DRUGS AND THE PHARMACEUTICAL SCIENCES
`
`VOLUME 157
`
`Pharmaceutical
`NH)eal
`
`SHRUTI
`
`IV_AER’s
`
`DiscoveryDevelopment Review Marketing
`Pre-clinical
`_Clinical
`i, vu
`Approval
`
`Continuous Learning — Manufacturing Science
`
`Pre-formulation
`
`Formulation (Clinical)
`Optimization
`
`(Optimization)
`Scale-Up
`
`Manufacturing
`Changes
`
`Quality by Design
`
`&
`Efficacy
`
`Appropriate labeling and risk management
`
`edited by
`Michael Levin
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 1 of 116
`
`
`
`

`

`Pharmaceutical
`Process Scale-Up
`Second Edition
`
`edited by
`Michael Levin
`Metropolitan Computing Corporation
`East Hanover, New Jersey, U.S.A.
`
`New York London
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 2 of 116
`
`

`

`Published in 2006 by
`CRC Press
`Taylor & Francis Group
`6000 Broken Sound Parkway NW, Suite 300
`Boca Raton, FL 33487-2742
`
`© 2006 by Taylor & Francis Group, LLC
`CRC Press is an imprint of Taylor & Francis Group
`
`No claim to original U.S. Government works
`Printed in the United States of America on acid-free paper
`10 9 8 7 6 5 4 3 2 1
`
`International Standard Book Number-10: 1-57444-876-5 (Hardcover)
`International Standard Book Number-13: 978-1-57444-876-4 (Hardcover)
`
`This book contains information obtained from authentic and highly regarded sources. Reprinted material is
`quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts
`have been made to publish reliable data and information, but the author and the publisher cannot assume
`responsibility for the validity of all materials or for the consequences of their use.
`
`No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic,
`mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and
`recording, or in any information storage or retrieval system, without written permission from the publishers.
`
`For permission to photocopy or use material electronically from this work, please access www.copyright.com
`(http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive,
`Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration
`for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate
`system of payment has been arranged.
`
`Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only
`for identification and explanation without intent to infringe.
`
`Library of Congress Cataloging-in-Publication Data
`
`Catalog record is available from the Library of Congress
`
`Visit the Taylor & Francis Web site at
`http://www.taylorandfrancis.com
`
`Taylor & Francis Group
`is the Academic Division of T&F Informa plc.
`
`and the CRC Press Web site at
`http://www.crcpress.com
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 3 of 116
`
`

`

`Contents
`
`Introduction . . . .
`Preface . . . . xi
`Contributors . . . . xxi
`
`v
`
`1. Dimensional Analysis and Scale-Up in Theory and Industrial
`Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
`Marko Zlokarnik
`Introduction . . . . 1
`Dimensional Analysis . . . . 2
`Determination of a Pi Set by Matrix
`Calculation . . . . 8
`Fundamentals of the Theory of Models
`and of Scale-Up . . . . 12
`Further Procedures to Establish a Relevance List . . . . 14
`Treatment of Variable Physical Properties by
`Dimensional Analysis . . . . 23
`Pi Set and the Power Characteristics of
`a Stirrer in a Viscoelastic Fluid . . . . 29
`Application of Scale-Up Methods in Pharmaceutical
`Engineering . . . . 31
`Appendix . . . . 52
`References . . . . 53
`
`2. Engineering Approaches for Pharmaceutical Process Scale-Up,
`Validation, Optimization, and Control in the Process and
`Analytical Technology (PAT) Era . . . . . . . . . . . . . . . . . .
`Fernando J. Muzzio
`Introduction and Background . . . . 57
`
`57
`
`xv
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 4 of 116
`
`

`

`xvi
`
`Contents
`
`Model-Based Optimization . . . . 62
`Process Scale-Up . . . . 65
`Process Control
`. . . . 66
`Conclusions . . . . 68
`References . . . . 69
`
`3. A Parenteral Drug Scale-Up . . . . . . . . . . . . . . . . . . . . . .
`Igor Gorsky
`Introduction . . . . 71
`Geometric Similarity . . . . 72
`Dimensionless Numbers Method . . . . 74
`Scale-of-Agitation Approach . . . . 75
`Scale-of-Agitation Approach Example . . . . 78
`Latest Revisions of the Approach . . . . 80
`Scale-of-Agitation Approach for Suspensions . . . . 83
`Heat Transfer Scale-Up Considerations . . . . 85
`Conclusions . . . . 86
`References . . . . 87
`
`. . . . . . . . . . . . . .
`
`4. Non-Parenteral Liquids and Semisolids
`Lawrence H. Block
`Introduction . . . . 89
`Transport Phenomena in Liquids and Semisolids and Their
`Relationship to Unit Operations and Scale-Up . . . . 91
`How to Achieve Scale-Up . . . . 111
`Scale-Up Problems . . . . 123
`Conclusions . . . . 124
`References . . . . 125
`
`5. Scale-Up Considerations for
`. . . . . . . . . . . . . . . . . .
`Biotechnology-Derived Products
`Marco A. Cacciuttolo and Alahari Arunakumari
`Introduction . . . . 129
`Fundamentals: Typical Unit Operations . . . . 134
`Scale-Up of Upstream Operations . . . . 140
`Downstream Operations . . . . 146
`Process Controls . . . . 149
`Scale-Down Models . . . . 150
`Facility Design . . . . 150
`
`71
`
`89
`
`129
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 5 of 116
`
`

`

`Contents
`
`Examples of Process Scale-Up . . . . 151
`Impact of Scale-Up on Process Performance
`and Product Quality . . . . 154
`Summary . . . . 155
`Final Remarks and Technology Outlook . . . . 156
`References . . . . 157
`
`6. Batch Size Increase in Dry Blending and Mixing . . . . . . .
`Albert W. Alexander and Fernando J. Muzzio
`Background . . . . 161
`General Mixing Guidelines . . . . 162
`Scale-Up Approaches . . . . 165
`New Approach to the Scale-Up Problem
`in Tumbling Blenders . . . . 166
`Testing Velocity Scaling Criteria . . . . 173
`The Effects of Powder Cohesion . . . . 175
`Recommendations and Conclusions . . . . 178
`References . . . . 179
`
`7. Powder Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`James K. Prescott
`Introduction . . . . 181
`Review of Typical Powder Transfer Processes . . . . 182
`Concerns with Powder-Blend Handling
`Processes . . . . 182
`Scale Effects . . . . 189
`References . . . . 197
`
`xvii
`
`161
`
`181
`
`199
`
`8. Scale-Up in the Field of Granulation
`and Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`Hans Leuenberger, Gabriele Betz, and David M. Jones
`Introduction . . . . 199
`Theoretical Considerations . . . . 200
`The Dry-Blending Operation . . . . 201
`Scale-Up and Monitoring of the Wet
`Granulation Process . . . . 202
`Robust Formulations and Dosage Form Design . . . . 214
`A Quasi-Continuous Granulation and Drying Process
`(QCGDP) to Avoid Scale-Up Problems . . . . 214
`IPR2020-00770
`United Therapeutics EX2019
`Page 6 of 116
`
`

`

`xviii
`
`Contents
`
`Scale-Up of the Conventional Fluidized Bed Spray
`Granulation Process . . . . 220
`Summary . . . . 234
`References . . . . 235
`
`237
`
`9. Roller Compaction Scale-Up . . . . . . . . . . . . . . . . . . . . .
`Ronald W. Miller, Abhay Gupta, and
`Kenneth R. Morris
`Prologue . . . . 237
`Scale-Up Background . . . . 238
`Scale-Up Technical Illustrations . . . . 239
`Vacuum Deaeration Equipment Design Evaluation . . . . 241
`Conclusion . . . . 264
`References . . . . 265
`
`10. Batch Size Increase in Fluid-Bed Granulation . . . . . . . . .
`Dilip M. Parikh
`Introduction . . . . 267
`System Description . . . . 273
`Particle Agglomeration and Granule Growth . . . . 284
`Fluid-Bed Drying . . . . 288
`Process and Variables in Granulation . . . . 291
`Process Controls and Automation . . . . 300
`Process Scale-Up . . . . 305
`Case Study . . . . 310
`Material Handling . . . . 311
`Summary . . . . 316
`References . . . . 318
`
`11. Scale-Up of Extrusion and Spheronization . . . . . . . . . . .
`Raman M. Iyer, Harpreet K. Sandhu, Navnit H. Shah,
`Wantanee Phuapradit, and Hashim M. Ahmed
`Introduction . . . . 325
`Extrusion-Spheronization—An Overview . . . . 326
`Extrusion . . . . 328
`Spheronization . . . . 348
`Process Analytical Technologies (PAT) . . . . 361
`Summary . . . . 364
`References . . . . 365
`
`267
`
`325
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 7 of 116
`
`

`

`Contents
`
`xix
`
`371
`12. Scale-Up of the Compaction and Tableting Process . . . . .
`Alan Royce, Colleen Ruegger, Mark Mecadon, Anees Karnachi,
`and Stephen Valazza
`Introduction . . . . 371
`Compaction Physics . . . . 372
`Predictive Studies . . . . 375
`Scale-Up/Validation . . . . 388
`Case Studies . . . . 393
`Process Analytical Technology . . . . 405
`References . . . . 407
`
`13. Practical Considerations in the Scale-Up of Powder-Filled Hard
`409
`Shell Capsule Formulations . . . . . . . . . . . . . . . . . . . . . .
`Larry L. Augsburger
`Introduction . . . . 409
`Types of Filling Machines and Their Formulation
`Requirements . . . . 410
`General Formulation Principles . . . . 418
`Role of Instrumented Filling Machines
`and Simulation . . . . 420
`Scaling-Up Within the Same Design and Operating
`Principle . . . . 421
`Granulations . . . . 429
`References . . . . 430
`
`14. Scale-Up of Film Coating . . . . . . . . . . . . . . . . . . . . . . .
`Stuart C. Porter
`Introduction . . . . 435
`Scaling-Up the Coating Process . . . . 441
`Alternative Considerations to Scaling-Up
`Coating Processes . . . . 479
`Scale-Up of Coating Processes: Overall Summary . . . . 484
`References . . . . 484
`
`435
`
`15. Innovation and Continuous Improvement in Pharmaceutical
`Manufacturing
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`Ajaz S. Hussain
`Prologue . . . . 487
`The PAT Team and Manufacturing Science Working Group
`Report: A Summary of Learning, Contributions and Proposed
`IPR2020-00770
`United Therapeutics EX2019
`Page 8 of 116
`
`487
`
`

`

`xx
`
`Contents
`
`Next Steps for Moving Toward the ‘‘Desired State’’ of
`Pharmaceutical Manufacturing in the
`21st Century . . . . 488
`Bibliography and References . . . . 525
`
`Appendix . . . . 529
`Index . . . . 531
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 9 of 116
`
`

`

`4
`
`Non-Parenteral Liquids and Semisolids
`
`Lawrence H. Block
`Duquesne University, Pittsburgh, Pennsylvania, U.S.A.
`
`INTRODUCTION
`
`A manufacturer’s decision to scale-up (or scale-down) a process is ultimately
`rooted in the economics of the production process, i.e., in the cost of material,
`personnel, and equipment associated with the process and its control. While
`process scale-up often reduces the unit cost of production and is therefore
`economically advantageous per se, there are additional economic advantages
`conferred on the manufacturer by scaling-up a process. Thus, process scale-up
`may allow for faster entry of a manufacturer into the marketplace or improved
`product distribution or response to market demands and correspondingly
`greater market-share retention.a Given the potential advantages of process
`scale-up in the pharmaceutical industry, one would expect the scale-up task
`to be the focus of major efforts on the part of pharmaceutical manufacturers.
`However, the paucity of published studies or data on scale-up—particularly
`for non-parenteral liquids and semisolids—suggests otherwise. On the other
`hand, one could argue that the paucity of published studies or data is nothing
`
`a On the other hand, the manufacturer may determine that the advantages of process scale-up
`are compromised by the increased cost of production on a larger scale and/or the potential loss
`of interest or investment income. Griskey (1) addresses the economics of scale-up in some detail
`in his chapter on engineering economics and process design, but his examples are taken from the
`chemical industry. For a more extensive discussion of process economics, see Ref. 2.
`
`89
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 10 of 116
`
`

`

`90
`
`Block
`
`more than a reflection of the need to maintain a competitive advantage
`through secrecy.
`One could also argue that this deficiency in the literature attests to the
`complexity of the unit operations involved in pharmaceutical processing. If
`pharmaceutical technologists view scale-up as little more than a ratio
`problem, whereby
`Scale-up ratio ¼ Large-scale production rate
`Small-scale production rate
`
`ð1Þ
`
`then the successful resolution of a scale-up problem will remain an empirical,
`trial-and-error task rather than a scientific one. In 1998, in a monograph on
`the scale-up of disperse systems, Block (3) noted that due to the complexity
`of the manufacturing process which involves more than one type of unit
`operationb (e.g., mixing, transferring, etc.), process scale-up from the bench
`or pilot plant level to commercial production is not a simple extrapolation:
`
`‘‘The successful linkage of one unit operation to another defines the
`functionality of the overall manufacturing process. Each unit oper-
`ation per se may be scalable, in accordance with a specific ratio, but
`the composite manufacturing process may not be, as the effective
`scale-up ratios may be different from one unit operation to another.
`Unexpected problems in scale-up are often a reflection of the dichot-
`omy between unit operation scale-up and process scale-up. Further-
`more, commercial production introduces problems that are not a
`major issue on a small scale: e.g., storage and materials handling
`may become problematic only when large quantities are involved;
`heat generated in the course of pilot plant or production scale proces-
`sing may overwhelm the system’s capacity for dissipation to an extent
`not anticipated based on prior laboratory-scale experience (3).’’
`
`Furthermore, unit operations may function in a rate-limiting manner
`as the scale of operation increases. When Astarita (4) decried the fact, in
`the mid-1980s, that ‘‘there is no scale-up algorithm which permits us to
`rigorously predict the behavior of a large scale process based upon the beha-
`vior of a small scale process,’’ it was presumably as a consequence of all of
`these problematic aspects of scale-up.
`A clue to the resolution of the scale-up problem for liquids and semi-
`solids resides in the recognition that their processing invariably involves the
`
`b The term unit operations, coined by Arthur D. Little in 1915, is generally used to refer to
`distinct physical changes or unit actions (e.g., pulverizing, mixing, drying, etc.) while unit opera-
`tions involving chemical changes are sometimes referred to as unit processes. The physical
`changes comprising unit operations primarily involve contact, transfer of a physical property,
`and separation between phases or streams.
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 11 of 116
`
`

`

`Non-Parenteral Liquids and Semisolids
`
`91
`
`unit operation of mixing. Closer examination of this core unit operation
`reveals that flow conditions and viscosities during processing can vary by
`several orders of magnitude depending upon the scale of scrutiny employed,
`i.e., whether on a microscopic (e.g., mm to cm) or macroscopic (e.g., cm to m)
`scale. The key to effective processing scale-up is the appreciation and under-
`standing of microscale and macroscale transport phenomena, i.e., diffusion
`and bulk flow, respectively. Transport by diffusion involves the flow of a
`property (e.g., mass, heat, momentum, and electromagnetic energy) from
`a region of high concentration to a region of low concentration as a result
`of the microscopic motion of electrons, atoms, molecules, etc. Bulk flow,
`whether convection or advection, however, involves the flow of a property
`as a result of macroscopic or bulk motion induced artificially (e.g., by mech-
`anical agitation) or naturally (e.g., by density variations) (5).
`
`TRANSPORT PHENOMENA IN LIQUIDS AND SEMISOLIDS AND
`THEIR RELATIONSHIP TO UNIT OPERATIONS AND SCALE-UP
`
`Over the last four decades or so, transport phenomena research has
`benefited from the substantial efforts made to replace empiricism by funda-
`mental knowledge based on computer simulations and theoretical modeling
`of transport phenomena. These efforts were spurred on by the publication in
`1960 by Bird et al. (6) of the first edition of their quintessential monograph
`on the interrelationships among the three fundamental types of transport
`phenomena: mass transport, energy transport, and momentum transport.c
`All transport phenomena follow the same pattern in accordance with the
`generalized diffusion equation (GDE). The unidimensional flux, or overall
`transport rate per unit area in one direction, is expressed as a system prop-
`erty multiplied by a gradient (5)
`
`
`
`

`
`@G
`@t
`
`¼ d
`
`x
`
`@2G
`@x2
`
`
`
`
`
`!
`
`
`
`@G
`@x
`@x
`
`¼ d
`
` 
`
`¼ d
`
`@E
`@x
`
`ð2Þ
`
`where G represents the concentration of a property Q (e.g., mass, heat, elec-
`trical energy, etc.) per unit volume, i.e., G ¼ Q/V, t is time, x is the distance
`measured in the direction of transport, d is the generalized diffusion coeffi-
`cient, and E is the gradient or driving force for transport.
`Mass and heat transfer can be described in terms of their respective
`concentrations Q/V. While the concentration of mass, m, can be specified
`directly, the concentration of heat is given by
`
`c The second edition of Transport Phenomena was published in 2002, 42 years later, an
`indication of the utility of the first edition and its continuing acceptance by the engineering
`discipline.
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 12 of 116
`
`

`

`92
`
`mCpT
`V
`
`¼ rCpT
`
`Block
`
`ð3Þ
`
`where Cp is the specific heat capacity and T is temperature. Thus the speci-
`fication of rCpT in any form of the generalized diffusion equation will result
`in the elimination of rCp, assuming it to be a constant, thereby allowing the
`use of temperature as a measure of heat concentration (5). In an analogous
`manner, momentum transfer can be specified in terms of the concentration
`of momentum u when its substantial derivative is used instead of its partial
`derivative with respect to time
`
`¼ vH2u
`
`Du
`Dt
`
`ð4Þ
`
`where v is the kinematic viscosity. If pressure and gravitational effects
`are introduced, one arrives at the Navier–Stokes relationships that govern
`Newtonian fluid dynamics.
`When the flux of G is evaluated three-dimensionally, it can be repre-
`sented by (5)
`¼ @G
`@t
`
`dz
`@t
`
`ð5Þ
`
`dG
`dt
`
`þ @G
`@x
`
`dx
`@t
`
`þ @G
`@y
`
`dy
`@t
`
`þ @G
`@z
`
`At the simplest level, as Griskey (1) notes, Fick’s law of diffusion for
`mass transfer and Fourier’s law of heat conduction characterize mass and
`heat transfer, respectively, as vectors, i.e., they have magnitude and direc-
`tion in the three coordinates, x, y, and z. Momentum or flow, however, is
`a tensor which is defined by nine components rather than three. Hence,
`its more complex characterization at the simplest level, in accordance with
`Newton’s law, is
`
` 
`
`dvx
`dy
`
`tyx ¼ Z
`where tyx is the shear stress in the x-direction, ðdvx=dyÞ the rate of shear,
`and Z is the coefficient of Newtonian viscosity. The solution of Equation (2),
`the generalized diffusion equation,
`G ¼ f ðt; x; y; zÞ
`
`ð6Þ
`
`ð7Þ
`
`will take the form of a parabolic partial differential equation (5). However,
`the more complex the phenomenon—e.g., with convective transport a part
`of the model—the more difficult it is to achieve an analytic solution to
`the GDE. Numerical solutions, however, where the differential equation is
`transformed to an algebraic one, may be somewhat more readily achieved.
`IPR2020-00770
`United Therapeutics EX2019
`Page 13 of 116
`
`

`

`Non-Parenteral Liquids and Semisolids
`
`93
`
`Transport Phenomena and Their Relationship to Mixing
`as a Unit Operationd
`
`As noted earlier, virtually all liquid and semisolid products involve the unit
`of operation of mixing.e In fact, in many instances, it is the primary unit
`operation. Even its indirect effects, e.g., on heat transfer, may be the basis
`for its inclusion in a process. Yet, mechanistic and quantitative descriptions
`of the mixing process remain incomplete (7–9). Nonetheless, enough funda-
`mental and empirical data are available to allow some reasonable predic-
`tions to be made.
`The diversity of dynamic mixing devices is unsettling: their dynamic,
`or moving, component’s blades may be impellers in the form of propellers,
`turbines, paddles, helical ribbons, Z-blades, or screws. In addition, one can
`vary the number of impellers, the number of blades per impeller, the pitch of
`the impeller blades, and the location of the impeller, and thereby affect
`mixer performance to an appreciable extent. Furthermore, while dispersators
`or rotor/stator configurations may be used rather than impellers to effect mix-
`ing, mixing may also be accomplished by jet-mixing or static-mixing devices.
`The bewildering array of mixing equipment choices alone would appear to
`make the likelihood of effective scale-up an impossibility. However, as diverse
`as mixing equipment may be, evaluations of the rate and extent of mixing and
`of flow regimesf make it possible to find a common basis for comparison.
`In low-viscosity systems, miscible liquid blending is achieved through
`the transport of unmixed material via flow currents (i.e., bulk or convective
`flow) to a mixing zone (i.e., a region of high shear or intensive mixing). In
`other words, mass transport during mixing depends on streamline or laminar
`flow, involving well-defined paths, and turbulent flow, involving innumer-
`able, variously sized, eddies, or swirling motions. Most of the highly turbu-
`lent mixing takes place in the region of the impeller, fluid motion elsewhere
`serving primarily to bring fresh fluid into this region. Thus, the characteriza-
`tion of mixing processes is often based on the flow regimes encountered in
`mixing equipment. Reynolds’ classic research on flow in pipes demonstrated
`
`dReprinted in part, with revisions and updates, by courtesy of Marcel Dekker, Inc., from L. H.
`Block, ‘‘Scale-up of disperse systems: Theoretical and practical aspects,’’ in Pharmaceutical
`Dosage Forms: Disperse Systems (H. A. Lieberman, M. M. Rieger, and G. S. Banker, eds.),
`Vol. 3, 2nd ed., New York: Marcel Dekker, 1998:366–378.
`eMixing, or blending, refers to the random distribution of two or more initially separate phases
`into and through one another, while agitation refers only to the induced motion of a material in
`some sort of container. Agitation does not necessarily result in an intermingling of two or more
`separate components of a system to form a more or less uniform product. Some authors reserve
`the term blending for the intermingling of miscible phases while mixing is employed for materials
`that may or may not be miscible.
`f The term flow regime is used to characterize the hydraulic conditions (i.e., volume, velocity,
`and direction of flow) within a vessel.
`IPR2020-00770
`United Therapeutics EX2019
`Page 14 of 116
`
`

`

`94
`
`Block
`
`that flow changes from laminar to irregular, or turbulent, once a critical
`value of a dimensionless ratio of variables has been exceeded (10,11). This
`ratio, universally referred to as the Reynolds number, NRe, is defined by
`Equations (8a) and (8b),
`
`NRe ¼ Lvr
`Z
`
`NRe ¼ D2Nr
`Z
`
`ð8aÞ
`
`ð8bÞ
`
`where r is the density, v the velocity, L the characteristic length, and Z is the
`Newtonian viscosity; Equation (8b) is referred to as the impeller Reynolds
`number, as D is the impeller diameter and N is the rotational speed of the
`impeller. NRe represents the ratio of the inertia forces to the viscous forces
`in a flow. High values of NRe correspond to flow dominated by motion
`while low values of NRe correspond to flow dominated by viscosity. Thus,
`the transition from laminar to turbulent flow is governed by the density
`and viscosity of the fluid, its average velocity, and the dimensions of the
`region in which flow occurs (e.g., the diameter of the pipe or conduit, the
`diameter of a settling particle, etc.). For a straight circular pipe, laminar
`flow occurs when NRe < 2100; turbulent flow is evident when NRe > 4000.
`For 2100  NRe  4000, flow is in transition from a laminar to a turbulent
`
`regime. Other factors such as surface roughness, shape and cross-sectional
`area of the affected region, etc., have a substantial effect on the critical value
`of NRe. Thus, for particle sedimentation, the critical value of NRe is 1; for
`some mechanical mixing processes, NRe is 10–20 (12). The erratic, relatively
`unpredictable nature of turbulent eddy flow is further influenced, in part, by
`the size distribution of the eddies which are dependent on the size of the
`apparatus and the amount of energy introduced into the system (10). These
`factors are indirectly addressed by NRe. Further insight into the nature of
`NRe can be gained by viewing it as inversely proportional to eddy advection
`time, i.e., the time required for eddies or vortices to form.
`In turbulent flow, eddies move rapidly with an appreciable component
`of their velocity in the direction perpendicular to a reference point, e.g., a sur-
`face past which the fluid is flowing (13). Because of the rapid eddy motion,
`mass transfer in the turbulent region is much more rapid than that resulting
`from molecular diffusion in the laminar region, with the result that the
`concentration gradients existing in the turbulent region will be smaller than
`those in the laminar region (13). Thus, mixing is much more efficient under
`turbulent flow conditions. Nonetheless, the technologist should bear in mind
`potentially compromising aspects of turbulent flow, e.g., increased vortex for-
`mation (14) and a concomitant incorporation of air, increased shear and a
`corresponding shift in the particle size distribution of the disperse phase, etc.
`IPR2020-00770
`United Therapeutics EX2019
`Page 15 of 116
`
`

`

`Non-Parenteral Liquids and Semisolids
`
`95
`
`Although continuous-flow mixing operations are employed to a limited
`extent in the pharmaceutical industry, the processing of liquids and semisolids
`most often involves batch processing in some kind of tank or vessel. Thus, in the
`general treatment of mixing that follows, the focus will be on batch operationsg
`in which mixing is accomplished primarily by the use of dynamic mechanical
`mixers with impellers, although jet mixing (17,18) and static mixing devices
`(19)—long used in the chemical process industries—are being used to an
`increasingly greater extent now in the pharmaceutical and cosmetic industries.
`Mixers share a common functionality with pumps. The power impar-
`ted by the mixer, via the impeller, to the system is akin to a pumping effect
`and is characterized in terms of the shear and flow produced as
`P / QrH
`
`or
`
`H / P
`Qr
`
`ð9Þ
`
`ð10Þ
`
`N
`
`dyne
`
`where P is the power imparted by the impeller, Q the flow rate (or pumping
`capacity) of material through the mixing device, r the density of the mate-
`rial, and H is the velocity head or shear. Thus, for a given P, there is an
`inverse relationship between shear and volume throughput.
`The power input in mechanical agitation is calculated using the power
`number, NP,
`NP ¼ Pgc
`
`
`rN 3D5
`¼ g  cm  sec
`where gc is the force conversion factor gc ¼ kg  m  sec
`2
`2
`, N the
`1), and D is the diameter of the impeller. For a
`impeller rotational speed (sec
`given impeller/mixing tank configuration, one can define a specific relationship
`between the Reynolds number [Eq. (8)]h and the power number [Eq. (10)] in
`which three zones (corresponding to the laminar, transitional, and turbulent
`regimes) are generally discernible. Tatterson (20) notes that for mechanical agi-
`
`tation in laminar flow, most laminar power correlations reduce to NpNRe¼ B,
`where B is a complex function of the geometry of the system,i and that this is
`equivalent to P / Z h N2D3; ‘‘if power correlations do not reduce to this form
`
`g The reader interested in continuous-flow mixing operations is directed to references that deal
`specifically with that aspect of mixing such as the monographs by Oldshue (15) and
`Tatterson (16).
`for mixing is defined in SI-derived units as NRe ¼
`h Here,
`the Reynolds number
`5ND2 r)/Z, where D, impeller diameter, is in mm.; Z is in Pas; N is impeller speed,
`(1.667 10
`in r.p.m.; and r is density.
`i An average value of B is 300, but B can vary between 20 and 4000 (20).
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 16 of 116
`
`

`

`96
`
`Block
`
`
`
` ¼ v/ND;
`Figure 1 Various dimensionless parameters [dimensionless velocity, v
`pumping number, NQ ¼ Q/ND3; power number, NP ¼ Pgc=rN 3D5
`; and dimension-
` ¼ tmN] as a function of the Reynolds number for the analysis of
`
`less mixing time, t
`turbine–agitator systems. Source: Adapted from Ref. 22.
`
`for laminar mixing, then they are wrong and should not be used.’’ Turbulent
`correlations are much simpler: for systems employing baffles,j NP¼ B; this is
`equivalent to P / rN3D5. Based on this function, slight changes in D can
`result in substantial changes in power.
`Impeller size relative to the size of the tank is critical as well. If the ratio of
`impeller diameter D to tank diameter T is too large (D/T is > 0.7), mixing
`efficiency will decrease as the space between the impeller and the tank wall will
`be too small to allow a strong axial flow due to obstruction of the recirculation
`path (21). More intense mixing at this point would require an increase
`in impeller speed, but this may be compromised by limitations imposed by
`impeller blade thickness and angle. If D/T is too small, the impeller will not
`be able to generate an adequate flow rate in the tank.
`Valuable insights into the mixing operation can be gained from a
`consideration of system behavior as a function of the Reynolds number,
`NRe (22). This is shown schematically in Figure 1 in which various dimension-
`less parameters (dimensionless velocity, v/ND; pumping number, Q/ND3;
`power number, NP = Pgc=rN 3 D5
`; and dimensionless mixing time, tmN)
`are represented as a log–log function of NRe. Although density, viscosity,
`mixing vessel diameter, and impeller rotational speed are often viewed by
`
`
`
`
`
`j Baffles are obstructions placed in mixing tanks to redirect flow and minimize vortex formation.
`Standard baffles—comprising rectangular plates spaced uniformly around the inside wall of a
`tank—convert rotational flow into top-to-bottom circulation.
`
`IPR2020-00770
`United Therapeutics EX2019
`Page 17 of 116
`
`

`

`Non-Parenteral Liquids and Semisolids
`
`97
`
`formulators as independent variables, their interdependency, when incorpo-
`rated in the dimensionless Reynolds number, is quite evident. Thus, the sche-
`matic relationships embodied in Figure 1 are not surprising.k
`Mixing time is the time required to produce a mixture of predetermined
`quality; the rate of mixing is the rate at which mixing proceeds towards the
`final state. For a given formulation and equipment configuration, mixing
`time, tm, will depend upon material properties and operation variables. For
`geometrically similar systems, if the geometrical dimensions of the system
`are transformed to ratios, mixing time can be expressed in terms of a dimen-
`sionless number, i.e., the dimensionless mixing time, ym or tmN
`tmN ¼ ym ¼ f NRe; NFrð
`Þ ¼) f NReð
`Þ
`
`
`ffiffiffiffiffiffi
`pð
`The Froude number, NFr ¼ n=
`Þ, is similar to NRe; it is a measure
`
`ð11Þ
`
`Lg
`of the inertial stress to the gravitational force per unit area acting on a fluid.
`Its inclusion in Equation (11) is justified when density differences are
`encountered; in the absence of substantive differences in density, e.g., for
`emulsions more so than for suspensions, the Froude term can be neglected.
`Dimensionless mixing time is independent of the Reynolds number for both
`laminar and turbulent flow regimes as indicated by the plateaus in Figure 1.
`Nonetheless, as there are conflicting data in the literature regarding the sen-
`sitivity of ym to the rheological properties of the formulation and to equip-
`ment geometry, Equation (11) must be regarded as an oversimplification of
`the mixing operation. Considerable care must be exercised in applying the
`general relationship to specific situations.
`Empirical correlations for turbulent mechanical mixing have been
`reported in terms of the following dimensionless mixing time relationship (24)
`ð12Þ
`
`a
`
` 
`
`T D
`
`ym ¼ tmN ¼ K
`
`where K and a are constants, T is tank diameter, N is impeller rotational speed,
`and D is the impeller diameter. Under laminar flow conditions, Equation (12)
`reduces to
`
`ð13Þ
`ym ¼ H0
`where H0 is referred to as the mixing number or homogenization number. In
`the transitional flow regime,
`H0 ¼ C NReð
`
`Þa
`where C and a are constants, with a varying between 0 and 1.
`
`ð14Þ
`
`k The interrelationships are embodied in variations of the Navier–Stokes equations, which
`describe mass and momentum balances in fluid systems (23).
`IPR2020-00770
`United Therapeutics EX2019
`Page 18 of 116
`
`

`

`98
`
`Block
`
`Flow patterns in agitated vessels may be characterized as radial, axial,
`or tangential relative to the impeller, but are more correctly defined by the
`direction and magnitude of the velocity vectors throughout the system, par-
`ticularly in a transitional flow regime; while the d