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Computers and Chemical Engineering 42 (2012) 30–47

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Computers and Chemical Engineering

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An integrated approach for dynamic flowsheet modeling and sensitivity analysisof a continuous tablet manufacturing process

Fani Boukouvala, Vasilios Niotis, Rohit Ramachandran, Fernando J. Muzzio, Marianthi G. Ierapetritou∗

Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854, United States

a r t i c l e i n f o

Article history:

Received 17 September 2011

Received in revised form 14 January 2012Accepted 18 February 2012

Available online 27 February 2012

Keywords:

Dynamic flowsheet simulation

Pharmaceutical manufacturing

Sensitivity analysis

Population balance modeling

a b s t r a c t

Manufacturing of powder-based products is a focus of increasing research in the recent years. The main

reason is the lack of predictive process models connecting process parameters and material properties to

product quality attributes. Moreover, the trend towards continuous manufacturing for the production of

multiple pharmaceutical products increases the need for model-based process and product design. This

work aims to identify the challenges in flowsheet model development and simulation for solid-based

pharmaceutical processes and show its application and advantages for the integrated simulation and

sensitivity analysis of two tablet manufacturing case studies: direct compaction and dry granulation.

The developed flowsheet system involves a combination of hybrid, population balance and data-based

models. Results show that feeder refill fluctuations propagate downstream and cause fluctuations in the

mixing uniformity of the blend as well as the tablet composition. However, this effect can be mitigated

through recycling. Dynamic sensitivity analysis performed on the developed flowsheet, classifies the

most significant sources of variability, which are material properties such as mean particle size and bulk

density of powders.

Published by Elsevier Ltd.

1. Introduction

Historically, the pharmaceutical industry has been very inno-vative and successful in the field of new drug discovery anddevelopment. However, this has drawn the focus away from

the development of efficient manufacturing methods and processunderstanding (Gernaey & Gani, 2010; Huang et al., 2009; Klatt &Marquardt, 2009; McKenzie, Kiang, Tom, Rubin, & Futran, 2006).In addition, one of the fears that the industry is facing today is

the significant decrease in profit due to the expiration of impor-tant patents and the difficulty of the development of new drugsto replace them. This fact drives the focus towards efficient man-ufacturing strategies, which would significantly make products

competitive in a market where generic manufacturers are alsoinvolved.

Due to the lack of knowledge of how critical material attributesand process parameters affect end-point product attributes,

combined withineffective control strategies, pharmaceutical man-ufacturing processesgenerate productsthat areoften characterized

∗ Corresponding author. Tel.: +1 732 445 2971; fax: +1 732 445 2581.

E-mail addresses: [email protected], [email protected]

(M.G. Ierapetritou).

by a relatively large amount of variability that would not be

tolerated in other process industries (e.g. petrochemicals orfoods) (McKenzie et al., 2006). One additional challenge for theestablishment of efficient, controlled, and automated manufactur-ing methods is the considerable variability in new raw material

properties, since any new formulation has unique molecular struc-ture, physico-chemical and biological properties. In addition, themajority of pharmaceutical products (∼80%) are in a solid basedform of tablets or capsules, composed from bulk powder materi-

als, which are far more complex and challenging to handle thanliquid or gas phase materials. Even though significant progress hasbeen made recently in particle technology research, there is a gapbetween fundamental science and applied engineering due to the

need for integration of multiscale knowledge (Ng, 2002). All of the above reasons have been the source of consensus and legacybased heuristic production strategies, conducted overwhelminglyin batch mode; with product quality being traditionally verified

offline through acceptance sampling. This approach has lead toadditional sources of variability, which arethe effects of theanalyti-cal method, andthe human factor, since it is commonfor operatorsto regulate the process based on their individual knowledge and

experience.Recently, the Food and Drug Administration (FDA) has recog-

nized theneed for modernizing pharmaceutical manufacturingand

0098-1354/$ – seefront matter. Published by Elsevier Ltd.

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F. Boukouvala et al. / Computers and Chemical Engineering 42 (2012) 30–47 31

Nomenclature

Symbol

A surface area (m2)C API API concentration (–)d50 mean particle size (m)F PBM density function (particles)

H height (m)

h0 half of ribbon thickness (m)m mass flow (kg)P compaction pressure (MPa)

R radius (m)RSD Relative Standard Deviation (−)RT residence time (s)u feed speed (m/s)

W width (m)˛ nip angle (rad)ı effective angle of friction (rad)ε porosity (−)

in inlet angle (rad)bulk powder bulk density (kg/m3) material stress (MPa)

R rate (particles/s)ω rotation rate (rpm)ah heckel parameterbi (i = 1, 2, 3, 4) feed frame response surface parametersC rc

1 stress-angle empirical parameter

kbreak breakage kernelk g process gainkh heckel parameterK rc stress-angle empirical parameter

delay time constant

Domain

g gasn componentr particle size

s1 APIs2 excipient z time delay z 1 axial

z 2 radial

Subscript

in inlet streamout outlet streamP pressuresp set point

u speedω rotation rate

Superscript

delayed delayeddisc feed frame disc f feeder

ff feed framem mixermil millrc roller compactor

rib ribbonrol roller compactor rolltablets tabletstp tablet press

has launched an initiative for enhancing process understandingthrough Quality by Design (QbD) and Process Analytical Tech-

nology (PAT) tools (Garcia, Cook, & Nosal, 2008; Lionberger, Lee,Lee, Raw, & Yu, 2008; Nosal & Schultz, 2008; Yu, 2008). Themajor goals of these efforts include the development of scien-tific mechanistic understanding of a wide range of processes;

harmonization of processes and equipment; development of tech-nologies to perform online measurements of critical materialproperties during processing; performance of real-time con-trol and optimization; minimization of the need for empirical

experimentation and finally, exploration of process flexibilityor design space (Lepore & Spavins, 2008). To achieve thesegoals, the industry needs the modeling tools and databasesfor measuring, controlling and predicting quality and perfor-

mance.In the last five years, one of the main approaches for mod-

ernizing pharmaceutical manufacturing, transition of productionfrom batch to continuous mode, is becoming increasingly more

appealing to the industry and regulatory authorities (Betz, Junker-Bürgin, & Leuenberger, 2003; Gonnissen, Goncalves, De Geest,Remon, & Vervaet, 2008; Leuenberger, 2001; Plumb, 2005). Theadvantages of this change have been proven very beneficial in

many aspects when applied in other fields, such as petrochemicals

and specialty chemicals (Gorsek & Glavic, 1997). Firstly, contin-uous manufacturing allows the use of the same equipment forthe production of smaller and larger quantities, which minimizes

the need for scale-up studies and the time-to-market significantly(Leuenberger, 2001). At the present time, processes developed insmall-scale equipment used for initial clinical studies must bescaled-up (empirically)and subsequentlyvalidated experimentally

and further optimized, since their operation is always poten-tially different at the larger scale. This leads to another advantageof continuous integrated manufacturing, which is the minimiza-tion of the plant footprint, since the entire continuous process

typically fits inside a much smaller space. A well controlled con-tinuous process involves the handling of small aliquots of materialthroughout the unit operations, increasing the ability to monitor

a significant fraction of the process streams, which is impossiblein a large-scale batch process. In addition, continuous opera-tions can produce higher throughputs under better control, whichimplies the optimal use of the invested capital (space, raw mate-rials and equipment), as well as the reduction of waste (Plumb,

2005). Also, in a continuous setting, the human factor is sig-nificantly decreased through automation of operation and thuslabor costs can be reduced. Finally, risks associated with materialhandling, such as contamination and undesired segregation and

agglomeration are reduced since less time is necessary for filling,emptying and cleaning equipment. A detailed economical analy-sis and comparison of batch versus continuous operating mode forthe production of pharmaceuticals has been performed by Schaber

et al. (2011), demonstrating the possibilities and advantages of the

latter.However, a switch from the already established batch to contin-

uous operation involves many challenges, and could lead to failure

if not performed correctly. Firstly, pharmaceutical substances arehighly sensitive to environmental conditions, such as humidity andtemperature and a possible larger residence time than requiredcan cause significant material degradation. This can cause dan-

gerous product contaminations and should be avoided. In a batchsetting, the residence time is more easily controlled whereas ina continuous setting this is more challenging. Subsequently, in acontinuous production, the process does not reach steady state

from the beginning, and this may cause off-specification productto be produced duringa particular time interval. However,becauseregulatory authorities require detailed and time-consuming docu-

mentation for the establishment of a manufacturing strategy, and



32 F. Boukouvala et al./ Computers and Chemical Engineering 42 (2012) 30–47

because in many cases companies currently have unused capac-ity, it is still debatable by pharmaceutical companies whether the

modification of an already established batch manufacturing pro-cedure to a continuous one is worth the risk and the up-frontexpense. In addition, one of the most discussed topics involvedin the batch-to-continuous transition is the definition of a batch

in a continuous setting, since this must be clearly defined dueto regulatory aspects. However, the steady-state nature of con-tinuous processing as well as the ability to process less materialat a unit time, will facilitate monitoring and efficient control. All

of the above together with process knowledge and tools such asthe one developed in this work, can be used to identify possibleproblems ahead of time and be able to predict which fraction of the production to discard. Ultimately, as we move towards better

process knowledge and improve the available models and con-trol strategies, more and more perturbations can be handled andalleviated before even affecting the final product quality (feedforward control). In other words, as we move forward, our abil-

ity to predict and control a continuous process should be theaspects which will define the conception of a batch in a continuousline.

Continuous manufacturing cannot be performed successfully

unless each sub-process is well understood in terms of the effect

of material properties, operating parameters and environmen-tal conditions on critical product quality attributes. If processunderstanding is then translated into models, computer aided

simulation tools, such as flowsheet modeling, allow the pro-posed continuous integrated process to be designed, analyzedand optimized. Flowsheet modeling is one of the most influen-tial achievements of computer-aided process systems engineering,

which has enabled the design, analysis and optimization of robustprocesses in the chemical industry. A robust and detailed flow-sheet simulation is an approximate representation of the actualplant operation, which also helps in the establishment of suc-

cessful control strategies that will regulate the process whengiven a desired set-point change or when a problem occursduring the operation of the integrated process (Ramachandran,

Arjunan, Chaudhury, & Ierapetritou, 2011; Ramachandran andChaudhury, 2011). Process control aims to maintain the processin a desired state. Through accurate simulations, one can predictthe time interval of the transitional stage during which prod-uct has not yet reached desired state, and the control actions

to take when the system deviates from the desired state (feed-back control) or when perturbations are detected as they enterinto the system (feed-forward control). Accurate modeling of the residence time distribution of material in the process also

allows discarding a small percentage of faulty product whennecessary, which is more profitable than production of failingbatches.

A developed flowsheet simulation can also facilitate the iden-

tification of possible process integration bottlenecks, conflicting

design and control objectives, simulation of the effect of recyclestreams as well as process start-up and shut-down. For these andother reasons, flowsheet synthesis is an extremely important first

step in a wide range of industries, during which the optimal pro-cess configuration is decided upon according to the desired designobjectives (Biegler, Grossmann, & Westerberg, 1997). This proce-dure enables the investigation of design alternatives through the

formulation of superstructure networks and the solution of mixedinteger optimization problems which have operating conditionsand designparameters as decision variables (Biegler & Grossmann,2004; Biegler et al., 1997; Henao & Maravelias, 2011). In the litera-

ture and in industrial practice, flowsheet simulations have helpedidentify global optimal operating conditions and design configu-rations that lead to robust, flexible and economically profitable

processes.

Research in flowsheet building for fluid-based processes com-mon to the chemical industry (i.e. petrochemicals) has become a

mature activity, resulting in a variety of state of the art softwarepackages (e.g. ASPEN, gPROMS, CHEMCAD, etc.) that contain allthe needed capabilities. Using thedeveloped software is easy sincea user can simply ‘drag-and-drop’ the necessary unit operations

from established model libraries and connect them appropriatelyto simulate a specific integrated process. On the contrary, flow-sheet models and software for solid based processes are only in aprimitivestage fora variety of reasons (Gruhn, Werther,& Schmidt,

2004;Ng & Fung, 2003;Ng, 2002; Werther, Reimers,& Gruhn, 2008,2009).

First of all, due to the predominantly batch configuration inwhich essentially all solid pharmaceuticals are manufactured, the

need for a preliminary flowsheet synthesis step appeared unnec-essary. More importantly, the lack of knowledge of the criticalmaterial properties, design, and process variables, as well as thelack of unit operation process models have inhibited the devel-

opment of model-based flowsheet simulators. Due to the highcomplexity of the raw materials and the lack of standardizedprocedures, another obstacle is the inexistence of comprehensivematerial property databases for a wide range of used excipi-

ents and APIs. In fact, material characterization of pharmaceutical

powders is a non standardized procedure which differs amongstthe different companies. Universal material property libraries arevital to model libraries, if one wants to produce a wide ranging

multipurpose flowsheet model, independent of specific productapplications.

Lastly, solid-based flowsheet modeling has been held back dueto the lack of software with capabilities for handling dynamic

changes of distributed parameters (i.e. particle size distribu-tions). This problem has recently been tackled in incipient formby a variety of software developers such as gPROMs/gSOLIDsand SolidSim (Werther, Toebermann, Rosenkranz, & Gruhn,

2000).In this work, gPROMs is used as a platform for building a

flowsheet model for two production schemes for pharmaceu-

tical tablets. gPROMs is an equation-based (Oh & Pantelides,1996; Winkel, Zullo, Verheijen, & Pantelides, 1995) and dynamicsoftware, which is widely accepted in a variety of fluid basedproduct industries. The specific objectives of this work include(1) model development for a variety of powder unit opera-

tions, (2) integration and simulation of the developed modelsand models obtained from literature in gPROMS and (3) dynamicsensitivity analysis of the developed flowsheet simulation forthe identification and quantification of critical sources of uncer-

tainty.The remainder of the paper is organized as follows. Section

2 is a description of the models developed and implemented todescribe each unit operation and how these models are integrated

to simulate actual production scenarios for direct compaction and

dry granulation. The theoretical background of dynamic sensitivityanalysis is described in Section 3. Results for the two case studiesandsensitivity analysis are discussed in Section 4. Finally,the paper

concludes with Section 5 with a discussion of this work and futureplans.

2. Flowsheetmodeling for integrated continuous

pharmaceutical systems

2.1. Unit operation models

2.1.1. Feeders

In the majority of powder handling industries (i.e. pharmaceu-

tical, food, ceramics, catalysts), feeding of powder materials into a




continuous processing line is performed through gravimetric feed-ers. The main purpose of the unit operation of feeding is thesupply

of raw materials to the subsequent unit operation at desired andconsistent flowrates in order to match the desired mixture com-position and total material throughput. A typical Loss-In-Weight(LIW) feeder is comprised of a hopper that can hold up to a certain

amount of powder material, which is fed to the next processingunit through a rotating screw. The output feedrate of a gravimetricfeeder is calculated based on the loss in the weight of the mate-rial contained in the feeder over time. This mode of operation

allows the accurate monitoring of the exact amount of materialprovided to the next unit operation, since any accumulation of powder in the hopper will be captured by the change in the totalweight.

Currentlyavailable feedersare operatedin closed-loop. Throughthe modification of the rotation rate of the feeder screws (manip-ulative variable) the equipment can achieve the desired outputfeedrate set point. Different screw designs and sizes are avail-

able to accommodate different types of materials and differentflowrate throughputs. In Boukouvala, Muzzio, and Ierapetritou(2010b) a method is developed based on experimental data anddata-based response surface models, that can aid in identifying

the optimal design and size of the screw based on the desired

flowrate and material properties of the powder which is han-dled.

Even though significant work has been performed in the area of

feeder design developmentfrom an equipment vendor perspective,powder feeding has not been studied extensively from a model-ing viewpoint. In the literature, first-principle models describingpowder feeding are absent, which leads to the need of black-box

dynamic models. In order to capture the dynamics of the process, amodel is requiredfor theaccuratecalculation of theoutput flowrateand the description of the feedrate response in the case of possi-ble feedrate set-point changes. Thus, an experimental design was

performed in order to collect dynamic data of the output flowrateafter different magnitudes of step changes under different oper-ating conditions. Specifically, dynamic step change experiments

are performed using a system of three gravimetric LIW feeders(API, excipient and lubricant feeder). Two different formulationsare tested (3% and 30% active pharmaceutical ingredient) and threedifferent operating flowrates. Once the system reaches steady-state, step changes (±10%) to the feedrate set point are performed

and the material exiting the three-feeder system is monitored, inorder to calculate the transient response of the total and indi-vidual flowrates. Analysis of the collected data suggests that theclosed-loop feederdynamics canbe describedby a first order delay

differential equation. Throughout the process of feeding, the mate-rial is assumed to retain its original particle size distribution andbulk density, which is something that is validated experimentallyfor the types of fine excipients, API’s and lubricants handled in

this work. However, such an assumption must be validated for

materials which are complex, show tendency to break or aggre-gate and especially in cases where mixtures are fed through aLIW feeder. The equation for a DDE system is given in Appendix

A.

2.1.2. Mixers

Several modeling approaches exist in the literature for powder

mixing processes. The current modeling approaches can be cate-gorized into Monte-Carlo methods (Mizonov, Berthiaux, Marikh,Ponomarev, & Barantzeva, 2004), continuum and constitutivemodels (Sudah, Chester, Kowalski, Beeckman, & Muzzio, 2002),

data-driven statistical models (Boukouvala, Muzzio, & Ierapetritou,2010a; Boukouvala et al., 2010b; Portillo, Ierapetritou, & Muzzio,2009; Wu, Heilweil, Hussain, & Khan, 2007), compartment mod-

els (Portillo, Muzzio, & Ierapetritou, 2006, 2008), RTD modeling

approaches (Gao, Ierapetritou, & Muzzio, 2011; Gao, Muzzio, &Ierapetritou, 2011; Gao, Vanarase, Muzzio, & Ierapetritou, 2011),

hybrid-models (Portillo, Muzzio, & Ierapetritou, 2007; Wassgren,Freireich, Li, & Litster, 2011) and discrete element method (DEM)based models (Bertrand, Leclaire, & Levecque, 2005; Dubey, Sarkar,Ierapetritou, Wassgren, & Muzzio, 2011; Hassanpour et al., 2011;

Remy, Khinast, & Glasser, 2009, 2010; Remy, Canty, Khinast, &Glasser, 2010; Sarkar & Wassgren, 2009, 2010). The broad portfolioof mixing models showcase the potential of using different mod-els for a specific use. For instance, statistical/RTD models could be

used for online control and dynamic optimization whilst constitu-tive and hybrid models could be used for design and simulation.Hybrid models especially have the potential to incorporate multi-scaleinformationfrom theparticlelevel to theunit-operation level.

In this work, we describe an alternative hybrid methodology basedon population balance modeling. The developed population bal-ance accounts for n solid components, axial and radial coordinatedirections.

A hierarchical solution strategy is employed for the solution of the multi-dimensional population balance model, that explicitlycasts the population balance equation in terms of its rate pro-cesses (Immanuel & Doyle, 2005; Poon et al., 2009; Ramachandran

& Barton, 2010; Ramachandran, Immanuel, Stepanek, Litster, &

Doyle, 2009). The technique involves the discretization of the sys-tem domain with respect to the internal and external coordinatesfollowed by recasting the population balance partial differen-

tial equation into finite volumes wherein each finite volumeis now an ordinary differential equation in terms of the rateprocesses. The continuous partial differential equation is alsotransformed into discrete ordinary differential equations over the

domain of the finite volumes. The ordinary differential equa-tions are then integrated over time via a first order explicit Eulerpredictor–corrector method (Immanuel & Doyle, 2005). Initial con-ditions for the model must be prescribed, which, are the initial

API and excipient feedrates. More details on the developmentof the PBM can be found in Boukouvala, Dubey, Vanarase, andMuzzio, Ierapetritou (2012), however, the specific equations of

the mixing module developed for this flowsheet are given inAppendix B.

2.1.3. Roller compactor

Roller compaction is the process of compacting a blended

mixture of powders into a thin ribbon between two rotat-ing rolls. Compaction of powders into ribbons aims to producecompacts which are subsequently milled to give powder mix-tures with improved mechanical and uniformity characteristics

(Am Ende et al., 2007; Cunningham, Winstead, & Zavaliangos,2010; Hein, Picker-Freyer, & Langridge, 2008; Soh et al., 2008).Roller compaction has been studied in literature and severalmodeling approaches have been proposed, ranging from sim-

pler data-based (Turkoglu, Aydin, Murray, & Sakr, 1999) to more

complex FEM and/or DEM simulations (Cunningham et al., 2010;Dec, Zavaliangos, & Cunningham, 2003; Zinchuk, Mullarney, &Hancock, 2004), that link input material properties and process

variables to properties of the produced ribbon. An interestingreview of the most significant modeling attempts of roller com-paction is found in (Dec et al., 2003). The first significant effortwas a contribution of Johanson et al. in the 1960s ( Johanson,

1965) which can predict the steady-state ribbon density andthickness of a produced ribbon given various processing condi-tions, inlet powder material properties and design aspects. Eventhough this model is based on a series of simplistic assump-

tions, it has been verified against experimental data and has beenused often in the roller compaction literature. More recently, Hsu,Reklaitis, and Venkatasubramanian (2010) extended the capa-

bilities of this model to capture the dynamics of the process.




Details about the derivation of the model can be found in thereferenced publication, however the equations and their link-

age to input and output streams are described in AppendixC.

2.1.4. Mill

A three-dimensional population balance model is implementedto describe the dynamics of the milling process. Unlike the mix-ing process, the milling process is assumed to be homogenouswith respect to spatial position (i.e. uniform velocities within the

process geometry) but heterogeneous with respect to its inter-nal coordinates which in this case are particle size, bulk densityand API composition. Similar to Verkoeijen, Pouw, Meesters, andScarlett (2002) a volume-based PBM is described in this study. The

specifics for this PB model are given in Appendix D. One of thebasic parameters of this model is the breakage function, whichdescribes how fragments, resulting from the breakup of largerparticles, are distributed in terms of their volumes. There are sev-

eral possible functional forms for this distribution, given eitherby continuous (e.g. normal or lognormal) or discrete (e.g. binary)distributions. The breakage function used in this study is basedon the work of Pinto, Immanuel, and Doyle (2007, 2008). Based

on the probabilities of particles in a particular finite volume (bin)

breaking to form daughter particles in one or more smaller finitevolumes, a numerical operation was performed that was able todescribe the distribution of these fragments (Ramachandran et al.,

2012).The milling model also incorporates product classification

(essentially 2 sieves) which sorts particles of particular size. Thesesorted particles are tracked to monitor the bulk density and API

composition, with the intention of maintaining their values withincertain specifications. Particle size distribution can be obtained viathis approach but is not considered in this study as the focus ison an integrated systems approach of lumped properties. Specifi-

cally, a simplified version of the model is solved for the purposesof this work, in order to calculate solely mean particle size infor-mation, which is required for the connection of the milling model

with downstream processes. The model is solved via a finitevolume method, previously developed by Immanuel and Doyle(2005) f or multi-dimensional systems, in combination witha back-ward differential formula (BDF) implicit integrator (built-in ingPROMS).

2.1.5. Hopper

Hoppers are unit operations which are a supplementary com-ponent of processes such as tablet presses and roller compactors

and aim to collect powder from an upper opening and feed mate-rial to the actual process from the bottom orifice. Modeling thebehavior of coarse (<500m) particulate mixtures in handling sys-tems such as conical hoppers has been studied in the literature

(Savage, 1965; Savage & Sayed, 1981; Weir, 2004). Conical shaped

hoppers have been also studied experimentally, where a numberof problems have been observed depending mainly on the prop-erties of the processed material and the geometry design of the

process. Typical examples include arching or bridging – whichprevents material from flowing out of the hopper, and ratholing– which limits the capacity of the hopper due to a formation of a stagnant layer of material around the walls of the hopper. In

order to overcome these problems, modifications to the geome-try of the hopper may be performed (i.e. change of slope or shape),addition of inserts such as inverted cones and finally, addition of flow enhancing material such as glidants (i.e. Silicon Dioxide or

Magnesium Stearate) can be added to the mixture. Above all, theproperties of the processed raw materials (i.e. cohesiveness, fric-tion angle, flowability) can suggest the optimal design in order

to attain the operation of the hopper in the ‘mass flow’ regime,

where all of the material inside the hopper is moving towards theexit, where it is discharged with a relatively constant flowrate.

The output flowrate from a hopper in tableting or capsule filling issometimes controlled throughthe presenceof a feeding screw(sys-tem equivalent to gravimetric feeders), or through the feed framein the tablet press. It is important, however, to make sure that

the hopper is carefully designed (height, angle and outlet diam-eter) such that mass flow is achieved and stagnation of materialin “dead” zones is avoided. For the materials processed in thisstudy, experimental studies will be employed to determine con-

ditions that achieve ‘mass flow’ independently from the geometrydesign of the conical hopper, due to the concentration of MgStpresent in the mixture (Faqih, Alexander, Muzzio, & Tomassone,2007).

This model is a combination of literature data and mass balanceequations, in order to capture the expected effects of this interme-diate piece of equipment as part of an integrated flowsheet model(see Appendix E). It is realized that the series of assumptions made

for the development of this model, introduce some uncertaintyin the quantitative results of this model, however, qualitatively,this model can guarantee to capture the realistic behavior of thepowder when passing through a conical hopper. Recently, hop-

pers have been studied in more detail through DEM simulations

which provide significant qualitative insight (Baxter, Abou-Chakra,TüZün, & Mills Lamptey, 2000; Ketterhagen, Curtis, Wassgren, &Hancock, 2008), however the capabilities of the current flowsheet

simulation cannot handle such computationally expensive mod-els.

2.1.6. Tablet press

The next process of an integrated tabletproduction line is tabletcompaction, during which small portions of blended powders arecompressed into a tablet of desired size and shape between twopunches. The most common type of tablet press equipment used

in the pharmaceutical industry are rotary tablet presses whichhave been studied both experimentally and computationally (Heinet al., 2008; Jain, 1999; Michaut et al., 2010; Sinka, Cunningham, &

Zavaliangos, 2003). Initially, the material,which has usually passedthrough a hopper, enters the “feed frame” which is a small cham-ber with rotating blades that fill the dies of the tablet press. Thepowder in the dies is then compressed. Significant work has beenperformed in order to model the effectof process parameters of the

feed frame on powder properties and die filling (Mendez, Muzzio,& Velazquez, 2010). In fact, the feed frame could be considered asan additional unit operation, however, in this work it is consideredas part of the tablet press model.

The models available in literature can be categorized betweentwo extremes: purely empirical (Akande, Rubinstein, & Ford, 1997;Gonnissen et al.,2008; Haware,Tho, & Bauer-Brandl,2009; Michautet al., 2010; Seitz & Flessland, 1965) and high fidelity FEM or

DEM simulation models. Since the aim of this work is to gen-

erate a computationally tractable flowsheet model that can beused for optimization purposes and aims to capture the dynam-ics of the process, expensive models in the form of FEM or DEM

simulationsshouldbeavoidedorintroducedasreducedordermod-els based on the actual expensive simulation. In this work, thetablet press is represented as a simple empirical model, basedon the popular Heckel equation (Seitz & Flessland, 1965; Jain,

1999).Thecorrelations usedto connect powder to tablet properties are

given in part F of the Appendix. It is important to account for thetimenecessary for powder thatis processed upstream to propagate

to the tablet press and thus affect properties of outcoming tablets.However, evidencefrom the sameexperimental studyshows thatafraction of thematerial processedthroughthe feed frame is further

mixed according to their residence time, which might affect their




flow properties and RSD. In this work, however, it is assumed thatno further mixingof thematerial is performed prior to die filling. It

is realized that this is a simple model, which disregards potentiallysignificant information such as the effects of particle size distribu-tion and powder bulk density on the properties of the producedtablets. However, the online prediction of porosity is a significant

result, which can be used to evaluate the quality of the producedtablets online.

3. Sensitivity analysis for dynamic integrated systems

Sensitivity analysis quantifies uncertainty in any type of com-plex model and helps identify the inputs and initial conditions

that are critical to the outputs. The purpose of applying a dynamicglobal sensitivity approach for the developed flowsheet simula-tion is not only the identification of the most significant variablesand parameters, but also the assessment of the model forms and

parameters using global variance-based techniques. For any inte-grated process where every unit operation interacts with otherunits and a variation of a parameter in one operation might affectthe outcome in another process, theapplicationof sensitivity anal-

ysis is beneficial since uncertain input stream, control or design

variables may cause high uncertainty in the design. Additionalsources of uncertainty are the developed model parameters, whichare based on noisy experimental data. There have only been a

few recent publications where global sensitivity analysis tech-niques have been applied to flowsheet simulationmodels. Schwier,Hartge, Werther, and Gruhn (2010) used optimization methods topropose a strategy for the sensitivity analysis of flowsheet simu-

lation of solid processes which consists of an effect analysis andan influence analysis. In another application of global sensitivityanalysis in bio-manufacturing processes, Chhatre et al. (2008) usedvariance-based methods to extend the sensitivity analysis stud-

ies performed in individual unit operations to an entire flowsheetprocess.

There are a multitude of global sensitivity analysis methods

being used such as Fourier Amplitude Sensitivity Test (FAST),regression-based methods, and the Sobol’ method (Saltelli, Chan,& Scott, 2000; Sobol, 2001). Global sensitivity analysis techniquesevaluate the effect that an input parameter xi has on the outputwhile all other inputs x j, j /= i arealso varied based on their assigned

distributions and a quasi-random experimental design. The sensi-tivity indices are the quantitative measures of sensitivity; the maineffect of the input parameter on the output variance is defined bythe first-order sensitivity index S i, the interaction effects the input

parameters xi and x j have on the output variance are measured bythe second order sensitivity index S ij, and accordingly higher-orderindices can measure higher-order interactions between parame-ters. The total sensitivity index S Ti is the sum of all sensitivity

indices involving xi and describes the total variance accounted for

by factor xi individually and in all possible interactions with otherparameters.

The Sobol’ method is able to calculate the first-order, all

higher-order sensitivity indices and the total sensitivity indicesto quantitatively determine the interaction between parameters.However, as the number of indices to be calculated is increased sodoes the computational cost and calculation time. If the S Ti is high

then xi is an influential parameter, if S i and S Ti are both small then xi

is not an influential parameter neither alone nor by its interactionwithanother parameter. If boththe first-order S i and total-order S Ti

sensitivity indices aresimilar thenthereare no interaction between

xi and another parameter. Finally very different first-order S i andtotal-order S Ti imply high interactions of xi with other parameters.

In computationally expensive models with a very large num-

ber of parameters, screening methods are used to identify the

subset of parameters that mostly control the output variability(Saltelli, Chan, et al., 2010; Saltelli, 2004). The advantage of screen-

ing methods is their low computational cost with the trade-off of only providing a qualitative sensitivity measure and ranking theparameters by the order of importance i.e. they do not quantifyhow much more important is one parameter from another. The

most effective of the screening methods, which is in good agree-ment with results from the Sobol’ method, is the Morris methodwhich uses the mean and the standard deviation of local sensitiv-ity measures to quantify the global importance of input parameters

(Campolongo & Saltelli, 1997; Campolongo, Saltelli, & Cariboni,2009, 2011; Saltelli, Tarantola, & Campolongo, 2000; Saltelli, Ratto,Tarantola, Campolongo, & Commission, 2006). High mean valuesidentify an important parameter while a high standard deviation

identifies non-linear effects and interactions with other inputs.In the present work, the need to assess both quantitatively

and qualitatively how the different variables of a process dynam-ically affect an output is a challenge that has been tackled in

multi-compartment models in systems biology (Hu & Yuan, 2006;Marino, Hogue, Ray, & Kirschner, 2008), where the complexity of the interactions among the compartments resembles the inter-actions between the compartments of a flowsheet simulation.

Time-varying sensitivity indexes, which can be calculated for spe-

cific time points of interest, provide insight in questions such aswhich parameters are the most important at those time pointsor how long after the perturbation is completed, the outcome is

still influenced by the perturbation. This allows the assessment of significant changes of the effects of one parameter over an entiretime interval during model dynamics, the quantification of whichof the output variables and compartments is most sensitive to a

perturbation and the determination of which unit operation of themulti-compartment model requires particularattention during thecontrol of the process.

The application of sensitivity analysis to any simulation model

at first involves assigningprobability density functions (i.e. normal,uniform, lognormal, etc.) to each of the input parameters accordingto the available data and knowledge. If there is no a priori knowl-

edge of a parameter’s nominal value, then a uniform distributionwithminimumand maximum values is assigned to thatparameter.Otherwise if there is a nominal value for the parameter availablefrom data, normal distributions are assigned setting the nominalvalue as the mean and adjusting the standard deviation accord-

ing to the parameter’s uncertainty. Sampling is performed withMonte Carlo simulations where random or pseudo-random num-bers are used to sample from the parameter probability densityfunctions, generate an input matrix and perform multiple model

output evaluations. The results of these evaluations are used toassess the influenceor relativeimportance of eachinput parameteron the outputvariable (Saltelli,Chan, et al., 2010; Saltelli, Tarantola,et al., 2010). The sensitivity analysis is carried out at different time

points for a dynamic approach, researching parameter perturba-

tion scenarios in different operating conditions such as in processstartup andduring process steady state. The approaches have beenimplemented using SimLab developed at the Joint Research Cen-

tre (Simulation Laboratory for Uncertainty and Sensitivity Analysis, JRC, Italy, 2006).

4. Results

4.1. Case Study 1: Direct compaction

Tablet production through direct compaction is the simplestmethod involving the least number of processing steps of theraw powders to actual pharmaceutical tablets. Typically, the sys-

tem has as many feeders as the number of components in the




Fig. 1. Flowsheet model for direct compaction.

pharmaceutical blend, which feed the material into the mixerwhere it is blended. Subsequently, the blended material is sentto a hopper from which it is fed to the tablet press through the

feed frame. This type of processing is used when the raw mate-rials are easy to handle and there are no problems in terms of segregation, cohesiveness and flowability, which are determined

through a series of material property characterization tests prior toproduction. Through the development of the model library forthe unit operations described in the previous section, a dynamicflowsheet model for this case study can be simply built bydragging-and-dropping into a flowsheet (Fig. 1) and setting mate-

rial property, design andmodel parameter valuesfor a specific casestudy. Here, the production of Acetaminophen tablets is simulated,where the formulation consists of: 3% Acetaminophen (API), 96%Avicel (Excipient) and 1% MgSt (lubricant). Lubrication is a very

important aspect of tablet manufacturing since the presence andconcentration of lubricants can improve flowability and reducepowder adherence to metal walls (Wang, Wen, & Desai, 2010).However, an increased concentration of MgSt can lead to tablets

with reduced hardness and lower dissolution rate. In fact it has

been shown that the number of revolutions that a lubricated blendundergoes inside the mixer is correlated to the compaction forceof a tablet (Kushner & Moore, 2010). Thus, it is critical to know

how much MgSt reaches the tablet press and its history in terms of the mixer residence time at the point it reaches the tablet press.However, in this work, the concentration of MgSt in the pow-der stream can be predicted at all times and throughout all units,

but there is no correlation between the lubricant concentrationand tablet properties. This feature will be incorporated in futurework.

For any desired formulation, the simulation requires informa-

tion about the total flowrate or throughput, and the compositionof the blend, as well as the particle size distribution and bulk den-sity of each raw powder material. Through this information, the

flowsheet can calculate the necessary rotation rates of each of the

screw feeders in order to supply the system with the desired pow-der blend at steady state. In addition, due to the experimentally

observed variability of the processed powder flowrates, noise isadded to the dynamic feeder outlet flowrates by drawing valuesfrom a normal distribution with a standard deviation of 0.05 every2 s of simulation time. This feature can identify whether this vari-

ability affects the dynamic profiles of downstream properties. Dueto the assumption of mass flow through the hopper, no mixing of the material is assumed. Thus, properties of the material such asconcentration and Relative Standard Deviation are passed through

the unit operation with a time delay equal to the mean residencetime of the material in the hopper. The mean residence time canbe calculated approximately equal to the hopper volume dividedby the volumetric powder flowrate. Similarly, the same assump-

tions of no mixing and average residence time delayed propertiesare incorporated for the feed frame operation, however, the meanresidence time is a function of the process parameters (AppendixF). Finally, the final tablet porosity is controlled solely by the pro-

cess parameter of compaction force, but the average compositionof materials in the tablets is approximated based on the powdermaterial properties exiting the feed frame. Fig. 2 is a more detailedrepresentation of the system containing all the variables, param-

eters and design aspects which should be defined in each process

and are passed from one process to the next.The first assessment of the flowsheet simulation is performed

through the verification of the overall mass balances for each unit

operation (Fig. 4) as well as for the overall system, such that allmass that enters from thefeeders exits in theform of tablets. A fur-ther assumption for the uniformity of the average weight of tabletsis necessary for this calculation. However, this type of dynamic

simulation can be very useful in identifying how possible pertur-bations during the operation of a process can affect the output of the same process or further processes downstream. For example, atypical perturbation which will be inevitably encountered during

continuous direct compaction is feeder refilling. In fact, strategiesand equipment for feeder hopper refilling is a major concern inthe powder processing industry (Engisch & Muzzio, 2010), since

it is important to balance between flowrate fluctuation, frequencyof refilling and equipment cost. Through the developed flowsheetmodel, however, it is possible to simulate any operating sequencein order to study its effects on final and intermediate product prop-erties. Fig. 3 represents the overshoot in the API flowrate which

is caused when the hopper is refilled with material at t =1000s.The downstream effects of this fluctuation can be seen in Figs. 4–6.Specifically, from Fig. 4 it can be verified that the mass balance issatisfied in the mixing module as well as that the feedrate over-

shoot is filtered out at the output of the mixer. This is expecteddue to the residence time of the powder inside the blender andsince the overall fraction of the API concentrationin this simulationis only 3%. However, the API must be present in the final prod-

uct (tablets) in very specific concentrations. Thus, based on this

integrated dynamic model, the imposed perturbation causes theAPI concentration to increase from the desired value of 0.03–0.034(Fig. 5) within a small time window.

In addition, due to the knowledge of the residence times of thematerial in the hopperand feed frame, it is possible to approximatewhich fraction of the produced tablets to discard, if the predictedAPI concentration is not within the acceptable bounds, based on

Critical Quality Attributes (CQA) specifications. Finally, due to thediscretization of the mixer in small compartments for thepurposesof the PBM model, the calculation of Relative Standard Deviation(RSD) of the API concentration is also made possible. This measure

is used widely to characterize blend uniformity and is suggestedby regulatory agencies to be monitored for quality assurance pur-poses. The value of RSD is calculated as the standard deviation of

the predicted API concentration between the different bins located




Fig. 2. Detailed representation of flowsheet model for direct compaction.

at the exit of the blender divided by their mean value. In Fig. 6,

the RSD profile has two peaks, one during the initial stage of theprocess and one which is caused by the refilling perturbation. Theinitial larger peak can be explained since the material exiting the

mixer has not reached steady state yet and is bound to have morevariability. The second milder increase is caused by the suddenintroduction of additional API intothe system. Thisresult, however,must be further experimentally verified.

Another advantage of flowsheet simulation is the simulationof different process operation scenarios including recycle dynam-ics. Thus for this specific case study the effect of adding a secondmixing tank in the process through which a fraction of the mixer

outlet will be re-processed and sent to the mixer inlet is assessed

(Fig. 7a). This approach shows promising filtering abilities of

feedrate fluctuations (Fig. 7b). Therecycling benefitsare alsoshown

in Fig. 5 where the final API concentration of the produced tabletsis not affected significantly compared to the case with no recy-cling. However, this increases the cost of the system significantly

andcan cause the system response to be slow in responseto onlinecontrol actions. However, theseaspects will not be the focus of thispaper, which aims only to be an initial attempt for pharmaceuticalflowsheet model building.

Finally, the application of the methodology for dynamic sen-sitivity analysis is applied to the integrated process of directcompaction. Collecting all possible inputs for the sensitivity anal-ysis of this large case study leads to approximately 120 inputs

including parameters, design variables and process conditions.

These include: material properties for the three ingredients




Fig. 3. Feedrate of API during simulation of refilling.

Fig. 4. Mixer inlet and output total flowrates during refilling.

Fig. 5. API concentration throughout the different units during refilling.

(particle size distributions, bulk densities), model parameters(axial, radial and backward fluxes of PB model for each compart-

ment of the mixer geometry based on the geometry discretization,Heckel model parameters, empirical parameters of feeder model),design variables (height, aperture diameter of the hopper) and

operating variables (mixer rpm, feed frame rotation speed and

Fig.6. RelativeStandardDeviation (RSD)of APIconcentration in mixeroutletduring

refilling.

speed, tablet press compaction force). The outputs of interest are

the final properties of the produced tablets as well as intermediateproduct properties, such as process stream RSD and composition

(Table 1).An initial screening method based on Morris technique is

performed in orderto minimizethe number of variables and conse-quently minimize the required sampling cost. The large number of

parameters is a characteristic of population balance models sincethis is a multiple of thenumber of bins forwhichthe process geom-etry is discretized spatially. A screening technique, however, canidentify whether the relative effect of the total number of these

parameter values is significant compared to all the other uncer-tain parameters. After the process of initial screening, 11 inputs areidentified as important relatively to the remaining ones (Table 2).ThePBM parameters arefound insignificantin thiscase study, how-

ever, this does notmean that these parameters areredundant. Thisresult simply denotesthat for thechosenoutputsconsidered,whichare in their majority bulk output stream properties, these param-eters are not significant compared to the 11 uncertain inputs of

Table 2.Following the methodology described in Section 4, the flow-

sheet is simulated for 1500s for a total number of 1040 times. Theselection of 1040 input parameter vectors results from the genera-

tion of two 80 by11 randominput matrices where 80(11+ 2)= 1040inputvectorsare created (Saltelli, Chan, et al., 2010). Quasi-randomnumbers are used to generate these random data matrices forthe computation of the Monte Carlo integrals. Other sampling

techniques such as the Latin Hypercube sampling can be used tocompute the sensitivity indices but it has been shown that the

Sobol’ LPT sampling schemes used here perform better (Saltelli,Tarantola, et al., 2010). For each of the stochastic simulations the

vector of values for the 11 uncertain input parameters is chosenand sent to gPROMS for the computation of the outputs. Values of the selected outputs (Table 1) are exchanged every 10s in orderto perform the calculations for the SA indices for each small time

interval. As a result, dynamic profiles of the sensitivity analysisindices are calculated to produce profiles such as the ones shownin Figs.8 and 9.

Fig. 8 depicts the dynamic sensitivity profiles for the RSD of the

mixer output stream. As expected, it is evident that the two mostsignificant variables are the mean particle size of the API and theexcipient, as well as their bulk densities to a lesser extent. Surpris-ingly the effect of the mixer rotation rate is overshadowed relative

to the effects of these four parameters; and this result does not




Fig. 7. (a) Flowsheet model with recycle and (b) effect of recirculation of powder

material during refilling.

Table 1

Output of global sensitivity analysis.

Output

1 Mixer total output flowrate

2 Mixer output bulk density

3 Mixer output RSD

4 Mixer output API concentration

5 Hopper output density

6 Hopper output RSD

7 Hopper output API concentration

8 Hopper mean residence time

9 Hopper mass holdup

10 Hopper height

11 Feed frame mean residence time

12 Tablet porosity

13 Tablet API concentration

Fig. 8. Dynamic sensitivity analysis profile of mixeroutput Relative Standard Devi-

ation.

necessarily agree with experimental observations. An explanation

to this is perhaps a wrong choice of the range of the uniform distri-butionof this specific inputwhichis toosmall tocapturethedesiredeffects of this parameter, or else the inability of the model to cap-ture the significant effectof the mixer rotationrate.Oneof the goals

of performing sensitivity analysis is always the validation and anal-ysis of the model accuracy and effectiveness. In addition, the profilereveals a few fluctuations in the relative effects of the significantinputsat the initial stages of operation, whichfinally converges to a

steady-stateprofile. This result is dueto the transition time neededto reach steady state inside the mixer.

The contributionof effects of all the uncertain inputs to thefinalAPI concentration of the produced tablets is shown in Fig. 9. Based

on the cumulative area of the mean particle size of the excipient,this is found to be the most significant uncertain parameter forthis specific output. The high concentration of excipient in thislow-dose drug formulation (96% excipient) is one of the reasons

that may explain this result. The insignificant variations observedbetween1200and 1500 s maybe attributed to numericalnoise thatis often encountered in flowsheet simulations, sincethe system hasreached steady state at this stage.

Figs. 8 and 9 represent the total sensitivity indices (S Ti) sincefor this case study they are found to be very similar to the firstorder indices. This resultimplies that thereare no significant inter-actions between input parameters which affect the RSD and API

concentration. Fig. 10 represents an intensity plot of the signifi-cant contributions of inputs to each output, when the system hasreached steady state. Value of 1 indicates strong influence whilevalue close to zero indicates no correlation at all.

Certain outputs depend solely on a single input, such as tabletporosity which is only affected by the compaction pressure. Thiseffect is expected since the current flowsheet model does not takeintoaccount the effect of particle sizeand other material properties

on the tabletporosity. Thus,it becomes clear that such an approachof global sensitivity analysis may be used not only to draw signifi-cant conclusions about the interactions between specific uncertaininputsto outputs, butalso to point outmissingcorrelations whicha

model fails to capture. This information is critical for model refine-ment in order to predict all the desired and expected trends and

correlations.




Table 2

Input to global sensitivity analysis.

Input Mean value Distribution SD/bounds Units

1 API bulk density 600 Normal 50 kg/m3

2 Excipient bulk density 325 Normal 35 kg/m3

3 Lubricant bulk density 160 Normal 10 kg/m3

4 API mean particle size 3.00E−05 Normal 5.00E−06 m

5 Excipient mean particle size 2.00E−04 Normal 2.00E−05 m

6 Lubricant mean particle size 2.00E−05 Normal 5.00E−06 m

7 Mixer rpm – Uniform [5–15] rpm8 Die disc speed – Uniform [0.509–1] –

9 Feed frame rotation rate – Uniform [0.33–1] –

10 Tablet press compression force set point – Uniform [8–12] MPa

11 Hopper aperture diameter – Uniform [0.05–0.06] m

Fig. 9. Dynamic sensitivity analysis for tablet API concentration.

Fig. 10. Intensity plot of total sensitivity indices of inputs (Table 2) to outputs

(Table 1) at steady state.

Finally, the same set of experiments is performed for 2200s,but this time a refill of the API feeder is scheduled at time t =1000s(Fig.4). The purpose of this simulation is to identifyhow such a per-

turbation willaffect thesensitivity indices of theintegratedprocessdynamically. Interestingly, not only the profiles of the SA indicesare drastically different (Fig. 11), but also parameters which werenot included previously are now found to be critical. Comparing

Fig. 9 with Fig. 11b it becomes obvious that after a refilling of theAPI concentration, process parameters such as mixer rotation rateand feed frame speed become so critical towards the final API con-centration of the produced tablets, that they overshadow the effect

of material properties. This result can be explained based on thefact that these two inputs control the mean residence time of thematerial inside the mixer and the feed frame, thus they will affectthe time necessary for the API concentration to reach a new steady

state.In addition, in this case the first order indices (Fig. 11a) are

different than the total indices (Fig. 11b) implying that the majorcontributions of the effects of mixing rotation rate and feed frame

speed are due to interactions with other inputs. Typically the sumof S Ti is greater than 1 because the various interactions arecounted

multiple times (Saltelli, Chan, et al., 2010). The difference between




Fig. 11. (a)Firstorder S i indices and(b) total order S T indices fortablet APIconcen-

tration after an API feeder refill at t =1000s.

the values of S i and S Ti is a measurement of the capacity in whichthis parameter participates in any interactions between otherparameters.

4.2. Case Study 2: Dry granulation

The second case study is a more complex processing line, whichprecompresses the powder blends intothin ribbons which are then

milled and then finally compressed into tablets (Fig. 12).As it has been mentioned earlier, this production scenario is

selectedwhenpowderproblems suchas segregationor aggregationdue to cohesion are observed, or in cases where the raw materi-

als are highly sensitive to water, or also in cases where high API

content causes the uncompressed powder to be poorly flowable.Due to the particle deformation mechanisms, compression of pow-ders into ribbons, which are then milled to form particles in the

50–400m range, produces powders with better flow abilities andmore consistent API composition. Following the same approach asin the previous case study, the necessary processes are linked tobuild a flowsheet model, using the model types described in Sec-

tion 3 (Fig. 13). Through this case study, the authors aim not onlyto show the capabilities of the resulting model, but also the prob-lems and gaps of this integration, due to the limits of the availablemodels.

In this case study, the initial stages are identical to direct com-paction, referring to feeding and mixing. The available model forthis process can predict ribbon output properties as a function

of process and design variables (Fig. 14), but does not consider

Fig. 12. Flowsheet model forCase Study 2: drygranulation.

the composition of ribbons and effects of RSD. Thus, this informa-

tion enters the process, but cannot be communicated to furtherdownstream processes. A simple assumption of the average rib-bon composition (API, excipient and lubricant) to be equal to thecomposition of the material entering the rolls is used, however,

further investigation is necessary for the validity of this assump-tion. Despite the fact that the integration of these two models ismissing certain significant correlations, it can still capture someinteresting effects. For example, a possible set point change in

the compression pressure in the roller compactor (Fig. 14), causesthe ribbons to be thinner but more dense, which will definitelyhave an effect in the milling process because denser ribbonswill be harder to break but are also likely to break into smaller

particles.It is also assumed that as the ribbons enter the mill, they are

broken into small pieces, and this is simulated through an initialcondition in the milling population balance of very large parti-

cle sizes. These particles are further broken up into smaller finesas the material is processed inside the mill. Despite its aforemen-

tioned gaps, the integration can successfully capture the effect of perturbations in the mixture composition to the average particle

size of the milled particles. In fact, during the same schedule forAPI feeder refilling as in the first case study, as more API entersthe milling process, a small increase in the average particle size isobserved, due to the change in the balance of API and excipient

volume fractions entering the system (Fig. 15), which the popu-lation balance can capture (see Appendix D). It is very importantto be able to accurately predict the average particle size of milledparticles, since this will play a very important role in tablet prop-

erties, such as hardness and dissolution, which are not studied inthis work.

Finally, based on the tablet press model, the effects of the pro-cess parameter of compaction pressure on tablet porosity can be

approximated (Fig. 16).




Fig. 13. Detailed description of flowsheet model for dry granulation.




Fig.14. Dynamic responseof ribbon propertiesfor set pointchange in compression

pressure of roller compactor.

Fig. 15. Effect of refilling in average particle size of milling process.

Fig. 16. Effect in tablet porosity due to a step change in tablet press compaction

pressure.

5. Conclusions andperspectives

This work aims to outline the necessary steps and challengesassociated with flowsheet model building for integrated pharma-

ceutical manufacturing processes. It is evident, that the currentstate of flowsheet model building in the pharmaceutical indus-try is very primitive compared to state of the art of fluid-based

flowsheet models. This initial approach aims to combine different

types of model types, ranging from semi-empirical population bal-ances to empirical models, in order to capture all the effects and

interactions of current knowledge of the necessary processes fortransforminga mixture of rawpowder materials to actualpharma-ceutical tablets. Results prove that the developed models capturethe expected trends and responses of stream variables during a

dynamic operation. Such results can be used to identify promisingcontrol strategies through the simulation of dynamic step changeexperiments. Most importantly, such a simulation can provideinsight in capturing the dynamics of a process through accurate

prediction of the residence time of powder throughout each pro-cess andthus itcan beusedto estimatethe time intervalfor off-specproduct in thecase of step-changes or unexpected events upstreamas well as the propagation of the variability of the inputs and their

effects on tablet properties.Dynamic sensitivity analysis which is enabled through stochas-

tic simulations of the flowsheet model based on a computerexperiment can lead to important conclusions about the quantifi-

cation of uncertainty effects towards specific outputs. The effectsof uncertainty of a large number of fluctuating inputs is impor-tant since this can lead the process to operate outside the designspace where process is outside of the validated operational inter-

val and the product might be out of specifications (OOS). Finally,

ranking the relative effect of the uncertain inputs on specific out-puts is vital when identifying efficient control strategies, which is afuture goal towards the implementation of an efficient continuous

tablet manufacturingprocess. Mostimportantly, these rankingscanhelp answer a critical question companies currently struggle with:which variables are critical?

Future goals include theincorporationof powder material prop-

erties into the flowsheet simulations, such as flowability metrics(flowindex) and interfacial properties (contact angle), which implythemodificationof thedevelopedmodelsin order to takethe effectsof these variables into account. In addition, significant interactions

between ribbon properties (density and thickness) and the inputvariables of the milling process are currentlybeing researched bothcomputationally and experimentally in order to be able to capture

thepropagation of effects and thecoupled dynamics between thesetwo processes. Finally, since the vast majority of modeling work forpowder based processes is in forms of computationally expensiveDEM or FEM simulations, incorporation of the predictions of suchmodels into a flowsheet simulation through reduced order models

is another future goal. Simulation of start-up and shut-down pro-cedures has been identified to require modifications in the modelparameters and willbe included in future versionsof thedevelopedflowsheet model library.

Acknowledgments

The authors would like to acknowledge the financial support

by ERC (NSF-0504497, NSF-ECC 0540855). In addition, the authorswould like to thank colleagues Bill Engisch and AdityaVanarase forproviding the experimental data.

Appendix A. Feeder

The parameters of thefeeder unit operationmodel consist of the

process gain parameter (k f g ), the time constant ( f ), and the time

delay factor ( f d

) (Eq. (A1)). The optimum parameter values wereobtained through minimization of the least-squares error of the

observed versus predicted flowrate values. As described in Section2, the inlet bulk density and mean particle size are assumed to beconstant and are input specifications of the material being fed to

the model.




f dmout (t )

dt +mout (t ) = k f

g ω f

f d

∂mdelayedout (t, z )

∂t = −

∂mdelayedout (t, z )

∂t with I.C. m

delayedout (t, z = 0) = mout (t )

bulk in(t ) = bulk out (t )d50 in(t ) = d50 out (t )

(A1)

where ω f is the feeder screw rotation rate, z is the time delay

domain, and mdelayedout is the actual output feedrate of the material

based on the experimentally observed time delay f d

.

Appendix B. Mixer

A multi-dimensional population balance model is constructed

to model blending processes that accounts for n solid componentsand two external coordinates (axial and transverse directions inthe blender) and one internal coordinate (size distribution due tosegregation). The equation is shown below:

∂F (n, z 1, z 2, r , t )

∂t +

∂

∂z 1

F (n, z 1, z 2, r , t )

dz 1dt

+∂

∂z 2F (n, z 1, z 2, r , t )

dz 2

dt + ∂

∂r F (n, z 1, z 2, r , t )

dr

dt

= R formation(n, z 1, z 2, r , t ) −Rdepletion(n, z 1, z 2, r , t ) (B1)

In Eq. (B1), the number density function F (n, z 1, z 2, r , t ) rep-resents the total number of moles of particles with property r atposition z = ( z 1, z 2) and time t . In addition, z 1 is the spatial coordi-

nate in the axial direction, z 2 is the spatial coordinate in the radialdirection, r is the internal coordinate that depicts particle size andn = 2 to indicate presence of two components (active pharmaceu-

tical ingredient and excipient). Hence dz 1/dt and dz 2/dt representthe axial and radial velocity, respectively.

z 2

miin

(n = i, z 1 = 0, z 2, t ) = miin

(t ) for i = 1, . . . , n

miout (t ) =

z 2

mi(n = i, z 1 = L, z 2, t ) for i = 1, . . . , n

bulk out (t ) =

ni

C (n = i, z 1 = L, z 2, t )ibulk in

d50 out (t ) =

ni

C (n = i, z 1 = L, z 2, t )di50 in

RSD(t ) =SD(n = " API ", z 1 = L, z 2, t )

mean(n=

" API ", z 1 =

L, z 2, t )

(B2)

The group of Eq. (B2) are included in the mixing model for thecalculation of the inlet mass flowrates of each material, the outlet

bulk density, mean particle size and RSD, which are passed on thenext unit operation. These equations are necessary for the con-nection of the population balance equation with preceding andsubsequent unit operations.

Appendix C. Roller compaction

The model introduced in (Hsu et al., 2010) is implemented in

order to relate the input powder bulk density (bulk in) of the pow-der and process parameters such as compression pressure (P rc

h ),

rotating roll speed (ωrc ) and inlet powder feed speed (min) to aver-age density (rib

bulk out ) and thickness (h0) of the produced ribbon.

The roller compactor is divided into two regions, the slip region– within which the powder is assumed to flow between the rolls,and the nip region – inside which the powder is compressed toform ribbons. The first equation is thematerial balance of the pow-

der entering the nip region which is exiting in forms of ribbons.An empirical correlation is used between applied ribbon stress anddensity,usingthe values of theparametersK rc and C rc

1 in theoriginal

publication. Design parameters such as roll radius Rrol, roll width

W

rol

, compact surface area A

rol

, effective angle of friction ı, inletangle in and nip angle ˛ need to be specified based on the geom-

etry of the equipment and the material properties of the powdermixture. The dynamics of the process in the case of step changesin the pressure, rotation speed and feed speed are captured by thefinal three first order differential equations.

d

dt

h0(t )

Rrol

=

ωrc

bulk in(t ) cos in(1+ (h0(t )/Rrol) − cos in)(uin(t )/ωrc (t )Rrol)− ribout (t )(h0(t )/Rrol)

in

0

( )cos( )d

P rc h

(t ) =W rol

Arol

out (t )Rrol

1+ sin ı

a

0

h0(t )/Rrol

(1+ (h0(t )/Rrol)− cos )cos

K rc

cos d

out (t ) = C rc 1 (ribout (t ))K

rc

rc P

dP rc h

(t )

dt + P rc

h (t ) = P rc

sp

rc ω

dωrc (t )

dt +ωrc (t ) = ωrc

sp

rc u

durc (t )

dt + urc (t ) = urc

sp

(C1)

Appendix D. Milling

The population balance model developed for this work is char-acterized by the internal coordinates API volume (s1), excipient

volume (s2) and gas volume ( g ) (see Eq. (D1)):

∂∂t

F (s1, s2, g , t ) = Rbreak(s1, s2, g , t )

Rbreak(s1, s2, g , t ) = R formationbreak

−Rdepletionbreak

R formationbreak

=

∞

s1

∞

s2

∞

g

kbreak(s1, s2, g )b(s1, s2, g , s1, s2, g )

×F (s1

, s2

, g , t )ds1

ds2

dg

Rdepletionbreak

= kbreak(s1, s2, g )F (s1, s2, g , t )

(D1)

Similarly to the mixing model, density function F (s1, s2, g , t )

represents the number of moles of particles of API, excipient andgas in time. Here,Rbreak is the breakage rate, which is described bythe difference between the rate of formation of new daughter par-

ticles and the rate of depletion of the original particle. In Eq. (D1),




the breakage rate is described by the breakage function (b) and thebreakage kernel (kbreak). As an initial condition, the mean particle

size of the material that enters the mill is set to a really large value,resembling the size of broken ribbons.

The breakage kernel used in this study was a modified kernelbased onthe work by Matsoukas, Kim, and Lee (2009), where kbreak

has a size and composition (c 1, c 2) dependency, where differentweights areassigned to the different components in order to intro-duce composition asymmetry in the model. The current kernel inthe literature is symmetrical and as a result deviations in the API

composition from the desired value cannot be observed. The out-puts of the PBM are particle size (d50), bulk density (bulk out ) andAPI composition (C API ), which are defined as follows:

d50(t ) =

6(s1(t ) + s2(t ) + g (t ))

1/3

bulk out (t ) =Mass of Solid(t )

Total Volume(t )

C API (t ) =

[(F (s1, s2, g , t )s1(t ))/(s1(t ) + s2(t ))]

F (s1, s2, g , t )

(D2)

Note that in this model the evolution of the average particle

diameter is tracked for all particle size ranges (i.e. fines, productand oversized particles).

Appendix E. Hoppers

A mass balance on the hopper system will be of the following

form (Eq. (E1)):

dm

dt = min −mout (E1)

where m is the mass holdup inside the hopper. Assuming con-

stantbulk density throughout the hopper the height of the materialinside thehoppercan becorrelatedto the mass holdupthrough (Eq.

(E2)):

m(t ) = H hop(t ) Ahopbulk(t ) (E2)

The area of the conical hopper is not constant and it is assumedto be a linear function of the height. This correlation can be easily

found from measuring the actual dimensions of the hopper. Thepropagation of individual component concentrations and RSD arecaptured taking into account the time delay caused by the meanresidence time of the material inside the hopper (Eq. (E3)).

rt ∂C iout (t, z )

∂t

= −∂C iout (t, z )

∂z

with I.C. C iout (t, z = 0) = C iin

(t ),

for i = 1, . . . , n

rt ∂RSDout (t, z )

∂t = −

∂RSDout (t, z )

∂z

with I.C. RSDout (t, z = 0) = RSDin(t )

(E3)

where H hop is the height, Ahop is the area of the hopper, bulk isthe bulk density and rt is the mean residence time of the material

inside the hopper. In other words, since it is assumed that all thematerial entering the hopper flows out at a constant flowrate, it issafe to deduce that the material is no further mixed and accordingto itsmeanresidence time allproperties of theblend will propagate

at the output of the hopper accordingly.

Appendix F. Tablet press

Accordingto Heckel analysis,the compression force of thepow-der can be linked to the porosity of the produced tablets, which isa very significant product quality attribute (Eq. (F1)).

ln

1

ε(t )

= khP tp(t ) + ah (F1)

where ε represents the porosity of a tablet, P tp

is the compactionforce, while kh and ah are empirical parameters which should becalculated through experimentation for thematerialwhich is being

processed. The porosity of a tablet is highly correlated to thedisso-lution andbioavailability of a tablet. The compression pressure hasbeenexperimentally observedto follow a firstorder linear responsegiven a set-point change, and this is introduced into the model in

order to capture the dynamics of the process. In order to accountfor the residence time of the powder in the feed frame, a responsesurface model is used, which correlates the die disc speed (udisc )and the feed frame speed (u ff ) to the average residence time of

the powder in the feed frame section. The model parameters arefitted based on the experimental data obtained in (Mendez et al.,2010) for the processed formulation (Eq. (F2)) through minimiza-tion of the least-squares error between measured and predicted

values. The investigatedranges of variables udisc and u ff are [29–57]and [24–72] rpm,respectively, but theyare normalized so thattheybelong in the same range ([0–1]).

RT ff = b1 + b2udisk

+ b3u ff + b4udisc u ff (F2)

Finally, simple material balances based on the rotation rate,mean tablet weight (wtablets) and desired output tablet productionrate (mtablets

out ) can be formed (Eq. (F3)). Again, the dynamics of themixture composition, which reflects the composition of the pro-

duced tablets takes into account the delay caused by the residencetime of thematerial in the feed frame and a differential equation isused to capture the dynamics of a set point change in compactionpressure (Eq. (F3)).

RT ff ∂C iout (t, z )

∂t = −

∂C iout (t, z )

∂z

with I.C. C iout (t, z = 0) = C iin

(t ), i = 1, . . . , n

m(t ) = int

min(t )

wtablets

udisc (t ) =mtablets

out (t )

60ndisc

tp dP tp(t )

dt + P tp(t ) = P tp

sp

(F3)

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