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Interaction of iron with wood pulp fibres Susilo, Robin 2003

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INTERACTION OF IRON WITH WOOD PULP FIBRES B y Robin Susilo B.Eng. (Chemical Engineering) University of Indonesia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL AND BIOLOGICAL ENGINEERING We accept this thesis as conforming to th£ required standard THE UNIVERSITY OF BRITISH COLUMBIA November 2003 © Robin Susilo, 2003 Library Authorization In presenting this thesis in partial fulfillment 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. Name of Author (please print) Date Title of Thesis: U t g r « * o f t ° y \ o f j ^ n uJoed pu[p £bu>* Degree: Master 04 fyyljd Sge^n Year: XQO\ Abstract Considerable research has been done to reduce water consumption by recycling the process water. The goal is to achieve zero liquid discharge or "closed-cycle" mill operation. However, there are still some problems due to the presence of some materials that are not needed in the pulping process and which tend to accumulate in the system and create operational problems. These materials mostly are metal ions that are known as Non-Process Elements (NPEs). They originate mainly from wood, and also from process water and the makeup lime. Therefore, understanding the interaction of these harmful metal ions with the fiber is needed to manage these metals in a closed-cycle pulp mill. Fibers have many functional groups such as: carboxyl acid, phenolic hydroxyl, hexenuronic acid, polysaccharide acids and catechol groups. These groups create a negatively charged fibre when they dissociate in water. Hence, fibres can interact with the metal ions like iron, manganese and copper electrostatically, chemically or both. The focus of this work is the interaction of iron with wood fibres. Pulp samples from British Columbia interior and coastal mills were investigated. Metal ion concentration on the fiber at various pulping stages was determined. The sampling points at the pulp mill were taken after brown stock washer, after oxygen delignification, and at various stages of the bleaching processes. It was found that fibre from a coastal mill has a higher iron concentration compared with fibre from an interior mill. The water used in transporting the log might introduce iron into the wood so that pulp from coastal mill would have more iron. It was also found that iron concentration in the fiberline did not change much because iron form precipitates and trapped inside the fiber mat. Metal ion removal methods using a combination of acid washing and chelation in four-washing stages was developed. A chelating agent (DTPA) was able to increase the iron removal substantially. The fiber properties such as the water retention value (WRV) and the charge properties were determined for the metal ion partitioning prediction. The fiber saturation point was found to increase as the pH increase due to swelling for all samples. Two charged groups were able to 11 represent the fiber charge on the fiber, one charge group dissociates at acidic condition and the other one dissociates at alkaline condition. The origin of these two functional groups was not identified. The acidic charge group might probably contain carboxyl acid bound to lignin (pK A »5-6 ) and uronic acid (pK B ~3-4). The alkaline charge group might be the phenolic hydroxyl bound to lignin. It was also found that the charge content decreases down the fiberline as the lignin content decreases. Partitioning experiments were conducted whereby we measured the iron concentration on the fiber and in the surrounding liquor. The fibres were previously acid washed with a chelating agent to "free" them from the metals. The results indicated that iron strongly stayed on the fiber even at acidic conditions where the fibre did not contribute any charge to attract the metal ion. S E M & E D X analysis confirmed the presence of iron precipitates on the fiber and trapped inside the fiber mat so that these precipitates become the fibre phase belonging. Iron might probably form complexes with the anionic group in the water, especially the hydroxyl group. A partitioning model based on Donnan equilibrium was used to compare equilibrium concentration of iron in fibre and the surrounding liquor. The model calculated values were not found to be in agreement with experiment data probably due to iron-compound precipitation. It should be noted that the model was able to predict manganese and copper partitioning, although the predictions were slightly lower than the experimental data especially at higher p H (pH > 7). Manganese and copper containing precipitates were encountered at p H 7 but not at p H 5. Manganese and copper data were obtained in another study in our laboratory. It can be concluded that the iron interaction with the charge groups on the wood fibres is not a chemical binding interaction, but due to the iron-compound precipitates which are trapped inside the fibre web. Hence, a strong water soluble ligand like those chelating agents can bind the metal ions from the suspension so that the harmful metal ions can be removed from the suspension. i i i Table of Contents Abstract ii Table of Contents iv List of Tables viii List of Figures xi List of Symbols xvi Acknowledgements xviii 1. Introduction 1 1.1. Chemical Pulping Technology and the Environment 1 1.2. Closed Cycle Operation and Non-Process Elements 2 1.3. Scope of Thesis 4 2. Literature Review and Research Objectives 5 2.1. Iron Chemistry 5 2.2. Non process elements (NPEs) in kraft mills 14 2.3. Metal ion removal 16 2.4. Charged groups in pulp fibres 18 2.5. Metal ion partitioning in pulp suspensions 22 2.6. Research objectives 26 3. Modelling Framework: Physical System and Mathematical Model. 27 3.1. Physical system 27 3.2. Mathematical Model 28 3.2.1. Dissociation of Fiber Charged Groups on Fibers 29 3.2.2. Electroneutrality 29 3.2.3. Water Dissociation Constant 30 3.2.4. Donnan Equilibrium 30 3.2.5. Charge Balances 30 3.2.6. Mass balances 31 iv 3.2.7. Inclusion of Binding Interaction 31 3.3. Fiber Charge and Binding Constant Determination 36 3.3.1. Fiber Charge Calculation from Potentiometric Titration 36 3.3.2. Binding Constant Determination 38 4. Experimental: materials, equipment and methods 42 4.1. Materials 42 4.1.1. Pulp Samples '. 42 4.1.2. De-ionized water 45 4.1.3. Di-ethylene tri-amine penta-acetic acid (DTPA) solution 45 4.1.4. HC1 (Hydrochloric acid) 46 4.1.5. Fe standard for A A Analysis 47 4.1.6. Spectrophotometer standard 47 4.2. Equipment 48 4.2.1. p H meters 49 4.2.2. Centrifuge 49 4.2.3. Atomic Absorption Spectroscopy ( A A S ) 50 4.2.4. Spectrophotometer (Colorimeter) 51 4.3. Experimental Methods 52 4.3.1. Moisture Content Determination 52 4.3.2. Ashing the Pulp Sample 53 4.3.3. Digestion of the Pulp Sample 53 4.3.4. FSP Water Determination 53 4.3.5. Potentiometric titration 54 4.3.6. Metal Profile of a Pulp Sample 55 4.3.7. Metal ion removal from pulp 58 4.3.8. Metal ion partitioning in a pulp suspension 61 4.4. S E M & E D X Analysis of A c i d Washed Pulp Samples 64 4.4.1. Sample Preparation 64 4.4.2. S E M & E D X Preparation 64 4.4.3. S E M & E D X Analysis Procedure 65 v 5. Results and Discussion 67 5.1. Water Retention Value (WRV) 67 5.1.1. Water Retention Value of BC Coastal Samples 67 5.1.2. Water Retention Value of BC Interior Samples 71 5.2. Potentiometric Titration 74 5.2.1. Potentiometric Titration: Acid-Washed Chelated Fiber Mat 74 5.2.2. Potentiometric Titration: Acid-Washed Chelated Fiber Mat with Metal 77 5.3. Iron Concentration Profiles 79 5.3.1. Iron Concentration of BC Coastal Samples 79 5.3.2. Iron Concentration of BC Interior Samples 81 5.4. Residual Iron Concentration 82 5.4.1. Residual Iron Concentration from BC Coastal Samples 83 5.4.2. Iron Concentration in Liquor from BC Coastal Samples 84 5.4.3. Residual Iron Concentration from BC Interior Samples 86 5.5. Fiber Charge Properties 88 5.5.1. Fiber Charge Properties of BC Coastal Mill Fiber 89 5.5.2. Fiber Charge Properties of BC Interior Mill Fiber 96 5.6. Binding Constant 100 5.7. Iron Partitioning 100 5.7.1. Iron Partitioning Experiment 100 5.7.2. Iron Partitioning Prediction 106 5.8. SEM & EDX Results 109 5.8.1. SEM & EDX of Acid Washed Pulp Not Containing A Precipitate 110 5.8.2. SEM & EDX of Acid Washed Fiber Mat Containing A Precipitate 111 5.8.3. SEM & EDX of Acid Washed Pulp after Introducing Iron at pH 3 115 6. Conclusions and recommendations 118 6.1. Conclusions 118 6.2. Recommendations 118 7. References 119 vi APPENDIX 123 APPENDIX A: WRV Measurement Data 124 APPENDIX B: Potentiometric Titration Data for Fiber Charge Calculation 127 APPENDIX C: Potentiometric Titration Data for Binding Constant Calculation.... 133 APPENDIX D: Metal Profile Analysis 137 APPENDIX E: Metal Removal Analysis 139 APPENDIX F: Metal Partitioning Analysis 141 APPENDIX G: Sample of Calculation 144 APPENDIX H: Error Analysis 145 APPENDIX I: Fiber Charge Program 146 APPENDIX J: Binding Constant Calculation 152 APPENDIX K: Iron Partitioning Prediction 157 List of Tables Table 2.1: Cumulative formation constants for ferrous and ferric hydroxyl complexes at 25°C (Langmuir, 1997) 7 Table 2.2: Median values of micro elements concentration (mg/kg-od fiber) in four different wood chips species (Bryant, P. S., et. al., 1993) 15 Table 2.3: Comparison of different methods in determining the anionic charge groups in pulps fiber, given in mmol/kg-od fiber (Lingren et al., 2002) 19 Table 2.4: Dissociation constant and fiber charge of oxygen bleached hardwood kraft fiber from p H 2 tolO (Rasanen et al., 2001) 20 Table 2.5: The fiber charge properties of unbleached softwood kraft fiber determined from a potentiometric titration data at p H 2 to 6 (Laine et al., 1994) 21 Table 2.6: The amount o f acidic groups in fibres (pmol/g) determined by conductometric and potentiometric titration using different ionic concentration (Athley et. al., 2001) 22 Table 2.7: Equil ibrium constant (pKa) from potentiometric titration (Athley et. al., 2001) 22 Table 2.8: Complex formation constant of manganese and calcium with carboxyl group on the fiber evaluated from potentiometric titration at ionic concentration of 0.02 M N a C l for hardwood (HW) and softwood (SW) pulp (Karin, A . , et al. (2001) 24 Table 4.1: Sampling points and pulp properties determined at the mi l l for B C Coastal 43 Table 4.2: Sampling points and pulp properties determined at the mi l l for B C Interior 45 Table 4.3: Stability constants of D T P A and E D T A (Rasanen and Karkkainen, 2003) 46 Table 5.1: W R V fitting parameter from the regression of the data of B C Coastal 70 Table 5.2: W R V fitting parameter from the regression of B C Interior 73 Table 5.3: Fiber charge fitting parameter from the regression of the potentiometric titration data of B C Coastal samples 90 Table 5.4: Fiber charge properties fitted using "Two-site" charge model of B C Coastal samples 94 Table 5.5: Fiber charge properties up to p H 8 (Laine et al., 1994) 95 Table 5.6: Fiber charge comparison between several authors 96 vin Table 5.7: Fiber charge fitting parameter from the regression of the potentiometric titration data of B C Interior Samples 97 Table 5.8: Fiber charge properties fitted using "two-site" charge model of B C Interior samples 99 APPENDIX Table A - l : W R V experimental data for Brown Stock Washer mat of B C Coastal M i l l 124 Table A-2: W R V experimental data for Post Oxygen Washer mat of B C Coastal M i l l 124 Table A - 3 : W R V experimental data for D c washer stage outlet of B C Coastal M i l l 124 Table A - 4 : W R V experimental data for E o p washer stage outlet mat of B C Coastal M i l l 125 Table A - 5 : W R V experimental data for D n washer stage outlet mat of B C Coastal M i l l 125 Table A - 6 : W R V experimental data for D 2 washer stage outlet mat of B C Coastal M i l l 125 Table A - 7 : W R V experimental data for Brown Stock Washer mat of B C Interior M i l l 126 Table A - 8 : W R V experimental data for Post Oxygen Washer mat of B C Interior M i l l 126 Table A - 9 : W R V experimental data for D c washer mat of B C Interior M i l l 126 Table B - 1 : Potentiometric titration for Brown Stock Washer (BSW) mat of B C Coastal M i l l 127 Table B-2 : Potentiometric titration results for Post Oxygen Washer mat of B C Coastal M i l l 128 Table B - 3 : Potentiometric titration results for D c washer stage outlet mat of B C Coastal M i l l 129 Table B-4: Potentiometric titration results for E o p washer stage outlet mat of B C Coastal M i l l 129 Table B-5 : Potentiometric titration results for D n washer stage outlet mat of B C Coastal M i l l 130 Table B-6: Potentiometric titration results for D 2 washer stage outlet mat of B C Coastal M i l l 130 Table B-7 : Potentiometric titration results for Brown Stock Washer (BSW) of B C Interior M i l l 131 Table B-8 : Potentiometric titration results for Post Oxygen Washer mat of B C Interior M i l l 132 Table B-9 : Potentiometric titration results for D c mat of B C Interior M i l l 132 IX Table C - l : Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of iron at 520 ppm from B C Coastal M i l l 135 Table C-2: Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of manganese at 600 ppm from B C Coastal M i l l 135 Table C-3: Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of copper from B C Coastal M i l l 136 Table D - l : Iron profile from A A S Analysis of B C Coastal M i l l 137 Table D-2: Iron profile from A A S Analysis of B C Interior M i l l 137 Table D-3: Iron profile from ICP Analysis of B C Coastal M i l l 138 Table D-4: Iron profile from ICP Analysis of B C Interior M i l l 138 Table D-5: Iron profile from Spectrophotometer Analysis of B C Coastal M i l l 138 Table E - l : Residual iron concentration from A A S Analysis of B C Coastal M i l l 139 Table E-2: Residual iron concentration from A A S Analysis of B C Interior M i l l 139 Table E-3: Residual iron concentration from ICP Analysis of B C Coastal M i l l 139 Table E-4 Residual iron concentration from ICP Analysis of B C Interior M i l l 140 Table E-5: Residual iron concentration from Spectrophotometer Analysis of B C Coastal M i l l 140 Table E-6: Liquor concentration at each washing stage from ICP Analysis of B C Coastal M i l l 140 Table F - l : Partitioning data from A A S Analysis of B S W from B C Coastal M i l l using filter paper 141 Table F-2: Partitioning data from A A S Analysis of B S W from B C Coastal M i l l using centrifuging 142 Table F-3: Partitioning data from A A S Analysis of D c washer mat from B C Coastal M i l l . . . . 143 x List of Figures Figure 2.1: p H range for the occurrence of aquo, hydroxo and oxo complexes for various oxidation states (Stumm and Morgan, 1995) 6 Figure 2.2: Mole fraction of total dissolve Fe(II) present as F e 2 + and Fe(II)-OH complexes as a function of p H in pure water at 25 °C (Langmuir, 1997) 8 Figure 2.3: Mole fraction of total dissolve Fe(III) present as F e 3 + and Fe(III)-OH complexes as a function of p H in pure water at 25 °C (Langmuir, 1997) 9 2_|_ Figure 2.4: Solubility diagram to show the effect of hydrolysis on dissolved Fe (Morel and Hering, 1993) 10 Figure 2.5: Solubility diagram for Fe (II) in the presence of carbonates and sulfide (Morel and Hering, 1993) 11 Figure 2.6: Haber-Weiss cycle (Fenton reaction) (Pierre and Fontecave, 1999) 13 Figure 2.7: Redox potentials for the H 2 O 2 / H O , C V C h * , Fe(III)/Fe(II) couples as a function of p H at 25°C (Liden and Ohman, 1998) 14 Figure 3.1: Physical system of pulp suspension: fiber with two charged-groups and water distributed between the solution phase (S) and the fiber phase (F) 28 Figure 4.1: B C Coastal M i l l samples from left to right: Brown Stock Washer mat (BSW); Post Oxygen Delignification mat (P -O2); D c ; E o p ; D n ; and D 2 washer outlet 44 Figure 4.2: Di-ethylene Tri-amine Penta-acetic A c i d (DTPA) structure 46 Figure 4.3: Water purifier E L G A U H Q II (a); Analytical Balance Mettler Toledo (b) 49 Figure 4.4: Ph meter (Metrohm 691) and Centrifuge (Hermle) 50 Figure 4.5: Atomic Absorption Spectroscopy 51 Figure 4.6: Spectrophotometer 51 Figure 4.7: Potentiometric titration (Mettler DL25 titrator and Mettler Toledo model DG111-SC glass electrode) 55 Figure 4.8: Pulp sample preparation procedure for metal profile and metal removal 57 Figure 4.9: Metal profile procedure to find the amount of metal bound to the fiber 58 Figure 4.10: Metal ion removal procedure in four washing stage 61 Figure 4.11: Metal ion-partitioning procedure 63 Figure 4.12: S E M & E D X preparation 65 x i Figure 5.1: Water retention value data and fitted curve of B C Coastal: Brown Stock Washer mat 68 Figure 5.2: Water retention value data and fitted curve for B C Coastal: Post Oxygen Washer mat 68 Figure 5.3: Water retention value data and fitted curve of B C Coastal: D c washer stage outlet 69 Figure 5.4: Water retention value data and fitted curve of B C Coastal: E o p washer stage outlet 69 Figure 5.5: Water retention value data and fitted curve of B C Coastal: D n washer stage outlet mat 70 Figure 5.6: Water retention value data and fitted curve of B C Coastal: D 2 washer stage outlet 70 Figure 5.7: Water retention value data and fitted curve of B C Interior: Brown Stock Washer mat 72 Figure 5.8: Water retention value data and fitted curve of B C Interior: Post Oxygen Washer mat 72 Figure 5.9: Water retention value data and fitted curve of B C Interior: ' D c ' mat 73 Figure 5.10: Potentiometric titration data of B C Coastal samples 74 Figure 5.11: Potentiometric titration data of B C Coastal samples zoomed at the zone of interest 75 Figure 5.12: Potentiometric titration data of B C Interior Samples 76 Figure 5.13: Potentiometric titration data of B C Interior Samples zoomed at the zone of interest 76 Figure 5.14: Potentiometric titration of B S W mat with iron addition from B C Coastal M i l l 78 Figure 5.15: Iron concentration comparison among A A S , ICP and Spectrophotometric analysis along the fiberline from B C Coastal M i l l 79 Figure 5.16: Comparison iron profile concentration at acidic condition as it was taken from the pulp m i l l to dilution p H at 1% consistency 81 Figure 5.17: Iron concentration comparison between A A S and ICP analysis along the fiberline from B C Interior M i l l 82 Figure 5.18: Original and residual iron concentration along the fiberline from B C Coastal M i l l using ICP analysis 83 Figure 5.19: Comparison of iron removal efficiency between ICP and A A S analysis from B C Coastal M i l l 84 Figure 5.20: Comparison the amount of iron removed from the pulp from its original with the amount of iron found on the liquor during acid-chelation washing 85 Figure 5.21: Iron found in the liquor at each washing stage for each B C Coastal samples 86 Figure 5.22: Original and residual iron concentration from ICP analysis for pulp samples from B C Interior M i l l 87 Figure 5.23: Comparison o f iron removal efficiency among ICP and A A S analysis from B C Interior M i l l 87 Figure 5.24: Calculated fiber charge distribution from potentiometric titration of B C Coastal samples 89 Figure 5.25: Fibre charge determined from the potentiometric titration data for Brown Stock Washer (BSW) mat from B C Coastal M i l l 91 Figure 5.26: Fibre charge determined from the potentiometric titration data for Post Oxygen washer mat from B C Coastal M i l l 91 Figure 5.27: Fibre charge determined from the potentiometric titration data for D c washer stage outlet mat from B C Coastal M i l l 92 Figure 5.28: Fibre charge determined from the potentiometric titration data for E o p washer stage outlet mat from B C Coastal M i l l 92 Figure 5.29: Fibre charge determined from the potentiometric titration data for D n washer stage outlet mat from B C Coastal M i l l 93 Figure 5.30: Fibre charge determined from the potentiometric titration data for D 2 washer stage outlet mat from B C Coastal M i l l 93 Figure 5.31: Calculated fiber charge from potentiometric titration of B C Interior samples 97 Figure 5.32: Fibre charge determined from the potentiometric titration data for Brown Stock Washer mat from B C Interior M i l l 98 Figure 5.33: Fibre charge determined from the potentiometric titration data for Post Oxygen Washer mat from B C Interior M i l l 98 Figure 5.34: Fibre charge determined from potentiometric titration data for "Dc" mat from BC Interior Mill 99 Figure 5.35: Iron partitioning comparison: separation of fiber from the suspension using filter paper and centrifuging of Brown Stock Washer from BC Coastal Mill 101 Figure 5.36: Iron partitioning between the fiber phase and the solution phase at pH = 3 for Brown Stock Washer of BC Coastal Mill 102 Figure 5.37: Partitioning ratio (k) at various iron concentrations in the pulp suspension for iron partitioning at pH = 3 for Brown Stock Washer pulp from the BC Coastal Mill 103 Figure 5.38: Iron partitioning between the fiber phase and the solution phase at pH = 3 for Dc washer mat of BC Coastal Mill 104 Figure 5.39: Partitioning ratio (k) at various iron concentration in the pulp suspension for iron partitioning at pH = 3 for Dc washer mat from the BC Coastal Mill 104 Figure 5.40: Iron partitioning comparison: total iron introduced into the suspension versus total iron found using mass balance relationship for Brown Stock Washer of BC Coastal Mill 105 Figure 5.41: Iron partitioning comparison: total iron introduced into the suspension versus total iron found using mass balance relationship for Dc washer mat of BC Coastal Mill .' 106 Figure 5.42: Iron partitioning prediction at 520 ppm iron concentration of Brown Stock Washer (BSW) mat from BC Coastal Mill 107 Figure 5.43: Manganese partitioning prediction at 600 ppm manganese concentration of Brown Stock Washer (BSW) mat from BC Coastal Mill 108 Figure 5.44: Copper partitioning prediction at 210 ppm copper concentration of Brown Stock Washer (BSW) mat from BC Coastal Mill 109 Figure 5.45: SEM from acid washed pulp where no precipitate is found 110 Figure 5.46: EDX from acid washed pulp where no precipitate is found I l l Figure 5.47: SEM from acid washed pulp where a precipitate is found ....112 Figure 5.48: EDX from acid washed pulp where a precipitate is found 113 Figure 5.49: EDX from acid washed pulp where another type of precipitate is found 114 Figure 5.50: SEM of acid washed pulp after introducing iron at pH 3 115 xiv Figure 5.51: E D X o f acid washed pulp after introducing iron at p H 3 116 APPENDIX Figure C - l : Potentiometric titration data of water (blank), acid-washed chelated pulp ( A W P ) without and with the addition of iron in a B S W sample from a B C coastal m i l l 133 Figure C-2: Potentiometric titration data of water (blank), acid-washed chelated pulp ( A W P ) without and with the addition of manganese in a B S W sample from a B C coastal m i l l 134 Figure C-3: Potentiometric titration data of water (blank), acid-washed chelated pulp ( A W P ) without and with the addition of copper in a B S W sample from a B C coastal m i l l 134 xv List of Symbols Total moles of anion j A W - C F M Acid-Washed Chelated Centrifuged Fiber Mat C Concentration measured from the analysis Q Total moles of cation j C F M - 1 Centrifuged Fiber Mat for Metal Profile C F M - 2 Centrifuged Fiber Mat for Metal Removal D a Divalent cationic F Volume of solvent in the fiber phase Fa Faraday constant Fe Iron concentration on the fiber F C Fiber charge FSP Fiber saturation point H W Hardwood fibres L - l Liquor obtained from D T P A Washed L-2 Liquor obtained from A c i d Washed using Hydrochloride A c i d L-3 Liquor obtained from D T P A + A c i d Washed using Hydrochloride A c i d L-4 Liquor obtained from Distil led De-ionized water wash rrij Molalities of species j M Mass of water M a Monovalent cationic M e 2 + Divalent metal ion O D Weight of oven dried sample R Gas constant S Total weight of digested solution sw Softwood fibres T Temperature V Volume of solvent in the solution phase W R V Water retention value xv i Greek Symbol P Equilibrium constant X Donnan equilibrium partition distribution constant ¥ Surface potential Subscript j Species j CI Chloride N a Sodium X Function group on the fiber A Ac id ic charge groups B Basic Charge groups M e Metal ions H Proton O H Hydroxyl Superscript F Fiber phase S Solution phase z Valence xv i i Acknowledgements I would like to thank Dr. Peter Englezos for his patient, constructive idea and guidance during the completion of this research project in "Metal-Fiber Interaction". I also would like to thank Dr. Chad Bennington for his advice and guidance in completing the work. I also want to express thanks to Dr. Xiaosen Li and Rajeev Chandraghatgi for their corporation and great discussions. Helps from technical, staff and fellow students in the Pulp and Paper Center at the University of British Columbia were highly appreciated. I would also like to show gratitude for the financial support from NSERC and pulp samples supply from CANFOR. xviii Chapter 1 1. Introduction A modern pulp and paper industry is characterized by a demand for high quality products, low consumption of chemical and minimizing or complete reduction of liquid and gaseous effluents. One of the main materials used in pulping operations that have the highest consumption is process water. Considerable researches has been done to reduce water consumption by recycling the process water but there are still some problems due to the presence of some materials that are not needed in the pulping process and tend to accumulate in the system and create some operational problems. These materials mostly are metal ions that are known as Non-Process Elements (NPEs). Fundamental studies are needed to understand the behaviour of NPEs to develop and implement zero liquid effluent or close cycle technology. 1.1. Chemical Pulping Technology and the Environment Pulping refers to any process by which wood or other fibrous raw material is reduced to a fibrous mass. This can be accomplished mechanically, thermally, chemically, or combination of these treatments (Smook, 1992). For mechanical pulping, the wood is converted into fibers mechanically. The yield is high; usually more than 90% of the original wood substance because lignin is still attached there but has a lower quality and strength (more fines). The products are usually used to make newsprints. Chemical pulping produces much less fiber, the yield is around 40-50% because it uses chemical compounds that dissolve the lignin chemically. However fiber is intact, much stronger and flexible. The two principle chemical pulping methods are the (alkaline) kraft process and the (acidic) sulphite process. The kraft process has become dominant compared to sulphite process because of the advantages in chemical recovery and pulp strength. In kraft process, the wood chip is cooked for several hours in a digester using a solution of sodium hydroxide (NaOH) and sodium sulphite ( N a S 2 ) to delignify the lignin molecule into smaller segment so it can dissolve into the 1 Chapter 1: Introduction liquor. These two chemicals are usually called "white liquor". Then the chips go to a blow tank where the softened chips are disintegrated into fibers, and then they are washed to recover the cooking chemical. The process is called brown stock washing where the outlet from this point goes to a bleach plant to reduce the lignin content down to a certain level of "kappa" number. The used cooking liquor after the digestion process is called "black liquor". It consists of cooking liquor plus dissolved lignin and some compounds that originate from the wood, such as extractive, metal ions, dirt, etc. To minimize the production cost and have a viable operation, one need to recover the chemical that is used during the process. What the industry does with the liquor is to concentrate it using a series of evaporators and then incinerate it in the recovery furnace to form inorganic smelt. The smelt is then dissolved in water to form green liquor, followed by causticizing with reburned lime to form white liquor for the next cooking cycle. Pulping processes need a significant amount of water, especially for washing. The water effluent from the pulp mill might be contaminated with materials that are removed from the fiberline, such as dirt, lignin, metal ions, etc. Thus, water effluent must be treated before it can be recycled or release to the environment. In order to minimize environmental concerns arising from the effluents from the pulp mills, a close cycle process was proposed where all of the materials involved in the process are recycled and only acceptable effluent (most probable in terms of solids and small amounts of gases) are generated (Bihani, 1996 and Reeve, et al., 1979). 1.2. Closed Cycle Operation and Non-Process Elements Continued concern about the environment maintains an interest in progressing toward low effluent, closed-cycle pulp and paper operations (Jemaa et al., 1999). This is not possible to apply in industry so far because of the imbalances of sodium / sulphur and caustic/chlorine and the build up of some materials that are not needed in the process. This build up tends to create some technical problems in the process: like scaling and corrosion, decreasing the quality of the paper product, and increasing the chemical usage during bleaching (decompose peroxide). These materials are industrially known as non-process elements (NPEs), which include 2 Chapter 1: Introduction potassium, chloride, magnesium, manganese, iron, barium, silicon, aluminium, copper, nickel, chromium, nitrogen, and zinc. The accumulation of NPEs, especially transition metal ions can significantly affect the selectivity of oxygen delignification, selectivity of bleaching reactions, quality of the product, and tendency to form deposits (Ala-Kaila et al., 1999). High transition metal content significantly reduces the selectivity of oxygen delignification and therefore the pulp quality. It also significantly worsens the strength properties, tear strength, burst strength, and zero span (Soini et al., 1998). Low fiber strength is caused by cellulose and lignin degradation that is catalyzed by the formation of free radicals from peroxides and transition metals in the process. Transition metals can also decompose the peroxide to form hydroxyl radical, which is responsible for the degradation of fiber cellulose; therefore it affects the breakage of chain cellulose molecules, shortens the length chain, and thus reduces pulp viscosity. The effects of transition metals depend on their redox characteristics. Even in small quantities like less than one ppm, these transition metals are sufficient enough to decompose peroxide. According to the Fenton reaction that will be discussed later, particular metal ions can catalyze the decomposition of hydrogen peroxide through a cyclic alteration of oxidation state. NPEs can partition between the fiber and surrounding water in pulp suspension. In general, they prefer to stay in the water under acidic conditions and attached to the fibers under alkaline conditions. It is believed that there are a variety of functional groups in the fiber that can bind NPEs, such as carboxyl acid in the lignin and also phenolic hydroxyl, hexenuronic acid, polysaccharide acids, and catechols groups in non-extracted hemicellulose. A recent study suggested that carboxylic acid groups in lignin and condensed phenolics might play an important role in the overall NPEs binding process. It is also suggested that there is a correlation between the amount of carboxyl and condensed phenolics present in kraft lignin and their metal binding capacity (Werner and Ragauskas, 2000). To implement a close cycle system, the major concern of effluent reduction is in terms of water effluent. Water reduction opportunities have been identified in different mill areas including wood and chip preparation, pulping, bleaching, pulp machine operation, chemical preparation 3 Chapter 1: Introduction and recovery; but still it's only for a certain degree of closure where the fresh water is still required by the process. In a fully closed cycle operation in a pulp mill, the behaviour of the NPEs is not fully understood yet, although it is very important to prevent operational problems and minimize chemical usage during the bleaching process thus reducing the production cost. Finding out the behaviour of NPEs in pulp suspensions under different pH conditions is very important to control NPEs in a close cycle system. Fundamental studies are needed to provide the basis for which the new technology can be developed in modern pulp manufacturing facilities. 1.3. Scope of Thesis Experiments will be performed with mill pulp suspensions in order to determine the iron concentration of pulp, iron removal and finally iron partitioning at different pH conditions. The results will then be compared with predictions from a thermodynamic model. 4 Chapter 2 2. Literature Review and Research Objectives Significant research efforts have been devoted in order to establish a close cycle pulp mill that will meet the environmental regulations. Fundamental studies have reached some points to understand the effect of the accumulation of the metal ions known as non-process element to the pulping process. Some methods have been investigated to remove the metal ions from the fiber using acid washing or chelation with DTPA. The other method to control the metal ions is by converting the iron into solid solution so that harmful metal ion becomes catalytically inactive against peroxide decomposition. The behaviour of metal ion partitioning in pulp suspension is still under investigation because fibres have many groups that can bind the metal ions depending on the pH of the suspension and electrolyte concentration. 2.1. Iron Chemistry Iron is in the first row of transition metals at the periodic table. It is known as the most abundant transition metal in nature and as an active participant in environmental redox reactions. Iron is one of the metals classified as Non-Process Elements (NPEs) and it has a detrimental effect in pulping process especially when close cycle technology is applied. Iron has two oxidation states; Fe + 2 and Fe+ 3. The changes in its oxidation state have a dramatic impact on both solubility and speciation. Above its solubility, combination of metal ions like iron with molecules or anions that have free pairs of electrons (usually bases) can form coordination or complex compounds. The complex can be formed by an electrostatic and/or covalent force. In this case metal cations will be called the central atom, and the anion or molecule with which it forms a coordination compound will be referred to as ligand. The most common ligands that can form complexes with iron are hydroxide (OFF) and carbonates (CO3). Functional groups on the fiber when dissociate can also contribute negative charges so that the fibre can behave as a ligand. Therefore, iron can form complexes with the ligands existed in the suspension and create problems in the pulping processes. 5 Chapter 2: Literature Review and Research Objectives Figure 2.1: pH range for the occurrence of aquo, hydroxo and oxo complexes for various oxidation states (Stumrn and Morgan, 1995) Depending on the oxidation state and pH, iron can be in the form of aqueous metal ion or as complex such as hydroxo and oxo complexes. As seen from figure 2.1, iron at the second oxidation state (ferrous) tends to be in aqueous metal ion state when the pH is below 8. If the pH increases then hydroxo iron complexes will be formed. The oxidized iron (ferric, third oxidation state) tends mostly to form hydroxo iron complexes from above pH 4 up to about pH 12. Aqueous ferric ions are formed only if the pH is below 4. At very high pH (above 12), oxo complexes of iron (ferric) are formed (Stumm and Morgan, 1995). 6 Chapter 2: Literature Review and Research Objectives In oxidized surface water, dissolved iron as Fe (ferric) ion or Fe (III) is mobile only at pH below 4. Under reducing conditions, iron as uncomplexed Fe 2 + (ferrous) ion is soluble and mobile up to pH 8. Thus, Fe 2 + generally forms weak complexes or ion pairs except with bisulfide ion. In contrast, Fe 3 + forms strong complexes with most ligands, especially with OFT. It can also be seen from the stability constant (cumulative formation constants), which is listed in the table 2.1 for the system that there are no carbonate carbons. As seen from table 2.1, almost all Fe 3 + usually exist as complexed whereas Fe 2 + occur as uncomplexed in natural waters. Reduction of surface groups from Fe (III) to Fe (II) increased the iron solubility by several orders of magnitude, thus it's more difficult to form precipitate. Thus, iron complex formation depends strongly on the pH and oxidation states (Langmuir, 1997). The rapid oxidation of iron can be seen by naked eyes by adding sodium hydroxide to dilute solution of Fe (II). The initial colourless solution rapidly turns brown and becomes turbid with the brown precipitates formed. Table 2.1: Cumulative formation constants for ferrous and ferric hydroxyl complexes at 25°C (Langmuir, 1997) Species -logp P Ferrous Iron Complexes FeOH + 10.1 1 0-l(].l Fe(OH) 2 u 20.5 1 0 - 2 0 . i Fe(OH)3" 29.4 io- i y - 4 Ferric Iron Complexes FeOH 2 + 2.19 1 0 " i y Fe(OH) 2 + 5.67 i o - 3 b / Fe(OH) 3 u 12.56 Fe(OH)4" 21.6 The oxidation state of iron plays an important role in the metal partitioning modelling since precipitations formation might effect the modelling prediction. Therefore understanding the oxidation state of iron at different pH condition is needed. Iron in water can form several iron species depending on the pH. The mole fraction of iron species under different pH condition for the two oxidation states are shown in figure 2.2 and 2.3. As seen in figure 2.2, most Fe (II) complexed is formed only at alkaline condition (above pH 8 7 Chapter 2: Literature Review and Research Objectives or 9). Below pH 8, most Fe (II) is in form of aqueous ions. The majority of complexed iron species is Fe(OFLV. Figure 2.2: Mole fraction of total dissolve Fe(II) present as Fe and Fe(II)-OH complexes as a function of pH in pure water at 25°C (Langmuir, 1997) 8 Chapter 2: Literature Review and Research Objectives Contrary to ferrous ion, ferric ion is formed under a narrow range of pH compared to ferrous ion as shown in figure 2.3. Ferric ions only exist at pH < 4 in the solution. At higher pH, more iron (III) complexed species are formed depending on the pH. 0 2 4 6 8 10 pH Figure 2.3: Mole fraction of total dissolve Fe(III) present as Fe 3 + and Fe(III)-OH complexes as a function of pH in pure water at 25°C (Langmuir, 1997) 9 Chapter 2: Literature Review and Research Objectives The effect of hydrolysis on dissolved Fe (II) concentration depends on pH. In figure 2.4, the iron species dependence on pH with the total iron concentration at 10"4 M is shown. Log C in the graph refers to the concentration of each species. "~*:2 *j ' H H rl * \ »—j i r; • 2 4 6 8 10 12 14 pH Figure 2.4: Solubility diagram to show the effect of hydrolysis on dissolved Fe 2 + (Morel and Hering, 1993) The heavy line on the top of all lines represents the total iron concentration, which is the sum of all dissolved Fe (II) species. The figure 2.4 consists of 5 regions, which are the follows: pH < 5.9 Fe is totally in solution as Fe 2 + 5.9 < pH < 6.6 Fe is mostly present as Fe but there might be FeS (s) precipitates 6.6 < pH < 10.1 Fe is mostly present as FeCO"3 (s), which coexist with FeS (s) 10.1 < pH < 12.1 Fe is mostly present as Fe(OH)2 (s), which coexist with FeS (s) 12.1 < pH < 14 Fe is precipitated as Fe(OH)2 (s) but dissolved species Fe(OH)3" becomes increasingly important with increasing pH 10 Chapter 2: Literature Review and Research Objectives If there is anionic species present in the iron solution, there will be a competition and coexistence among several solid phases. The most common anions that are found in water are carbonates ( C O 3 2 ) , sulfide (S2~) and hydroxide (OH"). All of them can form precipitates with iron under certain conditions. In 1M of iron solution that has 10~5 M of sulfide and 10"3 M of carbonates concentration (C in the figure 2.5 represent concentration), there are boundaries between each solid phase and solid coexistence as seen in figure 2.5. The boundaries for stability of various solids are given by lines A and E for FeS (s); lines B, F, and D for FeC0 3 (s); and C, G, D, H, and C for Fe(OH)2 (s) (Morel and Hering, 1993). 11 Chapter 2: Literature Review and Research Objectives In a system in which there are two solid phases such as (FeCCb (s) and Fe(OH)2 (s)), there will be a competition between them to control the solubility of iron. Although the solubility limit of Fe(OH)2 (s) is smaller than FeC03 (s), it doesn't mean that Fe(OH)2 (s) always precipitates to the exclusion of FeCC>3 (s). The equilibrium reaction and the equilibrium constants are given below. (Pankow, 1991) Fe(OH\{s) <-> Fe2+ + 20H~ K = 10"15 1 (2.1) FeC03(s) <-> Fe2+ + CO,1' K=10" 1 0 6 8 (2.2) The solid phase that controls the solubility limit is the solid that gives the lowest equilibrium activity of metal ion to reach the Gibbs free energy at minimum. This means the concentration of cationic and anionic species in the system will play an important role to determine the solubility limit. The equilibrium of this system is reached according to the following equation (Pankow, 1991): FeC03(s) + H20 4* Fe(OH)2 (s) + C02(g) K = pC02 = 10"543 (2.3) Based on the assumption that solid is pure and the activity is unity, the above two solids can coexist only when pco2 is equal to 10"5'43 atm. If pco2 > 10"5 4 3 atm, the above reaction will have a positive AG and spontaneously proceed to the left side. If pco2 < 10"543 atm, the reaction will have a negative AG and spontaneously proceed to the right. This means that at pco2 > 10"5'43 atm, FeCCb (s) is a stable solid compared to Fe(OH)2(s) and for pco2 < 10'5'43 atm, Fe(OH)2(s) is a more stable solid compared to FeCC"3 (s). Iron can also participate in a cyclic process between the second and third oxidation state through one transfer electron. This redox process can be fine-tuned by well-chosen ligands. Superoxide radical and hydrogen peroxide are involved to catalyze the cyclic process, which is known as a Fenton reaction. It was actually found by Haber and Weiss in 1934 and then Fenton modified it later. The Fenton reactions are shown below (Pierre and Fontecave, 1999). Fe 2 + + H 2 0 2 •» Fe 3 + + OH» + OH" (2.4) OH« + H 2 0 2 -» H 2 0 + H0 2 « (2.5) Fe 3 + + H0 2 « -> Fe 2 + + H + + 0 2 (2.6) Fe 2 + + H0 2 * Fe 3 + + H02" (2.7) Fe 2 + + OH* -» Fe 3 + + OH" (2.8) 12 Chapter 2: Literature Review and Research Objectives All of these reactions make a chain reaction through oxidation and reduction. Equation (2.4) serves as a chain initiation, equation (2.7) and (2.8) as the termination reactions. Equation (2.4), (2.5), and (2.6) form the chain cycle, which is the site of oxygen evolution (Kremer, 1999). Figure 2.6: Haber-Weiss cycle (Fenton reaction) (Pierre and Fontecave, 1999) In Fenton reactions, hydrogen peroxide oxidizes the reduced form of the metal and superoxide 02* reduces the oxidized form of the metal, so the metal ions become catalytically active to hydrogen peroxide decomposition. The changing in oxidation state creates a cyclic process. To make the catalytic action of iron thermodynamically feasible, the redox potential (EH) of the iron couple in oxidation/reduction states (EFe(iii)/EFe(ii)) must be above the redox potential of 02/02* couple and below H202/HO« couple. But if the redox potential (EH) of the metal ions (Fe /Fe ) is not between the range mention above, iron becomes catalytically inactive. Because redox equilibrium involves both protons and electrons, the redox potential will change according with the pH. It is very important to adjust the pH outside from the dangerous range. This is shown in figure 2.7 (Liden and Ohman, 1998). The plot of redox potential as a function of pH at 25°C has been established by Liden and Ohman for iron concentration of IO"5 mol/L and carbonate concentration of IO"3 mol/L. It is shown on figure 2.7 below. It can be seen that iron below neutral pH is very active for peroxide decomposition. > Fe(III) 13 Chapter 2: Literature Review and Research Objectives Figure 2.7: Redox potentials for the FFiCVHO*, 02/02*, Fe(III)/Fe(II) couples as a function of p H at 25°C (Liden and Ohman, 1998) 2.2. Non process elements (NPEs) in kraft mills N P E s are introduced in the kraft mi l l from wood chips, make-up chemicals, process water, and from the degradation of process equipment. The major source of N P E s is the wood itself. N P E s content in wood depends on geographical location, the available soil nutrients, and the wood species. Their concentrations vary from one mi l l to another depending on the type of raw material and the degree of closure (Jeema et al., 1999). N P E s content also varies within the tree itself. It varies in the stem, branches, and crown foliage. N P E s accumulate significantly i f the closure of water cycles is applied. Thus there is a need for a practical solution especially in a totally chlorine free (TCF) or elemental chlorine free (ECF) bleaching where the bleaching process incorporate H2O2 stages. 14 Chapter 2: Literature Review and Research Objectives Metals in wood chips are classified into two groups, macro and micro. The macro elements have concentrations higher than 50 ppm and include Na, K, S, Ca, Mg, and P. The microelements have concentrations of less than 50 ppm and include Cu, Mn, Fe, and Al. Other elements such as Cr, Ni, Co, Ti, Mo, Ba, and V are normally present in trace (<5 ppm) to non-detectable amounts. For most wood species, K and Ca contents are the highest (Jeema et al., 1999). The micro elements concentration of four different wood species are given in table 2.2 (Bryant, P. S., et. al., 1993). Table 2 .2 : Median values of micro elements concentration (mg/kg-od fiber) in four different wood chips species (Bryant, P. S., et. al., 1993) Metal Redwood Douglas-Fir S. Pine Gum / Oak Cu 2 1 1 2 Mn 18 35 39 20 Fe 33 22 20 8 Al 33 28 25 18 As seen in table 2.2, iron and other metal ions are found on the wood chips and enter the fiberline. Iron content on the pulp might also be a function of process-equipment corrosion. But according to Bryant et al. (1993), corrosion is not a reasonable explanation because the contribution of iron content in the pulp from the corrosion is much less than the iron content in the pulp itself unless the rate of corrosion is very high which is unlikely in the pulp mill. Bryant et al. (1993) also measured iron concentration down the fiberline. They found out that iron has fewer tendencies to acid desorption and often remains on the fiber even after acid treatment, where most of metal ions can be removed from the fiber. They also found out that there is instability of iron concentration down the fiberline where it might increase at the later washing stages. The source of the increased iron concentration is not fully understood. They assumed that iron is always present on the pulp and some of them are not detected because of the heterogeneous nature as a dirt or solid in the fiberline, not homogenous and bound to the fiber. 15 Chapter 2: Literature Review and Research Objectives 2.3. Metal ion removal Wood fibers have several functional groups which can create negative charges in the pulp suspension; therefore they have ion exchange properties where metal ions can interact with the fibers. There are two methods that are generally used to remove metal ions, which are by acid treatment at pH 1.5 to 3 and pre-treatment by chelation. Acid washing is a well-known metal removal method from the fiber and it used in most pulping operations to remove most of metal ions. But some metal ions still remain in the fiber after acid treatment; therefore chelation treatment is introduced to remove these residual metals on the fiber that cannot be removed effectively by acid washing. The best chelating agents are the aminocarboxylates such as ethylene di-amine tetra-acetic acid (EDTA) and di-ethylene tri-amine penta-acetic acid (DTPA), which are relatively cheap and effective compared to other chelating agents like phosphoric acids and their salts, such as di-ethylene tri-amine penta-methylene phosphoric acid (DTMPA). Chelating agents form water-soluble complexes together with the metal ions. Chelating agents can cut the cost of bleaching chemical consumption and inhibit cellulose decomposition reactions catalyzed by these metal ions. Acid washing of the pulp fiber removes most of the transition metal ions without any selectivity. Bouchard et al. (1995) commented that a chelation step has an advantage, because while it removes the metal ions, it leaves the alkali earth metals such as magnesium, which are associated with the pulp. Magnesium has been known to help to control peroxide decomposition and prevent cellulose de-polymerization. He recommended adding magnesium to prevent pulp degradation especially when acid washing is used. Ghosh et al. (1998) showed that two stages of chelation before oxygen delignification considerably improves the viscosity and brightness of pulp. They found that lignin-metal ion complexes are more coloured than DTPA-metal ion complexes so that the impregnation of DTPA solution can recover the brightness loss due to coloured lignin-metallic complexes. 16 Chapter 2: Literature Review and Research Objectives From the thermodynamics consideration, there are two ways to make metal ions catalytically inactive. The first one is by chelation. The second one is to bind the metal ion in a solid phase so that it cannot change its oxidation state. The latter approach is not popular because of the scaling problem. The last concept is called the solid solution method, which is able to protect the peroxide from decomposition. It has been reported that iron (II) and manganese (II) in the presence of pulp or an ionic polymer such as polygalacturonic acid can be protected against oxidation in highly alkaline and oxidative environments by adding magnesium hydroxide and carbonate precipitates. Magnesium can form co-precipitates with iron and manganese. Therefore these transition metals are unable to catalyze the decomposition of H2O2 through Fenton cycle (Liden and Ohman, 1998). Interaction between magnesium and iron can be understood in terms of solubility data. The less soluble the magnesium precipitate becomes, the more effectively iron can be protected from changing oxidation state in a Fenton reaction. From a chemical point of view, co-precipitation of iron or manganese with magnesium has a high probability if they are present in the +11 oxidation state. This is because they have similarities in ionic radii as well as solubility product for their hydroxide and carbonate solid phases. In addition, their chemical structure with respect to their hydroxide or carbonates is similar so that they can isomorphically replace each other in a crystalline lattice. In the presence of oxygen and above neutral pH, the stable oxidation of iron is +111. That means the ionic radius decreases and then the hydrolysis become much stronger. Iron(III) forms hydroxide precipitates at pH above 3 so that it needs to be kept unoxidized until the pH is sufficient enough to precipitate magnesium, therefore iron with the incorporation of magnesium can form co-precipitates. It is also found that the addition of carbonates increases the brightness of the pulp because the carbonate is required to further decrease the solubility of the solid formed since the hydroxide ion concentration at pH 11 or less is still too low to completely precipitate all Mg(II) as Mg(OH)2 (Liden and Ohman, 1997). Isomorphous substitution of Mg(II) by Fe(II) and Mn(II) in a solid phase at high Mg/Fe(Mn) molar ratio (usually more than 5) and high concentration of free hydroxide, carbonate or silicate in the aqueous phase lower the solubility of solid phase (Mg,Fe,Mn) and effectively prevent the catalytic action of iron and manganese towards hydrogen peroxide decomposition. Mg(II) is known as a redox stabilizer of Mn(II) and Fe(II) during alkaline oxygen delignification and 17 Chapter 2: Literature Review and Research Objectives peroxide bleaching by maximizing the concentration of Mg(II) at a given high pH so that the concentration of aqueous Fe(II) and Mn(II) are minimised and the solid state Fe(II) and Mn(II) are buried in a Mg(II)-dominated solid phase. A major concern in performing the experiment employing these metal ions at high pH is to maintain an oxygen-free environment in the system, to prevent the metal ion from being oxidized to solid metal (oxo) hydroxide (Wiklund, et al., 2001). The solubility of iron decreases when it becomes a minor component in the solid phase with the excess of magnesium (Liden and Ohman, 1997). 2.4. Charged groups in pulp fibres Fiber mainly consists of cellulose, hemicellulose and lignin. Cellulose is basically sugar with many glucose monomer linked to each other. Because cellulose is built out of a sugar monomer, it is called a polysaccharide. Hemicellulose is similar to cellulose, but it is more amorphous structure and less strength, so hemicellulose is not resisted to hydrolysis. Uronic acid can be resulted from hydrolysis of hemicellulose (Sjostrom, 1993). Lignin mainly consists of carboxyl acid and phenolic hydroxyl. These two are the major functional groups in lignin that contribute charges. These functional groups are proton bound so that when they are de-protonated, negative charges arise from the fiber surface and attract cations. The major charges of unbleached pulps are hexenuronic (HexA) and methylglucuronic (MeGlcA) acid with PKA = 3.1-3.3 (Rasanen et al., 2001). The other weaker acid is lignin-bound carboxyl with PKA = 5-6 (Laine et al., 1994). In alkaline region, the phenolic hydroxyl group on the lignin might contribute charge, the pK A varies in the range of 7.3-10.3 (Ragnar et al., 2001). The charged groups on the fiber dissociate at a certain pH. This creates an imbalance of ionic distribution across the fiber and water interface. The fiber dissociation reaction for one charge group is shown in equation 2.9. XHoX~+H+ (2.9) where XH is the protonated charged group, X" is the dissociated free charge on the fiber and H + is the proton. The dissociation constant can be written as follows: 18 Chapter 2: Literature Review and Research Objectives \X-JH+] KXH~ r -, (2-10) XH yXH^ Basically, there are 3 different methods that has been identified in determining the fiber charge properties. The first one is based on sorption, such as methylene blue sorption or polyelectrolyte sorption. The second method is using conductometric titration. The last method is by potentiometric titration. Lingren et al. (2002) and Fardim et al. (2002) did the comparison between the three methods and they are summarized in table 2.3. These authors found that methylene blue sorption is simpler, less laborious work and good repeatability. Conductometric titration method gives a similar result with methylene blue sorption. There are some limitations of these two methods because they can only determine the total acidic groups in the pulps but they cannot determine the acid base properties of the charge groups. The potentiometric titration method was found to be the best method because it can give the initial deprotonation level, the determination of different acidic group and its acid/base properties and also the total amount of charge. The limitation of potentiometric titration method is that it takes longer time for analysis and it's difficult to determine the charge group at alkaline condition due to the slow drifting of the pH toward the acidic condition (unstable). Table 2.3: Comparison of different methods in determining the anionic charge groups in pulps fiber, given in mmol/kg-od fiber (Lingren et al., 2002) Pulps Potentiometric titration Methylene blue Conductometric titration Unbleached kraft fibres Birch 95 115 124 Pine 56 81 79 Eucalypt 87 104 105 Bleached kraft fibres TCF Birch 62 68 66 TCF Pine 41 45 45 ECF Birch 52 65 65 ECF Pine 38 37 40 ECF Eucalypt 70 77 83 19 Chapter 2: Literature Review and Research Objectives Bygrave and Englezos (1998) found that two dissociation constants can represent the charge distribution on the fiber from a post-brown stock washer pulp between pH 2 to 11. They used a Donnan-based model to calculate the fiber charge from a potentiometric titration data. The dissociation constants were found to be 1.6E-4 (pKA = 3.8) and l.le-8 (pKA = 8.0). The total charge concentration was found to be 95 mmol/kg-od for the acidic group and 55 mmol/kg-od for the basic group. Rasanen et al. (2001) also determined the fiber charge based on Donnan theory from a potentiometric titration data from pH 2 to 10. They performed potentiometric titration of oxygen delignified hardwood kraft fiber. They assumed there are three charge groups available on the fiber. The pK values and the total charge are reported in table 2.4. Table 2.4: Dissociation constant and fiber charge of oxygen bleached hardwood kraft fiber from pH 2 tolO (Rasanen et al., 2001) Parameter Values pK A 3.77 pK B 5.97 pK c 8.58 QA 120 mmol/kg QB 12 mmol/kg Qc 9 mmol/kg Laine et al. (1994) calculated fiber charge from potentiometric titration using Gran plot. The authors also introduced an electrostatic correction at the fiber surface. This model became so popular and many researchers used their work to calculate fiber charge; mostly by Lingren et al. in 2000 and 2001 (total 4 journal papers), Athley et. al. in 2001 and Rasanen and Karkkainen in 2003. These authors suggested that the concentration of ions near the fiber surface is different from the concentration in the bulk solution. This is because of the negative charges on the fiber surface, which create work required to move the mobile ions across the bulk solution and the fiber. The ionic distribution depends on the surface potential (y/) and the charge of the ion (z) according to the Bolzman equation. Thus, the fiber charge concentration on the surface can be written as follows: 20 Chapter 2: Literature Review and Research Objectives [X-] =[X~U r t ) (2.11) L_ -i surface L_ -ibulk where \\i is the surface potential, F is the faraday constant, R is the gas constant, and T is the absolute temperature. Therefore dissociation constant can be written as follows: zy/F RT KXH(int) ~ FTTTTn ( 2 - 1 2 ) [X'J_H+]e{ JXH] The surface potential was calculated according to the constant capacitance model (CCM) of a double layer. Table 2.5: The fiber charge properties of unbleached softwood kraft fiber determined from a potentiometric titration data at pH 2 to 6 (Laine et al., 1994) Pulps Kappa Qlotal pK A pK B Unbleached Softwood kraft fibres 17.7 65 3.37 5.71 19.0 55 3.41 5.43 34.7 75 3.40 5.50 56.6 115 3.37 5.68 56.7 100 3.39 5.48 Laine et al. (1994) calculated the fiber charge of unbleached softwood kraft fiber at different kappa number from pH 2 to 8, as shown in table 2.5. They found that two charge groups can represent the fiber at acidic condition, the stronger acid correspond to the uronic acid in hemicellulose and the weaker acid corresponds to the carboxyl acid bound to lignin. Lingren and Ohman (2000) also calculated the fiber charge of fully bleached softwood kraft fibres at pH between 2 to 6. They found that the total acidic charge was 31 mmol/kg-od fiber and the pK value was 3.41. Athley et. al. (2001) reported the fiber charge for three different pulp samples: Hardwood (HW), Softwood 1 (SW1), and Softwood 2 (SW2) at two different ionic concentrations. The potentiometric titration and conductometric titration was used to calculate the fiber charge. They 21 Chapter 2: Literature Review and Research Objectives did the titration only at pH 3 to 6. They found out that hardwood fibre has more charge than softwood fiber. The amount of acidic groups in the pulps and their equilibrium constant are shown in table 2.6 and table 2.7. Table 2.6: The amount of acidic groups in fibres (umol/g) determined by conductometric and potentiometric titration using different ionic concentration (Athley et. al., 2001) Pulp sample Kappa number Potentiometric Titration Conductometric Titration Ionic concentration (NaCl) 0.02 mol/ L 0.1 mol/L 0.001 mol/ L HW 11 126 128 140 SW1 9.9 68 73 80 SW2 8.4 50 Not Done 59 Table 2.7: Equilibrium constant (pKa) from potentiometric titration (Athley et. al., 2001) Pulp sample Ionic concentration pK A HW 0.02 M 3.45 HW 0.1 M 3.04 SW1 0.02 M 3.25 SW1 0.1 M 2.88 SW2 0.02 M 3.20 Rasanen and Karkkainen (2003) also determined the fiber charge of oxygen delignified hardwood kraft fibres from pH 2 to 10. They found that the pK values are 3.1 and 5.6 with the charge content of 128 and 22 mmol/kg-od fiber. 2.5. Metal ion partitioning in pulp suspensions Metal ions are present in different quantities during the pulping process. Their presence depends strongly on pH and constantly partition in the fiber line. The first partitioning of NPEs happens during pulping from the digester, brown stock washer, oxygen delignification, bleaching plant and up to stock preparation where metals can associate either with the pulp or liquor. The distribution of metal ions between the fiber and the surrounding solution depends on the amount 22 Chapter 2: Literature Review and Research Objectives of negative charge on the fiber, which is related to the amount of acid groups in the fiber and their degree of deprotonation (Athley et al., 2001). The methods that have been applied so far to model the metal ion partitioning are: (i) the ion exchange model; (ii) complex formation model; (ii) Donnan equilibrium model; and (iv) Donnan theory with the integration of complex formation model. These models basically consider two interactions between the functional group on the fiber with metal, which is the electrostatic interactions (Donnan theory) or the chemical binding interactions (ion exchange or complexation) for predicting the metal ion partitioning. In ion exchange model, fiber charge is considered as ligands (L) that interact with the monovalent and divalent cations through chemical binding in the ion exchange model as shown in equation 2.9 and 2.10 (Bryant and Edwards, 1996). M + + L" <-»• M L M + 2 + 2L" <-> M L 2 (2.13) _ [ML] [ML,] K ^ - ^ ¥ ] K ^ ' ^ F f ( 2 - 1 4 ) Each metal ion ( M ) has its own equilibrium constant with the fixed charge groups on the pulp fibers (L~). The metal partitioning can be predicted only after the equilibrium constant of binding reaction is known. They found that the concentration of iron and aluminium on the fibre had little dependence on pH, thus the ion exchange model cannot predict their partitioning behaviour (Bryant and Edwards, 1996). In the complex formation model (Athley, 2001); metal ions can form complexes with the anionic charged groups of the fibers, such as carboxylate groups. The general expression for this complex-formation reaction is given as follows: p H + + q M 2 + + r =COO~ <-> HpMq(=COO) (p+2q~r ) (2.15) This complex reaction formation involved protons (H+), metal ions (M), and carboxylate groups (=COO~), where its quantity is denoted as p, q. and r. These charged groups on the surface will give rise to a surface potential. This phenomenon will affect the apparent equilibrium constant, K , , and distribution of ions at the interface. 23 Chapter 2: Literature Review and Research Objectives K -K e<p+2"^FKRT) (2 16) where F is Faraday constant, R the gas constant, T the absolute temperature, and Kpqrm is the intrinsic constant, which can be considered to be the equilibrium constant at a surface without any influence from the surface charge. So the apparent or binding constant will be: \HBMea(=COO~) (P+2^F Kh... = ^—^ — ^ e RT (2.17) binding p - i n r- ., -\q r- -\r \ / [H+J[Me+2][=COO-] Potentiometric titration was used to determine the binding constant. They assumed a specific complex formation is formed by metal ions (manganese and calcium) with the carboxyl group under different combinations of proton, metal ions and carboxyl, as shown in equation (2.15). The metal complexes they tested were Me(COO)+ , Me(COO)2 , MeOH(=COO) , Me(=COOH)22+ , Me(COOH)2+ and Me(= COOH\= COO)+ . Only Me(COO)+ and Me(COO)2 have been used successfully to describe divalent metal ion affinities for the oxygen-delignified kraft pulp (Athley, 2001). The binding constants are given in table 2.8. The binding reactions for the two complexes are shown in equation 2.18 and 2.19. Me2++2(=COO~)^Me(=COO)2 (2.18) Me2++(=COO-)^Me(=COO)+ (2.19) Table 2.8: Complex formation constant of manganese and calcium with carboxyl group on the fiber evaluated from potentiometric titration at ionic concentration of 0.02 M NaCl for hardwood (HW) and softwood (SW) pulp (Karin, A., et al. (2001) Pulp Complex formation constant (- loglO Kb i n d i n l,) sample Mn(COO)+ Mn(COO)2 HW 1.44 4.51 SW 0.67 3.99 Models based on chemical binding have disadvantages, because the equilibrium constant from the experiment is needed before the model can be used as a predictive tool. 24 Chapter 2: Literature Review and Research Objectives The electrostatic interaction was based on Donnan theory, which was developed to describe the uneven distribution of ions across a membrane separating a solvent and a solution. Based on Donnan equilibrium, when the acidic groups in the pulp are deprotonated, negative charges arise and affects the distribution of ions between the two phases. Thus, the concentration of metal ion in the fiber solution depends on the amount of acid groups on the fiber, their degree of dissociation, the charge of the metal ion, and its total concentration compared to the total concentration in the suspension. The distributions of all metal ions and charged groups in the suspension will be constant, depending on the ionic strength (valence) and described by distribution constant X (Towers and Scallan, 1996). A = H+ H+ M + M+ ( \M' \ 1/ \/2 (2.20) + 2+ where M and M are the metal ions and A" anions. Bygrave and Englezos (1998; 2000) extended the model to take into account the activity coefficients of the ions to predict the metal ion partitioning. Calcium, magnesium and sodium were the metal ions of their interest. They found that partitioning can be modeled by using electrostatic interaction only. An extension of the Donnan equilibrium model that takes into account complexation equilibria in the solution with a chelating agent has also been developed (Rasanen and Stenius, 2001 and Rasanen and Karkkainen, 2003). Due to the negative charge at the fiber surfaces, the ligand from the chelating agent is distributed in the external solution where they form ionic complexes with free metal ions. They evaluated the applicability of the extended Donnan model with chelation of metal ions in hardwood kraft pulps. Donnan equilibrium was combined with complex formation of metal ion with ligand from the chelating agent and hydroxyl group. They used oxygen delignified kraft pulp samples from a Finnish pulp mill. They assumed that two fiber charged groups exist on the fiber. The fiber charge was determined using potentiometric titration. The equilibrium experiments were done in a jar for 12 hours during the night after adjusting the pH and bubbling with argon gas. The chelating agents were DTPA and EDTA, which were assumed to have five and four carboxylic groups respectively that bind with metal ions. 25 Chapter 2: Literature Review and Research Objectives Finally, Norberg, et al. (2001) found that anionic charge from the pulp fibres is balanced with Na" ion, while divalent metal ions were present as solid carbonates in oxygen-delignified pulps. They found that the presence of carbonate ions contributed negative charges in the solution together with hydroxyl ions; so to maintain the charge balance in the suspension, most of divalent metal ions have to be in solid form. Monovalent ions in the other hand stay at their ionic form because they cannot form a solid phase at these conditions. So this indicates that a monovalent ion such as sodium binds to the fiber to a point that corresponds to the ion exchange capacity in the fibre. It won't be washed out from the pulp but stays in the fiber to the bleach plant. It can be described clearly by the reaction below to maintain the charge balance: 2 Ma + + 2 X" <r>2 MaX Da 2 + + C0 3 2" <-» DaCCb (2.21) 2 H + +20H" o 2 H 2 0 where Ma is monovalent cationic; Da is divalent cationic and X" is the fiber charge. At acidic conditions, the carbonates dissolve and consume two protons to produce carbon dioxide gas. The divalent cations predominantly replace Na+ in the fibre wall if do not react with anions to maintain the balance of the charge in the suspension. The metal carbonates can be prevented from dissolving by adding sodium carbonates into the suspensions. 2.6. Research objectives A. Pulp samples from a British Columbia interior and a coastal mill will be used in order to: 1. Determine iron concentration profile in the pulp suspension at several sampling points down the fiberline. 2. Determine residual iron concentration after washing with acid and chelating agent. 3. Determine the total charge on each pulp sample down the fiberline and its acid-base properties. 4. Perform partitioning experiments with acid washed pulps to measure how iron partitions between the fiber and surrounding liquor. B. Compare model prediction with partitioning data 26 Chapter 3 3. Modelling Framework: Physical System and Mathematical Model Metal ions interact with wood pulp fiber based on the electrostatic interaction as well as chemical binding. A fundamental factor in predicting the metal ion partitioning is the charge properties. The binding constants are also required before chemical binding interaction can be used to predict metal ion partitioning. Therefore, the modelling will be divided into two sections. The first one is to describe the metal ion partitioning prediction in the pulp suspension and the second one is to determine the fiber charge properties and the binding constants. Modeling of the iron interaction with the wood fiber in the pulp suspension will be described in the following order. Physical system of the pulp suspension will be illustrated at first and then mathematical model will be derived next. 3.1. Physical system The fiber is basically celluloses, hemicelluloses, and lignin with many functional groups in it. These functional groups might dissociate in water and give off proton to form negative charges so that they can attract or bind cations. Pulp suspension consists of water as the solvent and the fiber itself. Wood fibre is very porous and hygroscopic, which is like gel. So the water can be distributed between the fiber and the bulk solution. Consequently, it induces a two-phase system that consists of Solution phase (S) and Fiber phase (F). Water in the solution phase is called 'external water' and in fiber phase is called 'internal water'. So pulp suspension can be modelled as a two-phase system where each phase is separated by a membrane-like, which allows anions and cations in the system to diffuse through the membrane till they reach equilibrium (Towers and Scallan, 1996). At equilibrium, the energy is at minimum where the pressure, temperature, and electro-chemical potential between the two phases are equal according to Gibbs free energy. The physical system of pulp suspension is illustrated in figure 3.1. 27 Chapter 3: Modelling Framework: Physical System and Mathematical Model Solution Phase (S) Figure 3.1: Physical system of pulp suspension: fiber with two charged-groups and water distributed between the solution phase (S) and the fiber phase (F) The water in the internal solution is the water bound within the fiber wall . It's not the lumen water, which is the water inside the pores of a fiber. Since fiber is hollow, the lumen water can be removed easily by centrifuging. The amount of internal water is determined using the water retention value ( W R V ) , which is equal to the fiber saturation point (FSP) for the pulp samples at FSP less than 1.8 g-water/g-od fiber. Metal ions partition between the fiber and the solution phase because of the attraction from the charged groups present on the fiber phase. When these charged groups on the fiber dissociate, they w i l l create a negative charges so there wi l l be a potential gradient for cations like metal ions towards the fiber phase. On the contrary, the anion wi l l be expelled from the fiber phase, as shown in figure 3.1. 3.2. Mathematical Model Based on the physical system, a general mathematical model based on electrostatic interaction and chemical binding interactions w i l l be presented here. Since there are two phases in the system, superscript S and F w i l l be used throughout the chapter which refer to solution phase 28 Chapter 3: Modelling Framework: Physical System and Mathematical Model and fiber phase. The equations used in the model are fiber dissociation constant, electroneutrality, water dissociation constant, Donnan equilibrium, charge balances and mass balances. 3.2.1. Dissociation of Fiber Charged Groups on Fibers It is assumed that fiber can be represented by introducing two charged groups (A~ and B). The dissociation reaction of two-charged groups on the fiber is given in equation 3.1: AH^>H++A~ (3.1a) BH<^H++B~ (3.1b) where A' and B~ are the deprotonated fiber charge and Ft is the proton. AH and BH are the protonated fiber charge. It is assumed that fiber groups are monovalent, so the dissociation constant of fiber in the solution can be described as follows: {H'){A-} K - ) K - ) m = ( « ) {BH) K„) 3.2.2. Electroneutrality The concentrations of the two free charged groups are denoted by mF and mF. The valence of iron as a metal ion is considered as two throughout the calculations, because iron at the second oxidation state tends to stay in the solution phase up to pH 8 as shown in figure 2.2. On the contrary, iron in the third oxidation state tends to form complexes as shown in figure 2.3. The model does not accommodate any precipitation to occur. This is the limitation of the model. The electroneutrality of each solution, F and S, is expressed by equations (3.3) and (3.4). j X v < + E v < = o * MH+ +ML+ ~ma--KH- =° (3-4) j k 29 Chapter 3: Modelling Framework: Physical System and Mathematical Model where 'z/ is the valence of each ion, 'Zk' is the valence of the charged group on the fiber which is equal to one, 'm/ is the molality of each ion and 'mk' is the molality of the free charged group on the fiber. 3.2.3. Water Dissociation Constant Dissociation constant of water relates the molality of H+ and OH~ in the fiber phase and solution phase. KW = AH^0H- = K+KH- = mlMOH- ^ ^ -14 The dissociation constant of water is 10 3.2.4. Donnan Equilibrium The fibre with the imbibed water is considered as a homogeneous bulk phase separate from the external solution. The presence of fixed ionic species, like the carboxyl and other charged groups on the fibres induces Donnan equilibrium. Thus, the concentrations of mobile metal ions inside and outside the fibre phase are not equal. Ideal solution behaviour is adopted in this model because the ionic concentration in the pulp suspension is very dilute, so the activity coefficient is considered as unity. Bygrave (1997) showed that introducing activity coefficient has no significant benefit and it adds more complication on the model. Donnan equilibrium expression is described as following (Towers and Scallan, 1996): i ( s \mcr Na* (mj lma- J J ms + V Na+ J S [mj J where is the molality of ion j , z. is the valence of ion j, and X is Donnan constant. 3.2.5. Charge Balances The charge balance can give the moles of fixed charged groups within the F solution. These charged groups can be bonded to protons or exist in deprotonated form. The charge balances for the two groups are shown in equation (3.7): ^ F = mFAH+mFA. (3.7a) 30 Chapter 3: Modelling Framework: Physical System and Mathematical Model % = mFH+mF. (3.7b) M' where QA and QB are respectively the total moles of fixed charged group within the F solution, MF is the mass of water in the F solution. 3.2.6. Mass Balances The mass balance expressions for all mobile ions are shown as follows: Cj =MS (mSj) + MF(mF) (3.8) Aj =Ms(mSj) + MF(mF) (3.9) where C.is the total moles of cations (Na+, Me2+), A} is the total moles of anion (CI"), M^is the mass of water in the internal solution, M 5 is the mass of water in the external solution. Me 2 + is the metal ion, which could be Fe 2 + or Mn 2 + or Cu 2 + . 3.2.7. Inclusion of Binding Interaction The metal-fiber binding interaction is modeled using the equilibrium constant for each metal with the functional group on the fibre. The affinity of metal ions for the pulp fibres can be explained by metal ions forming complexes with the anionic groups of the fibre, e.g. carboxylate groups or other charged groups on the fiber. The expression for the complex-formation reactions of two functional groups with the divalent metal is given by Equation (3.10): Me 2 + + 2A~ <z> MeA, (3.10a) Me2+ + 2B~ <=> MeB2 (3.1 Ob) where Me2+ denotes the metal ion (Fe2+ or Mn 2 + or Cu2 +) and (A~) and ( B~) are the deprotonated charged group on the fiber respectively. If KMeA and KMeB are the binding constants, we have: {MeA,} _ (mLeA2) {Me }{A } (mMe2.)(™A_) 31 Chapter 3: Modelling Framework: Physical System and Mathematical Model {MeB2} (mLeB2) K ^ = {Me^}{By= «,)(<. )2 ( 3 - U b ) Due to the metal ion and fiber binding, the charge balances have to be modified. The charge balance equations (3.7) are now replaced by equation 3.12 below. M % = mFBH+mF +mFB_ (3.12b) The mass balance equation (3.8) is now replaced by equation 3.13 below. CMe=MF (mFMe2+) + Ms (msMel+) + MFmFeA2 + MFmFMeBi (3.13) In the mathematical model described in section 3.2, there are 13 equations to describe the partitioning model. They are listed below: • Two equations from electroneutrality (equation 3.3 and 3.4) • Two equations from water dissociation constant (equation 3.5) • Four equations from Donnan equilibrium (equation 3.6) • Two equations from the charge balances (equation 3.12) • Three equations from mass balances (equation 3.8, 3.9 and 3.13) There are 20 variables in the model. Four variables can be determined from the potentiometric titration of acid washed fiber that will be described in section 3.3. They are the fiber charge properties: KAH, KBH , QA and QB . The binding constant KMeA and KMeB are also determined by a potentiometric titration as described in section 3.3 later. Thus, only 14 variables are left. The variables are listed below: • Five variables from the dissociation of acidic groups on the fiber F F F F F - ™AH - MBH - MA- - M B - " " V • Eight variables from the electroneutrality F S F S - mK, + " mM * - m r r ' m r r 32 Chapter 3: Modelling Framework: Physical System and Mathematical Model mOH- 'KM- " " C i - < e « • One variable from Donnan equilibrium - A The model equations are manipulated as follows. From the water dissociation constant, the molality of hydroxyl group in the fiber and solution phase can be related to the molality of proton in the fiber and solution phase respectively as given in equation 3.14 and 3.15. ( 3 - 1 4 ) mH+ <H-=jjh (3-15) From Donnan equilibrium, the molality of proton, sodium, chloride and metal ion in the fiber phase can be related to the molality of these ions in the solution phase as given in equation 3.16, 3.17, 3.18 and 3.19. mF+ = msH+A (3.16) s m From the mass balances and substituting Donnan equilibrium, the molality of sodium ion in the solution phase can be related the total moles of the sodium as shown in equation 3.20. msN + = . F C m , (3.20) Na (MFA + MS) 33 Chapter 3: Modelling Framework: Physical System and Mathematical Model From the binding interaction (equation 3.11), the molality of metal bound on the fiber can be written in terms of the binding constant. (<e,2) = ^ 2 (<^)K-) 2 (3.21a) (<B2) = KMeBi(mFMe2+)(mFry (3.21b) Using equation 3.19 and 3.21; the mass balance of metal ion (equation 3.13) becomes: C » = (mL» )(MS+*2MF) + « 2 + ) X2MF \KMeA2 «_ )2 + KMeBi (<_ )21 (3.22) Hence, the molality of metal ions in the solution phase can be obtained as follows: C m Me MS+X2MF ^KMeA2(mFJ+KMeBi(mFB.) (3.23) From the dissociation of acidic groups, the molality of protonated acid charged groups can be written in terms of the dissociation constant of the fiber as given in equation 3.24. {MBH) = ("OK-) KAH K (3.24a) (3.24b) BH Substituting the molality of protonated acid charged groups (equation 3.24) into the charge balance equation (equation 3.7), the charge balance equations become: QA « • ) « - ) MF (KAH) QB _ « . ) « - ) • + m M' (KBH) + mr (3.25a) (3.25b) 34 Chapter 3: Modelling Framework: Physical System and Mathematical Model The molality of the free charged groups on the fiber (mA_ and m r ) can be related to their dissociation constant and their total charge concentration by re-arranging the charge balance equations and substituting the Donnan equation for proton (equation 3.16): m \MF j K AH Q, M K BH KBH +mH+A (3.26a) (3.26b) After substituting all molalities of mobile ions from equation 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20, 3.23, and the free charged groups from equation 3.26, it can be shown that the electroneutrality equations (equation 3.3 and 3.4) is a function of Donnan constant and the molality of chloride in the solution phase (equation 3.40 and 3.41). So it will end up having two equations and two variables. K ) . (MFA+MS) X K QA M' K AH MF K BH " V 1 KAH + "V A KBH + " V A + Ms +X2Ml ^KMeA2(mF_)2+KMeB2(mF_)2 ^r = 0 K ) + c Na (MFA+MS) K. m H* 2C. Me Ms +X2MF = 0 (3.27) (3.28) When the binding constants are set at zero, the above equations become: 35 Chapter 3: Modelling Framework: Physical System and Mathematical Model + K r ) K rw | me \ / w (MFA + MS) (MFA2+MS) -X mSH+A MF M (3.29) BH K AH (msH+)A KBH+(msH+)A = 0 ms H — 1 — "+ (MFZ+MS) (MFA2+MS) 2C„ K • m . cr (3.30) m H+ The unknowns in equation 3.29 and 3.30 are X and ms . The two equations can be solved to obtain values for these variables. Subsequently the metal ion (Me2+) partitioning can be calculated from equation 3.19 and 3.23. It is noted that in the above equation the mass of water in the solution {M S ), the total moles of metal (CME), total moles of sodium (CNA) at a given pH (m +^) are known from the partitioning experiment. The mass of water in the fiber phase {^MF) is known from the water retention value (WRV) measurement. The other four variables (KA H, KBH, QA and QB) were obtained from the fiber charge calculation described in section 3.3 and the other two binding constants (KMeA^ and KMeBi) were calculated as described in section 3.3. 3.3. Fiber Charge and Binding Constant Determination Fiber charge is calculated from the potentiometric titration data of acid washed-chelated fiber mat for all pulp samples. The titration is done with NaOH. Hence the ions of interest are Na+, OH", H + , and CI" (background ion). The above model is then employed to determine the four parameters (KAH, KBH , QA and QB). The binding constants (KMeAi and KMeBi) are determined from the potentiometric titration data of acid washed-chelated fiber mat but in the presence of the metal ion (Me2+) e.g. Fe 2 + or Mn 2 + or Cu 2 + . These calculations are explained below. 36 Chapter 3: Modelling Framework: Physical System and Mathematical Model 3.3.1. Fiber Charge Calculation from Potentiometric Titration From the water dissociation constant, the molality of hydroxyl group in the fiber and solution phase can be related to the molality of proton in the fiber and solution phase respectively as given in equation 3.14 and 3.15. From Donnan equilibrium, the molality of proton, sodium, chloride and metal ion in the fiber phase can be related to the molality of these ions in the solution phase as given in equation 3.16, 3.17, 3.18 and 3.19. From the mass balances and substituting Donnan equilibrium, the molality of sodium ion in the solution phase can be related the total moles of the sodium as given by equation 3.20. The molality of chloride ion in the solution phase can be related the total moles of the chloride as given by equation 3.31. mi - A«X ( 3 3 1 ) a (MF+MSA) The molality of the free charged groups on the fiber (mF_ and mF_) can be related to its dissociation constant and its total charge concentration as given in equation 3.26. So the total concentration of free charge will be the sum of the concentration of the two and is given by equation 3.32. mF_ = mF + mF_ X A B F mx = MF \MF j (3.32) BH + m\A Substituting all molalities from equation 3.14, 3.15, 3.16, 3.17, 3.18, 3.20, 3.31 and equation 3.32 into the electroneutrality equations (3.3 and 3.4) we obtain: m\A+( C m X / a , -J^-m* =0 (3.33) H (MFA + MS) (MF+MSA) m^A x 37 Chapter 3: Modelling Framework: Physical System and Mathematical Model ms + ^ 2 Ac£_ J ^ = O (3 34) H+ (MFX + MS) (MF+MSX) msH+ 1 ^ Equation 3.33 and 3.34 are the two final independent equations. These two equations contain six unknowns: X , mF_ , KAH , KBH , QA and QB . The other variables are known from the potentiometric titration experiment: msH+ ,CNa ,Aa ,MF and Ms. The way to solve the set of equations is by solving for X in equation 3.34 first and then use this X value in equation 3.33 to calculate mF_. The other four variables (KA H, KBH, QA and QB ) are fitted by using equation 3.32. 3.3.2. Binding Constant Determination As explained above, the potentiometric titration data of acid washed chelated pulp in the presence of Me 2 + are used to determine the binding constants. The Donnan model with binding interaction is used. The titration data below pH 7 and above pH 7 were treated separately in order to compute KMeA^ and KMeB^ respectively. The calculations were done according to the following equations. From the water dissociation constant, the molality of hydroxyl group in the fiber and solution phase can be related to the molality of proton in the fiber and solution phase respectively as given by equation 3.14 and 3.15. From Donnan equilibrium, the molality of proton, sodium, and metal ion chloride in the fiber phase can be related to the molality of these ions in the solution phase as given by equation 3.16, 3.17, 3.18, and 3.19. From the mass balances and substituting Donnan equilibrium, the molality of sodium and chloride ion in the solution phase can be related to the total moles of the sodium and chloride as shown in equation 3.20 and 3.31. 38 Chapter 3: Modelling Framework: Physical System and Mathematical Model From the dissociation of acidic groups, the molality of protonated acid charged groups can be written in terms of the acid dissociation constant of the fiber as given in equation 3.24. For one charged group (for example the acidic charged, A"), the mass balance of metal ion given by equation 3.22 can be rewritten as follows: \2" c » = K » ) K + x l M F ) + ) ^ F k ^ 2 K ) (3.35) Hence, the molality of metal ion in the solution phase (equation 3.23) can be rewritten as follows: m Me Me" Ms +A2MF (3.36) Substituting the molality of protonated acid charged groups (equation 3.24), Donnan equation for proton and metal ion (equation 3.16 and 3.19) and metal bound with the acid charged groups (equation 3.21) into the charge balance equations (equation 3.12), it becomes: /jy- \ MeA2 v Me1+' v A ' \ A ] M (3.37) After substituting the molality of metal ion in the solution phase (equation 3.36) into the charge balance equation (equation 3.37) and re-arranging the charge balance equation, it can be shown that the charge balance will be a function of the free acid charged group and the binding constant as shown in equation 3.32. Q. M A _ (KAH) K-)+ KMeACMeA\mFJ Ms +A2Ml l + K MeA. K ) (3.38) The binding constant can be written by re-arranging equation 3.38 so that it will be a function of Donnan constant [X) and free charged group on the fiber {niF_): 39 Chapter 3: Modelling Framework: Physical System and Mathematical Model (MS+MFA2) K M> K AU H) MeA, KAH K - K (3.39) Substituting all molalities of mobile ions from equation 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20, 3.31, 3.36 and the binding constant from equation 3.39, it can be shown that the electroneutrality equations (equation 3.3 and 3.4) is a function of Donnan constant (A) and the free acid charged group on the fiber {mF_ ). + K (MFA + MS) (MF+MSA) msH+A • 0 ™S 1 \ A I 2 C M e ^ Ms +A2M' C, Na K. H+ (MFA + MS) (MF+MSA) msH+ + 2C Me \MS +A2M' ^KMeAi(mFJ (3.40) (3.41) Equation 3.40 can be simplified by introducing co : CNaX K.. ^Na" ™Cl '^w (MFA + MS) (MF +MSA) mSH+A (3.42) We can simplify equation 3.41 by introducing an extra variables: n = mu+ + C AAA S { ^Na •"•CI'* '^w " + (MFA + MS) (MF +MSA) msH+ (3.43) Substituting co and n into equation 3.40 and 3.41, we obtained: 40 Chapter 3: Modelling Framework: Physical System and Mathematical Model 2 C M e ^ MS+A2MF l + K MeA, -K)=° (3-44) 71 + 2C Me Ms +X2Ml l + K MeA3(™FA-)2 (3-45) At this point, there are two simplified equations from the electroneutrality equations in the fiber and solution phase (equation 3.44 and 3.45) with two unknowns left: X and mF_. The two new introduced variables (a>,n) are not considered as unknowns because both of them are a function of A . After solving these two unknowns, the binding constant can be calculated by using equation 3.39. This calculation is repeated for the other charged group (B"). The other variables are known from the potentiometric titration experiment: ,CN a, Aa ,MF and Ms. The other four variables (KAH , KBH , QA and QB ) can be obtained from fiber charge properties as described in section 3.3.1. 41 Chapter 4 4. Experimental: materials, equipment and methods This chapter will describe all procedures used in conducting the experiments. The materials and equipments used during the experiments will be discussed and the method for carrying out the experiments will be described afterwards. 4.1. Materials Materials used in the experiments were: • Softwood Kraft pulp from a coastal mill and an interior mill in British Columbia. • Distilled and de-ionized water. • 0.1 N NaOH solution from Fisher Scientific for adjusting the pH of the pulp suspensions and potentiometric titration. • Di-ethylene tri-amine penta-acetic acid (DTPA) solution from Fluka Chemie Gmbh., available at 40% concentration for the chelating stage. • 6M of Hydrochloric acid (HC1) (trace metal grade) from LabChem Inc. for adjusting the pH of the pulp suspensions, acid washing and digestion of the ash. • 1M of Hydrochloric acid (HC1) from Fisher Scientific for the potentiometric titration. • Fe standard solution available at lOOOppm from Aldrich Chemical Company for preparing the calibration standards of Atomic Absorption Spectrophotometric (AAS) analysis • Hydroxylamine from Fisher Scientific for Spectrophotometric analysis. • O-phenanthroline from Fisher Scientific for Spectrophotometric analysis. • Sodium acetate from Fisher Scientific for Spectrophotometric analysis. 4.1.1. Pulp Samples A pulp sample was obtained from British Columbia coastal mill. The mill consists of two fiber lines: Thermo-Mechanical Pulping for Newsprint and Kraft pulp as market pulp. This mill manufactures 1200 TPD of bleached kraft pulp from softwood, which consists of 50% of Cedar 42 Chapter 4: Experimental: material, equipment and methods and 50% of SPF (mixture of Spruce, Pine and Fir), commercially known as HSLP-400. I used the kraft pulp in the experiments. The kappa number was determined down the fiberline. At the Digester, the kappa number was found at 35 with the final brightness of the pulp sheet was 90.4 % and the viscosity was 17.4cp. The pH was taken from the mill. The rest of the kappa number was determined in our laboratory using the standard procedure from TAPPI. Table 4.1 lists the complete sampling points and pulp properties. The pulp samples can be seen in figure 4.1. Table 4.1: Sampling points and pulp properties determined at the mill for BC Coastal Sample Number Sample name Consistency (%) Kappa Number pH 1 Post-Brown Stock Washer (BSW) 14.05 35.1 > 13 2 Oxygen Delignification Washer Mat (P-02 Washer Mat) 16.75 19.1 > 13 3 D c Washer stage outlet 12.32 12.5 2.3 4 E0p Washer stage outlet 9.76 10.5 10.6 5 D n Washer stage outlet 13.41 6.7 4.5 6 D 2 Washer stage outlet 14.39 4.5 3.4 Note: This pulp was received in December 2001. 43 Chapter 4: Experimental: material, equipment and methods Figure 4.1: B C Coastal M i l l samples from left to right: Brown Stock Washer mat (BSW); Post Oxygen Delignification mat (P -O2); D c ; E o p ; D n ; and D 2 washer outlet 44 Chapter 4: Experimental: material, equipment and methods Another pulp sample was obtained from an interior mill. The consistency and kappa number of this pulp was determined in our laboratory. The pH at 1% consistency was also determined at our laboratory. We also received bleached dried pulp sheets. The pulp characteristics are tabulated in table 4.2. Table 4.2: Sampling points and pulp properties determined at the mill for BC Interior Pulp Sample Original Pulp Consistency (%) Kappa Number pH (1% consistency) Brown Stock Washer (BSW) 18.2 35.7 9.85 Post Oxygen Washer (P-O2) 28 18.9 9.83 'Dc' Mat (Dc) 11.95 12.2 4.35 Dried Pulp 94.28 Not Determine Not Done Note: This pulp was received in October 2001. 4.1.2. De-ionized water De-ionized water was used to avoid the contamination of unwanted metal ions during the experiments. To maintain the purity and reduce the load of the filter in the water purifier, distilled water was used as the input to the water purifier to produce de-ionized water. The purity of de-ionized water was very important in this experiment because we were dealing with a very small quantity of metal ion in the pulp sample so we wanted to make sure that there are no inorganic contaminants in the water. De-ionized water was mainly used to rinse all of the equipment used in the experiment after washing with hydrochloride acid (HC1) and also used to make up chemical during dilution or adjusting the consistency of pulp suspension. 4.1.3. Di-ethylene tri-amine penta-acetic acid (DTPA) solution In the experiments, di-ethylene tri-amine penta-acetic acid (DTPA) solution was available at 40% concentration, and could be further diluted to any concentration needed during experiment. The structure of DTPA is shown in figure 4.2. 45 Chapter 4: Experimental: material, equipment and methods Figure 4.2: Di-ethylene Tri-amine Penta-acetic Acid (DTPA) structure DTPA is a chelating agent. There are many types of chelating agents used to bind metal ions; EDTA and DTPA are the common ones. Basically, chelating agents have several charge groups that dissociate at different pH conditions to bind the metal ion so that the metal ions become inactive. EDTA for instance, it has four charge groups. DTPA has five charged groups, so DTPA is a stronger chelating agent compare to EDTA. When these charge groups dissociate, they create negative charges so that they are expelled from the fiber charge groups. Metal ions have higher affinity towards chelating agent than fiber because the complex of metal ion and DTPA is much more stable than the metal ion to pulp complexes. It is characterized by the solubility constants of DTPA compared to the pulp. The stability constant of these chelating agent are summarized in table 4.3. Table 4.3: Stability constants of DTPA and EDTA (Rasanen and Karkkainen, 2003) Stability constant DTPA EDTA PK! 1.08 2.07 pK2 2.55 2.75 pK3 4.33 6.24 PK4 8.60 10.34 pK5 10.58 -4.1.4. HC1 (Hydrochloric acid) 6M of hydrochloric acid (HC1) was readily available to use for the acid-wash step, digestion and pH adjustment for the partitioning experiments. Under acidic conditions, metal ions tend to go 46 Chapter 4: Experimental: material, equipment and methods to the solution instead of the fiber because the active site in the fibre is protonated with H and release the cations to the solution. HC1 was also used to digest the ash of pulp sample. The concentrated HC1 dissolved the ash to form a solution so that metal concentration in the solution can be analyzed and the absolute amount of metal ion in the solution could be calculated. This concentrated HC1 could be diluted to 1M and used to clean all of equipments that were used during the experiments. This was done do maintain clean apparatus before doing any experiments and prevent the contamination to the measurements. Another 1M of HC1 from fisher scientific was used in the potentiometric titration as the background ions. 4.1.5. Fe standard for Atomic Absorption Spectrometric (AAS) Analysis Fe standard solution was available at lOOOppm (Fishers Scientific). It was used to make up the calibration standards in analyzing AAS. It was also used for metal addition in partitioning experiments. Iron has two different concentration ranges for the optimum AAS measurement, so I prepared my standard according to the concentration of my samples. The first concentration range is from 2 to 9 ppm and the next one is from 20 to 80 ppm. In my samples, the iron concentration never went up beyond 80 ppm, so I prepared the standard up to 80 ppm. For the first range, I made lppm; 2.5ppm; 5ppm; 7.5ppm; and lOppm. For the second range, I prepared 20 ppm; 30ppm; 50ppm; and 80ppm. Most of the sample I found later on falls between 2-9 ppm. To prepare the standard, I followed the method described in TAPPI standard (T 266 Om-94). Basically, I used the standard solution from Fisher Scientific and diluted it into the concentration I needed by adding de-ionized water. I also put 5 ml of 6M HC1 in every 50 ml of solution the same as I prepared the blank to prevent iron precipitation. I also used this iron solution to prepare the standard solution for the Spectrophotometric method, which was a suitable method for measuring low iron concentration (less than lppm). This standard solution was diluted to 2 ppm so that it could be diluted to the concentration desired from zero to one ppm. 47 Chapter 4: Experimental: material, equipment and methods 4.1.6. Spectrophotometer standard To perform the Spectrophotometric analysis, the following reagents were needed. The reagents were 10% Hydroxylamine solution as the reducing agent, 0.1% o-p phenanthroline solution as the complexing agent, and 10% sodium acetate as the buffer solution. These reagents was prepared by dilution base on the weight percentage. For the o-phenanthroline solution, hot water was used to dissolve the powder. It is because o-phenanthroline is an organic compound so that it's not easily dissolved under room temperature. 4.2. Equipment The equipments were mostly used to perform the mixing of pulp suspension, centrifuging the wet fiber mat, drying, ashing, digestion, potentiometric titration of the pulp suspension, Atomic Absorption Spectroscopy ( A A S ) analysis and Spectrophotometric analysis in the experiments. The equipment details are listed as follows: • 700mL and 1500mL Plexiglas vessels with baffles for mixing pulp suspension. • Dynamic Drainage Jar (DDJ) funnel and nylon mesh for the filtration. • Water purifier ( E L G A U H Q II, Great Britain) for producing de-ionized water. • A p H meter (Metrohm 691 p H meter, Switzland) for adjusting the p H . • Drying oven operating at 105°C for drying the wet fibers. • Muffle furnace operating at 575°C for ashing the pulp samples. • Atomic Absorption Spectroscopy ( A A S ) analyzer ( G B C 904 A A Spectrophotometer, G B C Scientific Equipment, Australia) for determining iron concentration in the pulp samples. • Spectrophotometer analyzer (Biochrom, Novaspec II, Cambridge, England). • 25mL glass vials with screw caps and 125-mL polyethylene bottles are used to store sample solution (ordered from Fisher Scientific). • A few crucibles and desiccators for the ashing process (Fisher). • Top balance accurate to 0.1 g and analytical balance accurate to O.lmg (Mettler Toledo). • Centrifuge (Hermle) for determining the internal water. • Mettler D L 2 5 titrator for potentiometric titration. • Mettler Toledo model DG111-SC glass electrode for potentiometric titration. 48 Chapter 4: Experimental: material, equipment and methods The pictures of the water purifier to produce de-ionized water and an analytical balance are shown in figure 4.3 below. (a) (b) Figure 4.3: Water purifier ELGA UHQ II (a); Analytical Balance Mettler Toledo (b) 4.2.1. p H meters The pH measurements were performed using the Metrohm 691 pH Meter. The accuracy of the instruments was ± 0.01. This instrument was supplied by Fischer Scientific Ltd (Edmonton, Alberta). The measurement was done at 1% consistency with dipping the probe into the pulp suspension and reading the number directly from the display. Repeating the measurement at several points in the pulp suspension was done to make sure that the pH reading represented the whole suspension. 4.2.2. Centrifuge Centrifuge was used to separate the external water from the internal water in the fiber using a water retention value (WRV) method. The fiber mat retained after the filtration was placed in 49 Chapter 4: Experimental: material, equipment and methods the insert with a stainless steel filter below it and put inside the tube for centrifuging. Centrifuge was used to remove the lumen water inside the fiber that remained after filtration and also the free water. Centrifuge took 30 minutes at 2590rpm. The weight of fiber mat before and after the centrifuge was noted down. Figure 4.4: Ph meter (Metrohm 691) and Centrifuge (Hermle) 4.2.3. Atomic Absorption Spectroscopy (AAS) The metal ion concentration was detected using Hol low Cathode Atomic Absorption Spectroscopy. The analysis was performed using G B C 904 A A Spectrophotometer supplied by G B C Scientific Equipment Pty Ltd, Australia. To maintain the accuracy o f the measurement, A A S standard solution was used to calibrate the A A S machine according the optimum working range given in the A A S manuals, depending on the metal concentration in the solution that was going to be measured. Two working ranges were used between 2-9 ppm and 20-80 ppm for iron. The A A standard was prepared according to T A P P I standard (T 266 Om-94). The critical point to get a reliable measurement and a good calibration curve was to prepare the blank and the standard solution accurately. 50 Chapter 4: Experimental: material, equipment and methods Figure 4.5: Atomic Absorption Spectroscopy 4.2.4. Spectrophotometer (Colorimeter) A spectrophotometer was used as an analytical quantitative analysis of iron at a very low concentration. The optimum working range for iron was O.lppm tolppm. Usually the iron concentration of the pulp sample was much more than lppm, so the solutions were diluted to less than 1 ppm and then applied the dilution factor to calculate the actual concentration. Figure 4.6: Spectrophotometer 51 Chapter 4: Experimental: material, equipment and methods Basically, spectrophotometer measured the absorbance from the sample, so calibration of the instrument was needed. The calibration used the iron standard solution with a known concentration and then correlated the absorbance with the concentration. To determine total iron, ferric iron has to be reduced with hydroxylamine hydrochloride and the resulting ferrous iron is then complexed with o-phenanthroline. Ferrous iron forms a colored complex with o-phenanthroline (1,1 O-phenanthroline). Three o-phenanthroline molecules combined with each ferrous ion to yield a complex. This complex is called "ferroin". Once formed, the color of the complex is stable for long periods of time. Quantitative formation of the complex is observed in the pH region between 2 to 9. The pH is adjusted to 6-9 by addition of sodium acetate as the buffer. The colored solution obeys Beer's law. The iron concentration from the solution can be seen by its color, which is orange. The more iron in the solution; the color of the solution becomes darker. 4.3. Experimental Methods The method used in the experiment is based on the TAPPI standard. Method to find the moisture content, ashing, digestion, fiber saturation point (FSP), potentiometric titration, metal profile, metal removal and metal partitioning will be described as follows. 4.3.1. Moisture Content Determination TAPPI standard T 412 om-94 was used to measure the consistency of all pulp samples. The moisture content in the pulp sample was measured by putting the sample in the oven at 105 + 2°C for approximately 3 to 4 hours, depending on the quantity of the sample used. Then, the sample was put in the desiccator for approximately 30 minutes until it reached the room temperature. After that, the sample was weighed on the analytical balance and the ratio of dried fibers over wet fibers was calculated to find the pulp consistency. This was repeated several times until the weight did not change anymore; making sure that all moistures had gone. 52 Chapter 4: Experimental: material, equipment and methods 4.3.2. Ashing the Pulp Sample The pulp sample was put in the crucible and ashed in the muffle furnace for at least 10 hours or overnight to make sure that the pulp was properly ashed. In the furnace, all of the organic material was burned and only inorganic material stayed in the crucible. The colour of the ashed sample was usually white and very dry. After ashing, the sample was removed from the furnace and kept in the desiccator for about 30 minutes in order to cool it down to room temperature. Then the pulp sample was then ready for digestion. 4.3.3. Digestion of the Pulp Sample After ashing, the ash was placed inside the fume hood to perform the digestion. A few drop of de-ionized water was put into the ash to wet the ash and prevented it from flying over during the digestion since the ash is very light. Then 6M HC1 was added into the ash to digest the ash. For lOg of OD pulp, approximately 10-20ml of 6M HC1 was added in order to digest the pulp sample completely. If some particles found in the solution, the solution was heated on a heater for some time to dissolve the particles. Then the solution was diluted with de-ionized water up to the desired total volume of solution for analysis, approximately 25 ml. Finally, the solution was transferred into the vial which was already labelled. The crucible and the lid was rinsed with de-ionized water twice to make sure no metal ion remained and transferred to the corresponding vial for analysis. 4.3.4. FSP Water Determination Fiber saturation point (FSP) is a method to measure the moisture content inside the cell of wood fibers. In 1972, Scallan and Carles showed that FSP could be easily obtained from the water retention value (WRV) at the specific centrifuge conditions of 900g (2590 rpm) and 30 minutes (Bygrave, 1997). The WRV value equals to the FSP at the value up to 1.8 g of water/g OD fiber under this centrifuge conditions. The value of FSP depends on the pH of the pulp fiber. So the water retained by a wet pulp sample after centrifuging under standard condition is defined as the water retention value (TAPPI UM 256, 1991). WRV was determined by using a centrifuge with a fixed 45° rotor and centrifuge tubes with plastic inserts designed to hold 100 mesh screen half way up the tube. The mesh screen is supported from the below by a porous plastic plate for mechanical strength. Six samples could be centrifuged at once. 53 Chapter 4: Experimental: material, equipment and methods Here is the Water Retention Value (WRV) procedure: 1. The pulp was dispersed in de-ionized water at 1% consistency overnight. Then it was filtered on a Buchner runnel and vacuum flask until the fiber mat was at 20% consistency. 2. The wet fiber mat was placed into each centrifuge insert with the equivalent of lg-oven dry fiber each. The insert was fitted with the tube and balanced by adding water. 3. The tube was centrifuged for 30 minutes at 2590rpm. 4. After 30 minutes, the insert was removed and the mass of the fiber mat recorded. 5. The centrifuged fiber mat was dried in an oven at 105 + 2°C. Then the sample was placed in a desiccator to cool down and the mass of oven dried the fiber mat was recorded. The WRV was calculated based on the mass difference of wet fiber mat after centrifuging with the mass of the oven dry fiber for the corresponding mass of oven dried fiber, see equation 3.1. _ Wet Fiber Mat - OD Fiber Mat OD Fiber Mat 4.3.5. Potentiometric titration Potentiometric titrations were conducted to determine the fiber charge and the binding constants as described in chapter 3. The potentiometric titration procedure is described below: 1. The pulp sample was washed using a metal ion removal procedure, which will be described later in section 4.3.7. It was assumed that most metals had been removed by applying four stages of washing. The fiber mat was called acid washed centrifuged fiber mat (AW-CFM-2). 2. The corresponding 0.6g of oven dried AW-CFM-2 was used. 0.6g of 1M HC1 was added into the pulp to provide background ions. Finally, the fiber mat was diluted to 60g to make 1% consistency of pulp suspensions. This pulp suspension was then mixed and equilibrated for 1-2 hours with a three-blade vinyl impeller. For the binding experiment, 54 Chapter 4: Experimental: material, equipment and methods a known amount of metal ions was added into the suspension while maintaining the volume at 60 ml. 3. A Mettler DL25 titrator was used to perform titration with lOOmmol/L NaOH solution. During the titration, nitrogen injection was fed into the titration vessel to prevent carbon dioxide absorption. Each injection of NaOH was followed by mixing before the electric potential (pH) was read, which was at equilibrium. If the pH was still drifting, the pH reading was delayed until the pH became constant. The volume of NaOH added versus pH reading from the instrument was noted down from the original pH to about pH 11. Figure 4.7: Potentiometric titration (Mettler DL25 titrator and Mettler Toledo model DG111-SC glass electrode) 4.3.6. Metal Profile of a Pulp Sample Substantial experimentation was performed in order to establish an experimental procedure. It is well described in figure 4.8 and 4.9. According to the preliminary trials, 20g of corresponding OD pulp sample was good enough to analyse the full metal profile and metal removal. The pulp sample was divided into two samples. The first sample was to find out the metal ions on the fiber phase (metal profile). The second sample was to find the effect of acid washing and 55 Chapter 4: Experimental: material, equipment and methods chelation for metal ion removal, where the residual of metal ions in the fiber phase was measured. The initial preparations of both pulp samples for metal profile and also metal removal were the same, which is shown in figure 4.8. Here is the procedure for pulp sample preparation: 1. Jacketed glass vessel (2 L and 1 L) and all tools that were used during the experiment (beaker, insert, flasks) were cleaned using 6M HC1 solution. Acidic condition removed all residual ions from previous experiment. These tools were rinsed twice with distilled water and three times using distilled de-ionized water and dried at room temperature. 2. The platinum crucible and lid was cleaned using a few drops of 40% DTPA solution for overnight followed by acid washing for several minutes to remove all metal ions. The crucible was rinsed using distilled de-ionized water for three times and dried in the muffle furnace at 575°C for 15 minutes. Then cooled down for about 30 minutes in the desiccator to reach room temperature. The crucible was weighed once it cooled down. 3. The consistency of the pulp sample was determined using three replicates. The average consistency was taken. A corresponding of 20g OD pulp sample was prepared. 4. Each pulp sample was divided into two for metal profile and metal removal, which corresponds to lOg OD pulp sample each. The sample was put into the vessel and diluted with distilled de-ionized water to get 1% consistency. 5. The pulp sample was washed with distilled de-ionized water for 5 minutes at 1% consistency and 500 rpm, followed by filtration using Dynamic Drainage Jar (DDJ) to remove all of the dirt material and residual cooking chemical in the pulp sample. Note that during the dilution to 1% consistency, the pH might change from the original pH into a naturally occurring pH upon the dilution, which was usually close to neutral pH depending upon the original pH. If the original pH was found at about alkaline, it might drop to pH 8 to 9 whereas if the original pH was acidic, it might go up to pH about 5-7. 6. The empty insert for separating the fiber and free water was weighed and then the fiber mat was put into the six inserts evenly. The fiber mat with the insert was weighed. All inserts were placed inside the tube for centrifuging. 7. The fiber mat was centrifuged at 2590 rpm for 30 minutes. 8. The centrifuged fiber mat (CFM) was weighed and retained for the next step. The procedure for metal profile itself is shown on figure 4.9 and described below: 56 Chapter 4: Experimental: material, equipment and methods 1. The centrifuged fiber mat-1 (CFM-1) was placed in the crucible and oven dried inside the oven at 105 + 2°C for 3-4 hours. The dried sample was cooled down to room temperature inside desiccator and the corresponding oven dried weight was measured. 2. Then the oven dried sample was ashed in the muffle furnace at 575 + 25°C for overnight. The ash was cooled down to room temperature inside desiccator and then digested with a few drops of de-ionized water and 6 M HC1. 3. The solution was transferred into the vials for analysis. Some portion of the samples was sent to a private laboratory in Burnaby, B C for ICP analysis. The rest portion of the samples was analyzed using Atomic Absorption Spectroscopy ( A A S ) analysis. Two pulp samples were also analyzed with calorimetric method using Spectrophotometer to verify the accuracy of the measurements. This allowed the comparison among the ICP result, A A S analysis and Spectrophotometer analysis. The results from analysis corresponded to the total metal ion on the fiber in the pulp sample. 20g Pulp Sample (PS) 10g Pulp Sample 1 (PS-1) DDW Washing at 1% Consistency Filtration Centrifuge Centrifuge Fiber Mat-1 (CFM-1) 10g Pulp Sample 2 (PS-2) DDW Washing at 1% Consistency Filtration Centrifuge Centrifuge Fiber Mat-2 (CFM-2) Figure 4.8: Pulp sample preparation procedure for metal profile and metal removal 57 Chapter 4: Experimental: material, equipment and methods Centrifuge Fiber Mat-1 (CFM-1) Oven-dry Ashing + Digestion Figure 4.9: Metal profile procedure to find the amount of metal bound to the fiber 4.3.7. Metal ion removal from pulp Removing metal ions from the fiber phase requires understanding the characteristic and interaction between fiber and each metal in the suspension. Although the metal of interest here was iron, some other metals were also under investigation at the same time because they are responsible for peroxide decomposition and cellulose degradation. The other metals of interest were manganese and copper. Finding out the best metal ion removal efficiency of all metals from the pulp suspension required preliminary experiment, and it was done by Chen, B . Y . (2002) in her B . A . S c . thesis. According to the result shown in Chen's thesis, the optimum metal removal procedure had been established for all these three metals. In her thesis, she determined the metal ion removal efficiency through various methods for each metal ion individually and came up with a suggestion for the removal of all three metal ions in the pulp suspension. She found out that for iron, it was best removed by the combination of acid and D T P A . Manganese was effectively removed under acidic condition and copper was mostly removed by using D T P A under non-acidic condition. So based from the result of her experiment the metal ion removal procedure for the entire three metal ions of interest was developed. The metal removal required three stages washing in series to remove these three metals. First, 50ppm D T P A was used to remove copper, then using 6 M HC1 to adjust p H at 1.5 « 2 to remove 58 Chapter 4: Experimental: material, equipment and methods manganese, and the last using combination of acid and DTPA to remove iron. Each of the washing removal was done at 2.5% consistency for one hour at 500 rpm mixing. After each washing the suspension was filtered using drainage jar (DDJ). The liquor after each washing stage was collected for analysis. The retained fiber mat was maintained the consistency back to 2.5% by adding fresh de-ionized water. The washing was done at 2.5% consistency because at higher consistency it was difficult to mix the pulp suspension as for lower consistency it required more process water and chemical. After finishing all the three stages washing, the residual metal ion left on the fiber was analyzed. The removal efficiency was found not quite satisfactory, so another set of experiments were done by applying one more washing stage with distilled de-ionized water (DDW) at the end of the three washing stage. An improvement in term of metal removal efficiency was found. The washing with DDW at the end probably removed more iron complexes that was trapped inside the fiber mat. So only the metal removal procedure with washing using DDW is described here. The metal removal procedure is shown on figure 4.10 and described below: 1. Jacketed glass vessel (2 L and 1 L) and all tools (beaker, insert, flasks) that were used during the experiment were cleaned using 6M HC1 solution. Acidic condition removed all residual ions from previous experiment. These tools were rinsed twice with distilled water and three times using distilled de-ionized water and dried under room temperature. 2. The centrifuged fiber mat from the pulp sample preparation (CFM-2) described in section 4.3.6 was collected, which corresponded to lOg oven dry. This sample was put into the vessel and diluted with distilled de-ionized water until approximately around 200g of pulp suspension, which corresponded to 5% consistency. 3. The first washing step is called "DTPA wash" as shown in figure 4.10. 1% DTPA which correspond to 50 ppm (2g) and distilled de-ionized water was added, so the total pulp suspension was 400g which corresponded to 2.5% consistency. The pulp sample was washed with 50 ppm DTPA for one hour and then followed by filtration using DDJ. The liquor was collected for analysis and the fiber mat was weighed for the next washing stage. The liquor was called L-l.The weight of fiber was used to calculate the amount of water needed in the next washing stage that corresponded to 2.5% consistency. 59 Chapter 4: Experimental: material, equipment and methods 4. The second washing is called "HC1 wash" as shown in figure 4.10. The retained fiber mat from the previous washing was washed in acidic condition by using HC1 for another one hour. The fiber mat was put back into the vessel and then distilled de-ionized water was added till 395g approximately, before adding the 6M HC1. The pH was adjusted at around 1.5-1.75 by adding a few drops of HC1 followed by adding distilled de-ionized water to get 2.5% consistency. After one hour, the suspension was filtered once again to collect the liquor and the acid washed fiber mat was weighed. The liquor was called L-2. 5. The third washing is called "HC1 + DTPA wash" as shown in figure 4.10. The fiber mat after acid washing from the previous stage was collected and put into the vessel. Distilled de-ionized water was added up to 350g and then the pH was adjusted to 1.5-1.75. More distilled de-ionized water was added until the weight of the pulp suspension was 398g. Then the pulp was washed with acid for the first half an hour followed by chelation for another half an hour. The chelation was done by adding 2g of 1% DTPA to get 50 ppm concentration. After one hour, the suspension was filtered using DDJ to collect the liquor and the acid washed fiber mat was weighed. The liquor was called L-3. 6. The last washing stage is called "De-ionized water washing" as shown in figure 4.10. After all three washing stages was done, the retained fiber mat was washed again with distilled de-ionized water for 5 minutes at 1% consistency in order to displace some of the metal ion that might be complexed by DTPA and trapped inside the fiber mat. The pulp suspension was filtered to retain the fiber mat and the liquor for analysis (L-4). The fiber mat was centrifuged to remove all external water from the fiber. 7. The acid washed chelated centrifuged fiber mat (AW-CFM-2) was dried in the oven, follow by ashing and digestion. The solution was transferred into the vial for analysis. 8. Then all solutions (all washing liquors and digested acid washed centrifuged fiber mat) were analyzed using AAS analysis. Some portion of the sample was also sent for ICP analysis. 60 Chapter 4: Experimental: material, equipment and methods Centrifuge Fiber Mat-2 (CFM-2) DTPA Wash 50 ppm, 2.5% Consistency HCI Wash pH~1.5-2, 2.5% Consistency HCI + DTPA Wash pH«1.5-2, 2.5% Consistency De-ionized Water Washing at 1% Consistency Acid Washed Centrifuged Fiber Mat-2 (AW-CFM-2) Liquor-1 (L-1) Liquor-2 (L-2) Liquor-3 (L-3) Liquor-4 (L-4) Oven-dry, Ashing + Digestion A A N A L Y S I S Figure 4.10: Metal ion removal procedure in four washing stage 4.3.8. Metal ion partitioning in a pulp suspension The samples used in the partitioning experiments were only two samples, which were from B C Coastal samples: Brown Stock Washer (BSW) and D c . In the partitioning experiment, all metal ions on the pulp sample were removed by the acid washed-chelation stage. It followed the metal removal procedure that was described in the chapter 4.3.7. The centrifuged fiber mat ( A W -C F M - 2 ) shown in figure 4.10 was collected and used in the partitioning experiment. The centrifuged fiber mat ( A W - C F M - 2 ) was diluted to 1% consistency with de-ionized water and mixed for an hour. The p H was adjusted to the desired p H , which was set at pH=3 for iron. Partitioning experiment at p H higher than 3 was not done because of the iron precipitations (see figure 2.3). The suspension was divided into three replicates inside 125ml polyethylene bottles. Then iron from the A A S standard solution was added accordingly, which was at 1, 2, 4 and 10 61 Chapter 4: Experimental: material, equipment and methods times the initial concentration of metal ion measured in the fiber. The suspension was mixed under nitrogen injection overnight in an orbital shaker. It was assumed that the suspension had reached equilibrium overnight. Afterwards, the fiber mat was filtered, centrifuged, oven dried, ashed, and digested for determining the iron concentration in the fiber phase. The liquor was also analyzed for iron concentration in the solution phase. The complete procedure for metal ion partitioning is shown in figure 4.11 and is described below: 1. All equipments used in the experiment were cleaned using 6M HC1 solution, rinsed with distilled de-ionized water three times and dried at room temperature. Metal ion removal procedure as described in chapter 4.3.7 was performed, which corresponded to lOg oven dried fiber. The acid-washed chelated centrifuged fiber mat (AW-CFM-2) was collected. 2. Acid-washed chelated centrifuged fiber mat (AW-CFM-2) was diluted with distilled de-ionized water up to 1% consistency. Then the pulp suspension was mixed. After a while, nitrogen gas line was opened and the pulp suspension was injected with nitrogen for several minutes to prevent carbon dioxide absorption and carbonate precipitation. The mixing was done for an hour. 3. The pH of the pulp suspension was adjusted at 3 by adding HC1 or NaOH solution and followed by sweeping with nitrogen for several minutes. The pH measurement was done at several points for several time to make sure that pH in the suspension was stable. 4. Once the desired pH had been reached and stable, the pulp suspension was splitted into three polyethylene bottles (Nalgene) using 100 ml beaker. Each bottle had lOOg suspension that corresponded to lg oven-dried fibers. This was done very quickly after stopping the mixer to maintain the homogeneity of the pulp suspension. 5. A known amount of iron was added to the suspension based on the iron metal profile concentration found in the pulp originally at a variation of 1, 2, 4 and 10 times more than the iron metal profile. Iron standard solution from AAS was used to avoid any contaminant from other ions. 6. The pulp suspension was mixed using orbital shaker under nitrogen injection to avoid carbon dioxide absorption for overnight. 62 Chapter 4: Experimental: material, equipment and methods 7. The next day, the pulp sample was filtered using DDJ, the fiber mat and the filtrate was collected. The DDJ filter is a 70 mesh one. 8. The fiber mat was centrifuged or passed through 5 urn filter paper followed by oven-drying, ashing and digestion. The acid-digested pulp sample was analyzed using AAS analysis. As seen from figure (4.11) this step was done in two ways, see p. 100 for explaination. 9. The fiber mat was also analyzed with SEM and EDX analysis to see whether any precipitation was found and trapped inside the fiber mat. 10. The filtrate was kept for analysis. A c i d Washed Centrifuged Fiber Mat-2 ( A W - C F M - 2 ) Mix the suspension at 1 % consistency Adjust the pH of the pulp suspension Split into three replicates Metal ion addition at known concentration Let the pulp suspension equilibrate for overnight using orbital shaker under N2 atmosphere 1 Filter the pulp suspension using DDJ Fiber mat Centrifuge or use filter paper, Oven-dry, Ash ing + Digestion Filtrate * -C^SEwT&ED^> ( ^ N A L Y S r T ^ Figure 4.11: Metal ion-partitioning procedure 63 Chapter 4: Experimental: material, equipment and methods 4.4. SEM & EDX Analysis of Acid Washed Pulp Samples Scanning Electron Microscopy (SEM) is a tool used to scan for any small particle and Energy Dispersive X - R a y ( E D X ) is a tool used to analyze the atomic composition of the particle. Using S E M and E D X analysis, any inorganic precipitates on the fiber mat of acid washed samples can be identified. The sample preparation and the S E M - E D X preparation are both required before the analysis. 4.4.1. Sample Preparation The samples used in the analysis were: - A c i d washed chelated pulp ( A W - C F M - 2 ) A c i d washed chelated pulp, in which iron was added according to the partitioning experiment at p H 3 (Fe-AWCP3) The acid washed chelated pulp sample was prepared according to the metal removal procedure described in section 4.3.7 and the other sample was prepared according to the metal ion partitioning procedures described in section 4.3.8. A l l samples were oven-dried for S E M and E D X analysis. Each sample contained approximately lg-od fiber after the drying. The amount of pulp sample used for the analysis was approximately 0. 001.-od fiber and was obtained from the 1-g sample. 4.4.2. SEM & EDX Preparation The analysis proceeds as follows: 1. The 0.001-g dried sample was placed on the sample holder; which was covered by carbon adhesive so that the sample would stick to it. Five sample holders with the material under investigation could be mounted on a sampling table, as seen in figure 4.12. 2. The sampling table was placed under vacuum inside the coating equipment. Then, the samples were coated with carbon, which has a minimal effect on the X-ray spectrum. This was done in order to ground the electron charge from the samples. If no coating was applied on the fiber, there might be a built up of electron charge on the fiber while imaging the 64 Chapter 4: Experimental: material, equipment and methods samples with the electron beam in S E M analysis. High vacuum condition (no air in the samples) was also important because i f air was present, it might bum the carbon while heat was applied. The carbon coating procedure took 30 minutes. Sample holder Sampling table Figure 4.12: S E M & E D X preparation 4.4.3. SEM & EDX Analysis Procedure The instrument used for S E M analysis was the Hitachi - S3000N (Mito, Japan) and for E D X analysis was the Quartz - X O N E (Vancouver, Canada). The analysis procedure is given as follows. 1. The mounting table with five different samples was placed into a slot in the instrument. The analysis took place in a vacuum chamber. 2. The electron beam was turned on and the position of the mounting table was adjusted t i l l enough count rates were achieved for E D X analysis. The height of the mounting table was at 15 mm. 3. The S E M was set on backscattered mode (BSE), which gave a clear contrast in the grey scale picture. This is because the fibers consist of organic material such as carbon and oxygen, which is in dark grey colour, and the metal precipitates exist in a bright colour so that the contrast between the fiber and metal precipitates can be seen clearly. 65 Chapter 4: Experimental: material, equipment and methods 4. The metal composition in the precipitate was determined using the E D X technique, which gave the atomic composition of the precipitates based on the excitation energy of the constituent atoms. Some atoms have more than one free orbital so that it might have more than one peak on the E D X plot when it is excited by X-ray radiation. The subject of interest is metal precipitate in the fiber mat, which was manually searched by scanning the entire fiber mat. The focus and the magnification were adjusted to search for the precipitates. Once the precipitate was found, the camera was zoomed to the area of interest, which was usually marked by the dashed ellipse or dashed circle. Then, this area was analyzed with E D X to obtain its atomic concentration. Thus, different "spots" on the fiber mat can be focused to obtain S E M pictures and perform E D X analysis. 66 Chapter 5 5. Results and Discussion Values of the variables or parameters needed for the modelling of iron and other metal (copper and manganese) partitioning in aqueous wood fibre suspensions are presented first. Iron profiles and iron removal in the fiberline will be exposed next. Then the prediction results from the modelling of the metal partitioning will be discussed. Finally, the results from SEM and EDX analysis are presented. 5.1. Water Retention Value (WRV) The Water Retention Value (WRV) value equals to the Fiber Saturation Value (FSP) at the value up to 1.8 g of water/g OD fiber under centrifuging conditions at 2590 rpm. WRV will be used throughout this chapter for the modelling representing the moisture content in water-saturated cell of walls of wood fibers. Since the WRV value is a function of pH, thus a correlation is required. The fitting curve relates the relation between WRV and pH condition in the fiber suspension and described by a correlation of the form: WRV = A(pHs)2 + BpH s + C (g H20/g od fibre) (5.1) where A, B, and C are the parameters estimated from the regression of the data. The WRV experiments were performed three times for each pulp sample at each pH and the data are given in appendix A. 5.1.1. Water Retention Value of BC Coastal Samples The WRV versus pH plots for each pulp sample from BC Coastal Mill are shown in figure 5.1 to figure 5.6. Table 5.1 shows the estimated parameter values and their corresponding errors in parenthesis. 67 Chapter 5: Results and Discussion £ 1.38 4 S 1.3 Experimental Data Calculated FSP 4 6 8 10 pH of the external solution 12 Figure 5.1: Water retention value data and fitted curve of B C Coastal: Brown Stock Washer mat | 1.70 -\ g 1-62 -\ • | 1.54 1 1 " 4 6 H _ 1.38 1.30 * Experimental Data Calculated FSP 4 6 8 10 pH of the external solution 12 Figure 5.2: Water retention value data and fitted curve for B C Coastal: Post Oxygen Washer mat 68 Chapter 5: Results and Discussion 2 4 6 8 10 12 pH of the external solution Figure 5.3: Water retention value data and fitted curve of B C Coastal: D c washer stage outlet 2 1.70 ^ JO > 1.38 5 1.30 • Experimental Data — Calculated FSP 4 6 8 10 12 pH of the external solution 14 Figure 5.4: Water retention value data and fitted curve of BC Coastal: E o p washer stage outlet 69 Chapter 5: Results and Discussion g 1.70 g 1.62 4 • 11.54 H ? 1.46 > 1.38 1.30 Experimental Data Calculated FSP 4 6 8 10 pH of the external solution 12 Figure 5 .5 : Water retention value data and fitted curve of B C Coastal: D n washer stage outlet mat g 1.70 | 1.62 O) ^ 1.54 f 1.46 _ 1.38 4 S 1.30 Experimental Data Calculated FSP 4 6 8 10 pH of the external solution 12 Figure 5 .6 : Water retention value data and fitted curve of B C Coastal: D 2 washer stage outlet 70 Chapter 5: Results and Discussion Table 5.1: W R V fitting parameter from the regression of the data of B C Coastal Sample A B c B S W -0.0020 0.045 1.44 (0.0005) (0.006) (0.02) P - 0 2 -0.003 (0.004) 0.07 (0.005) 1.2 (0.1) Dc -0.003 0.06 1.35 (0.001) (0.01) (0.04) Eop -0.002 0.041 1.41 (0.001) (0.008) (0.03) D n -0.0019 0.04 1.41 (0.0008) (0.01) (0.03) D2 -0.002 0.04 1.39 (0.001) (0.01) (0.04) A l l W R V data demonstrated that W R V increases as the p H increases. Wood fibres are basically cellulose molecules, which are extremely hydrophilic, thus they loves water and attracts water so that the fibres swell. A s the fibres swell, intermolecular bonds are broken as a result of internal stresses produced by swelling, which increase the surface area of the fibre. A t higher p H , most fiber has the tendency to free itself rapidly from the fiber web, thus the fiber volume expands to create more room and accommodate more water. The pulp samples from B C Coastal m i l l do not have big variances in term of water content in the fiber down the fiberline. It is almost constant for all pulp samples, which increase from about 1.4 to 1.7 g-E^O/g-od fiber as the p H increase from 2 to about 11. 5.1.2. Water Retention Value of BC Interior Samples The plots of W R V versus p H for each pulp sample from B C Interior M i l l are shown in figure 5.7 to figure 5.9. 71 Chapter 5: Results and Discussion 1.35 £ 1.28 Q _ 1.21 H | 1.14 H > 1.07 or 1.00 Experimental Data Calculated FSP 4 6 8 10 12 pH of the external solution 14 Figure 5.7: Water retention value data and fitted curve of B C Interior: Brown Stock Washer mat 1.35 0 £ 1 28 -• Experimental Data — Calculated FSP 4 6 8 10 pH of the external solution 12 Figure 5.8: Water retention value data and fitted curve of B C Interior: Post Oxygen Washer mat 72 Chapter 5: Results and Discussion 1.00 4 - i 1 i 1 1 2 4 6 8 10 12 pH of the external solution Figure 5.9: Water retention value data and fitted curve of B C Interior: ' D c ' mat The W R V o f B C Interior m i l l also increase as the p H of the suspension increase, but the water content is less compared from B C Coastal pulp. There is also an increase of W R V as the pulps go down the fiberline. Table 5.2 shows the estimated parameter values and their corresponding errors in parenthesis. Table 5.2: W R V fitting parameter from the regression of B C Interior Type A B C B S W -0.0003 (0.0001) 0.007 (0.002) 1.055 (0.005) P - 0 2 -0.0006 (0.0003) 0.022 (0.004) 1.05 (0.01) Dc -0.0027 (0.0004) 0.054 (0.005) 1.06 (0.02) 73 Chapter 5: Results and Discussion 5.2. Potentiometric Titration A s explained previously two potentiometric titrations were conducted. The first one provided data for the calculation o f the fiber charge properties. The other titration was done with a known metal ions addition to determine the binding constants. 5.2.1. Potentiometric Titration: Acid-Washed Chelated Fiber Mat The potentiometric titration experimental data of acid-washed chelated fiber mat from B C Coastal M i l l is plotted in figure 5.10 below, showing the p H of the suspension versus the volume of sodium hydroxide (NaOH) consumed during the titration. 0 -I i 1 . i 1 0 2 4 6 8 10 V NaOH (mL) Figure 5.10: Potentiometric titration data of B C Coastal samples The blank titration was performed first to determine the effect of fiber inside the solution during the titration. The blank consisted of 60-ml of water and hydrochloric acid (HCI) with the concentration of 10-mmol/L. It was titrated with 100-mmol/L of sodium hydroxide (NaOH). Using simple hand calculation of acid-base reaction, the addition of 6 m l of 100-mmol/L N a O H was needed to neutralize the H C I in the solution. It is shown on figure 5.10 where the p H changes asymptotically after 6 m l of 100-mmol/L N a O H titrated into the solution. 74 Chapter 5: Results and Discussion From figure 5.10, all titration data lie close to each other so that it makes difficult to see the difference between each pulp sample. The critical point is at between p H 4 to 10 where the corresponding N a O H consumed at this p H range is about 5.0 to 8.0 ml , as shown in figure 5.11. The addition of N a O H at p H less than 4 neutralized HCI , because the titration of pulp is almost the same as the blank. This means the fiber has not dissociated yet so that it does not contribute any charges in the suspension to attract the sodium ions. Above p H 4, the charge groups on the fiber start to dissociate so it contributes charges that the amount of N a O H consumption increases compared to the blank as expected. The functional groups on the fiber attract the sodium so that the titration curve shifts to the right. The more the charge available in the fiber, the more it would consume N a O H until the fiber charge groups are saturated by the sodium ion. 2 -0 H 1 1 1 1 1 4 5 6 7 8 9 V NaOH (ml_) Figure 5.11: Potentiometric titration data of B C Coastal samples zoomed at the zone of interest Figure 5.11 shows that B S W sample consumed the highest sodium hydroxide among the other pulp samples followed by p-02 sample. The last four samples from the bleaching stages consumed the least amount of N a O H and lie between the blank and the p - 0 2 sample. 75 Chapter 5: Results and Discussion 14 -, 0 4 1 , , , 1 1 0 2 4 6 8 10 12 V NaOH (mL) Figure 5.12: Potentiometric titration data of B C Interior Samples 14 -I 12 0 4 , 1 , , , 1 5 6 6 7 7 8 8 V NaOH (mL) Figure 5.13: Potentiometric titration data of B C Interior Samples zoomed at the zone of interest 76 Chapter 5: Results and Discussion The potentiometric titration experiment for B C Interior mi l l is shown in figure 5.12 and 5.13. The titration result shows that all titration curves for each pulp sample lie on the right side from the blank titration. The titration curves from the right to the left correspond to the pulp sample from B S W , post-oxygen delignification and the first stage of bleaching. It can be seen that as the pulp goes down the fiberline, the N a O H consumption is less. This indicates that the lignin contribute charges in the pulp so when the lignin content is less, the charge is also less. This titration has the same trend as the one from B C Coastal M i l l samples. The earlier potentiometric titration (old titration) was done only with N 2 injection at the beginning o f the titration. It was assumed that there was no leakage in the vessel so that N 2 was not injected anymore while doing the titration. Later on, it was noted that the old titration never met the blank after a certain p H where all fibre charges had dissociated. It seems the carbon dioxide dissolved in the pulp suspension so that the p H drops, therefore the fibres appeared to have enormous charge content at p H higher than 8. A s a consequence, all titration was repeated with N 2 injection throughout the whole titration except B S W from B C Interior due to lack of pulp sample. A s seen in figure 5.12 and 5.13, the pulp samples from p - 0 2 and D c indeed meet the blank at p H higher than approximately 10.5 but not B S W sample. So for the fibre charge properties calculation, the titration data was cut up to p H 8. 5.2.2. Potentiometric Titration: Acid-Washed Chelated Fiber Mat with Metal The potentiometric titration of acid-washed chelated fiber mat with a known amount of iron addition was done to determine the binding constants. The iron was used from the iron standard solution for A A S . The iron was added at 520-mg/kg-od fiber concentration. The comparison of the titration between the blank, acid-washed chelated fiber mat with and without the metal addition is shown in figure 5.14. 77 Chapter 5: Results and Discussion Figure 5.14: Potentiometric titration of B S W mat with iron addition from B C Coastal M i l l From figure 5.14, the initial p H of fiber with iron is slightly lower than the blank. This is due to the addition o f iron solution, because the iron standard solution used in the experiment is dissolved in HC1 solution, thus the actual HC1 concentration in the suspension is more than the blank itself. It is also noted that the pulp suspension with iron consumes more sodium hydroxide. This is contradicting with the hypothesis where the presence of iron should interact with the free charge on the fiber so that the free charge content on the fiber w i l l be less and thus sodium hydroxide consumption w i l l be less. This could be attributed to formation of a complex between iron and the hydroxide group during the titration. A s a result, the charged groups on the fiber are free to attract the sodium. To maintain the charge balance, more sodium hydroxide is needed compared to a titration without metals at a certain p H . 78 Chapter 5: Results and Discussion 5.3. Iron Concentration Profiles The metal concentration from two pulp mills on the coastal and interior side in British Columbia were analyzed, especially iron. The samples were collected from different sampling points down the fiberline for analyzing its metal profiles. 5.3.1. Iron Concentration of BC Coastal Samples The pulp samples are taken after the brown stock washer, post oxygen delignification and at several bleaching stages. The iron concentration on the fiber in those samples was determined by ICP, A A S , and Spectrophotometric analysis. ICP Analysis B A A Analysis • Spectrophotometric B S W P-02 Dc Eop Dn Sampling Points D2 Figure 5.15: Iron concentration comparison among A A S , ICP and Spectrophotometric analysis along the fiberline from B C Coastal M i l l I did the spectrophotometric analysis only for the first two pulp samples, which were obtained after the brown stock washer (BSW) and post oxygen delignification (p-0 2 ) . Figure 5.15 shows the iron concentration in the fiber of the pulp samples from six points along the fiberline. A s 79 Chapter 5: Results and Discussion seen in figure 5.15, the measurements from ICP, A A S , and Spectrophotometric analysis are close to each other. So for the rest of the pulp samples, I analyzed them using A A S and ICP only. The iron content of the pulp samples collected after brown stock washer and the oxygen delignification unit were found at the same level. The pulp sample from the first chloride dioxide bleaching stage (Dc) where the p H was 2.3 had iron concentration of 28 mg/kg O D pulp. Then the fiber went to the alkaline extraction stage (Eop) where the p H in the suspension was increased to about 10.6 in order to solubilize the extracted lignin from the previous bleaching stage by using N a O H , thus the solubilized lignin could be removed from the suspension. Since the p H was alkaline, there was a slight increase in the iron concentration. The last two bleaching stages were operated at acidic conditions ( D n and D 2 ) , which were at p H 4.5 and 3.4. A s seen from figure 5.15, iron concentration dropped to 22 and 27 mg/kg O D pulp. The fact that iron concentration on the fiber was significant at acidic p H is a strong indication that iron might bind chemically with the functional groups on the fiber or as a complex form with the anionic group in water and trapped inside the fiber mat. It was noted that metal profile experiments were done at 1% consistency. Due to the dilution, the p H of the suspension changed from its original value given in table 4.1. The p H increased to values between 5 and 7 for the three acidic stages. Since there was a fluctuation on the iron concentration at acidic conditions especially at D n and D 2 , some of the iron especially at D 2 was probably complexed by the hydroxyl group at this dilution p H and redeposited on the fiber. Additional experiments were done to verify this assumption. The metal profile was determined again, but this time the p H of the pulp suspension was set at the same p H of the pulp as received from the m i l l by adding HC1. The result is shown in the figure 5.16. A s seen, the iron concentration decreases slightly at the acidic condition compared to the dilution p H . This indicates that some iron might be complexed by the hydroxyl group during the dilution to 1% consistency and this iron complexed is trapped in the fiber so that the iron that was measured by the A A S analysis was higher than the actual iron that was bound to the fiber. Because of precipitation, the amount of iron on the fiber becomes significant. 80 Chapter 5: Results and Discussion The iron concentration is stable at low pH where it was found at about 20-22 mg/kg od fiber at D n and D 2 . This raises a question whether this iron binds to the fiber or precipitated and trapped inside the fiber mat. It is likely that the iron is in form of precipitates because at a very acidic condition, the fiber has not dissociated yet so that iron cannot bind with the charged group on the fiber. A n extra analysis using S E M will verify the interaction of iron with the fiber, which will be discussed in section 5.8. Dilution pH • Original pH 35 30 § 5 25 £8 20 o o> C A r-O - 15 O O 8 | 10 0 21 20 Dc Dn D2 Pulp Sampling Point Figure 5.16: Comparison iron profile concentration at acidic condition as it was taken from the pulp mill to dilution pH at 1% consistency The maximum deviation from our measurement is 1 mg/kg-OD (1 ppm). So for all concentration measurement, the maximum and minimum concentration will be its concentration given on the graph plus or minus 1 ppm. The details of the error analysis calculation are given in appendix H . 81 Chapter 5: Results and Discussion 5.3.2. Iron Concentration of BC Interior Samples The pulp samples were collected after brown stock washer (BSW), oxygen delignification (p-0 2), first stage of bleaching (Dc) and the last stage of bleaching which was the dried mat. BSW P-02 Dc Dried Pulp Sampling points Figure 5.17: Iron concentration comparison between AAS and ICP analysis along the fiberline from BC Interior Mill As seen from figure 5.17, iron concentration on the fiber decreases by 1 mg/kg OD fiber after oxygen delignification. After the first bleaching stage the iron concentration decreases further to 5 mg/kg OD fiber and it keeps on decreasing down to about 4 mg/kg OD pulp at the dried sheet pulp. The trend for the iron concentration along the fiberline of the interior mill is similar to the coastal one where iron stay in the fiber line in a significant quantity and not being removed. However, the pulp sample from the coastal mill has four times more iron than the interior mill. It is suspected that the iron is introduced from the water used to transport log to the wood in the coastal region so that it has more iron in the fiber. However this is not a generalized conclusion. One has to look at several coastal and interior mills to reach a generalized conclusion. 82 Chapter 5: Results and Discussion 5.4. Residual Iron Concentration After metal ions was being removed from the fiber using the combination o f acid washing and chelation as described in section 4.3.7, the residual metal concentration that had not been removed by our washing procedures was obtained. The removal efficiency for the two pulp mills down the fiberline were analyzed and discussed in the following section. The liquor concentration after each washing was also analyzed to determine the metal removal efficiency after each washing. 5.4.1. Residual Iron Concentration from BC Coastal Samples Figure 5.18 shows the original iron concentration of the pulp samples together with the iron concentration after the pulps have been acid-washed with a chelating agent according to the metal removal procedure in section 4.3.7. Original Iron Concentration • R e s i d u a l Iron Concentration B S W P-02 Dc Eop Dn D2 Sampling points Figure 5.18: Original and residual iron concentration along the fiberline from B C Coastal M i l l using ICP analysis 83 Chapter 5: Results and Discussion It was noted that the last step of washing with distilled de-ionized water was not done for samples B S W and P-O2. From figure 5.18, iron was removed down to about 8 and 7-mg/kg O D pulp in the B S W and P-O2 samples. Iron was found at around 4 mg/kg O D pulp for the other samples. Perhaps the last washing with distilled deionized water was able to remove more iron so that the residual iron concentration for the last four pulp samples was less than the first two samples. • AA Analysis • ICP Analysis B S W Post 0 2 Dc Eop Dn D2 Sampling Points Figure 5.19: Comparison of iron removal efficiency between ICP and A A S analysis from B C Coastal M i l l The iron removal efficiency was then computed according to equation (5.2). The results are given in figure 5.19. r> , ~ . Iron original - Iron residual , .... Removal efficiency = - x 100% (5.2) Iron original 5.4.2. Iron Concentration in Liquor from BC Coastal Samples The amount of iron in the liquor after each washing stage was measured using ICP analysis. A A S analysis was not done here because the concentration o f iron in the solution was so dilute 84 Chapter 5: Results and Discussion that the A A S analysis could not detect its concentration. The total iron in the liquor was then obtained from the summation of each individual washing stage. The total iron in the liquor from the analysis was compared with the amount iron in the liquor calculated from a mass balance, which was the difference between the original and the residual iron concentration on the fibers. • Total iron in liquor measured • Total iron in liquor calculated 0.40 -r 1 o> 0-32 BSW P-02 Dc Eop Dn D2 Sampling Points Figure 5.20: Comparison the amount of iron removed from the pulp from its original with the amount of iron found on the liquor during acid-chelation washing From figure 5.20, the amount of iron calculated from the mass balance in the liquor is more than the amount of iron measured in the liquor, except for B S W samples. This raises a question why the mass balance does not hold. It was noted that the liquor samples contained precipitates that settle down, but only the liquor portion was analyzed. Therefore, the iron that was potentially included in the precipitates was not accounted for in the measurement. The iron concentration in the liquor obtained at each washing stage is shown in figure 5.21. This refers to the procedure given in figure 4.10. A s seen from figure 5.21, iron is removed at different quantities at each washing stage. Most of the liquors from the first washing stage using 85 Chapter 5: Results and Discussion D T P A have less iron except for B S W and D 2 . This is because the first washing stage was done using D T P A , which is a chelating agent that can form complexes with iron. The B S W sample has iron at the highest quantity due some precipitations accounted in the measurement (the liquor was analyzed before letting it settled down) but not at the other samples. For the acidic washing stage, which is the second washing stage, generally iron was found in the highest concentration compare to the other washing stages. There are also some fluctuations in the results that might be due to some precipitates not settling down being very small and hence included in the liquor that was analyzed. • DTPA washed • Acid washed • Acid + DTPA washed 0.16 i 1 BSW P-02 Dc Eop Dn D2 Sampling points Figure 5.21: Iron found in the liquor at each washing stage for each B C Coastal samples 5.4.3. Residual Iron Concentration from BC Interior Samples Residual iron concentration for B C interior mi l l is shown in figure 5.22. The iron removal efficiency is shown in figure 5.23. A s seen in figure 5.23, the removal efficiency is found to be between 45-79%. There is also a discrepancy between the A A S and ICP analysis for the B S W sample probably due to the small initial concentration numbers. 86 Chapter 5: Results and Discussion • Original iron concentration • Residual iron concentration 8 10 n BSW P-02 Dc Dried Pulp Sampling Points Figure 5.22: Original and residual iron concentration from ICP analysis for pulp samples from B C Interior M i l l IAA Analysis • ICP Analysis BSW P-02 Sampling Points Dc Figure 5.23: Comparison of iron removal efficiency among ICP and A A S analysis from B C Interior M i l l 87 Chapter 5: Results and Discussion 5.5. Fiber Charge Properties The potentiometric titration data was converted into fiber charge using the model that was described in chapter 3.3. The calculated fiber charge was then fitted into two different models. The first model was based on the "accurate charge" model where the potentiometric titration data were translated into charge versus internal p H data (Bygrave and Englezos, 1998). This model assumed that there were infinite charged groups on the fiber, which could be represented by a cubic equation. Therefore, a continuous charge distribution on the fibres from the experimental data was obtained by fitting a curve. The fitted curve gives the quantity of charge on the fibres at any given internal phase p H , and provides a convenient function to obtain the accurate charge on the fibres. There is no physical meaning of "accurate charge" model. It just gives a representative of charge distribution as a function of internal p H . The potentiometric titration data is described by a correlation of the form: 1000 mFx.MFw = A(pHF)3 + B (pHF)2 + C pHF + D (5.3) where A , B , C, and D are the constant parameters estimated from the regression of the data mF.MF versus the p H of the fiber phase. The other variables involved in the equation are: mF_ The molality of fixed charged groups within the fibres, MF The mass of water in the fibre phase, phf The p H in the fibre phase. The other model was a "two-site" charge model, meaning there were two charge groups on the fiber. So the charge properties from the "two-site" charge model were determined by fitting of the calculated fiber charge from the potentiometric titration. Both models are shown in the following section for both pulp samples from B C Coastal and Interior M i l l . 88 Chapter 5: Results and Discussion 5.5.1. Fiber Charge Properties of BC Coastal Mill Fiber The fiber charge calculated from the potentiometric titration at different pH condition is reported in figure 5.24 below. The fiber charge shown in figure 5.24 corresponds to the calculated fibre charge at the corresponding pH. 140 120 ra £ 100 51 o -o 80 5 9 LL O) •a t 6 0 Q) _ 3 I 40 o E ra w O 20 pHS = 5 B p H S = 7 D p H S = 9 B p H S = 11 0 BSW p -02 Dc Eop Dn D2 Sampling points Figure 5.24: Calculated fiber charge distribution from potentiometric titration of BC Coastal samples The calculated fiber charge increases as the pH increases as shown in figure 5.24. At higher pH, the fiber dissociates more so that it contributes more charges. The fiber charge also decreases down the fiberline. This indicates that the lignin on the fiber contribute charges because as the fiber goes down the fiberline the lignin content decreases as well as the charges. The pulp sample after the brown stock washer has the higher charge content followed by the post oxygen delignification samples. The last four pulp samples after each stage of bleaching have the lowest charge content. 89 Chapter 5: Results and Discussion The fitted parameters of the "accurate" model are given in table 5.3. Those parameters are valid only at the p H range given in the table. Below the p H range specified, the fiber charge is zero because the fiber has not dissociated yet. Table 5.3: Fiber charge fitting parameter from the regression of the potentiometric titration data of B C Coastal samples Sample p H s range A B C D B S W 3.3 < p Hs < 11.0 0.55 (0.04) -12 (1) 101 (6) -218 (13) P - 0 2 3.7 < p Hs < 11.0 0.70 (0.05) -16 (1) 130 (8) -293 (17) D c 4.0 < p Hs < 11.0 0.07 (0.05) -3 (1) 39 (9) -110 (20) 3.8 < p H s < 11.0 0.20 (0.02) -6.0 (0.5) 60 (3) -148 (V) D n 3.0 < p Hs < 11.0 0.07 (0.02) -2.3 (0.3) 25 (2) -54 (4) D 2 3.4 < p Hs < 11.0 0.08 (0.02) -2.4 (0.3) 26 (2) -56 (5) The values in the bracket in table 5.3 correspond to the standard error of the fitting parameter values. The calculated fiber charge and the fitted fiber charge using equation (5.3) versus the p H in the fiber phase for all pulp samples are shown in figure 5.25 to figure 5.30 below. 90 Chapter 5: Results and Discussion T3 9 o E E a> o 0) J3 140 120 100 80 60 40 20 0 • Fiber charge from potentiometric titration Fitted fiber charge 6 8 PH S 10 12 Figure 5.25: Fibre charge determined from the potentiometric titration data for Brown Stock Washer (BSW) mat from B C Coastal M i l l £ 120 .Q "O ? o E E, 0) L_ JC u o 100 80 60 -I 40 20 i l 0 • Fiber charge from potentiometric titration Fitted fiber charge 6 8 PH S 10 12 Figure 5.26: Fibre charge determined from the potentiometric titration data for Post Oxygen washer mat from B C Coastal M i l l 91 Chapter 5: Results and Discussion 70 SI % 60 9 o> 50 o 40 E £ 30 20 a> i_ ra .c o 10 0 • • Fiber charge from potentiometric titration Fitted fiber charge 8 10 12 Figure 5.27: Fibre charge determined from the potentiometric titration data for D c washer stage outlet mat from B C Coastal M i l l gT 60 Si -a 50 9 O) ^ 40 o | 30 i 20 ra « 10 -i_ o JD ii o -^ G^ S^ ^^ ^ r • Fiber charge from potentiometric titration Fitted fiber charge • • 6 8 PH S 10 12 Figure 5.28: Fibre charge determined from the potentiometric titration data for E o p washer stage outlet mat from B C Coastal M i l l 92 Chapter 5: Results and Discussion aT 50 1 § 45 J3 40 -T3 O j? 35 i 3 0 | 25 o 20 S> 15 co 10 -0 • F iber c h a r g e from potent iometr ic titration Fitted fiber c h a r g e 6 8 PH S 10 12 Figure 5.29: Fibre charge determined from the potentiometric titration data for D n washer stage outlet mat from B C Coastal M i l l oT 45 i 40 9 35 ^ 30 | 25 E 20 g, 15 (0 u 10 0 • F iber charge from potentiometric titration Fitted fiber charge 6 8 PH S 10 12 Figure 5.30: Fibre charge determined from the potentiometric titration data for D 2 washer stage outlet mat from B C Coastal M i l l 93 Chapter 5: Results and Discussion From the "two-site" charge model, the fiber charge properties can be fitted using equation 3.24. One charge was found dissociates at acidic condition and the other one dissociates at alkaline condition. The summary of fiber charge properties for all pulp samples down the fiberline are given in table 5.4. Table 5.4: Fiber charge properties fitted using "Two-site" charge model o f B C Coastal samples Pulp Samples Kappa number pKA pKB QA QB QTotal range (mmol/kg-od fiber) B S W 35.1 4.23 9.16 73 54 128 3.3 - 11.0 p-0 2 19.1 4.43 9.74 66 50 116 3.7-11.0 D c 12.5 4.61 7.59 41 17 58 4 .0-11.0 Eop 10.5 4.45 7.42 44 11 55 3.8-11.0 D n 6.7 3.73 6.58 27 16 43 3.0-11.0 D 2 4.5 3.80 6.75 25 12 37 3.4-11.0 Note: ' N D ' refers to Not Detectable From the fiber charge properties given in table 5.4, two charged groups were able to describe the charge distribution on the fibres. There is not any physical meaning of these two charge groups because we did not analyze the origin of these groups. According to Laine, et al. (1994) and quoted by many researchers, the two groups on the fiber contribute charges in acidic condition. They are uronic acid ( p K A « 3 - 4) and carboxyl acid bound to lignin ( p K A « 5 - 6). Ragnar et al. in 2001 suggested that another charge group exist at alkaline condition, which is the phenolic hydroxyl group ( p K A « 7.3 - 10.3). But no one has ever reported the alkaline charge groups due to the experimentation difficulties while doing the potentiometric titration. Most researchers found that the p H always drifts to the acidic condition at p H higher than 6, thus the charge calculation is not accurate. In our earlier work, we also found this behaviour so that the sodium consumption increase at higher p H (pH>6). Thus, the fibres appear to have enormous charge content. It was found that by bubbling nitrogen throughout the whole titration could eliminate the p H drifting towards the acidic condition, which was potentially caused by the absorption of the carbon dioxide. Therefore, the fiber charge was able to be calculated up to p H 11. This means there are 3 major charge groups exist on the fibre (uronic acid from the hemicellulose, 94 Chapter 5: Results and Discussion carboxyl groups bound to lignin, and phenolic hydroxyl bound to lignin) but using 2 charge sites was enough to represent the charge distribution. Table 5.5: Fiber charge properties up to p H 8 (Laine et al., 1994) Pulps Kappa Q A Q B Qlotal p K A p K B Reference Unbleached Softwood kraft fibres 56.7 N A N A 100 3.39 5.48 Laine, et al. (1994) 56.6 N A N A 115 3.37 5.68 34.7 N A N A 75 3.40 5.50 19.0 N A N A 55 3.41 5.43 17.7 N A N A 65 3.37 5.71 B S W 35.1 65 14 79 4.13 6.61 This work p - 0 2 19.1 66 16 82 4.23 6.80 D c 12.5 40 12 52 4.58 6.98 Eop 10.5 46 4 50 4.49 6.30 D n 6.7 25 9 34 3.69 5.43 D 2 4.5 19 14 33 3.59 5.21 Table 5.5 gives the fiber charge properties up to p H 8 obtained by Laine et al. (1994) and this work. The stronger acid group (pK A ) refers to the uronic acid and the weak acid group (pK B ) refers to the carboxyl acid bound to lignin. Laine et al. applied electrostatic correction at the fiber surface using Constant Capacitance Model ( C C M ) to fit the calculated fiber charge from the potentiometric titration data to obtain a better fitting so that the fitted constant become slightly lower than the one without the electrostatic correction. It can also be seen from table 5.5 that the p K values obtained by Laine et al. (1994) are lower than the values obtained by this work. Table 5.6 shows the fiber charge properties comparison between this work and other researchers for softwood kraft fibres. Athley et al. (2001), Laine et al. (1994), and Lingren and Ohman (2000) calculated fiber charge using the same methods. In general, their p K constant are lower than this work due to the electrostatic corrections. Their total charge contents are similar to this work for both unbleached kraft pulps and fully bleached kraft pulps, as summarized in table 5.6. Bygrave and Englezos (1998) calculated fiber charge using Donnan model, which is similar to this work. 95 Chapter 5: Results and Discussion Table 5.6: Fiber charge comparison between several authors Pulp samples P H S Kappa Q A Q B Qlotal p K A p K B Reference Oxygen delignified kraft fibres SW1 2-6 N A 68 - 68 3.25 - Athley, et al. (2001) SW2 N A 50 - 50 3.20 -B C Coastal softwood kraft fibres B S W 2-6 35.1 65 - 65 4.13 -This work p - 0 2 19.1 59 - 59 4.31 -Unbleached Softwood kraft fibres 2-8 34.7 N A N A 75 3.40 5.50 Laine, et al. (1994) 17.7 N A N A 65 3.37 5.71 Oxygen delignified kraft fibres SW1 2-9 N A N A N A 80 - - Athley, et al. (2001) SW2 N A N A N A 59 - -B C Coastal softwood kraft fibres B S W 2-8 35.1 65 14 79 4.13 6.61 This work p - 0 2 19.1 66 16 82 4.23 6.80 Post-brown stock washer (BSW) kraft fibres 2-11 N A 95 55 150 3.8 8.0 Bygrave and Englezos (1998) B C Coastal (BSW) softwood kraft fibre 2-11 35.1 73 54 127 4.23 9.16 This work Ful ly Bleached Softwood kraft fibres 2-6 N A 31 - 31 3.41 . - Lingren and Ohman (2000) B C Coastal softwood kraft fibres D n 2-6 6.7 27 - 27 3.74 -This work D 2 4.5 25 - 25 3.81 Note: ' N A ' refers to Not Available information. There is a slight variation in terms of p K values for each pulp sample due to the fitting. This is not true in reality since the p K values refer to the same charged group on the fiber, so the p K value does not depend on the pulp sample. 5.5.2. Fiber Charge Properties of BC Interior Mill Fiber The fiber charge was calculated from the potentiometric titration data using the equation given in chapter 3.3. The dissociated or free charge at each corresponding p H is shown in figure 5.31. From figure 5.31, it is clearly shown that the fiber charge increases as the p H increases and the fiber charge decrease down the fiberline as the lignin content decreases. This trend is the same as the one reported from the B C Coastal samples. The titration of B S W sample was affected by the carbon dioxide absorption, thus the fibre charge increases tremendously at p H 11. 96 Chapter 5: Results and Discussion • pHS = 5 • p H S = 7 dpHS = 9 • pHS = 11 9Qn BSW p-02 Dc Sampling points Figure 5.31: Calculated fiber charge from potentiometric titration of B C Interior samples I followed the same procedure as of B C Coastal samples and obtained table 5.7 for the parameter estimation of the "accurate charge" model. Those parameters are valid for the pH range specified only. A t the p H lower than the p H range given, the fiber charge is zero and at higher p H than the p H range given has the same charge quantity as given at the maximum pH range. Table 5.7: Fiber charge fitting parameter from the regression of the potentiometric titration data of B C Interior Samples Sample p H s range A B C D B S W * 3.4 < p H s < 8 . 0 1.1 (0.1) -23 (2) 170 (10) -353 (17) P - 0 2 3 . 7 < p Hs < 11.0 0.35 (0.05) -9 (1) 87 (V) -206 (16) Dc 3 . 9 < p Hs < 11.0 0.20 (0.04) -5 (1) 50 (7) -122 (15) Note: ' * ' refers to the old titration, without N 2 injection throughout the whole titration 97 Chapter 5: Results and Discussion The calculated fiber charge and the fitted fiber charge for each pulp sample versus the p H of the fiber phase is shown on figure 5.32 to figure 5.34 below. £ 140 S 120 9 100 o 80 E -E 60 <D co JZ u CD n 40 20 i l 0 • ^ • Fiber charge from potentiometric titration Fitted fiber charge 6 8 PHS 10 12 Figure 5.32: Fibre charge determined from the potentiometric titration data for Brown Stock Washer mat from B C Interior M i l l CD •a o o E E, o CO JZ o 0) J3 100 90 80 70 60 50 40 30 20 10 0 • Fiber charge from potentiometric titration Fitted fiber charge 8 10 12 Figure 5.33: Fibre charge determined from the potentiometric titration data for Post Oxygen Washer mat from B C Interior M i l l 98 Chapter 5: Results and Discussion oT 60 .£2 •a o • D) 50 40 o | 30 o E? as o S3 20 10 ii 0 • Fiber charge from potentiometric titration Fitted fiber charge 6 8 PHS 10 12 Figure 5.34: Fibre charge determined from potentiometric titration data for " D c " mat from B C Interior M i l l From the "two-site" charge model, the fiber charge properties can be fitted using equation 3.24 and summarized in table 5.8. The same trend is also found here, thus the explanation is the same as the pulp samples from B C Coastal mi l l . Due to the lack of B S W sample supply, the titration using N 2 injection throughout the titration could not be completed. A s the result, the fitting of the fibre charge properties were done using the earlier titration data up to p H 8 only (the N 2 was only injected before the start of the titration, assuming the vessel was tightly sealed). Table 5.8: Fiber charge properties fitted using "two-site" charge model of B C Interior samples Pulp Samples Kappa number pKA pKB QA QB QTotal pH s range (mmol/kg-od fiber) B S W * 35.7 3.7 6.3 86 35 121 3.4-8.1 p - 0 2 18.9 4.2 8.1 63 24 87 3.6-11.0 D c 12.2 4.5 8.8 38 18 56 5.1-11.0 Note: ' * ' refers to the old titration, without N 2 injection throughout the whole titration 99 Chapter 5: Results and Discussion 5.6. Binding Constant From the potentiometric titration result shown in figure 5.12, the binding constant was calculated using the equations described in chapter 3.4. A s seen from the titration data, fiber with the presence o f iron consumed N a O H more than the titration without the presence of iron. This disagreed with the hypothesis that the titration curve should lie between the blank and clean fiber. I f metal ions bind with the free charge on the fiber chemically, the amount of sodium needed in the titration should be less due to less active site on the fiber available to attract the sodium ion. Therefore, the binding constant calculation was found negative for all titration points to keep the charge balance in the suspension, meaning that chemical binding is not present. This is probably due to precipitates which iron forms with the hydroxyl group from N a O H . Consequently, the binding constants were set equal to zero for the partitioning prediction. The verification of precipitation w i l l be discussed further in section 5.8. 5.7. Iron Partitioning The iron partitioning result is presented in two sections. The first section discusses the partitioning experimental results and the second section discusses the partitioning prediction based on the model. 5.7.1. Iron Partitioning Experiment A s discussed in section 4.3.8 and figure 4.11, the partitioning experiments were done in two different ways (see page 61). The first approach was to separate the suspension using filter paper and the other one was to separate the suspension using a centrifuge. In the experiment using filter paper, the filter paper was also ashed. Figure 5.35 shows the iron on the fiber phase determined from the partitioning experiment with and without the filter paper. 100 Chapter 5: Results and Discussion 160 5 140 JD ? 120 0) c O (0 ro 100 D) 80 E 60 40 20 Iron found on the fiber phase using filter paper 1 4 2 Iron found on the fiber phase using centrifuge 31 62 125 312 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.35: Iron partitioning comparison: separation of fiber from the suspension using filter paper and centrifuging of Brown Stock Washer from B C Coastal M i l l A s seen in figure 5.35, there is a difference between the two. The filter paper appears to retain iron. It was noted that the original filter paper was examined by ashing and did not have any metals. The above results indicate the correct step is to use centrifuge and not filter paper. A l l subsequent experiments were done with a centrifuge. Iron partitioning was done at one p H only, p H 3, to minimize iron-complex formation. A s seen from figure 2.3, there are many iron complexes that can be formed when the p H is higher than 3. Iron-complex formation is not desirable because the experimental result cannot be compared to the partitioning model since the partitioning model does not support complex formations. The partitioning was done only for two pulp samples: B S W and Dc , which represent the pulp sample at high and low fiber charge. 101 Chapter 5: Results and Discussion 350 31 62 125 312 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.36: Iron partitioning between the fiber phase and the solution phase at p H = 3 for Brown Stock Washer o f B C Coastal M i l l A s seen in figure 5.36 above, iron has a high tendency to be in the fiber phase. A t low iron concentration, almost all iron is in the fiber phase. A s the amount o f iron in the suspension increases, the amount o f iron found on the fiber is also higher but the increase is not linear. To understand further this behaviour, let's consider the ratio o f the partitioning (X) o f iron between the fiber and the solution phase. From the fiber charge properties described in table 5.3, it was found that there was no charge available on the fiber at p H 3. This indicates that the partitioning ratio should be unity. Figure 5.37 shows the Donnan partition ratio as the iron concentration in the suspension is increased. 102 Chapter 5: Results and Discussion 15 13 12 9 6 7 6 5 co Q. 3 0 31 62 125 312 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.37: Partitioning ratio (k) at various iron concentrations in the pulp suspension for iron partitioning at p H = 3 for Brown Stock Washer pulp from the B C Coastal M i l l A s seen in figure 5.37, the partitioning ratio is greater than unity. It decreases as the iron concentration in the suspension increases. The fact that the ratio is greater than one can be attributed perhaps to iron complex formation. The iron complex is probably trapped in the fiber web and thus it is accounted as belonging to the fiber phase. The presence of this iron complex was verified by analyzing the pulp sample using Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray ( E D X ) , which w i l l be discussed in section 5.8. The partitioning results for Dc pulp sample are given in figure 5.38 and 5.39. Figure 5.38 also shows a high tendency of iron to be in the fiber phase for Dc pulp sample. It is also noted that the iron partition ratio is higher than unity. Iron complex precipitation in the fiber is a probable reason. 103 Chapter 5: Results and Discussion _ 300 0) 250 T3 O I ^ 200 o LL i, 150 E o 100 S 50 w re • Solution phase • Fiber phase 249 25 47 25 50 100 250 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.38: Iron partitioning between the fiber phase and the solution phase at p H = 3 for Dc washer mat of B C Coastal M i l l re 12 d. 9 o 2 c 6 "E o 0 10 25 50 100 250 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.39: Partitioning ratio (X) at various iron concentration in the pulp suspension for iron partitioning at p H = 3 for Dc washer mat from the B C Coastal M i l l 104 Chapter 5: Results and Discussion Each experiment was done three times and the repeatability was found quite satisfactory. The average of each iron concentration is plotted in figure 5.40 for B S W sample and in figure 5.41 for Dc sample. J2 350 300 "§ 250 200 CD L L i D) & 150 c o i 100 (A tt CO S 50 I Iron introduced into the suspension I Measured iron 317 319 37 34 31 62 125 312 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.40: Iron partitioning comparison: total iron introduced into the suspension versus total iron found using mass balance relationship for Brown Stock Washer of B C Coastal M i l l It is noted that the iron removal procedure does not remove iron entirely from the fiber. It was found that the acid-chelation washing removed 82% of iron from the fiber phase, so the total amount of iron on the fiber was the amount o f iron introduced in the suspension plus the residual iron on the fiber. The calculated iron from the mass balance was the summation of iron measured from the solution and fiber phase. The more iron introduced into the suspension; the less the deviation between measured iron and iron added as shown in figures 5.40 and 5.41. 105 Chapter 5: Results and Discussion 300 Iron introduced into the suspension (mg-Fe / kg-od fiber) Figure 5.41: Iron partitioning comparison: total iron introduced into the suspension versus total iron found using mass balance relationship for Dc washer mat o f B C Coastal M i l l A s seen from figure 5.41, the mass balances are satisfied. The amount of iron that was introduced was 25 mg of iron per 1 kg of oven dried-fiber, which was the amount found on the fibers and with the variation o f once, twice, four times, and ten times that correspond to 25ppm, 50ppm, lOOppm, and 250ppm. The deviation (the difference of iron introduced with the iron found using mass balance calculation) from three replicates was found to be 16%, 13%, 5% to 3%>, as the iron introduced increased from 25 ppm, 50 ppm, 100 ppm, to 250 ppm. 5.7.2. Iron Partitioning Prediction The fiber charge properties from the "two-site" charge model and the binding constant were used to predict the metal ion partitioning. A potentiometric titration o f acid-washed chelated fiber mat with the iron addition was used to determine how much sodium hydroxide needed to adjust the p H of the suspension. The iron partitioning was predicted for iron concentration at 520 mg-Fe/kg-od fiber (520 ppm) as shown in figure 5.42. 106 Chapter 5: Results and Discussion 0 I - i 1 1 1 1 2 4 6 8 10 12 pH of solution Figure 5.42: Iron partitioning prediction at 520 ppm iron concentration of Brown Stock Washer (BSW) mat from B C Coastal M i l l A s seen from figure 5.42, the iron concentration predicted in the fiber phase increases as the p H of the suspension increases. This is due to the electrostatic interaction where it follows the fiber charge dissociation curve shown in figure 5.25. The fiber has a higher capacity towards metal where the metal concentration on the fiber increases as the fiber dissociates. According to the partitioning model prediction shown in figure 5.42, there is almost no iron found on the fiber phase at p H 3. It is because the fiber has not dissociated yet so that there is no charge group available on the fiber at this pH. From the experimental result, we found that there was quite significant iron concentration on the fiber at p H 3. This iron-fiber interaction is clearly not an electrostatic or chemical binding interaction because there is no fiber charge available at this p H to attract the metal ion. The only possibility of iron found on the fiber at this p H is due 107 Chapter 5: Results and Discussion to the complex formation or precipitation between the iron and the anion group in the water. This precipitates might be trapped inside the fiber mat so that this iron is measured as belonging to the fiber phase. Iron that can form precipitates at p H 3 is only iron at the third oxidation state. Ferrous forms complexes only at p H higher than 8 as shown in figure 2.3. Ferric iron on the contrary can form different iron complex species depending on the p H as shown in figure 2.3. A t p H 3, F e O H 2 + is the probable complex that we found on the fiber. The precipitation identified w i l l be discussed in section 5.8. 0 1 ^ \ 1 1 1 -I 2 4 6 8 10 12 pH of solution Figure 5.43: Manganese partitioning prediction at 600 ppm manganese concentration of Brown Stock Washer (BSW) mat from B C Coastal M i l l On the contrary, manganese and copper partitioning from the batch experiment can be predicted by assuming the electrostatic interaction only as shown in figure 5.43 and 5.44. The experimental data were obtained by Chandraghatgi, 2003. From the S E M & E D X analysis of the fiber mat, no manganese-contained precipitate was found up to p H 5 and only very small 108 Chapter 5: Results and Discussion amount of manganese precipitates was found on the fiber mat at p H 7. A copper-contained precipitate was also found at p H 7. Consequently, the manganese and copper prediction at higher p H is slightly lower than the manganese and copper found on the fiber from the experiment. 0 f - i 1 1 1 1 2 4 6 8 10 12 pH of solution Figure 5.44: Copper partitioning prediction at 210 ppm copper concentration of Brown Stock Washer (BSW) mat from B C Coastal M i l l 5.8. SEM & EDX Results These investigations were carried out to identify any inorganic precipitates on the fiber mat of acid washed chelated samples with and without the iron addition. During the analysis, the sample was scanned thoroughly to find any precipitation which can be seen as a bright object on the picture. A n area of interest is zoomed and marked with a dashed-circle or ellipse in the picture and analyzed its concentration using the E D X , which gives the atomic composition. A 109 Chapter 5: Results and Discussion portion of a sample which has no precipitates was analyzed to get its atomic composition. Another portion of a sample which has a precipitates was also analyzed to find its atomic composition. 5.8.1. S E M & E D X of A c i d Washed Pulp Not Conta ining A Precipitate Wood fiber is basically organic material and metal ion is inorganic material, so it is very easy to distinguish their appearance in from the S E M picture. The organic material is shown in a dark colour and inorganic material is shown in a bright colour. Figure 5.45 shows the S E M picture of acid washed chelated pulp where no precipitates exist on the fiber mat. We want to see the actual atomic concentration on the fiber where no precipitates exist and compare to the one with precipitates in it. The atomic composition of the area marked in figure 5.51 was analyzed using E D X and the result shown in figure 5.46. Figure 5.45: S E M from acid washed pulp where no precipitate is found The notes on the S E M picture refer to the following: - B S E 2 is the backscattered mode that we used in S E M analysis. W D 15.0mm is the distance between the sample and the sensor for optimal E D X analysis. 110 Chapter 5: Results and Discussion 20.0kV is the voltage used during the analysis. x500 is the magnitude of magnification of the sample, which is 500 times. lOOum is the length o f the dotted line above the note. kCts-f Line Method Intensity K-ratio ZAF Concentration 2 Sigma Z A G KA 2660.24 0.354 1.665 58.99 wt% 0.21 wt% 0.978 1.704 o.m O KA PRZ 919.03 0.066 6.189 40.95 wt% 0.25 wt% 1.031 6.001 1.000 S KA PRZ 15.96 0.000 1.197 0.06 wt% 0.01 wt% 1.145 1.045 1.000 Figure 5.46: E D X from acid washed pulp where no precipitate is found A s expected, fibers have only carbon and oxygen with the concentration about 59% carbons and 41% oxygen. A small quantity of impurities was also found on the fiber, which is sulphur. It is not unlikely given kraft process. This might be originated from the cooking chemical in the digester ( N a 2 S ) . N o other substances were found in this fiber mat. I l l Chapter 5: Results and Discussion 5.8.2. S E M & E D X of A c i d Washed Fiber M a t Conta in ing A Precipitate A n acid washed chelated fiber mat sample was analyzed. A big precipitate was found in the acid-washed chelated fiber web, which had a brighter color than the surrounding fiber, as shown in figure 5.47. Figure 5.47: S E M from acid washed pulp where a precipitate is found A s seen in figure 5.47 a precipitate is trapped inside the fiber mat. Its atomic composition was determined from E D X analysis and shown figure 5.48. A s seen in figure 5.48, the precipitate mainly consists of iron, magnesium, aluminum, silica, and vanadium. A small quantity of sodium and manganese is also found in this precipitates. There are not many precipitates seen on the acid washed pulp. The size of this precipitate is quite big due to the presence of other metals as a co-precipitate. 112 Chapter 5: Results and Discussion This is the reason why iron cannot be removed further. The iron precipitates found on the fiber are the reason why iron tends to stay on the fiberline and are not removed even at acidic condition even although the fiber is in the protonated form. 0 4 6 8 keV Line Method Intensity K-ratio ZAF Concentration 2 Sigma Z A ¥ C KLA PRZ 174.43 0.048 4.907 23.38 wt*/0 6:53wt% 0.909 5.407 0:999 O K A PRZ 746.63 0.110 3.873 42.67 wt% 0.61 wt% 0.959 4.041 0.999 Na KA PR£ 4.60 0:000 3.502 0.08wt% 0.05 wt% 1.056 3.327 0:997 MgKA PRZ 474.45 0:022 2.314 5.l4\vt% 0.08 wt% 1.036 2.241 0.996 A i K A PRZ 595,84 0.027 1.960 5.35 wt% 0.08 wt% 1.074 1.831 0;997 Si KA. PRZ 810.90 0.041 1.679 6 90wt% 0.08wt% 1.048 L602 1.000 V LA PRZ 15.52 0.010 2.404 2.37 wt% 0.62 wt% 1.224 L97S 0.994 M n K A l PRZ 14.18 0.004 1.224 0.43 wt% 0.06 wt% 1.244 0.994 0.990 F e K A l PRZ 389.71 0.113 1.214 068wt% 0.19 wt% 1.225 0.991 1.000 Normalized, Factor : 1 Figure 5.48: E D X from acid washed pulp where a precipitate is found Three precipitates were found in 0.001-g oven dried fiber. The composition of one of the other two precipitates was similar to the one above and that of the third one is shown in figure 5.49. A s seen, this one is predominantly a calcium deposit. 113 Chapter 5: Results and Discussion kCts Line Method Intensity K-ratio Z A F Concentration 2 Sigma Z A V C K A PRZ 3196.29 0.292 1.798 52.54 wt% 0.17 wt% 0.962 .1.870 0.999 0 K A PRZ 1116.60 0.055 6.989 38.56 wt% 0.22 vyt% 1.015 6.886 1.000 Mg K A PRZ 71.20 0.001 2.081 0.23 wt% 0.01 wt% 1.096 1.899 0.999 A l K A PRZ 19.61 0.000 1.677 0.05 wt% 0.0.1 wt% 1.136 1.478 0:999 Si K A PRZ 13.57 0.000 1.390 0.03 wt% 0.01 wt% 1,109 1.256 0,998 S K A PRZ 26.45 0.001 1.184 0.07 wt% 0.01 wt% 1.127 1.059 0.992 Ca K A . PRZ 2501.17 0.075 1.131 8.52 wt% 0.03 wt% 1.161 0.974 l;000 Normalized, Factor TT Figure 5.49: E D X from acid washed pulp where another type of precipitate is found A l l precipitates found on the fiber mat mainly consist o f iron or calcium as the dominant metal precipitates with similar concentration to the one shown in figure 5.48 and 5.49. 114 Chapter 5: Results and Discussion 5.8.3. S E M & E D X of Acid Washed Pulp after Introducing Iron at pH 3 Figure 5.50: S E M of acid washed pulp after introducing iron at p H 3 The shiny particle in the middle of figure 5.50 corresponds to a precipitate found on the fiber mat. Its concentration was determined and shown in figure 5.51. There were five precipitates found in this sample. One of them is also shown in figure 5.50 in the right up comer. The concentration of all but one of the precipitate was similar to that in figure 5.50. The other one had mostly calcium as shown in figure 5.49. The size of this precipitate is smaller than the one shown in figure 5.47. It is noted that the majority of the precipitates have a size similar to that in figure 5.50. A s seen in figure 5.51, this precipitate consists mainly of iron with some other metals with small quantities. Mainly 31% of the precipitate is iron, and the rest are less than 1% such as: zinc, manganese, calcium, potassium, aluminium, silica, sulphur and chloride. The other precipitates 115 Chapter 5: Results and Discussion found on the fiber mat have similar concentration with iron as the dominant metal in all precipitates. kCtsI 20 15-J 10. 5 J Zn A j J ^ | ^ K Ca Fie T r Zn Zn keV Line Method Intensity K-ratio ZAP Concentration 2 Sigma Z A F C K A PRZ 1241.78 0.145 2.918 42.29 wt% 0.23 wt% 0.901 3.240 0.999 0 K A PRZ 866.29 0.055 4.692 25.63 wt% 0.17 wt% 0.951 4.939 0.999 A I K A PRZ 0.00 0.000 1.000 0.00 ^/o 0.00 wt% 1.000 1.000 1.000 S i K A PRZ 0.00 0.000 1.000 0.00 wt% 0.00 wt% 1.000 1.000 1.000 S K A PRZ 24.22 0.001 1.264 0.08 wt% 0.01 wt% 1.056 1.201 0.997 C1KA PRZ 18.35 0.001 1.231 0.07 wt% 0.01 wt% 1.107 1.117 0.995 K K A PRZ 27,20 0.001 1.125 0.11 wt% 0.01 wt% 1.108 1.033 0.983 C a K A PRZ 28.65 0.001 1.069 0.12 wt% 0.01 wt% 1.086 1.013 0.971 M n K A l PRZ 20.71 0.002 1.174 0.26 wt% 0.02 wt% 1.231 0.984 0.969 F e K A l PRZ 2082.25 0.257 1.190 30.63 wt% 0.11 wt% 1.212 0.984 0.999 Z n K A l PRZ 24.77 0.006 1.289 0.81 wt% 0.04 wt% 1.269 1.016 1.000 Normalized, Factor TT Figure 5.51: E D X of acid washed pulp after introducing iron at p H 3 Based on the S E M and E D X analysis, iron was found as precipitates and trapped inside the fiber mat for all pulp samples. This explains why fiber has a strong affinity towards the iron. For the same reason, the binding constant calculation and iron partitioning prediction fails. The residual iron found on the fiber after applying four washing stages is mostly the iron precipitates. 116 Chapter 5: Results and Discussion Chelating agent can improve the iron removal from the fiber and form iron complexes but the challenge now is how to remove these complexes from the fiber. 117 Chapter 6 6. Conclusions and recommendations 6.1. Conclusions Based from our experimental and modelling results, the iron interaction with the wood pulp fiber can be concluded as follows: • Iron tends to stay in the fiberline throughout the pulping processes. • D T P A assisted iron removal from the fiber substantially. • Fiber can be represented by two charge groups, one dissociates at acidic condition and the other one dissociates at the alkaline condition. • Iron has a high tendency to form precipitates even at acidic conditions. • Iron precipitates can be trapped in the fiber mat so that the fiber phase appears to retain more iron; as the consequence, the iron partitioning prediction fails. 6.2. Recommendations Due to the limitation in our model to predict the iron partitioning, a few recommendations are highlighted here such as: • Introducing a complex formation term into the partitioning model so that it can predict the iron partitioning more accurately. Identification of all complex species and known values of formation constants are needed. • Understanding how to remove the iron precipitates such as by introducing a ligand which is able to create a negative charge precipitate, thus it w i l l be expelled from the fiber phase and stay in the solution. 118 7. References Ala-Kai la , K . , A b , O . M . R . , and Alen , R., "Dynamic response in p H and the transient behaviour of some chemical elements in pulp-water suspensions", Nordic Pulp and Paper Research Journal Vol .14, No.2 ,p . l49-157, 1999 Athley, K . , Ulmgren, P., and Ohman, L . O . , "Acid-base properties of oxygen-delignified kraft pulps", Nordic Pulp and Paper Research Journal, Vol .16, No.3, p. 195-203, March 2001, Athley, K . , Ulmgren, P., "Interaction between divalent metal ions and oxygen-delignified kraft pulp", Nordic Pulp and Paper Research Journal, Vol .16, No.3, p.204-214, A p r i l 2001. Bihani, B . G . , "Goal of Closed-Cycle Operation hinges on Fiberline Developments", Pulp and Paper, p. 87-90, July 1996 Bouchard, J., Nugent, H . M . , and Berry, R . M . , " A Comparison between A c i d Treatment and Chelation Prior to Hydrogen Peroxide Bleaching of Kraft Pulps", Journal of Pulp and Paper Science, Vol .21 , No.6, p. J203-J207, June 1995 Bryant, P.S., Robarge, K . , and Edward, L . L . , "Transition-Metal Profiles in Open and Closed Kraft Fiber Lines", Tappi Journal, Vol .76, No. 10, p. 148-159, 1993 Bryant, P.S., and Edward, L . L . , "Cation Exchange of Metals on Kraft Pulp", Journal of Pulp and Paper Science, Vol .22 , N o . l , p. J37-J42, 1996 Bygrave, G . , and Englezos, P., "Fibre charge from potentiometric titration of kraft pulp and Donnan equilibrium theory", Nordic Pulp and Paper Journal, Vol .13, No.3, p.220-224, 1998 Bygrave, G.S. , "Thermodynamic Model and Data on the Partitioning of Non-Process Elements between Kraft Fibres and Water in a Pulp Suspension", M . A . S c . Thesis, University of British Columbia, 1997 Chandraghatgi, R. S., "Interaction of Manganese and Copper with the Wood Pulp Fiber", M . A . S c Thesis, University o f British Columbia, 2003 Chen, B . Y . , "Metal Ion Partitioning in Wood Fibre Suspensions: Investigation of Metal Ion Removal Efficiency by Various Methods", B . A . S c Thesis, University of British Columbia, 2002 Fardim, P., Holmbom, B . , Ivaska, A . , Karhu, J., Mortha, G . , and Laine, J., "Crit ical comparison and validation o f methods for determination of anionic groups in pulp fibres", Nordic Pulp and Paper Research Journal, V o l . 17, No.3, p. 346-351, 2002 Ghosh, A . , N i , Y . , L i , Z . , Heitner, C , and McGarry, P., "Phototostabilization of Bleached Mechanical Pulps with D T P A Treatment", Journal of Pulp and Paper Science, Vol.24, No.8, p.259-263, August 1998 119 Chapter 7: References GrOnroos, A . J . , PitkAnen, M . , and Vuolle, M . , "Radical Formation in Peroxide-Bleached Kraft Pulp", Journal o f Pulp and Paper Science, Vol .24, No.9, p.286-290, September 1998 Jeema, N . , Thompson, R., Paleologou, M . , and Berry, R . M . , "Non-Process elements in the kraft cycle, Part I: Sources, levels and process effects", Pulp and Paper Canada T292, 100:9, p.47-51, 1999 Jeema, N . , Thompson, R., Paleologou, M . , and Berry, R . M . , "Non-Process elements in the kraft cycle, Part II: Control and removal options", Pulp and Paper Canada T46, 101:2, p.41-45, 2000 Kremer, M . L . , "Mechanism of the Fenton reaction. Evidence for a new intermediate", Phys. Chem. Chem. Phys. Journal, V o l . 1, p. 3595-3605, 1999 Laine, J., Lovgren, L . , Stenius, P., Sjoberg, S., "Potentiometric titration of unbleached kraft cellulose fibre surfaces", Colloids and Surfaces A : Physicochemical and Engineering Aspects, V o l 88, p- 277-287, 1994 Langmuir, D . , "Aqueous Environmental Geochemistry", Prentice Hal l , 1997 L i , Z . , N i Y . , and V a n Heiningen, A . R . P , " A c i d washing and chelation in a displacement system: A comparative study", Journal of Pulp and Paper science: Vol .26, No.10, p.341-345, October 2000 Liden, J. , and Ohman, L . - O . , "Redox Stabilization of Iron and Manganese in the +11 Oxidation State by Magnesium Precipitates and Some Anionic Polymers. Implication for the Use of Oxygen-Based Bleaching Chemicals", Journal of Pulp and Paper Science, Vol .23, No.5, p. J193-J199, M a y 1997 Liden, J., and Ohman, L . - O . , "On the Prevention of Fe and M n Catalyzed H2O2 decomposition Under Bleaching Conditions", Journal of Pulp and Paper Science, Vol .24, No.9, p.269-275, September 1998 Lingren, J. and Ohman, L . - O . , "Characterization of acid/base properties for bleached softwood fibers as influenced by ionic salt medium", Nordic Pulp and Paper Research Journal, V o l . 15, N o . l , p . 18-23,2000 Lindgren, J. , Wiklund, L . , and Ohman, L . O . , "The contemporary distribution of cations between bleached softwood fibres and the suspension liquid, as a function of -log [H + ] , ionic strength and temperature", Nordic Pulp and Paper Research Journal, Vol .16, N o . l , p.24-32, 2001 Lingren, J., Persson, P., and Ohman, L . -O . , "Interaction of calcium(II), copper(II) and aluminum(III) ions with two chemically modified wood fibres", Nordic Pulp and Paper Research Journal, V o l . 16, No.3, p. 225-234, 2001 120 Chapter 7: References Lingren, J., Paperboard, I., Ohman, L . - O . , Gunnars, S. and Wagberg, L . , "Charge determinations of cellulose fibres of different origin - Comparison between different methods", Nordic Pulp and Paper Research Journal, V o l . 17, N o . l , p. 89-96, 2001 Morel , F . M . M , and Hering, J. G . , "Principles and Application of Aquatic Chemistry", A Wiley-Interscience Publication, John Wi ley & Sons Inc., 1993 N i , Y . , L i , Z . , and V a n Heiningen, A . R . P . , "Pulse chelation with D T P A " , Pulp and Paper Canada, T 3 8 2 , 100:12, p.110-113, 1999 N i , Y . , Ju, Y . , and Ohi , H . , "Further Understanding of the Manganese-Induced Decomposition of Hydrogen Peroxide", Journal of Pulp and Paper Science: V o l . 22, No.26, p.90-93, March 2000 Norberg, C , Liden, J., and Ohman, L . O . , "Modell ing the Distribution of "Free", Complexed and Precipitated Metal Ions in a Pulp suspension Using Donnan Equilibria", Journal of Pulp and Paper Science, Vol .27, No.9, p.296-300, September 2001 Pankow, J. F. , "Aquatic Chemistry Concepts", Lewis Publisher, Michigan, 1991 Pierre, J .L. , and Fontecave, M . , "Iron and Activated Oxygen Species in Biology: The Basic Chemistry", Biometals Journal, Vol .12, p. 195-199, 1999 Ragnar, M . , Lingren, C.T. , Nilvebrant, N . - O . , "On the dissociation constants of phenolic groups in lignin structures", Proc. 10 t h Intl. Symposium on Wood and Pulping Chemistry, Poster presentation, Yokohama, Japan, 1999 Rasanen, E . , Stenius, P., and Tervola, P., "Model describing Donnan equilibrium, p H and complexation equilibria in fibre suspensions", Nordic Pulp and Paper Research Journal, Vol.16, No.2,p . l30-139, 2001 Rasanen, E . , and Karkkainen, L . , "Model Complexation of Metal Ions in Pulp Suspensions", Journal of Pulp and Paper Science, Vol .29, No.6, p.196-203, 2003 Reeve, D . W . , Rowlandson, G . , Kramer, J. D . , Rapson, W . H . , "The closed-cycle bleached kraft pulp m i l l - 1978", T A P P I Journal, Vol .62 (8), p. 51-54, 1979 Sjostrdm, E . , "Wood chemistry: fundamentals and applications", Academic Press, 2nd edition, San Diego, 1993 Soini, P., Jakara, J., Koljonen, J., and Gullichsen, J., "Effect of transition metals on oxygen Delignification and Peroxide Bleaching", Paperi Ja Puu-Paper and Timber, Vol .80, No.2, p . l 16-121, 1998. Smook, G . A . , "Handbook for Pulp and Paper Technologist", 2 n d edition, Angus Wilde Publication, Vancouver, 1992 121 Chapter 7: References Stumm, W. , and Morgan, J., "Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters" 3 r d edition, Environmental Science and Technology, A Wiley-Interscience Publication, John Wi ley & Sons Inc., 1995 Towers, M . , and Scallan, A . M . , "Predicting the Ion-Exchange of Kraft Pulps Using Donnan Theory", Journal of Pulp and Paper Science, Vol .22, No.9, p. J332-J337, September 1996 Werner, J .A. , Ragauskas, J .A. , Jiang, J.E., "Investigations into the Intrinsic Non-Process Element Binding Capacity of Kraft Black Liquor Lignins", A I C h E Symposium Series, Vol .95, No.322, p.31-36, 1999. Werner, J .A. , Ragauskas, J .A. , Jiang, J.E., "Intrinsic metal Binding Capacity of Kraft Lignins", Journal of wood chemistry and technology, 20(2), p.133-145, 2000 Wiklund, L . , Ohman, L . O . , and Liden, J., "Sol id solution formation between M n (II) and M g (II) hydroxides in alkaline aqueous solution", Nordic Pulp and Paper Research Journal, Vol.16, March 2001. 122 APPENDIX 123 APPENDIX A: WRV Measurement Data Water Retention Value ( W R V ) of the pulp sample was measured at different p H . Each measurement was performed three times. The average values of W R V measurements and the standard deviation of each measurement is reported in the table. Table A-l: W R V experimental data for Brown Stock Washer mat of B C Coastal M i l l P H S Average value Standard External solution g water/g od fibre deviation 2.5 1.5296 0.0042 2.92 1.5641 0.0230 5.26 1.6251 0.0233 6.65 1.6458 0.0369 7.8 1.6669 0.0284 11.12 1.6934 0.0496 Table A-2: W R V experimental data for Post Oxygen Washer mat of B C Coastal M i l l P H S External solution Average value g water/g od fibre Standard Deviation 2.01 1.3261 0.006 3.98 1.4957 0.020 6.58 1.5216 0.010 10.53 1.6290 0.020 Table A-3: W R V experimental data for D c washer stage outlet of B C Coastal M i l l P H S External solution Average value g water/g od fibre Standard deviation 3.05 1.4815 0.0383 3.34 1.5239 0.0072 4.08 1.5532 0.0229 6.58 1.5975 0.0150 7.30 1.6219 0.0095 8.80 1.6288 0.0187 10.38 1.6363 0.0132 124 Table A-4: WRV experimental data for E o p washer stage outlet mat of BC Coastal Mill PH S Average value Standard External solution g water/g od fibre deviation 2.70 1.4943 0:0255 4.12 1.5617 0.0164 5.21 1.5687 0.0180 6.04 1.5872 0.0211 7.00 1.5905 0.0137 8.95 1.6122 0.0113 11.59 1.6213 0.0142 Table A-5: WRV experimental data for D n washer stage outlet mat of BC Coastal Mill PH S Average value Average External solution g water/g od fibre deviation 2.83 1.4890 0.0030 3.44 1.5255 0.0042 6.35 1.5684 0.0055 9.26 1.5865 0.0036 10.75 1.5925 0.0039 Table A-6: WRV experimental data for D 2 washer stage outlet mat of BC Coastal Mill PH S External solution Average value g water/g od fibre Average standard deviation 2.85 1.4848 0.0258 3.43 1.5258 0.0055 6.04 1.5702 0.0051 9.36 1.5962 0.0100 10.63 1.6033 0.0111 125 Table A-7: WRV experimental data for Brown Stock Washer mat of BC Interior Mill PH S Average value Standard External solution g water/g od fibre Deviation 2.02 1.0666 0.0328 2.62 1.0745 0.0238 3.86 1.0775 0.0310 6.28 1.0900 0.0336 8.54 1.0896 0.0346 11.57 1.0947 0.0375 Table A-8: WRV experimental data for Post Oxygen Washer mat of BC Interior Mill PH S Average value Standard External solution g water/g od fibre Deviation 2.12 1.0952 0.0249 2.55 1.0974 0.0258 4.68 1.1290 0.0310 5.93 1.1601 0.0266 6.89 1.1658 0.0158 9.47 1.2030 0.0089 11.31 1.2100 0.0378 Table A-9: WRV experimental data for D c washer mat of BC Interior Mill PH S External solution Average value g water/g od fibre Standard Deviation 3.08 1.1993 0.0222 5.16 1.2719 0.0181 7.97 1.3188 0.0044 10.74 1.3271 0.0063 11.51 1.3315 0.0250 126 APPENDIX B: Potentiometric Titration Data for Fiber Charge Calculation The potentiometric titration data is given in the term of volume NaOH added to the suspension and the corresponding pH at equilibrium. Table B-1: Potentiometric titration for Brown Stock Washer (BSW) mat of B C Coastal M i l l NaOH (mL) pH value NaOH (mL) pH value NaOH (mL) pH value 0.00 2.010 5.85 3.521 6.75 10.251 0.40 2.040 5.90 3.608 6.80 10.337 0.80 2.075 5.95 3.715 6.85 10.415 1.20 2.114 6.00 3.840 6.90 10.498 1.60 2.153 6.05 3.985 6.95 10.579 2.00 2.198 6.10 4.150 7.00 10.654 2.40 2.246 6.15 4.357 7.10 10.770 2.80 2.299 6.20 4.603 7.20 10.861 3.20 2.360 6.25 4.916 7.40 10.999 3.60 2.428 6.30 5.233 7.60 11.111 4.00 2.510 6.35 5.791 8.00 11.261 4.40 2.610 6.40 6.523 8.40 11.369 4.80 2.738 6.45 7.655 8.80 11.447 5.20 2.915 6.50 8.476 9.20 11.516 5.40 3.040 6.55 9.280 9.60 11.580 5.60 3.206 6.60 9.657 10.00 11.620 5.70 3.312 6.65 9.983 5.80 3.446 6.70 10.162 127 Table B-2: Potentiometric titration results for Post Oxygen Washer mat of BC Coastal Mill NaOH (mL) pH value NaOH (mL) pH value NaOH (mL) pH value 0.00 2.085 6.05 4.080 6.95 10.741 0.40 2.114 6.10 4.252 7.00 10.786 0.80 2.149 6.15 4.450 7.05 10.825 1.20 2.189 6.20 4.689 7.10 10.860 1.60 2.231 6.25 4.980 7.15 10.897 2.00 2.278 6.30 5.355 7.20 10.931 2.40 2.320 6.35 5.843 7.25 10.960 2.80 2.377 6.40 6.509 7.30 10.992 3.20 2.433 6.45 7.601 7.40 11.041 3.60 2.502 6.50 8.831 7.60 11.136 4.00 2.581 6.55 9.610 8.00 11.270 4.40 2.681 6.60 9.990 8.40 11.365 4.80 2.803 6.65 10.212 8.80 11.447 5.20 2.985 6.70 10.355 9.20 11.512 5.60 3.271 6.75 10.470 9.60 11.564 5.80 3.519 6.80 10.558 10.00 11.612 5.90 3.693 6.85 10.631 6.00 3.932 6.90 10.692 128 Table B - 3 : Potentiometric titration results for D c washer stage outlet mat o f B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.138 5.70 3.449 6.55 10.480 0.40 2.167 5.80 3.608 6.60 10.590 0.80 2.199 5.85 3.707 6.65 10.680 1.20 2.239 5.90 3.830 6.70 10.740 1.60 2.280 5.95 3.981 6.75 10.798 2.00 2.325 6.00 4.177 6.80 10.848 2.40 2.377 6.05 4.433 6.90 10.936 2.80 2.430 6.10 4.738 7.00 11.001 3.20 2.490 6.15 5.150 7.20 11.130 3.60 2.560 6.20 5.767 7.60 11.290 4.00 2.650 6.25 6.866 8.00 11.409 4.40 2.734 6.30 8.215 8.40 11.499 4.80 2.848 6.35 9.418 8.80 11.560 5.20 3.028 6.40 9.870 9.20 11.615 5.40 3.153 6.45 10.158 9.60 11.660 5.60 3.330 6.50 10.320 10.00 11.699 Table B -4 : Potentiometric titration results for E o p washer stage outlet mat of B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.152 5.70 3.421 6.55 10.533 0.40 2.180 5.80 3.563 6.60 10.620 0.80 2.214 5.85 3.652 6.65 10.690 1.20 2.250 5.90 3.759 6.70 10.753 1.60 2.288 5.95 3.887 6.75 10.810 2.00 2.330 6.00 4.055 6.80 10.856 2.40 2.377 6.05 4.280 6.90 10.943 2.80 2.427 6.10 4.586 7.00 10.975 3.20 2.484 6.15 4.927 7.20 11.110 3.60 2.550 6.20 5.430 7.60 11.275 4.00 2.625 6.25 6.410 8.00 11.386 4.40 2.720 6.30 8.088 8.40 11.469 4.80 2.847 6.35 9.539 8.80 11.540 5.20 3.020 6.40 10.040 9.20 11.600 5.40 3.142 6.45 10.275 9.60 11.651 5.60 3.309 6.50 10.420 10.00 11.690 129 Table B-5: Potentiometric titration results for D n washer stage outlet mat of B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.039 5.70 3.286 6.55 10.650 0.40 2.069 5.80 3.423 6.60 10.712 0.80 2.100 5.85 3.508 6.65 10.775 1.20 2.134 5.90 3.612 6.70 10.830 1.60 2.176 5.95 3.740 6.75 10.874 2.00 2.217 6.00 3.913 6.80 10.915 2.40 2.264 6.05 4.160 6.90 10.990 2.80 2.316 6.10 4.540 7.00 11.053 3.20 2.375 6.15 5.211 7.20 11.160 3.60 2.442 6.20 6.830 7.60 11.298 4.00 2.519 6.25 9.314 8.00 11.405 4.40 2.618 6.30 9.854 8.40 11.485 4.80 2.738 6.35 10.130 8.80 11.550 5.20 2.904 6.40 10.310 9.20 11.605 5.40 3.024 6.45 10.460 9.60 11.655 5.60 3.180 6.50 10.565 10.00 11.699 Table B-6: Potentiometric titration results for D 2 washer stage outlet mat of B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.000 5.70 3.279 6.55 10.704 0.40 2.028 5.80 3.428 6.60 10.762 0.80 2.061 5.85 3.522 6.65 10.814 1.20 2.098 5.90 3.638 6.70 10.858 1.60 2.138 5.95 3.773 6.75 10.900 2.00 2.180 6.00 3.966 6.80 10.941 2.40 2.224 6.05 4.244 6.90 11.011 2.80 2.278 6.10 4.687 7.00 11.075 3.20 2.337 6.15 5.520 7.20 11.162 3.60 2.403 6.20 7.540 7.60 11.305 4.00 2.482 6.25 9.661 8.00 11.402 4.40 2.579 6.30 10.068 8.40 11.490 4.80 2.705 6.35 10.297 8.80 11.557 5.20 2.881 6.40 10.448 9.20 11.602 5.40 3.002 6.45 10.551 9.60 11.653 5.60 3.166 6.50 10.634 10.00 11.699 130 Table B-7: Potentiometric titration results for Brown Stock Washer (BSW) of B C Interior M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.229 6.10 3.931 7.65 10.652 0.40 2.254 6.15 4.060 7.70 10.678 0.80 2.284 6.20 4.212 7.75 10.706 1.20 2.314 6.25 4.393 7.80 10.726 1.60 2.362 6.30 4.606 7.85 10.746 2.00 2.407 6.35 4.814 7.90 10.760 2.40 2.459 6.40 5.130 7.95 10.778 2.80 2.515 6.45 5.530 8.00 10.799 3.20 2.580 6.50 5.979 8.05 10.841 3.60 2.659 6.55 6.527 8.10 10.865 4.00 2.786 6.60 7.147 8.15 10.907 4.40 2.878 6.65 7.442 8.20 10.925 4.80 2.984 6.70 8.134 8.25 10.932 5.20 3.006 6.75 8.704 8.30 10.953 5.25 3.029 6.80 9.105 8.35 10.972 5.30 3.058 6.85 9.409 8.40 10.993 5.35 3.084 6.90 9.629 8.80 11.093 5.40 3.113 6.95 9.800 9.20 11.180 5.45 3.142 7.00 9.920 9.60 11.253 5.50 3.175 7.05 10.020 10.00 11.313 5.55 3.213 7.10 10.105 10.40 11.370 5.60 3.255 7.15 10.166 10.80 11.424 5.65 3.295 7.20 10.228 11.20 11.464 5.70 3.339 7.25 10.295 11.60 11.501 5.75 3.395 7.30 10.322 12.00 11.539 5.80 3.442 7.35 10.390 12.40 11.561 5.85 3.500 7.40 10.427 5.90 3.563 7.45 10.485 5.95 3.636 7.50 10.530 6.00 3.723 7.55 10.575 6.05 3.824 7.60 10.615 131 Table B-8: Potentiometric titration results for Post Oxygen Washer mat of B C Interior M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.068 6.05 4.110 6.95 10.801 0.40 2.101 6.10 4.292 7.00 10.850 0.80 2.138 6.15 4.511 7.05 10.897 1.20 2.180 6.20 4.768 7.10 10.948 1.60 2.220 6.25 5.099 7.15 10.989 2.00 2.265 6.30 5.634 7.20 11.034 2.40 2.317 6.35 6.401 7.25 11.068 2.80 2.369 6.40 7.605 7.30 11.095 3.20 2.430 6.45 8.660 7.40 11.149 3.60 2.498 6.50 9.540 7.60 11.243 4.00 2.584 6.55 9.953 8.00 11.380 4.40 2.687 6.60 10.184 8.40 11.490 4.80 2.818 6.65 10.338 8.80 11.558 5.20 2.994 6.70 10.456 9.20 11.614 5.60 3.288 6.75 10.551 9.60 11.677 5.80 3.535 6.80 10.638 10.00 11.710 5.90 3.715 6.85 10.694 6.00 3.958 6.90 10.751 Table B-9: Potentiometric titration results for D c mat of B C Interior M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.045 5.70 3.379 6.55 10.546 0.40 2.072 5.80 3.538 6.60 10.612 0.80 2.105 5.85 3.639 6.65 10.683 1.20 2.143 5.90 3.762 6.70 10.746 1.60 2.188 5.95 3.916 6.75 10.806 2.00 2.232 6.00 4.114 6.80 10.852 2.40 2.278 6.05 4.382 6.90 10.938 2.80 2.338 6.10 4.756 7.00 11.013 3.20 2.398 6.15 5.294 7.20 11.121 3.60 2.467 6.20 6.142 7.60 11.283 4.00 2.551 6.25 8.082 8.00 11.399 4.40 2.649 6.30 9.428 8.40 11.489 4.80 2.775 6.35 9.857 8.80 11.563 5.20 2.958 6.40 10.131 9.20 11.625 5.40 3.084 6.45 10.291 9.60 11.677 5.60 3.259 6.50 10.424 10.00 11.718 132 APPENDIX C: Potentiometric Titration Data for Binding Constants Calculation This potentiometric titration of acid washed chelated fiber with the addition of known amount of metal was done to calculate the binding constant and also used in the metal ion partitioning prediction model to adjust the suspension p H . A l l titration curves with metal addition (iron, manganese, or copper) lie to the right from the fiber itself without the presence of metal. The more metal added the more sodium hydroxide is consumed so that the titration curve shifts more to the right. Thus, all binding constant could not be calculated and the constant was set to zero for all metal ion. The titration with iron, manganese, and copper addition are shown in figure C - l to C-3. 0 2 4 6 8 10 12 Volume of NaOH (ml) Figure C-l: Potentiometric titration data of water (blank), acid-washed chelated pulp (AWP) without and with the addition of iron in a B S W sample from a B C coastal mi l l 133 14 Blank 0 2 4 6 8 10 12 Volume of NaOH (ml) Figure C-2: Potentiometric titration data of water (blank), acid-washed chelated pulp (AWP) without and with the addition of manganese in a BSW sample from a B C coastal mill 0 2 4 6 8 10 12 Volume of NaOH (ml) Figure C -3 : Potentiometric titration data of water (blank), acid-washed chelated pulp (AWP) without and with the addition of copper in a BSW sample from a BC coastal mill Table C - l : Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of iron at 520 ppm from B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 1.989 6.00 2.952 7.40 9.646 0.40 2.009 6.40 3.280 7.45 9.836 0.80 2.038 6.60 3.601 7.50 9.940 1.20 2.066 6.80 4.221 7.55 10.044 1.60 2.100 6.85 4.450 7.60 10.138 2.00 2.134 6.90 4.785 7.70 10.304 2.40 2.172 6.95 5.203 7.90 10.581 2.80 2.214 7.00 5.733 8.30 10.879 3.20 2.260 7.05 6.300 8.40 10.902 3.60 2.312 7.10 6.973 8.80 11.080 4.00 2.370 7.15 7.745 9.20 11.190 4.40 2.443 7.20 8.411 9.60 11.271 4.80 2.525 7.25 8.842 10.00 11.334 5.20 2.626 7.30 9.155 5.60 2.758 7.35 9.411 Table C - 2 : Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of manganese at 600 ppm from B C Coastal M i l l N a O H (mL) p H value N a O H (mL) p H value N a O H (mL) p H value 0.00 2.058 6.00 3.017 7.45 9.971 0.40 2.083 6.40 3.298 7.50 10.140 0.80 2.114 6.60 3.532 7.55 10.268 1.20 2.148 6.80 3.922 7.60 10.384 1.60 2.183 6.90 4.226 7.70 10.577 2.00 2.218 6.95 4.418 7.80 10.721 2.40 2.259 7.00 4.655 8.00 10.914 2.80 2.305 7.05 4.939 8.40 11.153 3.20 2.352 7.10 5.361 8.80 11.315 3.60 2.403 7.15 6.049 9.20 11.420 4.00 2.465 7.20 6.988 9.60 11.496 4.40 2.538 7.25 8.053 10.00 11.567 4.80 2.617 7.30 8.858 5.20 2.713 7.35 9.334 5.60 2.841 7.40 9.704 135 Table C-3: Potentiometric titration of acid-washed chelated Brown Stock Washer (BSW) mat with the presence of copper from B C Coastal M i l l N a O H (mL) p H value trial 1 (210ppm) p H value trial 2 (210ppm) p H value (600 ppm) 0.00 2.006 2.105 2.133 0.40 2.027 2.135 2.158 0.80 2.056 2.166 2.188 1.20 2.087 2.198 2.220 1.60 2.121 2.230 2.252 2.00 2.161 2.272 2.288 2.40 2.208 2.319 2.330 2.80 2.260 2.365 2.376 3.20 2.320 2.421 2.422 3.60 2.380 2.483 2.476 4.00 2.455 2.556 2.535 4.40 2.548 2.647 2.606 4.80 2.663 2.756 2.699 5.20 2.816 2.897 2.813 5.60 3.040 3.111 2.965 5.90 3.309 3.358 3.128 6.20 3.829 3.830 3.385 6.40 4.529 4.484 3.660 6.60 6.030 5.901 4.145 6.70 7.081 6.943 4.517 6.75 7.620 7.435 4.789 6.80 8.121 8.053 5.083 6.85 8.672 8.531 5.410 6.90 9.066 9.025 5.901 6.95 9.365 9.316 6.387 7.00 9.610 9.546 6.914 7.05 9.768 9.728 7.636 7.10 9.900 9.872 8.400 7.15 10.012 9.999 8.893 7.20 10.105 10.088 9.467 7.25 10.181 10.174 9.663 7.30 " 10.241 10.248 9.927 7.35 10.293 10.306 10.036 7.40 10.354 10.362 10.165 7.60 10.587 10.541 10.407 7.80 10.749 10.670 10.623 8.20 10.973 10.844 10.859 8.70 11.141 10.993 11.041 9.10 11.242 11.084 11.118 9.50 11.322 11.163 11.205 9.90 11.379 11.229 11.271 10.30 11.428 11.279 11.311 10.70 11.489 11.331 11.360 11.10 11.530 11.374 11.406 136 APPENDIX D: Metal Profile Analysis This appendix has six columns that correspond to the analysis of each sample. The first column (Description) refers to the number of sample. The second column (Symbol) refers to the metal profile ( C F M ) . The detail description of the symbol is given in the list o f symbol section. The next column (Pulp type) refers to each sampling points in the fiberline. The symbol in this column corresponds to table 4.1 and 4.2 in chapter 4. The fourth column (Weight or S) refers to the weight of the liquor after acid digestion of the pulp samples or the weight of the liquor itself after washing. The fifth column (Cone, or C) refers to the concentration from each sample after analysis. It is given in part per mil l ion (ppm). [Fe] refers to the iron concentration on the fiber given in mg-Fe / kg-OD fiber, c r ^ refers to the deviation from the mean values reported. The last column (%RSD) refers to the standard deviation of each measurement from Atomic Absorption Spectroscopy ( A A S ) . Each measurement from A A S was done six times the reported values are the average of six replicates. There is no replicate for the ICP measurements. Each pulp sample corresponds to 10.0000-g oven dried fiber (OD). Table D-l: Iron profile from A A S Analysis of B C Coastal M i l l Description Pulp type Weight (g) Cone, (ppm) [Fe] V] % R S D Sample 1 B S W 33.2117 9.7 31 1.0 4.19 Sample 2 P - 0 2 32.6868 7.9 28 1.1 5.34 Sample 3 Dc 7.9411 34.8 30 1.1 2.94 Sample 4 Eop 14.3377 28.3 38 0.8 2.84 Sample 5 D n 8.8471 23.0 21 0.3 3.00 Sample 6 D2 8.9099 29.4 26 0.3 4.01 Table D-2: Iron profile from A A S Analysis of B C Interior M i l l Description Pulp type Weight (g) Cone, (ppm) [Fe] V i % R S D 8.86 Sample 1 B S W 18.1869 4.6 9 0.6 Sample 2 P - 0 2 22.5668 2.5 6 0.7 17.65 Sample 3 Dc 16.1415 2.9 5 0.5 18.56 Sample 4 Dried sheet 15.3343 2.2 3 0.5 8.94 137 Table D-3: Iron profile from ICP Analysis of B C Coastal M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] V] Sample 1 B S W 33.2117 9.8 31 1.0 Sample 2 P - 0 2 32.6868 8.8 31 1.1 Sample 3 Dc 12.6854 21.6 28 0.4 Sample 4 Eop 14.3377 23.4 31 0.4 Sample 5 D n 17.3060 12.6 22 0.5 Sample 6 D2 19.2837 14.3 27 0.6 Table D-4: Iron profile from ICP Analysis of B C Interior M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] Vl Sample 1 B S W 18.1869 3.8 8 0.6 Sample 2 P - 0 2 22.5668 3.2 7 0.7 Sample 3 Dc 16.1415 2.9 5 0.5 Sample 4 Dried Sheet 15.3343 2.8 4 0.5 Table D-5: Iron profile from Spectrophotometer Analysis of B C Coastal M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] Sample 1 B S W 33.2117 10.3 33 1.0 Sample 3 P - 0 2 32.6868 8.4 30 i . i 138 APPENDIX E: Metal Removal Analysis The explanation of the table in this appendix is the same as the one in appendix D . Each sample corresponds to lOg oven dried fiber. Table E - l : Residual iron concentration from A A S Analysis of B C Coastal M i l l Description Pulp type Weight (g) Cone, (ppm) [Fe] V l % R S D Sample 1 B S W 31.5114 2.3 7 0.9 14.06 Sample 2 P - 0 2 30.7744 1.5 5 1.0 14.21 Sample 3 Dc 11.9870 3.4 4 0.4 11.41 Sample 4 Eop 12.5131 3.0 4 0.4 8.70 Sample 5 D n 15.9528 2.6 4 0.5 14.61 Sample 6 D2 18.2244 1.4 3 0.6 >20 Table E-2: Residual iron concentration from A A S Analysis of B C Interior M i l l Description Pulp type Weight (g) Cone, (ppm) [Fe] Vi % R S D Sample 1 B S W 16.1958 1.2 2 0.6 >20 Sample 2 P - 0 2 15.8127 1.0 2 0.5 >20 Sample 3 Dc 16.3697 1.1 2 0.5 >20 Table E-3: Residual iron concentration from ICP Analysis of B C Coastal M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] V] Sample 1 B S W 31.5114 2.7 8 0.9 Sample 2 P - 0 2 30.7744 2.2 7 1.0 Sample 3 Dc 11.9870 3.8 5 0.4 Sample 4 Eop 12.5131 3.7 4 0.3 Sample 5 D n 15.9528 2.6 4 0.5 Sample 6 D2 18.2244 1.8 3 0.5 139 Table E-4 Residual iron concentration from ICP Analysis of B C Interior M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] Vi Sample 1 B S W 16.1958 2.2 4 0.6 Sample 2 P - 0 2 15.8127 1.0 2 0.5 Sample 3 Dc 16.3697 1.5 3 0.5 Table E-5: Residual iron concentration from Spectrophotometer Analysis o f B C Coastal M i l l Description Pulp type Weight (gr) Cone, (ppm) [Fe] Vi Sample 1 B S W 31.5114 2.3 7 0.9 Sample 2 P - 0 2 30.7744 1.2 4 1.0 Table E-6: Liquor concentration at each washing stage from ICP Analysis of B C Coastal M i l l Description Symbol Pulp type Weight (gr) Cone, (ppm) Sample 1 L - l B S W 370.1504 0.4 Sample 2 L-2 370.6704 0.4 Sample 3 L-3 375.4904 0.2 Sample 4 L - l P - 0 2 356.077 0.1 Sample 5 L-2 360.857 0.3 Sample 6 L-3 362.6347 0.1 Sample 7 L - l Dc 353.5658 0.1 Sample 8 L-2 355.8258 0.2 Sample 9 L-3 362.1858 0.0 Sample 10 L-4 958.8750 0.0 Sample 11 L - l Eop 368.6981 0.1 Sample 12 L-2 369.5181 0.1 Sample 13 L-3 374.0381 0.1 Sample 14 L-4 959.9581 0.0 Sample 15 L - l D n 355.0508 0.1 Sample 16 L-2 357.7308 0.1 Sample 17 L-3 356.5008 0.1 Sample 18 L-4 959.4503 0.0 Sample 19 L - l D2 355.2520 0.1 Sample 20 L-2 359.0220 0.1 Sample 21 L-3 359.8320 0.1 Sample 22 L-4 959.7506 0.0 140 APPENDIX F: Metal Partitioning Analysis The partitioning experiment data introduces new symbols. The symbols have the following form: A X - B or A F - B . These two symbols are introduced to identify each sample during analysis. ' X ' refers to the fiber phase and ' F ' refers to the solution phase (filtrate). ' A ' refers to the multiplication o f the initial metal content from each pulp sample (one, two, four and ten times of the original iron concentration on the fiber) and ' B ' refers to the replicates of the same concentration. The explanations of the rest of the table in this appendix are the same as the one in appendix D . Each sample corresponds to l g oven dried fiber. Table F-l: Partitioning data from A A S Analysis o f B S W from B C Coastal M i l l using filter paper Description Symbol Pulp type Weight (g) Cone, (ppm) % R S D Sample 1 IX-1 B S W 5.8558 5.4 6.20 Sample 2 1X-2 B S W 6.7292 5.5 7.25 Sample 3 1X-3 B S W 7.4676 5.2 6.00 Sample 4 2X-1 B S W 6.9182 8.6 3.74 Sample 5 2X-2 B S W 7.0697 8.7 5.00 Sample 6 2X-3 B S W 7.522 8.2 2.44 Sample 7 4X-1 B S W 7.501 13.1 2.88 Sample 8 4X-2 B S W 6.6624 13.2 3.55 Sample 9 4X-3 B S W 6.8944 13.5 2.85 Sample 10 10X-1 B S W 8.053 17.4 3.75 Sample 11 10X-2 B S W 7.2595 20.2 2.31 Sample 12 10X-3 B S W 8.9034 17.3 1.48 Sample 13 1F-1 B S W 86.5383 0.0 0.00 Sample 14 1F-2 B S W 85.972 0.0 0.00 Sample 15 1F-3 B S W 85.4194 0.0 0.00 Sample 16 2F-1 B S W 87.9796 0.0 0.00 Sample 17 2F-2 B S W 86.7216 0.0 0.00 Sample 18 2F-3 B S W 87.0715 0.0 0.00 Sample 19 4F-1 B S W 88.3353 0.0 0.00 Sample 20 4F-2 B S W 90.0752 0.0 0.00 Sample 21 4F-3 B S W 90.0003 0.0 0.00 Sample 22 10F-1 B S W 90.6178 1.7 10.68 Sample 23 10F-2 B S W 85.453 1.9 10.40 Sample 24 10F-3 B S W 87.4312 1.9 18.63 141 Table F-2: Partitioning data from A A S Analysis of B S W from B C Coastal M i l l using centrifuging Description Symbol Pulp type Weight (g) Cone, (ppm) % R S D Sample 1 1X-1 B S W 4.1148 5.5 6.59 Sample 2 1X-2 B S W 4.4655 4.8 4.19 Sample 3 1X-3 B S W 4.7869 4.7 6.57 Sample 4 2X-1 B S W 5.0575 6.1 6.01 Sample 5 2X-2 B S W 5.6522 5.0 3.69 Sample 6 2X-3 B S W 4.8147 6.0 5.99 Sample 7 4X-1 B S W 6.2388 7.5 2.79 Sample 8 4X-2 B S W 5.8846 7.2 3.53 Sample 9 4X-3 B S W 5.8268 8.0 2.69 Sample 10 10X-1 B S W 5.7674 14.9 1.97 Sample 11 10X-2 B S W 6.2357 15.2 1.36 Sample 12 10X-3 B S W 5.5661 15.7 1.05 Sample 13 1F-1 B S W 102.9423 0.1 >20 Sample 14 1F-2 B S W 97.5135 0.1 >20 Sample 15 1F-3 B S W 97.5292 0.1 >20 Sample 16 2F-1 B S W 100.5308 0.3 15.76 Sample 17 2F-2 B S W 97.418 0.4 >20 Sample 18 2F-3 B S W 97.5449 0.4 >20 Sample 19 4F-1 B S W 97.3268 0.8 >20 Sample 20 4F-2 B S W 97.3709 0.8 17.64 Sample 21 4F-3 B S W 97.2211 0.8 >20 Sample 22 10F-1 B S W 98.2278 2.3 10.33 Sample 23 10F-2 B S W 97.9895 2.2 9.38 Sample 24 10F-3 B S W 97.8704 2.3 6.33 142 Table F-3: Partitioning data from A A S Analysis o f D c washer mat from B C Coastal M i l l Description Symbol Pulp type Weight (g) Cone, (ppm) %RSD Sample 1 1X-1 Dc 9.3632 1.5 10.91 Sample 2 1X-2 Dc 8.0726 1.9 7.75 Sample 3 1X-3 Dc 8.3992 1.8 9.56 Sample 4 2X-1 Dc 7.886 2.9 3.65 Sample 5 2X-2 Dc 7.4906 3.0 4.04 Sample 6 2X-3 Dc 8.3079 3.0 6.20 Sample 7 4X-1 Dc 10.9901 2.4 19.05 Sample 8 4X-2 Dc 10.5001 3.0 2.88 Sample 9 4X-3 Dc 11.4079 3.0 3.13 Sample 10 10X-1 Dc 11.1538 4.7 3.32 Sample 11 10X-2 Dc 11.9475 4.1 3.37 Sample 12 10X-3 Dc 11.7327 3.9 1.92 Sample 13 1F-1 Dc 97.2248 0.1 >20 Sample 14 1F-2 Dc 97.3742 0.1 >20 Sample 15 1F-3 Dc 97.2566 0.1 >20 Sample 16 2F-1 Dc 97.4579 0.3 >20 Sample 17 2F-2 Dc 97.3896 0.2 >20 Sample 18 2F-3 Dc 97.1564 0.2 >20 Sample 19 4F-1 Dc 97.5159 0.7 13.62 Sample 20 4F-2 Dc 97.6577 0.7 >20 Sample 21 4F-3 Dc 97.3894 0.7 >20 Sample 22 10F-1 Dc 97.4427 2.0 9.77 Sample 23 10F-2 Dc 97.5382 1.9 9.42 Sample 24 10F-3 Dc 97.6886 2.1 5.88 143 A P P E N D I X G: Sample of Calculation The iron concentration on the pulp was calculated based on the analysis result of ICP, A A S or Spectrophotometric. The concentration measured from the analysis was the concentration of iron in the digested solution (ppm or mg-Fe/kg-solution). Thus, the number was converted to the concentration o f iron on the fiber (mg-Fe/kg-od fiber). This was done by calculating the absolute mass of iron in the solution and divided by the appropriate mass of oven dried fiber. The equation is given as follows: Fe = OD where: Total weight of the digested solution Concentration measured from Analysis Weight of the oven dried sample Iron concentration of the fiber S c OD Fe [gr-solution] [mg-Fe/kg-solution] [g-oven dried fiber] [mg-Fe/kg-od fiber] For example the calculation of iron concentration on the fiber phase of B S W sample from B C Interior m i l l , as given in the first row from table D-2. The amount of solution from the digestion reported is 18.1869 g (S). The iron concentration measured reported is 4.6ppm (C). The weight of the oven dried sample is 10.0000-g od (OD). Thus, the iron concentration on the fiber w i l l be: mgFe kgod fiber 4.6 Fe mgFe kg solution (18.1869 [g solution]) (10.0000 [go d fiber]) = 8 The maximum error associated with the calculated iron concentration is 1 ppm, thus all concentrations reported here are rounded off without any decimal. The calculation of error analysis is given in appendix H . 144 APPENDIX H: Error Analysis The error from the calculation of iron concentrations are calculated using the equation 1-1 below: ' S [ F e p 2 ^ r n - . i V / - r _ , x 2 G\Fe\ = dS , x 2 fd\Fe] dc dOD (dOD) where: d[Fe] dS d[Fe] dC d[Fe] 80D C OD S OD S*C OD1 dS = 1E-4 g dC = 0.3 ppm dOD = 1E-4 g a = deviation from the mean value (H- l ) So equation 1-1 can be re-written as follows: C \ODj (IE-4) + f s f s-c^2 KODJ (0.3) + OD ( L 5 - 4 ) 2 (H-2) For example the calculation of iron concentration on the fiber phase o f B S W sample from B C Interior m i l l , as given in the first row from table D-2. f 4.6 \ 2 10.0000 ( l £ - 4 ) 2 + ^18 .1869V/„^2 ( 10.0000x18.1869 V 10.0000 (0.3) + 10.00002 ( l £ - 4 ) 2 < 1 = 0-3 °~\Fe\ = 0 6 mg Fe kgod fiber 145 APPENDIX I; Fiber Charge Program The fiber charge calculation program is a general program to calculate the charge properties. The input to the program is the titration experiment data which is given provided in a txt file and the fitting parameter for W R V measurement. The total moles of all anions and cations, the mass of oven dried fiber, and the total volume of the suspension has to be specified before using the program. The programs used to calculate the fiber charge are: 1. bsw.m The main program, B S W sample is reported here. 2. titrate.m Sub-routine to calculate the fiber charge. 3. bisect.m Sub-routine to solve non-linear equation using Bisection's method. 4. solution.m The electroneutrality function. 5. maqrt.m Sub-routine to fit fiber charge properties using "2-charge" model. 6. modeafit.m The fitting equation. 7. modeadfit.m The derivative o f fitting equation. % bsw blank % bsw.m i s a m - f i l e that i s used to input the data f o r c a l c u l a t i n g the % f i b e r charge and f i t the d i s s o c i a t i o n constant and the t o t a l charge % moles. % This m - f i l e c a l l s the sub-routine to c a l c u l a t e the f i b e r charge. c l e a r a l l Kw=le-14; % Assign T i t r a t i o n Data data=load('bsw.txt'); NaOH=data(1:end,1); pH=data(1:end,2); % Assign FSP constant A=-0.002; B=0.04 5; C=1.44; % C a l c u l a t e the exact f i b e r charge [mmhs, mmohs,mmcls,mmnas,lam,FSP,V,F,Cna,Acl] = t i t r a t e (NaOH,pH,A,B,C); 146 % Set the data, range f o r the re g r e s s i o n range=28:60; mhf=mmhs(range).*lam(range); mohf=Kw./mhf; mnaf=Cna(range).*lam(range)./(F(range).*(lam(range)-1)+ V(range)); mclf=Acl(range)./(F(range).*(1-lam(range))+ V(range).*lam(range)); % Set the input f o r the re g r e s s i o n xl=mhf; x2=F(range); y=mhf+mnaf-mohf-mclf; N=[y;xl;x2]; kk=[2.13e-9 2.48e-13 4.15e-5 7.38e-9]; % C a l c u l a t e the f i t t i n g parameter [bm,yfitm,varm]=marqrt ( N ,kk,'modeafit','modeadfit'); ql=bm(l)/bm(3); q2=bm(2)/bm(4); res=[ql q2 bm(3) bm(4)]; max=ql./x2*bm(3)./(bm(3)+mhf); mbx=q2./x2*bm(4)./(bm(4)+mhf); % P l o t the r e s u l t f i g u r e ( 1 ) plot(-loglO(xl),yfitm*1000.*FSP(range),-loglO(xl),y*1000.*FSP(range),'*') xlabel('pH^F') y l a b e l ( ' T o t a l f r e e charge (mmol/kg od)') title('BSW') f i g u r e ( 2 ) plot(-loglO(xl),max*1000.*FSP(range),'+',-loglO(xl),mbx*1000.*FSP(range),'*') xlabel('pH"F') y l a b e l ( ' F r e e charge of two f u n c t i o n a l groups (mmol/kg od)') t i t l e ( 'BSW ) fu n c t i o n [mmhs,mmohs,mmcls,mmnas,lamdaa,FSP,vv,ff, Cnat, A c l t ] = t i t r a t e (NaOH,pH,A,B,C) % This i s f o r K determination of metals with f i b e r % ' t i t r a t e . m ' i s a s c r i p t m - f i l e that uses Newton's i t e r a t i v e method to % solve the same p a i r of nonlinear equations. % The augmented Jacobian matrix i s c a l c u l a t e d i n the f u n c t i o n m - f i l e % 'coeff3.m' while the two nonlinear equations are defined i n % solution.m'. % The v a r i a b l e s used are: % V = volume of the suspension % F = volume of water satura t e d c e l l u l o s e (FSP) % Cna = T o t a l c a t i o n moles of natrium % A c l = T o t a l anion moles of c h l o r i d e % HpS = H+ i n s o l u t i o n I The input are: % NaOH = volume of t i t r a n t NaOH added-(ml) 147 % pH = pH read from the pot e n t i o m e t r i c t i t r a t i o n % A,B,C = f i t t i n g c o e f f i c i e n t from the FSP measurement c l c t i c g l o b a l V F Cna A c l Kw mhs % Assign constant ( I n i t i a l background concentration, Oven-Dried % f i b e r and volume of suspension) Vo=60/1000; OD=0.6/1000; Cna_o=0/1000; Acl_o=10/1000; Mnaoh=100/1000; Kw=le-14 ; Acl=Acl_o*Vo; % Assign T i t r a t i o n Data HpS=10. A(-pH); % Assign I n t i a l value m=length(pH); n=l:m; V=Vo; lamda=le-2; % I t e r a t i o n f o r each pH fo r i=l:m % Assign FSP constant FSP(i)=A*pH(i)~2+B*pH(i)+C; F=FSP(i)*OD; % [kg OD] % [mol/L] % [mol/L] % [mol/L] % Moles of C l -60-g (suspension) 0 . 6-g od f i b e r 0-mmol NaCl 10-mmol HC1 100-mmol NaOH [mol] [mol/L s o l u t i o n ] [kg water/kg OD] [kg water] C a l c u l a t i n g a new volume with the corresponding mole V=Vo-OD+NaOH(i)/1000; Cna=Cna_o*Vo+Mnaoh*NaOH(i)/1000; f f ( i ) = F ; vv(i)=V; mhs=HpS ( i ) ; Cnat(i)=Cna; A c l t ( i ) = A c l ; a l c u l a t e the two unknowns using Newton's method x = b i s e c t ( ' s o l u t i o n ' , l e - 2 , 1 0 0 , l e - 2 , l e - 6 ) ; mmhs(i)=mhs; % mhs mmohs(i)=Kw/mmhs(i); % mohs mmcls(i)=Acl/(F*(1/x(1)-1)+V); % mcls mmnas(i)=Cna/(F*(x(1)-1)+V); % mnas lamdaa(i)=x(1); % lamda T o t a l suspension volume [L] Moles of Na+ [mol] end toe 148 f u n c t i o n root = b i s e c t ( f , x i , x f , d x , t o l ) % bisect.m % Simple s c r i p t m - f i l e that uses the b i s e c t i o n method to % f i n d the sma l l e s t root of a f u n c t i o n 'fun' bounded by % [ x i , x f ] to a to l e r a n c e ' t o l ' . Incremental search with % an i n i t i a l increment 'dx' i s f i r s t used to "find an % i n t e r v a l [xold,xnew] which brackets the root. x l = x i ; y l = f e v a l ( f , x i ) ; i f yl==0 root= x l ; e l s e while xl<xf % Incremental search s e c t i o n x2=xl+dx; y2=feval(f,x2); i f yl*y2>0 xl=x2; yl=y2; e l s e while ( x 2 - x l ) > t o l % B i s e c t i o n s e c t i o n x3=(xl+x2)/2; y3=feval(f,x3); i f yl*y3>0 xl=x3; yl=y3; e l s e x2=x3; y2=y3; end end root=x3; r e t u r n end end disp('No root found i n search range') end f u n c t i o n y = s o l u t i o n (lamd) % This f u n c t i o n i s to c a l c u l a t e the e l e c t r o n e u t r a l i t y i n the % s o l u t i o n phase g l o b a l V F Cna A c l Kw mhs mhs=mhs; mohs=Kw/mhs; mnas=Cna/(F*(lamd-1)+V); mcls=Acl/(F*(1/lamd-l)+V) ; y=mhs+mnas-mohs-mcls; 149 f u n c t i o n [a, y f i t , var,k,AA,int] = marqrt(A,a,f,df) % Assign v a r i a b l e s r e q u i r e d by the f i t t i n g procedure [c,m]=size(A); cm=2:c; c p = l : c - l ; y=A(l,:); x(cp, :)=A(cm, :) ; t o l = l e - 4 ; maxit=200; r e l a x = l ; n=length(a); lamda=le-3; maxda=lelO; i t e r = 0 ; f l a g = l ; k ( l , : ) = a ; % C a l c u l a t i n g y f i t f o r i=l:m x x = x ( : , i ) ; y l ( i ) = f e v a l ( f , x x , a ) ; end % C a l c u l a t e e r r o r term S SSQ=sum((y-yl)."2); % Using combination Marquardts and Newton method while maxda>tol i t e r = i t e r + l ; i f iter>maxit f p r i n t f ( ' M a r q u a r d t s method f a i l e d to converged i n %2.0f i t e r a t i o n s \ n ' , i t e r ) r e t u r n end i f flag==l a l p h a = c o e f f ( f , d f , x , y , a ) ; f o r j = l : n d i a g ( j ) = a l p h a ( j , j ) ; end end % Using marquardt's method, i n t r o d u c i n g lamda lamdap=lamda+l; f o r j = l : n a l p h a ( j , j ) = d i a g ( j ) * l a m d a p ; end % Using Newton's method to f i n d a new f i t t i n g parameter %da=gauss(alpha); d=alpha(:,5); dd=[alpha(:,1) alpha(:,2) alpha(:,3) alpha( , 4 ) ] ; dda=dd\d; da=dda'; a new=a+relax*da; maxda new=max(abs(da./a)); f o r i=l:m x x = x ( : , i ) ; y f i t ( i ) = f e v a l ( f , x x , a new); end % C a l c u l a t e the new e r r o r term SSQ_new=sum((y-yfit). A2); % Check, whether the new e r r o r i s l a r g e r or l e s s % I f l a r g e r , increase lamda by ten, otherwise decrease lamda by ten. i f SSQ new<SSQ a=a new; lamda=0.l*lamda; SSQ=SSQ new; maxda=maxda new f l a g = l ; e l s e 1amda=10*1amda; flag=0; end k (iter+1, :)=a; 150 end % C a l c u l a t i n g the variance var=SSQ/(m-n); % C a l c u l a t e 95% confidence i n t e r v a l o f: the parameter d=length(alpha)-1; AA=inv(alpha(1:d,1:d)); f o r i = l : d t k ( i ) = s q r t ( v a r ) * s q r t ( A A ( i , i ) ) ; i n t ( i ) = 1 . 9 6 * t k ( i ) ; end f u n c t i o n y = modeafit ( x ,k) % This i s the o b j e c t i v e f u n c t i o n f o r f i t t i n g "2 charge" model mhf= x(l); F=x(2); k l = k ( l ) ; k2=k(2); kah=k(3); kbh=k(4); maf=kl/F/(kah+mhf); mbf=k2/F/(kbh+mhf); y=raaf+mbf; f u n c t i o n dy = modeadfit ( i , x , k ) % This i s the d e r i v a t i o n of the o b j e c t i v e f u n c t i o n with respect % with each parameter mhf=x(1); F=x ( 2) ; k l = k ( l ) ; k2=k(2); kah=k(3); kbh=k(4); i f i==l dy=l/F/(kah+mhf); e l s e i f i==2 dy=l/F/(kbh+mhf); e l s e i f i==3 dy=-kl/F/(kah+mhf) A2; e l s e dy=-k2/F/(kbh+mhf) A2; end 151 APPENDIX J: Binding Constant Calculation The binding constants calculation program is a general program to calculate the binding constants. The input to the program is the titration experiment data of acid washed chelated fiber (clean fiber with no metal) with a known addition of metal ion, in this case iron. The fiber property such as the W R V is needed as the input to the model. The total moles of all anions and cations, the mass of oven dried fiber, and the total volume of the suspension has to be specified before using the program. The programs used to calculate the binding constants are: 1. bswbindl609.m The main program, B S W sample is reported here. 2. t i t l609.m Sub-routine to calculate the binding constants. 3. newtonnonlinl609.m Newton's sub-routine to solve non-linear equations. 4. coefE.m Sub-routine to calculate the Jacobian matrix. 5. nonlinl609.m The objective function for solving the set of equations. % bswbindl60 9.m i s an m - f i l e that i s used to c a l c u l a t e the binding % constant from the po t e n t i o m e t r i c t i t r a t i o n data c l e a r a l l g l o b a l Kw Kah Kbh Qa Qb Cme % Assign constant Kw=le-14; % Assign T i t r a t i o n Data with metal datal=load('bbswfe.txt'); NaOHl=datal(1:23,1); pHl=datal(1:23,2); % Assign FSP constant A=-0.002; B=0.045; C=1.4 4; % Assign metal co n c e n t r a t i o n Me=520; % mg-Me/kg od Mme=56; % g/mol Mhcl=36.5; % [g/mol] (1% wt of the s o l u t i o n , not metal content) % Assign the f i b e r charge p r o p e r t i e s 152 Qa=5.6816e-005; Qb=0.00011197; Kah=3.2754e-005; Kbh=3.0444e-010; % So l v i n g the set of equations [maf, lamda, Kbind, mhf, mmes, mmef, mahf, mmeaf, t o t a l , f f, vv].=tit 1609 (NaOHl,pHl,A,B,C,Me,Mme,Mhcl) ; % Prepare the t a b l e of the r e s u l t m=l:length(NaOHl); tabl=[m;pHl';Kbind]' f u n c t i o n [maf,lamda,Kbind,mhf,mmes,mmef,mahf,mmeaf, t o t a l , f f , vv] = t i t 1609 (NaOH, pH, A, B, C, Me, Mme, Mhx) % 'tit2.m' i s a s c r i p t m - f i l e that uses Newton's i t e r a t i v e method to % solve the same p a i r of nonlinear equations. % The augmented Jacobian matrix i s c a l c u l a t e d i n the f u n c t i o n m - f i l e %'coeff2.m' while the two nonlinear equations are defined i n % solution.m'. % The v a r i a b l e s used are: % V = volume of the suspension % F = volume of water saturated c e l l u l o s e (FSP) % Cna = T o t a l c a t i o n moles of natrium % A c l = T o t a l anion moles of c h l o r i d e % HpS = H+ i n s o l u t i o n % x x l = fr e e charge [mol/L or mol/kg or mmol/g] % xx2 - Lamda' --> assuming i d e a l s o l u t i o n % The input are: % NaOH = volume of t i t r a n t NaOH added (ml) % pH = pH read from the po t e n t i o m e t r i c t i t r a t i o n % A,B,C = f i t t i n g c o e f f i c i e n t from the FSP measurement t i c g l o b a l V F A c l Cna Cme mhs Qa Qb Kah Kbh % Assign constant ( I n i t i a l background concentration, Oven-Dried f i b e i % and volume of suspension) Vo=60/1000; OD=0.6/1000; Cna_o=0/1000; Acl_o=10/1000; Mnaoh=100/1000; Kw=le-14; Acl=Acl_o*Vo+Me*OD/100/Mhx; Cme=Me*OD/Mme/1000; % Assign T i t r a t i o n Data [L] 60-g suspension [kg OD] 0.6-g od f i b e r [mol/L] 0-mmol NaCl [mol/L] 10-mmol HC1 [mol/L] 100-mmol NaOH % Moles of CI- [mol] % Moles of metal [mol] 153 HpS=l0. A(—pH); % [mol/L s o l u t i o n ] % Assign I n t i a l value-m=length(pH); n=l:m; V=Vo; lamda=l; % I t e r a t i o n f o r each pH fo r i=l:m % Assign FSP constant FSP(i)=A*pH(i) A2+B*pH(i)+C; % [kg water/kg OD] F=FSP(i)*0D; % [kg water] % C a l c u l a t i n g a new volume with the corresponding mole V=Vo-OD+NaOH(i)/1000; % T o t a l suspension volume [L] Cna=Cna_o*Vo+Mnaoh*NaOH(i)/1000; % Moles of Na + [mol] mhs=HpS(i); k=[le-3 1]; %[maf lamda] % C a l c u l a t e the unknowns using Newton's method r e s u l t ( i , :)=newtonnonlinl609(k); ma=result ( i , 1 ) ; l a m = r e s u l t ( i , 2 ) ; Kbind(i)=(V-F+F*lam A2)*(Qa/F-(l+mhs*lam/Kah)*ma)/lam A2/ma A2/ .. (Cme-Qa+(l+mhs*lam/Kah)*ma*F); mnas(i)=Cna/(F*(lam-1)+V); mcls(i)=Acl*lam/(F*(1-lam)+V*lam); mohs(i)=Kw/mhs; mhf(i)=mhs*lam; mnaf(i)=Cna*lam/(F*(lam-1)+V) ; mclf(i)=Acl/(F*(1-lam)+V*lam); mohf(i)=Kw/mhs/lam; mmes(i)=Cme/(V-F+F*lam-2*(1+Kbind(i)*ma A2)) ; mmef(i)=mmes(i)*lam A2; mahf(i)=ma*mhf(i)/Kah; ma f(i)=ma; mmeaf(i)=Kbind(i)*mmef(i)*ma A2; total(i)=ma+mahf(i)+mmeaf(i); lamda(i)=lam; f f ( i ) = F ; vv(i)=V; end toe 154 f u n c t i o n k = newtonnonlinl609 (k) % This i s a Newton's method to solve a set of non-linear equation % Assign parameter f o r Newton's method t o l = l e - 6 ; maxit=200; i t e r = 0 ; maxdx=lelO; % C a l c u l a t i n g the unknowns using Newton's method while iter<maxit & maxdx>tol i t e r = i t e r + l ; maxdx=0; a=coeff2('nonlinl609',k); aa=a(:,1:end-1); dd=det(aa); i f dd==0 f p r i n t f ( ' M a t r i x i s s i n g u l a r ' ) r e t u r n e l s e dk=gauss (a); end k=k+dk; maxdx=max(abs(dk)); end % E r r o r message i f i t e r a t i o n exceed the maximum number of i t e r a t i o n i f iter>maxit fprintf('\nMaximum i t e r a t i o n exceed! \n') end f u n c t i o n a = c o e f f 2 ( f , x ) % ' c o e f f 2 . m ' i s a f u n c t i o n m - f i l e that c a l c u l a t e s the augmented % Jacobian matr i x r e q u i r e d f o r the s o l u t i o n of a set of nonl i n e a r % equations having the general form: % f i ( x l , x 2 , . . . , x n ) = 0, i=l , 2 , . . . , n % coeff2.m evaluates the p a r t i a l d i f f e r e n t i a l s using f i n i t e % d i f f e r e n c e approximations. ' f' i s the dummy name of the f u n c t i o n % m - f i l e that contains the I.h.s. of each nonlinear equation. n=length(x); np=n+l; delx=le-6*x; f o r i = l : n a ( i , n p ) = - f e v a l ( f , i , x ) ; f o r j = l : n xtemp=x(j); x ( j ) = x ( j ) + d e l x ( j ) ; f t e m p = f e v a l ( f , i , x ) ; x(j)=xtemp; a ( i , j ) = (ftemp + a ( i , n p ) ) / d e l x ( j ) ; end end f u n c t i o n y = n o n l i n l 6 0 9 (i,k) 155 % 'nonlin2.m' i s a f u n c t i o n m - f i l e that defines the p a i r of nonlinear % equations with 'coeff2.m' c a l c u l a t i n g the Jacobian matrix using % f i n i t e d i f f e r e n c e s . % The input are: % x l = maf [mol/L or mol/kg or mmol/g] % x2 = Lamda' --> assuming i d e a l s o l u t i o n g l o b a l V F A c l Cna Cme mhs Kw Kah Kbh Qa Qb ma=k(1); lam=k(2); phi=mhs+Cna/(F*(lam-1)+V)-Acl*lam/(F*(1-lam)+V*lam)-Kw/mhs; omega=mhs *lara+Cna*lam/(F*(lam-1)+V)-Acl/(F*(1-lam)+V*lam)-Kw/mhs/lam; Kmea=(V+F*(lam A2-l))*(Qa/F-(l+mhs*lam/Kah)*ma)/lam A2/ma A2/(Cme-Qa+(l+mhs*lam/Kah)*ma*F); mmes=Cme/(V-F+F*lamA2*(l+Kmea*maA2)) ; i f i==l y=omega-ma+2*mmes*lamA2; el s e y=phi+2*mmes; end 156 APPENDIX K: Iron Partitioning Prediction Metal partitioning program require the input from the previous program listed in appendix I and J, which is the fiber charge and the binding constant. A potentiometric titration data of acid washed chelated fiber with a known amount of iron addition was used to adjust the pH. The sodium hydroxide needed in adjusting the pH of the suspension. The program and all sub-routine are listed below. 1. partitionfe.m The main program. 2. titl909a.m Sub-routine to calculate the partitioning prediction. 3. newtonnonlinl909a.m Newton's sub-routine to solve non-linear equations. 4. nonlinl909a.m The objective function for metal partitioning. % p a r t i t i o n f e . m i s an m - f i l e that i s used to p r e d i c t the metal i o n % p a r t i t i o n i n g using the f i b e r charge p r o p e r t i e s and bi n d i n g constant. % The p a r t i t i o n i n g p r e d i c t i o n consider both e l e c t r o s t a t i c i n t e r a c t i o n % and chemical b i n d i n g i n t e r a c t i o n . % From the chemical b i n d i n g program, the binding constant was found at % negatives, so i n t h i s p a r t i t i o n i n g model, the binding constant i s set % at zero, meaning the i n t e r a c t i o n of f i b e r - m e t a l i s e l e c t r o s t a t i c a l l y . % This m - f i l e c a l l s the sub-routine t i 11.90 9a. m to solve a set of % equations. c l e a r a l l g l o b a l Kw Kah Kbh Qa Qb A c l Cme Kw=le-14; % Assign T i t r a t i o n Data with metal datal=load('bbswfe.txt'); NaOHl=datal(l:end,1); pHl=datal(1 rend,2); % Assign FSP constant A=-0.002; B=0.045; C=l.4 4; % Assign metal co n c e n t r a t i o n Me=520; % mg-Me/kg od Mme=5 6; % g/mol Mhcl=36.5; % [g/mol] (1% wt of the s o l u t i o n , not metal content) 157 % Assign the f i b e r charge p r o p e r t i e s Qa= 4 . 4027e-005; Qb= 3. 2225e-005; Kah= 5 . 9218e-005; Kbh= 7 .1731e-010; % C a l c u l a t i n g the metal i o n p a r t i t i o n i n g [maf, mbf, mahf, mbhf,Total,lamda,mhf,mmes,mmef,mcls,mclf,Aclcal,FSP,ff,vv,mnas,m n a f ] = t i t l 9 0 9 a (NaOHl,pHl,A,B,C,Me,Mme,Mhcl); % Prepare the t a b l e of'the p a r t i t i o n i n g p r e d i c t i o n m=l:length(NaOHl); tabl=[m;pHl';maf,-mbf,-mahf,-mbhf;Total] ' tab2=[m;pHl';mmes;mmef;Aclcal;lamda]' % P l o t t i n g the r e s u l t plot(pHl,mmes*1000.*(vv-ff)*Mme*l/0.6e-3,'*',pHl,mmef*1000.*ff*Mme*l/0.6e-3,'+',pHl,ones(1,length(pHl))*Cme*1000*Mme*1/0.6e-3) xlabel('pH-S') ylabel('Moles of i r o n (mg/kg-od)') t i t l e ( ' B S W i r o n p a r t i t i o n i n g at 520ppm') f u n c t i o n [maf,mbf,mahf,mbhf,Total,lamda,mhf,mmes,mmef,mcls,mclf, A c l c a l , FSP, f f , vv,mnas,m naf] = t i t l 9 0 9 a (NaOH,pH,A,B,C,Me,Mme,Mhx) % 'titl909a.m' i s a s c r i p t m - f i l e that uses Newton's i t e r a t i v e method % to solve a set of nonl i n e a r equations. % The augmented Jacobian matrix i s c a l c u l a t e d i n the f u n c t i o n m - f i l e % ' coeff2.ni 1 while the two nonlinear equations are defined i n % nonlinl909a.m'. ' % The v a r i a b l e s used are: % V = volume of the suspension % F = volume of water saturated c e l l u l o s e (FSP) % Cna = T o t a l c a t i o n moles of natrium % A c l = T o t a l anion moles of c h l o r i d e % HpS = H+ i n s o l u t i o n % The input are: % NaOH = volume of t i t r a n t NaOH added (ml) % pH = pH read from the po t e n t i o m e t r i c t i t r a t i o n % A,B,C = f i t t i n g c o e f f i c i e n t from the FSP measurement t i c g l o b a l V F A c l Cna Cme mhs Qa Qb Kah Kbh % Assign constant ( I n i t i a l background concentration, Oven-Dried f i b e r % and volume of suspension) Vo=60/1000; % [L] 60-g suspension OD=0.6/1000; • % [kg OD] 0.6-g od f i b e r 158 Cna o=0/1000; % [mol/L] 0-mmol Na.Cl A c l 0=10/1000; '0 [mol/L] 10-mmol HC1 Mnaoh=100/1000; 9-o [mol/L] 100-mmol NaOH Kw=le-14; Acl=Acl_o*Vo+Me*OD/100/Mhx; o. ~o Moles of C l - [mol] Cme=Me*OD/Mme/1000; 0, Moles of metal [mol] % Assign T i t r a t i o n Data HpS=10. A(-pH); c. 'o [mol/L solution]: % Assign I n t i a l value m=length(pH); n=l:m; V=Vo; lamda=1; % I t e r a t i o n f o r each pH f o r i=l:m % Assign FSP constant FSP(i)=A*pH(i) A2+B*pH(i)+C; o. o [kg water/kg OD] F=FSP(i)*0D; 0. "O [kg water] % C a l c u l a t i n g a new volume with the corresponding mole V=Vo-OD+NaOH(i)71000; % T o t a l suspension volume [L] Cna=Cna_o*Vo+Mnaoh*NaOH(i)/1000; o, o Moles of Na+ [mol] mhs=HpS(i); k=[4.le-5 1]; o„ "o [mcls lamda] % C a l c u l a t e the four unknowns using Newton's method result(i,:)=newtonnonlinl909a(k) r mcl=result ( i , 1 ) ; lam=result ( i , 2 ) ; mnas(i)=Cna/(F*(lam-1)+V); mcls(i)=mcl; mohs(i)=Kw/mhs; mhf(i)=mhs*lam; mnaf(i)=mnas(i)*lam; m c l f ( i ) = m c l s ( i ) / l a m ; mohf(i)=Kw/mhf(i); mmes(i)=Cme/(V+F*(lam A2-l)) ; mmef(i)=mmes(i)*lam A2; maf(i)=Qa*Kah/F/(Kah+mhf(i)); ' mbf(i)=Qb*Kbh/F/(Kbh+mhf(i)); mahf(i)=maf(i)*mhf(i)/Kah; mbhf(i)=mbf(i)*mhf(i)/Kbh; matotal(i)=maf(i)+mahf(i); mbtotal(i)=mbf(i)+mbhf(i); T o t a l ( i ) = m a t o t a l ( i ) + m b t o t a l ( i ) ; lamda(i)=lam; • A c l c a l ( i ) = m c l s ( i ) * ( V + F * ( 1 / l a m - l ) ) ; f f ( i ) = F ; vv(i)=V; end toe 159 f u n c t i o n k = newtonnonlinl909a (k) % Assign parameter f o r Newton's method t o l = l e - 6 ; maxit=200; it e r = 0 ; maxdx=lelO; % C a l c u l a t i n g the unknowns using Newton's method while iter<maxit & maxdx>tol i t e r = i t e r + l ; maxdx=0; a=coeff2('nonlinl909a',k); aa=a(:,1:end-1); dd=det(aa); i f dd==0 f p r i n t f ( ' M a t r i x i s s i n g u l a r ' ) r e t u r n e l s e dk=gauss(a); end k=k+dk; maxdx=max(abs(dk)); end % E r r o r message i f i t e r a t i o n exceed the maximum number of i t e r a t i o n i f iter>maxit fprintf('\nMaximum i t e r a t i o n exceed! \n') end f u n c t i o n y = nonl i n l 9 0 9 a ( i , k ) % 'nonlin2.m' i s a f u n c t i o n m - f i l e that defines the p a i r of % equations with 'coeff2.m' c a l c u l a t i n g the Jacobian matrix % f i n i t e d i f f e r e n c e s . n o n l i n e a r using % This equation i s f o r e l e c t r o s t a t i c i n t e r a c t i o n only % The input are: % x l = maf [mol/L or mol/kg or mmol/g] % x2 = Lamda' —> assuming i d e a l s o l u t i o n g l o b a l V F Cna Cme mhs Kw Qa Qb Kah Kbh mcls=k(l); lam=k(2); mnas=Cna/ (F* (lam-1) +V) ; mmes=Cme/ (V+F* (lam / v2-l) ) ; mohs=Kw/mhs; mhf=mhs*lam; mnaf=mnas*lam; mmef=mmes*lamA2; mohf=Kw/mhf; mclf=mcls/lam; maf=Qa*Kah/F/(Kah+mhf); mbf=Qb*Kbh/F/(Kbh+mhf); i f i==l y=mhs+mnas+2*mmes-mohs-mcls; el s e y=mhf+mnaf+2*mmef-mohf-mclf-maf-mbf;' end 160 

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