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Dynamic simulation of brown stock washers and bleach plants Wang, Roseanne Xiaohong 1993

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DYNAMIC SIMULATION OF BROWN STOCK WASHERS AND BLEACH PLANTS by Roseanne Xiaohong Wang  M.Eng. General Research Institute for Non-Ferrous Metals, China, 1987.  A THESIS SUBMITTE D IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  July, 1993 © Roseanne Xiaohong Wang, 1993  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of ^ce4.19 The University of British Columbia Vancouver, Canada  Date  ^  DE-6 (2/88)  479  ABSTRACT  Dynamic process simulators of brown stock washers and multistage bleach plants were developed for process control. SIMNON, a dynamic simulation language, was employed as a platform for constructing the simulators. The washing process simulator was used to investigate dynamic behavior of a three-stage countercurrent washing plant and to evaluate process control strategies. Good understanding of interactions of the operating units and the dynamics of the washing system were achieved, and significantly improved washing by better control were shown. For dynamic modelling of the bleach plant, pulp flow patterns in the retention towers were modelled using tracer responses from different towers. A model consisting of a cascade of CSTR's and a PFR showed good correspondence with measurements. A linear relationship was derived to correlate delignification and brightening. Unit operation models for mixing, reactions and washing were formulated using mass balances on liquor, fibres, chromophores, chemicals, pH and dissolved solids. Bleaching kinetic models from the literature were evaluated and incorporated into the bleaching process simulator. Using the simulator and industrial conditions, a dynamic model of a CDEDED bleach plant was built and used to simulate responses of the CE kappa number and brightness to changes in the chemical charge, incoming kappa number and production rate. Dynamic characteristics of nonlinearity and long time delay were identified. This simulator could be applied to other bleaching sequences to study process dynamics and control strategies if the bleaching kinetics used in those sequences were known.  11  TABLE OF CONTENTS  ABSTRACT ^  ii  LIST OF TABLES ^  vi  LIST OF FIGURES ^  vii  NOMENCLATURE ^  xi  ACKNOWLEDGMENTS ^  xv  DEDICATION ^  xvi  1 GENERAL INTRODUCTION ^  1  2 MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS^5 2.1 Introduction ^  5  2.2 Process Description ^  6  2.3 Model Development ^  7  23.1 Introduction ^  7  2.3.2 Process Variables and Analysis ^  7  2.3.3 Modeling of Seal Tank ^  9  2.3.4 Modeling of Drum Filter ^  11  2.3.4.1 Mechanistic Approach ^  11  Mat Formation^  12  Dewatering and Displacement Washing^  12  2.3.4.2 Efficiency Approach ^ 2.3.5 Washing Stage and Plant Models ^ 2.4 Simulation of Process Dynamic Behavior ^  15 16 18  2.4.2 A Single Washer ^  18  2.4.3 Three Washers in Series ^  19  111  2.5 Control Strategy Evaluation ^  25  2.5.1 Washing Process Control ^  25  2.5.2 Results and Discussion ^  28  2.6 Conclusions ^  34  2.7 Recommendations and Suggestions for Future Work ^  34  3 MODELING AND SIMULATION OF A BLEACH PLANT ^  37  3.1 Introduction ^  37  3.2 Process Description ^  38  3.3 Model Development ^  40  33.1 Process Variables and Analysis ^  40  33.2 Modeling Flow Patterns in Retention Towers ^  43  33.2.1 Introduction ^  43  3.3.2.2 Observations and Models ^  43  3.3.3 Kinetic Models ^  54  3.3.3.1 Introduction ^  54  3.3.3.2 Chlorine Delignification ^  59  333.3 First Alkaline Extraction ^  61  3.3.3.4 Chlorine Dioxide Bleaching ^  66  33.3.5 Second Alkaline Extraction ^  68  3.3.4 Correlation of Light Absorption Coefficient with Kappa Number after the Ei Stage ^  69  33.5 Mathematical Models of Unit Operations ^  72  3.3.5.1 Mixer ^  73  33.5.2 Tower ^  74  CSTR (Continuous Stirred Tank Reactor)^  75  PFR (Plug Flow Reactor)^  76  33.5.3 Washer ^  77  33.6 CDEDED Plant Model ^  77  iv  3.4 Dynamic Behavior of a CDEDED Plant ^  80  3.5 Conclusions ^  85  3.6 Recommendations and Suggestions for Future Work ^  88  4 GENERAL CONCLUSIONS^  89  REFERENCES^  90  A LITERATURE REVIEW OF PULP WASHING^  98  A.1 Fundamental Washing Studies ^  98  A.1.1 Filtration ^  98  A.1.2 Two-phase Flow ^  98  A.1.3 Compression and Drainage Properties of Wood Fibrous Mat ^ 99  Density, pm, and Porosity, c^  99  Permeability, kp ^  99  Relative Permeability, kr^  99  A.1.4 Displacement Washing ^ A.2 Washing Efficiencies ^  100 100  B LITERATURE REVIEW OF PULP BLEACHING ^  103  B.1 Lignin and Chromophores of Wood Pulp ^  103  B.2 Bleaching Kinetics of Kraft Pulp ^  104  B.2.1 Experimental Methods ^  104  B.2.2 Mathematical Models ^  105  B.3 Mixing in Bleaching ^  108  B.3.1 Segregation and Flow Patterns ^  108  B.3.2 Mixing and Bleaching ^  110  B.3.3 Bleaching Mixers and Retention Towers ^  110  LIST OF TABLES  2.1 Mathematical model of a washing stage ^  17  22 Operating data of an industrial vacuum drum washing plant ^  19  2.3 Mean and variance of dissolved solids carryover resulting from three control strategies. . . ^ 32 3.4 Results from fitting CSTRS+PFR and CSTRS models to tracer experimental data. ^ 49 3.5 Experimental conditions used in bleaching kinetics studies for different bleaching stages. . . ^ 60 3.6 Kinetic data base for alkaline extraction of chlorine bleached Kraft pulps ^ 62 3.7 Kinetic data base of alkaline extraction for chlorine dioxide bleached Kraft pulps ^ 64 3.8 Comparison between our modified model and Axegird model ^  66  3.9 Rate constants A1 and A2 for C102 bleaching for different pulps ^ 67 3.10 Stoichiometric constants n and A3 for C102 consumption in C102 bleaching for different pulps ^  68  3.11 Data base of brightness versus kappa number after the first extraction stage and light absorption coefficient calculated using Kubelka-Munk equation. ^ 71 3.12 Operating conditions of a CDEDED bleach plant. ^  80  3.13 Input data for simulation of a CDEDED bleach plant ^  81  3.14 Comparison between predicted and experimental data at steady state after retention towers of a CDEDED bleach plant ^ B.15 Relative reaction/mixing rates for common pulp mixers^  vi  82 111  LIST OF FIGURES  1.1 Kraft pulp process schematic. ^  2  2.2 Flow diagram of a three-stage vacuum drum washing plant. ^  6  2.3 Schematic diagram of a vacuum drum washing stage. ^  8  2.4 Comparison of flow pattern models for a seal tank. ^  10  2.5 Operating zones in a drum filter. ^  11  2.6 Simulation model structure for a three-stage washing plant. ^  17  2.7 Dynamics of a single washer: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=60 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage 20 2.8 Dynamics of 1st stage of a three stage washing plant: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=60 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash 22  liquor applied on the last stage. ^ 2.9 Dynamics of 2nd stage of the three stage washing plant: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=60 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage. ^  23  2.10 Dynamics of 3rd stage of a three stage washing plant: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=60 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage vii  24  2.11 Bode diagrams of dissolved solids in washed pulp leaving a three-stage washing plant to changes in pulp production rate ^  25  2.12 Bode diagrams of dissolved solids in washed pulp leaving a three-stage washing plant to changes in wash liquor flow rate ^  26  2.13 Control layout of a three-stage vacuum drum washing plant. ^ 29 2.14 Process disturbances used in simulation of control strategies for a three-stage washing plant: fluctuations in (A) dissolved solids content in pulp feed and (B) pulp production rate.  30  2.15 Dissolved solids carryover of a three-stage washing plant using different control 31  strategies^  2.16 Liquor levels in three seal tanks under proportional control (Strategy 3 example). ^ 33 2.17 Effects of anti-windup on control performance. ^  35  3.18 Process flow diagram of a CDEDED bleach plant. ^  39  3.19 Process units and variables of a bleach stage. ^  41  3.20 Typical RTD in a low consistency tower ^  46  321 Typical RTD in a medium consistency tower. ^  47  322 Flow patterns, plots of associated residence time distributions and tracer responses for an upflow tower^  48  3.23 Measured residence time distribution and model predictions for an upflow C tower with bottom and mid circulators in operation. ^  50  3.24 Measured residence time distribution and model predictions for an upflow C tower with a bottom circulator in operation. ^  51  3.25 Measured residence time distribution and model predictions for a C tower. ^ 51 326 Measured residence time distribution and model predictions for a downflow El tower. . . ^ 52 VIII  3.27 Measured residence time distribution and model predictions for an upflow DI tower. . . . 52 3.28 Measured residence time distribution and model predictions for a downflow E2 tower. . . . 53 3.29 Measured residence time distribution and model predictions for an upflow  D2 tower.  . . . 53  3.30 Three sequences of a CSTRS+PFR model with two CSTR's. 54 3.31 Comparison between CSTRS+PFR and PFR model responses of residual chlorine to a step change in inlet kappa number. ^  55  3.32 Comparison between CSTRS+PFR and PFR model responses of residual chlorine to a step change in chlorine charge. ^  55  3.33 Comparison between CSTRS+PFR and PFR model responses of kappa number after C tower to a step change in inlet kappa number. ^  56  3.34 Comparison between CSTRS+PFR and PFR model responses of kappa number after C tower to a step change in chlorine charge^  56  3.35 Difference between CSTRS+PFR and PFR models responses of residual chlorine dioxide to a step change in chlorine dioxide charge. ^  57  3.36 Difference between CSTRS+PFR and PFR model responses of brightness after DI tower to a step change in chlorine dioxide charge. ^  57  3.37 Comparison between CSTRS+PFR and PFR model predictions of residual chlorine dioxide as a function of chlorine dioxide charge^  58  3.38 Comparison between CSTRS+PFR and PFR model prediction of brightness after D1 tower as a function of chlorine dioxide charge  ^58  3.39 Kappa number during El bleaching of chlorine bleached pulps as calculated by our modified model and Axegard's model^  65  3.40 Kappa number during El bleaching of a chlorine dioxide bleached pulp as calculated by our modified model and Axegfird's model. ^  67  3.41 Light absorption coefficient vs. kappa number after first extraction stage ^ 72 ix  ^  3.42 Block diagram of a bleaching unit operation model: mixer^  73  3.43 Block diagram of a bleaching unit operation model: reactor. ^ 75 3.44 Block diagram of a bleaching unit operation model: washer. ^ 77 3.45 Flowsheet of a typical CDEDED bleach plant and corresponding simulation block diagram. ^  78  3.46 CDEDED bleach plant response to step changes in total available chlorine charge in CD stage. ^  83  3.47 CDEDED bleach plant response to typical variations in incoming kappa number. ^ 84 3.48 CDEDED bleach plant response to a step change in pulp production rate ^ 86 A.49 A generalized washing system described by Norden model. ^ 101 B.50 An example of bleaching reaction characteristics  x  108  NOMENCLATURE Ai^ Constant in Equation 3.39, kg2,m-4, A2^  Constant in Equation 3.39, kg2/m4  A3^  Constant in Equation 3.40, m2"/Icgn-1  a^Coefficient in Equation 3.46, kg/m2 am^Specific resistance of mat, m/kg Constant in Equation 3.46, m2/kg Bj^  Constant in Equation 3.42, kg2.m-4.mor0.1.Lo.1.min-03  B2^  Constant in Equation 3.42, mo1"8.1,- 0.08• m3 m2 kg1 Dissolved solids concentration, kg/m3  Cm^  Fibre consistency, % on slurry Dimensionless dissolved solids concentration  DF^Dilution factor (refer to Equation 2.13) DR^Displacement ratio (refer to Equation 2.15)  Residence time distribution, %/min EN^ Norden efficiency factor, dimensionless  Ea^Activation energy of bleaching reaction, kl/mol Volume of filtrate collected per unit filtration area, m Gp(s)^Transfer fuction of washing plant, % .min/kg  Chlorine charge factor, % available C12 on o.d. pulp/unbleached kappa number Hm^  Mat thickness, m  Hs/^Liquor level in seal tank, % on total tank level Content of chromophores, expressed as kappa number in delignification stage and light absorption coefficient in brightening stage Ka^  Kappa number, dimensionless  Kat-^Floor level of kappa number, ie. the minimum value of kappa number reached in a delignification reaction Kai and Ka2^Kappa number of fast and slow bleaching reactions Kk^  Light absorption coefficient, m2/kg  Kicr^  Floor level of light absorption coefficient, m2/kg  Kpo and Kp^Gain of washing plant, %  xi  .min/kg  Constant of water dissociation, 10-14 mo12/L2 K'^Initial value of kappa number Rate constant of bleaching reaction/. kE•^Darcy's permeability, m2 kr^ Relative permeability, dimensionless ki and k2^Rate constants of fast and slow bleaching reactionf  Fow rate of liquor in pulp stream, kg/min Number of CSTR's in series Exponent in Equation 3.40 Pe^ Pee let number, dimensionless  AP^Pressure drop across mat, Pa Velocity of wash liquor through mat, m/s Ideal gas constant, 8.314 kJ/mol/K ^ Reflectance at 457nm (Brightness), %ISO Itoo Bleaching reaction rate, ie. rate of kappa number decrease in a delignification or rate of light absorption conefficient decrease in a brightening reaction RW^Wash liquor ratio (see Equation 2.9), dimensionless  Light scattering coefficient, m2/kg S,,,^ Saturation of mat, dimensionless  Laplace operator Temperature, K Time, min Mean residence time, min Mean residence time in CSTRS, min Residence time in PFR, min Mean residence time in retention tower, min At^Measuring time interval, min V^ Fow rate of liquor in non-pulp stream, kg,/min  Volume of seal tank, m3 W„,^Mass of dry mat deposited per unit filtration area, od kg/m2 Their units vary with different reaction orders.  xii  X  ^  Mass percentage of component in pulp liquor, % Mass percentage of component in non-pulp liquor, % Dimensionless distance  Greek Symbols:  A^Neutralized II+ and OH- during mixing and washing, % on liquor E^Mat porosity, dimensionless Liquor viscosity, Pa •s Liquor density, kg/m3 Pm^ Mat density, od kg/m3 o^ Standard deviation expressed as percentage of mean, %  Tp^  Dimensionless time Time constant of washing plant, min Stoichiometric coefficient of bleaching reaction, % on od. pulp/(kappa number) for delignification and % on o.d pulp/(light absorption coefficient) for brightening  Subscripts:  Filtrate off drum filter exp^Experimental value Bleaching liquor component, i = C (chemical), 1-1+, OH-, or DS (dissolved solids) pred^Predicted value Recirculated filtrate Vat slurry Wash liquor onto drum filter 0^ Pulp stream into process unit 1^ Stream (pulp or non-pulp) off process unit 2^ Non-pulp stream into process unit Superscripts:  Bleaching result of PFR determined by Equation 3.65  Abbreviations:  CSTR^Continuous stirred tank reactor CSTRS^Continuous stirred tank reactors in series DS^Dissolved solids PFR^Plug flow reactor RTD^Residence time distribution TAC^Total available C12, % on pulp Abbreviations for Bleaching Stage:  C/D^Chlorination with C12 and 002 substitution (10 - 70% as active chlorine) (C.+Dioo-x) ^Simultaneous addition of x% (as active chlorine) C12 and (100-x)% (as active chlorine) 002 CD^Chlorination with C12 and small percentage of 002 (5. 10% as active chlorine) DI^First 002 bleaching stage D2^ Second C102 bleaching stage Dc^Chlorination with 002 and small percentage of C12 ( <50%) (DxCloo-x) ^Chlorination with sequential addition of x% (as active chlorine) C102 followed by (100-x)% (312. Time delay between additions is not specified. Ei^First alkaline extraction stage Eo^First alkaline extraction with addition of 02 E2^ Second alkaline extraction stage 0^Oxygen delignification  x iv  ACKNOWLEDGMENTS  I extend my sincerest appreciation and thanks to my thesis supervisors, Dr. Patrick Tessier and Dr. Chad Bennington for their guidance, kind support, encouragement and valuable discussions throughout the course of this research, without which this work would not have been possible. I am also indebted to Dr. Bruce Bowen and Dr. Richard Branion for providing valuable advice and suggestions. I wish to thank Patti Turner of PAPRICAN for providing information for the simulation of brown stock washers. I would appreciate academic assistance of Dr. Yu Qian, Dr. Ruhe Zhao, Mr. Ky Vu and Mr. Scott Morgan. I would like to thank my colleagues and also my friends, Mr. Xingsheng Qian and Mr. Lijun Wang for sharing a pleasant time with them. The consistent computer network support from Mr. Rick Morrison and Mr. Kristinn Kristinsson is greatly acknowledged. I would like to express my special thanks to Ms. Rita Penco for her patient assistance in my literature search. I am thankful to the other members of the PAPRICAN group at UBC and the staff of the chemical engineering department office for their assistance. I would like to thank the National Sciences and Engineering Research Council of Canada for providing financial support and excellent computer facilities. I am grateful to my little daughter, my husband and my parents in law for their contributions to a happy family which is the most important for the success of my thesis. Finally, my greatest thanks go to my parents for their love and enormous sacrifices for their daughter.  XV  DEDICATION  x vi  CHAPTER I: GENERAL INTRODUCTION  CHAPTER 1 GENERAL INTRODUCTION Pulp and paper mills are made up of a wide variety of process units which transform wood into pulp and paper products. Numerous flows of pulp, water, chemicals and dissolved solids must be recycled, leading to a high degree of interaction among the process units. Complicated physical and chemical phenomena take place in the many unit operations. The kraft pulp process outlined in Figure 1.1 is considered to be typical. There are three important process operations in converting wood chips into bleached pulp: digestion, brown stock washing and bleaching. During digestion with chemicals and heat, the lignin and other alkali-soluble constituents of wood are dissolved in the cooking liquor and the fibres are liberated. The mixture of pulp and spent cooking liquor after digestion, referred to as brown stock, is fed to a series of washers, where the spent cooking liquor is separated from the pulp using fresh or reused water. The spent cooking liquor, also called weak black liquor, is then delivered to the recovery system to recycle cooking chemicals and recover thermal energy. The washed pulp is transferred to the bleach plant where the pulp is subject to a sequence of chemical treatments to increase pulp brightness. Industrial processes can be modeled mathematically based on mass, energy and momentum balances. Computer simulation can be of considerable help in solving design and operation problems. This is why there has been a tremendous increase in the use of computer simulation in the pulp and paper industry (Roche and Bouchard, 1982; McConnell et al., 1992). The most common applications have involved steady-state simulation, especially in areas of the process design and operation optimization. Many commercial steady-state simulators have been available for pulp and paper processes, such as GEMS (Edwards et al., 1983), MASSBAL (1983), PAPMOD (1988), FlowCale (1983) and MAPPS (1984). For use in process control design, a few simulators, such as GEMS, PAPDYN (1990) and MAPPS, have been modified by including the dynamics of storage tanks to provide time-dependent simulation. These simulators, basically consisting of steady-state unit models described by relatively simple algebraic equations, are inadequate to accurately characterize the dynamic behavior of various pulp and paper processes. In order to help the pulp and paper industry 1  Chapter 1: GENERAL INTRODUCTION  Wood Chips  Cooking Liquor  Digestion Brown Stock Wash Water  ^i  Make-up Chemicals  Recovered '41111Chemicals  Brown Stock Washing  Black Liquor  Recovery  lo Energy  Un leached Pulp ,  Bleaching  Bleaching Chemicals 4^ -41-- Heat  Bleached Pulp to Market or to Paper Machine  Figure 1.1: Kraft pulp process schematic.  increase process control abilities and understand the effect of dynamics on its operation, there is a need for a more realistic dynamic simulator which provides detailed dynamic models of the process units. Such a simulator can be used as a mathematical "pilot-plant" to investigate process behavior of an actual plant and to test different control strategies. Interactions among the process units would become evident and transient responses of the overall system to disturbances (such as changing feed rates, failure of equipment or different operating strategies) could be predicted. Dynamic simulators can also help new operators learn about the effects of operation changes and the benefits of properly tuned control systems. Powerful computer technologies are necessary to develop a new dynamic process simulator for the pulp and paper industry. From a software point of view, there are several alternatives 2  CHAPTER I: GENERAL INTRODUCTION  for our purpose: from general languages to equation-oriented simulators. FORTRAN and C may be employed but are unwieldy for complex applications. A good simulation package must be robust, well-structured, versatile and user-friendly. We think that SIMNON, an equation-oriented dynamic simulator, is a suitable choice. SIMNON was developed in the Department of Automatic Control of the Lund Institute of Technology in 1979 (SIMNON, 1991). It is designed for simulating dynamic systems whose behavior is represented by nonlinear, ordinary, differential or difference equations. A complex system may be described as an interconnection of simpler subsystems. This modular feature provides considerable flexibility for constructing plant models where unit models can be easily modified and rearranged for different flowsheets. Advanced integration algorithms are supplied to improve executive time and simulation accuracy for the long term as well as very fast response. External modules written in FORTRAN or C may be embodied into the SIMNON framework to enhance the capabilities in computation and system description. SIMNON has been used for education and research in such diverse disciplines as automatic control, biology, chemical engineering, economics and electrical engineering at many universities. The original version was implemented in PC/DOS computers and a new version can be also run under the UNIX operating system on Sun/Sparc workstations. Using SIMNON as a platform, dynamic simulators for brown stock washers and a multistage bleach plant have been developed. Firstly, we used the brown stock washers as an example to test the applicability of SIMNON . The model developed for the brown stock washer can also be used for describing the pulp washer in the bleach plant. A series of brown stock washers form a countercurrent system of pulp and wash liquor with significant recycle existing within each stage. We will show how the washer model incorporated into SIMNON can be used to study the dynamic behavior of a multistage countercurrent washing system, including interactions among the washing stages and the dynamic response of the washing plant to manipulation of the wash water flow rate and to major process disturbances. We will also test and compare different control strategies for the washing plant dueugh the use of the simulator. Once satisfied that SIMNON was able to handle a relatively simple but very representative process, our work moved on to a more difficult problem: a multistage bleach plant. Operations in the 3  Chapter I: GENERAL INTRODUCTION  bleach plant are very complicated mainly due to multistage chemical reactions with long retention times, complex compositions of process streams and the large number of recycled flows. Few attempts have been made to model pulp bleaching processes, particularly the dynamic behavior of the process. To describe the dynamics of such a system, detailed investigations of the kinetics of the bleaching reactions and the pulp flow in bleaching towers were made. A combination of SIMNON and a FORTRAN algorithm was used to solve the partial differential equations which represent the reactor behavior varying with position as well as time. The unit operation models and appropriate bleaching kinetics were combined together to describe each bleaching stages. The integrated model can be used to study transient responses in the final kappa number, brightness and residual chemicals to changes in various process variables. A simulation model of a five stage bleach plant having a CDEDED sequence was built up by connecting the corresponding stage models. The dynamic response of different stages of the bleach plant were obtained when changes were made to the unbleached pulp kappa number, production rate and chemical charge.  4  CHAPTER 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  CHAPTER 2 MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  2.1 Introduction  The primary purpose of the brown stock washing plant in a kraft pulp mill is to economically remove the maximum amount of dissolved organic and soluble inorganic materials present in the pulp at the end of the cooking or digestion of wood chips with the minimum amount of fresh or reused process water. Therefore it has two effects on the pulping process. Firstly, it cleans the pulp for bleaching treatments. Secondly, it is the first step in the recovery process which recycles the inorganic products and recovers the thermal energy of organic components extracted from the wood. Better washing leads to more pulping chemical recovery, less energy cost for the recovery evaporation, reduced bleach chemical demand and decreased mill discharges of BOD, COD and AOX. The washing plant possesses typical features of a pulp and paper process. It is a multiple input, multiple output system with recycle loops and countercurrent flows. Each stream contains water, fibres and dissolved solids. Therefore, this plant is a very good example to examine the capability of SIMNON for developing a dynamic simulation of other pulp and paper processes. The model developed for the brown stock washer is also useful in simulating washers in the bleach plant. Dynamic simulation of brown stock washers has been done in previous studies (Perry et al., 1975; Lundquist, 1980; Nase and Sjoberg, 1989; Turner et al., 1990), making it possible to compare our results with theirs. In this chapter, the dynamic mathematical model of a vacuum drum washer is described. Then applications of the dynamic washer simulator are demonstrated through open-loop and closed-loop simulations. The open-loop simulation was used to investigate the dynamic responses of a three-stage brown stock washing plant to changes in wash liquor flow and process disturbances. The closed-loop simulation was used to compare different control strategies. 5  Chapter 2: MODFI LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  2.2 Process Description  Brown stock washing is carried out in a series of washers that form a countercurrent system. Each washer represents a washing stage. The vacuum drum washer is the most commonly-used washer in brown stock washing and also in bleach plants (Crotogino et al., 1987). Figure 2.2 shows a flow diagram of a typical brown stock washing plant using three vacuum drum washers. The incoming pulp stream (brown stock) is fed into the first stage and the wash water is added countercurrently. The outgoing pulp stream from each stage goes to the next stage for further washing and the outgoing filtrate is recirculated as dilution liquor for the incoming pulp or is used as the wash liquor for the previous stage. The filtrate from the first stage is sent to the evaporator train. The washed pulp from the last stage goes to the bleach plant.  Figure 2.2: Flow diagram of a three-stage vacuum drum washing plant.  The operation of a vacuum drum washing stage consists of several steps. Pulp enters the washer at medium consistency (6-12%) and is diluted by recirculated filtrate to low consistency (0.75-2.5%) before entering a vat which contains a wire-cloth covered drum. As the drum rotates through the vat slurry, a lower pressure inside the drum extracts the liquid from the vat slurry with pulp forming a mat on the surface of the drum. After the mat emerges from the slurry, liquid is further extracted as it moves into the displacement washing zone where cleaner wash liquor is applied to displace the dirty vat liquor. The mat is further dewatered and finally removed from the wire surface at a 6  CHAPTER 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  medium consistency. The filtrate collected from the drum goes down through a drop leg to a seal tank for deaeration and then is recirculated as dilution liquor or used as shower liquor on the previous stage. The recirculated liquor flow rate is roughly ten times larger than the flow rate of the wash liquor to the previous stage. 2.3 Model Development 2.3.1 Introduction  The great dependence of the other parts of the mill on the brown stock washing plant explains the interest that has always been shown in it. Many projects have been carried out modelling washing process, particularly the works of Norden et al. (1966; 1987), Tomiak (1974) and Cullinan (1986). All these studies deal with the static operation of process, particularly for the purpose of designing the washing plants and choosing their operating conditions. To improve the control of these processes, it is necessary to know the connections between the action variables and the output variables in the form of dynamic models. Some such studies have been carried out especially by Perry et al. (1975), Perron and Lebeau (1977), Han (1989) and Turner et al. (1990). They all employed complicated mechanistic models, involving fundamental fluid flow and mass transfer principles. A model integrating the Norden efficiency factor with the dynamic tank seems to be best for describing mill washing systems (Lundquist, 1980; Nase and Sjoberg, 1989). The present study dims at identifying a methodology which can facilitate the simulation of washing plants and the evaluation of control strategies. The analysis and modelling of a vacuum drum washing system are presented in this section. 2.3.2 Process Variables and Analysis  A vacuum drum washing stage can be divided into the following three process units shown in Figure 2.3: 1. dilution vat, where the incoming pulp at medium consistency is diluted to low consistency by  the recirculated filtrate, 2. drum filter, where a portion of the dissolved solids are separated from the fibres by thickening and washing with cleaner wash liquor and 7  Chapter 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  3. seal tank, where the filtrate is deaerated and then is recirculated as dilution liquor or pumped to the previous washer as wash liquor. The pulp streams entering and exiting each unit are characterized in terms of the liquor flow rate  (L), fibre consistency (C.) and content of the dissolved solids (XDs). The dissolved solids include inorganics and soluble organics. The wash liquor and filtrate of each unit are characterized in terms of the liquor flow rate (V), and dissolved solids content (YDS). The fine fibres which are washed into the filtrate are neglected. First, it is necessary to compare the residence times of the different process units. This allows us to considerably simplify the description of the washing stage by dropping the dynamics of those that have very fast response times and thus don't affect the overall system dynamics. The seal tank  Wash Liquor V2, YDS2  Washed Pulp Li, Cntl , XDSI  Filtrate to Previous Washer 4^ VI, YDS/ ,  L - Pulp liquor flow rate V - Wash liquor flow rate C. - Fibre consistency XDS  -  YDS -  Dissolved solids content in wash liquor Dissolved solids content in pulp liquor  Figure 23: Schematic diagram of a vacuum drum washing stage. 8  CHAPTER 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  has a much longer residence time than the dilution vat and drum filter because of its large liquor inventory. The filtrate stays in the seal tank for about 10 minutes. Pulp remains in the vat for only a few seconds and passes over the drum in less than 1 minute. Therefore when modelling the dynamics of a complete washing stage, it is assumed that the dilution vat and drum filter are operated in quasi-steady state, i.e., their responses to changes in operating conditions are instantaneous. The transient behavior of the seal tank governs the overall stage dynamics and is considered alone. The models of the washing units, stage and entire plant are described below.  2.3.3 Modeling of Seal Tank To describe the dynamics of the seal tank, plug flow and perfectly mixed flow models were tested. The real seal tank should act somewhere between these two ideal limits. However, the effect of different flow patterns in the seal tank on the dynamic behavior of the entire washing system is diminished by strong interactions between the adjacent process units. Step responses of washed pulp predicted using the two ideal flow models are approximately the same whether for a single washer or a three-stage washing plant as shown in Figure 2.4. The perfectly mixed flow model was chosen to represent the seal tank. This model consists of the following equations: Overall mass balance: dffst^(rd—li-14) dt^Vst • PI  (2.1)  and dissolved solid mass balance: Carp^Vd • (YDSd YDS1)  irscHst.p,  (2.2)  where 1131 is the percentage of liquor level in the total seal tank level, Vit is the seal tank volume. The liquor density, pi, is a function of the temperature and dissolved solids concentration of the liquor. Some empirical correlations for black liquor density have been reported (Venkatesh, 1985; Terry, 1988; Branch, 1991). However, it is reasonable to assume a constant liquor density since the dissolved solid content of the filtrate in brown stock washing is fairly small (<20 %). 9  Chapter 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  2.64 --  2.62 0  I  2.6  2.56  •S - -*  2.54  *  A  0  0  I  r  Single Washer - - - - Perfectly mixed flow Plug flow  I  t  2.52  I  25  I  2'48 0  50^100^150^200^250^300  0.242 --  0.24 ts--2.° oo 0 ....  -  t  I? 4 3 rn  0  I  238  a. a a.  I  --  Three Washers in Series  0.238  - — Perfectly mixed flow Plug flow  rj 0.236  4 1 0.234 0 0 0.232 rz 0 al. .g 0.23 . 4 3 .5 0.228 -3"  E  0.226 0.224 ^ 0  100  ^  200  ^  300^400^500^600^700^800 Time (min)  Figure 2.4: Comparison of flow pattern models for a seal tank.  10  CHAPTER 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  Wash Liquor  Vat Slurry  1 - Mat Formation 3- Displacement Washing 2- Dewatering^4- Dewatering  Figure  2.5: Operating zones in a drum filter.  2.3.4 Modeling of Drum Filter  The operation of the drum filter involves complicated fluid flow and mass transfer. Therefore, a mechanistic analysis may be used for a detailed description of the drum filter operation. On the other hand, a simple efficiency approach, such as the Norden efficiency factor (Norden, 1966; Norden et al., 1973) or the displacement ratio (Perkins, 1954), can be used to represent the steady-state operation of a drum filter. The Norden efficiency factor is superior to the displacement ratio for washing process simulation since it is less sensitive to changes in the dilution factor — an important process condition representing the wash liquor applied (Crotogino et al., 1985). Both a mechanistic approach and the Norden model have been tested in order to find out which one is more practical for the simulation of mill washing systems. A detailed literature review of washing mechanisms and the concepts of the Norden efficiency factor and displacement ratio are presented in Appendix A. 2.3.4.1 Mechanistic Approach  The separation of dissolved solids from fibres in the drum filter consists of four operating zones: mat formation, dewatering, displacement washing and further dewatering, as illustrated in Figure 2.5. Various models have been proposed which describe the fundamental phenomena occurring during each phase (see Appendix A). Sperry's filtration, Han's two-phase flow and Brenner's axial dispersion models are employed for an overall description of the drum filter since they are relatively simple and generally accepted. 11  Chapter 2: MODFLUNG, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  Mat Formation As the drum rotates through the vat slurry, a lower pressure inside the drum extracts the liquid from the vat slurry and a mat forms on the surface of the drum. This action is described mainly based on Sperry's filtration equation (Sperry, 1916): dG ^AP dt = Wm  (2.3)  where: G^= volume of the filtrate collected per unit filtration area, m I^= residence time since the pulp slurry enters the filtration zone, s  AP = pressure drop across the mat, Pa pi^= liquor viscosity, Pa.s  am^= specific resistance of the mat, in/kg = mass of dry mat deposited per unit filtration area, od kg/m2 Both G and Wm can be expressed in term of the mat thickness, i.e., pm • Hm G = pi^ ‘-'171V • A  and Wm = pm • Hm^  (2.4)  where: H. = mat thickness, m  Cm, = vat consistency, % PI^= liquor density, kg/m3 Pm = mat density, od kg/m3  When these expression for G and Wm are substituted into Equation 2.3 and the latter is integrated, the mat thickness after filtration can be found for a given drum vacuum and vat consistency. Dewatering and Displacement Washing After the mat emerges from the slurry, dewatering, washing and further dewatering take place. The liquid flow through the mat during these steps is 12  ^  •  CHAPTER 2: MODFI J ING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  represented by two-phase flow model proposed by Han (1989): dS,,, dt  q kr kr) c • Hm  P  c•  HI . pi  (2.5)  where: S.^= saturation of the mat, dimensionless  = velocity of the wash liquor (zero for deWatering), m/s  •  1cD^= Darcy's permeability, m2  kr^= relative permeability, dimensionless = mat porosity, dimensionless  Integration of Equation 2.5 yields the saturations at different positions in the drum rotary direction (which is related to i). Then the profile of the mat consistency can be calculated from the saturation. Displacement washing occurs when the wash liquor is applied to the mat. The dissolved solids concentration profile in the mat during displacement washing and subsequent dewatering is described using the axial dispersion model suggested by Brenner (1962): Oc^1 02c_Oc Or P,Oz2 Oz  with initial and boundary conditions of = 0^at r = 0 for all z  ^c  Oc 8c OZ  = Pe • (c —1) at z = 0 for r > 0 = 0^at z = 1 for r > 0  where: = (CDs, — CDsm )/(CDsv — Cpsw), dimensionless dissolved solids concentration = Z1H„„ dimensionless distance  13  (2.6)  Chapter 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  •  = axial distance, m  Pe^= u • HmID,  Peclet number, dimensionless  •  = axial dispersion coefficient, m2/s  •  = velocity of liquid through the mat, mis  •  = t.^dimensionless residence time  CDSv • CDSm and CDSw  = dissolved solids concentration in vat, mat and wash liquor respectively, kg/m3  Brenner's model does not account for adsorption of dissolved solids on the fibre surface. According to the observations of Poirier et al. (Poirier et al., 1987a), this simplification may not be valid for the later stages of a washing plant, where the concentration of dissolved solids in the mat liquor becomes much lower than that in the early stages. An additional term can be included in the model to describe solute absorption (Sherman, 1964). Equations 2.3 to 2.6 together constitute a mechanistic model for the drum filter operation. This model describes the development of dissolved solids concentration and consistency across the drum for a given consistency, dissolved solids concentration and flow rate of the vat slurry. The model implies that there is no mixing of fluid along the drum rotary direction. Thus the outputs of the model, such as dissolved solids concentration and consistency in the washed pulp, have a pure time delay in response to input changes. This time delay, however, is negligible because of very short residence time in the drum filter. The model also addresses the effects of drum speed and vacuum on the washing results. Thus, this model could not only be used for designing the washing process control but also for optimizing the washer operation. Unfortunately, this approach has limited application to the mill washing operation since it requires complicated calculations and a great number of fundamental parameters. The mat porosity, mat density, Peclet number and permeability are complicated functions of process conditions as well as of fibre physical properties (compressibility, drainage, etc), which are difficult to obtain from mill measurements. 14  CHAPTER 2: MODPTI.ING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  2.3.4.2 Efficiency Approach  In contrast to the detailed mechanistic approach, the Norden model compares the drum filter with an ideal mixing-extraction line. This is not a true description of what happens in the real system. Nevertheless, results calculated by the Norden model agree with the results calculated from rigorous mechanistic models such as Brenner's dispersion model. The Norden efficiency factor for the drum filter is defined as: = {log lit  (xxDsv:Yyposs 2d)  when RW  log YtiA7  EN  ^ypsd^sz  ^L.  A  1  (2.8)  when RW = 1  DStr^DS1  where RW is the wash liquor ratio, defined as v2  RW = — Li  (2.9)  . We also have static mass balance equations for the liquor: (2.10)  Vd = V2 + Lv Ll  and for the dissolved solids: YDSd  V2 • YDS2 Lv • XDSv Ll • XDS1  (2.11)  Vd  By combining Equations 2.8 to 2.11, an expression for the dissolved solids content in washed pulp liquor is obtained in terms of the input variables of the drum filter: RW —1  XDS1 =  1 YDS2 + RwEN.Va/L„ —1 ( XDSv — YDS2) YDS2 +  k • ( xDst, — Ybs2)  mi  C  1 – Cmi  15  1  when RW = 1  where RW can be expressed in terms of the dilution factor,  RW = DF  when RW  (2.12)  DF:  1  (2.13)  Chapter 2: MODFI LING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  As shown in Equation 2.12, the Norden method provides a straightforward relationship between the dissolved solids content in washed pulp and the input variables of the drum filter. The value of the Norden efficiency factor is available from mill data collected under conditions similar to the proposed application. Therefore, this model is more practical for process simulation and control system design. The outlet mat consistency, C„,/, is another input parameter of this model. A combination with the simplified mechanistic model could be employed to account for the consistency as an independent variable. Since washing efficiency is often reported in tenns of displacement ratio in mills, it is useful to relate the Norden efficiency factor to the displacement ratio in order to facilitate the application of the Norden model to the process simulation. This relationship has been derived from the mass balances around the drum filter and is shown by Equation 2.14: log^(RIVIDDRR) EN=  log RW  (2.14)  where DR is the displacement ratio and defined by Perkins (1954) as: DR  = XDSv — XDS1 XDSv — YDS2  (2.15)  The ratio of the vat liquor flow rate to the filtrate flow rate leaving the filter, Lvilid, is approximately equal to one because the recirculated filtrate constitutes the major part of both vat liquor and the filtrate flow rate leaving the filter, roughly 90%. Therefore, Equation 2.14 can be simplified to be io, =  RW—DR  6  1—DR  log RW  (2.16)  The Norden efficiency factor can be calculated by Equation 2.16 if the displacement ratio and the corresponding wash liquor ratio are known. 2.3.5 Washing Stage and Plant Models  Table 2.1 summarizes the model equations used to simulate a single vacuum drum washing stage. The drum filter is described based on Norden efficiency factor, the dilution vat as a static perfect mixer and the seal tank as a dynamic perfectly mixed flow tank. This model retains the 16  CHAPTER 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  Table 2.1 Mathematical model of a washing stage. 1. Dilution vat:  = Lo + V, LO • XDSO Vr •  (2.17)  YDS1  2. Drum filter:  XDS1  L1 — LO  Cm')^1 Cml 1 — Cm° Cm1  _ YDS { 2 + RwERNZ1L._i (XDSv — YDS2)  when RW 1  — YDS 2 +^• (XDSt, — YDS2)  when RW = 1  (2.18)  Vd = V2 A- —L1 V2 • YDS2  Lv  • XDSv — L1  YDSd —^  3. Seal tank:  ^di ^di  XDS1  Vd  ^(Vd — — Vr) ^Vat • Pi  (2.19)  dYD^Vd • (YDSd YDS1)  di —^Vat • H at • pi  dynamic characteristics of the washing system and the effects of major process conditions such as dilution factor, production rate and incoming dissolved solids content. It has been written as a computer module in SIMNON. The dynamic process model of a multistage washing plant can now be constructed by connecting the separate washer modules. The structure of a simulation model corresponding to the three-stage washing plant in Figure 22 is shown in Figure 2.6.  Black liquor  Washer 1  .41.=.4111.  Wash liquor  Washer 2  Brown Stock  Washer 3 Washed Pulp  Figure 2.6: Simulation model structure for a three-stage washing plant.  17  Chapter 2: MODMING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  2.4 Simulation of Process Dynamic Behavior  The countercurrent flows between pulp and wash liquor as well as the substantial recycles within each unit lead to a complex dynamic behavior of the brown stock washing plant, which must be well understood before a control system can be designed. The dynamic responses of a single washer and a three-stage washing plant were investigated with the assistance of the washing process simulator written in SIMNON. Input changes were made in the pulp production rate, dissolved solids content in the pulp feed and wash liquor flow respectively. Changes in the pulp production rate and incoming dissolved solids content can be due to variations in pulp digestion, blow tanks or pumps, while the wash liquor flow is an important manipulated variable. The liquid levels in the seal tanks were considered to be constant for any change so that the case studies could focus on the dynamic behavior of the dissolved solids in the washed pulp and filtrate liquor. The initial steady-state conditions for the simulation were obtained from operating data collected from an industrial washing plant with a production rate of 400 odt/d (see Table 2.2).  2.4.2 A Single Washer For a 15% step increase made in the pulp production rate, incoming dissolved solids content or wash liquor flow rate, the responses of dissolved solids content in the washed pulp and in the washer filtrate of a single washer are shown in Figure 2.7. The response in the filtrate is a slow, first-order response. As a result of the very fast flow of the pulp stream, an instantaneous response is observed in the washed pulp. It then become a slow first-order response because of the effect of the recycle loop. The settling time (the time required for a step response to reach 95% of its new steady-state value) is approximately 160 minutes for the change in dissolved solids in the pulp feed. The settling time is about 70 minutes for both the change in wash liquor flow rate and the change in production rate. The response magnitude is also similar for the change in the wash liquor flow and for the change in the pulp production rate. The 15% change in these two variables produces about 12% steady-state change in the output dissolved solids content. 18  CHAPTER 2: MODFL LING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  Table 2.2 Operating data of an industrial vacuum drum washing plant.  Variable  Washer 1  Washer 2  Washer 3  Pulp onto washer Consistency (%) Dissolved solids (%)  6.90 22.8  8.50 8.47  12.8 2.65  Vat slurry Consistency (%) Dissolved solids (%)  1.0 19.4  1.1 6.73  1.1 1.53  Pulp off washer Consistency (%) Dissolved solids (%)  8.50 8.47  12.8 2.65  10.4 0.537  Wash liquor Dissolved solids (%)  6.71  1.50  0.0  Seal tank Volume (m3) Level (%) Dissolved solids (%)  1067 23.3 18.9  861 33.5 630  683 33.3 1.43  Dilution factor  2.58  2.52  2.59  Wash liquor ratio  1.24  1.37  1.3  Displacement ratio  0.83  0.75  0.6  Norden efficiency factor  4.29  2.96  2.25  2.43 Three Washers in Series  Figures 2.8 to 2.10 show the responses of each washing stage in a three washer plant to a step change in the pulp production rate, incoming dissolved solids content and wash liquor flow rate. It took less than 1 second CPU time of a Sun/SPARC station 2 to simulate these dynamic responses over a period 2000 minutes. The responses are much slower than those of the single washer due to strong interactions between the stages. It took more than ten hours to reach the new level of dissolved solids removal following the manipulation of the wash liquor flow rate. Such an unusually slow response can often confuse the operator, who may never see the full results of his action during 19  Chapter 2: MODFILING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  9.4  _ (A)  9.2  8.8 8.6 8.4 8.2  100  22 213  ^  300^400^500^600  (B)  21 20.5 20 19.5  .5  19 18$ 18 17$ 17  •  100^200^300^400^500^600 Time (min)  Figure 2.7: Dynamics of a single washer: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=50 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage.  20  CHAPTER 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  a shift An instantaneous response of washed pulp was observed when the pulp production rate or wash liquor flow rate was changed, but not when the incoming dissolved solids content changed. A transfer function between the dissolved solids content of the washed pulp leaving the third washer and wash liquor flow rate, Gp(s), was obtained from the simulated results. It is a sum of a pure gain and a first order terms as follows: Gp(s) = Kpo +  with  Kp rp • s + 1  Kpo = —1.1 X 10-4 (% •  (2.20)  min/kg)  Kp = -6.7 x 10-4 (% • min/kg) and rp = 223 (min) Where Kpo and Kp are the gains, rp is the time constant and s is the Laplace operator. This function was used to calculate the controller parameters of when different process control strategies were studied as shown in the next section. The frequency responses of the three-stage washing plant were simulated by using sinusoidal changes in the pulp production rate and wash liquor flow rate, respectively. The Bode diagrams in Figure 2.11 show the amplitude ratio and phase lag between the dissolved solids in the washed pulp and the production rate changes at different frequencies. The amplitude ratio decreases with the increase in the frequency and approaches a lowest limit when the frequency is about 10-3 rad/s. The phase lag decreases first and then increases with increasing frequency. This indicates that variations in production rate always disturb normal operation since the process response is not completely attenuated over high frequencies. The shape of the Bode diagrams for changes in the wash liquor flow rate are similar to those for changes in the production rate. As shown in Figure 2.12, however, the amplitude between the wash liquor flow and dissolved solids in the washed pulp is much smaller. The dynamic characteristics of the washing plant shown in the simulation agree with mill observations (Lundquist, 1980; 1985). This allowed the validity of the dynamic process model to be verified qualitatively. As well, the results are similar to previous dynamic studies (Perry et al., 1975; Turner et al., 1990) which used mechanistic models for brown stock washing. 21  Chapter 2: MODE]. LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  13  (A)  12 11 10  200^400^600^800 1000 1200 1400 1600 1800 2000  400^600^800^1000 1200  1400  1600  1800 2000  Time (min)  Figure 2.8: Dynamics of 1st stage of a three stage washing plant: step response in (A) dissolved solids in  washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at 150 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage.  22  CHAPTER 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  5.5  (A)  4.5  -S 33  A 13  200^400^600^800 1000 1200 1400 1600 1800 2000  11  (B)  10  200^400^600^800^1000 1200 1400 1600 1800 2000  Time (min)  Figure 2.9: Dynamics of 2nd stage of the three stage washing plant: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at t=50 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage.  23  Chapter 2: MOD LUNG, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  1.4  (A)  g=^1.2  .g  t .5 0.8 ;  A ,..).2 to  3  0.6  0.4  .  0  02 0^200^400^600^800^1000 1200 1400 1600 1800 2000  33  (B)  23  .,  03  0  '  200^400^600^800 1000 1200 1400 1600 1800 2000 Time (min)  Figure 2.10: Dynamics of 3rd stage of a three stage washing plant: step response in (A) dissolved solids in washed pulp and (B) dissolved solids in filtrate. A 15% increase is made at 160 minutes in (a) pulp production rate, (b) dissolved solids in pulp feed and (c) wash liquor applied on the last stage.  24  CHAPTER 2: MODMING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  :  10  0 -2 c 10 "-T5  cc a) -a  N-1,11-9"  -  E < 10^• -6  10  10  -5  -4  10 10 Frequency (rad/s)  -3  .^.  .  -2^1 10^10  -1 0  -40 -50  10  -6^  10  -5^  10  -4^  10  -3^  Frequency (rad/s)  10  -2  Figure 2.11: Bode diagrams of dissolved solids in washed pulp leaving a three-stage washing plant to changes in pulp production rate  2.5 Control Strategy Evaluation  2.5.1 Washing Process Control  Attention to brown stock washing has been growing for the following reasons: O Reduced dissolved solids carry over to bleach plant is suggested as a way to help meet more strict environmental regulations on bleaching effluents. O Increasing energy prices have made it very desirable to reduce the amount of water to be evaporated. O The importance of good washing for product quality is better understood. 25  ^•  Chapter 2: MODE! TING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS .  133 10 ..,e  -3  1^•I^  V^  I  E  .?  e . ... co  cr a) V e=. r). E-  <  10 -476—^ -5 10^10  '  .1 . . ..  10 -4^10 Frequency (rad/s)  -3^10 -2  170  -a (2) 160  -0  w Prs 150 .c  0_  140 10  -6^  10  -5^  -4^  10 10 Frequency (rad/s)  -3^  10  -2  Figure 2.12: Bode diagrams of dissolved solids in washed pulp leaving a three-stage washing plant to changes in wash liquor flow rate  Better washing process control has been recognized as a means of improving brown stock washing and has been studied in many projects. The comments made by some of these authors (Lundquist, 1980; 1985; /lase and Sjoberg, 1989; Han, 1989; Turner et al., 1990) are summarized as follows: El Control dilution factor: More wash liquor applied in washing results in less dissolve sold carryover but the more energy consumption in evaporation. Therefore, the dilution factor must be correctly chosen to achieve economic washing El Coordinate wash liquor flows: The control system should simultaneously adjust the wash liquor flows of all stages when the washing conditions are changed, for example, when the pulp production rate is altered. 26  CHAPTER 2: MODFI LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  O Coordinate liquid levels of seal tanks: Control of the seal tank levels and control of the dissolved solids removal are all based on manipulation of the countercurrent wash liquor flows. A proper control strategies for the seal tank levels is important to eliminate interactions between the tank levels and interactions between the tank levels and dissolved solids removal. O Control dissolved solids removal: The washing control system should have ability to reduce the process variability to maintain optimum dissolved solids removal. O Detect disturbances: Sensors to monitor disturbances are desired to decide the appropriate operating conditions when the washing system is disturbed. O Inform the operator about disturbances and efficiencies: This can give an early warning when a bad situation is developing. It can also provide a good basis for continuous tuning and more long-term improvements of the process. The dilution factor proposed by Korhonen (1979) has been widely accepted as a main control variable. Turner et al. (1991) designed a cascade feedforward control system which was able to eliminate oscillations of seal tank levels. However the vast majority of washing plants are still operated without any significant control systems, where operator involvement is the major control element. Automatic control of drum washers is limited primarily to level control loops (Tumer et al., 1990). The drum rotation speeds are adjusted to maintain the dilution vat levels constant and the flow rates of wash liquor are manipulated to maintain liquid levels constant in the seal tanks. In this work, the process dynamic simulator was used to study how washing plant control might be further improved. In particular, three control strategies for a three-stage vacuum drum washing plant are compared and evaluated. The process dynamic behavior of the washing plant was discussed in the previous section.  Strategy 1 only controls the liquid levels in the seal tanks with no action to correct dissolved solids removal. The control loops for the seal tank levels are shown as dot-dashed lines in Figure 2.13. Proportional controllers were used for the seal tank level.  Strategy 2 not only controls the seal tank levels but also the dissolved solids removal by means of feedback control. The feedback control system measures the dissolved solids content of washed pulp 27  Chapter 2: MODE!. LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  leaving the last washer and adjusts the wash liquor flow rate onto that washer to maintain the desired dissolved solids content in the washed pulp. It also simultaneously adjusts all upstream wash liquor flow rates by the same amount (dotted lines in Figure 2.13). The feedback controller for dissolved solids removal was a PI controller. The controller parameters were found by using Dahlin's tuning rule. This rule results in a first-order closed-loop response and requires only one tuning parameter.  Strategy 3 expands Strategy 2 by adding a feedforward control for dissolved solids removal. The feedforward control monitors the production rate as a function of the consistency and flow rate of the brown stock onto the first washer, and maintains the dilution factor by adjusting wash liquor flow rates in the washing system. The feedforward control is illustrated by dashed lines in Figure 2.13. The feedback control shown by the dotted line was used to determine the set point of the dilution factor. All these control strategies are based on existing on-line instrumentation for brown stock washing. Measurement of the liquid level in the seal tank is required for all the strategies. In addition, measurement of the dissolved solids concentration in washed pulp is required for Strategy 2 and Strategy 3. There is also a need for Strategy 3 to measure the incoming slurry flow rate and consistency. Measuring the tank level and slurry flow rate are already successful technology. There are different types of on-line consistency indicators on the market, such as blade type transmitters and microwave gauges (Woodard, 1988), etc. The dissolved solids carryover can be measured based on mat liquor conductivity (Wigsten, 1988). An optical sensor to monitor the dissolved solids concentration has recently been developed (Edlund et al., 1992). 2.5.2 Results and Discussion In order to give the control strategy simulation a realistic result, time series of the pulp production rate and the dissolved solids content in pulp feeds over a period of 10 days which we derived from a mill data were used as the process disturbances of the simulation. The power spectrum corresponding to the mill data showed eight peaks. We, therefore, selected the eight corresponding frequencies and amplitudes to represent the incoming dissolve solids variations as shown in Figure 2.14. Also shown in this figure are the production rate variation composed of a square wave with a period of two days and appropriate random noise. Figure 2.15 shows the dissolved solids carryover (kg dissolved 28  CHAPTER 2: MODE! LING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  I Frcedforward Control  T'41+  Redbrick Control  • Washed Pulp  Brown Stock  Seal Tank 2  Seal Tank 1  Seal Tank 3  Black Liquor 0 Analyzer Transmitter  Tank Level Controller  0 Dissolved Solids Controller  Figure 2.13: Control layout of a three-stage vacuum drum washing plant.  solids/odt pulp) obtained by the different control strategies in response to the process disturbances for the first five days. The CPU time for each response simulation was about 10 seconds. Large increase in the dissolved solids carryover resulted from the disturbances when the system was controlled using Strategy 1 (see dotted line in Figure 2.15A). In contrast, the dissolved solids carryover of Strategy 3 was relatively constant (see solid line in Figures 2.15A). Strategy 2 yielded a slower compensation for production rate disturbances than Strategy 3 (see Figure 2.15B). It took up to ten hours to pull the dissolved solids content in the washed pulp back to the set point. Table 2.3 lists the means and variances of dissolved solids carryover during the 10 days resulting from the three control strategies. It is apparent that both Strategy 2 and Strategy 3 can give much smaller means and variance of dissolved solids carryover than Strategy 1. This improvement has economic and environmental significance, not only for the washing plant but also for the other departments in the mill. Variations in the seal tank levels of Strategy 3 are larger than those of the other two control strategies because it requires more vigorous manipulation of the wash liquor flow rate for rapid 29  Chapter 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  28  \  26  \\` ii  1 /,  /k  22  1  \  —  1  I  \  \ 18  16  \  I I  I  1^2^3^4^5^6^7^8^9^10  315  (B)  310  i 305  I  g E :115 300  t c4  /  It  \,/  295  g 290  MI  ..=  8  \ A,,A  Z 285  2  280 275  270  0  1^2^3^4^5^6^7^8^9^10 Time (d)  Figure 2.14: Process disturbances used in simulation of control strategies for a three-stage washing plant: fluctuations in (A) dissolved solids content in pulp feed and (B) pulp production rate.  30  CHAPTER 2: MODELLING, SIMULATION AND COlVTROL OF BROWN STOCK WASHERS  80 ±2 .....  -.8 .....„  g 1.,^70 -> o  i' rn A 60  50  1.5  ^  2  51  50  49  48  47  46  45  44  0.5^1^1.5^2^2.5  ^ ^ 3 4  Time (d)  Figure 2.15: Dissolved solids carryover of a three-stage washing plant using different control strategies.  31  Chapter 2: MODELUNG, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  Table 23 Mean and variance of dissolved solids carryover resulting from three control strategies. Dissolved solids carryover  Strategy 1  Strategy 2  Strategy 3  Mean (kg/odt)  63.6  46.3  46.3  Variance (% on mean)  27  2.6  0.68  Initial operating conditions listed in Table 22. Process distubances shown in Figure 2.14. compensation for fluctuations in the production rate. Fig= 2.16 shows the simulation results for Strategy 3. The variations in the liquid level are within 2% in the first seal tank and become smaller as the number of washers increases. It should be noted that the variation in the tank level is affected by the magnitude of the process disturbances. For example, larger changes in the production rate will result in increased variations in the level. Normally, the increased level does not cause any problem while the decreased level could not provide a retention time sufficient for removing air from liquor. The acceptable decrease in the level is dependent on the mill but generally not more than 10% of its set point. In the above simulation experiments, the flow rate of wash liquor was determined by the control target. In the mill, manipulation of the wash liquor flow is often limited by the evaporators or simply by the washer showers. When an unexpectedly large disturbance enters the system, the wash liquor flow rate demanded by the dissolved solids controller could be beyond the process constraints. The response of dissolved solids in washed pulp will be then governed by the wash liquor constraint, leading to a sustained error input of the controller. Therefore, it is necessary to use a technique for protecting the controller from integral windup. Figure 2.17 shows the performance of Strategy 3 with and without anti-windup when the maximum constraint of wash liquor flow is 3200 L/min in the tested case. During the two day operation period when the production rate was increased by 10%, the wash liquor flow rate on the third washer could not be increased correspondingly. It saturated at the maximum value (see Figure 2.17A). The process disturbance was not fully suppressed, leading to the positive deviations in the control variable from its set point. Consequently, the integral term of the PI controller without anti-windup became very large. This integral term drove the saturation in the wash liquor flow to the period that the production rate was decreased, resulting in the negative  32  CHAPTER 2: MODELLING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  35 34.8 34.6 34.4 34.2 34 33.8 33.6 33.4 33.2 33  0  0.5  ^ ^ ^ ^ ^ ^ ^ ^ ^ 4 5 3.5 3 4.5 2.5 1.5 2 1  34 33.8  ,--,  33.6  63, 33.4 7. .) > 33.2  4  1 33 [-■ 32.8 1 32.6 15 i...^32.4 VI 32.2 32 0  0.5  i  1.5  2  2.5  3  3.5  4  4.5  5  Time (d)  Figure 2.16: Liquor levels in three seal tanks under proportional control (Strategy 3 example).  33  Chapter 2: MODF7 LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  deviations in the process response (See Figure 2.17B). Since the controller with anti-windup can give an integral modification when the saturation occurs, it can then follow rapidly the decrease in production rate and take the correct control action. 2.6 Conclusions  This chapter is concerned with the modelling, simulation and control of a countercurrent brown stock washing plant. The mathematical model based on the Norden efficiency factor and dynamic seal tank appears to accurately represent the mill washer operation. This model can be used as a simple but useful method for process simulation and control development. The open-loop responses of three stage washing plants were simulated for changes in the pulp production rate, incoming dissolved solids content and wash liquor flow rate. These examples showed strong interactions and quick-slow mixing dynamics of the countercurrent washing system. It is therefore very difficult to achieve good washing by manual control of a washing plant. It was also showed how a good dynamic simulator could be used to develop and evaluate process control strategies. Through use of typical process disturbances, three different control strategies were compared. Automatic control of wash liquor flow applied in washing system can efficiently compensate for the effect of process disturbances, resulting in uniform and reduced dissolved solids carryover. The combination of feedforward and feedback control has much faster suppression on the effect of variations in production rate than feedback control only. SIMNON was well suited to the washing plant simulations, showing promise in the development of dynamic simulators for other pulp and paper processes. Therefore, the use of SIMNON was extended in the remainder of this study to a bleach plant. 2.7 Recommendations and Suggestions for Future Work 1. To test the sensitivity of the washer discharge consistency to changes in process conditions.  The present model assumes that the discharge consistency is constant when the wash liquor flow or pulp production rate is changed. 34  CHAPTER 2: MODELLING, SIMULATION AND COIVTROL OF BROWN STOCK WASHERS  3300  (A) — With Anti-Windup — Without Anti-Windup  .... 3250 .1 b 3200  4 g V s.  en 3150 PA 5  80  CI'  ;:.^ -1 1  3100 I  3050  300° 0  1^2^3^4^5^6^7^8^9^10  79  (B) — With Anti-Windup — Without Anti-Windup -  70  61 ,-, t -a5 t,^52  k  v) A  • I  43 -  34  I I^ I %^ 1 %^ %^ 1 • • I %^.^,-•^I s• r% , ‘^, ... •^S...,^..^ 0%,  %^I^ ,..., ^  ,..  %  1^I ...,./  1^2^3^4^5^6^7^8^9^10 Time (d) Figure 2.17: Effects of anti-windup on control performance.  35  Chapter 2: MODE! LING, SIMULATION AND CONTROL OF BROWN STOCK WASHERS  2. To develop a simplified mechanistic model or modify the Norden model to show the effects of adsorption phenomena, drum speed, vacuum, vat consistency, etc. These factors are not accounted for by the present model. 3. To apply the model to more problems. Examples include extending the present simulator to other washing process flowsheets and washer configurations, optimizing wash liquor application levels, and simulating washing control systems which may include secondary loops (e.g., control of drum speed and recirculated liquor flow rate) in addition to the control loops of wash liquor flow.  36  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  CHAPTER 3 MODELING AND SIMULATION OF A BLEACH PLANT  3.1 Introduction  Pulp bleaching is the chemical treatment of cellulosic fibre to increase pulp brightness by removal or modification of the light-absorbing lignin left in the pulp while preserving pulp strength characteristics. Bleaching can also increase pulp cleanliness to make pulp suitable for the manufacture of printing and tissue grade paper. The primary objectives in operating a bleaching plant are product brightness, production rate, operation costs and environmental pollution. Today, environmental awareness is on the increase and the kraft pulp industry is facing tougher regulations on bleach plant effluents. A dynamic bleaching process simulator would be a very helpful tool for testing new bleaching operations and developing process control to meet this challenge. Possible benefits from improved bleaching process control include lower chemical demand and thus reduced pollution discharge while maintaining high pulp quality. However, early attempts to formulate mathematical descriptions of bleach plant operations have taken into account only the bleaching kinetics and the steady-state mass balances. No study has touched on the bleach plant as a whole to reveal interactions within the system. The dynamic process modelling presented in this chapter is based on fundamental flow phenomena as well as chemical kinetics. The flow patterns of pulp slurries in bleaching towers were studied and modeled by means of tracer responses. Based on the cluumophoric theory and experiments, a correlation, which relates models of the delignification and brightening processes, was established. Unit operation models for mixing, reaction and washing were formulated as mass balance equations. It is a difficult problem to determine what type of bleaching sequence to simulate since bleaching technology is rapidly changing in the 1990's due to environmental pressures. A CDEDED five stage bleach plant, which is a conventional sequence for producing fully bleached haft pulps, was chosen as an example in the present work. This choice is primarily due to the fact that there is sufficient information on pulp bleaching kinetics, available in the literature, for modelling a CDEDED 37  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  sequence. Another reason is that such chlorine-based bleaching sequences with modifications are still widely used in commercial bleached lcraft pulp manufacture. There are many chemical and physical similarities among the various pulp bleaching sequences in current use. The present study can be used as a basis for modelling other types of chlorine-based sequences and even bleaching processes with novel chemicals. The process simulator written using SIMNON's modular approach can be flexibly adapted to these new changes. Bleaching kinetic models from the literature were evaluated and incorporated in the process simulator. Some of them were modified and expanded. An overall model for the CDEDED plant is presented. The dynamic behavior of different stages in response to changes in the chemical charge, incoming kappa number and production rate are illustrated.  3.2 Process Description Bleaching is usually carried out in a continuous sequence made up of several stages with each stage utilizing different chemicals and conditions. In the earlier stages of the bleaching sequence the emphasis is on lignin removal while in the later stages the emphasis is placed on lignin decolourization to develop brightness. Each stage is a combination of mixing, reaction and washing, and consequently, different pieces of equipment are involved: 1) mixers to achieve a uniform mixture of fibres with bleaching chemicals and steam, 2) a retention tower to provide time for chemical diffusion and reaction and 3) a washer to separate the treated fibres from the soluble reacted material and spent chemicals. Steam may be used in the stage to heat the pulp slurry to the reaction temperature. Filtrate from each washer is recycled within the stage for dilution of the pulp slurry to the desired inlet consistency and may be delivered to the previous stages for pulp washing In the CDEDED bleaching sequence, the initial CDE sequence uses chlorine and chlorine dioxide followed by extraction with sodium hydroxide to solubilize and remove the lignin in pulp. Chlorine dioxide is applied at a low percentage in the order of 10% to the first chlorination stage to protect pulp strength. The succeeding DED sequence employs chlorine dioxide and sodium hydroxide to brighten the pulp. A flowsheet of a bleach plant with the CDEDED sequence is shown in Figure 3.18. In the first CD stage, the unbleached pulp is often diluted to low consistency (s, 3.5%) and mixed with 02 and 002. Then the bleaching reaction is completed in the CD tower and water-soluble 38  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  1:5-‹ Chanical or Steam Mixer^ED Washer^Seal Tank  Figure 3.18: Process flow diagram of a CDEDED bleach plant.  products in the chlorinated pulp are washed out in the washer after the tower. In the second stage, Eli the pulp is treated with sodium hydroxide and the alkali-soluble lignin fragments are removed. The pulp slurry in the El tower is at medium consistency (r- 10%) and it is diluted at the bottom of the tower with filtrate from the El washer so that it can be pumped out by conventional pumps. After the first two stages, most of the lignin (about 70-80%) is removed, but the pulp still appears dark. The brightness is about 30% ISO. In the following stages, DED, pulp brightness is increased by eliminating the chromophoric groups in the lignin without removing lignin. Chlorine dioxide is used as the bleaching agent in the DI stage. Alkali is also added to control the pH value within a range optimizing brightness development. Alkali and chlorine dioxide are used in the succeeding stages, E2  and D2, to further increase the pulp brightness. After the final stage, the brightness ranges from  88 to 92% ISO. Figure 3.18 also shows one countercurrent scheme for washing the pulp exiting the towers. Fresh water is applied to all of the showers of the second chlorine dioxide stage washer and to some of the showers of the other stage washers, while filtrate from each of the washers (except the C stage washer) is reused in the remaining showers of the previous stage washer. 39  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  In recent years, significant modifications in bleaching technology have taken place in order to meet the increasingly stringent environmental regulations. Chlorine dioxide has been substituted for most or all of chlorine in order to eliminate dioxin formation and decrease AOX generation. Oxygen has been used to enhance the alkaline extraction to permit the removal of additional lignin. Research is also underway to find economical and environmentally friendly chemicals for bleaching pulp. Nevertheless, all typical bleaching operations are involved in the CDEDED sequence. Major changes are usually associated with the use of different chemicals. Thus simulation of the CDEDED sequence can serve as a starting point for modeling current and future bleaching technologies.  3.3 Model Development  33.1 Process Variables and Analysis  The mathematical model developed for a multistage bleach plant should have the ability to address the interactions of important process variables within and between each bleaching stage. Fundamental chemical and physical aspects should be identified by the process analysis to allow an overall description of the bleach plant to be made. The process units and variables to be considered for a single bleach stage are shown in Figure 3.19. The pulp production rate of a bleaching plant is not constant due to variations in the flow rate and consistency of the slurry entering the plant. Higher production rates need more chemicals to achieve the desired product brightness. Increasing the production rate also decreases the slurry residence time in the bleaching system. Variation in the kappa number of the pulp entering the bleaching plant is an important disturbance. Fibre consistency, temperature and chemical charge of each stage determine the bleaching reaction rate. The pH of the bleaching liquor is another vital factor for some bleaching reactions. pH values could be changed due to mixing, washing and bleaching reactions. The dissolved solids, especially organic dissolved substances, could react with bleaching agents if they enter the bleaching process. Efficient washing is essential to decrease dissolved solids carryover and thus to reduce chemical consumption. In a CEDED bleach plant, the kappa number after the El 40  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  Inlet Kappa Nod Brightness Production Rate  Kappa Nod Brightness  Wash Liquor  Inlet Consistency" , Consistency  Chemical Charge  Chemical  Pulp out  Temperature Retention Tower  Residence Time  Chemical Residual PH  Filtrate  Inlet pH  DS Carryover  Pulp in  Inlet DS Wash Liquor Applied Figure 3.19: Process units and variables of a bleach stage.  stage indicates delignification intensity and thus is an important control target of CE delignification. The brightness after the DI and D2 stages is the control target for DED bleaching. The dynamics of the retention towers plays a dominant role in the overall transient behavior of a bleach plant. This is because they have a much longer residence time than other process units. The residence time of the pulp slurry in the retention towers ranges from 20 to 240 minutes, depending on the stage. The residence time in the mixers and washers is on the order of seconds. The time in all pipe lines is less than approximately two percent of the total residence time for a CDE0DED (Mackinnon, 1987). Therefore, attention must be paid to the dynamic behavior of the towers while the transient behavior of all other process units in the bleach plant may be neglected. Knowledge of the flow patterns of pulp slurries through the various retention towers is required in order to accurately model the tower dynamics. Mixing in the bleaching stages brings the pulp slurry together with bleaching chemicals, steam and dilution liquor. In particular, mixing to obtain a uniform distribution of the chemicals in the pulp is critical for pulp bleaching effectiveness. The unique rheology of pulp slurry makes it difficult to quantitatively represent mixing performance. A literature review of pulp mixing and 41  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  other fundamental knowledge relevant to pulp bleaching is presented in Appendix B. In the present work, all mixing processes are simply assumed to be perfect and instantaneous. Heat exchange that takes place during mixing has not been taken into account. The bleaching reactions occur in both the chemical mixer and the subsequent retention tower. The reaction in the mixer-is viewed as a process occurring after the perfect macroscale mixing is achieved (i.e. uniform distribution of the chemical reactant in the bulk liquid around each fibre). This treatment provides a reasonable representation of many actual cases, such as chlorine and chlorine dioxide high-shear mixer (Bennington et al., 1989), where the mixing occurs much faster than the reaction rate so that the time required for a desirable state in mixing is negligible compared to the time for bleaching reaction to take place. The rate of the bleaching reaction in each stage can be conveniently represented by kinetic models that lump the chemical reaction and mass transfer steps together. The pulp washer after the retention tower separates the fibres from the waste products and residual chemicals. The washer operation can be described by the Norden efficiency factor used earlier in our model of the brown stock washing (see Chapter 2). Since all phenomena occurring in the bleach plant washers are assumed to be instantaneous in comparison with the tower dynamics, the Norden model can be used for the entire washing stage including seal tank, dilution vat and filter. Acid-base neutralization, dissociation and hydrolysis could all take place in the bleaching process liquor due to the complex liquor composition. Therefore, infonnation on buffering capacities of fibres, and weak acids and bases in the liquor is required to accurately calculate pH values for various unit operations. The constant of water dissociation equilibrium is the most essential and used here for the calculation of the pH after washing and after the mixing. It is assumed that the pH change after the bleaching reaction is determined by the reaction as well as the water dissociation equilibrium. The chromophore content of pulp throughout the bleach plant is expressed by two distinct methods: the kappa number is used for the initial delignification stages (e.g. C and El) and the light absorption coefficient for the later brightening stages (eg. DI,  E2  and D2). Only after a  correlation between the light absorption coefficient and kappa number is established, can the models of these two bleaching sections be linked to form the model for a complete bleach plant. 42  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  3.3.2 Modeling Flow Patterns in Retention Towers  3.3.2.1 Introduction Retention towers are critical components that determine the transient behavior of a bleach plant. In order to model the dynamics of the retention tower, it is necessary to know the flow pattern of pulp slurries through the tower. The slurry flow not only determines the residence time distribution of the reacting fluid but also governs mixing of the fluid elements with different residence times and different chemical compositions. A pure plug flow model of the tower has been used in previous bleach process simulations (Ackert et al., 1975; Myers and Edwards, 1989; Ulinder, 1992). This model only leads to a pure time delay response, which has not been found to be the case for the real system. Deviations from plug flow could be caused by channeling, mixing and radial variations of flow velocity. A first order plus dead time model has also been used as an empirical approximation for the response signals of all key process variables, such as consistency, kappa number and brightness, in retention towers (Biallcowski, 1990). Our purpose in this work is to develop a suitable mathematical model for the pulp flow pattern in the industrial bleach tower by analysis of residence time distribution (RTD or E function) measurements. Different models for non-ideal flow were tested and compared with respect to their complexity and correspondence with the observed behavior. The best model was used to predict the dynamic responses of residual chemicals, kappa number and brightness to changes in various process conditions. Comparison between this model and a pure plug flow model was also conducted through simulation of the chlorine and the second C102 towers.  3.3.2.2 Observations and Models Extensive stimulus-response experiments using inert tracers have been done in previous projects for various bleach retention towers to study the residence time distribution and flow behavior of the towers. They showed that the pulp flow in the towers deviated to a greater or lesser degree from plug 43  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  flow. There is, therefore, a need to establish a mathematical model which more closely approximates reality. Observed E curves used for this work were obtained from the following sources: 1. Snyder (1966) conducted measurements of E curves for an upflow chlorine tower with circulators at the bottom, middle and upper sections. Employed in this work are the results for two circulators operating at the bottom and middle of the tower and one circulator in operation at the bottom of the tower. 2. Another E curve for the chlorine tower was taken from mill data. The records of tracer leaving a chlorine mixer and subsequent tower for the case of an impulse signal imposed on the pulp slurry entering the mixer were used to obtain the E curve by deconvolution of the tower response from the mixer response. 3. Perkins (1971) published impulse-response results observed in medium consistency towers, including the El, DI and E2 and D2 stages. E curves for these towers were obtained using a normalization procedure. The first consideration was naturally placed on two single parameter models which are widely used for non-ideal flow: an axial dispersion model and a CSTRS (Continuous Stirred Tank Reactors in Series) model. These models use quite different mechanisms but are often found to be consistently suitable for real systems. The CSTRS model was chosen since this model is governed by ordinary differential equations, which are more easily solved by SIMNON than the axial dispersion model, which involves partial differential equations. The E function of the CSTRS model is (Levenspiel, 1972)  (v)  N—1  E— ^  N  tt • (N —1)! exp  •t It  (3.22)  The adjustable parameter, N, is the number of the stirred tanks in series and represents the extent of mixing in the system. The larger  N  is, the less the mixing is. One tank represents perfect mixing;  an infinite number of tanks is equivalent to plug flow. The N value for an experimental tracer response can be determined using a least-squares method 44  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  with the objective function:  E (E,,ez.p —  Ek,pred)2^  where Ek/, is the measured residence time distribution at kth time point and  Ek,pred is  (3.23) the predicted  residence time distribution at that time point To obtain a best fit of the data, the mean residence time in the model, L should also be estimated by the least-squares method. However, the observed mean residence time can also be used in the model because we have found that this value is insignificantly different from the optimal one. For residence time distributions obtained at discrete times, It  =E  roc,  it can be approximated by the formula  tt,k • Ek,exp • L‘tt,k  ^  (3.24)  When the CSTRS model was used to represent the tracer experimental signals, poor fits resulted. Shown in Figures 3.20 and 3.21 are the bar plots of a typical RTD for low and medium consistency towers, respectively. The observed response is unsymmetrical with an extended tail as well as a long initial dead time over which the tracer is not detected at the tower outlet. On the other hand, a large N value of the CSTRS model yields a symmetrical gaussian-like curve with a long dead time. It is impossible for this model to account for both the initial dead time and the following unsymmetric response. Perkins (1971; 1985) blamed the non-ideal flow in retention towers on the radial nonunifomiity of velocity caused by fluid viscosity and wall drag. He suggested a parabolic velocity profile for laminar flow in the tower. We feel that the variation in flow velocity is not large enough to explain the typical shape of most tracer tests. In fact, the slurry cannot be maintained in the laminar flow regime throughout a tower. Any disturbing component within the tower (e.g., bottom mixer, agitator or circulator) may introduce an unstable condition to the fluid, leading to local turbulent flow. Only the slurry beyond the agitated zone can be treated as a laminar flow. Several authors (Forgacs et al., 1958; Moller et al., 1971; Moreira and Felders, 1979) have investigated the laminar flow behavior of pulp slurries in pipes and towers. They found that a central region exists in which the pulp slurry moves at an uniform velocity and occupies most of the cross section. The shear and velocity 45  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  25  20  15  10  0 ----/I 0  15  20 25 30 35  ao  45  Time after Injection (min)  Figure 3.20: Typical RTD in a low consistency tower.  variations occur primarily in the fluid near the wall. The radius of this core section approaches  the tower radius as the Reynolds number decreases and the pulp consistency increases. Even at a consistency as low as 2%, the core radius is very close to the vessel radius over a large range of Reynolds numbers. Also due to poor vertical dispersion, this laminar flow slurry behaves like a plug flow fluid, resulting in a narrow, symmetrical residence time distribution with a long tail. Figure 3.22 illustrates feasible flow patterns of a pulp slurry through an upflow tower and how the slurry tracer changes shape from an impulse input to the measured output. A reasonable interpretation for the unique flow behavior in the pulp retention tower can be obtained by connecting a number of CSTR's with a PFR (plug flow reactor) in a cascade form. The RTD in the PFR portion is a 5 function at tp, the residence time taken by the plug flow fluid. Thus the overall RTD in the CSTRS+PFR model is formed by delaying the RTD in CSTRS by  tp.  There  will not be a distinguishable boundary between the mixed flow zone and plug flow zone in a real tower. If it is assumed that the measured dead time is due only to the plug flow, the mean residence 46  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  7 Data from Perkins (1971) 6  5  4  3  2  1  00-4/  100^120^140  160^180^200  Time after Injection (min)  Figure 3.21: Typical RTD in a medium consistency tower.  time of the CSTRS is = —^  (3.25)  Table 3.4 lists the results obtained by fitting the CSTRS+PFR and CSTRS models to the experimental tracer responses. The standard errors of the CSTRS+PFR model predictions, e, are apparently smaller than those of the CSTRS model. The parameters obtained for the CSTRS+PFR model show good agreement for the C towers at low consistency and for the E and D towers at medium consistency. We found a value of 2 for N for the C towers and a value of 3 or 5 for the E and D towers. The percentage of the residence time taken by the plug flow, ipat, varies from 79 to 85% for the C towers while is in the range of 82-90% for the E and D towers. These values can serve as rough estimates of the model parameters needed to represent the industrial bleach towers. Figures 3.23 to 3.29 show the observed RTD's (bar plots) for pulp slurries in the C, El, DI, E2  and D2 towers, along with the best fit responses from the CSTRS+PFR and CSTRS models. 47  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Figure 3.22: Flow patterns, plots of associated residence time distributions and tracer responses for an upflow tower.  Also shown are the responses predicted by fitting a model with one CSTR connected with a PFR (CSTR+PFR) to the experimental data. They give a further indication that the CSTRS+PFR model provides much more satisfactory predictions for all of the observed residence time distributions than the CSTRS and CSTR+PFR models. The CSTR+PFR model is simpler but probably provides an inaccurate representation of the pulp flow. 48  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.4 Results from fitting CSTRS+PFR and CSTRS models to tracer experimental data. Model Towers  it  cr  mm n  %  CSTRS+PFR  N  CSTRS  ic  idie  fP  tp/it  e  Mill  %  min  %  %/min  N  e %/min  C  24.4  12  2  4.4  18  20.0  82  0.9  93  3.5  C  -^31.8  13  2  4.64  15  27.1  85  2.16  81  4.0  C  59.2  14  2  11.9  21  47.2  79  0.27  83  1.06  E1  75.9  7.9  3  7.78  10  68.1  90.  0.79  274  2.52  Di  138  7.3  3  15.5  11  122  89  0.55  278  132  E2  58.3  7.6  5  10.7  18  47.8  82  0.88  292  1.02  D2  141  7.6  3  16.0  11  125  89  0.45  338  1.07  o = Standard deviation of measured residence time distribution 0.= =... 1 tt  • vE^-  it)2 Ek,exp • Ati,k  (3.26)  e = Standard error of the predicted residence time distributions from the observed values e=  It can also  VE  (Ek,„  -  Ek,pred)2  n -1  (3.27)  be seen from these figures that the response peaks and tails predicted by the  CSTRS+PFR model are lower than the measured values. These underpredictions are believed to be a consequence of the fact that the model does not include the velocity gradients inherent to the vertical laminar flow. A more accurate description would require modification of the PFR, with its uniform velocity to a number of parallel plug flow channels with some velocity distribution. However, the calculations would be complicated significantly. The long tails observed in the measured responses indicate that only a small fraction of the slurry is held up by wall drag in the towers. This can also be evidenced by stagnant volumes, which are determined by comparing observed mean residence times and calculated values. It is shown in Perkins' paper (1971) that stagnant volumes were no more than 10% of the total volumes in the tested E and D towers. But stagnant volumes in the C towers are about 30%. This is mainly attributable to the channeling caused by undissolved C12 bubbles entering 49  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  25 CSTRS+PFR CSTR+PFR CSTRS  It  20  I  Data from Synder (1966)  Ii  15  10  5  15^20^25^30^35^ao^45 -  Time after Injection (min)  Figure 3.23: Measured residence time distribution and model predictions for an upflow C tower with bottom and mid circulators in operation.  the towers, which may be eliminated by good mixing. In tracer trials done on D towers in a mill (Bonar and Munro, 1979), no radial velocity gradients were detected. Since bleaching reactions are non-linear with respect to the content of chromophore in the pulp, a further consideration with the CSTRS+PFR model should be the sequence of CSI'RS and PFR. For example, the model with two CSTR's has three possible sequences as shown in Figure 3.30. For a given overall mean residence time and fraction of PFR, these three sequences all give identical tracer response signals, but act differently for the nonlinear reaction. Which one is the most reasonable can be easily determined from the configuration of the system to be studied. The upflow tower shown in Figure 3.22, for example, might best be represented by sequence b in Figure 3.30. The CSTRS+PFR model with reaction rate terms included is presented in Section 3.3.5. The different behaviors exhibited by the CSTRS+PFR and pure PFR models were compared using the reaction responses of the C and DI towers. The number of CSTR's was chosen to be 2 for the C tower and 3 for the DI tower. The residence time of the PFR was 80% of the overall residence time in the C tower and 90% in the D1 tower. Figures 3.31 to 3.34 show the results for the C tower. 50  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  25  20  15  5  0  25^30^35^40^45^50^55  lime after Injection (win)  Figure 3.24: Measured residence time distribution and model predictions for an upflow C tower with a bottom circulator in operation. 9^ CSTRS+PFR CSTR+PFR CSTRS  8 7  Confidential data  6 5 4 3 2 1 0  0^20  30^40^50^60  ^  70^80^90^100^110^120  Tune after Injection (win)  Figure 3.25: Measured residence time distribution and model predictions for a C tower.  51  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  16 14  II  I  12  CSTRS+PFR CSTR+PFR ^ CSTRS  II  -  '  I' I'  Data from Perkins (1971)  10 8 6 4 2  70^80 lime after Injection (min)  Figure 3.26: Measured residence time distribution and model predictions for a downflow El tower. 8 CSTRS+PFR CSTR+PFR CSTRS  7  Data from Perkins (1971)  6 5 4 3 2  ^t4.  110^120^130^140  ^  150^160^170  180  Time after Injection (min)  Figure 3.27: Measured residence time distribution and model predictions for an upflow D1 tower  52  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  14  12  10  8  6  4  2  Time after Injection (min)  Figure 3.28: Measured residence time distribution and model predictions for a downflow  E2 tower.  7  ^  CSTRS+PFR CSTR+PFR ^ CSTRS^-  6  Data from Perkins (1971)  5  4  4.1  3  2  1 ■  , ,  o—//^_.....,'^st;_..,.,;.. ;,........^mwakt. s--..:,.774-,qp.,..,...9.....„ _ o^100^120^140^160^180^200 Time after Injection (min)  Figure 3.29: Measured residence time distribution and model predictions for an upflow  53  D2 tower.  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Figure 330: Three sequences of a CSTRS+PFR model with two CSTR's.  The CSTRS+PFR and PFR models provide quite similar estimates for the steady-state kappa number and residual chlorine at the given operating conditions (see horizontal lines in the figures). This can be explained by the fact that the PFR occupies a large portion of the entire tower. On the other hand, the two models exhibit obviously different transient responses to changes in the chlorine charge and input kappa number. The CSTRS+PFR model is not only able to predict the dead time but also the low-order response appearing after the dead time and before the new steady state. The difference between the CSTRS+PFR and PFR models in simulating the dynamic responses in residual 002 and brightness after DI tower to an increase in 002 charge is illustrated in Figures 3.35 and 3.36, respectively. Similarities between the CSTRS+PFR and PFR models for steady state simulation are again clearly seen from the plots of 002 residual and brightness as a function of the 002 charge in Figures 3.37 and 3.38, respectively. The brightness predicted by the PFR model is about 1.0 ISO units higher than that predicted by the CSTRS+PFR models. 33.3 Kinetic Models 3.3.3.1 Introduction The most important aspect in modeling a pulp bleaching process is the knowledge of bleaching 54  ^  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  0.55  0.5  C-stage Conditions  New Steady State  C12 Charge: 5% Consistency: 3 % Inlet kappa: 25 to 20 40°C 32 min  0.45  0.4  a  0.35  0.3 Initial Steady State  PFR CSTRS+PFR  ^0.25 ^^ ^ 10^20^30 40^50^60 0  Time (min)  Figure 331: Comparison between CSTRS+PFR and PFR model responses of residual chlorine to a step change in inlet kappa number. 0.3  C - stage Conditions Q2 Charge: 5 to 4% Consistency: 3% Inlet kappa: 25 40°C 32 min  0.25  0.1 PFR CSTRS+PFR  0.050  10  s  20  30  40  ^  50  Time (min)  Figure 332: Comparison between CSTRS+PFR and PFR model responses of residual chlorine to a step change in chlorine charge.  55  60  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  12  C-stage Conditions cli Charge: 5%  Consistency: 3 % Inlet kappa: 25 to 20 40°C 32 min  113  9.5  9  PFR CSTRS+PFR  8.5 0  10  20  30  ao  50  60  Time (min)  Figure 3.33: Comparison between CSTRS+PFR and PFR model responses of kappa number after C tower to a step change in inlet kappa number. 15.5  C-stage Conditions 15  g^14.5  Co Charge: 5 to 4% Consistency: 3% Inlet kappa: 25 40°C 32 min  14 13.5  k^ eos 44  13  12.5 12  PFR CSTRS+PFR  11.5 0^10^20^30  40  50  Time (min)  Figure 334: Comparison between CSTRS+PFR and PFR model responses of kappa number after C tower to a step change in chlorine charge.  56  60  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  0.85  Di - stage Conditions C102 Charge: 1.2 to 1.4%  0.8 - Consistency: 10.9 % 0.75  ...  Inlet Brighteness: 37.5 70 °C 160 snin  i • • " .. --  t^0.7 3 o F  _ - - - - - - - - - - - - - - - - --  • ..^  •  fai^0.65  C")  I  0.55 -  : I I  I  0.45 •  0.4 --// 120 0^  I  PFR CSTRS+PFR  Ii  160  140  180  200  220  Time (min) Figure 3.35: Difference between CSTRS+PFR and PFR models responses  of residual chlorine dioxide to a step change in chlorine dioxide charge. 76 Di - stage Conditions C102 Charge: 1.2 to 1.4% Consistency: 10.9%  75.5 - Inlet Hz:leanness: 37.5 70 °C 160 min  * E  75  § 74.5 on  I , • , .. .... ----------------------  .0 ea  o r.' ^74  , -  73.5 PFR CSTRS+PFR 73-7 0  120^140^160^180^200  Time (mm) Figure 3.36: Difference between CSTRS+PFR and PFR model responses  of brightness after DI tower to a step change in chlorine dioxide charge.  57  220  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  33 DI-stage Conditions  Consistaicy: 10.9 % Inlet Brighteness: 375 70 °C 160 min  3.0  1.5  1.0  03  1.5^2^2.5  %55  ^ ^ 3 3.5  C102 Charge (% on od pulp)  Figure 3.37: Comparison between CSTRS+PFR and PFR model predictions of residual chlorine dioxide as a function of chlorine dioxide charge. 79  78 -  DI-stage Conditions  Consistency: 10.9 To Inlet Brighteness: 375 70°C 160 min  77  76  75  74  73  72 05  1.5  2  2.5  3  3.5  C102 Charge (% on od pulp)  Figure 3.38: Comparison between CSTRS+PFR and PFR model prediction of brightness after DI tower as a function of chlorine dioxide charge. 58  4  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  reaction kinetics. In the process kinetic models employed in this study, the removal of chromophores in the pulp is characterized by a decrease in the kappa number for delignification reactions and by a decrease in the light absorption coefficient for brightening reactions. After a comprehensive survey, we found that research in this area has not caught up with the rapid changes in pulp bleaching technology. It was difficult to evaluate and use the kinetic models for delignification with chlorine dioxide alone or with mixture of chlorine dioxide and chlorine developed by Germgird et al. (Germgard et al., 1982; Germgird and Lindberg, 1982) since neither the parameters nor the experimental data supporting the models were published. Furthermore, the (C+D) model is only valid for a simultaneous addition of chlorine dioxide and chlorine whereas sequential charges are usually employed in a modem chlorination stage. There has been no kinetic model published to describe Eo bleaching, which is another modification in bleaching 'craft pulp. An empirical model by Mackinnon (1987) failed to produce a representation of the Eo bleaching reaction rate although it is called a kinetic model by the author. Due to these circumstances, only kinetic models for the C, Er, DI,  E2  and D2 stages are incorporated in this study. As the kinetics  of these bleaching reactions were largely studied by laboratory experiments with constant chemical compositions, low fibre consistencies and good mixing, the experimental conditions may not be similar to mill scale practice. The experimental conditions and pretreatment on which the models are based are shown in Table 3.5. The table also gives the ranges for which the models are applicable. The type of pretreatment has a pronounced effect on the reactivity of the pulp towards the chemicals. 333.2 Chlorine Delignification  Of the kinetic models proposed by several authors for chlorine bleaching, one by Ackert et al. (1973) is identified as a combination of simplicity and accuracy. This model divides the lignin into three types: fast, slow and a floor level or unreactive lignin. The rate of fast lignin removal is given by  = -dKai = ki • [C12] • Kai ^ (3.28) dt while the rate of slow lignin removal is dKa2^  r" 1 r' T2 = -^= & 2 • 1%-,121  di  59  (3.29)  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.5 Experimental conditions used in bleaching kinetics studies for different bleaching stages.  Stage  Pretreatment kraft pulp  Chem. (mol/L)  pH  C12: 0.7-5.9x 10-2  Temp. (0  Consist. (%)  Author  18-39  0.3-0.7  Ackert et al. (1977)  E1  NaOH: 0.37-7.5x 10-5  9.5-12.5  40-80  0.4  Axegfird (1979)  E1  NaOH: 0.61-4.5x 10-5  10-12  60  , 0.4  Axegfird (1979)  DI  CE (DC)E 0(C+D)E 0(C+D)EH CEHH  C102: 1.0-20x 10-3  2-6  40-80  0.4 6  Ted (1977) and Tormund (1980)  E2  0(C+D)ED  NaOH: 0.61-61x 10-5  7.4-12  40-80  0.4  Axegird and Teder (1984)  D2  CEDE (DC)EDE 0(C+D)EDE  C102: 1.0-20x 10-3  2-6  40-80  0.4 6  Ted (1977) and Tormund (1980)  The reaction rate constants, ki and k2, are expressed as ki = 1123 .exp  ( :1_ 250) 7, T250)  k2 = 22.47•exp  [C12] is the concentration of chlorine (mol/L) and  Kai  (3.30)  and Ka2 are the contents of fast and slow lignin  respectively, expressed as kappa number. Kai + Ka2 + K01= Ka, which is the kappa number analyzed after the alkaline extraction with constant conditions. The initial values of the fast and slow kappa numbers, lea] and ra2, are given by = 0.5 Kai 2  =  0.3 • K  where K'0 is the unbleached kappa number. 60  (3.31)  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PL41VT  The stoichiometric relationship between chlorine consumption and decrease in kappa number is C12 consumption, % on od pulp = Wu, Kappa number decrease  (3.32)  where Wm, is the stoichiometric coefficient (rs, 0.208). Hydrogen ions are formed during the chlorination. If it is assumed that the substitution reaction - is the fast reaction and the oxidation reaction is the slow one, then each mole of reacted C12 produces one and two moles of H+, respectively, for the fast and slow reactions. The kinetics of chlorine bleaching with low C102 substitution are assumed to be the same as for C12 bleaching. Then, the total chlorine concentration includes chlorine dioxide as active chlorine. 1 kg C102 is equivalent to 2.63 kg chlorine based on their oxidizing power. 3.3.3.3 First Alkaline Extraction  The reaction kinetics and lignin solubilization mechanism during the first extraction stage are poorly understood. This lack of understanding is reflected by the fact that only three attempts at modelling delignification kinetics have been published, by AxegArd (1979), Mackinnon (1987) and Taylor et al. (1982). Axegard's model has some fundamental basis while Taylor's is completely empirical. Mackinnon continued Axegfird's work but did not obtain any significant improvement. AxegArd's model was tested and modified in the present study. Kinetic data bases published by AxegArd, including experimental conditions and results for extracting chlorine bleached pulp and chlorine dioxide bleached pulp, are shown in Table 3.6 and Table 3.7, respectively. AxegArd's model represents extraction of the chlorine bleached pulp by two parallel first-order reactions with respect to kappa number decrease: one is the fast lignin reaction and the other is the slow lignin reaction. The rates of these dtwoireactions are expressed as follows K ki • [0111 "Kai rl -dKdat2 r2 = - = k2 • [OH dt  -  ]0.05 Ka2  (3.33)  where Kai and Ka are fast and slow kappa numbers respectively and [OM is hydroxyl ion concentration (moVL). ki and k2 are the rate constants of the fast and slow reactions respectively. 61  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  They depend on the reaction temperature according to -4691)  k1 = 1.96 • 106 • exp ^T k2 = 0.0103 exp  (3.34)  -241)  The ratio of initial kappa numbers between the fast and slow reactions was determined as a function of initial alkalinity, chlorine charge and temperature as -1,,,C; 1  1-3368") = 1.75.^105 exp ^[011-}a25-f  (3.35)  02^ '  where K'01 + ra2 = ra, is the kappa number after chlorination and f is the chlorine charge factor (% available C12 on od pulp/unbleached kappa number). Axegird's model indicates that the hydroxide concentration has a very slight effect on both the fast and slow reactions while higher initial alkalinity results in a larger proportion of lignin in the fast reaction. Although the alkali concentration decreases during extraction in industrial practice, it was found that the kappa number could be satisfactorily predicted from the initial alkali concentration. Table 3.6 Kinetic data base for alkaline extraction of chlorine bleached Kraft pulps  C12 charge factor Data set  p0H  Temp (°c)  Time (min)  Kappa No.  Time (min)  Kappa No.  1  0.15  3  60  0.0 5.5 10 20  172 15.0 14.2 13.8  40 60 70  13.1 12.7 12.3  2  0.2  3  60  0.0 1.5 3 5  13.1 12.1 11.4 10.9  10 30 50 64  10.1 9.60 9.20 8.86  3  0.25  3  60  0.0 5.0 10  10.5 8.46 7.9  20 40 60  7.5 7.0 6.50  4  0.20  1.5  80  0.0 5 10  13.1 8.30 7.67  20 60  6.61 5.44  62  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.6 (Continued) 02 charge Data set^factor  Kinetic data base for alkaline extraction of chlorine bleached Kraft pulps  p0H  Temp (°C)  Time (min)  Kappa No.  Time (min)  Kappa No.  5  0.20  2.5  80  0.0 5 10  13.1 9.10 8.30  40 60  7.11 6.72  6  0.20  3.0  80  0.0 1.5 42 7.9  13.1 10.6 10.1 9.22  16 34 70  8.60 8.28 7.43  7  0.20  3.5  80  0.0 2.1 4.2  13.1 10.6 10.3  7.9 32 64  9.78 8.61 7.94  8  0.20  4.0  80  0.0 1.0 2.1 5.4  13.1 12.0 11.5 10.7  14 35 70  10.1 9.33 8.56  9  0.20  4.5  80  0.0 1.0 2.1 5.1  13.1 12.4 12.0 11.6  17 40 70  10.7 10.1 93  10  0.20  3  95  0.0 2.0 5.2  13.1 9.4 8.6  10 30 60  8.1 7.3 6.7  11  0.20  3  40  0.0 2.8 10  13.1 12.1 11  16 40 70  10.8 10.5 10.1  Data from Axegard (1979). Chlorination Conditions: Initial kappa no. = 29.5, charge factor = 0.15 - 0.25, 20 °C, 60 min, final pH = 1.8-2.3, 3% consist.. Consist. in extraction = 0.4 %.  The present work tested the Axegard model with his experimental data at different chlorine charge and found that the model fits the data quite well at a charge factor of 025. However, at lower chlorine charge factors, the model gives kappa numbers lower than measured experimentally. 63  ^ ^  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  This discrepancy increases as the chlorine charge decreases. The original model assumes that the intensity of chlorination influences the initial distribution between the fast and slow kappa numbers instead of the reaction rates. A more reasonable implication for the effect of chlorination intensity could be that the rate of lignin solubilization will be slower in both the fast and slow reactions if the pulp is treated with less chlorine. The modification of Axegfird's model proposed in this work assumes that the reaction constants are proportional to the chlorine charge factor but the ratio of initial kappa numbers is not dependent on chlorination intensity. By fitting the experimental data, the new reaction constants are determined as = 9.78 • 106 • exp  —4691  ^f (3.36)  —241 k2 = 0.0515 • exp^f and the ratio of initial kappa number as al = K' 2  Table  —3368) T  2.72 104^ • exp ^  (3.37)  [01110.25  3.7 Kinetic data base of alkaline extraction for chlorine dioxide bleached Kraft pulps Time (min)  Kappa No.  Time (min)  Kappa No.  Data set  p0H  1  2  0.0 2.2 5  15 12.8 12.1  20 60 120  112 10.7 10.1  2  3  2.2 5 10  13.8 13.5 13.0  20 60 120  12.6 11.9 11.3  3  4  10 60  13.63 12.85  120  12.3  Data from Axegird (1979). Chlorination Conditions: Initial kappa no. = 29.5, charge factor = 0.14, 20 °C, 60 min, 3 % consist., final pH = 2.0. Extraction Conditions: 60 °C, 0.4 % consist. 64  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  18 — Our Modified Model 16  - Axegard Model o Experiment  14 Z 12 10 8 6 4  0  10^20^30^40  50  60  70  80  Time (min)  Figure 3.39: Kappa number during E1 bleaching of chlorine bleached pulps as calculated by our modified model and Axegard's model.  Figure 3.39 shows a comparison between our modified model and the original Axegird's model  for fitting the kappa number during the alkaline extraction of different chlorinated pulps. The modified model represents the experimental data better than the original model when the chlorine charge factor is reduced. A better fit of the overall data base is also achieved; the modified model yielded a standard deviation of 0.6% compared to 0.8% for the original model. A further comparison is performed using the experimental results of Histed et al. (1985), as shown in Table 3.8, which were obtained over a wider range of chlorine charges. The modified model gives a much better prediction of Histed's data than Axegdrd's model. This suggests that the present description of the reaction dependence on chlorination intensity is more reliable. However, at chlorine charge factors beyond the range covered by the model data base, the model predictions are slightly poorer. This occurs probably because there is a complicated relationship between the extraction reaction rates and the charge factor. The linear correlation assumed in the model is an approximation which is only valid within a narrow range.  65  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.8 Comparison between our modified model and AxegArd model. CE Kappa No.  Cl2 charge factor  C kappa No.  Experimental  Predicted by our modified model  Predicted by Axegfird  0.16  16.1  6.1  6.1  5.7  02  13.0  4.8  4.7  4.1  0.22  10.5  3.7  3.7  3.1  0.26  7.7  3.0  2.6  2.1  0.29  6.0  2.6  1,9  1.5  0.32  5.0  1.9  1.5  1.2  Data from Histed et al (1985). C-Stage Conditions: Initial kappa no. = 30.4, 40-80 °C, 2.5% consist., time = to zero residual. E-Stage Conditions: 80 °C, 10% consist., 60 mm, NaOH charge = 3% on pulp  The two kinetic models were also compared for extraction of a chlorine dioxide bleached pulp using the data base in Table 3.7. Good agreement between prediction of the modified model and the experimental data was obtained if the reaction rate constants were adjusted to a lower value than CE bleaching while the other model parameters were kept the same. The reaction mechanisms and factors governing delignification rates seem to be the same in the extraction stage for both chlorine and chlorine dioxide bleached pulps. Axegárd's suggestion for DE bleaching was that the initial fast-slow ratio Kfai/IV.2 was higher than for CE bleaching. Shown in Figure 3.40 is the kappa number predicted by the modified and original AxegArd's models for the extraction of a chlorine dioxide bleached pulp at different alkali concentrations. It is clear that Axegfird's model is not applicable in this case. 33.3.4 Chlorine Dioxide Bleaching Ted and Tormund (1977; 1980) represented the kinetic characteristics of the first and second chlorine dioxide stages by the following equations: r=-  dKk dt  = k [C1021" • [WIT" k - K k f)3^(3.38)  with - Ea) k = A1 • (K72 + A2) • exP^ • 71)  66  (3.39)  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  16 14  — Our Modified Model - -. Axegard Model o Experiment  12  6 4  2  0^20^40^60  80  ^  100  ^  120  Time (min)  Figure 3.40: Kappa number during Ei bleaching of a chlorine dioxide bleached pulp as calculated by our modified model and AxegArd's model.  where Kk is the content of chromophores in the pulp expressed as the light absorption coefficient at 457 um (m2/kg), Kji is the floor level of Kk (r4.1 m2/kg), [C102] is the mole concentration of C102, [R] is the mole concentration of 11+, E. is the activation energy (rs,59 kJ/mol) and ICI is the initial Kk value.  The constants Ai and A2 are dependent of the type of prebleaching (see Table 3.9).  Table 3.9 Rate constants A1 and A2 for C102 bleaching for different pulps.  Prebleaching (DC)E  A1  A2  0.145x 1010  (DC)EDE  0.117x109  -0.435x 10-3 0.01  0(C+D)EH  0.096x 109  0.023  Data from Ted and Tormund (1980) 67  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.10 Stoichiometric constants n and A3 for C102 consumption in C102 bleaching for different pulps.  Prebleaching  A3  0(C+D)E  1.3  0284  CEHH  1.6  0.486  (DC)E  1.0  0.292  0(C+D)EH  1.15  0.398  (DC)EDE  2.5  0.527K'k  0(C+D)EDE  2.0  0.0675ICk  Data from Ted and Tormund (1980)  The stoichiometric relationship for C102 consumption is  C102 consumption, % on od pulp1 = A 3 • — = Tcio2 Light absorption coefficient decrease Kk  (3.40)  and for II+ generation is 11+ generation, % on od pulp Light absorption coefficient decrease =  H+  (3.41)  where n and A3 vary with pulp type, as listed in Table 3.10. In most cases, 1F H+ was found to be directly proportional to Tao, independent on pH, pulp type and temperature. The rate and stoichiometric constants for chlorine dioxide bleaching of the (DC)E prebleached pulp in Tables 3.9 and 3.10 were used in the DI stage for simulation of a CDEDED sequence in this work. The kinetic constants used for the D2 stage are discussed below.  3.3.3.5 Second Alkaline Extraction Axegard and Teder (1984) found that the E2 stage itself can not delignify or brighten pulp, as is the case for the El stage. The main effects of the E2 stage are to improve the reactivity of pulp and to decrease the C102 consumption in the subsequent D2 stage. The bleaching efficiency of the D2 stage can be increased by higher alkalinity, higher temperature or longer reaction time in the E2  stage. To account for the effects of E2 conditions on D2 bleaching kinetics, we have correlated the 68  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  rate and stoichiometric constants for  D2 bleaching  with E2 conditions on the basis of Axegard and  Teder's investigation, to obtain A2 = B1 • [0111" •^• exp  ai ( -----RE. T  (3.42) )  Ea2 ) A3 = B2 • [OH 1-1 1°8 • exp (-7----  (3.43)  R•T  where [OM, tr and T are the alkalinity, reaction time and temperature, respectively, in the  E2 stage  while A2 and A3 are the rate constant in Equation 3.39 and the stoichiometric constant in Equation 3.40 respectively, for the D2 stage. The constants in Equation 3.42 and 3.43 were determined to be: B./  = 9.1x 1012  B2 =  Ea/  0.02  = 15 kJ/mol  Ea2 = —8 kJ/mol  3.3.4 Correlation of Light Absorption Coefficient with Kappa Number after the E1 Stage  Kappa number is a chemical method which indicates the content of lignin in pulp during the delignification phase while the light absorption coefficient is an optical measurement which indicates the content of chromophores in pulp during the brightening phase. Norrstrtim (1972) has shown that a theoretical relationship exists between the absorption coefficient of pulp and the contents of different chemical species responsible for the pulp color. But none attempted to quantitatively correlate the light absorption coefficient with the lignin content or kappa number of a bleached pulp. A linear relationship between the light absorption coefficient and the kappa number was employed in this work in order to simulate the complete bleach plant and to study how changes in the early delignification stages transfer to the later brightening stages. It was derived from the theory (NorrstrOm, 1972) that the light absorption coefficient of pulp is directly proportional to the content of chromophores in the pulp: Kk =  E i  69  Kki • Ci^  (3.44)  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  where Ci is the content of chromophore species i (mass percentage in pulp) and Kki is its specific absorption coefficient (m2/kg). Since elimination of chromophores in the delignification phase is accomplished by removal of lignin, it is possible that the lignin content represents the chromophore content for a delignified pulp. Thus, Equation 3.44 can be rewritten as (3.45)  Kk = KkLI • CLI b  where the subscript LI denotes lignin and  b  represents the contribution from the other components  of pulp such as extractives and carbohydrates. It is assumed that  b has  a very small value compared  to the product KkIA • Cm because lignin is the main contributor to the light absorption of pulp. Furthermore, based on the fact that the kappa number is directly proportional to the lignin content, it is assumed that a linear relationship exists between the light absorption coefficient and the kappa number for the pulp after the E1 stage, i.e., Kk =  a  Ka  +  As the nature of the chromophoric groups in pulp is not well known, the values of  b a  (3.46)  and b can not  be theoretically estimated. They were obtained by fitting experimental data. Experimental data for the light absorption coefficient versus the kappa number were not directly available in the literature, but were calculated from corresponding brightness values using the Kubellca-Munk equation: Kk (1 — Roof S —  2  Roc,  (3.47)  where Roo denotes the reflectance of the pulp sheet to blue light at a 475 nm wavelength, i.e., the brightness. S, the light scattering coefficient, depends on the physical structure of the pulp sheet; it varies from 30 m2/kg for a thin sheet of kraft pulp to 50 m2/kg for a thick one (Teder and Tormund, 1977; 1980). In this work, a scattering coefficient value of 50 m2/kg was used to convert brightness values to light absorption coefficients or vice versa. An average value should be obtained from experimental data when simulating a given bleach plant. Table 3.11 shows the data base for the brightness versus kappa number results reported by Liebergott (1991) and Dubelsten (1992). The corresponding light absorption coefficients calculated 70  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.11 Data base of brightness versus kappa number after the first extraction stage and light absorption coefficient calculated using Kubelka-Munk equation. Delignification  Ka  Rao % ISO  CE (C97+D3)E CE0 (C97+D3)E0  62 6.2 4.3 4.1 5.4  32 32 41 42 39  2.8 5.3 5.0 5.5 5.4  54 35.8 38.1 39.2 42.3 47.1 51.5  (D 15 C85)E (315C85)E0 (C90+1310)E ()30070)E (350050)E ()30070)E (C90+D1o)E0  Kk m2/kg  362 36.2 21.3 20.0 19.7 9.80 28.8 25.2 23.6  Source Liebergott (1991)  Dubelsten et al (1992).  23.9 14.9 11.4 13.1 10.6  3.0 2.7 (D30070)E0 52.8 3.1 (1350050)E0 3.2 49.2 (D30C70)Eo Reaction Conditions: Chlorination Liebergott 6.8 tTAC (% on pull)) Temperature (°C) 20-60 Time (min) 4-30 Consistency (%) 3.5 C102 Substitution (% ) 0-15 Liebergott Extraction NaOH (% on pulp) 3.5-4.0 Temperature (°C) 70 Time (min) 30-60 Consistency (%) 10 0.5 02 (% on Pulp) t Total available C12 = C12 + 2.63x C102 % on od pulp Correlation coefficient of the Kk with Ka = 0.93  71  Dubelsten 4.74-5.04 40 3 3.0 10-70 Dubelsten 2.22 70 60 10  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  40 35 30  25  20  10  5  2.5^3^3.5^4^4.5^5  5.5  6  6.5  Kappa Number after Et Stage  Figure 3.41: Light absorption coefficient vs. kappa number after first extraction stage.  with the Kubelka-Munk equation are also listed in the table. The coefficient of correlation of the  Kk  with Ka is 0.93. The results from the linear optimization is shown in Figure 3.41. For this data base, the light absorption coefficient — kappa number correlation is Kk =  4.69 K a + 0.01 (3.48)  This equation can be used to convert the kappa number after the El stage into the corresponding light absorption coefficient. It is valid in the kappa number range of 2.5-6.5 for several types of delignified pulps (CE, CE0, C/DE and C/DE0 ). 33.5 Mathematical Models of Unit Operations  The process in industrial bleach plants can be broadly divided into three unit operations: mixing, reaction and washing. Mathematical models for mixing, different bleaching reactions and washing were formulated and incorporated into the SIMNON framework. By assembling the unit operation models, process models for each bleach stage and an entire bleach plant can be constructed. The generic forms of the unit operation models are described below. 72  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  33.5.1 Mixer This model is used to describe the mixing of the pulp slurry with chemicals and steam, or dilution with recycled liquor or other process liquor. The model has two or more inlet streams which are pulp, chemical, steam and/or dilution liquor. The model block diagram depicted in Figure 3.42 has two inlet streams. The components in the incoming and outgoing pulp streams are water, fibres, chromophores (i.e. ligniaceous materials), bleaching chemicals, H+ and dissolved solids. The dissolved solids include chemicals and other soluble substances. The second input stream (chemical stream, steam or dilution liquor) consists of water, bleaching chemicals, H+ and dissolved solids. When perfect mixing and quasi-steady state are assumed, the  mass balance equation for liquor is:  LI = LO + V2 ^  (3.49)  Cm,i^Cmo Li ^ --= Lo ^ 1— Cmi^1 — Cmo  (3.50)  for fibres:  for chromophores: (3.51)  = Ko and for chemical and dissolved solids: Li • Xii = Lo Xio + V2 • Yi2  i = C and DS^(3.52)  where L and V are the flow rates of the liquor in the pulp streams and second input stream (kg/min), respectively, Cm is the fibre consistency (% on slurry), K is the chromophore content expressed as the Incoming Pulp  01"  Lo,Cmo,Ko, Xco,Xxio,XDso  Chemical, Steam or Dilution Stream  Mixer  Outgoing Pulp ow LI ,Cml , KI, XCI,X}f1,XDS1  V2, YC2, YH42, YDS2  Figure 3.42: Block diagram of a bleaching unit operation model: mixer. 73  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  kappa number or the light absorption coefficient, and Xi and Yi represent the contents of the chemical and dissolved solids in the pulp streams and second input stream (% on liquor), respectively. To determine the outlet H+ content, the following reaction is considered: H+ + OH- H20^  (3.53)  The governing equilibrium relationship is 17. [OH-] [H+] 17 x Kw  XOH- • XH+^2  pf  where X0H- and XH+ are the contents of the OW and H+ (% on liquor), respectively;  (3.54)  m is the  liquor density (g/L); 17 is the product of molar molecular weights of OH- and 1-1+; and ICH, is the constant of water dissociation (10-14 mo12/L2 ). If the above relationship is applied to the liquor in all streams entering and leaving the mixer, the mass balance for W becomes (X11+1 + A) = Lo • X0 +  V2 • YH+2^  (3.55)  and for 01-1-: L1  ^ ,,,^  ,^ Kw P)= L i:t •K .(,K„^ :KT; + v2 yiri. 2  (3.56)  where A is the content of the neutralized H+ and OH- (% on liquor). Simultaneous solution of Equations 3.54 to 3.56 yields XH+1. It is noted that OH- is the bleaching agent in the extraction stages. An 'effective' initial concentration of OH- for these stages can be determined using Equations 3.54 to 3.56, instead of using Equation 3.52, if the inlet pulp stream carries a significant amount of acid. 3.15.2 Tower  We have shown that pulp flow patterns in a retention tower can be represented by linking a number of CSTR's with a PFR in a cascade (CSTRS+PFR). For modeling the overall operation in the retention tower, both the flow behavior and bleaching kinetics must be considered. The CSTR and PFR models having bleaching reaction terms are shown below. 74  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  CSTR (Continuous Stirred Tank Reactor) is used not only to represent the local operation in  the retention tower, but also for the bleaching reaction in the mixer before the tower due to the very short residence time of the former, even though flow in some mixers is quite close to plug flow (Bennington et al., 1989). Figure 3.43 gives a general illustration for the CSTR and also the PFR. Constant density of the pulp fluid is assumed. Thus the mass balance for liquor is Ll  = LO  (3.57)  for fibres: dCmi Cm o — Cmi dt  (3.58)  for chromophores: Cmo _• (Ko —  (3.59)  dt^t, • Cmi  and for components in the liquor: dXii X0 — Xii^Cmi dt^I^1 — Cnii^• r where i is the mean residence time of the CSTR,  r  i = C, DS and II+^(3.60)  is the rate of chromophore removal (kappa  number or light absorption decrease) and the product, Cmi 1(1 — Cmi)•Ti.r, is the reaction rate of the bleaching liquor components.  W,  the stoichiometric coefficient, is positive for the reactant: bleaching  chemical (i.e. when subscript i = C), and negative for the products: H+ and dissolved solids (i = II+ and dissolved solids). The bleaching kinetics and the stoichiometry for the chlorination, chlorine dioxide bleaching and alkaline extraction were described previously. The stoichiometry relationship for dissolved solids generation is found from the amount of dissolved lignin in the delignification stages, and is assumed to be zero in the brightening stages.  Incoming Pulp Lo,Cmo,Ko,Xco,X1ro,XDso  Bleach Reactor CSTR and/or PFR  Outgoing Pulp ow Li. Crn,, K , XCI, X11+1,XDSI  Figure 3.43: Block diagram of a bleaching unit operation model: reactor. 75  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  PFR (Plug Flow Reactor) is part of the model for the retention tower. If constant density of the pulp fluid is assumed, the mass balance for liquor becomes (3.61) for fibres:  ac„,^ac,„ at^at  (3.62)  OK OK =—— at^at  (3.63)  _  for chromophores:  and for components in liquor: OXi^OXi^Cm = — Ti • r — Ot^Ot^1C„,  i = C, DS and II+^(3.64)  Equations 3.62 to 3.64 are two-dimensional partial differential equations with respect to the operating time, t, and the residence time, i They cannot be directly solved by SIMNON. They are converted as follows:  '-y /\  67  = c7no ( t — t p )  (t — ip) =^— ip)  K1(t) = K(t — tp) K(t  — tp) = Ko(t — tp) — Jr. dt  X ii(t) = X(t  —  ^  (3.65)  fp) tp  C„,o(t fp) Ti • r• dt X(t — fp) = Xio(t — fp)^ 1 — C,,o(t — tp) —  These equations mean that the output stream variables of the PFR,^Kj and X11 are delay functions of the variables CO3 IC,:; and ,c1.0, respectively. i,, is the time delay and also the residence time of the reactor. C7n0, K61` and X:0 at the time t - ip are the reactor outputs at the same time under the steady-state operation but, under the dynamic operation, they are the outputs of ip later. The time delay function is provided by the SIMNON's internal library while a Runge-KuttaFehlberg algorithm, written as a FORTRAN subroutine, was added to SIMNON to solve the integration in the I direction (i.e., along the flow path). 76  CHAPTER 3:  MODELING AND SIMULATION OF A BLEACH PLANT  3.3.5.3 Washer For the bleach plant simulation, this model can represent the whole washing stage (including washer, dilution and seal tank) or the washer only. The model schematic is shown in Figure 3.44. The dissolved solids include dissolved organic substances and all residual chemicals. The content of lignin remaining in the pulp is unchanged through the washer. The equations for the dissolved solids in washed pulp and filtrate are formulated based on the Norden efficiency factor, analogous to Equation 2.18. For determining 11+ in the outgoing streams, Equation 2.18 is expanded to include the neutralization reaction. The resulting equations for II+ and OH- in the washed pulp liquor are  XH+ =  { liff+  2 + RWERNI:V1711 -1L0-1 (XH+ 0 -111+2) - A  when RW = 1  YHF 2 + 117," • (Xlie- 0 - YH+2) - A RW-1  XOlr  YOH- 2 + RWEN •VaLo-1 (X0H- - YOH- 2) - A 1 -  YoH-2  when RW 1  + k • ( x0H-0 — YoH-2)— A  when RW 1 when RW = 1  (3.66)  (3.67)  where A is the content of the neutralized H+ and OH- (% on liquor). XH+1 is found by simultaneously solving Equations 3.66, 3.67 and 3.54.  Unwashed Pulp  L Washed Pulp^op.  mol  Li, Cna, Ki, MP, XDS/  Lo,Cmo, Ko, Kat, XDSO  Washer -411^  Filtrate  Wash Liquor  V/ YH'/, YDS/  V2, YHF2, YDS2  Figure 3.44: Block diagram of a bleaching unit operation model: washer.  3.3.6 CDEDED Plant Model Figure 3.45 shows the block diagram of the simulation model for a CDEDED plant, along with the process flowsheet. The model consists of five stages:  CD,  El, D1,  E2  and D2. Each stage  is a combination of modules: mixer, CSTR, PFR and washer. The generic descriptions for these modules of different stages were given above. The mixer module is used to calculate the total flow 77  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Wash Liquor  Wash Liquor  NaOH  Wash Liquor  NaOH  C102  Wash Liquor  NaOH Seam  Steam  C102  Bleached  • pulp  _T  Co Tower Tow  Ea Tower  Dl Tower  Filtrate  Filtrate  Filtrate  CEI2  NaOH  -0- WD21--110CD22  Bleached Pulp  1  I c,E13  Steam  MC Unbleached Pulp  Wash Liquor  PD2  PEI  -0- WC^MEI  Minor  CD23  CBI I  Wash Liquor  PC  Mute^  Washer^Seal Tank  ^ Chemical or Steam Mixer  Cl2  D2 Tower  E2 Tower  V Patrols  Alava  Module Notation Stage Module^S^bol Mixer CSTH  C - Stage MC CC1, CC2  El - Stage  Di- Stage  E2 - Stage  02 - Stage  ME1  MD1  ME2  MD2  CE11, CE12, CE13  CD11, CD12, CD13  CE21, CE22, CE23  CD21, CD22, CD23  PPR  PC  PEI  PD1  PE2  P02  Washer  WC  WEI  WD1  WM  WD2  Figure 3.45: Flowsheet of a typical CDEDED bleach plant and corresponding simulation block diagram.  78  CHAPTER 3: MODELJNG AND SIMULATION OF A BLEACH PLANT  rate and initial chemical(s) composition of the bleaching reaction after the pulp slurry is mixed with the chemical (02, NaOH and C102) and steam. A combination of CSTRS with a PFR is used to estimate the state of pulp leaving the retention tower. The CSTRS+PFR structure is changeable in the process simulator. Figure 3.45 shows a typical case. The bleaching reaction occurring in each tower distinguishes it from the other towers. The bleaching kinetics involved in all the tower models have been discussed in the section 3.3.3. The bleaching reaction occurring in the actual mixer is lumped into the tower model. But the mixer reaction can be represented separately if necessary, for example, by studying the sensor response after the mixer and local process control. The washer module is used to determine the dissolved solids carryover of the pulp leaving each stage. Equation 3.48 was used to convert the kappa number leaving the El stage into the light absorption coefficient entering the D1 stage. The model was formulated along the pulp flow path through the plant and, therefore, does not account for any recycled streams. Inclusion of recycle for dilution and washing could result in changes in the dissolved solids content, pH values and temperatures which will in turn affect the pulp bleaching reactions. The model assumes that the pulp liquors are neutral before mixing with acidic or basic chemicals and that the dissolved solids in the pulp do not consume chemicals. Also, the reaction temperatures are taken as input parameters since an energy balance is not included in the model. However, these aspects can be incorporated into the simulation later according to the needs of the particular problem to be studied. Bleaching kinetics, flow patterns and mass balances along the pulp flow path are regarded as the essential features for modeling the dynamic behavior of a multistage bleach plant and are already covered by the present model. The model can simulate the dynamic responses of the kappa number after the delignification stages, brightness (from light absorption coefficient) after the brightening stages, residual chemicals, final pH and dissolved solids carryover for changes in chemical charges, unbleached kappa number, incoming dissolved solids content and production rate. The input variables include bleaching kinetic constants; temperature of bleaching reactions; mean residence time of retention towers; parameters of the tower flow performance (CSTR number and PFR fraction); liquor density; Norden efficiency factor and outlet consistency of washers; consistency, 79  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.12 Operating conditions of a CDEDED bleach plant. Consist.  Temp.  (%) 3  (0c)  Time (min)  Chemical Charge (% on pulp)  40  40  02: 4.54 002: 0.19 TAC: 5.04  10  70  60  NaOH: 2.22  D  6  70  120  002: 0.6 NaOH: 0.35  E  10  70  60  NaOH: 0.5  6  70  120  002: 0.3 NaOH: 0.05  Stage CD  Data from Dubelsten et al. (1992).  kappa number, dissolved solids content, pH and liquor flow rate of unbleached pulp feed; chemical content, pH, and flow rates of chemical streams; flow rate of steam; dissolved solids content, pH and flow rate of wash liquors. Correctness of the model presented was judged by its ability to simulate the steady-state operation of an industrial scale bleachery of softwood kraft pulp (Dubelsten et. al., 1992). The operating conditions are shown in Table 3.12. The input data for the simulation are listed in Table 3.13. The simulated and experimental output results for each bleaching tower are shown in Table 3.14. Good agreement between the simulation and experiment is clearly seen. Although only one set of experimental data was used for the comparison, the agreement is sufficient to create confidence in the use of the model for further dynamic simulations.  3.4 Dynamic Behavior of a CDEDED Plant The CDEDED plant model has been used to investigate the dynamic effects of changes in the  chemical charge in the CD stage, incoming kappa number and pulp production rate on kappa number 80  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  Table 3.13 Input data for simulation of a CDEDED bleach plant. CD  C12 Flow, kg/min Conc., %  E  D  E  D  19.5 100  002  Flow, kg/min Conc., %  8.2 10  / /  26 10  / /  13 10  NaOH Flow, kg/min Conc., %  / /  137 7  22 7  31 7  3 7  Steam, kg/min  /  581  581  581  581  Tower p1, kg/m3 Temp, °C 4, min IA N  1000 40 40 0.8 2  1000 70 60 0.9 3  1000 70 120 0.9 3  1000 70 60 0.9 3  1000 70 120 0.9 3  3 3696 12  3 6099 7.8  3 3696 12  Kinetics  See Section 3.3.3  Washer EN  Wash liquor, kg/min Outlet consist., %  3 3696 12  3 5934 8.0  Unbleached pulp^Liquor flowrate = 13921 kg/min, Consist. =3%, Kappa No. =25.2, Dissolved solids content = 0.2 %, pH = 7  after the Ei stage and brightness after the Di and  D2 stages.  The results obtained in the previous  steady-state simulation were employed as the initial state for the dynamic simulations. Figure 3.46 shows the responses to step changes in the total available chlorine charge (TAC) to the CD stage. The TAC was decreased at t = 0 by 20% and increased at t = 400 minutes by 20% of the initial value of 5.04% (see Figure 3.46A). As expected, it took 86 minutes (sum of 81  Chapter 3: MODELING AND SIMULATION OF A BLEACH PL4iV7'  Table 3.14 Comparison between predicted and experimental data  at steady state after retention towers of a CDEDED bleach plant.  Stage CD  Chromophores cal.^exp. kappa:12.6  Residual chem.  pH  (% on liquor) C12: 3.25x 10-2  cal.^exp. 1.6  Dissolved solids (% on liquor) 0.481  E  kappa:5.6^5.3  NaOH: 5.81x 10-3  11.2^11.0  0.628  D  bright.:74.9^75.3  C102: 5.33x 10-3 NaOH: 1.16x 10-1°  3.5^3.7  0.169  E  bright.:74.9  NaOH: 9.60x 10-2  12.4  8.93x 10-2  3.9^3.8  3.78x 10-2  C102: 8.05x 10 -3 NaOH: 3.44x 104° Experimental data from Dubelsten et al. (1992). Operating conditions are listed in Table 3.12. D  bright.:88.8^89.2  PFR residence times of the CD and El stages) and a short-time dynamic process for the CE kappa number to respond to each input change (see Figure 3.46B ). The CED brightness and final brightness responded more slowly and with lower magnitude than the CE kappa number (see Figures 3.46C and 3.46D). It took about 230 minutes for the CED brightness to decrease from 74.9 to 68.5% ISO and 410 minutes for the final brightness to decrease from 88.8 to 87.5% ISO after the 20% decrease was made in the TAC. Due to the nonlinearity of bleaching kinetics, the response gain of each stage for the decrease in the chemical charge was apparently different from that for the chemical charge increase. The former is approximately double that of the latter in the simulated case. Step responses of the bleach plant to ±20% changes in the incoming kappa number have also been simulated and the results are similar to those shown in Figure 3.46. Another dynamic simulation employed incoming kappa number fluctuations derived from on-line measurements in Swedish mills (Edlund, Lundquist and Hansson, 1992). The simulated disturbances duplicated the magnitudes and frequencies of the actual disturbances. Referring to Figure 3.47A, large magnitude variations in the incoming kappa number over a period of 5000 minutes proceeded quite slowly in comparison with the process dynamics. Consequently, they all passed through the system 82  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  (A)  6 riR  5.5 5  c.5  .5  4.5 4  7.9  (B)  7A 6.9 6.4 e  5.9 5.4  4 .9 4.4  78 •  (C)  76 74  •  72 70  •  68  (D) tsR  89 88 87  .o 86  0^200^400^600^800^1000 Time (min)  Figure 3.46: CDEDED bleach plant response to step changes in total available chlorine charge in CD stage.  83  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLAM'  (A) ..  _  _ 9.4 8.9 8.4 7.9 7.4 6.9 6.4 5.9 5.4 4.9  _  4.4 80 75 70 65 60 55 90 89 88 87 86 85 84 0  1000  3000  2000  4000  5000  Time (min)  Figure 3.47: CDEDED bleach plant response to typical variations in incoming kappa number.  84  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  without control, resulting in the obvious changes in CE kappa number, CED and final brightness as shown in Figures 3.47B, 3.47C and 3.47D. The CPU time taken for this simulation was 70 minutes. Figure 3.48 shows the bleach plant responses when the pulp production rate was raised from 431 to 647 kg/min at t.-0 (i.e., a 15% step change). These responses were much more complex than those for the changes in chemical charge and incoming kappa number. The response of the second stage (E1) consisted of three distinct parts; the response in the third stage (D1), four parts and the response in the fifth stage (D2), six parts. This was attributable to the fact that the change in production rate caused changes in both the residence time and initial chemical concentration for all stages. The initial response of each stage resulted from the decrease in its residence time. The residence time decrease was gradual in the plug flow portion of the tower and produced a smaller time delay. The second response was due to the reduction in the initial chemical concentration. It followed that the responses to the changes in the previous stages (decrease in residence time and initial concentration) appear one at a time. Again, insensitivity of the final stage to the input change was found. For a 15% increase in production rate, the CE kappa number rose by 25% of its initial value after 110 minutes. The CDED brightness decreased by 6% while the final brightness only dropped by 1%.  3.5 Conclusions It was the objective of this work to develop a dynamic model of a multistage bleach plant. Through an analysis of the process operations in a typical bleaching sequence, the tower flow pattern, bleaching kinetics and relationship between the different chromophore indicators were identified as fundamental aspects which needed detailed study. From the tracer responses of typical bleaching towers, the pulp flow in the tower was found to be a combination of agitated mixing and plug flow. Among all the models tested, a cascaded CSTR's and PFR model was found to give the best representation of the experimental results. This model is proved to be the most successful at characterizing the retention tower for the purpose of bleach process control. The typical extent of mixing and fraction of plug flow in this model were also obtained. The CSTRS+PFR and PFR models were compared with respect to their ability to predict 85  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  IS;  500  4 490  .s  A. 1  .......  ...  (A) -  480 470 460  ■■1  450  ■■1  440 430 7.0 (B) -  6.8 6.4 6.2 6.0 5.8  -  _  5.6 5.4 75  Response to residence time decrease  b- 74 co a*  (C) -  _ _  to finial concentration decrease of Di-stage .411---- to El-stage changes  to CD-stage changes  70 88.8 88.6 88.4 88.2 88.0 87.8 87.6 87.4  87.2  0  50^100^150^200^250^300  ^  350  ^  400  ^  450  Time (min) Figure 3.48: CDEDED bleach plant response to a step change in pulp production rate.  86  500  CHAPTER 3: MODELING AND SIMULATION OF A BLEACH PLANT  the reaction responses of the chlorine tower and the first chlorine dioxide tower. The CSTRS+PFR model was able to more realistically represent transient responses in kappa number, brightness and residual chemicals than the PFR model when the chemicals charge or incoming kappa number was changed. The former can not only describe long-time delay but also low-order dynamic response of the tower. The choice between the CSTRS+PFR and PFR models did not seem to significantly affect the calculations of the steady-state bleaching results. So far, kinetic studies have been conducted for chlorine delignification, alkaline extraction and chlorine dioxide bleaching of kraft pulp. From the published kinetic models, those considered to be reliable and suitable for process simulation were incorporated in this work. The model for the first extraction was modified and the new model gave a better prediction for the effects of changing chlorine or chlorine dioxide charge. A theoretical analysis showed that the light absorption coefficient may be linearly related to the kappa number for a delignified pulp. The linear correlation between the light absorption coefficient and the kappa number after the El stage was determined using experimental data. It allows the connection of the delignification and succeeding brightening phase, and thus makes possible the simulation of the whole bleach plant. The dynamic model of the CDEDED bleach plant was assembled by linking the unit operation models for mixing, reaction and washing. The model was validated by checking the steady-state simulation against available experimental results. The applicability of the CDEDED bleach plant model was illustrated by following the dynamic behavior of the system due to changes in chlorine charge, incoming kappa number and production rate. The responses of CE kappa number as well as CED and final brightness to step changes in the chemical charge had strong nonlinearity and a long time delay. The responses of later stages were less sensitive than those of the earlier stages. When the production rate was changed, the system demonstrated complicated interactions. In conclusion, this study has established a base for further work in the process simulation and control of multistage bleach plants by use of the dynamic simulation package, SIMNON. The 87  Chapter 3: MODELING AND SIMULATION OF A BLEACH PLANT  simulator developed has been successfully used in predicting both the steady-state and dynamic behaviors of the a CDEDED bleaching sequence. For modelling other types of sequences where different bleaching agents are used, more information on bleaching kinetics is necessary; but the methodologies developed for describing the tower flow pattern, connection of the delignification with brightening phases and the unit operations should be directly adaptable. 3.6 Recommendations and Suggestions for Future Work  The major recommendation for future work is to develop dynamic simulators for commercial bleach plants on the basis of the present work and apply them to improve process control strategies. This general recommendation gives rise to the following specific suggestions. 1. To study and model chemical kinetics of modern bleaching technologies such as delignification N...  with high chlorine dioxide substitution, alkaline extraction with addition of oxygen, etc. This is the most essential step towards simulating a commercial bleaching sequence. 2. To account for the heat effects due to dilution, heating, washing and chemical reaction. 3. To study the buffering capacities of different components in bleaching liquor in order to provide an accurate estimates of pH. 4. To incorporate recycle schemes into the simulation. 5. To test the predictions of the developed models against mill measurements. 6. To apply the dynamic simulator to process control practices.  88  CHAPTER 4: GENERAL CONCLUSIONS  CHAPTER 4 GENERAL CONCLUSIONS  In this study, dynamic process simulators for brown stock washing plants and multistage bleach plants have been developed and preliminarily validated. SIMNON software has been used as the main tool to construct computer models and perform simulations. The simulator of the brown stock washing system provides a simple but accurate method to quantify the interactions among the process components and to predict system dynamic response to changes in major process variables. The model has been used to investigate the dynamic behavior and evaluate the process control strategies for a three-stage countercurrent washing plant. The simulator of the bleach plant gives realistic descriptions for the dynamic characteristics of the process such as long-time delays and strong nonlinearity. It can be used not only to simulate a CDEDED plant but also other types of bleach plants as long as the bleaching kinetics used in these sequences are available. Connection of these two simulators will constitute simulation for a process from the brown stock after digestion through to the final bleached product. This is significant for understanding the dynamics of an entire kraft pulping process and thus designing better control systems. Through the course of this study, it becomes obvious that a successful dynamic process simulator can only be constructed on the basis of accurate mathematical models, a sufficient data base and powerful computer technology. There is still much work that needs to be done in these three areas to develop useful models of the complex processes in the pulp industry.  89  REFERENCES Ackert, J. E., "Kraft Pulp Chlorination Kinetics", Ph.D. Thesis, University of Idaho, Moscow (1973). Ackert, J. E., D. D. Koch, and L. L Edwards, "Displacement Chlorination of Kraft Pulps — An Experimental Study and Comparison of Models", TAPPI J. 58(10), 141 (1975). AxegArd, P., "Kinetics of Alkaline Bleaching for the Kraft CE Sequence", Svensk Papperstiding 81(12), 361-367 (1979). AxegArd, P., U. Jansson, and A Teder, "The E2 Stage Improves the Reactivity of Pulp Towards Chlorine Dioxide", J. Pulp Paper Sci. 10(1), 1-5 (1984). AxegArd, P., S. Moldenius, and L. Olin, "Basic Chemical Kinetic Equations are Useful for an Understanding of Pulping Processes", Svensk Papperstiding 81(5), 131-136 (1979). Bennington, C. P. J., R. J. Kerekes, and J. R. Grace, "Mixing in Pulp Bleaching", J. Pulp Paper Sci. 15(5), 186-195 (1989). Biallcowski, W. L., "Bleach Plant Process Control", in "1990 Bleach Plant Operations", TAPPI Seminar Notes (1990), pp. 189. Bonar, L., and J. D. Munro, "Improvements in C12 Mixing at Crofton", in Prodeedings of CPPA Spring Conference (1979), pp. 136-140. Branch, C. A., and S. Muller, "Physical Properties of Kraft Pulp Black Liquor", Appita 44(5), 339-341 (1991). Brenner, H., "The Diffusion Model of Longitudinal Mixing in the Beds of Finite Length, Numerical Values", Chem. Eng. Sci. 17, 229-236 (1962). Brownell, L. E., and D. L. Katz, Chem. Eng. Progr. 43(11), 602 (1947). Carman, P. C., "Flow of Gases Through Porous Media", Academic Press., New York (1956). Chapnerka, V. D., "A Kinetic Study of the Chlorination of Unbleached Kraft Pulp", Ph.D. Thesis, University of Florida (1961). 90  Cholette, A., and L. Cloutier, "Mixing Efficiency Determination for Continuous Flow Systems", Can. J. Chem. Eng. 37, 105-112 (1959). Crotogino, R. H., N. A. Poirier, and D. T. Trinh, "The Principles of Pulp Washing", TAPPI J. 70(6), 95-103 (1987). Crotogino, R. H., D. T. Trinh, N. A. Poirier, and D. T. Wearing, "Pulp Washing' 83 — A Review", in Proc. of International Chemical Reconvery (TApPI) (1985). Darcy, H., "Les Fontaines Publiques de La Ville de Dijon", Victor Dalmint, Paris (1856). Dubelsten, P., S. G. Arinobu, and C. J. Kanters, "The Compatibility of C/D with Oxidative Extraction", Pulp Paper Can. 93(4), 24-27 (1992). Edlund, S. G., S.-0. Lundquist, and A. Hansson, "Experiences from the STFI OPTI-Kappa and its Use for the Control of Pulping Processes", Pulp Paper Can. 93(12), 118-122 (1992). Edwards, L. L., R. Baldus, and R. Abbot, "GEMS Documentation Describing Data Input, Simulation Control and Simulation Options", University of Idaho, Chemical Engineering Department (1983). Edwards, L. L., G. Hovsenius, and H. Norrstrtim, "Bleaching Kinetics: A General Model", Svensk Papperstidning 76(3), 123-126 (1973). Edwards, L. L., Peyron M., and Minton M., "Models for Cross-flow Pulp Washing Calculations", Pulp Paper Can. 87(1), 67 (1986). Forgacs, 0. L., A. A. Robertson, and S. G. Mason, "The Hydrodynamic Behavior of PaperMaking Fibres", Pulp Paper Mag. Canada 59(5), 117 (1958). Germgard, U., "Stoichiometry of Chlorine Dioxide Prebleaching of Softwood Kraft Pulp", Svensk Papperstiding 85(6), R43-50 (1982a). Genngird, U., "Stoichiometry of Prebleaching of Softwood Kraft Pulp with Chlorine Dioxide and Small Fractions of Chlorine", Cellulose Chem. Technol. 48(17), 35-48 (1982b). GermgArd, U., and R.-M. Karlsson, "Kinetics and Stoichiomentry of CE-Prebleaching of Softwood Kraft Pulp", Svensk Papperstiding 88(85), R146-150 (1985). 91  GermgArd, U., and H. Lindberg, "A Mathematical Model for (D+C)-Prebleaching", Svensk Papperstiding 85(18), R172-176 (1982). GermgArd, U., and B. SjOgren, "Ozone Prebleaching of Modified-Cook and Oxygen-Bleached Softwood Kraft Pulp", Svensk Papperstiding 88(15), R127-132 (1985). GermgArd, U., and A. Teder, "Kinetics of Chlorine Dioxide Prebleaching", Trans. Tech. Sect. CPPA 5(6), 31-36 (1980). GermgArd, U., A. Teder, and D. Tormund, "The Relative Rates of Consumption of Chlorine and Chlorine Dioxide During (D+C) Bleaching Softwood Kraft Pulp", TAPPI J. 65(5), 124-126 (1982). GermgArd, U., A. Teder, and D. Torrnund, "Mathematical Models for Simulation and Control of Bleaching Stage", Nordic Pulp Paper Res. 2(1), 16-22 (1987). Han, S. T., and W. L. Ingmason, "A Simplified Theory of Filtration", TAPPI J. 50(4), 176 (1967). Han, Y., "Flow through Porous Media: Impact of Flow on Wood Pulp Washer Performance", Master's Thesis, University of Idaho, Moscow (1985). Han, Y., "Modelling and Simulation of Wood Pulp Washers", Ph.D. Thesis, University of Idaho, Moscow (August 1989). Hisey, R. W., "An Investigation of the Mechanism of the Dewatering of Compressible Beds", TAPPI J. 39(10), 690 (1956). Histed, J. A., and C. R. Vega, "Optimum Chlorination Stage Conditions", Pulp Paper Can. 88(1), T22-25 (1987). Hsu, C., and J. S. Hsieh, "Reaction Kinetics in Oxygen Bleaching", AIChE J. 34(11), 116-122 (1988). Ingmason, W. L., and B. D. Andrews, "High-Velocity Water Flow Through Fibre Mats", TAPPI J. 35(3), 150-155 (1963). Karter, E. M., "The Role of Physico-Chemical Rate Phenomena in Wood Pulp Chlorination", Ph.D. Thesis, University of Maine, Orono (1968). 92  Kerekes, R. J., R. M. Soszynsky, and P. A. Tam Doo, "The Flocculation of Pulp Fibres", in Transactions of the Eight Fundamental Research Symposium, Oxford, vol. 1 (1985), pp. 265-310. Korhonen, 0., "Brownstock Washing: A Review of Current Technology", Pulp Paper J. (9), 104 (1979). Kovasin, K., H. V. Norden, and L. Ahonen, "Modelling the Filtration Stage of a Pulp Washer", Filtration & Separation 25(1), 42 (1988). Kubellca, P., and F. Munk, Z. Tech. Physik 12, 593 (1931). Kuo, M. T., "Filtrate Cake Washing Performance", AIChE J. 6(4), 566 (1960). Lee, P. F., "Optimizing the Displacement Washing of Pads of Wood Pulp Fibres", TAPPI 62(9), 75-78 (1979). Levenspiel, 0., "Chemical Reaction Engineering", John Wiley & Sons Inc., New York, 2nd Ed (1972). Liebergott, N., "General Principles of Pulp Bleaching", PAPRICAN Course Notes (1991). Lundquist, S.-0., "Pulp Washing Control: Principle and Results", Pulp Paper Can. 86(11), 72-76 (1985). Lundquist, S.-0., and H. Nordstrom, "The Development of a Control System for a Pulp Washing Plant Through the Use of Dynamic Simulation", in 1FAC./PRP 4 Automation Symposium Proc., Belgium (June 1980), pp. 3-5. Luthi, 0., "Different Approaches to Model Displacement Ratios", in Proc. of Pulp Washing Symposium (Tech Sect., CPPA), Quebec (September 1983), pp. 9. Luthi, 0., "Mechanics of Thick Mats", in Pulp Washing Symposium Proc., Marihamn, Finland (May 1987), pp. 1987. Mackinnon, J., "Dynamic Simulation of the First Two Stages of a Kraft Softwood Bleach Process", Master's Thesis, McGill University (1987). MAPPS, "MAPPS User's Guide", The Institute of Paper Chemistry, Appleton, WI (1984). 93  MASSBAL, "MASSBAL MKII System Documentation", SACDA, University of Western Ontario (1983). McConnell, R. R., 0. Syberg, and N. W. Wild, "Introduction to Process Simulation", TAPPI Press, 2nd Ed (1992). Moller, K., G. G Duffy, and A. L. Titchener, "The Laminar Plug Flow Regime of Paper Pulp Suspensions in Pipes", Svensk Papperstidning 74,829 (1971). Moreira, R. M., and R. M. Felder, "Residence Time Distributions of Paper Pulp Slurries in Vertical Laminar Flow", AIChE J. 25(1), 131-143 (1979). Myers, M. R., and L. L Edwards, "Development and Verification of Predictive Oxygen Delignification Model for Hardwood and Softwood Kraft Pulp", TAPPI J. 72(9), 215-219 (1989). NNse, T., and K.-E. Sjoberg, "Advanced Control of a Drum Washing Plant", Pulp Paper Can. 90(9), 108-111 (1989). Norden, H. V., "Analysis of a Pulp Washing Filter", Kemian Te,ollisuus 23(4), 344-351 (1966). Norden, H. V., "Statistical Analysis of Pulp Washer on an Industrial Rotary Drum", Pulp Paper Mag. Can. 74(10), 83-90 (1973). Norden, H. V., and M. Peldcanen, "General Calculation Method for Stagewise Models of Pulp Washing and Other Mass and Heat Transfer", in Pulp Washing'87 Symposium (CPPA Trans. Techn. Sect.) (September 1987), pp. 237. NorrstrOm, H., "Light Absorption of Pulp and Pulp Components", Svensk Papperstiding 75(22), 891-899 (1972). Olin, L., and A. Teder, "The Kinetics of Oxygen Bleaching", TAPPI J. 62(43-50), 12 (1979). PAPDYN, "PAPDYN Process Simulation Package", Pulp and Paper Research Institute of Canada (1991). PAPMOD, "PAPMOD Process Simulation Package", Pulp and Paper Research Institute of Canada (1988). 94  Paterson, A. H. J., and R. J. Kerekes, "Fundamentals of Mixing in Pulp Suspensions: Measurement of Microscal Mixing of Chlorine", J. Pulp Paper Sci. 11(4), 108-113 (1985). Paterson, A. H. J., and R. J. Kerekes, "Fundamentals of Mixing in Pulp Suspensions: Measurement of Microscal Mixing in Mill Chlorination Mixers", J. Pulp Paper Sci. 12(3), J78–J83 (1986). Pattyson, G., "Kamyr MC Mixer for Chlorine Dioxide Mixing at Great Lakes Forest Products, Thunder Bay, Ontario", in Proc. of the 70th Annual CPPA Meeting, Monteal (1984), pp. A63–A68. Pellet, G., "Longitudinal Dispersion, Intrapartical Diffusion and Liquid-Phase Mass Transfer During Flow Through Multiparticle System", TAPPI J. 49(2), 75-82 (1966). Perkins, J. K., "Channeling in Continuous Bleaching Cells (Pulp Behavior Patterns in Bleach Towers)", in Prodeedings of TAPPI 25th Alkaline Pulping Conference (1971), pp. 191-198. Perkins, J. K., "Mixers, Pumps and Towers — Design and Performance", in "Bleaching Plant Operations", TAPPI Seminar Notes (1985), pp. 127-134. Perkins, J. K., H. S. Welsh, and J. H. Mappus, "Brown Stock Washing Efficiency", TAPPI J. 37(3), 83-89 (1954). Perron, M., and B. Lebeau, "A Mathematical Model of Pulp Washing on Rotary Drums", Transactions of the Techn. Sect., CPPA 3(1), TR1–'TR5 (1977). Perry, J. F., M. Gottlieb, and R. A. Hohn, "Dynamic Simulation of a Brown Stock Washer", in ISA/75 Pulp and Paper Division Symposium Proc., Milwaukee, Wisconsin (1975), pp. 45-56. Poirier, N. A., R. H. Crotogino, and W. J. M. Douglas, "Displacement Washer of Wood Pulp — A Model with Source Term for Low Initial Liquor Concentration", in Pulp Washing '87 Symposium (CPPA/TS), Mariehamn, Finland (1987a). Poirier, N. A., R. H. Crotogino, and W. J. M. Douglas, "Displacement Washer of Wood Pulp — A Model with Source Term for Higher Initial Liquor Concentration", in Pulp Washing '87 Symposium (CPPA/TS), Mariehamn, Finland (1987b). 95  Poirier, N. A., R H. Crotogino, D. T. Trinh, and W. J. M. Douglas, "Displacement Washer of Wood Pulp — An Experimental Study at Low Initial Liquor Concentration", in Pulp Washing '87 Symposium (CPPA/TS), Mariehamn, Finland (1987c). Rapson, W. H., "TAPPI Monograph Series", TAPPI, 27 (1963). Reynolds, E., J. D. Gibbon, and S. Attowood, "Smoothing Quality Variations in Storage Chests Holding Paper Stock", Trans. Instn. Chem. Engrs 42, T13-T21 (1964). Roada, R. H., "FlowCalc: A Flowsheet Calculation Program for Microcomputers", Simulation Software, Custer, WI (1983). Roche, A., and D. Bouchard, "Process Simulation in the Pulp and Paper Industry", Technical Report M22, Pulp and Paper Research Institute of Canada (1982). Russel, N. A., "A Study of the Initial Phase of the Aqueous Chlorination of Kraft Pulp Mills", Ph.D. Thesis, Institute of Paper Chemisty, Lawrence College, Appleton (1966). Sherman, W. R., "The Movement of a Soluble Material During the Washing of a Bed of Packed Solids", AIChE J. 64(10), 855-860 (1964). SIMNON, "SIMNON User's Guide for Unix System", Lund Institute of Technology, Sweden (1991). Sinn, S., "State-of-the-Art Chlorine Dioxide Mixer Installed at Weyerhaeuser", Pulp Paper Can. 58(6), 119-121 (1984). Snyder, J., "Measuring Bleaching Tower Retention Times", TAPPI J. 49(12), 105-106 (1966). Sperry, D. R., "Deduction of Filtration Equation Including Term for Cloth Resistance and Experiments to Verify Same", Chem. Met. Eng. 15, 198 (1916). Taylor, R. A., Vega C. R., and J. A. Histed, "Numerical Simulation of the Extraction Stage Stoichiometry and Rate", in Int'l Pulp Bleach Conf. (CPPA/TAPPI), San Diego (1982), pp. 107-113. Teder, A., and D. Tormund, "Kinetics of Chlorine Dioxide Bleaching", Trans. Tech. Sect. CPPA 3(2), 41-46 (1977). 96  Teder, A., and D. Tormund, "Mathematical Model for Chlorine Dioxide Bleaching and its Applications", AIChE Symp. Ser. 76(200), 133-142 (1980). Terry, N. A., and Wm. J. Frederick, "Kraft Recovery Boiler Physical and Chemical Processes", American Paper Institute (1988), Ch. 2, pp. 62-64. Tomiak, A., "Purging Calculations for Cascades of Mixing Stages", Can. J. Chem. Eng. 52(8), 502 (1974). Torregrossa, L. 0., "Effect of Mixing on Chlorine Dioxide Bleaching", in TAPPI Pulping Conference, Houston, TX (1983), pp. 635-641. Trinh, D. T., N. A. Poirier, and R. H. Crotogino, "Displacement Washer of Wood Pulp — An Experimental Study at High Initial Liquor Concentration", in Pulp Washing '87 Symposium (CPPA/TS), Mariehamn, Finland (1987). Turner, P. A., B. J. Allison, and J. K. Oei, "Brown Stock Washer Control (Part II: Filtrate Tank Level Control)", in CPPA Annual Meeting Proc. (Book B), Techn. Sect., Quebec (December 1991), pp. 109-113. Turner, P. A., A. A. Roche, J. D. McDonald, and A. R. P. Van Heiningen, "Dynamic Behavior of a Brown Stock Washing Plant", in CPPA Spring Conference of Pacific Coast and West Branches (CPPA, Techn. Sect.) (May 1991). Ulinder, J. D., "Fixed Time Zone Methodology for Plug Flow Simulation as Applied to an Oxygen Delignification Reactor", in Proc. of Control Systems' 92, Wistler (1992), pp. 181. Venkatesh, V., and X. N. Nguyen, "Chemical Recovery in the Alkaline Pulp Processes", TAPPI Press. (1985), Ch. 3, pp. 17-18. Walker, 0. J., and A. Cholette, "Determination of the Optimum Size and Efficiency of Stock Chests I. The Ideal Chest", Pulp Paper Mag. Can. 59,113-117 (1958). Wigsten, A. L., "Conductivity—Based Shower Water Control In Brown Stock Washing", in TAPPI Pulping Conf. Proc. (Book 1), New Orleans (November 1988), pp. 1-13. Woodard, E. R., "A New Sensor for Brown Stock Washer Control", in TAPPI Pulping Conf. Proc. (Book 1), New Orleans (November 1988), pp. 15-17. 97  APPENDIX: A: LITERATURE REVIEW OF PULP WASHING  APPENDIX A LITERATURE REVIEW OF PULP WASHING Pulp washing has been traditionally described by two distinct approaches. One, called mechanistic model here, is based on the knowledge of fundamental physical phenomena which control the washing performance, such as filtration, two-phase flow, and displacement washing. The other, called efficiency model, is based on a efficiency concept that lumps various phenomena together. A literature review of the fundamental washing studies and washing efficiency concepts is presented below. A.1 Fundamental Washing Studies A.1.1 Filtration  The wood pulp fibres themselves are a porous media although the fluid within these pores is not likely to flow. When the mat is formed during filtration, the filtrate is driven through the mat by the pressure difference across the mat. Darcy's law (Darcy, 1856) can be used for liquid flow through a porous media. On the basis of Darcy's law, Sperry (1916) suggested a model for filtration in a cake which is growing in thickness, and has been proven useful in many applications. Many who followed Sperry's model were mainly with finding a correlation for the resistance term in the model for various filtration media. The resistance of a wood fibre mat depends on the compressible nature of the fibre since the fibres form highly compressible mats during filtration. Comprehensive research into the filtration and compression of wood pulp fibres has been carried out by 1ngmanson and coworkers (Hisey, 1956; 1ngmason and Andrews, 1963; Han and 1ngmason, 1967) but also by others (Han, 1985; Kovasin, 1988; Luthi, 1987). A.1.2 Two-phase Flow  Two-phase flow occurs in the partially saturated fibre mat during dewatering, through which liquid and air flow simultaneously. Darcy's law has been extended to the two fluid phases by correlating the permeability of each phase to the saturation of the mat. The saturation is the ratio of interfibre void volume occupied by the liquid to the total void volume of the mat. Calculation of the permeability for the two-phase flow has been studied by a few authors (Brownell and Katz, 1947; 98  APPENDIX: A: LITERATURE REVIEW OF PULP WASHING  Nelson and Dahlsi, 1957; Han, 1985). An empirical correlation by Han has been used for describing the dewatering operation in vacuum washers (Han, 1989). A.1.3 Compression and Drainage Properties of Wood Fibrous Mat  Here list a number of equations for calculation of compression and drainage properties of the wood fibrous mat. They could be applicable for the purpose of modelling industrial brown stock washing. 1. Density, pm, and Porosity, E Ingmason and Andrews (1963) expressed the mat density as a  function of the pressure drop, AP, in the form of: = (1  2  —  J • API^  2  (A.68)  where I and J are the compressibility constant. The mat porosity is calculated from the mat density by: c = 1 — p„, •  v^  (A.69)  where v is the specific volume of the fibres (m3/od kg fibres). 2. Permeability, kD Kozeny-Carman equation (Carman, 1956) for the Darcy's permeability is: E3  = ko  772  (1 —  (A.70)  where ri is the specific surface of the fibres (rn21m3) and ko is Kozeny constant. 3. Relative Permeability, kr The equation for the relative permeability proposed by Han (1985)  is:  0_211 2- , I. _Qr $  (A.71)  where p is the porosity distribution index. Sr is the reduced saturation, estimated by: Sr  Soo =^ — 1 — Soo  (A.72)  and Soo, the residual saturation, is given by = 1 (kij • AP ) -0.264 Soo 4Ok Hm, • 7 where Hm is the mat thickness and  -y is  the surface tension of fibres (N/m). 99  (A.73)  APPENDIX: A: LITERATURE REVIEW OF PULP WASHING  A.1.4 Displacement Washing  Displacement washing is the extraction of liquor in the mat by a piston effect with wash liquor containing less solutes. Ideal displacement happens when no solute transfers between the wash liquor and the original liquor in the mat. However, mixing and diffusion are unavoidable in actual displacement washing. In addition, there is an adsorption/desorption equilibrium of the solute on fibre surface if any solute is adsorbable. Brenner (1962) suggested an axially dispersed plug flow model to represent non-ideal displacement using a single parameter, ie. Peclect number. This model was extended by addition of a source term to account for adsorption (Sherman, 1964) and for intrafibre diffusion (Pellet, 1966). Poirier and his coworkers (1987a; 1987b; 1987c) modelled displacement washing of pulp for both high and low initial mat liquor concentration. They found that the axial dispersion model without the source term was adequate for high solute concentrations, but inclusion of a sorption isotherm was needed at low solute concentrations. Several studies (Pellet, 1966; Lee, 1979; Poirier et al., 1987c; Trinh et al., 1987) are available on the Peelet number of pulp fibre mats. Displacement washing has also been modelled by Kuo (1960) and Han and Ingmason (1967) in a quite different way from the dispersion model. The basic assumption of their model is that the mat has been dewatered to its residual saturation such that the wash liquor passes through the empty channels in plug flow and washing is primarily achieved by diffusion. But this assumption does not fit pulp washing. Only a small portion of the mat liquor can be removed prior to washing in any existing pulp washing equipment.  A.2 Washing Efficiencies  There are many methods of evaluating the efficiency of removal of dissolved solids from pulp by various pulp washing systems. Displacement ratio factor and Norden efficiency are two of them useful for simulation of industrial washing processes (Crotogino et al., 1985). Displacement ratio, originating from Perkins (1954) is defined as the ratio of actual reduction of dissolved solids to the maximum possible reduction. For most types of washing configurations including the vacuum drum washer, displacement ratio is a strong function of the quantity of wash 100  APPENDIX: A: LITERATURE REVIEW OF PULP WASHING  water applied but is less dependent on other process variables within the normal operation range (Luthi, 1983). The concept of Norden efficiency factor (Norden, 1966; Norden et al., 1973) was derived by comparing an real washing system to a hypothetical system comprising of a series of countercurrent ideal dilution-thickening stages. The Norden efficiency factor is interpreted as the number of ideal mixing stages needed to achieve the same washing performance as the system under consideration. This concept is usually used for a washing stage including a seal tank but can also be applied to a washing unit within the stage or a complete washing plant. The Norden efficiency factor for a generalized washing system shown in Figure A.49 is expressed as: ^Z:3  logjxrg:;:1  EN =^togV21 Li Lo  Ync,—Y11S2 XDSO -XDS1  Filtrate  when V2 = L1  (A.74)  Washed Pulp  Unwashed Pulp Lo,XDSO  when V2 0 L 1  Washing System  V I ,YDS1  XDSI  Wash Liquor V2, YDS2  Figure A.49: A generalized washing system described by Norden model.  Norden et al. (1973) have investigated the effects of the wash liquor ratio ( ratio of wash liquor  flow to washed pulp liquor flow ) and several other washing variables — production rate, drum speed, consistencies and alkali concentrations on the washing efficiency of vacuum drum filters in a mill. Regression analysis on measured data showed that Norden efficiency factors were remarkably different for different pulps or different washing stages in series but changed slowly with the operating variables. Therefore, the Norden efficiency factor is often treated in practice as a constant (Crotogino et al., 1985). 101  APPENDIX: A: LITERATURE REVIEW OF PULP WASHING  Washing efficiency is a steady state concept, representing the long-term performance of an actual washing system. Thus, for modeling of dynamic behavior of a washing plant, the efficiency concept can only be used to describe the washing component which has a negligible transient period compared to the slow process component. The Norden efficiency factor has been used for the vacuum drum filter in dynamic-simulations of brown stock washing systems (Lundquist, 1980; Nase and Sjoberg, 1989).  102  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  APPENDIX B LITERATURE REVIEW OF PULP BLEACHING  B.1 Lignin and Chromophores of Wood Pulp  Pure cellulose is white and does not contribute to pulp color. It is the chromophores contained in the pulp which are responsible for absorbing light and thus for the color of pulp. Cluomophores are coloured compounds, which absorb radiation in the ultra-violet and visible regions. The colourproducing species of pulp are mainly lignin or lignin breakdown products. Lignin is a highly branch, aromatic, three-dimensional polymer. In the lignin molecule, there are chemical groups containing chromogenic structures (eg. carbonyl groups and double bonds). Chromogens form chromophoric systems when they are present in suitable combination with benzene rings and auxomochromes (eg. OH, OMe, Cl). The lignin in wood contains a number of coloured constituents. However, some of lignin chromophoric groups result from reactions occurring during pulping and bleaching treatments. The carbohydrates and extractives in pulp also contain chromophoric groups but contribute much less to light absorption of pulp compared to lignin. Bleaching of lignin in a lcraft pulp is achieved by lignin removal followed by lignin decolourization which allows production of the desired brightness with minimal loss in pulp strength. The principle of dilignification is to convert the remaining lignin into soluble fragments by chemical treatment. For instance, lignin during chlorination reacts with chlorine to form chloro-lignins which are partly water-soluble in the washing step and readily alkali-soluble in the next extraction stage. Pulp in the delignification phase is characterized by its lignin content. The lignin content is usually measured by the kappa number in bleaching physical chemistry as well as in the industry. The kappa number is defined as the number of cubic centimeters of 0.1N potassium permanganate solution consumed by 1 gram of moisture-free pulp. It relates linearly to the lignin content for all types and grades of pulps up to yields of 70%. The content of lignin for unbleached softwood pulp is approximately 0.13 to 0.15 times the kappa number. For bleached pulp, the relationship between lignin and kappa number is also a function of the extent of delignification and oxidation of the pulp since the kappa number is determined by the reduction of potassium permanganate. 103  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  The decolourizing or brightening of pulp is concerned with selective elimination of chromophoric groups in lignin without lignin removal by using an oxidizing agent or a reducing agent. Chlorine dioxide is a conventional oxidant for bleaching kraft pulp. Pulp in this brightening phase is characterized by its chromophore content. The overall content of the chromophores is expressed in terms of brightness or by the light absorption coefficient of pulp. The brightness is a standardized method of measuring the reflectance of a pulp sheet using blue light at a wavelength of 457nm. It not only depends on the content of the light-absorbing components in pulp but also on the physical structure of the pulp sheet. In contrast, the light absorption coefficient at 457m wavelength, in the Kubelka-Munk equation (Kubelka and Munk, 1931; Rapson, 1963), is theoretically directly proportional to the absorptivity of the material and thus to the chromophore content (NorrstrOm, 1972). Therefore, the light absorption coefficient is preferable for studying the kinetics of pulp brightening reactions while the brightness is usually used as a technical unit to report the product quality. Assuming a light scattering coefficient of the standard pulp brightness sheet, the light absorption coefficient of the bleached pulp can be converted to the brightness using the KubelkaMunk equation. B.2 Bleaching Kinetics of Kraft Pulp B.2.1 Experimental Methods  Two principal methods have been used for obtaining experimental data and studying a bleaching reaction from the kinetic point of view. The first is the constant condition method, in which concentrations of active chemicals in bleaching solution are held constant throughout the bleaching. This method has many advantages, eg. O Simple mathematical treatment of the data. O No assumption concerning the stoichiometry has to be made. O Stoichiometry data are obtained if the liquor reactants are added continuously at the same rate as they are consumed and the added amounts are measured. O It is easy to separate different effects from each other. 104  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  0 The mathematical model is easier to relate to reaction mechanism.  The disadvantage is divergence from an industrial bleaching process where the bleaching chemicals are charged to the pulp at the start, and concentrations of all reactants then decrease as the reaction proceeds. The second is the differential method, in which the bleaching conditions resemble a mill bleaching. The advantage and disadvantage of the differential method are quite opposite to those of the constant conditions methods. The first method has been more frequently used than the second method. B.2.2 Mathematical Models  The reaction rate is directly governed by composition and temperature if a reaction is homogeneous, i.e. takes place in a single phase. In a heterogeneous reaction more than one phase is involved, hence heat and reacting material transportation between different phases may be a controlling step in determining the rate of overall reaction. Only when the chemical reaction is the rate controlling step, can a heterogeneous process be treated as a homogeneous reaction. Bleaching processes are heterogeneous reactions because they occur between fibre particles and gas or liquid chemical reagents. Chlorination with chlorine is a gas-liquid-solid three phase reaction. Alkaline extraction requires the presence of two liquid and solid phases. The factors that influence the rate of the bleaching reaction are quite complex, due to complex mechanisms of the lignin reactions as well as heterogeneity. Few attempts have been made to formulate kinetic models for pulp bleaching based on analysis of chemical reaction mechanisms and multi-phase transportation phenomena. The overall rate of the bleaching reaction is usually described by a process kinetic model of the following form (Edwards et al., 1973): r  dt = k • [A]a • [le • Ke (B.75)  Where K is the lignin content, measured as kappa number in a dilignification stage or the chromophore content measured as the light absorption coefficient in a brightening stage. [Al and [3] are the reactant concentrations in the process liquor, expressed in terms of mol/L. The rate orders, a, b and c are not necessarily the stoichiometric coefficients and need not be integers. The reaction rate constant, k, is 105  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  a function of the reaction temperature and can be expressed by the Arrhenius' law: k = kip •  exp ( 7,#)^(B.76) -  Where ko is called the frequency factor and E. is called the activation energy of the reaction. The main purpose of such a model is to summarize the experimental results and to simulate bleaching processes. The model has nothing to do with predicting the bleaching mechanisms at the molecular level. It might be no longer valid when the operating conditions and pulp properties are beyond the range from which the model is derived. Another important point is that the model is a homogeneous-like form since it only gives explicit composition-dependent and temperature-dependent terms. It can not tell how a change in the mass transfer rate of the reactant affects the bleaching rate when the reaction rate is controlled by the physical steps such as diffusion. For pulp bleaching systems, the effects of transporting chemicals from bulk liquor into the fibre wall or reverse might be significant. For example, increased pulp consistency might result in increased diffusion resistance originating from fibres overlapping each other (Ackert et al., 1975). A modification coefficient was added in the kinetic model of chlorination to account for consistency by Chaperka (1961) and Karter (1968). This type of model has been widely used in kinetic studies of pulp bleaching: O Delignification with oxygen (0) (Teder and Olm, 1979; Hsu and Hsieh, 1988; Myers and Edwards, 1989); O Ozone bleaching (Z) (Germgird and SjOgren, 1985); O Delignification with chlorine (C) (Chapnerka, 1961; Russel, 1966; Karter, 1968; Ackert, 1973; Mackinnon, 1987; Germgárd and Karlsson, 1985), chlorine dioxide (D) (Germgara and Teder, 1980; Germgird, 1982a; 1982b) and chlorine dioxide+chlorine (D+C) (Germgfird et al., 1982; Genngärd and Lindberg, 1982); O First alkaline extraction stage (E1) (Axegard, 1979; Mackinnon, 1987); O Bleaching with chlorine dioxide (Teder and Tormund, 1977; Teder and Tormund, 1980); O Second alkaline extraction stage (E2) (Axegard et al., 1984). 106  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  Two common factors in the bleaching kinetics of different stages were found and incorporated into the mathematical models in some general way. High Order: It is found that the bleaching reaction initially proceeds very fast, but the rate decreases considerably with increasing reaction time even though the concentration of the bleaching agent is kept constant. Figure B.50 gives an example of the decrease in the light absorption coefficient during the first chlorine dioxide bleaching. In a mathematical sense ,a fairly high reaction order is required to fit the experimental curve of kappa number or light absorption coefficient as a function of reaction time. The reaction order with respect to kappa number or light absorption coefficient is between 3 and 5 in most cases. From a mechanistic standpoint, it is improbable that 3-5 lignin fragments react with each other. A explanation was that the bleaching reaction is more likely to consist of a number of simultaneous reactions (AxegArd et al., 1979). When the bleaching effects of all these reaction are combined, they give the impression of high reaction order. Some authors (Ackert, 1973; Mackinnon, 1987; AxegArd et al., 1979; Myers and Edwards, 1989) accounted for the significant decrease in the bleaching reaction rate with time by assuming the existence of two categories of lignins, 'fast' and 'slow', which separately have a low order reaction rate. Asymptotic Level: It is also observed that most bleaching reactions never go to completion in a finite time. Usually, the chromophore content in pulp reaches a constant level after a very long reaction time rather than continues to decrease. This irremovable part is subtracted form total chromophores as a non-reactive component in kinetic expressions (Chapnerica, 1961; Karter, 1968; Teder and Tormund, 1980; Mackinnon, 1987; GermgArd et al., 1987; Myers and Edwards, 1989). GermgArd, Teder and etc. at the Swedish Forest Products Laboratory carried out research on bleaching kinetics for different stages for more than ten years. Their work was summarized in the paper by GermgArd et al. (1987). They found that the reaction order with respect to the chromophore content, expressed as kappa number or light absorption coefficient is 2-5, the order with respect to the bleaching chemical is 0.5 in most cases and the activation energy is 50-75 kJ/mol for all cases expect for ozone bleaching where it is lower, about 30 kJ/mol. 107  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  002 0.01 mol/L pH 8 70 °C  60  ^ ^ ^ 100 120 80  Reaction Time (min)  Figure B.50: An example of bleaching reaction characteristics.  B.3 Mixing in Bleaching B.3.1 Segregation and Flow Patterns Mixing is caused by relative movement within the fluid and usually has two overlapping aspects: the degree of segregation of the fluid and the earliness of mixing. The degree of segregation or non-uniformity is classified based on the range of physical dimensions over which the mixing occurs. For a pulp slurry system, there are the following three categories of mixing scales (Bennington et al., 1989):  Scale Designation^Approximate Size (mm) macroscale^> 10 Fibre-scale^0.05 - 10 microscale^<0.05 Macroscale mixing can be achieved by substantial backflow, i.e., bulk movement of the suspension over relatively large distances. Although 10 mm is chosen as a lower limit of macroscale  108  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  mixing, dimensions of a pipe diameter or more are of practical interest. Fibre-scale mixing is small scale mixing achieved primarily by shear, i.e., by local relative fluid movement induced by velocity gradients or turbulence, and by diffusion, i.e., molecular movement induced by concentration gradients. The other small scale mixing, microscale is mainly attained by molecular diffusion. It is aided by clump breaking and stretching that greatly increases the surface area available for diffusion. Uniformities on the three levels, particularly on the small scales depend strongly upon pulp slurry theology as well as the forces driving mixing such as velocity and concentration gradients. Pulp slurries are continuous fibre networks that possess structure and strength resulting from interaction between neighboring fibres. In the slurry having consistencies above 0.5%, cohesive strength occurs from mechanical forces bending and hooking fibres (Kerekes et al., 1985). At consistencies above 20%, the character of the slurry changes from mass concentration of fibres in water to a network of wet fibre aggregates. To produce flow in a pulp slurry or expose fibres to a chemical at an addition point, sufficient stress must be applied to rupture the fibre network as well as the flocs within it. Thus, pulp network strength is an important factor in the mixing of pulp slurry. As the consistency of the slurry increases, the network strength will increase with increase in the number of fibre to fibre interactions. Flocs with higher local consistency have greater strength than the surrounding slurry. Kerekes et al. (1985) and many other investigators found that the network strength is directly proportional to slurry consistency raised to a certain exponent. The earliness of mixing means whether fluid mixes early or late as it flows through the vessel. It concerns the bulk flow pattern through the vessel. There are two idealized flow patterns: ideal mixed flow and plug flow. Though real reactors never fully follow these patterns, a large number of reactors are designed to approach these ideals with negligible error. For example, tubular vessels can be considered as plug flow while continuous stirred tank reactors can be accounted for ideal mixed flow. To characterize the actual flow within a vessel which is neither in plug nor ideally mixed, many types of non-ideal flow models have been used. Some draw an analogy between mixing in the actual flow and diffusional process. These are called dispersion models. Others build a chain or network of ideal mixers. One parameter non-ideal flow models, i.e. the axial dispersed models and CSTRS, are known as adequate representatives of tubular vessels (Levenspiel, 1972). 109  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  B.3.2 Mixing and Bleaching  Since bleaching involves multiple simultaneous chemical reactions with lignin and carbohydrate components in the pulp, mixing uniformities as well as flow pattern affect the product quality and chemical consumption for a desired degree of bleaching. The potential impact of segregation is dependent on whether the time required for a desirable state in mixing is long or short with respect to time for bleaching reaction to take place. Relative reaction/mixing rates for major bleaching reactions in common mixers were obtained by Bennington et al. (1989) and are listed in Table B.15, where Tr  is the inverse of the reaction rate constant, and rm is the time required to produce a mixture of  specific quality, which characterizes mixing rate. Three cases are of interest: 1. Mixing occurs much faster than the reaction rate, rdrm>>1: Here mixing has achieved the ultimate state in which the chemical agent is uniformly distributed in the bulk liquid around each fibre before chemical reaction has proceeded to any significant extent. The only remaining distribution is transfer of the chemical from phase to phase. The overall bleaching rate is therefore governed by the reaction kinetics. Bleaching with chlorine, chlorine dioxide and oxygen in highshear mixer appears to be in this category. 2. Mixing and reaction proceed at approximately the same rate, i.e., rr/rm Here, both mixing and reaction kinetics determine the bleaching rate. 3. Reaction occurs much faster than mixing, rirm<<1: Here mixing is slow compare to the effective reaction rate. Consequently, the reaction performance, such as residual chemical, product quality, is determined by mixing: the rate at which mixing proceeds as well as the degree of the mixture uniformity. As shown in Table B.15 chlorination in CST falls into this category. B.33 Bleaching Mixers and Retention Towers  Mixing of pulp slurries is very complex owing to the unique rhe,ology of the slurry caused by their substantial network strength. The correlation between mixing quality and its factors is not well known and it is difficult to make direct measurement of this quality. Because each flow pattern of fluid through the vessel has associated with it a clearly defined residence time distribution (RTD) or exit age distribution function (E), the flow pattern can be estimated by measurement of residence time 110  APPENDIX: B: LITERATURE REVIEW OF PULP BLEACHING  Table B.15 Relative reaction/mixing rates for common pulp mixers. Trirm  Mixer Type  CST Static High-Shear  Bleaching Chemicals C12  C102  02  6.0x 10-2 4.5 180  0.39  4.6  29  350  1.2x 103  1.4 x 04  distribution (Cholette and Cloutier, 1959; Walker and Cholette, 1958; Reynolds, 1964; Levenspiel, 1972). By comparing the measured E curves with various models, the ability of the mixer to attenuate incoming fluctuations can be determined and the existence of short circuiting or dead zones within the vessel can be identified. For pulp mixing, there are a number of methods for assessing macroscale mixing besides using E curves (Torregrossa, 1983; Pattyson, 1984; Sinn, 1984). A direct measure of small-scale mixing may be the intensity of segregation (Paterson and Kerekes, 1985; 1986). However, a quantitative relationship between the behavior of the bleaching process and this small scale mixing has not been well established while there are various flow pattern models available for correlating to macroscale mixing. The flow in bleaching retention towers has been approximated as plug flow. Deviation from this ideality is sometimes considerable due to channeling, vertical mixing (Snyder, 1966) or creation of stagnant regions (Perkins, 1986). Mixing behavior in mixers used for bleaching is much more complex since the initial mixing between the chemical and fibre occurs here while the retention tower provides the additional time to complete the distribution of chemical throughout the slurry not accomplished by the mixer, and additional diffusion into the interstices of the fibre. The mixing behavior of typical bleaching mixers, CST, static mixers and high-shear mixers has been evaluated by Bennington et al. (1989). The flow pattern in these mixers changes from baclunixing to plug flow. CST for low consistency pulp produces good macroscale mixing through sufficient bacicmixing, but with non-uniform fibre-scale mixing. The static and high-shear mixers improve the fibre-scale uniformity, but at the expense of macroscale mixing.  111  

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