A Review of Dynamic Models of Hot-Melt Extrusion

Hot-melt extrusion is commonly applied for forming products, ranging from metals to plastics, rubber and clay composites. It is also increasingly used for the production of pharmaceuticals, such as granules, pellets and tablets. In this context, mathematical modeling plays an important role to determine the best process operating conditions, but also to possibly develop software sensors or controllers. The early models were essentially black-box and relied on the measurement of the residence time distribution. Current models involve mass, energy and momentum balances and consists of (partial) differential equations. This paper presents a literature review of a range of existing models. A common case study is considered to illustrate the predictive capability of the main candidate models, programmed in a simulation environment (e.g., MATLAB). Finally, a comprehensive distributed parameter model capturing the main phenomena is proposed.

[1]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[2]  P. Anderson,et al.  Simulation of distributive mixing inside mixing elements of co-rotating twin-screw extruders , 2013 .

[3]  João M. Nóbrega,et al.  Computer aided rheological design of extrusion dies for profiles , 2001 .

[4]  Bruno C. Hancock,et al.  Process modeling in the pharmaceutical industry using the discrete element method. , 2009, Journal of pharmaceutical sciences.

[5]  S. Chiu.  Developing commercial applications of intelligent control , 1997 .

[6]  H. Brenner.  The diffusion model of longitudinal mixing in beds of finite length. Numerical values: H. Brenner, Chem. Engng Sci.17: 229–243, 1962 , 1995 .

[7]  James L White,et al.  Simulation of non‐isothermal flow in modular co‐rotating twin screw extrusion , 1994 .

[8]  Timothy A. Haley,et al.  On-line system identification and control design of an extrusion cooking process: Part I. System identification , 2000 .

[9]  H.,et al.  Three-Dimensional Flow Modeling of a Self-wiping Corotating Twin-Screw Extruder. Part II , 2004 .

[10]  Stefan Heinrich,et al.  DEM–CFD modeling of a fluidized bed spray granulator , 2011 .

[11]  Bernard Gosselin.  Multilayer perceptrons combination applied to handwritten character recognition , 2004, Neural Processing Letters.

[12]  Jean-Francois Hetu,et al.  Immersed boundary finite elements for 3D flow simulations in twin-screw extruders , 2013 .

[13]  A. Isambert,et al.  Development of a global mathematical model for reactive extrusion processes in corotating twin-screw extruders , 2010 .

[14]  Kazumori Funatsu,et al.  3-D non-isothermal flow field analysis and mixing performance evaluation of kneading blocks in a co-rotating twin srew extruder , 2001 .

[15]  D. Kalyon,et al.  Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip , 2008 .

[16]  Bruno Vergnes,et al.  A study of residence time distribution in co-rotating twin-screw extruders. Part II: Experimental validation , 2003 .

[17]  Justin Rae Elsey.  Dynamic Modelling, Measurement and Control of Co-rotating Twin-Screw Extruders , 2002 .

[18]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[19]  M. Booy.  Isothermal flow of viscous liquids in corotating twin screw devices , 1980 .

[20]  Ernst Dieter Gilles,et al.  Development, analysis and validation of population models for continuous and batch crystallizers , 2002 .

[21]  V. Vanhoorne,et al.  Conceptual framework for model-based analysis of residence time distribution in twin-screw granulation. , 2015, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[22]  W. Michaeli,et al.  An Analytical Model of the Conveying Behaviour of Closely Intermeshing Co-rotating Twin Screw Extruders , 1996 .

[23]  Arthur Ritter,et al.  In vitro analysis and mechanical properties of twin screw extruded single-layered and coextruded multilayered poly(caprolactone) scaffolds seeded with human fetal osteoblasts for bone tissue engineering. , 2011, Journal of biomedical materials research. Part A.

[24]  Y.-H. Zhu,et al.  Application of neural network modelling in fuzzy extrusion control , 1992 .

[25]  Dana Barrasso,et al.  MULTI-SCALE MODELING OF WET GRANULATION PROCESSES , 2015 .

[26]  M. A. Barrera,et al.  Three-dimensional modelling of flow curves in co-rotating twin-screw extruder elements , 2008 .

[27]  David Jones,et al.  Digital image processing for measurement of residence time distribution in a laboratory extruder , 2006 .

[28]  Modelling extrusion cooking , 2001 .

[29]  Dana Barrasso,et al.  A Multi-Scale Hybrid CFD-DEM-PBM Description of a Fluid-Bed Granulation Process , 2014 .

[30]  M. Sheikhzadeh,et al.  Model predictive control of a twin-screw extruder for thermoplastic vulcanizate (TPV) applications , 2012, Comput. Chem. Eng..

[31]  Philippe A. Tanguy,et al.  Adaptive finite element simulations of fluid flow in twin-screw extruders , 2003, Comput. Chem. Eng..

[32]  Jean-Robert Clermont,et al.  Numerical simulations of non-isothermal three-dimensional flows in an extruder by a finite-volume method , 2005 .

[33]  D. Kalyon.  An analytical model for steady coextrusion of viscoplastic fluids in thin slit dies with wall slip , 2010 .

[34]  Ingmar Nopens,et al.  Model-based analysis of high shear wet granulation from batch to continuous processes in pharmaceutical production--a critical review. , 2013, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[35]  Use of Adjustable-Gap On-Line and Off-Line Slit Rheometers for the Characterization of the Wall Slip and Shear Viscosity Behavior of Energetic Formulations , 2006 .

[36]  W. Yacu.  MODELING A TWIN SCREW CO‐ROTATING EXTRUDER , 1985 .

[37]  Riitta L. Keiski,et al.  Modeling continuous high-shear wet granulation with DEM-PB , 2016 .

[38]  Michael J. Hounslow,et al.  Tracer studies of high‐shear granulation: II. Population balance modeling , 2001 .

[39]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[40]  Dilhan M. Kalyon,et al.  Apparent slip and viscoplasticity of concentrated suspensions , 2005 .

[41]  Otilia Popescu,et al.  A NEW APPROACH TO MODELING AND CONTROL OF A FOOD EXTRUSION PROCESS USING ARTIFICIAL NEURAL NETWORK AND AN EXPERT SYSTEM , 2001 .

[42]  Y. L. Gorrec,et al.  Dynamic Modeling of the Reactive Twin-Screw Corotating Extrusion Process: Experimental Validation by Using Inlet Glass Fibers Injection Response and Application to Polymers Degassing , 2012 .

[43]  Han E. H. Meijer,et al.  The modeling of continuous mixers. Part I: The corotating twin-screw extruder , 1988 .

[44]  Julian Morris,et al.  Artificial neural networks in process estimation and control , 1992, Autom..

[45]  Ashish Kumar.  Experimental and model-based analysis of twin-screw wet granulation in pharmaceutical processes , 2015 .

[46]  P. A. Taylor,et al.  On the dynamics and control of a plasticating extruder , 1982 .

[47]  Dilhan M. Kalyon,et al.  Mechanisms of mixing in single and co-rotating twin screw extruders , 1995 .

[48]  G. Hassan,et al.  Model reference optimal steady‐state adaptive computer control of plastics extrusion processes , 1981 .

[49]  C. Gogos,et al.  Mat formation and unstable flows of highly filled suspensions in capillaries and continuous processors , 1989 .

[50]  D. Kalyon,et al.  Twin Screw Extrusion Based Technologies Offer Novelty, Versatility,Reproducibility and Industrial Scalability for Fabrication of TissueEngineering Scaffolds , 2013 .

[51]  Nathalie Cayot,et al.  Dynamic modelling for a twin screw food extruder: Analysis of the dynamic behaviour through process variables , 1995 .

[52]  C. Gogos,et al.  Development of experimental techniques and simulation methods to analyze mixing in co‐rotating twin screw extrusion , 1988 .

[53]  Charles E. Martin,et al.  Pharmaceutical Applications of Hot-Melt Extrusion: Part II , 2007, Drug development and industrial pharmacy.

[54]  Anders Rasmuson,et al.  A volume-based multi-dimensional population balance approach for modelling high shear granulation , 2006 .

[55]  Grigore Bozga,et al.  Residence time distribution in a corotating twin-screw extruder , 2000 .

[56]  Hervé Bourlard,et al.  Neural networks for statistical recognition of continuous speech , 1995, Proc. IEEE.

[57]  Justin A. Gantt,et al.  High-shear granulation modeling using a discrete element simulation approach , 2005 .

[58]  Runyu Yang,et al.  DEM study of the transverse mixing of wet particles in rotating drums , 2013 .

[59]  L. Janssen,et al.  Twin screw extrusion , 1978 .

[60]  Lara Wakeling,et al.  Nutritional aspects of food extrusion: a review , 2007 .

[61]  Runyu Yang,et al.  Discrete particle simulation of particulate systems: A review of major applications and findings , 2008 .

[62]  M. Malik,et al.  3D Finite Element Simulation of Processing of Generalized Newtonian Fluids in Counter-rotating and Tangential TSE and Die Combination , 2005 .

[63]  M. Malik,et al.  An Integrated Approach for Numerical Analysis of Coupled Flow and Heat Transfer in Co-rotating Twin Screw Extruders , 2007 .

[64]  James D. Litster,et al.  Fundamental studies of granule consolidation Part 1: Effects of binder content and binder viscosity , 1996 .

[65]  Christian Jallut,et al.  Generic Dynamic Model for Simulation and Control of Reactive Extrusion , 2004 .

[66]  D. Kalyon,et al.  Development of extrudate distortions in poly(dimethyl siloxane) and its suspensions with rigid particles , 2006 .

[67]  M. Hanna,et al.  Modeling Selected Properties of Extruded Waxy Maize Cross‐Linked Starches with Neural Networks , 2003 .

[68]  Dana Barrasso,et al.  Multi-component population balance modeling of continuous granulation processes: A parametric study and comparison with experimental trends , 2013 .

[69]  Stefan Radl,et al.  A novel design for hot-melt extrusion pelletizers , 2010 .

[70]  D. Kalyon,et al.  An experimental study of distributive mixing in fully intermeshing, co-rotating twin screw extruders , 1989 .

[71]  I. Manas‐Zloczower,et al.  Distributive mixing in conveying elements of a ZSK-53 co-rotating twin screw extruder , 1998 .

[72]  D. J. van Zuilichem.  Extrusion cooking : craft or science? , 1992 .

[73]  Zou Lin,et al.  Optimization of die profile for improving die life in the hot extrusion process , 2003 .

[74]  H. Meijer,et al.  Tools to simulate distributive mixing in twin-screw extruders , 2012 .

[75]  Dilhan M. Kalyon,et al.  Assessment of the Degree of Mixedness of Filled Polymers , 2005 .

[76]  Bruno Vergnes,et al.  A study of residence time distribution in co‐rotating twin‐screw extruders. Part I: Theoretical modeling , 2003 .

[77]  H. D. Ruyck.  Modelling of the residence time distribution in a twin screw extruder , 1997 .

[78]  Bruno Vergnes,et al.  Computer simulation of starchy products' transformation by twin-screw extrusion , 1993 .

[79]  R. Altomare,et al.  An Analysis of Residence Time Distribution Patterns in A Twin Screw Cooking Extruder , 1986, Biotechnology progress.

[80]  G. D. Valle,et al.  A Basic Model for a Twin‐Screw Extruder , 1989 .

[81]  A. Yu,et al.  Microdynamic analysis of particle flow in a horizontal rotating drum , 2003 .

[82]  Wilhelm H. Többen,et al.  Improved Design of Shearing Sections with New Calculation Models Based on 3D Finite‐Element Simulations , 2002 .

[83]  D. Kalyon,et al.  Effects of air entrainment on the rheology of concentrated suspensions during continuous processing , 1991 .

[84]  James J. Feng,et al.  Constitutive modeling and flow simulation of polytetrafluoroethylene (PTFE) paste extrusion , 2006 .

[85]  Gregory R. Ziegler,et al.  Residence time distribution in a co-rotating, twin-screw continuous mixer by the step change method , 2003 .

[86]  P. V. Danckwerts.  Continuous flow systems , 1953 .

[87]  D. Kalyon,et al.  Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process , 2006 .

[88]  Philippe Bogaerts,et al.  Biological reaction modeling using radial basis function networks , 2004, Comput. Chem. Eng..

[89]  K. Narh,et al.  Evaluation of numerical simulation methods in reactive extrusion , 2005 .

[90]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[91]  Dave A. Miller,et al.  Fusion production of solid dispersions containing a heat-sensitive active ingredient by hot melt extrusion and Kinetisol dispersing. , 2010, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[92]  D. Kalyon,et al.  Time-dependent tube flow of compressible suspensions subject to pressure dependent wall slip: Ramifications on development of flow instabilities , 2008 .

[93]  B. H. Ng,et al.  Analysis of particle motion in a paddle mixer using Discrete Element Method (DEM) , 2011 .

[94]  Thomas F. Edgar,et al.  Process Dynamics and Control , 1989 .

[95]  Ecevit Bilgili,et al.  Population balance modeling of non-linear effects in milling processes , 2005 .

[96]  Rohit Ramachandran,et al.  A multi-dimensional population balance model approach to continuous powder mixing processes , 2013 .

[97]  Francis J. Doyle,et al.  Experimental validation studies on a multi-dimensional and multi-scale population balance model of batch granulation , 2009 .

[98]  E. Mitsoulis,et al.  Thixotropic flow of toothpaste through extrusion dies , 2011 .

[99]  L. Delamare,et al.  A global computer software for polymer flows in corotating twin screw extruders , 1998 .

[100]  Runyu Yang,et al.  DEM investigation of energy distribution and particle breakage in tumbling ball mills , 2012 .

[101]  Michael Thompson,et al.  Modelling the solids inflow and solids conveying of single-screw extruders using the discrete element method , 2005 .

[102]  Krist V. Gernaey,et al.  Model-based analysis of a twin-screw wet granulation system for continuous solid dosage manufacturing , 2016, Comput. Chem. Eng..

[103]  Ian T. Cameron,et al.  Process systems modelling and applications in granulation: A review , 2005 .

[104]  Frantisek Stepanek,et al.  A combined experimental and computational study of wet granulation in a Wurster fluid bed granulator , 2009 .

[105]  J. Kokini,et al.  Effect of mixer geometry and operating conditions on mixing efficiency of a non-Newtonian fluid in a twin screw mixer , 2013 .

[106]  R. L. Mallett,et al.  Stress and deformation analysis of the metal extrusion process , 1977 .

[107]  Dave A. Miller,et al.  The use of inorganic salts to improve the dissolution characteristics of tablets containing Soluplus®-based solid dispersions. , 2013, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[108]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry, Expanded Edition , 1987 .

[109]  T. Eerikäinen,et al.  Neural networks in extrusion process identification and control , 1994 .

[110]  Brian Scarlett,et al.  Population balances for particulate processes - a volume approach. , 2002 .

[111]  Dana Barrasso,et al.  A multi-scale, mechanistic model of a wet granulation process using a novel bi-directional PBM–DEM coupling algorithm , 2015 .

[112]  D. Chan,et al.  Dynamic behavior of a single screw plasticating extruder part II: Dynamic modeling , 1986 .

[113]  D. Kalyon,et al.  Electrical properties of composites as affected by the degree of mixedness of the conductive filler in the polymer matrix , 2002 .

[114]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[115]  Dilhan M. Kalyon,et al.  An experimental study of the degree of fill and melt densification in fully-intermeshing, co-rotating twin screw extruders , 1991 .

[116]  David Jones,et al.  Modeling residence time distribution in a twin-screw extruder as a series of ideal steady-state flow reactors , 2008 .

[117]  P. V. Danckwerts.  Continuous flow systems. Distribution of residence times , 1995 .

[118]  James L. White,et al.  Isothermal transient startup of a starved flow modular co-rotating twin screw extruder , 2000 .

[119]  Q. Lu,et al.  Model and strategies for computer control of a twin-screw extruder , 1993 .

[120]  E. Rodriguez.  Numerical Simulations of Reactive Extrusion in Twin Screw Extruders , 2010 .

[121]  B. Evrard,et al.  A review of pharmaceutical extrusion: critical process parameters and scaling-up. , 2015, International journal of pharmaceutics.

[122]  Steven J. Mulvaney,et al.  Modeling and process control of twin-screw cooking food extruders , 1994 .

[123]  L. Janssen,et al.  The modelling of counter-rotating twin screw extruders as reactors for single-component reactions , 1994 .

[124]  O. Levenspiel.  Chemical Reaction Engineering , 1972 .

[125]  Alain Vande Wouwer,et al.  Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB , 2014 .

[126]  D. Laforgia,et al.  Numerical study of the extrusion process in cereals production: Part I. Fluid-dynamic analysis of the extrusion system , 2006 .

[127]  L. Janssen,et al.  A novel model predicting the residence-time distribution during reactive extrusion , 1997 .

[128]  Dilhan M. Kalyon,et al.  Rheology and extrusion of medical‐grade thermoplastic polyurethane , 2003 .

[129]  D. Kalyon,et al.  A hybrid twin screw extrusion/electrospinning method to process nanoparticle-incorporated electrospun nanofibres , 2008, Nanotechnology.

[130]  Three‐dimensional flow modeling of a self‐wiping corotating twin‐screw extruder. Part I: The transporting section , 1996 .

[131]  Hans J. Herrmann,et al.  Modeling granular media on the computer , 1998 .

[132]  G. D. Valle,et al.  Theoretical Computation of the Isothermal Flow Through the Reverse Screw Element of a Twin Screw Extrusion Cooker , 1988 .

[133]  Samir Eddine Choulak.  Modélisation et Commande d'un procédé d'Extrusion Réactive , 2004 .

[134]  Johannes Khinast,et al.  Mechanistic modeling of modular co-rotating twin-screw extruders. , 2014, International journal of pharmaceutics.

[135]  Bruno Vergnes,et al.  Experimental and theoretical study of twin‐screw extrusion of polypropylene , 2000 .

[136]  J. B. Gerrish,et al.  Feedforward control model for a twin-screw food extruder , 1990 .

[137]  Maitraye Sen,et al.  Multiscale modeling and validation of particulate processes , 2015 .

[138]  D. Kalyon,et al.  Wall slip and extrudate distortion of three polymer melts , 2003 .

[139]  D. Kalyon,et al.  Extrusion of poly(ether imide) foams using pressurized CO2: Effects of imposition of supercritical conditions and nanosilica modifiers , 2014 .

[140]  D. Kalyon,et al.  Computational study of chaotic mixing in co‐rotating two‐tipped kneading paddles: Two‐dimensional approach , 1993 .

[141]  Charles E. Martin,et al.  Pharmaceutical Applications of Hot-Melt Extrusion: Part I , 2007, Drug development and industrial pharmacy.

[142]  E. Mitsoulis,et al.  Steady flow simulations of compressible PTFE paste extrusion under severe wall slip , 2009 .

[143]  P. V. Danckwerts.  Continuous flow systems. Distribution of residence times: P. V. Danckwerts, Chem. Engng Sci.2: 1–13, 1953 , 1995 .

[144]  Haiyan Liu,et al.  Application and Research of Fuzzy Control Simulation in Twin Screw Extruder , 2012 .

[145]  W. Johnson,et al.  The mechanics of metal extrusion , 1962 .

[146]  Liuping Wang,et al.  Continuous-time model predictive control of food extruder , 2008 .