquid mobile phases, and dissolved feed mixtures. The following definitions are made: The solid onto which adsorption occurs is defined as the adsorbent. The adsorbed molecule is defined in its free state as the adsorptive and in its adsorbed state as the adsorpt. There are typically different solutes, which are often called components (for example, A and B, Figure 2.1).
On a molecular level the adsorption process is the formation of binding forces between the surface of the adsorbent and the molecules of the fluid phase. The binding forces can be different in nature and strength. Basically, two different types of binding can be distinguished (Atkins, 1990; IUPAC, 1972):
Table 2.1 gives estimated values for adsorption enthalpies. In gaseous systems these enthalpies are proportional to the heat of vaporization hvap.
Table 2.1 Adsorption enthalpies.
As periodic chromatographic processes require complete reversibility of the adsorption step, only adsorption processes based on physisorption can be exploited. The related energies are sufficient to increase the temperature of gases due to their low volumetric heat capacities (Ruthven, 1984). Fluids, however, are characterized by volumetric heat capacities 102–103 times higher. Thus, the energies connected to adsorption processes have not much influence on the local temperatures. All of the following processes can, therefore, be considered to be approximately isothermal.
2.1.2 Chromatographic Process
In liquid phase chromatography the mobile phase is forced through a column, packed with a multitude of adsorbent particles (the stationary phase). Figure 2.2 illustrates the injection of a homogeneous binary mixture (components A and B represented by triangles and circles) into the system at the column inlet. Hereby the triangles represent the component B with the higher affinity to the stationary phase. Therefore, the mean adsorption time of this component on the stationary phase surface is higher than that of component A with the lower affinity (circles).
Figure 2.2 Principle of adsorption chromatography.
The difference in affinities, and thus adsorption time, results in a reduced migration speed through the column of the more adsorbed component B. This delays its arrival at the column outlet compared with the less adsorbed component A. If the process conditions are chosen well, the two substances can be completely separated and collected as pure components at the column outlet.
2.2 Basic Effects and Chromatographic Definitions
2.2.1 Chromatograms and Parameters
Basic information regarding the development of a chromatographic separation process provides the chromatogram. A typical chromatogram resulting from the injection of three different components in analytical amounts is shown in Figure 2.3.
Figure 2.3 Chromatogram of two retained and one unretained component.
The interaction strength of each component with the stationary phase is proportional to its retention time tR,i. Instead of the retention time, it is often useful to consider the retention volume, which is obtained by multiplying tR,i with the volumetric flow rate.
In the case of symmetrical peak shapes, the retention time can be determined from the peak maximum. For well-packed columns symmetrical peaks should be achieved as long as the amounts injected into the column are small, restricting the concentrations to the linear range of the adsorption isotherms. If increased amounts of substances are injected, that is, in the nonlinear range of the adsorption isotherms, the peaks are often distorted and asymmetrical. In that case the retention time has to be calculated from the point of gravity of the peaks applying the method of moments (Equation 2.38).
The total dead time ttotal is the time a nonretained substance needs from the point of sample introduction to the point of detection. It depends on the holdup within the column itself as well as on further holdup in the system or plant, which is, for instance, influenced by pipe lengths and diameters, pump head volumes (if the sample is introduced via a pump), and detector volumes. Therefore, the dead time of the plant without the column tplant has to be determined as well to get the correct dead time of the column t0 by subtraction of tplant from ttotal. Typically, tracer molecules are used to determine the dead time. These molecules should not be retained by the solid phase and should have the similar molecular sizes as the components to be separated to penetrate the pore system in a comparable way.
The overall retention time tR,i of a retained component i is the sum of the dead time t0 and the net retention time tR,i,net. The net retention time represents the time during which molecules of a substance are adsorbed onto the surface of the adsorbent.
Because the retention time of a substance depends on the column geometry, the porosity and the mobile phase flow rate, a normalization is expedient. For this the capacity factor , which is also called the retention factor, is defined according to Equation 2.1:
(2.1)
The capacity factor depends only on the distribution of the component of interest between the mobile and the stationary phases. It indicates the ratio of the time a component is adsorbed to the time it is in the fluid phase. It can also be expressed as a ratio of amounts of substance i in the stationary and mobile phases (Equation 2.2):
(2.2)
Both the capacity factor and the net retention time might depend on the nature of the tracer substance, which is used to determine t0. Therefore, only values that are based on experiments with the same tracer substance should be directly compared and used to calculate selectivities.
Every LC process aims to separate dissolved components. Therefore, the distance between the peak maxima of two or more components is of great importance. A selectivity α of a separation of two components i and j can be quantified by dividing their capacity factors (Equation 2.3):
(2.3)
Hereby, by convention, the capacity factor of the more retained component is placed in the numerator. Thus, the selectivity of two separated components is always >1. The selectivity is also called separation factor.
2.2.2 Voidage and Porosity
Other important information that can and should be derived from standard chromatograms is the column porosities and the void fractions. These parameters have to be carefully determined as an important basis for quantification and simulation of the purification process. As illustrated in Figure 2.4, the total volume of a packed column (Vc) is divided into two subvolumes: the interstitial volume of the fluid phase (Vint) and the volume of the stationary phase (Vads) (Equation 2.4):
(2.4)
Further, Vads consists of the volume of the solid material (Vsolid) and the volume of the pore system, Vpore (Equation 2.5):
(2.5)
From these volumes different porosities can be calculated (Equations 2.6–(2.8)):
(2.6)
(2.7)
(2.8)
Practical determination of the porosities often experiences difficulties. The most common method for determining the total porosity is the injection of nonretained, pore-penetrating tracer substances (gray and small black circles in Figure 2.5). In normal phase chromatography, toluene or 1,3,5-tri-tert-butylbenzene is often used, while in reversed phase chromatography uracil is typically selected as the component of choice.
Figure 2.4 Structure of packed beds.
Figure 2.5 Chromatography of tracer components.
The interstitial velocity of the mobile phase is given by Equation 2.9:
(2.9)
It is useful to measure the volumetric flow rate delivered by the pump during the determination of the column dead time. The total porosity is then calculated according to Equation 2.10:
(2.10)
To obtain the void fraction or interstitial porosity of a column the same methodology can be used based on injecting a high molecular weight substance that is unable to penetrate into the pores (large black circles in Figure 2.5). Figure 2.5 also shows an ideal chromatogram obtained from the injection of two tracer substances characterized by different molecular weights. For a nonretained and nonpenetrating molecule the dead time of the column and the interstitial velocity are connected by Equation 2.11:
(2.11)
Severe experimental problems often occur during the injection of high molecular weight tracers. Ideal high molecular weight substances should be globular and exhibit no adsorption or penetration into any pore but should, however, be highly mobile. Obviously, from these prerequisites, there is no ideal high molecular weight volume marker. Therefore, alternative methods for determining the void fraction are of interest. If the adsorbent parameters can be determined with high accuracy from physical measurements, the porosities can also be calculated from the mass of the adsorbent msolid, its density , and the specific pore volume vsp (determined, for example, by nitrogen adsorption or mercury porosimetry). The volume of the solid material is then calculated by Equation 2.12:
(2.12)
The pore volume can be obtained from Equation 2.13:
(2.13)
The sum of solid volume and pore volume gives the volume of the stationary phase, which, subtracted from the column volume, leads to the interstitial volume (Equation 2.14):
(2.14)
The void fraction can then be determined using Equation 2.6. Subsequently, the other porosities can be obtained by Equations 2.7 and 2.8.
An alternative method for easy and exact determination of total porosities can be used for small-scale columns. As long as a column can be weighed exactly, the mass difference of the same column filled with two solvents of different densities can be used to determine the porosity. The column is first completely flushed with one solvent and then weighed; afterwards, the first solvent is completely displaced by a second solvent of different density. For normal phase systems methanol and dichloromethane can be used; for reversed phase systems water and methanol are quite commonly employed. The volume of the solvent, representing the sum of the interstitial volume and the pore volume, is determined by Equation 2.15:
(2.15)
The total porosity is again calculated by Equation 2.8.
High-efficiency adsorbents are very often spherical and monodisperse in order to reduce pressure drops. In this case void fractions for spherical particles lie theoretically in the range 0.26 < ε < 0.48 and mean values of ε of approximately 0.37 can be roughly applied (Brauer, 1971).
Particle porosities lie in the range 0.50 < εp < 0.90, meaning that 50–10% of the solid is impermeable skeleton. In practice, the total porosity is often in the range 0.65 < εt < 0.80. With monolithic columns total porosities lie in the range 0.80 < εt < 0.90. At large porosities, sufficient stability of the bed has to be ensured.
2.2.3 Influence of Adsorption Isotherms on Chromatogram Shapes
A chromatogram is influenced by several factors, such as the fluid dynamics inside the packed bed, mass transfer phenomena, and, most importantly, the equilibrium of the adsorption processes taking place.
The adsorption equilibrium is typically described by isotherms, which give the correlations between the loadings of the solute on the adsorbent, qi, as a function of the fluid phase concentrations, ci, at a given temperature. Single-component and competitive adsorption isotherms are discussed in more detail in Section 2.5.
The elution profile of an ideal chromatogram depends only on the courses of the equilibrium functions characterizing the chromatographic system. To understand and predict real chromatograms additional mass transfer resistances and details regarding the fluid dynamics have to be taken into account.
The influence of the shape of the adsorption isotherm on the shape of a chromatogram is illustrated in Figure 2.6.
Figure 2.6 Influence of the type of equilibrium isotherm on the chromatogram.
In an ideal analytical chromatogram, that is, in the linear range of the adsorption isotherms, the retention time is a function of the isotherm slope, quantified by the Henry constant Hi (Figure 2.6a), according to the basic equation of chromatography (Equation 2.16) (Guiochon et al. 2006):
(2.16)
Thus, under linear conditions the retention time does not depend on the fluid phase concentration (Figure 2.6d).
In contrast, under nonlinear conditions peak deformations occur and the retention times become functions of concentration. This leads under thermodynamically controlled ideal conditions to the formation of disperse waves and shock fronts (Figure 2.6e and f).
The “retention times” of specific concentrations in waves are then related to the local slopes of the specific adsorption isotherm as follows:
(2.17)
For convex isotherms (Figure 2.6b) the desorption branch of the peak (the “tail”) forms a wave (Figure 2.6e), whereas for concave isotherms (Figure 2.6c) the adsorption branch forms a wave (“peak fronting,” Figure 2.6f).
The second type of branches of overloaded ideal peaks is characterized by shock fronts having retention times described by Equation 2.18:
(2.18)
Real chromatograms illustrated in Figure 2.6g–i are shaped not only by thermodynamics but also by kinetics of mass transfer and deviations from plug flow conditions. A rectangular concentration profile of the solute injected at the entrance of the column soon changes into a bell-shaped Gaussian distribution, if the isotherm is linear. Figure 2.7a shows this distribution and some characteristic values, which will be referred to in subsequent chapters. The degree of peak asymmetry T can be evaluated from the difference between the two peak halves at 1/10th of the peak height (Figure 2.7b) (Equation 2.19):
Figure 2.7 Determination of peak asymmetry: (a) symmetrical peak; (b) asymmetrical peak.
(2.19)
Another calculation method to evaluate peak asymmetry can be found in the different pharmacopoeias, for example, United States Pharmacopoeia (USP) or Pharmacopoeia Europea (PhEUR). These pharmacopoeias calculate peak tailing from an analysis at 5% of the peak height (Equation 2.20):
(2.20)
2.3 Fluid Dynamics
All preparative and production-scale chromatographic separations aim to collect target components as highly concentrated as possible. The ideal case would be a rectangular signal with the same width as the pulse injected into the column. This behavior cannot be achieved in reality. In every chromatographic system nonidealities of fluid distribution occur, resulting in broadenings of the residence time distributions of the solutes. Hydrodynamic effects that contribute to the total band broadening are frequently captured in an axial dispersion term. Figure 2.8 illustrates the effect of the axial dispersion. The rest of the band broadening results from finite adsorption rates and mass transfer resistance.
Figure 2.8 Band broadening in a column due to axial dispersion.
Figure 2.8 shows that the rectangular pulse, which is introduced at the column inlet (x = 0), is symmetrically broadened as it travels along the column. As a consequence of the band broadening, the maximum concentration of the solute is decreased. This causes an unfavorable dilution of the target component fraction.
Main factors that influence axial dispersion are discussed below.
2.3.1 Extra Column Effects
Every centimeter of tubing, as well as any detector, between the point of solute injection and the point of fraction withdrawal contributes to the axial dispersion of the samples and thus decreases the concentration and separation efficiency. Obviously, the length of connecting lines should be minimized. Critical are smooth connections of tubing and column, avoiding any dead space where fluid and, especially, sample can accumulate. The tubing diameter depends on the flow rate of the system and has to be chosen in accordance with the system pressure. The tubing should contribute as little as possible to the system pressure drop, without adding additional holdup volumes.
2.3.2 Column Fluid Distribution
Critical points for axial dispersion in column chromatography are the fluid distribution at the column head and the fluid collection at the column outlet (Section 4.3.3.2). Especially with large-diameter columns, these effects have to be carefully considered. Fluid distribution in the column head is widely driven by the pressure drop of the packed bed, which forces the sample to be radially distributed within the inlet frit. It is, therefore, important to use high-quality frits, which ensure an equal radial fluid distribution. In low-pressure chromatography with large dimensions, as well as with new types of adsorbents, such as monolithic packings, which exhibit much lower pressure drops, the fluid distribution is of even greater importance. Several approaches to optimize the distribution have been made by column manufacturers to overcome this problem of low-pressure flow distribution. The introduction of specially designed fluid distributors has greatly improved the situation (Section 4.3.3.2).
2.3.3 Packing Nonidealities
The packed bed of a chromatographic column will never attain optimum hexagonal dense packing due to the presence of imperfections. Those imperfections can be divided into effects due to the packing procedure and influences from the packing material. During the packing procedure several phenomena occur. The two most important are wall effects and particle bridges. Knox, Laird, and Raven (1976) determined a layer of about 30dp thicknesses where wall effects influence the column efficiency. Therefore, attention has to be paid to this effect with small-diameter columns. The larger the column diameter, the less severe is this effect. The second reason why imperfect packing may occur in columns is inappropriate packing procedures. If the particles cannot arrange themselves optimally during the packing process, they will form bridges, which can only be destroyed by immense axial pressure, with the danger of damaging the particles. One way to reduce particle bridging is to pack the column by vacuum and, afterwards, by axial compression of the settled bed. For more details see Section 4.6.
Insufficient bed compression, which leads to void volumes at the column inlet, is another source of axial dispersion. Preparative columns should therefore preferably possess a possibility for adjusting the compression of the packed bed.
2.3.4 Sources for Nonideal Fluid Distribution
The reasons for nonidealities in fluid distribution can be divided into macroscopic, mesoscopic, and microscopic effects (Tsotsas, 1987). The different effects are illustrated in Figure 2.9.
Figure 2.9 Fluid distribution nonidealities according to Tsotsas (1987): (a) microscopic; (b) mesoscopic; (c) macroscopic; (d) eddy diffusion.
Microscopic fluid distribution nonideality is caused by fluid dynamic adhesion between the fluid and the adsorbent particle inside the microscopic channels of the packed bed. Adhesion results in a higher fluid velocity in the middle of the channel than at the channel walls (Figure 2.9a). Solute molecules in the middle of the channel thus have a shorter retention time than those at the channel walls.
Local inhomogeneities of the voidage are a second source of broadening the mean residence time distribution. For small particles, the formation of particle agglomerates, which cannot be penetrated by the fluid, is another reason for axial dispersion. Figure 2.9b illustrates this mesoscopic fluid distribution nonideality. This effect results in local differences in fluid velocity and differences in path length of the solute molecules traveling straight through the particle agglomerates compared with those molecules moving around the particle aggregates. The second effect is also known as eddy diffusion (Figure 2.9d). Due to its similar origin, this statistical phenomenon is related to mesoscopic fluid dynamic nonidealities.
Macroscopic fluid distribution nonidealities are caused by local nonuniformities of the void space between the particles, which might occur especially in the wall region (Figure 2.9c).
All the above-mentioned effects cause an increase of the peak width and contribute, besides mass transfer resistances discussed below, to total band broadening.
2.3.5 Column Pressure Drop
In chemical engineering the Ergun equation (Equation 2.21) is well known for the estimation of friction numbers and corresponding pressure drops for fixed beds with granular particles:
(2.21)
It covers the broad span from fine particles to coarse materials (Brauer, 1971). For chromatographic columns small, more or less spherical particles are used. Therefore, the Reynolds numbers are very small and inertial forces can be neglected. Equation 2.21 then reduces to its first term, which represents the pressure drop because of viscous forces only.
The friction number is defined (Equation 2.22) as
(2.22)
where u0 is the velocity in the empty column (superficial velocity) (Equation 2.23):
(2.23)
Introducing Equation 2.22 in the reduced Equation 2.21 leads to Equation 2.24:
(2.24)
This equation is identical to Darcy's law (Equation 2.25), which is well known among chromatographers (Guiochon, Golshan-Shirazi, and Katti, 1994):
(2.25)
with
(2.26)
The coefficient k0 typically lies between 0.5 × 10−3 and 2 × 10−3. This agrees with Equation 2.26 where a void fraction of 0.4 results in a corresponding value of 1.2 × 10−3. If more precise values are required, k0 has to be measured for a given packing.
Another parameter derived also from Darcy's equation, which is often used to characterize a column, is the column permeability B (Equation 2.27):
(2.27)
Comparing Equations 2.25 and 2.27, the permeability is related to k0 by
(2.28)
