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Low consistency refining of mechanical pulp : the relationship between plate pattern, operational variables… Elahimehr, Ali 2014

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  Low Consistency Refining of Mechanical Pulp: The Relationship Between Plate Pattern, Operational Variables and Pulp Properties   by Ali Elahimehr  B.Sc. Mechanical Engineering, University of Tehran, 2005 M.Sc. Aerospace Engineering, Amirkabir University of Technology, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2014 © Ali Elahimehr, 2014  - ii - Abstract In this dissertation we propose a framework to predict pulp properties of mean fibre length and freeness from low consistency (LC) refiner operating conditions and present correlations between those properties of pulp and hand sheet paper properties of tear, tensile and bulk. This framework is not new and was proposed by Luukkonen [1] however, studying the effect of plate pattern in this work based on the methodology presented in this dissertation is a novel approach. We accomplish this objective through the introduction of two geometrical parameters: Bar Interaction Length,    , and Bar Interaction Area,    . To do so, a comprehensive modelling of the geometry of disc refiner plates used in LC refining of mechanical pulp is done. We develop analytical and numerical models to estimate important geometrical parameters such as bar crossing area, leading edges of bar crossings and number of crossing points in a disc refiner with parallel distribution of bars. We will then use these models to predict pulp properties of mean fibre length and freeness from refiner operating conditions by running pilot-scale refining trials of mechanical pulp over a wide range of plate pattern, rotational speed and gap size. From this stage, we present correlations between hand sheet paper properties of tear, tensile, bulk and pulp properties of freeness and fibre length. We also demonstrate a relationship between net power, plate pattern and refiner operating parameters such as plate gap and rotational speed based upon a classical dimensional analysis in which a reduced parameter space is related to each other through the use of statistical modelling.  - iii - Preface In this section, we briefly explain the contents of the journal papers and conference papers that are published from this thesis and clarify the contributions of co-authors in the papers.  Journal Papers  Elahimehr A., Olson J.A., Martinez D.M., “Understanding LC Refining: The Effect of Plate Pattern and Refiner Operation” Nordic Pulp and Paper Research Journal, 28 (3) 2013, pp. 386-391. This paper proposes and presents the results of an experimentally grounded framework to investigate the effect of refiner plate gap, rotational speed and patterns of disc refiner plates on performance and energy consumption of LC refining. We propose a non-dimensional power-gap relationship to determine the specific energy and refiner plate gap through the introduction of a new geometrical parameter, i.e. Bar Interaction Length. Chapter 6 includes the contents of this publication. The author of the thesis is the principal contributor to this publication. Professor James Olson assisted with writing the paper and designing refining experiments. Professor Mark Martinez assisted with developing the geometrical indicator of Bar Interaction Length.    Elahimehr A., Olson J.A., Martinez D.M., and Heymer J., “Estimating the Area and Number of Bar Crossings between Refiner Plates” Nordic Pulp and Paper Research Journal, 27 (5) 2012, pp. 836-843. In this publication, we present results of a computational analysis of the geometry of refiner plates used in LC refining with parallel distribution of bars on rotor and stator plates. Chapter 5 includes the contents of this publication. The author of this thesis was the principal contributor of this publication. Professor Mark Martinez assisted with code development, and Professor James Olson supervised the research. Dr. Jens Heymer helped with the analysis of results.  - iv - Contributions to Refereed Conference Proceedings   Elahimehr A., Martinez D.M., Olson J.A., “Understanding LC Refining: The Effect of Plate Pattern and Refiner Operation” Proceeding of International Paper Physics Conference, 2012, pp 82-87. This publication has mostly focused at understanding the role of plate pattern, rotational speed and gap size in power consumption of LC refining. Chapter 6 includes the contents of this publication. The author of this dissertation was the principal contributor to this publication by planning refining trials, running experiments and analyzing data collected. The writing of this paper was conducted by Professor James Olson. Professor Mark Martinez and Professor James Olson supervised the research.   Elahimehr A., Olson J.A., Martinez D.M. “On the Characterization of the Geometry of Low Consistency Refiner Plates” Proceedings of 7th International Seminar on Fundamental Mechanical Pulp Research IFMPRS, 2010, pp. 82-90. In this publication, a basic computational code has been developed to study the change in bar interaction area of a disc refiner with a single bar. Development of computational code and the writing of the publication were performed by the author of this thesis. Chapter 5 includes a part of the contents of this publication. Professor James Olson and Professor Mark Martinez supervised the research.      - v - Table of Contents Abstract ........................................................................................................................ ii Preface ......................................................................................................................... iii Table of Contents ........................................................................................................ v List of Tables ............................................................................................................. vii List of Figures ........................................................................................................... viii Nomenclature ........................................................................................................... xiii Acknowledgements .................................................................................................. xvi Dedication ............................................................................................................... xviii Chapter 1. Introduction ......................................................................................... 1 1.1. Change in Fibre Morphology ........................................................................ 1 1.2. Types of Refiner ........................................................................................... 2 1.3. Thermo Mechanical Pulping (TMP) ............................................................. 3 1.4. LC Refiner Plates .......................................................................................... 5 1.5. Bar Edge Length (BEL) ................................................................................ 6 1.6. No-Load Power ............................................................................................. 9 1.7. Pulp and Paper Properties ........................................................................... 10 Chapter 2. Literature Review ............................................................................. 14 2.1. Specific Edge Load Theory ........................................................................ 18 2.2. Specific Surface Load Theory .................................................................... 19 2.3. Number and Intensity of Impacts Theory ................................................... 20 2.4. C-factor Theory ........................................................................................... 21 2.5. Fibrage Theory ............................................................................................ 22 2.6. Summary of Literature ................................................................................ 22 Chapter 3. Research Objectives and Proposed Framework ............................ 24 Chapter 4. Modelling of the Geometry of Intersection Formed Between Refiner Plates: Analytical Approach ...................................................................... 26 4.1. The Mosaic Problem ................................................................................... 27 4.2. Estimating the Average of the Area of Bar Crossing, Length of Bar Crossing Edges and Number of Crossing Points in a Disc Refiner ........................ 29  - vi - 4.3. Summary ..................................................................................................... 34 Chapter 5. Modelling of the Geometry of Intersection Formed Between Refiner Plates: Numerical Approach ...................................................................... 35 5.1. The Toy Problem ........................................................................................ 35 5.2. Characterizing the Intersecting Pattern of Refiner Plates ........................... 39 5.3. Comparison of Analytical Solution with Computational Results ............... 48 5.4. Discussion ................................................................................................... 50 5.5. Summary ..................................................................................................... 52 Chapter 6. Pilot Scale Refining Trials of Mechanical Pulp.............................. 54 6.1. The Experimental Set up ............................................................................. 55 6.2. Power-Gap Relationship ............................................................................. 57 6.3. Bar Interaction Length (BIL) ...................................................................... 65 6.4. Relationship between Operational Variables, Plate Design and Pulp Properties ................................................................................................................ 68 6.5. Predicting Bulk and Tear Index from Pulp Properties ................................ 71 6.6. Development of Tensile Index .................................................................... 74 6.7. Summary ..................................................................................................... 83 Chapter 7. Summary and Conclusions .............................................................. 84 Chapter 8. Recommendations for Future Work ............................................... 86 References………………………………………………………………………..… 87 Appendix A. Two Intersecting Circles .............................................................. 93 Appendix B. Refiner Plate Simulator (RPS) ..................................................... 94 Appendix C. Table of Experimental Data ......................................................... 95  - vii - List of Tables Table ‎2-1. Different energy-based methods characterizing refining action . ............................... 23 Table ‎5-1. 8 cases studied in Figure 5-6 with various bar width, groove width and bar angle . ............................................................................................................................................ 41 Table ‎6-1. Operating conditions for the pilot-scale refining trials of mechanical pulp . .............. 55 Table ‎6-2. Specification of the four refiner plates used in the experiments (Note:    is the inside diameter and    is the outside diameter of the plate pattern,    is the groove depth and   is the bar angle)  . ......................................................................................... 56 Table ‎C-1. Pilot scale refining trial results for plate number 3 in Table 6-2 . .............................. 95 Table C-2. Pilot scale refining trial results for plate number 4 in Table 6-2 . .............................. 97 Table C-3. Pilot scale refining trial results for plate number 2 in Table 6-2 . .............................. 99 Table ‎C-4. Pilot scale refining trial results for plate number 1 in Table 6-2 . ............................ 101                            - viii -  List of Figures Figure 1-1: A schematic configuration of a single disc refiner with corrugated patterns of bars on rotor and stator discs obtained from [4]. ........................................ 2  Figure 1-2: (a) A low consistency refiner plate with parallel distribution of bars in 24 repeating segments or clusters. (b) A segment of a spiral plate having the advantage of constant intersecting angle between opposing bars. ................................................. 6  Figure ‎4-1: A schematic of one refiner plate is shown in this figure. The left image is a schematic of the entire plate which is composed of (in this case) 24 repeating segments or clusters. The image on the top right is a schematic of one cluster. Here   and    represent the inner and outer radii of the working surfaces of the refiner;   is the cluster angle; and   is the bar angle measured relative to the radius. The image on the bottom right shows the cross-section of the machined pattern on the surface of the plate.   and   represent the bar and groove widths, respectively. ....................... 28  Figure 4-‎7KH‎³0RVDLF´‎SUREOHP‎FURVVLQJ‎RI‎‎URWRU‎Ears on 2 stator bars creates 4 number of crossing points. Here,     is the area of intersection between one rotor bar-groove and one stator bar-groove representing 1 number of crossing point between bars. ............................................................................................................................. 28  Figure 4-3: Configurations of a stator segment with bar angle of   and cluster angle of  . The stator segment intersects with 1 rotor bar and creates 4 number of bar crossings. ..................................................................................................................... 30  Figure 5-1:  (a) The geometry of two intersecting squares    and    contained in a larger rectangle  .    and   are squares with an edge length of    and   and are centered at       and      , respectively. (b) An image of each polygon in (a) is defined through use of Equation (48). This image is created by summing all the functions at each grid point. ........................................................................................ 37  Figure 5-2: The relative error in the estimate of the intersecting area        using   equally spaced nodes in    and   directions respectively. The exact value of the area of intersection was determined using an analytical solution. .............................. 38  Figure 5-3: (a) A representative image of a stator SODWH‎ZLWK‎WKH‎FOXVWHU‎DQJOH‎RI‎ȕ‎The value of 1 represents the surface of the bars. (b) A representative image of the rotor LQ‎ZKLFK‎WKH‎DQJXODU‎YHORFLW\‎RI‎WKH‎SODWH‎Ȧ‎PHDVXUHG‎UHODWLYH‎WR‎WKH‎KRUL]RQWal is defined. Here,   represents time. (c) The summation of the images given in (a) and (b). ............................................................................................................................... 40   - ix - Figure 5-4: A schematic of the complex intersection pattern created when the rotor passes over the stator plate. Four images are given at different times: (a)             ; (b)           ; (c)            ; and, (d)         . ....................... 40  Figure 5-5: An estimate of the sensitivity of the area   as a function of number of grid points  , in the   and   directions. For this simulation          ,          ,         ,          ,           , and             . ........ 41  Figure 5-6: The variation of area  , as a function of rotational position for a number of different plate configurations. In (a) the bar angle   is held constant at a value of      In (b) the value of   is set to      For all the configurations shown,  ,    and    are equal to               and         respectively. The roman numeral in these figures refer to various bar and groove widths and are defined in Table 1. The average value as well as the standard deviation of all 8 cases is summarized in Table 5-1. .............................................................................................................................. 43  Figure 5-7: The relationship between the normalized average value of instantaneous area of bar crossings and its standard deviation with the cluster angle of       . The results shown are for the cases with        . .............................................. 44  Figure 5-8: The probability distribution of the area of bar crossings for 2 different plate configurations (i.e. (i) and (iii)) reported in the Table 1. In (a),          ,          ,       ,        and            . In (b),          ,          ,       ,        and            . ................................... 46  Figure 5-9: (a) The relationship between    and the dimensionless group     ⁄  For clarity, this relationship is shown at two different bar angles   and two different cluster angles  . The results shown are for the cases with         ,            , and             . The roman numeral in this figure refers to various bar and cluster angles and are: (i):         and       (ii):         and       , (iii):           and      , (iv):          and        , In (b), we display the goodness of the fit between the numerical results (abscissa) and the predictions using Equation (50). ........................................................................... 47  Figure 5-10: The relationship between the dimensionless perimeter    and area    for all cases simulated.    represents the ratio of the sum of the perimeters to the total length of the edges of the bars. ................................................................................... 48  Figure 5-11: (a) Comparison between total perimeter of bar crossings [ ] estimated with our computational simulations (     ) and those reported analytically through the use of Equation (35) (      ) for 320 different low consistency refiner plates. (b) The comparison between our analytical solution for the average number of bar crossings; Equation (45) with our computational results obtained in Chapter 5. ....... 49   - x - Figure 5-12: (a) The distribution of the total number of bar crossings,           , as a function of rotational position. Here,        ,          ,              and              (b) The relationship between    and the dimensionless group          This relationship is shown at cluster angle         ,             and        . The different marks in this figure refer to various bar angles and are:          ż,        Ÿ,         ¸ and          Ƒ. Different slopes in the graph refer to: (i)          , (ii)          , (iii)         and (iv)            In total, 80 cases have been studied. ............... 51  Figure 5-13: (a) The relationship between the sum of the perimeters   and the     defined using Equation (3). (b) The relationship between    and the    . This relationship is shown at cluster angle         ,             and        . .................................................................................................................................... 52  Figure 6-1: Illustration of the UBC pilot LC refiner used for these trials. ................. 57  Figure 6-2:  Total power versus gap for 3 rotational speeds of        ,          and          for both water and pulp. The plate number 3 with                 has been used in both trials. ............................................................... 58  Figure 6-3: Net power plotted against the inverse of gap for 3 refiner speeds using plate 3 (               ). .................................................................................... 60  Figure 6-4: Mean length weighted fibre length for various plate gaps for plate number 3 (               ).  The critical gap for fibre length reduction is near 0.25 mm and increases slightly with increasing    . ............................................................. 61  Figure 6-5: Power over angular velocity cubed versus inverse of gap for 4 plates used in these trials showing that over industrial ranges of gap sizes power is approximately proportional to ω3 and the inverse of gap for: (a) plate number 3 with                , (b): plate number 4 with                , (c): plate number 2 with                 and (d) plate number 1 with                . .. 63  Figure 6-6: Dimensionless power and gap for 4 plates (plate 1, 2, 3 and 4 corresponding to     of 5.59, 2.74, 0.99 and 2.01       ) for three angular velocities of 800, 1000 and 1200     in the industrial range (Gap > 0.2 mm)........ 64  Figure ‎6-7: The front view of the leading edge of rotor bar approaching the leading edge of stator bar capturing a fibre in an edge called Bar Interaction Length (left). The figure on the right shows the top view of a rotor bar over a stator segment with 5 bars creating an interaction length for fibres/bars. At the local position shown, 4 number of bar crossing events (            ) are created. ..................................... 66  Figure ‎6-8: Correlation between the predicted power number from Equation (56) and the measured power number from the trials for 3 plates (plate 1, 2 and 4  - xi - corresponding to     of 5.59, 2.74 and 2.01       ) for three angular velocities of 800, 1000 and 1200     in the industrial range (Gap > 0.2 mm). ........................... 67  Figure ‎6-9: Canadian Standard Freeness plotted versus specific refining energy for all samples taken. ............................................................................................................. 68  Figure ‎6-10: Prediction of length weighted fibre length from different intensity equations: (a) Specific Edge Load (SEL), (b) Modified Edge Load (MEL), (c) Tangential force per bar crossing and (d) net energy per leading edges of bar crossings. ..................................................................................................................... 70  Figure 6-11: (a) Correlation between bulk and freeness. (b) Correlation between bulk and specific refining energy. ....................................................................................... 73  Figure 6-12: Correlation between tear index and average fibre length. ..................... 74  Figure ‎6-13: Tensile index increase plotted versus specific refining energy for plate number 3 with                 at 3 rotational speeds of        ,          and         . ...................................................................................... 75  Figure ‎6-14: Tensile index increase plotted versus: (a) specific refining energy over rotational speed, (b) intensity of refining defined by SEL. This figure is shown for plate number 3 at 3 different rotational speeds of        ,          and         . ................................................................................................................. 77  Figure ‎6-15: Tensile index plotted versus specific refining energy at 3 different intensities taken from [51]. In these refining trials, the pulp was refined through multiple passes of refining at a constant intensity. ..................................................... 78  Figure ‎6-16: Tensile index increase per unit specific refining energy as a function of intensity for plate number 3 at 3 different rotational speeds of        ,          and         . .......................................................................................................... 79  Figure ‎6-17: (a) Tensile index increase per unit specific refining energy as a function of intensity for 3 plates (plates 1, 2 and 3 in Table 6-2) and a wide range operating conditions. In (b), we achieve a performance curve for multiple plates of case (a) by plotting tensile index increase per unit specific refining energy as a function of net energy per unit of bar interaction area ........................................................................ 79  Figure ‎6-18: Bulk versus tensile index increase for a wide range of operating conditions. Results plotted for 3 plates (plates 1, 2 and 3 in Table 6-2) with              ,               and                 at 3 rotational speeds of        ,          and         . ............................................................... 82   - xii - Figure ‎6-19: Light scattering coefficient of a handsheet as a function of tensile index at 3 different rotational speeds of        ,          and          for plate number 2 in Table 6-2. ................................................................................................ 82  - xiii - Nomenclature Symbols                 Instantaneous area of bar crossings,                     Normalized average value of instantaneous area of bar crossings                  Area of a single bar/groove crossing,                   Total working surface,                  Bar width,                    Bar edge length,       ⁄                  Bar edge length of rotor,       ⁄                  Bar edge length of stator,       ⁄                   Bar interaction area,                         Bar interaction length,      ⁄                     Consistency,                     C-factor                  Canadian Standard Freeness,                    Inner diameter,                    Outer diameter,                   Groove width,                     Plate gap clearance,                    Critical gap size,                    Groove depth,                   Refining intensity,                      Fibre length,                   Average bar length,                         Length of refining impacts,                   Effective edge length per revolution,                         Length weighted average fibre length,                   Number of grid points in x and y direction   ̇               Mass flow rate of fibre into the refiner,          - xiv -  ̅               Average mass of fibre,                    Rotation frequency,                         Bar density,                      Average value of instantaneous number of crossing points                   Number of bar crossings (analytically driven)                Instantaneous number of crossing points                  Number of impacts per unit mass of fibre,                      Number of refining impacts,                        Number of impacts experienced by a fibre                 Number of bars on the rotor                 Number of bars on the stator                Total perimeter of bar crossings,                  Normalized average value of instantaneous perimeter of bar crossings                 Probability of a fibre impact by bars                   Net refining power applied to fibres,                   No-load power in refining,                 Total power applied by refiner,                    Radius of disc refiner,                    Inner radius,                    Outer radius,                     Specific Edge Load,                       Specific Refining Energy,                           Specific Surface Load,                           Time,                   Coarseness of fibre,                        Length of bars on rotor,                   Length of bars on stator,        - xv - Greek     Bar angle, o    Cluster angle, o    Average intersecting angle, o    Average bar angle, o    Residence time, s    Density of water,            Rotational speed, rpm            Angle between the rotor bar and radius            Angle between the stator bar and radius    - xvi - Acknowledgements I would like to convey my gratitude to all people who gave me the possibility to complete this dissertation.  Firstly, I would like to express my sincere gratitude to my supervisors, Professor James Olson and Professor Mark Martinez for the continuous support of my PhD study, for their patience, enthusiasm and friendly help in various ways.   This work was funded by the Natural Sciences and Engineering Research Council of Canada through the Collaborative Research and Development program and through the support of our partners West Fraser Quesnel River Pulp, BC Hydro, FP Innovations, Catalyst Papers, Howe Sound Pulp and Paper, Canfor, Andritz, Arkema, Honeywell, WestCan Engineering, Advanced Fiber Technologies, Ontario Power Authority and CEATI international. I am deeply grateful to Professor Richard Kerekes for his advice and guidance from the early stage of this research.  I would like to thank the Pulp and Paper Center staff specifically Mr. George Soong and Mrs. Nici Darychuk for assisting me with performing the experiments. The experimental part of the work would not have accomplished without your help. I gratefully acknowledge the help of work-study students in the process of running refining trials, sampling and hand sheet making/testing Mr. Zaid Aljawadi, Mr. Ian Wong, Ms. Christine Saville and Ms. Kimberly Chin.  I am so thankful to my best friends Mr. Amir Saffari, Mr. Arash Saghafi and Mr. Milad Madinei for their support and encouragement throughout this entire journey. It was an honor to work beside my good friends in the Pulp and Paper Center of UBC Dr. Ali Vakil, Dr. Ario Madani, Dr. Eranda Harinath, Mr. Hamed Ghasvari, Dr. Nina Rajabi Nasab, Mr. Ata Sina, Mr. Ehsan Zaman, Mr. Jiyang Gao, Mr. Francisco Fernandez and Mr. Pouyan Jahangiri.  Finally, I would like to express my heartiest gratitude to my wonderful parents, Hosseinali and Ezzat whom this dissertation is dedicated to, my sister, Dr. Nasrin Elahimehr, and my brother, Dr. Reza Elahimehr for their continuous encouragement,  - xvii - support, and love during my education. I have always felt them beside me in Canada, even though they are living far away.                                        - xviii - Dedication  To my role-model, my wonderful father who worked hard, learned passionately, and loved unconditionally. He stood by me and supported me through my entire life with his guidance and encouragement.    To the angel of my life, my mother who took care of me and made me the man I am today. I am forever thankful for having you in my life.  To Nicole, I love you dearly.                  - 1 - Chapter 1. Introduction The purpose of this Chapter is to briefly introduce some of the commonly used terms LQ‎ WKLV‎ GLVVHUWDWLRQ‎ VXFK‎ DV‎ ³%DU‎ (GJH‎ /HQJWK´‎ ³1R-/RDG‎ 3RZHU´‎ ³)UHHQHVV´‎³%XON´‎DQG‎³7HQVLOH‎,QGH[´‎WKHVH‎WHUPV‎DUH‎H[WHQVLYHO\‎XVHG‎LQ‎LQGXVWU\‎WRGD\‎ We start by introducing how refining changes morphological properties of fibres and familiarizing the reader with the process of thermo mechanical pulping.  1.1. Change in Fibre Morphology This work will concentrate on the mechanical pulping process. During mechanical pulping the fibres are separated primarily by mechanical forces. Here wood chips are comminuted to pulp through several stages of treatment in devices termed refiners.  Refiners are mechanical devices employed to modify the morphology of papermaking fibre. They are rotary devices having bar patterns machined onto a rotor and a stator, see Figure 1-1. The rotor and stator plates are disc or conical in shape and are separated by a gap of about     to      . These plates rotate relative to one another and the consequent bar crossings create the mechanical action of refining. Refining results in multiple complex changes in fibre morphology. These changes in turn make multiple complex changes in paper quality and performance.  A simple description of the fibre morphological changes is that refining increases fibre flexibility and the degree of lumen collapse which allows the fibres to form denser sheets, increasing the relative bonded area available between fibres. Further, refining increases bond strength by increasing the exposed cellulose through fibrillation of the fibre surface.  These morphological changes increase paper strength and smoothness while decreasing porosity and bulk. Papermaking fibres flow in the grooves of the plate and are trapped between leading edges of opposing bars by reaction forces from the applied compression in WKH‎QDUURZ‎JDS‎EHWZHHQ‎WKH‎URWRU‎DQG‎VWDWRU‎7KH‎ILEUHV‎DUH‎³EHDWHQ´‎RU‎³UHILQHG´‎E\‎repeated impacts between the bars. Through repeated impacts of the crossing bars the wall of the fibres starts to break down. The outer part of the wall becomes fibrillated  - 2 - as layers of microfibrils are peeled away, significantly increasing the surface area of the fibres. The inner wall becomes delaminated which increases the conformability of the fibres. The increased surface area and conformability increases the bond area and strength when forming paper, making a higher tensile strength product.  The morphology and paper property changes are comprehensively reviewed by Page [2] and Ebeling [3].   Figure 1-1: A schematic configuration of a single disc refiner with corrugated patterns of bars on rotor and stator discs. Figure obtained from ref. 4.   1.2. Types of Refiner There are typically two different types of refiners used in the manufacture of high quality pulp in mechanical pulping process; conical refiners and disc refiners.   Conical refiners: This refiner is known to cause fibre cutting. However when plates with narrow bars are used, they provide a high level of fibre development for all kinds of fibres.  - 3 - The problem with this type of refiner is its low capacity and the change of plates which is relatively difficult.   Disc refiners: This type of refiners can be divided into three groups; single disc, double disc and twin disc.  1. Single disc: This refiner is one of the first types of refiners employed in mechanical pulping which is still used in new installations. Lowest capital cost and smaller capacities are known as characteristics of this type of disc refiner.  2. Double disc: This refiner is designed for high intensity refining. It requires less energy to obtain the same freeness.  3. Twin disc: This refiner is used for low intensity and high capacity refining because of its larger refining surface, however there are some operational problems associated with this type.  1.3. Thermo Mechanical Pulping (TMP) Much effort has been spent over the years to reduce electrical energy consumption in mechanical pulping. A major early solution for this was the use of high temperature to soften the lignin by generating steam in the process. This process is known today as Thermo Mechanical Pulping (TMP). The TMP process contains a number of different refining treatments. The type of this treatment is usually categorized by the concentration of the feed suspension. The industrial term used to define this FRQFHQWUDWLRQ‎LV‎³FRQVLVWHQF\´‎DQG‎LV‎GHILQHG‎DV‎WKH‎UDWLR‎RI‎PDss of fibres to the mass of suspension. Low consistency (LC) refining of pulp at    to    consistency followed after a primary and a secondary stage of high consistency (HC) refining, typically at     to     straightens fibres, decreases bulk and increases tensile strength of end use paper. Pressurized steam is applied before and during refining to  - 4 - increase the wood chips temperature and soften the lignin. Chips are preheated and refined in pressurized refiners in a primary stage and a second stage.  Energy consumption in TMP mills is still considerable due to the required energy to remove lignin and make suitable papermaking fibres.  $‎W\SLFDO‎WKHUPR‎PHFKDQLFDO‎SXOSLQJ‎SURFHVV‎DOVR‎FRQWDLQV‎D‎³ODWHQF\‎UHPRYDO´‎stage. Latency is a high curl developed in fibres during refining which is removed to some extent upon cooling after refining. The curl in fibre reduces the length of it, stiffens the fibre and diminishes its ability to make strong paper. This curl is removed LQ‎D‎³ODWHQF\‎FKHVW´‎LQ‎ZKLFK‎WKH‎SXOS‎LV‎Keated at low consistency in a stirred tank at elevated temperature making the fibres to untangle and straighten out to a large degree.  The mechanical pulping process is extremely electrical energy intensive. The refiners are powered by 10-30 MW motors and consume approximately 80% of the total energy in the mechanical pulping process. Mechanical pulp refiners in the province of British Columbia consume more than 8‎RI‎WKH‎%C‎+\GUR¶V‎FXUUHQW‎electrical energy production. Also, the experimental work done by Ottestam and Salmen [5] showed the efficiency of pulping to be about 10-15% in mechanical pulping based on fracture mechanics energy. With globally increasing energy costs, the survival of the mechanical pulping industry depends on the ability of mills to reduce energy consumption in mechanical refiners by improving the efficiency of refining. One method of reducing mechanical pulping energy is to diminish the number of refining treatments at high consistency (HC) and supplement the treatments at lower consistency. Low consistency (LC) refining has been shown to be a more energy efficient means of improving pulp quality. The precise reason for the higher efficiency of LC treatment in comparison to HC refining is still unclear. One of the most likely reasons may be the uniformity of treatment. At high consistency, the papermaking suspension resembles that of a paste. At this consistency, steam is formed due to frictional heating and this creates a very complicated heterogeneous three-phase system of wood fibres, water and steam in the refiner. Details of this are given in [6], [7], [8], [9] and [10]. At low consistencies, the suspension behaves as a  - 5 - single phase non-Newtonian fluid which may be pumped through the refiner using an external pump. Although more energy efficient, optimal operating conditions in LC refining are still unknown. LC refiners have the potential to cut the papermaking fibre. This is a deleterious effect damaging strength properties of paper. One solution to this is the use of proper design for the geometry of plates used in LC refining.  1.4. LC Refiner Plates Refiner plates are the governing components when paper quality and process is concerned. Various designs of LC refiner plates can be found in modern pulp and paper processes and each plate has its own characteristics. Small size refiner plates are typically made of one solid piece while in bigger size refiners, plates are manufactured from several segments or clusters. In both cases, the pattern of bars and grooves is repeating at each segment. Most typical LC refiner plates are manufactured by casting. The basic design parameters are bar width, groove width, groove depth, bar angle and plate diameter. These form the pattern of refiner plates.  Since the fibres have different physical dimensions, the bar width that should be used for LC refining of softwood pulp is different than the one that should be used for hardwoods. Long and strong softwood fibres require wider bars and wider grooves than do shorter and weaker hardwood fibres. Typically a bar width of     to       is recommended for softwoods while for hardwoods this width should be between    to    .  Initially, plates with straight bars, i.e. radial bars with no bar angle, were used for both stator and rotor plates but these plates were noisy and had a high level of fibre cut. Then, inclined bars with a bar angle of   to    were used to make less noise and allow refiners to run both in pumping and opposite to pumping direction. The importance of bar angle has been discussed in a few works. Vomhoff [11] studied the influence of bar angle on the refining process in a disc refiner. He tried to simulate the passing of rotor over the stator to determine the total intersecting area, number of bar crossings and total length of cutting edges. Siewert and Selder [12] found that  - 6 - refining pulp under the same specific refining energy but with different bar angles result in different freeness drops. Brecht et al. [13] shows that to achieve certain freeness drop, refining time was shorter and consequently the energy consumption was lower for smaller bar angles. Refiner plates with spiral pattern of bars and grooves provide a constant intersecting angle between rotor and stator bars resulting in a more uniform treatment in LC refining. Figure 1-2 shows two common industrially used patterns of plates in LC refining of mechanical pulp: a plate with parallel bars and a plate with spiral pattern. In this dissertation, we study refiner plates with similar parallel distribution of bars for both stator and rotor plates; however the results can be extended for other patterns as well.  Bar edges must have a good resistance to wear and corrosion so they can maintain their shape and not get deformed. The flat bar surface must not get polished and slippery. Deformation of bars results in increased energy consumption and less development in fibre morphology.   Figure 1-2: (a) A low consistency refiner plate with parallel distribution of bars in 24 repeating segments or clusters. (b) A segment of a spiral plate having the advantage of constant intersecting angle between opposing bars.   1.5. Bar Edge Length (BEL) Plate patterns are conventionally characterized by the total length of bar edges swept by bar crossing during a single rotation of the disc. This term is related to the  - 7 - intensity of refiner plate to provide a measure of the severity of refining. Definition of intensity incorporates both the operation of the refiner in terms of the power, rotational speed and the pattern RI‎WKH‎UHILQHU‎SODWH‎FKDUDFWHUL]HG‎E\‎WKH‎WHUP‎³Bar (GJH‎/HQJWK´‎   ).     is a standard measure in industry and is determined using TAPPI standard TIP [14]:      ∫                          (Eq. 1)  In which       and       are the number of bars on the rotor and stator plate at a given radius,  ,    and    are the inner and outer radii of the disc plate and   is the average bar angle measured at the mid bar of the segment. To calculate this integral, we need to approximate number of rotor and stator bars at each radial increment from geometrical parameters of bar width,  , and groove width,  . To do so, the number of bars on each radial increment can be estimated crudely by setting:                     (Eq. 2)  With this, Equation (1) can be integrated directly to give:                 (             ) (Eq. 3)  If the refiner has rotor and stator plates with different patterns,     should be calculated separately for rotor plate and stator plate and the resultant bar edge length would be as follows:      √          (Eq. 4)      is a modified form of the equation popularized by Brecht [15]. He proposed that the intensity of refining was related to the pattern of opposing bars and characterized the bar pattern as the effective edge length per revolution,         ⁄  , using the equation:  - 8 -           (Eq. 5)  And defined the intensity of impact as:             (Eq. 6)  Where    is the number of rotor bars,    is the number of stator bars,   is the average bar length per revolution        ,   is rotation frequency (rad/s) and      is the net refining power applied to fibres by the refiner (kW). The intensity of treatment was later related to the plate pattern by replacing    with     defined in Equation (3).              (Eq. 7)  Other researchers advanced different functional forms between plate pattern and the intensity of refining. Danforth [16] as an example considered   as:           (Eq. 8)  Where    and    are the length of bars on rotor and stator respectively. These definitions provide an estimate for   as machine intensity. However under the same energy distribution among bar crossings in a refiner, the energy expenditure on fibres per bar crossing impact varies for different fibres with different characteristics. Kerekes [17] suggested a fibre-based intensity that takes into account the probability of fibre impact at a bar crossing event and relates the intensity of refining that fibres experience to plate pattern as:                      (Eq. 9)  These equations have proved useful in practice, but have differences in relating the intensity of refining to the geometry of refiner plates.    - 9 - In addition to this debate, there are some authors, i.e. Kline [18], who suggest characterization of refiner plates based on the area of refining and relating   to the effective refining area rather than the length of the bar edges. Clearly, there is very little agreement on the impression of plate on the intensity of refining. To address this situation, Roux and his co-workers [19] recently proposed a new concept for assessing the intensity of refining by using a physical analogy between a slice of a beater and an annulus of a disc. They demonstrate a relationship between changes in pulp properties, such as fibre length and freeness, to intensity defined as:                            (  )                 (Eq. 10)  In this equation   is the bar angle and   is the cluster angle (The angle between two adjacent segments). In their work, they neglect the temporal variation of quantities such as bar angle and use average quantities in the first order as representative values. This estimate is quite reasonable to predict fibre length reduction and °SR evolution on fibres. Beyond this work, the deviations from the average of the local variables have not been estimated numerically. Our understanding of the role of plate pattern in LC refining is very minimal; it is from this point that this dissertation is motivated. An extensive analysis of the geometry of LC disc refiner plates with similar parallel distribution of bar on rotor and stator is presented in Chapters 4 and 5 of this dissertation.  1.6. No-Load Power No load power is defined as the energy per unit of time used by the refiner for purposes other than changing morphological properties of fibre. This energy has been reported to be        of total refiner motor energy and is a result of losses due to mechanical friction in the bearings, hydraulic losses through turbulences and pumping losses due to the fibre suspension flow.   - 10 -  There is no widely accepted protocol or standard to measure no-load power. In this dissertation the following definition for no-load power is used: No-load power is the energy required per unit of time to operate the refiner at its desired speed, consistency and flow rate at a gap size such that there is no change in morphology of fibre. In mechanical pulping, the energy requirement to operate refining under these conditions is the same as energy required to operate refining without the existence of fibres. With this, we can now determine the key variable for controlling the changes in fibre morphology, Specific Refining Energy (   ), defined as the ratio of the net power to the mass flow rate of fibres.                       ̇      ̇ (Eq. 11)  Where        is the total power applied to the refiner,          is the no-load refiner power and ̇  is the mass flow rate of fibre into the refiner.  1.7. Pulp and Paper Properties We refer to some pulp and paper properties throughout this dissertation in different sections that we report our results. These properties are freeness, fibre length, bulk, tear index and tensile index which we attempt to describe the industrial standard test methods and define each parameter below.  1. Freeness is the most important quality control test in the stock preparation area of the paper mill. It is not only a measure of the drainage of the pulp, but also an indicator of fine content, degree of refining and specific surface of fibres. Refining decreases pulp freeness by generating fines. This in turn, increases the specific surface of fibres which results in an increase in relative bonded area available between fibres to make a stronger sheet. Different standard measures of pulp drainage include: Canadian Standard Freeness, Schopper-Rieglor and William Slowness. In this dissertation, we measure this property based on Canadian Standard Freeness (   ) [ml] which is a measure  - 11 - of the volume of water collected from a pulp and drained from one exit nozzle in a specialized dewatering cell. Higher     implies a pulp which is easier to drain.  2. Fibre Length [mm] is one of the most frequently used parameters in this dissertation. There are various automated methods to measure frequency distribution of fibre lengths. These automated methods are able to report the average value of fibre length distribution. The average fibre length for softwood fibres is       and       for hardwood fibres before refining. In this work, we report the average value of fibre length according to the length weighted average fibre length:     ∑     ∑     (Eq. 12)  In which    is the number of fibres with the length   . 3. Bulk [cm3/g] indicates the inverse of sheet density calculated from the thickness and basis weight of hand sheets. Higher bulk is desired for absorbent papers. 4. Tear Index [mNm2/g] is an index indicating the strength of a paper in tear. Tear is the mean force required to continue the tearing of paper from an initial cut under standardized conditions. Tear index is measured by dividing tear strength [mN] of paper sheet by its basis weight [g/m2]. 5. Tensile Index [Nm/g] is an index indicating the strength of a paper to break when pulled at opposite ends. It is measured by dividing the tensile strength per unit width [N/m] of a paper sheet to its basis weight [g/m2]. The tensile index is a measure of the ultimate strength of a paper.  6. Opacity [%] is the measure of how much light is kept away from passing through a sheet. A perfectly opaque paper is the one that is absolutely impervious to the passage of all visible light. It is the ratio of diffused reflectance and the reflectance of single sheet backed by a black body. Opacity is important in printing papers, book papers, etc. The opacity of paper is influenced by thickness, amount of filler and degree of bleaching.  - 12 -  In this dissertation, a novel framework to analyze the relationship between low consistency refining operating variables, plate design and final pulp and paper properties is described in different Chapters of this thesis. Since the pattern of low consistency refiner plates is the key in characterizing LC refining of mechanical pulp, we start presenting our findings by characterizing the geometry of refiner plates.  In Chapter 2, we present a brief overview of the literature with the focus of characterizing refining action and the role of plate pattern into this characterization.  Chapter 3 explains the objectives of this dissertation and the framework suggested to achieve these objectives.  In Chapter 4, we model the geometry of disc refiner plates with parallel distribution of bars and present analytical equations to estimate the average values for number of bar crossing points, bar crossing area and length of bar crossing edges.  In Chapter 5, a novel computational method to determine time-dependant variations of bar crossing area, number of crossing points, and length of bar crossing edges between two refiner discs is introduced. We determine the time-dependent variations for approximately 320 different low consistency refiner plates and empirically propose equations to estimate important geometrical quantities. In this Chapter, findings form our numerical results have been compared with the analytical solutions of Chapter 4.   In Chapter 6, we analyze pilot scale refining trials of mechanical pulp to investigate relationships between refining operating variables, plate design and final pulp and paper properties of refining. In the first part, we relate operating conditions of refining such as rotational speed, gap size and plate design to changes in fibre length and freeness. We approach this problem by proper characterization of the geometry of refiner plates used in these experiments based on our findings in Chapters 4 and 5.  - 13 - The relationship between power consumption and operating conditions has also been studied. In the second part, we build correlations between pulp properties of freeness and fibre length and end use paper properties of bulk, tear index, opacity and tensile index from experimental data collected.    - 14 - Chapter 2. Literature Review The actual energy transfer mechanism into the fibres inside the refiner and how this mechanism is affected by the geometry of plate and refining operating variables is still unknown. Various hypotheses and theories have been proposed to describe the mechanism by which fibres interact with refiner bars. In this Chapter, we present an overview to the various attempts to develop a refining theory which can be used to quantify refining action for the purpose of comparing one refiner to another. This is a desirable object. Although the LC refining literature is vast, the focus of the present dissertation is to investigate the role of plate pattern and refining operating variables in the behaviour of mechanical pulp in LC refining. It should be stated that most of the refining theories have been developed for chemical pulp LC refining and the literature in the mechanical pulping process is not as complete.  The LC refining action has been characterized in a number of disparate, conceptually different methods. One way of describing refining action is to approach the analysis as a classic lubrication problem [20]. Here, the fibre suspension is considered as completely yielded and the equations of motion are linearized as the gap is considered small in comparison to the area. Here, the inertial terms have been eliminated.  This approaches lead to findings which have been observed industrially. In essence the results of this approach indicate that the shear is inversely proportional to the spacing or gap between the plates. In the limit of parallel plates, the analysis UHGXFHV‎WR‎WKDW‎RI‎CRXHWWH‎IORZ‎,Q‎WKH‎ODWH‎¶V‎DQG‎HDUO\‎¶V‎WKH‎DFWLRQ‎RI‎WKH‎refiners was characterized in an engineering fashion through traditional dimensional analysis. Here they considered the rHILQHU‎WR‎EHKDYH‎DV‎LI‎LW‎ZHUH‎D‎³SXPS´‎RU‎D‎SLHFH‎of turbo machinery, and scaled the governing parameters accordingly. In this method, the power consumption has been divided into three different parts as the required power to rotate the fluid, power for the pumping action and power to treat the fibres. In early work, this approach had limited success as one of the significant parameters, the gap size between the plates, could not be adequately measured. This limited the usefulness of such correlations. In more recent finding from our laboratory [1], it has been reported that like the lubrication work, the power applied scales linearly with the  - 15 - inverse of gap size.  In addition to lubrication problem approach, another way of describing refining action is to consider that as a piece of turbo machinery. A large body of literature exists which attempts to characterize the refining action based upon either the force or energy applied to the fibre suspension during bar crossing and study the structural effects on fibres and consider the refining process somewhat related to a fatigue-failure mechanism. Here mechanical force is applied to the fibre mat and property development occurs after repeated application of this force. The conceptual framework for this mechanism was built around measurements of force on the surface of raised corrugated sections of the stator bar. The first attempts to measure the mechanical force applied during a bar crossing ZHUH‎UHSRUWHG‎LQ‎WKH‎ODWH‎¶V‎)RU‎H[DPSOH‎*RQFKDURY‎HW‎DO‎[21], [22] and [23] measured the pressure distribution on the bar surface by replacing a portion of a bar inside a disc refiner by a beam instrumented with strain gauges and measuring the normal and shear forces acting over the entire surface of a refiner. They found a peak normal pressure of 3.5 MPa in a low consistency laboratory refiner operating at 2-3% consistency. Furthermore, the peak pressure was found to occur over the first 2-3 mm of the bar and was approximately 13 times greater than the average pressure.  Similar work by Nordman et al. [24] showed pressure distribution two orders lower than those of Goncharov but similarly having its maximum on the leading edges of bars. This is in support of those who believe that the fibre capture mechanism happens when leading edges of bars cross each other at a small gap between rotor and stator plate. In 1994, Martinez et al. [25] measured the maximum shear force on the surface of a single bar refiner by a strain gauge for different gap sizes and consistencies. They found that above an upper limit for gap size, the shear force is zero, meaning the fibre floc remains intact, and below a lower limit for gap size the shear force decreases significantly as a result of fibre rupture. For the gap sizes between the lower limit and the upper limit, with decreasing the gap size, the maximum shear force on the bar increases linearly.  In a subsequent work, Martinez and Batchelor [26] and [27] derived expressions to predict the normal and shear force acting on a fibre floc undergoing compression  - 16 - between passing bars of a refiner. Their equation was based on the assumptions that fibres are evenly spaced in any cross-section and the fibres display linear elastic behaviour under compression in a specific regime. In their model, they had predicted the existence of an additional force arising from the bar edge which acts to shear and compress the fibre floc in initial stages (corner force).  Batchelor et al [28] proposed a theory to predict the tensile force on fibre flocs that are trapped between the passing bars of refiner plates and sheared in the gap between plates. Their results showed that the heterogeneity of the refining process affects the magnitude of tensile force that fibres experience. The theory predicts that the tensile force experienced by individual fibres within a single floc can vary widely and depend significantly on the location of fibre within the floc, the orientation of the fibre relative to direction of bar travel and the point at which the fibre is trapped.   In 2001, Batchelor [29] developed equations to predict the number of impacts and the force of each impact on fibres by the rate at which fibres were trapped and the thickness of the captured fibres in low consistency refining. He then compared his analytical equations with a series of refining trials at 3 different consistencies and specific edge loads. It was found that for the refining trials, the numbers of fibres captured and the area and thickness of the flocs did not depend on the consistency at which refining was undertaken. Senger [4] showed later that stress-strain relationship becomes non-linear at strains greater than 30%. He found that for mechanical pulp fibres, fibre bending accounts for 65% of the total normal stress while fibre compression explained the other 35 %.  Kerekes et al. [30] advanced the argument that there are some factors which should also be considered in characterizing refining action such as: fractional bar coverage, gap size, specific edge load, bar material, edge sharpness and most importantly the distribution of fibres between bars. In fact, they argue that fibre orientation determines the type of strain imposed on that. Tensile strain within fibres is likely to be caused by shear forces acting on fibres. Bending results in axial tensile, axial compressive and shear stresses. Shear creates strain both within fibres and on their surfaces.   - 17 - In addition to these key studies, Senger and co-workers [31] used a refiner force sensor to measure normal and shear force on the bar surface by replacing one part of the bar with the sensor. Each sensor generates two voltage signals, which are converted to normal and shear force signals based on a method described by Siadat [32]. They found that with increasing the rotational speed, the coefficient of friction will increase. Also, at a given rotational speed, the co-efficient of friction decreases with decreasing plate gap.  Roux and his co-workers [19] in 2009 predicted the average number of bar crossings in a disc refiner with parallel distribution of bars and proposed a new definition for the intensity of refining as: the net normal force per bar crossing. Their definition of the intensity was very similar to the equation used in     theory, i.e. Equation (7), but they replaced      with a modified term taking into account the effect of the geometry of a refiner plate. They succeeded to predict refining pulp properties of freeness and average fibre length from their definition of intensity, i.e. Equation (10), and Specific Refining Energy.  Kerekes [33] describes a force-based refining intensity by estimating forces on bars and then relating them to forces on fibres through fibre distribution over bars and gap size. He then compares those forces to experimental measurements in mechanical pulping. The predicted and measured forces were in good agreement for low consistency refining of mechanical pulp. Prairie et al. [34] measured normal force, shear force and coefficient of friction over a range of Specific Edge Load from 0.33 to 0.5   ⁄  in a laboratory scale conical refiner running at 3% consistency. They replaced a portion of a bar with a 5mm piezoceramic sensor and measured the distribution of peak normal and shear force during different bar passing events. They found out that normal force in a bar crossing event increases with increasing Specific Edge Load while coefficient of friction decreases.  Although force is the key to understanding the change in fibre properties, an understanding of the force applied can be obtained through the use of indirect  - 18 - measurements which are more easily obtained. For example as energy by definition is defined as the force times the distance applied, many authors have characterized the refining action through use of energy (or more precisely power) estimates by describing its amount and nature. These theories are used to control refining conditions, plate pattern and to evaluate refining. Over the past fifty years, a number of refining theories has been presented in the literature. These methods relate the average energy per unit mass applied to the fibres to the power applied and some measure of the geometry of refiner plates.  Despite the lack rigor in calculating the geometrical parameter, the energy methods have had widespread acceptance industrially as the energy per unit mass correlates quite well to changes in both fibre morphology and end-use paper properties. These methods have engineering value but are severely limited tools in understanding the fundamental mechanisms involved in the refining process. In this part of the dissertation we present a brief overview of the theories of refining.  2.1. Specific Edge Load Theory Brecht [15] characterized refining by two parameters: the amount and nature of refining. He advanced the work of Wultsch and Flucher [35] who introduced the term ³UHILQLQJ‎LQWHQVLW\´‎DQG‎XVHG‎WKHLU‎GHILQLWLRQ‎RI‎LQWHQVLW\‎WR‎HYDOXDWH‎WKH‎QDWXUH‎RI‎refining (   ). He proposed the term specific refining energy (   ) as an indicator of the amount of refining. The form of these terms are shown in Equations (7) and (11) of this dissertation. From the derivation of intensity in their theory, the specific edge load is a measure of the energy expended per unit length per bar crossing. His analysis was based on a laboratory scale conical refiner and he concluded that the effective power is applied by the edges of the bars. He initially assumed that the edges of the bars as well as the area of refining which controls the shear forces are important during refining. In his experiments he varied the edge length of bars and area of refining at constant powers and found that small change in total edge length had a greater effect than change in the size of refining area.  This theory is one of the best known and most widely used refining theories in industry because all the factors can easily be calculated but it fails to consider many  - 19 - important factors having influence on the final refining results. For example, it does not consider such factors as refining consistency, width of bars, gap size and bar angle.  2.2. Specific Surface Load Theory Lumiainen [36] questioned the assumption regarding the refining effect over the bar edge and developed the idea of specific edge load. He assumed that the net energy is transferred to fibres from the edges of the bars (   ) as well as from the edge to surface contact phase. He proposed that the amount of refining evaluated by net energy, is a result of the number and energy content of refining impacts and the nature of refining is a result of the intensity measured by specific surface load and length of refining impacts. In other words, the amount of refining or specific refining energy (   ) becomes the result of three factors: number of refining impacts, intensity of impacts measured by     and length of refining impacts. This is shown in the following equation:                (Eq. 13)  Where         ⁄   is the number of refining impacts experienced by a fibre as it passes through the refiner,         ⁄   is the specific surface load and        is the length of refining impact or bar width factor. These three factors are calculated as:        ̇ (Eq. 14)             (Eq. 15)             ⁄   (Eq. 16)  Where    and     are calculated according to equations (5) and (7).   is the bar width of the plate and   is the average intersecting angle.  - 20 -  The specific surface load theory seems to work when fibres cover the whole width of the bar surface during a refining impact. This theory has partly replaced the specific edge load theory but it still does not take into account factors such as groove width [57].  2.3. Number and Intensity of Impacts Theory In this theory, the effective refining energy is considered to be the attribute of the number and intensity of impacts. The refining action was characterized in this way for the first time by Lewis and Danforth in 1962 [37]. Later in 1977 Leider and Nissan [38] carried out an analysis aimed to determine the intensity,              by calculating the energy necessary to stretch a fibre to its elastic limit and the number of impacts    by estimating the residence time. They postulated that the intensity of refining can be quantified by the energy per impact transmitted to pulp and that the duration of refining can be quantified by the number of impacts (  ) experienced by a fibre as it passes through the refiner. They suggested the following equation to determine   :              (Eq. 17)  Here,    and    are the number of rotor and stator bars,          is the rotation frequency,       is the residence time and    is the probability of a fibre to be in a position to be impacted by bars. Once    is determined, they calculate the intensity of refining (        ) by:         ̅   (Eq. 18)  Here ̅  is the average mass of fibre and     is specific refining energy defined in Equation (7).   - 21 - 2.4. C-factor Theory ³C-IDFWRU´‎SURSRVHG‎E\‎ .HUHNHV‎[17] is aimed to quantify refiner action for the purpose of comparing refiners. It estimates the number and intensity of impacts on fibres by representing the capacity of a refiner to apply changes in fibre morphology. ³C-IDFWRU´‎DVVXPHV‎WKDW‎WKH‎H[SHQGLWXUH‎Rf energy,         , is described by two basic variables: the number of impacts per unit mass of fibre           and the intensity of each impact      .             ̇        (Eq. 19)  It is well accepted that a large number of impacts of small intensity results in fibrillation while a small number of impacts at high intensity leads to cutting. In other ZRUGV‎HTXLYDOHQW‎UHILQLQJ‎DFWLRQ‎LV‎DFKLHYHG‎ZKHQ‎³  ´‎DQG‎³ ´ RI‎HDFK‎UHILQHU‎DUH‎equal not necessarily when their specific energy, E, are equal. Then Kerekes developed the C-factor representing the probability of refining on fibres to be a combination of plate pattern, rotational speed, fibre length, consistency and coarsness. If rotor and stator plate have similar patterns, and if the gap size between plates is smaller than groove depth, the C-factor for a disc refiner is:                                             (Eq. 20)  Where       is groove depth,           is density of water,   is pulp consistency,      is length of fibre,   is bar density,           is rotational speed,   is average bar angle and          is the coarsness of fibre.  Before these theories were introduced to literature, in 1887, Jagenberg (cited in Roux et al., [19], p52) studied the case of a hollander beater with parallel rotor and stator bars relative to the axis of the roll and realized that the bar crossing area is the key parameter in quantifying the refining action on fibres. In 1906, Kirchner (cited in Roux et al., [19], p54) confirmed the findings of Jagenberg and proposed equations to calculate bar crossing area in case of a beater with inclined bars.  - 22 - In 1922, Smith [39] considered many aspects of the flow in a beater as well as the mechanism by which fibres enter the beating zone to understand the action of beaters. He hypothesized that the rotor bar in passing through the stock picks up fibres on its edges and these were then trapped against the stationary bar. Work by others has also supported the fibre edge (fibrage) theory. The sketches of Banks [40] taken from his cine-films show fibres concentrated at the edges of bar crossings. Similarily Fox [41] showed cine-films that were interpreted as revealing fibrage theory.  2.5. Fibrage Theory This theory was proposed by Smith [39] who studied the action of beaters and postulated that the moving bar through pulp collects fibres on the leading edges as does the bed plate bar with fibres travelling over it. He assumed that the beating action is caused by the moving bars shearing through the leading edges of bars when a pair of bar edges cross over each other. He considered the fact that the wear of the front surface of the rotor bars occurred     above the leading edges as an evidence for his fibrage theory. Maskalov [42] also studied the refining process from a fibrage theory viewpoint. He observed that the amount of fibres on the leading edges of bars for an unrefined pulp was around            for a wide variety of disc refiners and softwood pulps.   2.6. Summary of Literature Many theories have been suggested during the years to describe the action of energy transfer and fibre morphology change in refiners. Each theoretical approach has had success under limited conditions and weakness under other conditions. Typically only two types of work transfer mechanism were accounted for: (i) cutting of fibres between the leading edges of crossing bars, and (ii) crushing or rubbing of fibres in the refining area between the opposing stator and rotor bars [3]. This shed lights on the importance of the geometry of refiner plates in characterizing the refining process and resulting paper properties. What is clear from the examination of the energy  - 23 - approaches is that even after 50 years of calculation, the shape of the corrugated surfaces, i.e. the projected areas of intersection between the land area of the bars and the leading edges of bar crossings, and optimum refining conditions under which desired changes in fibre morphology is achieved has yet to be determined properly. This is the key in understanding LC refining. It is from this point that our research is motivated.  Table 2-1: Different energy-based methods characterizing refining action Method Equations Comments Specific Edge Load NBELPSEL net. .fibrenetmPSRE   the most widely used method in industry similar pulp properties are expected from fibres subjected to similar     and      Modified Edge Load BGBSELMEL  .tan21.  accounts for parameters such as bar and groove width  applies an average value for bar angle  Number and Intensity of Impacts _.mINSRE I splits the energy into: number of impacts,  , and the intensity of each impact,   considers refining from the perspective of fibre not refiner  C-factor                                            considers the probability of a refiner to treat fibres takes into account bar and groove geometry  provides a more accurate description of refining intensity but not about its distribution  - 24 - Chapter 3. Research Objectives and Proposed Framework There are different models to characterize LC refining but the majority of these theories have been created for chemical pulps. Their accuracy with mechanical pulps remains unknown. Also, the relevant literature shows the complexity of LC refining and specifically the impression of plate design in energy transfer mechanism and optimal refining results.   As a result the specific objectives of this research are:  To characterize the influence of plate pattern on the changes to fibre morphology.  To derive analytically an estimate of the length of bar crossings edges (perimeter), number of bar crossing points and the area of refining under bar crossings.  To develop a computational model that can accurately simulate time-dependant variations of geometrical parameters and most importantly the area of bar crossings, number of bar crossing points and total length of bar crossing edges.  To investigate experimentally the effect of plate pattern and rotational speed on power-gap relationship for a wide range of plate design, rotational speeds and gap sizes.  To relate plate design and refining operating conditions to changes in fibre length and freeness.  To predict tensile index development from low consistency refining operating conditions.   To advance guidelines for optimal LC refining operation by relating the changes in fibre length and freeness to paper properties.  The framework is built on the hypothesis that:  - 25 -  Pulp properties of fibre length and freeness can predict most of sheet properties such as bulk and tear index but do not correlate well with tensile index development.  Dimensionless power is related to dimensionless gap by plate design and feed furnish.  Specific Edge Load theory does not predict mechanical pulp refining performance properly. This could be caused by defining the intensity of refining as the net energy per bar crossing per bar length. Defining the intensity of refining as the net energy per bar crossing surface or the net energy per length of bar crossing leading edges may lead to a better understanding of the intensity of refining.  - 26 - Chapter 4. Modelling of the Geometry of Intersection Formed Between Refiner Plates: Analytical Approach One of the open remaining questions in the area of low consistency refining is the inter relationship between the plate pattern, energy consumption, and the changes in fibre morphology. It is widely accepted that the plate pattern is the key to understanding the changes in fibre morphology. Understanding how plate design affects this relationship is difficult, as the number of contact points between these plates is vast and the local area of intersections between the plates form a system of closed-polygons whose shape evolve and translate as a function of time.  In this section we turn our attention to derive analytical equations for the average area of bar crossing, number of bar crossing points and the length of bar crossing edges in a low consistency disc refiner plate with parallel distribution of bars and grooves. 1 Figure 4-1 shows a schematic of a refiner plate with the geometrical parameters used in this work to characterize such patterns. It should be noted that there are many different patterns of plate for the application in low consistency refining. For example, a group of plates have their segments filled with bars such that there is no groove space between two adjacent segments while another pattern has a relatively big size groove space, i.e. master groove, between adjacent segments. We model a general case here that represents both patterns: (i): plates with master grooves (     and (ii): plates with no master grooves (   ).  In order to familiarize the reader with  basic equations used in this Chapter to estimate the geometrical parameters of bar crossing area, number of bar crossings and the length of bar crossing edges (perimeter) in a disc refiner, we begin by introducing D‎VLPSOH‎H[DPSOH‎RI‎D‎³0RVDLF´‎SUREOHP‎‎                                                  1 In disc refiner plates with parallel distribution of bars and grooves, each bar is parallel to another bar in the same segment or cluster with a distance of a grove width, G. The equations derived in this Chapter are limited to such patterns. The geometry of intersection formed between this type of bar patterns creates the shape of a parallelogram.   - 27 - 4.1. The Mosaic Problem Figure 4-2 illustrates an intersecting pattern formed between the geometry of 4 rectangular bars. This pattern is similar somewhat to the case of 2 rotor bars crossing 2 stator bars in a disc refiner with a bar width of  , a groove width of   and an intersecting angle of  . The total area of the mosaic,   , is covered by 4 smaller mosaics with an area of     each created by the intersection of 1 set of bar-groove and another set of bar-groove.  If    be the total surface of the mosaic, then the number of bar crossings can be calculated by the formula:            (Eq. 21)  In which     is the area of a single crossing created from bar and groove intersection.                 (Eq. 22)  Once the number of crossing points is determined, we can simply calculate the total length of crossing edges between bars ( ) and the total area of bar crossings ( ) as:                         (Eq. 23)                          (Eq. 24)  Now we extend the model of a mosaic to the case of a single disc refiner with parallel distribution of bars and grooves at each segment.    - 28 -  Figure 4-1: A schematic of one refiner plate is shown in this figure. The left image is a schematic of the entire plate which is composed of (in this case) 24 repeating segments or clusters. The image on the top right is a schematic of one cluster. Here    and    represent the inner and outer radii of the working surfaces of the refiner;   is the cluster angle; and   is the bar angle measured relative to the radius. The image on the bottom right shows the cross-section of the machined pattern on the surface of the plate.   and   represent the bar and groove widths, respectively.     Figure 4-2: The “Mosaic” problem; crossing of 2 rotor bars on 2 stator bars creates 4 crossing points. Here,     is the area of intersection between one rotor bar-groove and one stator bar-groove representing 1 crossing point between bars.  - 29 - 4.2. Estimating the Average of the Area of Bar Crossing, Length of Bar Crossing Edges and Number of Crossing Points in a Disc Refiner A single disc refiner is first considered as depicted on Figure 4-3. A full rotor bar is delimited by a segment of stator plate with parallel bar distribution. The stator segment has a bar angle of   and a cluster angle of   as they are defined in Figure 4-1. We assume that stator and rotor bars have the same width of B, groove width of   and the intersection angle between them is  . This geometry is very often met in the paper industry.  For the patterns of plates that there is no master groove between plate segments, the total working surface,    is equal to the area of the disc. Therefore the total length of bar crossing edges and the total area of bar crossings become independent of bar angle. By substituting:                 (Eq. 25)  Into Equations (21) to (24), we can estimate the total length of bar crossing edges, total area of bar crossings and the number of crossing points as:                        (Eq. 26)                         (Eq. 27)                            (Eq. 28)  As the rotor bar rotates over the stator segment, the shape of intersecting polygons and their intersecting angle   evolves and translate as a function of time.  Also, it is very common for disc patterns used in industry to have master grooves. As it is shown in Figure 4-3, the total working surface,    , in this case is not equal to the total area of the disc calculated in Equation (25). This motivates us to follow an  - 30 - integration method to estimate the mean number of bar crossings, area of bar crossings and length of bar crossing edges from our characterizing parameters introduced in Figure 4-1.   Figure 4-3: Configurations of a stator segment with bar angle of   and cluster angle of  . The stator segment intersects with 1 rotor bar and creates 4 number of bar crossings.   If the total length of bar crossing edges on an elementary annulus with radius of   shown in Figure 4-3 is measured, it is:                      (Eq. 29)                            (Eq. 30)  In which    is the angle between rotor bar and the radius at the point of bar crossing and     is the angle between stator bar and the radius at the point of bar crossing such that:            (Eq. 31)   - 31 - Also, for the elementary annulus with radius of  :                    (Eq. 32)  In which      is the number of segments in an entire disc.     is a function of the radius of the elementary annulus and the bar angle  . It can be determined by solving the system of equations:  {                (       )    (Eq. 33)  The total length of bar crossing edges can then be calculated by integration from inner to outer radius of the disc as follows:            ∫                     (       )       (Eq. 34)  This gives:                                        (Eq. 35)                              {                     (         (        )      )        (  (        ) )   } (Eq. 36)  Similarly, the total area of bar crossings can be calculated by integrating the area of crossings on an elementary annulus from inner to outer radius of the disc:  - 32 -                                         (Eq. 37)  It may be noticed that       is the intersecting angle of the bars. For the stator, Figure 4-3, clearly demonstrates that    varies between   for the first full bar located on the right side of circumference of radius    and     for the last bar located on the left side of the segment. Assuming a similar plate pattern for rotor, during the relative motion of rotor plate on stator plate:           (Eq. 38)            (Eq. 39)  Hence, during the relative motion, the number of bar crossings varies between:                   (Eq. 40)  And                      (Eq. 41)  The average value for the total number of crossing points on the elementary annulus may be calculated by a double integration:                  ∫ ∫                          (Eq. 42)  The first integral gives:  ∫                                         (Eq. 43)  And the second one:  - 33 -  ∫ [                     ]                                      (Eq. 44)  By substituting Equation (32) for     into Equation (42) and integrating these partial results over the complete annulus between the radii    and    and with the help of some trigonometric calculations we can calculate the average total number of bar crossings as:                             {                                   } (Eq. 45)                   is defined in Equation (36). This is the general form of the equation for determining the average value for the total number of bar crossings in a disc refiner with parallel distribution of bars. The special case of this equation is when there is no master groove in a segment (    . In this case, Equation (45) will have the same form of the one reported by [43]:                                     ⁄  ⁄   (Eq. 46)  This is an average value for the number of crossing points between rotor and stator plates with parallel distribution of bars in a segment. It should be stated that from Equations (31), (38) and (39),   and   have positive values such that:         (Eq. 47)   - 34 - 4.3. Summary In this Chapter of the dissertation, we derived analytical equations to estimate the average quantities of bar crossing area, total length of bar crossing edges and number of bar crossing points in a disc refiner characterized such as Figure 4-1. These equations neglect the temporal variation of quantities such as bar angle and use average quantities in the first order as representative values.  In the next Chapter, the deviations from the average of the local variables are estimated numerically.  We believe that the time-dependent variations in the patterns formed may lead to insights into the beating effect and a better definition of the intensity.                 - 35 - Chapter 5. Modelling of the Geometry of Intersection Formed Between Refiner Plates: Numerical Approach In this Chapter,  a novel methodology for estimating the area and perimeter of intersection between two or more intersecting surfaces, without having to determine or order the points of intersection, is presented. No restriction is placed on complexity of the intersecting geometry except that it must represent a closed region. This method is well-suited for cases in which the area and perimeter of intersection are complicated, are not strongly peaked in a very small region, and when relatively low accuracy is tolerable. Although this work is presented for disc refiner plates, the methodology proposed can be used for any type of refiner plates. In this study, we examine the time-dependent evolution of the area, perimeter and number of bar crossings for 320 different low consistency refiner plate configurations with similar geometrical patterns for rotor and stator plates using this methodology and compare these results with those analytical equations obtained in Chapter 4. Empirical correlations are presented to relate the plate parameters to bar crossing area. Finally, we interpret our findings in terms of the industrially accepted parameters used to characterize the action of refiner plates.  To familiarize the reader of this thesis with the methodolRJ\‎XVHG‎ZH‎VWDUW‎E\‎LQWURGXFLQJ‎D‎FODVVLFDO‎³7R\‎3UREOHP´‎  5.1. The Toy Problem Computing the area and perimeter of intersecting objects is one of the most fundamental aspects of computational geometry. As the region of intersection forms a polygon itself, its area and perimeter can be calculated once the points of intersection are determined and the vertices are ordered so that a simple path can be formed. The degree of complexity of this problem varies if the polygon is concave or convex. Convex polygons are those in which every internal is less than 180ƕ; a polygon that is not convex is concave. The convex problem is considered the simpler of the two  - 36 - cases as the ordering of the vertices is relatively straightforward. Shamos & Hoey [44]‎2¶5RXUNH‎HW‎DO‎[45] and Saab [46] present efficient methods for doing so. With concave polygons, Chazelle & Dobkin [47] demonstrate a methodology of decomposition to form a system of convex polygons. In this work we present a methodology that avoids the computationally intensive steps of ordering the vertices and detecting the intersecting points between intersecting polygons. We advance a methodology, which (somewhat) resembles a Monte-Carlo approach.  Before we highlight our method through a simple example we must formally define the terms used. Let                    be collection of polygons in    that intersect and let int     and ext     denote the points of       that are interior and exterior, respectively, to   . To specify particular regions within  , we define       to represent                  . Further, we define                        to be a collection of functions evaluated over a discrete set of points,          where                , using the following functional form:     {                                   (Eq. 48)  To highlight this, we consider the intersection of the polygons    and    as shown in Figure 5-1(a). We create two separate functions    and    through use of Equation (48) and visualize the domain by summing these functions at each   and   position to create one image (Figure 5-1(b)). Here we see that the common intersecting region        is given by the region in which the function is equal to two. Once the image of the region of interest is created, the area   and perimeter   can be deduced through standard image analysis techniques.   - 37 -  Figure 5-1:  (a) The geometry of two intersecting squares    and    contained in a larger rectangle  .    and    are squares with an edge length of    and    and are centered at       and      , respectively. (b) An image of each polygon in (a) is defined through use of Equation (48). This image is created by summing all the functions at each grid point.   To highlight the utility of this method we report the error in determining the area of        as a function of number of nodes   (Figure 5-2). Here we see that the relative error diminishes somewhat linearly with increasing grid size. A relatively crude estimate, i.e. a relative error of 10í3% can be achieved with approximately      grid points in each direction; this is a relatively low-accuracy result. Higher accuracy results can be achieved with higher-order segmentation algorithms to determine the edges of the object.   - 38 -  Figure 5-2: The relative error in the estimate of the intersecting area        using  equally spaced nodes in    and   directions respectively. The exact value of the area of intersection was simply determined using direct mathematical calculations for the geometry presented in Figure 5-1(a).   There are a number of benefits to this numerical methodology as opposed to using the exact solution. To begin, this method produces reasonable estimates for cases in which the area and perimeter of intersection are not strongly peaked in a very small region. This methodology is general and can be applied for any shape of closed bodies that can be represented as a polygon. To highlight this we present another toy problem in Appendix A. to demonstrate this. Finally, we realize the true benefit of this approach when we have a vast number of intersecting objects in the image. With the exact method, i.e. determining the vertices and then ordering the problem, the computational intensity increases with the number of intersecting objects. The true benefit of this method is when we extend the problem to estimating the area and perimeter of thousands of simultaneously  - 39 - intersecting bodies. With this methodology, the computational requirements do not increase as rapidly with increasing number of intersecting objects.  5.2. Characterizing the Intersecting Pattern of Refiner Plates At this point we turn our attention to reporting on the algorithm for the industrially relevant case of two overlapping disc refiner plates, see Figure 5-3. Images of the stator and rotor are represented in the first two panels of this figure. The rotational speed of the rotor is defined by   and its angular position at any time   is defined by  . We used Equation (48) to generate the images. As with the toy problem, we highlight the region of interest by adding the functions which represent the rotor and stator. In Figure 5-3(c), the regions which are assigned the value of two represent the intersecting regions between opposing bars of the rotor and stator. It should be noted that the case illustrated in this figure is considered as a very coarse bar pattern. We use this pattern for clarity in the presentation. Industrially relevant patterns contain approximately 30 times more bars on each rotor and stator. Four snapshots of the intersection patterns at different positions of the rotor are given in Figure 5-4. We see that the most common object of intersection formed is a parallelogram with equal adjacent length (lozenge). The unique property of such a parallelogram is that its area is proportional to the square of its perimeter. We can see that for different angular positions, the number of intersecting points as well as the magnitude of each intersection area changes from      to    . In total 320 simulations were conducted in which [          ]  [           ]  [         ]  [          ]  [          ]  [               ]  The sensitivity of the solution is shown in Figure 5-5 as a function of the number of grid points in   and   directions for one time step. Here, we see that although the estimated value of   generally diminishes with increasing , we find that the solution varies by less than 2% for cases with         . All simulations were conducted with         .   - 40 -  Figure 5-3: (a) A representative image of a stator plate with the cluster angle of β. The value of 1 represents the surface of the bars. (b) A representative image of the rotor in which the angular velocity of the plate ω, measured relative to the horizontal is defined. Here,   represents time. (c) The summation of the images given in (a) and (b).    Figure 5-4: A schematic of the complex intersection pattern created when the rotor passes over the stator plate. Four images are given at different times: (a)             ; (b)           ; (c)            ; and, (d)         .    - 41 -  Figure 5-5: An estimate of the sensitivity of the area   as a function of number of grid points , in the   and   directions. For this simulation          ,          ,         ,          ,           , and             .   At this point we turn our attention to the main findings in this Chapter and examine the evolution of area with rotational position. In Figure 5-6, eight simulations are presented with the conditions given in Table 5-1.   Table 5-1: 8 cases studied in Figure 5-6 with various bar width, groove width and bar angle               (i) (ii) (iii) (iv) (i) (ii) (iii) (iv)       3.2 3.2 1.3 1.3 3.2 3.2 1.3 1.3       2.4 4 2.4 4 2.4 4 2.4 4      0.57 0.44 0.35 0.25 0.57 0.44 0.35 0.25    0.214 0.138 0.084 0.040 0.13 0.082 0.05 0.025     0.013 0.008 0.005 0.002 0.009 0.006 0.003 0.001                3817 2417 7818 3987 3393 2138 7212 3675     342 213 636 303 329 221 642 314   The first observation that can be made from this figure is that there are two dominant frequencies comprising the signal. The low frequency signal has a period of the  - 42 - FOXVWHU‎DQJOH‎ȕ‎7KH‎KLJK‎IUHTXHQF\‎VLJQDO‎KDV‎D‎ZDYH‎OHQJWK‎RI‎DSSUR[LPDWHO\       .  The second observation is that with decreasing bar size (i and iii, or, ii and iv) the area of intersection diminishes.  The third observation that can be made is that the average value of   in each one of these traces is related to the ratio of         .  Finally, quantitatively we observe that the variance in each of these signals diminishes with the magnitude of the area. This is quantified in Figure 5-7, in which the average area, normalized by the area of the plate, defined as:                   ∫         (Eq. 49)  is shown as a function of the standard deviation (  ) of the signal.   - 43 -  Figure 5-6: The variation of area  , as a function of rotational position for a number of different plate configurations. In (a) the bar angle   is held constant at a value of       In (b) the value of   is set to      For all the configurations shown,  ,    and    are equal to               and         respectively. The roman numeral in these figures refer to various bar and groove widths and are defined in Table 1. The average value as well as the standard deviation of all 8 cases is summarized in Table 5-1.   - 44 -   Figure 5-7: The relationship between the normalized average value of instantaneous area of bar crossings and its standard deviation with the cluster angle of       . The results shown are for the cases with        .   We also notice that for a plate with smaller bar size, more homogeneity in the area of bar crossings is expected. In order to prove this, we have compared 2 different configurations of plates in the Table 5-1 (i.e. (i) and (iii)) in which we have a coarser distribution of bar patterns in (i) with           comparing to (iii) with          . These 2 plates have similar groove width of          , bar angle of        and cluster angle of       . Figure 5-8 shows this comparison. Although the magnitude of area of bar crossings is smaller for the plate with smaller width, a more uniform distribution in the area of bar crossings is achieved. At this point, we turn our attention to developing a rule of thumb regarding the relationship between    to the plate parameters. We do so empirically and attempt to fit an equation of the form:  - 45 -                                   (Eq. 50)  We also highlight the importance of variations in the distribution of instantaneous area in Figure 5-7. By changing a plate configuration in a way which a larger area of bar crossings is provided, a higher variation in the magnitude of bar crossings is expected. This result is in accordance with findings of Brecht [13] where he finds a higher noise level with smaller bar angles. This might be a result of the higher variation in the area distribution of bar crossings at smaller angles. In Figure 5-9(a), we highlight the utility of the correlation by plotting    as a function of           IRU‎WZR‎Į‎DQG‎WZR‎GLIIHUHQW‎ȕ‎7KH‎XWLOLW\‎RI‎WKH‎ILW‎IRU‎DOO‎cases was tested and is shown in Figure 5-9(b). Excellent agreement is found as the correlation coefficient    was determined to be 0.99. In the final part of this section we examine the length of the perimeter formed during intersection. As mentioned previously, most polygons formed in the domain are parallelograms with sides of equal length. With such parallelograms, the area is proportional to the square of its perimeter. In Figure 5-10 we demonstrate that for all cases tested, we find that this relationship, too, does hold.   - 46 -  Figure 5-8: The probability distribution of the area of bar crossings for 2 different plate configurations (i.e. (i) and (iii)) reported in the Table 1. In (a),          ,          ,       ,        and            . In (b),          ,          ,       ,        and            .   - 47 -  Figure 5-9: (a) The relationship between    and the dimensionless group        For clarity, this relationship is shown at two different bar angles   and two different cluster angles  . The results shown are for the cases with        ,            , and            . The roman numeral in this figure refers to various bar and cluster angles and are: (i):         and       (ii):         and       , (iii):          and      , (iv):          and        , In (b), we display the goodness of the fit between the numerical results (abscissa) and the predictions using Equation (50).   - 48 -  Figure 5-10: The relationship between the dimensionless perimeter    and area    for all cases simulated.    represents the ratio of the sum of the perimeters to the total length of the edges of the bars.   5.3. Comparison of Analytical Solution with Computational Results In this part of the thesis, we validate our computational results for the 320 different low consistency refiner plates that were analyzed in this Chapter with the analytical equations derived in Chapter 4. This comparison is illustrated in Figure 5-11 where we show numerical estimates of the perimeter and number of bar crossing intersections versus the analytical values obtained from Equations (35) and (45). Excellent agreement is found between them.  - 49 -  Figure 5-11: (a) Comparison between total perimeter of bar crossings [ ] estimated with our computational simulations (      ) and those reported analytically through the use of Equation (35) (       ) for 320 different low consistency refiner plates. (b) The comparison between our analytical solution for the average number of bar crossings; Equation (45) with our computational results obtained in Chapter 5.    - 50 - 5.4. Discussion Another outcome of the current work is the possibility to detect the instantaneous and average number of bar crossings at each rotational position which seems to play a significant role in the intensity of refining. To make clear what we mean by the instantaneous number of bar crossings, in Figure 5-3(c) each segment has 7 number of bar crossings which leads to a total of 56 bar crossings at      for the case shown. As the location of rotor bars vary both temporarily and spatially along the radius of the refiner plate, a different number of bar crossings is created. Figure 5-12(a) shows the total number of bar crossings for a plate with        ,          ,              and            .  The average number of bar crossings is also shown to be a function of the dimensionless group of          as weOO‎ DV‎ WKH‎ EDU‎ DQJOH‎ Į as the area and perimeter of bar crossing [Chapter 4 of the thesis]. In Figure 5-12(b) a correlation between   ,           DQG‎Į‎KDV‎EHHQ‎VKRZQ‎IRU‎D‎FRQVWDQW‎SODWH‎VL]H‎RI‎             and       . Different slopes on the graph represent different bar widths to be: (i)          , (ii)          , (iii)         and (iv)          .  One of the main findings of this graph is that at a constant  , increasing   will decrease the average number of bar crossings while decreasing   at a constant   will increase the number of crossings in one revolution of rotor disc in front of the stator disc. This can also be seen in Table 5-1 where decreasing bar width from           to           at a constant groove width of           and bar angle of       , (i.e. (i) to (iii)) will decrease the averaged normalized area of bar crossings from          to         . It should be noted that in this case, the standard deviation of normalized area will decrease as well while the average number of bar crossings increases from         contact/rev to         contact/rev. Here,    is the average number of bar crossings over the time domain, i.e.        ∫                     (Eq. 51)    - 51 -       Figure 5-12: (a) The distribution of the total number of bar crossings,           , as a function of rotational position. Here,        ,          ,                        and              The average number of bar crossing, i.e.        , has been shown on the graph. (b) The relationship between    and the dimensionless group          This relationship is shown at cluster angle         ,             and        . The different marks in this figure refer to various bar angles and are:          (○),        (▲),        (◊) and          (□). Different slopes in the graph refer to: (i)          , (ii)          , (iii)         and (iv)            In total, 80 cases have been studied.   In addition to this, we attempt to interpret    , as defined by Equation (3), in terms of the output of our code. The natural starting point for this comparison is  . We do however find that     is proportional to          , as shown in Figure 5-13(b). These results may imply that BEL is not a very good predictor of length of bar crossing edges but is an excellent representation of the number of crossing points; a parameter advanced by Roux et al. [19] as important in understanding the relationship between plate parameters to the beating effects.   - 52 -  Figure 5-13: (a) The relationship between the sum of the perimeters   and the     defined using Equation (3). (b) The relationship between    and the    . This relationship is shown at cluster angle         ,             and        .   5.5. Summary In this Chapter of the dissertation, we first introduced a novel numerical method to estimate the area and perimeter of polygons formed between intersecting bodies. This ZDV‎VKRZQ‎WKURXJK‎WKH‎VLPSOH‎H[DPSOH‎RI‎D‎³7R\‎3UREOHP´   This methodology is fast and robust and does not need to detect the points of intersection between overlapping objects. The main benefit of this methodology is  - 53 - seen in the industrially relevant case of low consistency refiners where the crossing of thousands of moving polygons (rotor bars) on top of stationary polygons (stator bars) create a complex geometry of intersection whose shape and magnitude change and transfer as a function of time.   We used this methodology to simulate the patterns formed between 320 different disc refiner plates with parallel distribution of bars at each segment and estimated the instantaneous area, perimeter and number of crossing points between overlapping bars. From the distribution of these geometrical parameters over 1 revolution of rotor plate, an average value of bar crossing area, length of bar crossing edges (perimeter) and number of crossing points was assigned to each plate as its characteristics. This enabled us to propose a statistical model to predict the average area of bar crossing in a disc refiner with parallel distribution of bars.   The validity of this methodology to use in disc refiner plates was tested by comparing the numerical results with analytical equations obtained in Chapter 4. We observed that the average area and perimeter of bar crossing is a function of the dimensionless parameter    , bar angle   and cluster angle  . Also, we demonstrate that the perimeter formed from the intersecting bars is proportional to the square root of its area and is not proportional to the industrially known parameter of    .                      - 54 - Chapter 6. Pilot Scale Refining Trials of Mechanical Pulp In this Chapter, we propose an experimentally based framework to develop low consistency LC refining performance equations that can be used to design and optimize LC refining systems.  The framework is built on the hypothesis that (1) plate design is the key in understanding the changes in performance of LC refining of mechanical pulp, (2) pulp properties of fibre length and freeness can be determined from operating conditions in refining and plate design, (3) fibre length and freeness can predict sheet properties such as bulk and tear index but do not correlate well with tensile index [48].  In the first stage of this framework, we derive correlations between pulp properties of fibre length and freeness and operating conditions of refining such as rotational speed, plate design and plate gap. We propose a new definition for the intensity of refining which predicts changes in fibre length by properly characterizing the geometry of plates used in LC refining. We also show that the change in freeness or drainage of pulp slurry is dependent on the energy applied to the suspension. In the second stage, we present correlations between pulp properties of fibre length and freeness and final sheet properties of tear index and bulk. We also demonstrate that these two properties are not good indicators of tensile index. We attempt to improve two parameter characterization methods so that we can derive a good correlation between tensile index and operating conditions of LC refining in mechanical pulping.     We rely on experimental measurements and dimensional analysis to determine the relationships between refiner operation, design, and the resulting pulp property changes.  The results of these studies are presented and we propose a new framework for interpreting the experimental data and the development of new models for the effect of refiner operation and design in terms of power, diameter, velocity and the details of plate geometry on pulp and final sheet quality changes.   - 55 - 6.1. The Experimental Set up The Pulp and Paper Centre at the University of British Columbia has recently installed a new low consistency refining pilot facility in partnership with Aikawa and FineBar. This flow loop consists of two large tanks with the capacity of    each, a centrifugal pump, and a single     disc LC refiner with a variable speed drive with a maximum rotational speed of          and        motor. The refiner facility has D‎QXPEHU‎RI‎)LQH%DUŒ‎SODWHV‎ZLWK‎D‎EURDG‎UDQJH‎RI‎EDUJURRYH‎JHRPHWULHV. In all experiments, softwood CTMP market pulp from Northern British Columbia (Quesnel River Pulp) was used.  The pulp is approximately       CSF (the standard procedure for this measurement is described in TAPPI T227),     mm mean fibre length and is refined at      consistency. The fibres are screened and there is nearly zero detectable debris using a        flat screen. The stock temperature was held constant at approximately      for all trials. The flow rate was held constant at         for all trials.  The stock was pumped from a     tank through a       pump and through the LC refiner in a single pass and into a second tank.  At each trial, we varied power over practical ranges of plate gap with a minimum of 15 samples collected per trial to provide repeatability and high resolution. The trials were run at 3 different rotational speeds;        ,          and          for a wide range of plate geometries that are listed in Table 6.2.   Table 6-1: Operating conditions for the pilot-scale refining trials of mechanical pulp Parameter Condition Refiner Speed        ,         ,          Refiner Plate BEL:     ,     ,     ,             Consistency    Flow Rate         Number of Gap Sizes    Pulp Type Softwood,      SPF  - 56 -  The refiner is instrumented with magnetic flow meters, pressure and temperature sensors in the inlet and outlet of refiner, power meters, plate actuation and variable speed drives on the pump and refiner.  The refiner is operated and data collected using a LA%9,(:Œ‎LQWHUIDFH‎7KH‎UHILQHU‎LV‎HTXLSSHG‎ZLWK‎D‎/9'7‎WR‎GHWHUPLQH‎plate position and thus plate gap.  We assume that the diameter of the pilot refiner is small enough relative to its mechanical stiffness to ensure accurate gap determination from plate position sensing. The zero-point of plate position is determined by bringing the plates together and recalibrating before each trial. Each plate used in these trials has been worn in using abrasive material in a stock suspension before these trials were conducted to ensure plate parallelism.  Table 6-2: Specifications of the four refiner plates used in the experiments (Note:    is the inside diameter and     is the outside diameter of the plate pattern,    is the groove depth,  is the bar width,   is the groove width and   is the bar angle)  Plate    [mm]    [mm]   [mm]   [mm]   [mm]   [o]     [     ⁄ ] 1     406 1 2.4 4.8 15 5.59 2 229 406 1.6 3.2 4.8 15 2.74 3 229 406 3.2 4.8 4.8 15 0.99 4 229 406 2 3.6 4.8 15 2.01  - 57 -  Figure 6-1: Illustration of the UBC pilot LC refiner used for these trials.   6.2. Power-Gap Relationship As previously described, power affects both the specific refining energy applied to the pulp and the intensity of the energy transfer. Power is controlled by actuating the plate position to change the gap between the plates. The reduction of plate gap causes the fibres, that are trapped on the bar leading edges, to be compressed and sheared and results in an increase in friction between the plate and fibre which increases the required power. The interaction of fibres and rapidly rotating bars results in a complex relationship between the operating and design variables of the refiner and the resulting pulp and paper quality changes. This section of the dissertation examines some of the basic relationships that exist in refining. In the first part, we focus on the effect of plate gap and rotational speed on power consumption of refining by studying only   plate used in the experiments; i.e. plate number   in Table 6.2 with                 and then in the second part, we study the effect of plate pattern on power versus gap relationship. The main question  - 58 - that needs to be answered is: how does plate pattern and rotational speed change power versus gap relationship? Figure 6-2 shows the total power consumption of refining as a function of gap for plate number   at   different rotational speeds:        ,          and          for both water and pulp. We can see that as we reduce the gap, power increases. This is in accordance with what we expect but this increase in power becomes more significant for the gap sizes smaller than      . Also we observe that at a constant gap, the refining trial with higher rotational speed transfers more energy to the pulp. In order to find out what portion of this energy is actually transferred to fibres, we need to determine the no-load power.    Figure 6-2:  Total power versus gap for 3 rotational speeds of        ,          and          for both water and pulp. The plate number 3 with                 has been used in both trials.    - 59 - Figure 6-2 also shows power-gap relationship for the same plate and rotational speeds with water as our suspension. This experimental measurement of no-load power is in accordance with those of reported by Rajabi Nasab et al. [49] . From this figure, we choose the no-load power at the point where the total power consumption for water and pulp starts deviating, i.e. the industrial gap size of       is a good approximation for measuring the no-load power. The work by Mohlin [50] and Luukkonen et al. [51] have all shown that over a practical range power and refiner gap size have the following relationship:           (Eq. 52)  Figure 6-3 shows the relationship between the net power applied and the inverse of plate gap for our current trial with plate number  . For this trial, a gap of       is observed in which the significant increase in energy transfer to fibres is seen for gap sizes smaller than this. After this gap that refiner loading starts, i.e. the gap size of      , up to a certain critical gap,   , net power shows linearly proportional to the inverse of gap size. This critical gap is a function of rotational speed of the refiner and is smaller for smaller rotational speeds. For gap sizes smaller than the critical gap size, the relationship between the net power and inverse of gap deviates from linearity. The reason for this is not clear for us but it can be related to a different mechanism in refining at small gap sizes. The figure also shows that the power-gap relationship is strongly affected by angular velocity (   ) and that at a high angular velocity significantly higher powers can be reached at the same gap.   - 60 -  Figure 6-3: Net power plotted against the inverse of gap for 3 refiner speeds using plate 3 (               ).   The same experiments were run for a different flow rate of        through the refiner with the same results, i.e. the power is independent of flow rate.  This is similar to the finding of Luukkonen [51].  Fibre length is known to be reduced when the gap reaches a certain critical gap,   , Mohlin [52]. Figure 6-4 shows fibre length as a function of plate gap.  For these trials, the plate gap was decreased and the power increased while the mass flow rate remained constant.  Thus for this trial, both specific energy and intensity increased.   The figure shows that for all three angular velocities, the fibre length was unchanged until the plate gap reaches a critical gap, near 0.25 mm, corresponding to that measured by Mohlin [52]. From Figure 6-4, we see that the angular velocity affects the critical gap at which cutting occurs and that the lower the angular velocity the smaller that gap at which cutting occurs.    - 61 -  Figure 6-4: Mean length weighted fibre length for various plate gaps for plate number 3 (               ).  The critical gap for fibre length reduction is near 0.25 mm and increases slightly with increasing    .   Intuitively, we assume that the intensity of treatment increases as gap reduces and not with specific refining energy.  Unfortunately, as power increases so does the specific refining energy and the intensity of treatment. Therefore it may not be readily apparent what causes fibre shortening, either high intensity treatment or high specific energy treatment. However, we know that if the energy is applied at relatively low intensity (gap > critical gap) through a large number of treatments (stages) fibre length is not decreased and we know that if the intensity is high, below the critical gap, then fibre shortening occurs at low specific energy. The onset of cutting is known to be an important operating point for optimizing fibre quality improvements. For example, Luukkonen et al. [1] shows that the  - 62 - maximum tensile strength increase occurs near the critical gap and similar findings were reported by Olson et al. [53]. We will study the development of tensile index increase in Section 6.6 of this dissertation.  In addition, it is expected that the feed pulp compressibility and friction characteristics strongly affect the power-gap relationship. Experimentally we observe that power varies with angular velocity cubed and the inverse of gap, as seen in Figure 6-5. This relation was first observed in the work by Luukkonen [51] using a wide range of refiner conditions. We investigate this for a wide range of plate patterns and observe the same relationship between power, rotational speed and gap size over the ranges of gap sizes between       and      .  Figure 6-5 shows the power-gap relationship for plate gaps smaller than those conventionally used in industry.  At large     or small gaps the power-gap relationship begins to deviate for different rotational speeds.  This deviation appears to be a function of refiner angular velocity and plate pattern.   For plate number 3, the deviation approximately corresponds to the onset of fibre cutting as indicated in Figure 6-4.  It is hypothesized that the sudden change in the slope in Figure 6-5 indicates a mechanistic change in energy transfer to fibres and may correspond to a reduction of the number of fibres between the bars.  However, we do recognize that the measurement error is substantial at large   . The cubic relationship means that if you use     to estimate gap then the faster refiner will have a higher calculated     at the same gap.  This has important implications to those that use     to size and develop performance criteria for LC refiners and is most likely responsible for much of the difficulty in applying     theory and other mechanistic models of refining throughout the industry where refiner angular velocity varies significantly.  If the refiners are compared at the same critical plate gap, where the cutting should be identical, then the higher speed refiner will have the same degree of cutting at a higher     than the lower speed refiner. That is, the refiners will have different performance at the same calculated    .   - 63 -  Figure 6-5: Power over angular velocity cubed versus inverse of gap for 4 plates used in these trials showing that over industrial ranges of gap sizes power is approximately proportional to    and the inverse of gap for: (a) plate number 3 with                , (b): plate number 4 with                , (c): plate number 2 with                 and (d) plate number 1 with                .    Figure 6-5 shows that power-gap data collapse to a single curve for the gap sizes bigger than       when power is divided by angular velocity cubed for all the 4 plates used in our refining trials. However, the slope of this curve is a function of plate pattern. This cubic relationship can be determined directly from non-dimensionalizing power with the basic design and operating variables: density  ,  - 64 - outer diameter    (in this study         ) and rotation frequency   (rad/s), which yields:                   (Eq. 53)   Figure 6-6: Dimensionless power and gap for 4 plates (plate 1, 2, 3 and 4 corresponding to     of 5.59, 2.74, 0.99 and 2.01       ) for three angular velocities of 800, 1000 and 1200     in the industrial range (Gap > 0.2 mm).   Figure 6-6 shows that the slope of the power-gap relationship is strongly affected by the geometry of the plate.  For the plate gap range of industrial interest and the type of pulp used in the experiments, plate pattern determines the function,    given in the following equation:                         (Eq. 54)  Where    quantifies the effect of plate pattern on refiner performance.  - 65 - At a constant gap size of 0.33 mm, (           ), plate number 1 consumes almost twice more energy than plate number 2 at the same rotational speeds.  We observed that for the coarsest plate studied in our experiments, i.e. plate number 3 with         and         a different trend in power-gap relationship is seen. This corresponds to an almost second order polynomial relationship between the dimensionless groups of power number and the inverse of gap. The exact reason for this phenomenon is not clear to us. One possible reason could be the wide bar and groove width of this plate. We are aware of different shape of vortices formed in plates with wide grooves which results in a different fibre capture mechanism for plates with coarse distribution of bars and grooves [49]. We assume that this theory works for fine bar plates where the bar width and groove is less than fibre length. For example we observe:          (Eq. 55)  In which   is the average fibre length used in the trials. However, this is without further justification. We exclude the non-linear behavior of plate number 3 and perform a linear regression analysis for the plates with linear relationship. Figure 6-6 also shows that     is not a good predictor of    and that a different geometry factor needs to be determined. In the next section, we will introduce a new geometrical parameter referred as Bar Interaction Length (   ) in this dissertation and show that Bar Interaction Length is a better indicator of the role of the plate geometry in energy consumption and cutting effects of refining.  6.3. Bar Interaction Length (BIL) The importance of the leading edges of bar crossings in beaters and refiners has been studied in different works published on theories of refining and is reviewed in Chapter 2 of this dissertation. We refer to these OHDGLQJ‎HGJHV‎RI‎EDU‎FURVVLQJV‎DV‎³%DU‎,QWHUDFWLRQ‎/HQJWK´‎DV‎ZH‎EHOLHYH‎LW‎LV‎WKH‎OHDGLQJ‎HGJHV‎RI‎URWRU‎DQG‎VWDWRU‎EDUV‎WKDW‎staple fibres on their edges and drag them into the small gap between refiner plates.  Since the common shape of intersecting polygons in a disc refiner with parallel  - 66 - distribution of bars and similar patterns of rotor and stator plate is a parallelogram, the length of the leading edges of bar crossings is equal to half the perimeter of intersecting polygons described in Chapters 4 and 5 of this dissertation elaborately.  A plate pattern with a larger bar interaction length provides a longer edge for fibres to get captured and receive the energy expenditure of refining on them. Figure 6-7 is illustrated to clarify this concept. The figure on the left shows a rotor bar approaching a stator bar while an individual fibre is present in the gap between plates. The figure on the right shows bar interaction length when a rotor bar passes a segment of stator plate and creates 4 number of bar crossing events.   Figure 6-7: The front view of the leading edge of rotor bar approaching the leading edge of stator bar capturing a fibre in an edge called Bar Interaction Length (left). The figure on the right shows the top view of a rotor bar over a stator segment with 5 bars creating an interaction length for fibres/bars. At the local position shown, 4 number of bar crossing events (            ) are created.   From the observed relationship between our dimensionless groups in Figure 6-6, a correlation to predict    is sought for an experimental multiple regression form. A total of    data points are used for a least square fit to solve for the regression  - 67 - coefficients, and the following form to predict dimensionless power number is obtained:                                      (Eq. 56)  In this equation     is Bar Interaction Length and             .  To determine the quality of the proposed correlation between the non-dimensional groups, measured power number values are plotted with values from the proposed model, i.e. Equation (56) in Figure 6-8.  Figure 6-8: Correlation between the predicted power number from Equation (56) and the measured power number from the trials for 3 plates (plate 1, 2 and 4 corresponding to     of 5.59, 2.74 and 2.01       ) for three angular velocities of 800, 1000 and 1200     in the industrial range (Gap > 0.2 mm).  - 68 - A good correlation between the predicted and measured net power number values         is seen. 6.4. Relationship between Operational Variables, Plate Design and Pulp Properties  In this section, we relate changes in freeness and mean fibre length to LC refining operating conditions and plate design.  Figure 6-9 demonstrates that for all the pulp refining samples and for a wide range of plate pattern and rotational speed, the freeness measured by Canadian Standard Freeness (CSF) correlates well with the changes in specific refining energy introduced by Equation (11). The impact of the plate design and rotational speed is transferring a higher energy to pulp rather than changing freeness directly. Once more energy is transferred to pulp, a higher drop in freeness is observed.    Figure 6-9: Canadian Standard Freeness plotted versus specific refining energy for all samples taken.  - 69 - We studied the relationship between fibre length reduction and gap size in Figure 6-4 by reporting the mean length weighted fibre length as a function of gap size. The gap size in which fibre shortening starts is a function of rotational speed and plate pattern. Also, decreasing the gap size between plates increases both the intensity of refining described by     and the net specific refining energy transferred to pulp at the same time. Therefore it may not be readily apparent what causes fibre cutting, either high intensity treatment or high specific energy treatment.  For all the refining samples, Figure 6-10(a) demonstrates that     is not a good predictor of change in fibre length. At constant     different patterns of plates cause different levels of fibre shortening. This could be caused by not properly considering the geometry of plate in     characterization.  Efforts have been made to propose better definitions for the intensity of refining so that it can provide a better practical prediction of the changes in pulp and paper properties. Modified Edge Load (   ) theory proposed by Meltzer et al. [54] is another term proposed to develop a unified concept for the intensity of refining. The relationship between the intensity proposed by Modified Edge Load theory and length weighted average fibre length is shown in Figure 6-10(b). Not a good correlation between refining intensity and change in fibre length is found.  In one of the most recent works by Roux et al. [19], tangential force per number of bar crossing is claimed to be a better universal term that can predict changes in fibre shortening and freeness. This is compared with other refining intensity definitions in Figure 6-10(c). This plot is very similar to the prediction of fibre length from     theory. The reason for this is similar bar and cluster angles of all the plates used in our experimental trials. By re-DUUDQJLQJ‎5RX[¶V‎HTXDWLRQ‎IRU‎WKH‎LQWHQVLW\‎RI‎refining, we get:                (Eq. 57)  In which:  - 70 -                                   (Eq. 58)  This equation is similar to those reported by     for refiner trials run with our experimental plates.   We observe that conventional intensity definitions do not predict change in fibre length properly.  Figure 6-10: Prediction of length weighted fibre length from different intensity equations: (a) Specific Edge Load (SEL), (b) Modified Edge Load (MEL), (c) Tangential force per bar crossing and (d) net energy per leading edges of bar crossings.    - 71 - Defining the intensity of refining as: the net energy per leading edges of bar crossings provides an excellent term for predicting fibre length reduction in LC refining of mechanical pulp. This is shown in Figure 6-10(d).  A critical intensity of          is observed as the point where fibre shortening occurs for all the plates and rotational speeds tested.  6.5. Predicting Bulk and Tear Index from Pulp Properties We begin by analysing the results of trials in a traditional manner. Most mills relate the operation of the refiner by examining the changes in tear index, tensile index and bulk as a function of refining operational conditions.  Dried bales of market CTMP pulp, made from a mix of spruce, pine and fir (SPF) with a low chemical chip pre-treatment from Northern British Columbia were shipped to the pulp and paper center at the University of British Columbia. The dried bales were re-pulped at the beginning of each trial to 3% consistency and refining trials were then conducted with the conditions described in Section 6.1.  175 samples of refined pulp were collected from our sampling line and tested for freeness (using TAPPI standard T227) and fibre length (using a Fibre Quality Analyzer). Hand sheets were then made and paper properties of bulk (using TAPPI standard T500), tear index (using TAPPI standard T414) and tensile index (using TAPPI T494) were measured.  At this point we turn our attention to the work of Forgacs [48] and investigate his K\SRWKHVLV‎WKDW‎³WKH‎structural composition of mechanical pulps is defined in terms of two factors, namely distribution by weight of fibre length, and a characteristic particle shape parameter, which was related to the bonding potential of the particles LQ‎PHFKDQLFDO‎SXOSV´ We choose freeness      as an indicator of particle shape and the average length weighted fibre length     as an indicator of fibre length distribution and study the relationship between these properties and paper properties of tear index, tensile index and bulk.  Figure 6-11(b) shows bulk as a function of specific refining energy. For all the samples taken and for different rotational speeds and plate patterns, bulk can be predicted from specific refining energy. For the refining trials of mechanical pulp  - 72 - studied in this dissertation, the dependency of freeness on specific refining energy is shown in Figure 6-9. This concludes that the paper property of bulk is correlated with the pulp property of freeness. This correlation is shown in Figure 6-11(a).   However, the paper property of tear index does not show to be correlated with pulp property of fibre length as it was shown in the work of Forgacs [48]. Figure 6-12 shows the relationship between tear index and average fibre length. As the gap size decreases, up to a critical gap, tear index increases with no change in the length of fibre. After this critical gap, fibres start shortening and tear index drops drastically. Significant scatter is seen when we plot tensile index as a function of mean fibre length or freeness. These results validate the hypothesis of Forgacs [48] predicting mechanical paper property of bulk from key pulp properties of mean fibre length and freeness but they do not provide a good correlation between paper properties of tensile index and tear index and pulp properties. This motivated us to improve this 2-parameter characterization by introducing new terms that can better predict tensile index development of mechanical pulp as a function of operating conditions. We will discuss this in Section 6.6.  - 73 -  Figure 6-11: (a) Correlation between bulk and freeness. (b) Correlation between bulk and Specific Refining Energy.  - 74 -  Figure 6-12: Correlation between tear index and average fibre length.   6.6. Development of Tensile Index We demonstrated in Section 6.5 that paper property of bulk is correlated with pulp property of freeness. However, relating tear and tensile to pulp properties does not provide any correlations in our experimental data collected.  Alternatively, much effort has been spent over years to predict tensile development form key operational conditions of refining. Some of these methods are explained in Sections 2.1 to 2.4 of this dissertation. However, the methods proposed do not predict performance of refining in developing tensile properly.  This motivates us to propose a new characterization method to predict changes in tensile index due refining.    - 75 -  Figure 6-13: Tensile index increase plotted versus specific refining energy for plate number 3 with                 at 3 rotational speeds of        ,          and         .   We begin by showing tensile index increase as a function of specific refining energy for plate number 3 with                 at 3 rotational speeds of        ,          and         .  The first observation is that there is an optimum specific refining energy for improving tensile index. This optimum specific refining energy depends on the rotational speed of refiner operation. For the refining trial at         , we were able to achieve the highest tensile index increase of         at the specific refining energy of           while running the refiner at         increases tensile index less than       at about            specific refining energy transfer into refiner. It should be noted that tensile index for the pulp used in our experiments before refining is          . The optimum specific refining energy for tensile index corresponds to the onset of fibre cutting discussed in Figure 6-4. We have showed the specific refining energy that corresponds to critical gaps for different rotational  - 76 - speeds in Figure 6.13. Once we reach the critical gap in which the fibres start shortening, the tensile index starts decreasing. This is in accordance to findings of Luukkoneon [51]. The second observation is that under low specific refining energy, the rotational speed of refiner does not make a difference in improving tensile index, however as it is shown in Figure 6-3 rotational speed does affect specific refining energy. In other words, under the same low specific refining energy and different speeds of refiner, same increase in tensile index occurs. Similar specific refining energies at different rotational speeds can be achieved by changing the gap size between plates. This is shown in Figure 6-13 where all different rotational speeds in the first region of the diagram (specific refining energy             ) show similar trends.   The third observation is that the optimum specific refining energy for tensile index increase changes linearly with rotational speed. This is demonstrated in Figure 6-14(a) where tensile index increase is plotted as a function of specific refining energy over rotational speed of refiner. Since the flow rate is held constant in all refining trials, the x-axis of Figure 6-14(a) is proportional to the intensity of refining defined by Specific Edge Load, i.e.         . We have replaced the x-axis with Specific Edge Load to determine the magnitude of intensities for reader in Figure 6-14(b). For the plate shown in this figure, we can conclude that tensile index reaches its maximum value at the intensity of about      . Higher rotational speed allows to achieve a higher specific refining energy and tensile at the same intensity.    - 77 -  Figure 6-14: Tensile index increase plotted versus: (a) specific refining energy over rotational speed, (b) intensity of refining defined by SEL. This figure is shown for plate number 3 at 3 different rotational speeds of        ,          and         .   - 78 -   Previous studies show that tensile index increase is linear if refined at constant intensity [51]. This was shown over a large range of specific refining energy and it can be seen in Figure 6-15.   Figure 6-15: Tensile index plotted versus specific refining energy at 3 different intensities taken from [51]. In these refining trials, the pulp was refined through multiple passes of refining at a constant intensity.   Figure 6-15 shows that as we increase the intensity, the slope of tensile index versus specific refining energy decreases. This strongly suggests the refining of mechanical pulp at low intensities where we obtain a higher increase in tensile index per unit of energy per mass of fibre.   - 79 - Also, for the refining trials studied in this dissertation the efficiency of refining to increase tensile index, a parameter shown by plotting the increase in tensile index per unit specific refining energy required for this increase, is a function of intensity defined by SEL. This is shown in Figure 6-16 for plate number 3 at 3 different rotational speeds.   Figure 6-16: Tensile index increase per unit specific refining energy as a function of intensity for plate number 3 at 3 different rotational speeds of        ,          and         .    Figure 6-16 strongly emphasizes the importance of low intensity refining for those interested in improving strength properties of paper sheets made from mechanical pulping.  The results presented up to this point were limited to a single plate (plate number 3 in Table 6-2) used in the pilot refining trials. Figure 6-16 fully characterizes tensile performance of a single plate geometry for a wide range of intensity, specific refining energy and rotational speed.  We investigate the validity of this theory in predicting tensile performance in low consistency refining for multiple plates (plates 1,2 and 3 in Table 6-2) by plotting  Figure 6-17(a).  - 80 - Figure 6-17: (a) Tensile index increase per unit specific refining energy as a function of intensity for 3 plates (plates 1, 2 and 3 in Table 6-2) and a wide range operating conditions. In (b), we achieve a performance curve for multiple plates of case (a) by plotting tensile index increase per unit specific refining energy as a function of net energy per unit of bar interaction area.  - 81 - Under the same specific refining energy and intensity, totally different behaviours for tensile index is achieved for different designs of plates used in the experiments. This proves the obvious shortcoming of     theory in predicting paper property of tensile index. However, defining the intensity of refining for tensile development as the net energy per unit of bar interaction area (   ) provides a much better performance curve for predicting tensile performance for a wide range of rotational speeds, intensities and plate patterns. We believe that through the use of the analytical and computational modelling of the geometry of refiner plates used in our pilot refining trials, a better geometrical pattern can be used to describe the development of tensile index. The results demonstrate that net energy per area of bar crossings can lead to a better understanding of tensile index increase than     term. This is shown in Figure 6-17(b) where a good correlation between tensile index increase, specific refining energy and net energy per unit area of bar crossings (        ) is seen. It should also be noted that this observation is seen for the trials in which each data point has a different Specific Refining Energy and Specific Edge Load.  We study the relationship between tensile development and change in bulk in Figure 6-18. This figure shows that as the strength property of tensile increases, the sheet gets denser and the bulk decreases. This relationship shows a linear trend. While the slope of this linear relationship is negative, i.e. the bulk decreases as tensile increases, it is desirable for paper making mills to optimize the refining operation somehow that it results in a small slope in bulk versus tensile relationship.   - 82 -  Figure 6-18: Bulk versus tensile index increase for a wide range of operating conditions. Results plotted for 3 plates (plates 1, 2 and 3 in Table 6-2) with              ,               and                 at 3 rotational speeds of        ,          and         .   Figure 6-19: Light scattering coefficient of a handsheet as a function of tensile index at 3 different rotational speeds of        ,          and          for plate number 2 in Table 6-2.  - 83 - Figure 6-19 shows development of light scattering coefficient as a function of tensile index. For the range of specific refining energy used in our refining trials, light scattering coefficient increases from           ⁄ to           ⁄ . This contradicts previous results reported by [55] and [56] where no development in light scattering coefficient was seen in LC refining of mechanical pulp.   6.7. Summary Although the physical mechanism for fibre development in LC refining still remains unknown, in this Chapter we have been able to propose an improved framework to predict:  1- Pulp properties of fibre length and freeness from operating variables of refining and the geometrical variable of Bar Interaction Length (BIL). This confirms the findings of those researchers who believed that fibres get captured and cut under shear stress between bars and fibres on the leading edges of bars. 2- Paper property of bulk from pulp properties of fibre length and freeness. There is no correlation between development of tensile index and pulp properties. We introduce a novel 2-parameter model that can predict tensile index development from operating variables of refining and the geometrical variable of refining area. This confirms the findings of those who believe that fibre strength properties develop in a compression mechanism in the area of refining between crossing bars.    - 84 - Chapter 7. Summary and Conclusions We simulate the geometry of LC refiner plates and propose analytical and statistical equations to predict the average values for area of refining, leading edges of bar crossings and number of crossing points.  In addition to this, computational modelling of the geometry, predicts temporal variations of the geometrical parameters mentioned above. We observe that area of refining is proportional to square of leading edges of bar crossings. Also, a more uniform refining treatment is achieved in refiners with finer distribution of bars and grooves. Bar Edge Length (   ), a parameter used to describe plate pattern and introduced in Section 1.5 of this dissertation, does not correlate to the leading edges of bar crossings but is a good representative of the number of crossing points.  A novel methodology is presented to characterize the patterns formed through the intersection of grinding surfaces. The methodology is fast and robust and is useful for cases in which a low-order accuracy result is tolerable. The benefit of the methodology is that no ordering of the vertices, formed in the region of intersection, is required. The utility of the code is tested for the industrially relevant case of low consistency refiners. We simulated the patterns formed between 320 different plates and characterized the area, perimeter and number of crossing points. An empirical relationship was advanced between the plate parameters and the average area of intersection. We demonstrate that the length of bar crossing edges (perimeter) formed from the intersecting bodies is proportional to the square root of its area and is not proportional to the industrially known parameter of BEL. We also showed the relationship between the average area of intersection and its variations. A smaller bar and groove pattern provides a more uniform treatment of refining. Plate pattern plays an important role in power-gap relationship. This relationship can change from a linear correlation to a polynomial depending on the geometry of the refiner plate.  From a total number of 175 samples collected in our pilot-scale refining trials, we experimentally demonstrated that net power consumption is proportional to rotational speed cubed and the inverse of gap for the ranges of gap larger than a  - 85 - critical gap, i.e.     . This critical gap corresponds to the onset of fibre cutting and the maximum development of tensile index in LC refining. We observe that the critical gap and the change in mean fibre length defined by Equation (12) can be predicted from the intensity of refining defined as: net energy per unit length of bar interaction length, i.e.         . Change in Canadian Standard Freeness, an industrial standard related to pulp dewatering, is related to Specific Refining Energy defined by Equation (11). Also, we present a correlation between paper property of bulk and changes in freeness. We also observe that there is an optimum Specific Refining Energy applied to a single-pass refining that creates the most development in paper property of tensile index. This optimum specific refining energy is linearly proportional to the rotational speed of refining. Consuming more energy than this optimum value in a single-pass LC refining, will damage the strength property of tensile index. The development of tensile index can be predicted from a single curve performance plotting: Specific Refining Energy and intensity defined as net energy per bar interaction area of refining, i.e.         . The contribution of this dissertation to LC refining of mechanical pulp is in particular to propose a two-parameter characterization by properly considering the plate pattern into this characterization. Once the geometry of plate is well considered, good correlations are found to identify key operating variables effecting pulp and paper quality development.         - 86 - Chapter 8. Recommendations for Future Work We recommend the future work to include different feed furnish, consistency and mass flow rates as these two factors were held constant in this dissertation. Power consumption in LC refining can be determined by a combination of two functions; one that describes refiner plate geometry,       and the other describes the feed furnish,                     reflects the stress-strain characteristics of the fibre network and       is a function of the bar interaction length for which expressions have been developed from the basic geometrical parameters. We recommend the future work to focus on experimental determination and theoretical understanding of the function that defines         . Also, the consistency of refining changes the power consumption and the critical gap in which fibre cutting starts. This results in a significant drop in tensile strength and tear index. We suggest future work to focus on how different refining consistencies change the critical gap discussed in this work. This is of significant importance in industry since continuously operating refiners at a constant consistency is difficult to maintain.               - 87 -  References [1] A. Luukkonen, "Development of a methodology to optimize low consistency refining of mechanical pulp," PhD Thesis, University of British Columbia, Vancouver, Canada, 2011.  [2] D. Page, "The beating of chemical pulps±the action and the effects,"9th Fundamental Research Symposium on Fundamentals of papermaking, Cambridge, vol. 1, pp. 1-37, 1989.  [3] K. Ebeling, "A critical review of current theories for the refining of chemical pulps," Int. Symposium on Fundamental Concepts of Refining, Appleton, USA, pp. 1-34, 1980. [4] J. J. Senger, "The forces on pulp fibres during refining," Master Thesis, University of British Columbia, Vancouver, Canada,1998.  [5] C. Ottestam and L. 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Kerekes, "Characterizing fibre shortening in low-consistency refining using a comminution model,"  Powder Technol, vol. 129, pp. 122-129, 2003.   - 92 - [54] F. Meltzer and R. Rautenbach, "Neue moeglichkeiten zur vorherbestimmung des technologischen mahlergebnisses,"  Das Papier, vol. 48, pp. 578-583, 1994.  [55] C. Sandberg, L. Sundstrom, S. Andersson and E. Nelsson, "New TMP line improves pulp quality and reduces energy consumption," Proc. Intl. Mech. Pulp. Conf., China Light Industry Press, Xi'an, China, pp. 472-475, 2011. [56] S. Andersson and C. Sandberg, "Mill experiences from a 72" LC refiner at holmen Paper Braviken mill," Proc. Intl. Mech. Pulp. Conf., China Light Industry Press, Xi'an, China, pp. 138-143, 2011.  [57] J. Lumianen, "Refining of chemical pulp, papermaking part 1, stock preparation and wet end," Jyväskylä: pp. 86-122, 2010.     - 93 - APPENDIX A. TWO INTERSECTING CIRCLES The method that is introduced in this work is not just limited to simple polygons. Since any curved edge can be created by infinite number of straight lines, we expect our method to work for curved objects as well if we represent that as a high-order polynomial. Intersecting two circles is one example of curved overlapping objects. Here, for simplicity, we consider two intersecting circles centered at (0, 0) and (d, 0), formed by polygons with a large number of vertices, (6281 vertices). These are labeled as    and    in Figure A.1. The exact value of the area of intersection was determined using an analytical solution. With         we estimate the area to be         which is accurate to 5 significant figures. The relative error in this case is 1.7 × 10í2.    Figure A-1: The area of intersection between two intersecting circular bodies consist of 6281 vertices and with        . The radius of each circle is 0.5m   - 94 - APPENDIX B. REFINER PLATE SIMULATOR (RPS) Refiner Plate Simulator is a software developed using 0$7/$%Œ‎interface. This software enables the user to either customize a LC refiner plate or use one of the common patterns of plates for the purpose of simulating the rotation of a rotor disc in front of a stator disc.  Figure B-1 shows a simulation case in which similar rotor and stator plates with a bar width of      , groove width of       , bar angle of       and a cluster angle of       are used. The outer radius of the disc is assumed to be          and there are 4 similar bolts (with a radius of    ) on each disc. We chose to show the simulation for 20 degrees of rotor rotation.  The outcome of the simulator is a video showing the rotation of a number of rotor bars (filled in yellow in Figure B-1) on top of a number of stator bars (filled in green in Figure B-1). The red rectangles in Figure B-1 represent the area of bar interaction. The simulator also produces plots showing temporal variations of bar interaction length     and bar interaction area        Figure B-1: Refiner Plate Simulator (RPS)    - 95 - APPENDIX C. TABLE OF EXPERIMENTAL DATA Table C-1: Pilot scale refining trial results for plate number 3 in Table 6-2. Plate Number Bar Width (mm) Groove Width (mm) Groove Depth (mm) Bar Angle Cluster Angle Ri (mm) Ro (mm) AWF141615103030 3.2 4.8 4.8 15 7.5 111.125 203.2  BIA* BIA (m2) BIL* BIL (m) Nc  Nseg BEL(km/rev)  0.070 0.006 0.291 4.309 510.849 48 0.99  Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 0.070 791 28.8 19.6 47.336 1.501 1.562 291.05 2.91   40.514 0.078 792 26.8 17.6 43.342 1.346 1.649        0.105 793 25.5 16.3 39.119 1.245 1.71 307.95 2.775 8.53 41.483 0.114 793 25 15.8 37.924 1.207 1.714        0.154 794 21.2 12 29.247 0.915 1.801 351.6 2.907 8.991 41.769 0.178 795 19.2 10 25.301 0.762 1.868        0.202 797 17.3 8.1 19.644 0.615 1.88 365.25 2.859 9.511 40.646 0.268 799 13.7 4.5 10.935 0.341 1.882        0.346 799 12 2.8 6.835 0.212 1.879        0.414 799 11.1 1.9 4.699 0.144 1.879 380.6 3.054 9.506 38.204 0.513 799 10.6 1.4 3.427 0.106 1.899        0.718 799 10.1 0.9 2.112 0.068 1.928        1.086 800 9.6 0.4 0.953 0.030 1.884 376.55 3.005 9.777  2.569 800 9.2 0 0 0 1.877        0.086 990 44.9 28.5 61.417 1.744 1.462 251.8 2.58 7.628  0.106 990 44.5 28.1 60.623 1.720 1.529 252.2 2.629 8.501  0.170 992 38.6 22.2 47.166 1.356 1.645        0.178 992 37.5 21.1 45.253 1.289 1.695 310.65 2.926 8.876  0.193 993 36.1 19.7 42.816 1.202 1.76 324.5 2.8 9.087 42.099 0.220 994 32.7 16.3 35.245 0.993 1.814 341.75 2.772 9.232 41.122 0.245 995 29.9 13.5 28.978 0.822 1.828 328.75 2.685 10.545 40.568 0.278 996 26 9.6 20.887 0.584 1.882        0.350 999 22.1 5.7 12.465 0.345 1.902 363.4 2.939 10.192 40.109 0.409 1000 20 3.6 7.897 0.218 1.882        0.508 1001 18.7 2.3 5.157 0.139 1.868        0.660 1001 17.9 1.5 3.222 0.090 1.885        1.123 1001 17.2 0.8 1.687 0.048 1.841 378.7 3.105 10.58 37.416 2.546 1001 16.4 0 0 0 1.864 379.7 2.824 10.531   - 96 - Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 0.082 1189 63.1 36.6 81.703 1.865 1.201 164.1 2.426     0.100 1189 62.4 35.9 80.323 1.829 1.221         0.124 1189 61.1 34.6 78.236 1.763 1.3 195.05 2.497 6.997   0.142 1190 60.4 33.9 75.064 1.726 1.323 194.9 2.587 7.771  0.166 1190 58.6 32.1 70.606 1.634 1.455 230.75 2.71 7.695 42.142 0.186 1191 57.1 30.6 67.438 1.557 1.498        0.216 1191 54 27.5 60.739 1.399 1.596 270 2.644   43.354 0.248 1192 50.2 23.7 53.437 1.205 1.712        0.279 1193 45.8 19.3 43.491 0.980 1.777 324.15 2.7 9.25 43.362 0.340 1194 40.6 14.1 31.824 0.715 1.816 337 2.909 10.162  0.402 1198 33.7 7.2 16.546 0.364 1.821 357.5 3.014 9.457 39.938 0.509 1199 30.1 3.6 8.237 0.181 1.817        0.657 1199 28.4 1.9 4.300 0.096 1.829        1.128 1199 27.8 1.3 2.849 0.065 1.893 353.15 3.084    2.571 1199 26.5 0 0 0 1.838 375.5 3.018 10.54                              - 97 - Table C-2: Pilot scale refining trial results for plate number 4 in Table 6-2. Plate Number Bar Width (mm) Groove Width (mm) Groove Depth (mm) Bar Angle Cluster Angle Ri (mm) Ro (mm) AWF141615102330  2 3.6 4.8 15 7.5 111.125 203.2  BIA* BIA (m2) BIL* BIL (m) Nc  Nseg BEL(km/rev)  0.065  0.005  0.278  6.109  1029.34  48 2.01  Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) 0.024 800 20 11.2 24.363 0.417 1.843     0.041 800 19 10.2 22.900 0.380 1.854 348.75 2.924 9.71 0.075 800 17.1 8.3 18.603 0.309 1.855 359.25 2.875 9.829 0.106 800 16 7.2 15.630 0.268 1.907 355.65 2.941 9.845 0.127 800 15.4 6.6 14.721 0.246 1.882 385.7 3.045 9.663 0.164 800 14.2 5.4 12.082 0.201 1.896 386.1 3.017 9.405 0.180 800 13.8 5 11.227 0.186 1.9      0.219 800 12.7 3.9 8.585 0.145 1.923      0.245 800 12.1 3.3 7.504 0.123 1.906      0.301 800 11.4 2.6 5.584 0.097 1.922      0.414 800 10.8 2 4.309 0.074 1.904 396.5 2.986 9.481 0.521 800 10.4 1.6 3.374 0.059 1.914      0.705 800 9.7 0.9 1.933 0.033 1.913      1.083 800 9.2 0.4 0.823 0.014 1.908      2.595 800 8.8 0 0 0 1.914 386.25 2.978   0.072 994 33.4 17.1 35.558 0.513 1.795 353.6 2.837 8.814 0.080 996 31.3 15 30.665 0.449 1.865 356.45 2.839 9.784 0.111 996 29 12.7 26.545 0.380 1.889 348.55 2.979 9.758 0.128 996 27.8 11.5 23.929 0.344 1.860      0.176 998 25.5 9.2 19.660 0.275 1.881 373.15 2.952 10.804 0.260 1000 22.6 6.3 13.480 0.188 1.887      0.310 1000 21 4.7 9.797 0.140 1.902 376.9 2.879 9.956 0.392 1000 20 3.7 7.708 0.110 1.932      0.507 1001 19.5 3.2 6.597 0.095 1.925      0.608 1001 19 2.7 5.452 0.080 1.934      2.464 1001 16.3 0 0 0 1.931      0.079 1200 54.8 27.7 56.587 0.689 1.752 288.15   8.968 0.085 1200 52.7 25.6 53.264 0.636 1.791 311.9 2.831 9.471 0.104 1200 50 22.9 48.145 0.569 1.807      0.115 1200 48 20.9 43.156 0.519 1.837 338.55 2.913 9.33 0.143 1200 44.1 17 34.844 0.42 1.839 367.9 2.938 9.826  - 98 - Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) 0.188 1200 41.3 14.2 29.273 0.353 1.857      0.233 1200 39.3 12.2 25.069 0.303 1.869 392.7 2.901 9.784 0.295 1200 36 8.9 18.642 0.221 1.828      0.360 1200 34.6 7.5 15.459 0.18 1.851      0.444 1200 32.2 5.1 10.397 0.126 1.904 384.9 3.018 9.831 0.587 1201 31 3.9 8.105 0.096 1.88      0.858 1201 29.9 2.8 5.766 0.069 1.847      2.554 1201 27.1 0 0 0 1.865 391.05 2.9 9.85                                      - 99 - Table C-3: Pilot scale refining trial results for plate number 2 in Table 6-2. Plate Number Bar Width (mm) Groove Width (mm) Groove Depth (mm) Bar Angle Cluster Angle Ri (mm) Ro (mm) AWF141615102030 1.6 3.2 4.8 15 7.5 111.125 203.2  BIA* BIA (m2) BIL* BIL (m) Nc  Nseg BEL(km/rev)  0.040  0.003  0.214  5.673  1340.2  48 2.74  Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) CSF (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 0.068 794 25.4 16 37.227 0.441 1.791 328.4 2.965 9.327 40.154 0.078 796 20.2 10.8 25.752 0.297 1.835 349.15 2.981 9.776 40.802 0.086 798 17.4 8 19.55 0.219 1.848 370.65 3.036 9.845 40.193 0.106 800 16.4 7 16.931 0.191 1.861       39.671 0.134 800 15.3 5.9 13.970 0.161 1.881 356.533 3.022 9.854 40.086 0.179 800 14.3 4.9 11.895 0.134 1.859 370.45 2.918 10.534 39.732 0.188 800 13.8 4.4 10.469 0.120 1.844         0.203 800 13 3.6 8.653 0.098 1.862         0.231 800 12.2 2.8 6.529 0.076 1.893 368 2.909 9.818 39.389 0.257 800 11.7 2.3 5.425 0.062 1.894         0.315 800 11.3 1.9 4.341 0.052 1.875 371 3.042 9.853   0.349 800 11 1.6 3.664 0.043 1.867         0.423 800 10.8 1.4 3.062 0.038 1.847         0.685 800 10.1 0.7 1.633 0.019 1.896         0.837 800 9.9 0.5 1.153 0.013 1.888         2.516 800 9.4 0 0 0 1.868 369.05 2.924     0.045 993 34.5 17.1 37.983 0.377 1.789 321.1 2.835 8.92 40.656 0.070 992 32.4 15 32.305 0.331 1.821 334 2.775 9.48 41.113 0.100 993 31.2 13.8 30.694 0.304 1.840 337.65 3.003 10.494   0.120 994 30.1 12.7 27.608 0.279 1.831 333.75 2.938 9.774 41.218 0.151 994 27.9 10.5 23.530 0.231 1.841         0.185 996 25.8 8.4 18.995 0.184 1.859         0.208 996 24.4 7 15.686 0.153 1.886         0.243 997 22.8 5.4 12.036 0.118 1.895 364.15 2.895 10.147 39.917 0.291 997 21.5 4.1 8.933 0.090 1.883         0.337 999 20.3 2.9 6.483 0.063 1.87         0.441 1000 19.5 2.1 4.647 0.045 1.852         0.593 1000 18.9 1.5 3.263 0.032 1.888         0.837 1000 18.3 0.9 1.949 0.019 1.845         1.084 1000 18.1 0.7 1.504 0.015 1.852         2.558 1000 17.4 0 0 0 1.887 385.25 3.027 10.019    - 100 - Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) CSF (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 0.035 1193 58.6 29.8 64.987 0.546 1.703 268.75 2.798 8.753   0.049 1193 56.6 27.8 60.049 0.510 1.725         0.071 1194 55.2 26.4 55.401 0.484 1.752 294.05     46.033 0.090 1195 52.4 23.6 49.535 0.432 1.781 312.3 2.86 9.143 41.109 0.116 1195 50.3 21.5 45.618 0.393 1.803 302.55 2.82 9.47 41.633 0.152 1196 46.6 17.8 38.125 0.325 1.834 315.95 2.821 9.858 42.245 0.187 1197 43.4 14.6 31.715 0.267 1.883         0.206 1197 41.5 12.7 27.486 0.232 1.897 347.1 2.977 10.045 41.412 0.255 1198 38.1 9.3 20.364 0.169 1.876         0.331 1200 35 6.2 14.170 0.113 1.886 361.9 2.941 10.247 40.325 0.411 1200 32.8 4 8.700 0.072 1.87         0.510 1200 31.6 2.8 6.240 0.051 1.856         0.727 1200 30.7 1.9 4.144 0.034 1.858         1.128 1200 30.1 1.3 2.731 0.023 1.852         2.518 1200 28.8 0 0 0 1.846 359.9 3.065                                 - 101 - Table C-4: Pilot scale refining trial results for plate number 1 in Table 6-2. Plate Number Bar Width (mm) Groove Width (mm) Groove Depth (mm) Bar Angle Cluster Angle Ri (mm) Ro (mm) AWF141615101530 1 2.4 4.8 15 7.5 111.125 203.2  BIA* BIA (m2) BIL* BIL (m) Nc  Nseg BEL(km/rev)  0.047  0.004  0.230  9.099  2689.504  48 5.59  Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 0.064 796 22.6 14.7 33.717 0.198 1.818 341.15 2.793 9.193 40.674 0.075 798 21.8 13.9 32.047 0.186 1.839        0.101 798 18.4 10.5 25.135 0.141 1.866 358.6 2.972 10.016 39..385 0.113 799 17.3 9.4 22.449 0.126 1.864 366.1 2.952 9.391 38.966 0.135 800 15.7 7.8 19.455 0.104 1.88        0.155 800 14.1 6.2 15.004 0.083 1.889 363.666 2.838 9.305 39.054 0.174 800 13.1 5.2 12.441 0.069 1.882        0.188 800 12.2 4.3 9.963 0.057 1.841 386.15 2.857 8.975  0.202 800 12.1 4.2 9.995 0.056 1.901        0.246 800 11.3 3.4 8.131 0.045 1.856 392.85 2.961 10.178 38.172 0.296 800 10.9 3 6.794 0.040 1.885        0.355 800 10.7 2.8 6.254 0.037 1.868 405.3 2.934 9.009  0.404 800 10.4 2.5 5.677 0.033 1.852        0.495 800 10.1 2.2 5.019 0.029 1.811        0.642 800 9.6 1.7 3.768 0.022 1.842 408.85 2.954 9.261 38.395 0.993 800 8.8 0.9 2.020 0.012 1.85        2.539 800 7.9 0 0 0 1.896 403.25 2.925    0.066 993 35.3 20.6 47.649 0.222 1.788        0.087 993 31.6 16.9 38.882 0.182 1.838        0.103 994 30.3 15.6 35.857 0.168 1.845 351.9 2.811 9.046 40.536 0.121 996 27.9 13.2 31.259 0.142 1.804        0.151 996 26.8 12.1 29.145 0.130 1.869 356.6 2.883 9.26 40.321 0.179 996 25.5 10.8 25.891 0.116 1.892        0.211 996 23.7 9 20.846 0.096 1.866 361.1 2.949 10.953 39.277 0.244 998 21.8 7.1 16.987 0.076 1.87        0.280 998 20.7 6 14.210 0.064 1.869        0.343 999 19.5 4.8 10.868 0.051 1.839 368.25 2.976 9.27 39.899 0.407 1000 18.9 4.2 9.466 0.045 1.882        0.516 1000 18.4 3.7 8.103 0.039 1.876        0.664 1000 17.8 3.1 7.060 0.033 1.851 381.45 2.98 10.528 39.362 0.885 1000 17 2.3 5.261 0.024 1.901 375.9 2.985 10.733 38.426  - 102 - Gap(mm) Rotational Speed (rpm) Total Power (kW) Net Power (kW) SRE (kWh/ton) SEL (J/m) Lw (mm) CSF (ml) Bulk (cm3/gr) Tear Index (mNm2/gr) Tensile Index (Nm/gr) 2.508 1000 14.7 0 0 0 1.887 379.55 2.778 10.173   0.061 1191 54.8 29.1 64.679 0.262 1.77        0.062 1191 54.5 28.8 64.012 0.259 1.783 261.7 2.779 8.875  0.068 1191 53.6 27.9 62.012 0.251 1.793 280.25 2.728    0.072 1192 52.7 27 60.012 0.243 1.798 299.87 2.778 9.787  0.108 1193 48.7 23 51.121 0.206 1.821 288.4 2.892 9.027 40.772 0.128 1194 45.1 19.4 43.119 0.174 1.827        0.172 1194 42.8 17.1 38.007 0.153 1.8465 347.25 2.885 9.352 40.294 0.209 1195 40 14.3 31.784 0.128 1.8305 336.8 2.951 9.898 40.871 0.240 1195 37.8 12.1 26.894 0.108 1.849 354.25 2.825 10.289 40.81 0.289 1196 35.6 9.9 22.004 0.088 1.82        0.373 1197 32.4 6.7 14.891 0.060 1.877        0.517 1197 31 5.3 11.780 0.047 1.905 372.3 2.931    0.721 1199 29.8 4.1 9.112 0.036 1.903 342.45 2.975 10.393 38.893 2.567 1200 25.7 0 0 0 1.863 375.25 3.035     

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