Course Number: ETD 0708102, Fall 2008

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MODELING ADSORPTION OF CANE SUGAR SOLUTION COLORANT IN PACKED-BED ION EXCHANGERS A Thesis Submitted to the Graduate Faculty of the Louisiana State Unversity and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering in The Department of Chemical Engineering by Hugh Anthony Broadhurst B.S., University of Natal, 2000 August, 2002...

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ADSORPTION MODELING OF CANE SUGAR SOLUTION COLORANT IN PACKED-BED ION EXCHANGERS A Thesis Submitted to the Graduate Faculty of the Louisiana State Unversity and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering in The Department of Chemical Engineering by Hugh Anthony Broadhurst B.S., University of Natal, 2000 August, 2002 ACKNOWLEDGEMENTS The author wishes to thank all of the staff at the Audubon Sugar Institute that had an input on the project. Particular thanks must be given to Dr P.W.Rein for his guidance and motivation, Brian White and Lee Madsen for their expertise in the field of HPLC analysis, and Len Goudeau and Joe Bell for their assistance in the crystallization test. Thanks go to the sponsors, Tongaat-Hulett Sugar Limited and Calgon Carbon Corporation for providing the funds for this research. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS........................................... ii GLOSSARY OF TERMS.................................................. v NOMENCLATURE...........................................vii ABSTRACT....................................................................... ix CHAPTER 1. INTRODUCTION......................................... 1 1.1. The White Sugar Mill Process....................... .... 1 1.2. Research Objectives.......................... .....4 2. BACKGROUND....................................... 6 2.1. Cane Sugar Colorant................................. ..... 6 2.2. Quantifying Colorant.................................... ..... 8 2.3. Removal of Cane Sugar Colorant..................... . 10 2.4. Color Transfer in Crystallization.......... ......... 17 3. THEORY............................................... 20 3.1. Axially Dispersed Packed-Bed Adsorption Model.20 3.2. Plug Flow Adsorption Model................... ......... 23 3.3. Numerical Solution Technique................... ... 28 4. MATERIALS AND METHODS................. .................31 4.1. Experiments................................ 31 4.2. Sample Analysis......................................................................... 38 5. RESULTS AND DISCUSSION...................... ............. 45 5.1. Color Formation Investigation.................. ..... 45 5.2. Ultrafiltration.......................... 54 5.3. Strong-Acid Cation Resin....................................................... 56 5.4. Weak-Base Anion Resin............................................................. 66 5.5. Decolorizing Resin............... ................. 71 5.6. Regeneration Aids.......................................... 75 5.7. Color Transfer in Crystallization............................ 77 6. CONCLUSIONS........................................... 80 6.1. GPC as an Analytical Tool..................................... 80 6.2. Validity of the Plug-Flow Model............................ 80 6.3. SAC Resin.................. ........... 81 6.4. WBA Resin................................ .... 82 6.5. Decolorizing Resin......................... ....... 83 6.6. WSM Process Design........................... ..... 83 6.7. Future Research Directions.................... ........84 iii REFERENCES.................................................................. 86 APPENDIX A. SAMPLE CALCULATIONS............ ............. 91 B. SAC RESIN RESULTS.................. ........ 102 C. WBA RESIN RESULTS........................... ..... 120 D. DECOLORIZING RESIN RESULTS. 138 E. MATLAB CODE......... 151 VITA...................................................................... 161 iv GLOSSARY OF TERMS Affination The process of removing the molasses film from sugar crystals with a saturated sugar solution Ash ABS Breakthrough Inorganic dissolved solids Absorbance When the adsorbent can no longer absorb all of a solute species from the feed. Brix Chromatography Total dissolved solids (%m/m) A term for methods of separation based upon the portioning of a solute species between a stationary phase and a mobile phase DECOL GPC HPLC ICUMSA Decolorizing resin Gel Permeation Chromatography High performance liquid chromatography International Commission for Uniform Methods of Sugar Analysis MW Pol Purity RI SAC WBA Molecular weight Apparent sucrose content (% m/m) Percent of pol (or true sucrose) to brix Refractive index Strong-acid cation ion exchange resin Weak-base anion ion exchange resin v WSM White Sugar Mill The process of making white sugar directly from sugarcane using ultrafiltration and ion exchange. vi NOMENCLATURE Symbol A As C C* C0 Ci da dp D DAB E F JD k' kLa kc kr(T) k0 K K(t) KC0 Keq K0, K1 L MA n q q0 Q R Re Sc St t t0 T u u0 ui Vbed Vliquid Vresin Description Column cross-sectional area Sample absorbance at 420nm Concentration in bulk fluid Concentration of fluid in equilibrium with adsorbent Feed concentration Concentration of component i FEMLAB Time derivative coefficient matrix Particle diameter Axial dispersion coefficient Diffusivity of component A in B Activation energy FEMLAB Remaining terms in PDE vector Chilton-Colburn analogy J-factor Effective mass transfer coefficient Mass transfer coefficient Mass transfer coefficient in Geankoplis correlation Reaction rate Term in Arrhenius expression Adsorption parameter q = K.C* Time varying adsorption parameter Adsorption parameter based on initial concentration Equilibrium adsorption parameter Parameters in K(pH) Column length Molecular weight FEMLAB Outward normal on domain boundary Concentration on solid phase Initial resin concentration Volumetric fluid flow rate FEMLAB Dirichlet boundary condition vector or Universal Gas Constant Reynolds number Re = dui/ Schmidt number Sc = /DAB Stanton number St = k'L/ui Time variable Peak time of Gaussian distribution or Initial time parameter in batch tests Temperature FEMLAB Dependent variables vector Superficial fluid velocity Interstitial fluid velocity Volume of resin in packed-bed (voidage measurement) Volume of liquid (batch tests) Resin volume measured as a packed-bed in a measuring cylinder (batch tests) Units m2 AU mV mV mV g/ml or mV m m2/min m2/s J/mol [-] 1/min 1/min m/s 1/min 1/min [-] [-] [-] [-] [-] M [-] AU AU m3/min [-] [-] [-] min min K m/min m/min ml ml ml vii Symbol VT Vwater xi(t) xmax X(t) z Description Total volume (voidage measurement) Volume of water added (voidage measurement) Gaussian distribution i Maximum value of a Gaussian distribution Cumulative Gaussian distribution Distance from top of column Units ml ml m Symbol Description Time constant in batch tests Packed-bed void fraction Dimensionless relative time scale variable FEMLAB - First derivatives of distance variables vector Dimensionless distance Rate constant in K(pH) Dynamic viscosity Density Standard deviation in Gaussian distribution Relative time scale variable FEMLAB PDE domain Units 1/min [-] [-] [-] Pa.s kg/m3 min Subscript i 0 Description Component or interstial Feed/initial or superficial viii ABSTRACT The removal of cane sugar solution colorant by packed-bed ion exchangers was modeled using a linear driving force (LDF) adsorption model. Adsorption of colorant is of interest to the developers of the White Sugar Mill (WSM) process as it is a complex subject. The problem is that color is an indiscrete mixture of many components making it difficult to measure and even more challenging to model. Colorant formation was investigated using gel permeation chromatography (GPC) with the objective of developing a method to define pseudo-components representative of cane sugar solution colorants. WSM is a process for producing white sugar directly from sugarcane in the raw sugar mill by using ultrafiltration and continuous ion exchange technology. The ion exchange resins employed were a strong acid cation (SAC) resin in the hydrogen form, a weak base anion (WBA) resin in the hydroxide form and a decolorizing resin in the chloride form. Decolorization using the three resins was then analyzed using the GPC pseudo-component technique. Batch testing of the resin allowed the development of equilibrium isotherms that could be substituted into a standard LDF model. Column testing was then performed to investigate the dynamics of adsorption of colorant in packed-beds. Linear isotherms were measured for each of the three resins, indicating that the colorant is dilute. Results indicated that a plug-flow model with a constant linear isotherm was sufficient in all cases except the SAC resin. The SAC adsorption parameter decreased sharply as the pH increased, causing colorant to be ix desorbed from the resin. This situation must be avoided if optimal decolorization is to be achieved. The adsorption models can be utilized in the design of a WSM process to optimize the decolorizing capacity of the resins. x CHAPTER 1. INTRODUCTION 1.1 The White Sugar Mill Process 1.1.1 The Production of White Cane Sugar The production of white cane sugar is currently a two-step operation. Raw sugar is light brown in color and is produced in sugar mills. Mills are located close to the cane growers to minimize cane degradation and transportation costs. The raw sugar is subsequently transported to a refinery where the remaining impurities are removed. Figure 1.1 shows the basic steps in the production of raw sugar from sugarcane. Sucrose is first extracted from sugar cane with water, by counter-current milling or cane diffusion. The juice is screened, heated to its boiling point, and then flashed. Suspended solids and colloidal materials are then precipitated with milk of lime (calcium hydroxide solution) and settled in a clarifier. The resulting clear juice is evaporated to approximately 65% dissolved solids in a multiple effect evaporator train. Sugar is then crystallized from the syrup in a three-stage crystallization process. After each crystallization step, sugar crystals are separated from the mother liquor in centrifuges. The raw sugar is then transported to the refinery where it is dissolved, purified and re-crystallized to white sugar. Cane Extraction DJ Heating MJ Clarification CJ Evaporation Sy. 3 Stage Crystallization Ma. Centrifugation RS Mol Key: DJ = Draught juice; MJ = Mixed Juice; CJ = Clear Juice; Sy. = Syrup; Ma. = Massecuite RS = Raw sugar; Mol. = Final Molasses Figure 1.1: Raw sugar mill flowsheet 1 1.1.2 The White Sugar Mill There are three main areas in which the profitability of the raw sugar mill may be increased (Fechter et al., 2001): 1. Improve the quality of the sugar produced 2. Increase overall recovery of sugar 3. Make use of products in the molasses The sugar refinery is a simple and relatively low cost operation except for the significant costs in transporting raw sugar from the mill and sugar losses in the refining process. These costs could be removed by producing white sugar at the raw sugar mill. Recent advances in membrane and continuous ion exchange technology have been utilized by Tongaat-Hulett Sugar Limited and S.A. Bioproducts Limited in the development of a process to produce white sugar directly in the raw sugar mill (Rossiter, 2002). The process design may be incorporated into an existing raw sugar mill (see Figure 1.2). Cane Extraction Juice Heating 4 Stage Crystallization Clarification Evaporation Centrifugation White Sugar Whitestrap Molasses Ultrafiltration Refrigeration & HX Cation ISEP Anion ISEP Decolorization Figure 1.2: White sugar mill flowsheet 2 Juice from the existing first evaporation effect at 20 to 25% brix is first ultrafiltered. This removes high molecular weight material from the syrup that would otherwise irreversibly foul the ion exchange resins. The retentate (the material rejected by the membrane) may be used as a feedstock to a neighboring distillery or may be recycled to the clarifiers. Impurities leave the system in the clarifier mud. The permeate from the membrane unit must be refrigerated to 10oC as in the subsequent ion exchange separations low pH conditions are experienced. Under acidic conditions, sucrose breaks down to fructose and glucose. This reaction is termed inversion in the sugar industry. The heart of the process is the continuous ion-exchange demineralization using Calgon Carbon Corporations ISEP technology (Fig 1.3). An ISEP is similar to a conventional Simulated Moving Bed (SMB) that uses switching valves to achieve a continuous process. The ISEP differs in that it uses a rotating carousel of packed-beds about a central feed valve that is made up of a stationary and rotating element. ISEPs have been used in the South African sugar industry at the TongaatHulett Sugar Refinery to deash high-test molasses (HTM). The inorganic constituents of sugar solutions are commonly termed ash and so the demineralization resins have been named deashing resins. Two demineralization resins, a strong acid cation (SAC) and a weak base anion (WBA), are used in series to remove inorganic and charged organic impurities (primarily organic acids). Despite some decolorization, the resulting high purity juice still has significant color that must be removed in the decolorization ISEP. The decolorizing resin used is a sugar industry standard, a strong base anion resin in the chloride form. The decolorized juice produced from the WSM process is of 3 such high purity and low color that four crystallization stages maybe performed. The benefits of the process include (Rossiter, 2002): i. ii. iii. iv. v. Increase in yield Increase in sugar quality: white sugar not raw sugar is produced Production of high-grade molasses (termed whitestrap molasses) No fouling in evaporators and vacuum pans Higher heat transfer coefficients in pans and evaporators Figure 1.3: A pilot scale ISEP 1.2 Research Objectives Ion exchange demineralization has been shown to remove 95% of the ash content of the ultrafiltered syrup (Fechter, 2001). In parallel with the ash removal, is an 80% reduction in color. It is of significant interest to the process developers to investigate the removal of color by ion exchange resins. If the color adsorption could be modeled then the process design could be optimized to make best use of 4 the resins. operation. This may reduce the currently high loading on the decolorizing There is currently no complete model of cane sugar colorant (Godshall & Baunsgaard, 2000). The sugar industry standard color measurement groups all colored bodies as one component. This is a major assumption. For modeling purposes, it would be useful to define pseudo-components that represent cane sugar colorant. An investigation into cane sugar color formation will give valuable insights on how to define these components. Interaction between components could be assumed negligible since colorants are so dilute. This would allow the use of a number of single component models to represent adsorption of color onto the resins. The specific goals in the research are: Develop an analysis technique to measure color Use this analysis to investigate color formation Apply results from the color formation trials to define pseudocomponents to be used in modeling Perform batch adsorption tests to investigate the resin equilibrium properties Develop a packed-bed adsorption model using the equilibrium properties Perform column loading experiments and regress model parameters for each resin 5 CHAPTER 2. BACKGROUND 2.1 2.1.1 Cane Sugar Colorant Color in the Sugar Industry The goal of any production process is to produce as large a quantity of product within the quality criteria. One of the most important criteria in the sugar industry is the color of both raw and white sugar. Consumers and other users (e.g. carbonated beverage manufacturers) of white sugar expect a white product. Raw sugar (light brown in color) produced in the mills is also subjected to a quality standard. Higher color raw sugar requires more effort on behalf of the refiner to produce a white product. 2.1.2 Types of Colorant Sugar colorant is unfortunately not one single molecular species. It consists of a wide range of materials each with its own molecular weight (MW), pH sensitivity, charge, and chemical structure (Godshall & Baunsgaard, 2000). Research into the complex organic nature of cane sugar colorants has been a major area of interest in the sugar industry since its beginning. Understanding more about the character of color allows for fine-tuning existing separation processes and for designing new and better techniques for its removal. Colorants are often named from their origin and mechanisms of formation (Godshall et al, 1988). Caramelization and alkaline degradation are similar thermal mechanisms except that alkaline degradation occurs at high pH and forms much darker colorant (Godshall, 2000). The Maillard reactions occur throughout the factory and have many complex pathways (Van der Poel et al, 1998). They proceed 6 under almost all conditions, as reducing sugars and amines or amino acids are always present except in the purest of solutions. Iron also plays an important role, particularly in plant-derived colorants (Godshall, 1996). Many polyphenolic compounds found in cane juice are able to produce highly colored iron complexes. It must be noted that just as important as the colorants themselves are the compounds that are color precursors. These, often colorless, compounds can react to form highly colored species. Table 2.1 summarizes the general types of colorant found in a cane sugar mill (adapted from Godshall, 2000). Cane sugar colorant is a difficult issue as it is so difficult to define. Table 2.1: Types of sugar colorants General Characteristics Low MW colorless to light yellow precursors; darken at high pH; oxidize to form yellow and brown polymers; react with polyphenol Colorant Type Phenolic oxidase to form light yellow to dark brown colorants. Darken in presence of iron. The result of thermal degradation of sucrose; low net charge; wide Caramel color range from yellow to brown; MW 500 to about 1,000; MW and color increases as thermal destruction proceeds. Alkaline Degradation Products (ADPs) Melanoidin Similar to caramels, but much darker in color; form at high pH. Maillard reaction reaction products of amino acids with reducing sugars; reaction occurs rapidly at alkaline pH; products are dark brown. Polysaccharides formed in cane have phenolic groups and dicarboxylic Colorant Polysaccharide Complex acid functionalized lipids that can bind with colorant to make a very high MW product. Occludes preferentially into the crystal. 7 2.2 2.2.1 Quantifying Colorant ICUMSA Color The industry standard sugar solution color measurement is the International Commission for Uniform Methods of Sugar Analysis (ICUMSA) color method. A sugar juice free of suspended solids, corrected to pH 7, and of known solids concentration is analyzed using a spectrophotometer set to 420nm (SASTA1 laboratory manual). The color is calculated as follows: ICUMSA 420 color = AS 10,000 bc (2.1) The absorbance, AS , is divided by the product of the dissolved concentration, c (g/ml), and the cell width, b (mm). ICUMSA 420 color is a measurement to give an indication of the overall color of the juice. This is useful in evaluating the color removal performance of a process. Clearly, no information is given about the specific types of colorants present in the sample. Knowing the types of colorant is useful, for example, if a syrup has a high concentration of a substance with no affinity for the sugar crystal it will be of high ICUMSA color. According to the ICUMSA color the syrup would produce a high color product but in practice it would not. Similarly, low ICUMSA color mother liquor can produce sugar of higher color than would normally be expected. 2.2.2 Gel Permeation Chromatography Gel permeation chromatography (GPC) is a liquid chromatography method that separates a sample based on molecular size. A small sample is injected into a 1 South African Sugar Technologists Association 8 stream of a buffer solution that flows into a column packed with a gel of precisely controlled pore size. The gel pores are arranged in such a size distribution that small molecules are able to diffuse into the pores whereas larger molecules are excluded. A detector is used at the end of the column to measure the concentration of the material exiting the column. Typically, a refractive-index (RI) or an ultraviolet-visible (UV-VIS) detector is used. The analysis may be calibrated by injecting standards of precise molecular weight into the column. If the samples to be analyzed are of the same molecular size and shape as the standards, their weights may be read off the calibration curve. The buffer solution masks the gel from any ionic behavior of the sample, as no interaction is wanted between the analyte and the stationary phase. Many authors have made use of GPC to analyze sugar solutions, including Shore et al (1984), Godshall et al (1988, 1992a, 2000), Bento et al (1997) and Saska & Oubrahim (1987). Of particular interest is the work of Godshall (1992a). The removal of high molecular weight colorants in batch experiments was measured using GPC. The resulting chromatograms all had three distinct peaks. Each peak was treated as a single pseudo-component to investigate the decolorizing ability of a number of different adsorbents. Saska & Oubrahim (1987) report that GPC is a reliable method to investigate the molecular weight effects of decolorization mechanisms. The WSM process has been investigated using this principle except that it was applied to the dynamics of the process and not just the overall decolorization. 9 2.2.3 Advanced Techniques The fluorescent nature of sugar colorant has been extensively studied (Carpenter & Wall, 1972). Recently using advanced equipment and techniques researchers have been able to use this property to provide more information about sugar colorants (Bro, 1999, Baunsgaard, 2000 & Godshall & Baunsgaard, 2000). This research is still in its beginnings and is outside the scope of this investigation. Gas chromatography with mass selective detection (GC-MS) has also been used in the identification of colorants and other impurities (Letcher & Whitehead, 1996, Godshall, 1996 & Papageorgiou, 1999). The biggest downfall of this method is that most of the highly colored compounds have a molecular weight greater than 1,000 (Godshall, 1996), which is the operating limit of most gas chromatographs. 2.3 2.3.1 Removal of Cane Sugar Colorant Membrane Filtration Membrane filtration is a pressure filtration process whereby a number of components are separated by a membrane of a precise pore size. Any material of molecular diameter greater than the pore diameter will be rejected by the resin. The pore size is often represented as a molecular weight cut-off (MWCO). The stream passing through the membrane, termed the permeate, is purified by removal of larger material to the retentate stream. Membranes are typically constructed of ceramic, stainless steel or polymeric materials. It is important that the membrane is able to withstand high cross-membrane pressures, that is the differential pressure between feed and permeate side of the membrane. Higher pressures give rise to higher fluxes but lead to increased operating costs. Chemical resilience is also 10 important, as the membrane must be able to withstand the harsh cleaning chemicals used to remove buildup of foulants in the pores. In many industrial separation processes membrane filtration has been used effectively. This unit operation has, however, only been incorporated into one sugar production facility (in Hawaii, using the New Applexion Process), despite considerable interest by many researchers (Steindl, 2001). The Sugar Research Institute in Australia has been researching ultrafiltration since 1975. Membrane filtration can drastically increase sugar quality, and give rise to higher crystal growth rates (Crees, 1986) but it was concluded that capital and operating costs were excessive. Suspended solids, colloidal particles and soluble high molecular weight material can be removed using membrane filtration. Average performance data (Steindl, 2001) show the effectiveness of this unit operation in removing impurities from clarified juice: Purity rise Removal of Turbidity Dextran Starch Total polysaccharides ICUMSA Color 95% 98% 70% 80% 25% 0.45 units Membrane suppliers offer a wide range of pore sizes, however no major difference in color removal is experienced (Crees, 1986; Kochergin, 1997; Patel, 11 1991) unless the pore size is reduced to below 20,000MW. Use of the lowest MWCO is not practical as the sugar produced is not of significantly less color than of sugar produced from membranes of higher MWCO (Cartier et al, 1997). Membranes may be sized primarily on minimizing the membrane area (capital cost) and maximizing the permeate flux (Fechter et al, 2001). One of the problems associated with membrane separation is that the retentate stream contains sucrose. It is not economic to simply dispose of this stream and so a number of researchers have proposed methods to recycle the retentate or use it for some other purpose. Proposals include: Dilution of the retentate stream followed by a secondary filtration (Steindl, 2001) Clarification of the retentate using a flotation clarifier (Steindl, 2001) Recycling the retentate to the existing settling clarifiers (Rossiter et al, 2002) Using the retentate as a feed to an attached ethanol facility (Rossiter et al, 2002) Membrane technology may be applied to raw cane sugar mills after the lime defecation and clarification stage. Steindl (2001) reports that raw juice clarification removes the insoluble solids and some soluble material. The lower impurity concentration found in clarified juice allows higher filtration fluxes and reduces the risk of erosion on the membrane surface. 12 Urquhart et al, (2000) report that filtering clarified juice with a membrane unit allows the production of high pol, low color sugar to satisfy the Australian QHP (Queensland High Pol) standard. Another installation allowed the production of a super VLC (very low color) sugar (Kwok, 1996). High quality sugar produced using this technique allowed the Crockett refinery in California to eliminate both the affination and the remelt stations. Balakrishnan et al (2000) investigated the use of ultrafiltration to produce a plantation white sugar with a color of approximately 150 ICUMSA units. Ultrafiltration has also been suggested as a pretreatment since it generally cannot produce a syrup of high enough quality to directly crystallize white sugar (Steindl, 2001). Ion exchange and chromatography require a very clean feed, to protect the resin from fouling. Membrane filtration has proved to be a very effective pretreatment (Fechter et al, 2001), allowing the use of a single set of resin for a period longer than the length of an average South African season (about 9 months). Saska et al (1995) proposed the use of nanofiltration following ultrafiltration to produce an upgraded syrup from which white sugar could be crystallized. Monclin and Willett (1996) proposed using adsorptive decolorization of ultrafiltered juice. Amalgamated Research Inc. has developed and patented a direct white sugar production process using ultrafiltration followed with chromatography (Kearny, 1999a). Lancrenon et al (1998) propose the use of microfiltration in the sugar refining process. Despite the numerous investigations into membrane separations in the cane sugar industry there has been no widespread adoption of the unit operation (Steindl, 13 2001). It is likely that the next major installation of a membrane unit will be as a pretreatment to either ion exchange or chromatography. The use of ultrafiltration in the sugar industry is limited by economics. This unit operation will not make an appearance in the sugar industry until a process with proven economics is developed. It is likely that ultrafiltration will be used in series with another separation process. 2.3.2 Decolorization with Ion Exchange Resins Since the 1970s, with the advent of macroporous strong-base anion ion exchange resins, ion exchange resins in the chloride form have become the sugar refinery workhorse decolorizer. Despite increased effluent disposal problems, the lower capital and operating costs of fixed-bed ion-exchangers have caused them to replace activated carbon and bone char decolorization (Van der Poel et al, 1998). Factors affecting the ion exchange process are: Color to ash ratio Color content Type of colorant Impurity concentration (viscosity) Sugar colorants are fixed to strong-base anion exchange resins by ionic bonding and/or by hydrophobic interactions (Bento et al, 1996). Bento (1996) investigated the removal of colorants by Rohm & Haas Amberlite 900 resin: Caramels Melanoidins Alkaline degradation Products 62.8% 97.5% 98.0% 14 Caramels are least retained by the resin, as they are relatively uncharged whereas the other colorants are anionic in alkaline medium. Morley (1988) made a detailed study of fixed-bed decolorizing ion exchangers. Color was measured by the ICUMSA color method. An analytic mathematical model was derived assuming no axial dispersion and constant linear isotherms. Model parameters were estimated from experimental data giving an average correlation coefficient of 0.91. Batch tests were also performed to measure the equilibrium properties of the resin, expressed as an isotherm. A Langmuir isotherm was measured but in the concentration (color) range used, a linear fit was deemed acceptable. This model was used to improve the Tongaat-Hulett refinery in Durban, South Africa. The model does however, display the shortcomings of the ICUMSA color method on which it is based. An early breakthrough of a component that is strongly transferred to the crystal on crystallization could easily go unnoticed. 2.3.3 Chromatography Sugar solutions may also be purified using chromatography. This is a technique where a pulse of sugar solution is injected into a mobile phase that passes through a media, typically an ion exchange resin. In a favorable case different components in solution have differing affinities for the resin. If a pulse of material is introduced at the top of a packed-bed, into the mobile phase, the components will move down the columns at differing speeds causing separation. For an industrial operation, a simulated moving bed (SMB) design is often used, as it simulates a counter-current separation process, reducing the amount of resin required. The 15 French process engineering company, Applexion, have designed a process to give a column efficiency increase of 100% (Paananen & Rousset, 2001). There are numerous possibilities in applying chromatographic separation techniques to the cane sugar industry (Paillat & Cotillon, 2000; Kearney, 2002). Desugarization of final molasses is possible providing that the feed material is free of suspended solids. This is a significant problem for cane final molasses desugarization as the pretreatment to remove the suspended solids is difficult (Kearney & Kochergin, 2001). This process is more effective in the beet sugar industry as higher final molasses purities are experienced helping the process economics. Kearney & Kochergin (2001) report that the process economics are marginal for cane sugar operations. One of the problems associated with sucrose recovery from final molasses is the inhibiting effect of divalent cations, particularly calcium. Softening is also required as a pretreatment. A similar process is described by Lancrenon et al (1998) for the chromatographic separation of refinery molasses. Another option is the removal of non-sucrose products from molasses. Glycerin and other products can be recovered from cane molasses stillage after the production of ethanol (Kampen & Saska, 1999). Peacock (1999) showed that syrup rich in invert sugars could be separated from final molasses. Unlike, sucrose recovery, the above-mentioned processes were not affected by divalent cations in laboratory and pilot scale studies. The economics of these processes is determined by the product prices (Kearney & Kochergin, 2001). 16 Chromatography of refinery syrup is also possible. Kearney (1999b) showed that refinery syrup at 84% purity could be upgraded to 90% with 90% color removal and 96% invert sugar removal. Extensive testing has been performed on the chromatography of evaporator syrup prior to crystallization in the raw sugar mill (Kearney, 1997). The syrup must be filtered and softened (removal of calcium) prior to chromatography. The chromatography upgrades the syrup to 98% purity and removes enough color to allow the direct crystallization of white sugar (Kochergin et al, 2000, 2001). 2.4 Color Transfer in Crystallization A colorant (or impurity) can be transferred to the sucrose crystal on crystallization in three mechanisms (Godshall & Baunsgaard, 2000): Adsorption onto the crystal surface Co-crystallization into the crystal matrix (occlusion) Trapped by liquid inclusions inside the crystal Godshall & Baunsgaard (2000) focused on occlusion (co-crystallization) of colorants into the crystal matrix. Carbohydrate-type material was found to have a greater tendency to be occluded in the crystal. In addition, the higher the molecular weight the greater the occlusion. As a whole, color transferred 10-20% into the crystal, but color is not one entity, and different types of colors will have a greater or lesser affinity for the crystal. One of the greatest problems are polysaccharides as these species are indigenous in the cane and complex with color molecules, pulling them into the sugar crystal as the polysaccharide material is occluded. 17 Lionnet (1998) extensively studied the incorporation of impurities into the sucrose crystal on crystallization. It was concluded that color (and other impurities) were not transferred exclusively by liquid inclusions. Two mechanisms for transfer were investigated: adsorption isotherms and partition coefficients. Impurities can be adsorbed into crystals by an equilibrium process, governed by an isotherm (Donovan & Williams, 1992; Grimsey & Herrington, 1994). Witcamp and von Rosmalen (1990) and Zumstein et al (1990) proposed the use of a partition coefficient to measure transfer of impurities into a crystal. The partition coefficient method was found to be applicable to the case of sugar crystallization. The partition coefficient of a particular species i is defined as: Pi = {Ci }crystal {Ci }solution (2.2) Ideal behavior occurs when Pi is constant for a wide range of impurity concentrations. Factors such as rate of crystallization, temperature and crystal size must be kept constant. Lionnet (1998) applied the partition coefficient theory to the case of sugar crystallization and measured an ICUMSA color transfer coefficient of 0.02 (color in crystal/color in feed liquor) to affinated sugar. The issue of color transfer on crystallization needs further discussion. In the past color has been treated as a single component measured as ICUMSA color. By using more advanced techniques, as discussed earlier in this chapter, color may be split into a number of components or pseudo-components, depending on the complexity of the analysis. Owing to differences in the characteristics of these components, it is likely that different components will have different partition 18 coefficients (affinities) for the sucrose crystal on crystallization. This leads to the concept of good and bad color. Good color is color that does not transfer into the sucrose crystal and conversely bad color is material that displays high affinity for the sucrose crystal. Color separation processes need only focus on bad color, as good color will ultimately leave the process in the final molasses and not the crystal. 19 CHAPTER 3. THEORY 3.1 Axially Dispersed Packed Bed Adsorption Model This model considers a binary liquid mixture being contacted with a porous solid adsorbent in a packed bed reactor. One of these components is selectively adsorbed onto the spherical particles. If the physical adsorption process is assumed to be extremely fast relative to the convection and diffusion effects, then local equilibrium will exist close to the adsorbent beads. represented as an adsorption isotherm. An adsorption isotherm is an equation that relates the concentration in the film around the resin to the concentration on the resin bead itself. There are many different isotherms used in practice. For a liquid-solid contacting process, generally three isotherms are used: the linear, Langmuir or Freundlich isotherm. (See Figure 3.1) This equilibrium may be Concentration on solid Concentration in liquid Langmuir Freundlich Linear Figure 3.1: Common liquid phase isotherms 20 3.1.1 Fluid Phase Consider a portion of the packed column (Figure 3.2) of length dz, cross- sectional area A, and constant porosity . Q,C(z) q(z) z q(z+dz) Q,C(z+dz) z + dz Figure 3.2: A differential slice of a packed adsorption column Assuming that radial effects are negligible, an unsteady-state material balance on the solute may be performed. C C C q QC z QC z + dz + A D Adz + (1 ) Adz A D = 14 244 4 3 z z z z t 3 43 4 t 3 144444244444+ dz 1 24 14 244 Fluid flow Axial Dispersion Accumulation in fluid phase Accumulation in solid phase (3.1) Dividing by Adz and taking limits, (Note: set u 0 = Q ) A (3.2) C q C 2C + (1 ) u0 + D 2 = t t z z Two fluid phase concentration boundary conditions are required. i.) ii.) C ( z = 0, t ) = C 0 C ( z = , t ) = 0 (3.3) The first boundary condition is a simple Dirichlet condition that controls the feed concentration to the column. The second condition arises by imagining a column of infinite length. Since the column is infinitely long, it also has the capability to adsorb an infinite amount of solute insuring that no solute ever reaches 21 the end of the column. The initial condition comes from the assumption that the column has been properly cleaned and is free of solute when loading commences. C (z, t = 0) = 0 3.1.2 Solid Phase The concentration on the solid phase is controlled by the rate of uptake of solute from the liquid. Many complex expressions have been used for the (3.4) interphase transport in the literature. Two expressions have been used in particular: the bidisperse pore model and the linear driving force (LDF) approximation. The bidisperse pore model (Ruckenstein, 1971) models the adsorbent particle as a macrosphere made up of many small microspheres. Spaces between the micro and macrosphere (macropores) allow the solute to diffuse into the particle. The microspheres are also porous, allowing the solute to further diffuse. The bidisperse pore model is described by two equations. One more is required for the fluid phase resulting in a very complex system of three differential equations. Glueckauf (1947) formulated the classical linear driving force (LDF) model. The LDF model assumes a single film mass transport coefficient controls the rate of uptake from the liquid phase. It is also possible to use the same model even when the intraparticle diffusion is important (Rice, 1982). The film coefficient is simply renamed as an effective mass transfer coefficient. The rate of accumulation in the solid phase is equal to the rate of uptake from the liquid phase according to the LDF approximation. * (1 ) q Adz = k L a(C C4Adz ) 1442 43 14 2t 4 4 4 3 Rate of accumulation in the solid phase (3.5) Rate of uptake from the liquid phase (LDF) 22 Simplifying, (1 ) q = k (C C * ) t An initial condition is required for this equation, q(z, t = 0) = 0 (3.6) (3.7) 3.2 3.2.1 Plug Flow Adsorption Model Governing Equations The axial dispersion term in equation 3.2 may be negligible as Carberry and Wendel (1963) report that this is likely if the bed depth exceeds fifty particle diameters. In the experiments performed, the ratio of column length to particle diameter is approximately ten times this value and so plug flow is likely. The governing equations are the same as in the previous case (3.2 & 3.6), except that the second derivative term is ignored in the fluid phase equation. ui C C 1 q + + =0 z t t (3.8) 1 q = k C C* t ( ) (3.9) An analytical solution is available for this system (3.10) in the case of the linear isotherm using Laplace transforms (Rice & Do, 1995 & Morley, 1988). k uz i k z t C (t , z ) = C0 1 e exp u i 0 K (1 ) d (3.10) k z I o 2 t u K (1 ) i 23 A linear isotherm will be substituted into equation 3.9, but unlike in the classical solution (substituting for q), it will be substituted for C * . Morley (1988) reports that the measured, ICUMSA color isotherm is Langmuir but is linear under normal column operating conditions. Langmuir and linear isotherms have also been experienced in the adsorption of basic yellow dye from aqueous solution using activated carbon (Lin & Liu, 2000). On substitution of a linear isotherm: 1 q q = k C t K ( pH ) (3.11) Experimental results suggest that K, the equilibrium constant, is a function of pH (this will be discussed in section 5.3.2). Since pH is a variable that varies with time, it makes sense to substitute for C * , as it does not appear in any of the derivative terms. This has the advantage of not requiring the derivative of the pH with respect to time. A number of authors (Chern et al, 2001; Wu et al., 1999 & Guibal et al, 1994) have experienced pH effects on adsorption isotherms. 3.2.2 Similarity Transformation The above equations may be put into a more concise form by using the similarity transform (method of combination of variables). Defining the variable: =t z ui (3.12) This is a relative time scale, the difference between real time (from the start of the experiment) and the local fluid residence time. Making the substitution of equation 3.12 into the governing equations is known as combination of variables or the similarity transformation and is carried out below. 24 Using the chain rule: C C C C dz + dt = dz + d z t t z z z Also, from 3.12: d = dt dz ui (3.14) (3.13) Equating the multipliers of dz on each side of the 3.13: C C 1 C = z t z u i Using the same approach for dt, C C = t z Similarly, q q = t z (3.17) z (3.15) z (3.16) z Substituting the variable transformations into the governing equations (3.8 and 3.11) yields, C 1 C C 1 q ui z u + + = 0 i q 1 q = k C K (3.18) (3.19) It is convenient to substitute equation 3.19 into 3.18 to remove the derivative. ui C q = k C z K (3.20) 25 3.2.3 Conversion to Dimensionless Form Reduction to dimensionless form is performed using and , as defined below, where x is a parameter still to be defined. = x = z L (3.21) Making the variable transformation and substituting for the Stanton number, St = k L : ui C q = St C K q ui q = x St C L 1 K Equation 3.23 can be simplified by defining x as, 1 L ui (3.22) (3.23) x= Yielding (3.24) q q = St C K Substituting x into the definition of , (3.25) = 1 = 1 ui L ui z t u L i (3.26) The boundary and initial conditions are essentially unchanged in the transformation, 26 C ( = 0, ) = C0 C ( , = 0) = 0 q ( , = 0 ) = 0 3.2.4 Plug Flow Model Summary C q = St C K ( pH ) q q = St C K ( pH ) 3.2.5 Estimation of Stanton Number The correlation of Wilson and Geankoplis (1966) may be used to estimate the mass transfer of liquids in packed beds. For a Reynolds number range of 0.0016-55 and a Schmidt number range of 165-70,600: 1.09 (3.28) (3.27) (3.29) JD = where, Re = d p u0 , JD = Re 2 3 (3.30) k c (Sc )2 3 , and Sc = ui DAB (3.31) The fluid properties of an aqueous sugar solution at 20 brix at 10oC are (Bubnik et al, 1995): = 2.64 10 3 Pa.s = 1083 kg/m3 Yielding a Re = 0.34 and a J D = 3.30 . 27 The diffusivity of colorant can be approximated using the semi-empirical equation of Polson (1950) which is recommended for biological solutes of molecular weight greater than 1,000: D AB = 9.40 10 15 T (K ) (3.32) (M A ) 1 3 At 10oC and assuming a molecular weight of 6,000, D AB = 5.64 10 11 m2/s. The Schmidt number can then be calculated, Sc = 43,194.7 . Noting that: k = kc dp (3.33) The Stanton number may then be calculated St = k c == 1.091 dp This estimation of the Stanton number will be useful in confirming the estimated Stanton number from the regression of the model. 3.3 3.3.1 Numerical Solution Technique The Finite Element Method In the 1950s the term finite element was coined by aeronautical engineers that used early computers for structural analysis (Baker & Pepper, 1991). The method is founded in the calculus of variational boundary value problems. The finite element (FEM) technique has been used to solve complex structural (finite element) and fluid (computational fluid dynamics CFD) problems. It is not necessary for the engineer to understand the rich theory of variational calculus, as a stepwise approach has been presented by Baker and Pepper (1991). This stepwise procedure has been programmed into FEMLAB, an application that uses MATLAB 28 as its basis. Systems of differential equations and their associated boundary and initial conditions may be entered and solved over a domain that has been discretized by a user-defined mesh. Since the theory is well developed and the software readily available the discussion will revolve around the methods used to get FEMLAB to solve the system defined in section 3.2. 3.3.2 Solving Using FEMLAB The first step to a FEMLAB solution is to define the domain and geometry, over which the governing equations are to be solved. It is clear that this is a onedimensional problem so a straight-line is chosen as the geometry. At first glance, the obvious domain to use is from zero to one. The second boundary condition is at infinity so an extended domain must be used, as a mesh point is required for each boundary condition. For the purposes of this problem, a value of non-dimensional distance of twenty is sufficient. The solution to this problem forms a front that moves down the column. Care must be taken to ensure that the front never reaches the end of the domain. To solve the system the general partial differential equations (PDE) module of FEMLAB is used. The general form of a time-dependent (dynamic) problem is: da u + = F in t (3.34) The above equation is the general system of PDEs in the domain . The solution vector of the dependent variables is u. The time derivative is preceded by the coefficient matrix d a and represents the vector of partial derivatives with respect to the independent distance variable. Any remaining terms are placed into the vector F. 29 The boundary conditions of the domain, on , are represented for the Neumann (constant derivative) case as: n = 0 on (3.35) In the above equation n is the outward normal, and as in equation 3.34. For the simpler Dirichlet conditions (dependent variable equal to a constant), R = 0 on (3.36) is used. The expression is substituted into the vector R. Expanding the above PDE to the derived case yields: d a ,11 d a , 21 3.3.3 d a ,12 u1 F + 1 = 1 F d a , 22 t u 2 2 2 in (3.37) FEMLAB Parameters Converting the governing PDEs (3.28 and 3.29) and associated boundary conditions to this general form yields the parameters to enter into FEMLAB. C u = q 0 0 da = 0 1 C = 0 q St C K ( pH ) F = q St C K ( pH ) (3.38) The boundary conditions are all of the Dirichlet form: C + C0 R= q (3.39) These expressions may be substituted into FEMLAB to generate a solution. More details on the numerical analysis will be given in Appendix A.5. 30 CHAPTER 4. MATERIALS AND METHODS 4.1 4.1.1 Experiments Feed Preparation The first step before any resin experimentation is to prepare the feed material. Syrup (at 66%brix) was collected from the Cinclaire mill and stored in a refrigerator at 35oF for use during the research. ultrafiltration through a 0.45m membrane. The feed was prepared by The unit used was a PallSep Vibrating Membrane Filter (See Figure 4.1a) containing polymeric membranes (Figure 4.1b). The flowsheet is shown in Figure 4.2. Figure 4.1 (a,b): PallSep Vibrating Membrane Filter and membrane 31 Retentate Steam Permeate Figure 4.2: Ultrafiltration Flowsheet The ultrafiltration procedure is as follows: a.) Dilute required amount of stock syrup to approximately 30% brix and place in feed tank b.) c.) d.) e.) f.) Heat to approximately 65oC with steam Open feed valve and start pump Set cross membrane pressure to 100psi by adjusting flow control valve Start oscillating motor and set vibration to recommended amplitude Alter motor setting throughout run to maintain constant amplitude throughout concentration g.) h.) i.) j.) k.) l.) When feed runs low turn-off oscillating motor and feed pump Washout feed tank and fill with water Heat to scalding and add a small amount of bleach Start pump and motor and clean membrane for 10 to 15min Empty tank and refill with water Heat and use to rinse membrane 4.1.2 Batch Tests Batch tests are an important part of the research as they are a simple way of developing an isotherm for the resin. An isotherm is an equilibrium expression, 32 relating the concentration of a species in solution to that on the resin. This is useful in modeling packed-bed adsorption, as a similar equilibrium will exist. The name isotherm arises from the fact that the expression is only applicable at the temperature the data was collected. To maintain constant temperature conditions a 250ml jacketed glass beaker was used for all tests, circulating water at 10oC from a Neslab refrigerated water bath through the jacket. A Corning magnetic stirrer plate and stirrer bar was used to mix the resin and syrup in the beaker. Normally an equilibrium test involves leaving a sample in contact with the resin for approximately six hours (Morley, 1988) to ensure equilibrium is achieved. When the resins H+ or OH- form are released, the pH of the solution changes significantly. As discussed in Chapter 2, significant amounts of color can form under these conditions. The testing procedure was shortened to thirty minutes, and samples were taken every five minutes. This enabled an equilibrium value to be projected from the dynamic results. This experiment also yields data on the speed of the resin; that is how long it takes the resin to achieve equilibrium. This is of interest, as similar mass transfer speeds will be exhibited in changes in process conditions in a column experiment. The experiment is carried out by placing 150ml to 160ml of feed material into the beaker and cooling it to 10oC. Different regions of the isotherm are Volumes of resin are investigated by altering the concentration of the feed. measured as their packed-bed volume in a measuring cylinder. Approximately 15ml of resin (the exact value is not important at this stage) is measured, and the water 33 removed by vacuum filtration using a Buchner funnel and Whatman No. 4 qualitative filter paper. The dried material is then added to the beaker and a timer started. Samples are taken at five-minute intervals, starting with the initial material, using an Eppendorf adjustable-volume pipettor. Care must be exercised when sampling so that no resin is removed. It is advisable to turn off the stirrer 5-10 seconds before the sample time so that the resin in the top layer of liquid can settle. After all the samples have been taken, the exact resin is volume is measured in a measuring cylinder. 4.1.3 Void Fraction Measurement An important parameter in all the resin experiments is the resin packed-bed void fraction, or the resin voidage. This is simply measured by drying approximately 5ml of resin in a vacuum oven. The dry resin is placed into a 10ml measuring-cylinder and 5ml of water is added by pipette. The cylinder is then plugged and inverted a number of times to ensure complete mixing of the water and resin. Extra water may be added to wash down any beads from the cylinder walls above the liquid level by pipette. The resin packed-bed volume, volume of water added, and the total volume may be used to calculate the voidage. 4.1.4 Column Loading Three resins were investigated in the column loading experiments (Table 4.1), with three runs performed on each resin at different flow rates. Jacketed 25mm OD glass columns of 600mm length were connected to a Neslab circulating refrigerated water-bath set to 10oC. FMI piston pumps were used to control the 34 liquid flow rates in and of the column. Two pumps were used on the column as it allowed simpler control of the liquid level above the column (Figure 4.3). The pump at the column exit was set and not adjusted during an entire run. The level of liquid above the resin bed was controlled by setting the flow-rate of the inlet pump. An Oakton pH meter was placed after the column to continuously monitor the product pH. Table 4.1: Ion-exchange resins investigated Resin Rohm & Haas Amberlite 252 RF Rohm & Haas Amberlite IRA 92 RF Rohm & Haas Amberlite IRA 958 Type Strong acid cation (SAC) Weak base anion (WBA) Strong base anion (decolorizing) Form H+ OHCl- Feed 20%brix UF syrup Cation product 10%brix UF syrup WaterBath 10oC Feed Resevoir pH Figure 4.3: Column loading apparatus Before the run, the column is washed with deionized water to ensure that the bed is free of any contaminants. At the start of the experiment, the feed is switched from water to the appropriate solution and the time noted. A 25ml sample is drawn at intervals and the pH noted. Different feed materials are used for each resin to simulate the WSM process. To reduce the complexity of the investigation, a single 35 resin is loaded in each experiment, as it is important to have a constant feed composition to the column of interest. Beforehand sufficient feed must be produced by passing ultrafiltered syrup through the appropriate resins (Table 4.1). In the case of the decolorizing resin, 10%brix UF feed was used as this is of higher color, shortening the required length of experiment. Each sample is analyzed with GPC and for conductivity. determined. 4.1.5 Resin Regeneration After a run, the column is washed with water until the product stream is free of color. The required regenerant (Table 4.2) must be made up and 5 to 6 bed volumes is passed though the column at a low flow-rate (typically 30ml/min). After regeneration, the column is washed with deionized water until the product pH reaches a stable value. Table 4.2: Column Regeneration Resin SAC WBA Decol. Regenerant 6% HCl 10% NaOH 10% NaCl; 0.2% NaOH Temperature 25oC 60 oC 60 oC The ICUMSA color of a number of samples is also The use of methanol and ethanol washes were investigated to determine if more color could be removed from the resin thereby increasing the capacity of the resin in subsequent runs. 4.1.6 Color Investigation A GPC investigation was done on a number of color formation reactions, the aim being to determine suitable pseudo-components for modeling purposes. 36 Materials: Evaporator syrup was obtained from the Cinclaire mill for the caramelization and alkaline degradation tests. Molasses was obtained from stock at the Audubon Sugar Institute for investigation of the Maillard reactions. Cane juice was produced by disintegrating cane with water in a stainless steel environment using a Jeffco disintegrator. Caramelization and Alkaline Degradation: Syrup was boiled under constant reflux in an atmospheric laboratory still for 30 minutes. In the case of alkaline degradation, the syrup pH was increased with sodium hydroxide to pH 8.8. Maillard Reactions: Conditions favoring the Maillard reactions (Newell, 1979) were used: high temperature and brix but low purity. Molasses was maintained at 75oC in a constant temperature bath for 24 hours. The Effect of Iron on Cane Juice: Cane juice was heated at 50oC in a water bath for one hour. The effect of iron on cane juice was investigated by placing rusty and acid cleaned coiled wire of equal lengths into the heating tubes. Non-enzymatic effects were investigated by autoclaving (at 110oC for 10 minutes) the juice prior to exposure to iron and also by the addition of one part mercuric chloride to 5,000 parts juice to denature any enzymes (Meade, 1963). For each treatment, a control experiment was performed to check the effects without any iron in contact with the juice. 4.1.7 Color Transfer in Crystallization A batch pilot-plant crystallizer and centrifuge were used to produce raw sugar from ultrafiltered syrup. Syrup form the St James mill was used in place of the normal syrup as supplies had run out. The feed syrup, sugar and final molasses 37 were analyzed with GPC and ICUMSA color to measure the color transfer experienced. The color transfer data will be useful in investigating good and bad color. A detailed description of the crystallization equipment is given by Saska (2002). 4.2 4.2.1 Sample Analysis ICUMSA Color As mentioned in Chapter 2 ICUMSA color is the sugar industry standard color measurement. A small amount of the sample to be analyzed (approx. 10ml) is placed in a vial and corrected to pH 70.1 using HCl and NaOH solutions (0.5N works best). This is a difficult task for deashed samples, as they contain little or no buffering capacity. It is useful to use some of the initial sample to correct the pH if pH 7 is overshot. The sample is then diluted to a light golden color and filtered through a 0.45m syringe filter. The permeate is then analyzed with a spectrophotometer set to 420nm. The brix of the sample analyzed is then determined using a refractometer. ICUMSA color is defined as: ICUMSA 420nm Color = {Abs(420nm )}10,000 {Concentration (g/ml)} {Cell length (mm )} (4.1) The concentration term is taken from Table 8 in the SASTA Laboratory manual relating brix to concentration. Interpolation between points can be simplified by fitting a curve to the line. A quadratic equation was found to be suitable as the correlation coefficient (r2) was unity. Concentration (g/100ml) = 4.02110 2 {Brix} + 0.9978{Brix} 2 (4.2) 38 Equipment used: Spectronic Genesys 2 Spectrophotometer Bellingham and Stanley Ltd. RFM90 Refractometer Orion 410A pH meter 4.2.2 Conductivity The conductivity of every column-loading sample was analyzed using a Fischer Acumet conductivity meter. Conductivity gives an indication of the ash content of a sample, as solutions with more inorganic dissolved solids will generally be conductive. Samples from the cation column have very high conductivity as they have low pHs (high H+ ion concentration). Two probes with different cell constants were used for solutions of different conductivity (see Table 4.3). Table 4.3: Conductivity probes Conductivity 10S/cm 1mS/cm >1mS/cm Cell constant 1cm-1 10 cm-1 4.2.3 Gel Permeation Chromatography GPC is a separation process based on molecular size. A small sample is injected into a stream of a buffer solution that flows into a precisely controlled pore size gel column. The gel pores are arranged in such a size distribution that some small material is able to diffuse into the pores whereas larger molecules are excluded. The column may be calibrated by injecting standards of precise molecular weight into the column. If the samples to be analyzed are of the same molecular size shape as the standards, their weights may be read off the calibration 39 curve. The buffer solution masks the gel from any ionic behavior of the sample, as no interaction is wanted between the analyte and the stationary phase. All ion exchange and color testing samples were analyzed with GPC. A Bio-Rad AS-100 HRLC autosampler was used to inject 100l of sample into a mobile phase of 0.1M sodium nitrate (NaNO3), pumped isocratically at 0.5ml/min by a Waters 515 HPLC pump (Figure 4.4). Separation was achieved using two Waters Ultrahydrogel HPLC columns (Linear and 120) in series to give a molecular weight (MW) range of 6,000,000 to 100. Column Heater Solvent Resevoir Pump ABS 420nm Detector RI Detector Autosampler Computer Interface Fraction Collector Drain Signal Liquid flows Figure 4.4: Schematic of GPC Arrangement A Dionex AD20 absorbance detector set to 420nm was used to determine color and a SpectraSYSTEM RI-150 differential refractometer to measure dissolved solids. Each unit was computer controlled using the Dionex Peaknet system Dextran standards, sucrose and water were used to generate a (Version 4). molecular weight calibration curve (Figure 4.5). The detectors can be calibrated to 40 concentration using standards. This was not performed as this brings greater ambiguity to the data, as the choice of standard will affect the calibration. Different dextran standards behaved very differently in their signal response for the same concentration owing to differences in their chemical nature. For this reason all GPC data has been reported in terms of their measured signal as this is a measure of concentration. 10000000 1000000 100000 MW 10000 1000 100 10 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Retention Tim e (m in) Figure 4.5: GPC Molecular Weight Calibration Samples were prepared by diluting to 7-10 %brix and filtering through a 5.0m syringe filter. Godshall et al (1988) show that a 0.45m filter removes very high molecular weight material. This was confirmed by GPC analysis. A 5.0m membrane filter was found to be sufficient to remove insoluble material but not remove any dissolved high molecular weight material. 4.2.4 Analysis of GPC Chromatograms Refractive Index Quantitative analysis of GPC refractive index (RI) chromatograms of a distribution of a single species is a simple numerical integration task (Figure 4.6a). 41 The same applies for a number of non-overlapping species (Figure 4.6b). It may be assumed that each peak will be made up of a normal or a Gaussian distribution (Equation.4.3 Skoog et al, 1996): x(t ) = xmax e (t t 0 ) 2 2 (4.3) where xmax is the maximum concentration attained, t 0 is the retention time at the peak and 2 is the standard deviation of the curve (See figure 4.7a). The standard deviation is a measure of the spread or the width of the peak. xmax t0 2 x 0 1 2 3 4 t 5 6 7 8 Single species x 0 1 2 3 4 t 5 6 7 8 Two Species (No deconvolution required) Figure 4.6(a,b): GPC RI chromatograms requiring no deconvolution When peaks overlap, deconvolution is required. Numerical deconvolution can be performed in a straightforward manner using a least-squares curve fitting procedure (Katz et al, 1998). At any given time the overall signal is the sum of the individual component peaks (Figure 4.8). 42 X 0 2 4 6 8 10 12 t x1 x2 X Figure 4.8: Two Gaussian distributions deconvoluting a chromatogram For N components the recorded signal X is: X (t ) = x1 (t ) + x2 (t ) + .... + x N (t ) = xmax,i e i =1 N (t t0 ,i ) i2 (4.4) By minimizing the sum-of-squares between the fitted and measured parameter using a non-linear regression algorithm, the best-fit parameters can be determined. MATLAB 6.1 Optimization Toolbox has a Sequential Quadratic Programming routine that as applied to equation 4.4. Provided a reasonable initial guess and the correct number of components is supplied a reasonable fit was obtained. 420nm Absorbance The deconvolution technique used in the case of the RI chromatogram is only suitable if the number of peaks can be determined by inspection. Using the number of peaks as a free variable in the regression is not possible as it gives the 43 algorithm too much freedom. By using several thousand components, one could represent any chromatogram. In the case of the typical absorbance at 420nm chromatogram, there are no distinct peaks and so it is not possible to determine the number of components (Gaussian distributions) to use in the regression. A more simple technique was used in this case. Color tests were performed to determine the changes in concentration and color in different MW ranges (Broadhurst & Rein, 2002). Using this data, retention times were picked at which the absorbance was measured. These values were then tracked through the experiments giving a color-MW profile of the processes. 44 CHAPTER 5. RESULTS AND DISCUSSION 5.1 Color Formation Investigation The results to the color formation experiments will be presented starting from the simplest measurement technique, ICUMSA Color. This will be followed by the more informative GPC analysis. The GPC analysis in this section (5.1) has been performed by a slightly different technique since the method proposed in 4.2.4 relies on the results from this section (5.1.2). Peak-split points were chosen and the area between them integrated. Figure 4.5 has been used to convert these points into molecular weight (MW) ranges. 5.1.1 Caramelization and Alkaline Degradation Simple ICUMSA Color measurement shows a threefold increase in color for alkaline degradation, considerably more than for caramelization owing to the harsh reaction conditions (See Figure 5.1). 30000 25000 ICUMCSA Color Units (IU) 20000 15000 10000 5000 0 Syrup Caramel ADP Figure 5.1: ICUMSA Color of Caramelization and Alkaline Degradation 45 GPC is a more insightful analysis into the formation of sugar colorants. The resulting refractive index (RI) chromatograms are overlaid in Figure 5.2(a). Figure 5.2(b) shows the region of interest. Since sucrose overloads the detector, that peak may be ignored. 1.40x103 ADP 1.20x103 Sugar Peak Caramel 1.00x103 8.00x102 RI Response (mV) Syrup 6.00x102 4.00x102 2.00x102 0 -2.00x102 0 5.00 10.00 15.00 Retention Time (min) 20.00 25.00 30.00 Figure 5.2(a): RI GPC chromatograms for Caramelization and Alkaline Degradation 120 ADP 100 Caramel 80 60 RI Response (mV) Syrup 40 20 0 -20 -40 8.00 10.00 12.00 14.00 Retention Time (min) 16.00 18.00 20.00 22.00 Figure 5.2(b): Region of interest in GPC chromatograms 46 700 600 RI area response 500 400 300 200 100 0 >2,600k 2,600k - 300k 300k - 32k 32k - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 Molecular Weight Range Syrup Caramel ADP Figure 5.3: Caramelization and Alkaline Degradation RI Areas A number of peaks may be identified from the chromatograms, as indicated on the chromatogram. By comparing these molecular weight ranges with the initial syrup, the concentration effects of caramel and alkaline degradation product (ADP) mechanisms as a function of molecular weight may be determined. The integrated results are displayed as a bar chart in Figure 5.3. Increases in concentration are noticeable in all ranges showing that sugar range material (<650MW) is being polymerized into larger molecules. This explains why such large increases are noticed in the lower ranges. In all the ranges, alkaline degradation produces more material. The color chromatograms produce a similar result (see Figure 5.4), except that ADPs show more highly colored than the caramel products. Figure 5.4 shows that ADPs and caramels are produced from material of molecular weight less than 650 as increases are viewed in all ranges. Clearly, sugars are being polymerized. 47 16000 Absorbance (420nm) area response 14000 12000 10000 8000 6000 4000 2000 0 >2,600k 2,600k - 300k 300k - 32k 32k - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Syrup Caramel ADP Figure 5.4: Caramelization and Alkaline Degradation - Absorbance at 420nm Response HPLC analysis of the samples was performed, analyzing the organic acid concentrations. The difference between caramelization and alkaline degradation is strikingly different (Table 5.1). Alkaline degradation causes the formation of organic acids. In the thirty-minute period every acid except for aconitic acid, approximately doubled its concentration. Table 5.1: Organic acid concentrations (ppm) in caramel and ADP formation Acetic 1040 687 2058 Aconitic 2999 1141 3243 Citric 310 186 365 Formic 220 153 437 Lactic 1418 937 2392 Malic 413 234 492 Oxalic 33 19 108 Propionic 43 n/d 82 Sample Syrup Caramel ADP n/d non-detected 5.1.2 Maillard Reactions A similar analysis was performed simulating the Maillard reactions. Figure 5.5 shows the significant increase in ICUMSA color. It is interesting to note that 48 the same GPC molecular weight ranges were obtained for the Maillard reactions as for ADP and caramelization, except that the highest range had to be extended. Substantial increases in concentration are seen in all ranges (Figure 5.6). 160000 140000 120000 100000 80000 60000 40000 20000 0 Molasses Maillard Figure 5.5: Increase in ICUMSA Color from the Maillard Reactions 3500 3000 RI Detector - Area response 2500 2000 1500 1000 500 0 >5,000k 5,000k - 300k 300k-32k 32k - 8,000 8,000 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Molasses Maillard Figure 5.6: Maillard Reactions RI Areas 49 Figure 5.7 shows how the high molecular weight ranges contain insignificant amounts of color in this reaction compared to the ranges, 32kMW and below. It is interesting to compare the ICUMSA color data with GPC data. A greater increase in the absorbances (Figure 5.7) is seen compared to the ICUMSA color results (Figure 5.5). This is a result is caused by ICUMSA color being an intensity parameter: the color per unit dissolved solid. Taking the increase in the RI areas (Figure 5.6) into account shows the ICUMSA data to be reasonable. 120000 Absorbance (420nm) - Area response 100000 80000 60000 40000 20000 0 >5,000k 5,000k - 300k 300k-32k 32k - 8,000 8,000 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Molasses Maillard Figure 5.7: Maillard Reactions - Absorbance area at 420nm Response 5.1.3 Cane Juice and Iron It is well established that enzymes play an important role in the formation of color (Coombs & Baldry, 1978). Before these enzymes are denatured by thermal conditions in the process, they can form significant amounts of color. Iron is also implicated in the mechanisms of color formation. Godshall (2000) reports that the 50 ferrous iron (Fe2+) can form complexes with phenolics and caramels to form darker products. To investigate these effects three experiments were performed. i. ii. Untreated cane juice was exposed to iron enzymes still active Cane juice was autoclaved before exposure to iron thermally sterilized iii. Cane juice treated with Mercuric chloride (HgCl2) enzymes chemically denatured Untreated cane juice shows small but significant increases in color when heated (Figure 5.9). The samples exposed to iron show a similar behavior (add or subtract 5 units) except in the 7,500 to 4,000MW range where a large jump in color is seen relative to the initial juice and the control experiment. The changes in concentration are however too small to be significant (Figure 5.8). remainder of this analysis the RI changes will not be included. 50 45 For the RI Detector - Area response 40 35 30 25 20 15 10 5 0 >300k 300k - 32k 32k - 9,500 9,500 - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Juice Control Clean Fe Rusty Fe Figure 5.8: The effect of iron on untreated cane juice RI Area Response 51 250 ABS (420nm) - Area response 200 150 100 50 0 >300k 300k - 32k 32k - 9,500 9,500 - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Juice Control Clean Fe Rusty Fe Figure 5.9: The effect of iron on untreated cane juice ABS (420nm) Area Response 250 ABS (420nm) - Area response 200 150 100 50 0 >300k 300k - 32k 32k - 9,500 9,500 - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Juice Control Clean Fe Rusty Fe Figure 5.10: The effect of iron on autoclaved cane juice ABS (420nm) Area Response Autoclaved juice that is exposed to iron also shows the increase in color in the 7,500-4,000 MW range (Figure 5.10). The other ranges show either no change or a slight decrease in color. The data shows that the color increase 4,000 to 2,000 MW range is enzymatic as an increase is viewed for untreated juice but not for the tests 52 when the enzymes were denatured prior to exposure. The control experiment shows only a small change in this range and so the effect seen is the action of iron. This suggests that color formation in the presence of iron leads to a colorant of a specific molecular weight and that enzymes form relatively small amounts of colorant in ranges. To confirm this conclusion a second test was performed. If after denaturing the enzymes with mercuric chloride, cane juice produces colorant in the 7,500 to 4,000MW range, this must be due to the formation of colorant by the action of iron. The addition of mercuric chloride showed a very similar effect (Figure 5.11). The only major increase in color is observed in the same range, confirming our conclusion. No conclusive evidence can be obtained by comparing the effects of rusty and clean iron. 250 ABS (420nm) - Area response 200 150 100 50 0 >300k 300k - 32k 32k - 9,500 9,500 - 7,500 7,500 - 4,000 4,000 - 2,000 2,000 - 1,200 1,200 - 650 MW Range Juice Control Clean Fe Rusty Fe Figure 5.11: The effect of iron on cane juice with 1:5000 parts Mercuric Chloride ABS (420nm) Area Response 53 5.1.4 Times for Color Pseudo-Components The results presented in the above investigation suggest the following times (Table 5.2) to use in the determination of color pseudo-components. The times were picked by examining the important molecular weight ranges, for example the 7,500 to 4,000MW range in the cane juice experiments. Table 5.2: Definition of pseudo-components A 14.4 10,000 B 16.6 6,000 C 18 3,000 D 19.2 1,800 E 20.4 1,200 F 21.2 800 Pseudo-Component Retention time (min) Molecular weight 5.2 Ultrafiltration The removal of dissolved solids and color by ultrafiltration may be analyzed with GPC. Figure 5.12 shows that the 0.45m membrane has a molecular weight cut-off (MWCO) at approximately 10.4min, or 1,000,000 MW. Material larger than the MWCO is removed from the feed syrup, and so will not be passed to the resin where fouling would be likely. (The retention times displayed for the UF analysis have been offset by +1min as no Guard column was in place at the time of analysis as it was being cleaned.) The syrup feed to the ultrafilter has a significant colorant centered at 8 minutes in the GPC ABS chromatogram (Figure 5.13). This peak is of colored material of very high molecular weight and is very significant to sugar processing. Godshall and Baunsgaard (2000) report how the larger the MW of the colorant the greater the occlusion into the crystal on crystallization. By ultrafiltering the syrup 54 prior to ion exchange, not only is the resin protected from fouling but some of the color that is likely to transfer to the crystal (bad color) is removed. 200 180 160 140 RI Signal 120 100 80 60 40 20 0 0 5 10 15 20 25 Retention time (min) Feed Syrup Permeate Figure 5.12: Effect of ultrafiltration: GPC-RI 400 350 300 ABS 420nm Signal 250 200 150 100 50 0 0 5 10 15 20 25 Retention time (min) Feed Syrup Permeate Figure 5.13: Effect of ultrafiltration: GPC-ABS 420nm 55 5.3 Strong-Acid Cation Resin 5.3.1 SAC Batch Tests The batch tests are particularly useful in analyzing the equilibrium properties of the resin. For the cation resin, the calculated adsorption parameter increased as the resin reached equilibrium. The most significant result of the batch testing is that the resulting isotherms were linear (See Appendix B.1 & Figure 5.14). 9000 8000 7000 6000 q(t) 5000 4000 3000 2000 1000 0 0 50 100 150 200 250 C*(t) A Linear (A) B Linear (B) C Linear (C) D Linear (D) E Linear (E) F Linear (F) Figure 5.14: SAC Isotherms after 30 minutes Linear isotherms are simple to work with and indicate that the solute, in this case the colorant is dilute (Seader & Henley, 1998). The modeling technique using pseudo-components depends on the assumption that the color components are dilute so that multi-component isotherms and mass transfer relations are not required. From the adsorption equilibrium parameter versus time (based here on the initial concentration), K C 0 (t ) , the final equilibrium value may be calculated (see Appendix C.4, Equation 5.1). This relationship is plotted in Figure 5.15. 56 K (t ) = K eq (1 e t ) 30 (5.1) 25 20 KC0(t) 15 10 5 0 0 5 10 15 20 25 30 35 Time (min) A A (calc) B B (calc) C C (calc) D D (calc) E E (calc) F F (calc) Figure 5.15: SAC equilibrium parameter (based on C0) versus time (10oC) Table 5.3 displays the equilibrium parameters obtained from Figure 5.14 as Figure 5.15 shows that after 30 minutes equilibrium has been reached. Higher adsorption parameters are measured for the higher molecular weight components. This means that the resin has a higher affinity for the larger colorants and will be more effective at removing them than the low MW material. Table 5.3: SAC isotherm parameters Component Keq A 56.11 B 67.67 C 31.62 D 22.00 E 17.38 F 18.05 The refractive index detector can give information about what happens to the non-colored high molecular weight material when it is contacted with the resin. The RI deconvolution technique was used on the SAC isotherm GPC data. One peak in particular (named Peak 5 in the deconvolution) was affected by the resin. The GPC retention time decreased from its starting value of 18.8 to 20.55 minutes (see Figure 57 5.16), showing a decrease in molecular weight from 2,000 to 900. The low pH conditions are splitting the initial material into lower molecular weight species. 20.8 20.6 20.4 GPC Retention time (min) 20.2 20 19.8 19.6 19.4 19.2 19 18.8 18.6 0 5 10 15 20 25 30 35 Time (min) Figure 5.16: Peak 5 retention time variation in SAC batch tests 5.3.2 SAC Column Tests A typical breakthrough curve for the cation column is displayed in Figure 5.17. On the horizontal axis is plotted the relative time scale variable, , (defined in equation 3.26) and on the vertical axis, the color concentration (measured response from detector). The pH and conductivity are also plotted. The product from the column is of low pH and high conductivity up until = 30 . During this period hydrogen ions ( H + ) attached to the resin exchange for cations ( Na + , K + , Ca 2+ & Mg 2+ etc.) in the syrup feed, lowering the pH (see equation 5.2). pH = log10 H + [] (5.2) 58 180 160 140 120 16 14 10 100 C 8 80 6 60 40 20 0 0 10 20 30 40 50 60 70 80 90 4 2 0 100 D D (feed) pH Conductivity Figure 5.17: A typical SAC breakthrough curve (SAC6-D) Conductivity is closely related to the pH as the more ions in the solution, the higher the conductivity. As the resins supply of hydrogen ions is exhausted, the conductivity begins to drop. It is interesting that at = 46 the conductivity drops below the feed conductivity and the increases again. This may be caused by a softening effect, as divalent cations in solution can exchange with monovalent cations on the resin. The resin shows some affinity for the colored species in solution (in this example, pseudo-component D). The colorant increased continuously up until = 35 , where it reaches the feed value. After this point a curious effect occurs, the product from the column increases above the feed concentration for approximately 20 time units. This effect was found in all experiments for the lower MW species (components D,E and F). In the governing equations, (equations 3.28 and 3.29) there are two parameters that govern the dynamics of the system, namely, the Stanton number and 59 Conductivity (mS/cm) or pH 12 the adsorption equilibrium constant. If a constant linear isotherm is used, then the slope of the breakthrough curve will be constantly decreasing owing to the driving q force term, St C , tending to zero. This is shown graphically in Figure 5.18. K The mass transfer conditions in the bed therefore cannot force the concentration to go above the feed value even if the Stanton number is pH dependent. A change in Stanton number would result in a change of slope. 200 180 160 140 120 C 100 80 60 40 C C 20 S t = 1; K = 18; C = 180 0 0 0 0 20 40 60 80 100 120 Figure 5.18: Constant linear isotherm model solution If the resins affinity for solute the species (the colorant) were somehow decreased during the run it would drastically alter the dynamics. Going back to the linear isotherm, if K decreases, then q is forced to decrease, releasing material already absorbed to the resin. This effect appears to explain the phenomena 60 occurring in Figure 5.17. In addition, it is interesting to note that the effect appears to occur in parallel to the change in the pH and conductivity of the product. Changing the pH of a colorant solution drastically affects it color, indicating a pH sensitivity of the colorant molecule. It appears, in this case, that either or both the resin and the colorant display a change in affinity for each other as the pH increases. Essentially the equilibrium constant becomes a function of pH (as mentioned in section 3.2.1). It will be assumed that this dependence will be similar to the Arrhenius equation (5.2) that applies to the dependency most rate constants on temperature (Fogler, 1999). k r (T ) = k 0 e E RT (5.3) Since the pH is defined as a logarithmic function, this equation will be adapted slightly so that K (pH ) is high at low pH conditions and decreases exponentially to a constant value at low pH conditions (Figure 5.19; Equation 5.4). K ( pH ) = K 0 e pH + K1 14 (5.4) 12 10 K(pH) 8 6 4 2 0 0 1 2 3 4 5 6 7 pH Figure 5.19: Proposed functionality of K with pH 61 Applying this to the model and solving, using some typical pH values, yields a breakthrough (Figure 5.20) with very similar profile to that displayed in Figure 5.17. The model is not perfect, as it does not result in a breakthrough curve as linear as the measured data but it is a lot more accurate than the constant isotherm case. Possible causes for this are: Expression for K (pH ) is not perfect Similar mass transfer effects i.e. St ( pH ) 220 200 C C 0 180 160 140 120 C 100 80 60 40 20 S t = 1; K = 18; K = 7; = 1 0 1 0 0 10 20 30 40 50 60 70 80 90 100 110 Figure 5.20: Linear isotherm with K a function of pH model solution Parameters may then be regressed using the non-linear regression algorithm (Appendix A.5.1). The results (absorbance 420nm, pH, conductivity) for the column tests are displayed in Appendix B.2. Regressed model parameters are reported in Table 5.4 and Table 5.5. The regression operation was relatively 62 successful as most cases displayed a coefficient of correlation (R2) above 0.9. The Regressed Stanton numbers were similar to those calculated using correlations from the literature (see section 3.2.5). Components A and B have not been reported here as component A was too close to the detection limit of the detector to produce reliable results and component B displayed different dynamics. Component B (Figures F.11, F.20 & F.29) appears to have a much larger affinity for the resin than the other components; this corresponds to the batch data (Table 5.3). A pH effect is viewed as in the other components. In Table 5.4, the Stanton number remains relatively constant with changes in velocity over the region investigated. This is interesting as it means that the mass transfer coefficient, k , is proportional to the superficial velocity. The increase in k is likely to be a result of the smaller film thickness around the resin beads. The mass transfer coefficient, k , is extracted from the Stanton number and plotted versus the superficial velocity in Figure 5.21. Table 5.4: k L as a function of superficial SAC Stanton number St = ui velocity SAC u0 (m/h) C D E F 6 3.75 0.96211 1.0308 1.0415 1.0799 8 4.89 0.90784 0.91952 1.1358 1.4159 9 6.21 0.8535 1.0431 1.0079 0.9710 63 Table 5.5: Regressed SAC column isotherm parameters as a function of superficial velocity K0 K1 9 6.21 16.80 18.82 17.90 17.51 6 3.75 18.57 6.18 4.65 4.50 8 4.89 21.22 11.98 5.37 3.20 9 6.21 10.23 4.17 3.94 3.73 6 3.75 1.034 1.097 1.016 0.960 8 4.89 1.798 2.009 1.388 1.152 9 6.21 0.807 1.163 1.130 1.062 SAC u0 (m/h) C D E F 6 3.75 25.73 19.70 19.94 20.11 8 4.89 29.51 30.88 22.31 22.36 40 35 30 25 k' (1/h) 20 15 10 5 0 3 3.5 4 4.5 5 5.5 6 6.5 u0 (m/h) C D E F Figure 5.21: SAC mass transfer coefficient versus superficial velocity Equations 3.30 and 3.31 can be used to form a relationship between the superficial velocity and the mass transfer coefficient. k (ui ) 3 1 (5.5) 64 Figure 5.21 shows some resemblance to this proportionality. Another check on the Stanton number is to compare it to a correlation as in section 3.2.5. The correlation indicates that the measured data is in the correct range. There is some variation in the equilibrium expression parameters (Table 5.5). Ideally, this equilibrium expression should remain constant as only the flow rate is changing in each case. There are a number of possible explanations for this. Despite appropriate measures taken, the resin may not have been returned to the same initial condition at the start of each run. Another likely possibility is that since the model does not perfectly emulate the dynamics measured, the regression package alters the equilibrium parameters unnecessarily in searching for a best fit. For design purposes, a constant equilibrium should be used. It would be useful to measure this expression experimentally. This could be done by spiking the solution with a inorganic salt (e.g. NaCl) to force more hydrogen ions into solution, lowering the pH. For high pH values, it becomes more complicated. Two possibilities would be: Adding a pH buffer Making the feed material basic prior to resin addition It is also interesting to compare the values of the adsorption parameter obtained in the column tests (Table 5.5) to the value obtained in the batch tests (Table 5.3). The batch test adsorption parameters were significantly higher than the values measured in the column test. There is a clear need for further investigation into this resin. The dynamics of the process have been identified but data is required over a wider range of flows to find optimum operating conditions. 65 5.4 Weak-Base Anion Resin 5.4.1 WBA Batch Tests The WBA resin showed results slightly different from the SAC in the batch tests (Appendix C.1, Graph 5.22). Components B through D have an adsorption isotherm that does not pass through the origin. 3000 2500 2000 q(t) 1500 1000 500 0 0 5 10 15 20 25 30 35 40 45 C*(t) A Linear (B) B Linear (C) C Linear (D) D Linear (E) E Linear (F) F Figure 5.22: WBA Isotherms after 30 minutes Morley (1988) reports an isotherm of form, q = KC * + q0 (5.6) The parameter q0 represents the resin having some initial color loading before it is contacted with the fluid. Initial conditions of the model would then have to become q ( , = 0 ) = q0 Fortunately by defining a dimensionless concentration parameter q = q q0 (5.8) (5.7) 66 The initial condition is returned to zero and q0 can be ignored in the governing equations. This is particularly convenient as the actual values of q are not as important as the values of C . The adsorption isotherms were measured as a function of time, as was done in the SAC case, and are plotted in Figure 5.23. Time to equilibrium is clearly longer for the WBA resin than for the SAC resin (Figure 5.15). 16 14 12 10 KC0(t) 8 6 4 2 0 0 5 10 15 20 25 30 35 40 Time (min) B B (calc) C C (calc) D D (calc) E E (calc) F F (calc) Figure 5.23: WBA equilibrium parameter based on C0 versus time (10oC) The equation to determine the equilibrium value had to be altered form the form used for the SAC resin (equation 5.1) by adding a parameter, t 0 , to take into account K (t ) not passing through the origin. K (t ) = K eq 1 e (t t0 ) ( ) (5.9) It has been determined above that the WBA resin is slower in reacting to changes in concentration (i.e. time to equilibrium), producing the similar effect viewed here. 67 Table 5.6 displays the parameters obtained from the data for time thirty as this is close to equilibrium. Table 5.6: WBA isotherm parameters Component Keq b B 45.35 205.20 C 47.29 461.97 D 47.82 424.75 E 40.62 360.51 F 50.99 219.33 5.4.2 WBA Column Tests The WBA column test results proved to be far simpler than the SAC resin. A typical breakthrough curve is displayed in Figure 5.24. The pH starts from a high value as hydroxide ions ( OH ) are released from the resin. As the resins supply of hydroxide ions is exhausted, the pH drops since the feed is syrup that has already past through the SAC resin and has a low pH. The conductivity starts low, as the ash content of the product is extremely low, having been removed by the two resins. The conductivity rises as the resins hydroxide ion supply runs out. 120 12 100 10 80 8 60 C 6 40 4 20 2 0 0 5 10 15 20 25 30 35 0 D D (feed) pH Conductivity Figure 5.24: A typical WBA breakthrough curve (WBA6-D) 68 10xConductivity (mS/cm) or pH The product color starts low and increases until it reaches the feed value. Unlike the SAC resin, no strong pH effects are visible. There does appear to be some change in dynamics as the pH drops but the effect is so small that it has been neglected in the modeling. The WBA resin may therefore be modeled with the linear constant isotherm (Figure 5.18), allowing the use of the analytic model (Equation 3.10). The FEMLAB regression technique was still used even though the model is analytic, as the technique was well developed for the SAC case. The regressed parameters are displayed in Tables 5.7 and 5.8. The regression was successful, yielding correlation coefficients above 0.95 in most cases. The Stanton number showed considerable increases as the fluid velocity increased. Mass transfer strongly controls this resin, as seen by the slow behavior, and as the surrounding fluid velocity increases the resistance decreases drastically causing an increase in the Stanton number. Extracting the mass transfer coefficients and plotting versus the superficial velocity (Figure 5.25), shows a different behavior to the SAC in this fluid velocity region. The mass transfer conditions increase significantly at higher flow rates. Table 5.7: WBA Stanton number as a function of superficial velocity WBA u0 (m/h) B C D E F 5 3.10 0.54166 1.6502 1.9882 1.9848 2.0038 6 3.76 0.91915 1.8763 2.1675 2.0009 1.9517 7 4.28 1.1748 2.5726 3.4093 2.8938 2.8066 69 40 35 30 25 k' (1/h) 20 15 10 5 0 3 3.2 3.4 3.6 3.8 4 4.2 4.4 u0 (m/h) B C D E F Figure 5.25: WBA mass transfer coefficient versus superficial velocity The adsorption equilibrium parameter (Table 5.8) for the resin remains constant for the two higher velocity runs. Figure 5.26 shows that the changes observed for the lower velocity may be experimental error as some components show an increase and others a decrease. The value measured in the batch test did not correlate well with the regressed column data. This finding may occur because of the different mass transfer conditions in the column as to those in the batch tests. As in the SAC case, further experimental work is required to confirm these findings. Table 5.8: Regressed WBA column isotherm parameters as a function of superficial velocity WBA u0 (m/h) B C D E F 5 3.10 4.60 18.46 22.72 22.53 22.93 6 3.76 13.15 12.12 13.99 14.51 15.61 7 4.28 10.38 12.56 12.43 13.96 14.36 70 25 20 15 K 10 5 0 3 3.2 3.4 3.6 3.8 4 4.2 4.4 u0 (m/h) B C D E F Figure 5.26: WBA isotherm equilibrium constant versus superficial velocity 5.5 Decolorizing Resin The decolorizing resin was controlled by a linear isotherm, as discussed by Morley (1988). Unlike Morleys model, the product color, in a number of cases did not reach the feed value (See Figure 5.27). The same effect viewed here was observed for the ICUMSA color measurements (Figures D.2,D.9 & D.16). In one case, the experiment was allowed to run for eight hours and still the color did not increase. From visual inspection of the column during a run the reason for this effect is obvious. A black ring forms at the top of the resin and slowly moves down the column. The resin has more affinity for this dark colorant than any of the others. The yellow colors breakthrough first and presumably the dark colorant would breakthrough at some point, but this was not reached in any of the experiments. 71 100 90 80 70 60 50 40 30 20 10 0 0 50 100 150 200 12 8 6 4 2 0 250 F F (feed) pH Conductivity Figure 5.27: A typical decolorization breakthrough curve (DECOL7-F) Again no major pH or conductivity dependence was observed so a constant linear isotherm model was used in the regression. Since the product did not reach its feed value, the feed color concentration was used as a third variable, in addition to the adsorption parameter and the Stanton number. This gives rise to a portion of decolorization that goes unmodeled and would be a constant in a design process. The regression was particularly successful, yielding a lowest correlation coefficient of 0.963 and in most cases greater than 0.99. Morleys model regresses to an average correlation coefficient of 0.91 (Morley, 1988). Table 5.9 shows that mass transfer conditions are favorable. The Stanton numbers are considerably larger than for the SAC and WBA resins. Plotting the mass transfer coefficient against superficial velocity (Figure 5.28) shows an almost linear relationship. Higher velocities give rise to more favorable mass transfer conditions. Interestingly, the higher the molecular weight of the component the faster the mass transfer. 72 pH or Conductivity (mS/cm) 10 C Table 5.9: DECOL Stanton number as a function of superficial velocity DECOL u0 (m/h) B C D E F 7 3.68 9.092 5.710 3.939 3.383 3.310 8 5.50 13.269 7.766 3.654 3.242 2.685 9 6.36 14.335 8.418 4.596 4.213 4.093 The adsorption equilibrium constant (Table 5.10, Figure 5.29) remains relatively constant as the superficial velocity changes. As in the WBA case, this parameter should be kept constant in designing a decolorization system. The decolorizing resin has the strongest affinity for colorant of all three resins. It is interesting to note that similar constants are obtained for the different pseudocomponents. Table 5.10: DECOL column isotherm parameter as a function of superficial velocity DECOL u0 (m/h) B C D E F 7 3.68 142.50 113.47 104.16 110.32 97.94 8 5.50 152.65 119.50 152.53 164.04 161.28 9 6.36 148.98 119.38 140.08 137.18 114.97 73 160 140 120 100 k' (1/h) 80 60 40 20 0 3 3.5 4 4.5 5 5.5 6 6.5 7 u0 (m/h) B C D E F Figure 5.28: DECOL mass transfer coefficient versus superficial velocity 180 160 140 120 100 K 80 60 40 20 0 3 3.5 4 4.5 5 5.5 6 6.5 7 u0 (m/h) B C D E F Figure 5.29: DECOL adsorption parameter versus superficial velocity It is important to examine the amount of colorant that goes unmodeled (Table 5.11). In designing a process, a certain percentage of the feed color concentration will be completely removed and need not be modeled. Again, the material has least affinity for the resin that is most important. There is a large 74 amount of scatter in this data (Figure 5.30) making it impossible to determine the exact dynamics of this parameter. Further experimentation is required. Table 5.11: DECOL unmodeled color removal as a function of superficial velocity DECOL u0 (m/h) B C D E F 7 3.68 20.3% 2.5% 6.0% 3.4% 9.7% 8 5.50 37.3% 21.1% 0.0% 0.0% 4.5% 9 6.36 32.6% 18.9% 7.6% 11.9% 38.2% 45% 40% % Unmodeled color removal 35% 30% 25% 20% 15% 10% 5% 0% 3 3.5 4 4.5 5 5.5 6 6.5 7 u0 (m/h) B C D E F Figure 5.30: DECOL unmodeled color removal versus superficial velocity 5.6 Regeneration Aids Since bonds between the colorant and the resin can be hydrophobic in nature (Bento et al, 1996), it makes sense to investigate the possibility of using a methanol 75 wash to remove colorants from the resins. A 50% aqueous solution of methanol was used to good effect on the SAC column removing a significant amount of color. No significant color was observed in the effluents of the other resins. After washing the SAC resin with two bed volumes of methanol, a sample of the effluent was placed in a vacuum oven to evaporate the methanol. The sample was then analyzed with GPC. A significant amount of color was detected (Figure 5.31) at retention times less than 15 minutes (8,000MW). The evaporated sample was also analyzed for ICUMSA color, yielding a result 40,700 IU. This color was not removed in a typical regeneration. An increase in resin capacity for colorant should be obtained by performing methanol washes. It has been noticed that the decolorizing potential of the SAC resin does decrease after many cycles1. This may be caused by inadequate removal of color from the resin in regeneration. 300 200 100 Response 0 0 -100 5 10 15 20 25 30 -200 -300 Retention time (min) RI ABS 420nm Figure 5.31: GPC analysis of SAC methanol wash effluent 1 Rolf Reiman, Personal communication 76 Ethanol washes were also investigated and gave very similar results to the methanol case but have not been reported here. Prior to GPC analysis, all the organic solvent must be removed. Ethanol forms an azeotrope with water and so cannot be completely removed form the sample. Rossitter et al (2002) showed substantial benefits in using UF retentate as a feedstock to an ethanol distillery. This would make the possibility of regularly SAC ethanol washes attractive. The resin could be washed with ethanol from the distillery and the effluent returned directly to the process. The colorant would leave the process in the distillery effluent. 5.7 Color Transfer in Crystallization Sugar was crystallized from ultrafiltered syrup to investigate the transfer of color to the sugar crystal. The samples analyzed are the UF syrup feed, raw sugar and affinated sugar. The affination was performed by the method suggested in the SASTA Laboratory handbook. This removes the outer layer of the crystal removing the molasses coating. Measuring the color of the affinated sugar gives the color transfer to the crystal. Raw sugar color is the color transferred to both the molasses film and the crystal. It must be noted that only one crystallization has been performed so these results may only be used as an indication of the color transfer. By the time all the syrup was ultrafiltered, a significant amount of dextran had formed. This can be seen clearly by comparing Figure 5.32 for this case, to Figure 5.12 for regular ultrafiltered syrup. This caused difficulty in boiling, yielding small, elongated crystals. 77 4 3.5 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 GPC-RI Signal / Brix Dextran formation Retention Time (min) Raw Sugar UF Syrup Affinated Sugar Figure 5.32: Sugar Crystallization: GPC-RI chromatograms The partition coefficient of ICUMSA color was measured as 17.4% to the raw sugar and 1.8% to the crystal. The transfer to the crystal is very similar to the average 2% measured by Lionnet (1998). All the color concentrations are defined as color (absorbance) per unit brix. The samples were also analyzed using GPC, and reported as a response per unit brix. The refractive index chromatograms are displayed in Figure 5.32. A large amount of material is transferred to the film around the crystal, the difference between the raw and affinated chromatograms. Most of the film is removed in affination. Figure 5.33 shows the GPC-ABS chromatograms. The pseudo-components may then be determined using the standard technique and their transfer factor calculated (Figure 5.34). In each case, approximately a half to a third of the color appears to be in the sugar crystal itself. Component F has not been calculated as at the high concentrations used, an enlarged water peak (negative) occurs. 78 This reduces the measured color in the F range. It is interesting that all the color using the GPC technique appears to be bad color. Component E transfers more than the others do and so careful attention must be paid to it in designing a process. 1200 1000 GPC-ABS Signal / Brix 800 600 400 200 0 0 5 10 15 20 25 30 Retention Time (min) Raw Sugar UF Syrup Affinated Sugar Figure 5.33: Sugar Crystallization: GPC-ABS chromatograms 30% 25% Transfer Factor, Pi 20% 15% 10% 5% 0% A B C D E Pseudo-Component Pi,raw Pi,affinated Figure 5.34: Sugar Crystallization: Pseudo-component transfer 79 CHAPTER 6. CONCLUSIONS 6.1 GPC as an Analytical Tool The ICUMSA color method has serious shortcomings in measuring the dynamics of a process owing to the indiscrete nature of cane sugar colorant. The problem is that colorant is made up of many components that behave differently in a process. Using GPC as a tool to measure color pseudo-components has been particularly useful as it allows the components to behave differently in a process model. Essentially the functionality has been stepped up from one equation, to a set of equations, one for each defined pseudo-component. The different behaviors viewed in the adsorption experiments suggest that GPC may be a useful tool in analyzing other sugar solution color related processes. For a decolorizing process to be designed for maximum color removal it must be designed for the component that is least removed. ICUMSA cannot give any information about this issue. 6.2 Validity of the Plug-Flow Model A number of assumptions were made in the modeling process. The first was that the color pseudo-components may be used independently of each other. In other words, multi-component models are not required. The only coupling between the governing equations is in the equilibrium expression. component Langmuir isotherm: qi = q max,i K i Ci 1 + K i Ci (6.1) Consider the multi- As Ci 0 , qi q max,i K i Ci . Clearly if our colorant components are dilute enough, the equilibrium expressions can be considered independently. In our case 80 q max,i K i was grouped as a single parameter K for each component. The high molecular weight components in cane sugar solutions are in the parts per million concentration range. The refractive index detector showed no correlation to the absorbance detector, showing that the non-colored components are present in far greater concentrations. It may therefore be concluded that cane sugar colorants are extremely dilute and so modeling of their adsorption dynamics may be performed using single component models. It was also assumed that the fluid passing through the packed-beds is in plug-flow. This assumption was validated by performing a regression using the axial dispersion model (Equations 3.2 and 3.6). The regression terminated with a Peclet number in excess of 35. Froment and Bischoff (1990) recommend Peclet number based on particle diameter between 1 and 2. Multiplying the regressed Peclet number by the length to diameter ratio yields an extremely large particle based Peclet (over 1,000). The Peclet number appears as its inverse in equation 3.2, making the axial dispersion term very small. It is reasonable to use the plug-flow model to model the color adsorption process. 6.3 SAC Resin The SAC showed particularly interesting dynamics. Affinity of colorants for this resin is seriously affected by pH. As the pH increases, the adsorption parameter greatly decreases causing some components to elute from the column and others to be retained less by the resin. The decrease was modeled using an adapted Arrhenius equation allowing prediction of this phenomenon. The regressed model parameters were found to be reasonable. The mass transfer coefficient showed relationships 81 close to those in literature. The resin was shown to have particularly strong affinity for the high molecular weight component B. Components E,D and F were severely affected by the pH change causing major drops in decolorization. If the resin is to be operated making use of its full decolorizing power the pH must not be allowed to increase in the column. The conductivity of the product appeared to be a good indicator of the state of the resin. A falling conductivity gave some advanced warning of the impeding color problem. Operating in the low conductivity, softening, region allows the removal of divalent cations (e.g. calcium, magnesium) increasing the ash capacity of the resin. This becomes less attractive when the decolorizing ability of the resin is considered. The use of a methanol wash was effective in quickly removing a large portion of color from the SAC resin that was not removed in regeneration. Ethanol washing become particularly attractive when operating a distillery on the WSM retentate and molasses. Despite not being investigated here, the drop in decolorizing ability of the SAC resin over many loading/regeneration cycles may be attributed to incomplete regeneration. A more thorough investigation into the use of methanol or ethanol washes is recommended. 6.4 WBA Resin The weak-base anion exchange resin showed much simpler dynamics than the SAC resin. Unlike the SAC resin, pH did not influence the adsorption parameter strongly. Constant K values were found sufficient, allowing the use of the analytic model. The resin also showed differing mass transfer effects as the mass transfer coefficient increased greatly at higher flow rates. The batch test also indicated 82 stronger mass transfer limitations than the SAC resin, causing the WBA resin to take longer to reach equilibrium. Higher affinities for colorant were observed for the WBA resin, particularly for the low molecular weight material. The lack of a pH effect makes the resin simple to design as only the deashing conditions need be considered. The resin is a good follow up to the SAC resin, as the SAC resin has a higher affinity for the large material, whereas the WBA material has higher capacities for the low molecular weight material. 6.5 Decolorizing Resin The affinity of the decolorizing resin for colored bodies is far higher than any of the other resins. The constant linear isotherm model was found to be sufficient, except that the feed concentration (unmodeled color removal) was used as a variable in the regression. The decolorizing resin also showed far higher mass transfer coefficients than the SAC and WBA resins. Further experimentation is required to investigate the unmodeled color removal as scatter was observed in the regressed data. 6.6 WSM Process Design The model data may be used to size a WSM ion exchange process in conjunction with the current design techniques. decolorization would follow these steps: i. Designing for optimal Set the SAC resin volume by deashing requirements. The operating condition must be constrained to the high conductivity region; 83 otherwise, the decolorization capacity of the resin will be greatly reduced. ii. Since the WBA resin displays constant adsorption parameters, this resin may be sized only on deashing considerations. iii. The models for the resins must then be employed to calculated the WBA product. First, the SAC model used on the UF syrup feed, and subsequently the WBA model on the SAC product. iv. The model for the decolorizing resin is then used to calculate the required volume of resin. 6.7 Future Research Directions More advance GPC detectors have been used in studying colorant. Bento et al (1997) used Evaporative Light Scattering (ELS) detection in place of the RI detector and a Diode Array Detection (DAD) instead of the absorbance detector. DAD allows the absorbance measurement over a large range of wavelengths instead of just one. Colorants show absorbance in the UV region and so this gives a lot more information about the colorant. Analysis of DAD chromatograms is complex as they are three dimensional, having retention, response and wavelength axes. It may be more practical to analyze colorants at a single UV wavelength making use of the higher absorbances in this region. There is a clear need for more experimental data. More column tests would allow a complete picture to be developed over a range of fluid velocities. 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Witcamp, G.J. & von Rosmalen, G.M. (1990). Continuous crystallization of calcium sulphate phase from phosphoric acid solutions. Crystallization as a separation process, Amer. Chem. Soc. Symposium Series, 438: 381-394. Wu, F.-C., Tseng, R.-L. & Juang, R.-S. (1999). Role of pH in metal adsorption from aqueous solutions containing chelating agents on chitosan, Ind. Eng. Chem. Res., 38: 270-275. Zumstein, R.C., Gambrel, T. & Rousseau, R.W. (1990). Factors affecting the purity of L-isoleucine recovered from batch crystallization. Crystallization as a separation process, Amer. Chem. Soc. Symposium Series, 438: 381-394. 90 APPENDIX A. SAMPLE CALCULATIONS A.1 ICUMSA Color Set pH to 7.0 0.1 and dilute sample to give a 420nm absorbance between 0.1 and 0.9 AU. Measure 420nm absorbance, A = 0.562 Cuvette length = 10mm Measure brix of sample in cuvette, b = 6.77 Convert to concentration using equation 4.2 Concentration (g/100ml) = 4.021 10 2 {6.77} + 0.9978{6.77} = 6.94 g / 100ml = 0.0694 g / ml 2 Calculate ICUMSA color (round to nearest hundred) ICUMSA 420 = 10,000 A c l 10,000 0.562 = 0.0694 10 = 8100 A.2 A.2.1 a.) b.) c.) d.) GPC Chromatogram Analysis Refractive Index Deconvolution Algorithm Obtain initial guess Load chromatogram Set baseline (user input) see Figure A.1 Set sugar peak see graph A.1 The sugar peak is set by fitting a Gaussian curve to the front-leg of the sugar peak 91 e.) Using the initial guesses, a set number of Gaussian distributions are added together to fit the chromatogram. Zoom to bes t view for s ugar peak detec tion (P res s enter when done) 1000 800 600 400 200 Sugar Peak Baseline 12 14 16 18 20 22 24 0 Graph A.1: Setting of baseline and Sugar peak The regression is carried out in three constrained steps. This is required as if the algorithm is allowed to use all values at once convergence is poor, depending on the accuracy of the initial guesses. f.) The first regression is on the standard deviations as these are difficult to estimate. A least-squares nonlinear regression is performed on the first derivative, since it sharpens up the chromatogram. g.) h.) The second regression is on the retention times using the first derivative. The third regression is on standard deviation and maximum value on the original chromatogram 92 i.) Each Gaussian curve (Graph A.2) is integrated to determine the peak area. j.) The sum of the peaks is compared with the original curve to determine the correlation coefficient R2. (Graph A.3) 120 100 80 60 RI 40 20 0 12 14 16 18 Retention tim e (m in) 20 22 Figure A.2: Regression of RI Chromatograms with seven Gaussian profiles 93 140 M easured Calc ulated 120 100 80 RI 60 40 20 0 -20 -40 10 12 14 16 18 Retention tim e (m in) 20 22 Figure A.3: Comparison of regressed and measured data (R2 = 0.997) A.2.2 Absorbance Detector Algorithm A program was written to generate the values of the chromatogram at the determined time intervals. This is required, as the absorbance chromatograms did not display enough functionality (peaks) to deconvolute in a similar manner to the RI detector (See Figure A.4). analysis. A baseline correction is also performed in this 94 200 C 150 B D E F Absorbance 100 50 A 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 -50 Retention time (min) Figure A.4: Color pseudo-component measurement The data may be read directly of the chromatogram (Table A.1). The molecular weights of each pseudo-component may be read-off the GPC calibration curve (Figure 4.6). Table A.1: Absorbance pseudo-components from Graph A.4 Pseudo-Component Retention time (min) Molecular weight Absorbance signal A 14.4 10,000 10.64 B 16.6 6,000 142.66 C 18 3,000 177.87 D 19.2 1,800 150.79 E 20.4 1,200 105.61 F 21.2 800 91.87 A.3 Void Fraction Calculation The packed bed void fraction (equation A.1) of each resin is a required parameter in the adsorption calculations. = void volume (m 3 ) bed volume (m 3 ) (A.1) 95 The following values are measured: Vwater VT Vbed Volume of water added (ml) Total volume in measuring cylinder (ml) Volume of resin bed (ml) The voidage can be derived in terms of the measured variables: = For the cation resin, Vvoid Vbrd Vre sin V Vwater = = 1 T Vbed Vbed Vbed (A.2) Vwater = 5.5ml VT = 7.38ml Vbed = 5.8ml Calculating the voidage as in A.2: = 1 7..38 5.5 = 0.676 5.8 A.4 Isotherm Measurement Batch tests were performed in jacketed beakers were used to measure the resin isotherms. For the SAC and WBA resin, the isotherms were measured as a function of time since the solutions would degrade if left overnight owing to the harsh pH conditions. The decolorizing resin isotherm was measured overnight and so the parameters measured are the equilibrium values. This case will not be discussed here since it follows exactly the same steps except no transient analysis is required. The cation resin will be used as a sample calculation. 96 From the experiment the following is obtained: Vre sin Resin volume (ml) measuring cylinder packed-bed Liquid volume (ml) Absorbance responses for pseudo-components form GPC analysis At time, t , the absorbance (analogous to concentration) on the resin may be calculated after correcting for the dilution factor used in the analysis. qi (t ) = Vliquid Ci (t ) - [Ci (t = 0) Ci (t )] Vliquid 1 Vre sin (A.3) For component C the calculation is performed in Table A.2. Table A.2: Calculation of concentration (color) on resin (using 20brix data for the SAC resin) 0 355.4 0 5 264.8 3636.2 10 235.0 4831.6 15 233.7 4885.246 20 230.3 5023.2 25 219.2 5465.6 30 219.0 5473.9 t (min) CC(t) qC(t) This is repeated over all initial concentrations and plotted as Ci (t = 0 ) on the horizontal axis and qi (t ) on the vertical axis. For each time an isotherm may be regressed (Table A.3). In this case a straight-line with slope, K i (t ) , is used. Using the complete set of CC (t = 0 ) versus qC (t ) data, the K C (t ) data is determined (Table A.3) using Microsoft Excel Solver. 97 The K i (t ) data may then be fitted to determine the final equilibrium value using the following equation: K i (t ) = K i ,eq (1 e t ) (A.4) Least-squares regression using this equation yields K C ,eq = 16.37 Table A.3: Calculation of adsorption constants as a function of time from qC (t ) data (SAC) C C (t = 0) 46.7 613.3 641.9 685.2 683.6 622.4 722.7 106.7 1321.9 1676.7 1661.1 1696.0 1824.2 1952.9 129.6 1612.1 1949.2 2200.1 2301.0 2392.8 2593.4 216.5 2200.9 2984.6 3284.2 3503.4 3495.4 3678.8 220.6 1896.6 2620.4 2933.4 3064.5 3312.3 3357.2 355.4 3636.1 4831.6 4885.2 5023.2 5465.6 5473.9 425.3 5384.8 6372.2 6966.6 7355.3 7725.0 7549.5 t 0 5 10 15 20 25 30 K C (t ) 11.21 14.11 15.126 15.83 16.73 16.78 A.5 Packed-Bed Parameter Regression Parameter regression is performed using the MATLAB Optimization Toolbox nonlinear solver routine on a user-defined programming function. The function accepts input model parameters, pH and times at which the solution is required. The breakthrough curve is the returned result. The solver routine 98 minimizes the sum-of-squares by varying the model parameters using the Sequential Quadratic Programming (SLP) technique. A.5.1 Regression Algorithm a.) Define input vectors: Ci ,meas ( ) pH ( ) b.) - Dimensionless relative time (3.25) Measured component concentration Measured pH Define feed concentration and first guess of model parameters: C0 St K 0 , K1 , Measured feed concentration First guess of Stanton number Equilibrium parameter c.) The minimization may be described mathematically as St , K 0 , K1 , min 2 [F (St , K 1 j 0 , K1 , , pH , j ) Ci ,meas ( j ) ] 2 (A.5) d.) As mentioned above the function F (St , K 0 , K1 , , pH , j ) is calculated in FEMLAB and will be discussed in a separate algorithm below. e.) The result is then displayed and the correlation coefficient (R2) calculated A.5.2 a.) b.) c.) d.) FEMLAB Algorithm Create Geometry Define mesh on which to solve the solution Define PDE coefficients (3.37) Define Boundary coefficients (3.38) 99 e.) Create user defined expression for K ( pH , ) : K ( pH , ) = K 0 e pH ( ) + K1 (A.6) Since the pH term is a function of time measured at discrete points, a one-dimensional interpolation routine using Hermite polynomials was used for the pH. f.) FEMLAB uses the derivative of K ( pH , ) in its calculations. The expression is calculated symbolically by FEMLAB. The derivative of pH ( ) may not be calculated symbolically. The derivative may be evaluated numerically but this is a lot slower than using a defined expression. The advantage of using the interpolation routine is that it contains the derivative of pH ( ) using the Hermite polynomials. This greatly decreases the time to generate a solution. g.) The model solution may then be calculated: C (, ) q (, ) Fluid concentration for all positions and times Resin concentration for all positions and times There are a number of options in the FEMLAB function, femtime, that require alteration from the default settings if the problem is to be successfully solved. i. Streamline diffusion stabilization is an option that is used for hyperbolic PDEs. This option instructs FEMLAB to make use of the PDE characteristics1 (preferred directions). The solution goes unstable without making use of this option. 1 FEMLAB Version 2.2 Reference Manual, Comsol Inc. (2001) 100 ii. The highly nonlinear problem option must be checked as this reduces the damping parameters used in the solver. h.) From this data the breakthrough curve, F (St , K 0 , K1 , , pH , j ) , is then extracted as the function return. F (St , K 0 , K1 , , pH , j ) = C ( = 1, ) (A.7) 101 APPENDIX B. SAC RESIN RESULTS B.1 SAC Resin Isotherms 700 600 500 Color in Resin 400 300 200 100 0 0 5 10 15 20 25 Initial Color in Solution 5 Linear (5) 10 Linear (10) 15 Linear (15) 20 Linear (20) 25 Linear (25) 30 Linear (30) Figure B.1: Color component A - SAC isotherm as a function of time 9000 8000 7000 Color in Resin 6000 5000 4000 3000 2000 1000 0 0 50 100 150 200 250 300 350 400 In...