modeling adsorption of cane sugar colorant in packed-bed

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Louisiana State University LSU Digital Commons LSU Master's eses Graduate School 2002 Modeling adsorption of cane sugar colorant in packed-bed ion exchangers Hugh Anthony Broadhurst Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: hps://digitalcommons.lsu.edu/gradschool_theses Part of the Chemical Engineering Commons is esis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's eses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. Recommended Citation Broadhurst, Hugh Anthony, "Modeling adsorption of cane sugar colorant in packed-bed ion exchangers" (2002). LSU Master's eses. 3447. hps://digitalcommons.lsu.edu/gradschool_theses/3447

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Page 1: Modeling adsorption of cane sugar colorant in packed-bed

Louisiana State UniversityLSU Digital Commons

LSU Master's Theses Graduate School

2002

Modeling adsorption of cane sugar colorant inpacked-bed ion exchangersHugh Anthony BroadhurstLouisiana State University and Agricultural and Mechanical College

Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses

Part of the Chemical Engineering Commons

This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSUMaster's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected].

Recommended CitationBroadhurst, Hugh Anthony, "Modeling adsorption of cane sugar colorant in packed-bed ion exchangers" (2002). LSU Master's Theses.3447.https://digitalcommons.lsu.edu/gradschool_theses/3447

Page 2: Modeling adsorption of cane sugar colorant in packed-bed

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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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.

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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

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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

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GLOSSARY OF TERMS

Affination The process of removing the molasses film from sugar

crystals with a saturated sugar solution

Ash Inorganic dissolved solids

ABS Absorbance

Breakthrough When the adsorbent can no longer absorb all of a solute

species from the feed.

Brix Total dissolved solids (%m/m)

Chromatography A term for methods of separation based upon the portioning

of a solute species between a stationary phase and a mobile

phase

DECOL Decolorizing resin

GPC Gel Permeation Chromatography

HPLC High performance liquid chromatography

ICUMSA International Commission for Uniform Methods of Sugar

Analysis

MW Molecular weight

Pol Apparent sucrose content (% m/m)

Purity Percent of pol (or true sucrose) to brix

RI Refractive index

SAC Strong-acid cation ion exchange resin

WBA Weak-base anion ion exchange resin

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WSM White Sugar Mill – The process of making white sugar

directly from sugarcane using ultrafiltration and ion

exchange.

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NOMENCLATURE

Symbol Description Units A Column cross-sectional area m2 As Sample absorbance at 420nm AU C Concentration in bulk fluid mV C* Concentration of fluid in equilibrium with adsorbent mV C0 Feed concentration mV Ci Concentration of component i g/ml or mV da FEMLAB – Time derivative coefficient matrix dp Particle diameter m D Axial dispersion coefficient m2/min

DAB Diffusivity of component A in B m2/s E Activation energy J/mol F FEMLAB – Remaining terms in PDE vector JD Chilton-Colburn analogy J-factor [-] k' Effective mass transfer coefficient 1/min

kLa Mass transfer coefficient 1/min k’c Mass transfer coefficient in Geankoplis’ correlation m/s

kr(T) Reaction rate 1/min k0 Term in Arrhenius expression 1/min K Adsorption parameter q = K.C* [-]

K(t) Time varying adsorption parameter [-] KC0 Adsorption parameter based on initial concentration [-] Keq Equilibrium adsorption parameter [-]

K0, K1 Parameters in K(pH) [-] L Column length M

MA Molecular weight [-] n FEMLAB – Outward normal on domain boundary q Concentration on solid phase AU q0 Initial resin concentration AU Q Volumetric fluid flow rate m3/min R FEMLAB – Dirichlet boundary condition vector or

Universal Gas Constant

Re Reynold’s number Re = duiρ/µ [-] Sc Schmidt number Sc = µ/ρDAB [-] St Stanton number St = k'L/ui [-] t Time variable min t0 Peak time of Gaussian distribution or

Initial time parameter in batch tests min

T Temperature K u FEMLAB – Dependent variables vector u0 Superficial fluid velocity m/min ui Interstitial fluid velocity m/min

Vbed Volume of resin in packed-bed (voidage measurement) ml Vliquid Volume of liquid (batch tests) ml Vresin Resin volume – measured as a packed-bed in a measuring

cylinder (batch tests) ml

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Symbol Description Units VT Total volume (voidage measurement) ml

Vwater Volume of water added (voidage measurement) ml xi(t) Gaussian distribution i xmax Maximum value of a Gaussian distribution X(t) Cumulative Gaussian distribution

z Distance from top of column m

Symbol Description Units β Time constant in batch tests 1/min ε Packed-bed void fraction [-] φ Dimensionless relative time scale variable [-] Γ FEMLAB - First derivatives of distance variables vector η Dimensionless distance [-] λ Rate constant in K(pH) µ Dynamic viscosity Pa.s ρ Density kg/m3 σ Standard deviation in Gaussian distribution ξ Relative time scale variable min Ω FEMLAB – PDE domain

Subscript Description i Component or interstial 0 Feed/initial or superficial

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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

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x

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.

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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

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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 Clarification

Evaporation 4 Stage Crystallization Centrifugation White

Sugar

Whitestrap Molasses

Ultrafiltration Refrigeration & HX

Cation ISEP

Anion ISEP Decolorization

Figure 1.2: White sugar mill flowsheet

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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 Corporation’s 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. ISEP’s have been used in the South African sugar industry at the Tongaat-

Hulett 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

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such high purity and low color that four crystallization stages maybe performed.

The benefits of the process include (Rossiter, 2002):

i. Increase in yield

ii. Increase in sugar quality: white sugar not raw sugar is produced

iii. Production of high-grade molasses (termed whitestrap molasses)

iv. No fouling in evaporators and vacuum pans

v. 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

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5

the resins. This may reduce the currently high loading on the decolorizing

operation.

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 pseudo-

components 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

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CHAPTER 2. BACKGROUND

2.1 Cane Sugar Colorant

2.1.1 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

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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

Colorant Type General Characteristics

Phenolic

Low MW colorless to light yellow precursors; darken at high pH;

oxidize to form yellow and brown polymers; react with polyphenol

oxidase to form light yellow to dark brown colorants. Darken in

presence of iron.

Caramel

The result of thermal degradation of sucrose; low net charge; wide

color range from yellow to brown; MW 500 to about 1,000; MW and

color increases as thermal destruction proceeds.

Alkaline Degradation Products (ADPs)

Similar to caramels, but much darker in color; form at high pH.

Melanoidin

Maillard reaction – reaction products of amino acids with reducing

sugars; reaction occurs rapidly at alkaline pH; products are dark brown.

Colorant Polysaccharide Complex

Polysaccharides formed in cane have phenolic groups and dicarboxylic

acid functionalized lipids that can bind with colorant to make a very

high MW product. Occludes preferentially into the crystal.

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2.2 Quantifying Colorant

2.2.1 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:

bcAS 000,10color 420ICUMSA ×

= (2.1)

The absorbance, , is divided by the product of the dissolved concentration, c

(g/ml), and the cell width, b (mm).

SA

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

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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.

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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 Removal of Cane Sugar Colorant

2.3.1 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

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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 0.45 units

• Removal of

Turbidity 95%

Dextran 98%

Starch 70%

Total polysaccharides 80%

ICUMSA Color 25%

Membrane suppliers offer a wide range of pore sizes, however no major

difference in color removal is experienced (Crees, 1986; Kochergin, 1997; Patel,

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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.

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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,

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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 1970’s, 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 62.8%

• Melanoidins 97.5%

• Alkaline degradation Products 98.0%

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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

Page 27: Modeling adsorption of cane sugar colorant in packed-bed

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

Page 28: Modeling adsorption of cane sugar colorant in packed-bed

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

Page 29: Modeling adsorption of cane sugar colorant in packed-bed

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:

solution

crystal

i

ii C

CP = (2.2)

Ideal behavior occurs when 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.

iP

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

Page 30: Modeling adsorption of cane sugar colorant in packed-bed

19

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.

Page 31: Modeling adsorption of cane sugar colorant in packed-bed

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. This equilibrium may be

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)

Concentration in liquid

Con

cent

ratio

n on

sol

id

Langmuir Freundlich Linear

Figure 3.1: Common liquid phase isotherms

20

Page 32: Modeling adsorption of cane sugar colorant in packed-bed

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 ε. Q,C(z)

q(z) z

q(z+dz) z + dz

Q,C(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.

( )44344214342144444 344444 21

44 344 21

phase solidin onAccumulati

phase fluidin onAccumulatiDispersion Axial

flow Fluid

1 AdztqAdz

tC

zCDA

zCDAQCQC

dzzzdzzz ∂

∂−+

∂∂

=

∂∂

−−

∂∂

−+−+

+εεεε

Adz

(3.1)

Dividing by and taking limits, (Note: set AQ

=0u )

( )tq

tC

zCD

zCu

∂∂

−+∂∂

=∂∂

+∂∂

− εεε 12

2

0 (3.2)

Two fluid phase concentration boundary conditions are required.

i.) ( ) 0,0 CtzC ==

ii.) (3.3) ( ) 0, =∞= tzC

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

Page 33: Modeling adsorption of cane sugar colorant in packed-bed

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 (3.4) ( ) 00, ==tz3.1.2 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

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.

( ) ( )44 344 21

4434421(LDF) phase liquid

thefrom uptake of Rate

*

phase solid in theonaccumulati of Rate

1 AdzCCakAdztq

L εε −=∂∂

− (3.5)

22

Page 34: Modeling adsorption of cane sugar colorant in packed-bed

Simplifying,

( ) ( εε *1 CCktq

−′=∂∂

− ) (3.6)

An initial condition is required for this equation,

( ) 00, ==tzq (3.7)

3.2 Plug Flow Adsorption Model 3.2.1 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.

01=

∂∂−

+∂∂

+∂∂

tq

tC

zCui ε

ε (3.8)

( *1 CCktq

−′=∂∂−

εε ) (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).

( ) ( ) ( )

−′

−′

−−= ∫⋅′

− αε

αε

εα d

uzt

KkI

uzt

KkeCztC

io

uzk

i

i

12

1exp1,

00

(3.10)

23

Page 35: Modeling adsorption of cane sugar colorant in packed-bed

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:

*

( )

−′=

∂∂−

pHKqCk

tq

εε1 (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:

iuzt −=ξ (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

Page 36: Modeling adsorption of cane sugar colorant in packed-bed

Using the chain rule:

ξξξ

dCdzzCdt

tCdz

zC

zzt ∂∂

+∂∂

=∂∂

+∂∂ (3.13)

Also, from 3.12:

iu

dzdtd −=ξ (3.14)

Equating the multipliers of dz on each side of the 3.13:

zit

Cuz

CzC

ξξ ∂∂

−∂∂

=∂∂ 1 (3.15)

Using the same approach for dt,

zz

CtC

ξ∂∂

=∂∂ (3.16)

Similarly,

zz

qtq

ξ∂∂

=∂∂ (3.17)

Substituting the variable transformations into the governing equations (3.8 and 3.11)

yields,

011=

∂∂−

+∂∂

+

∂∂

−∂∂

ξεε

ξξqCC

uzCu

ii (3.18)

−′=

∂∂−

KqCkq

ξεε1 (3.19)

It is convenient to substitute equation 3.19 into 3.18 to remove the derivative.

−′−=

∂∂

KqCk

zCui (3.20)

25

Page 37: Modeling adsorption of cane sugar colorant in packed-bed

3.2.3 Conversion to Dimensionless Form

Reduction to dimensionless form is performed using η and φ, as defined

below, where is a parameter still to be defined. x

xξφ =

Lz

=η (3.21)

Making the variable transformation and substituting for the Stanton number,

iuLkSt′

= :

−−=

∂∂

KqCStC

η (3.22)

−⋅

−=

∂∂

KqCStx

Luq i

εε

φ 1 (3.23)

Equation 3.23 can be simplified by defining as, x

iuLx

εε−

=1 (3.24)

Yielding

−=

∂∂

KqCStq

φ (3.25)

Substituting into the definition of , x φ

−=

−=

i

i

i

uzt

LuLu

εε

ξε

εφ

1

1 (3.26)

The boundary and initial conditions are essentially unchanged in the transformation,

26

Page 38: Modeling adsorption of cane sugar colorant in packed-bed

( ) 0,0 CC == φη

C ( ) 00, ==φη

(3.27) ( ) 00, ==φηq

3.2.4 Plug Flow Model Summary

( )

−−=

∂∂

pHKqCStC

η (3.28)

( )

−=

∂∂

pHKqCStq

φ (3.29)

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:

3

2Re09.1 −

=εDJ (3.30)

where,

µρ0Re

ud p= , ( ) 32

i

c Scuk′

=DJ , and ABDρ

µ=Sc (3.31)

The fluid properties of an aqueous sugar solution at 20 brix at 10oC are (Bubnik et

al, 1995):

Pa.s 31064.2 −×=µ

kg/m3 1083=ρ

Yielding a and a . 34.0Re = 30.3=DJ

27

Page 39: Modeling adsorption of cane sugar colorant in packed-bed

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:

( )( ) 3

1

151040.9

A

ABM

KTDµ

−×= (3.32)

At 10oC and assuming a molecular weight of 6,000, m2/s. The

Schmidt number can then be calculated, . Noting that:

111064.5 −×=ABD

7.194,43=Sc

p

c

dkk′

=′ (3.33)

The Stanton number may then be calculated

091.1==′

=p

c

dkSt τ

This estimation of the Stanton number will be useful in confirming the estimated

Stanton number from the regression of the model.

3.3 Numerical Solution Technique

3.3.1 The Finite Element Method

In the 1950’s 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

Page 40: Modeling adsorption of cane sugar colorant in packed-bed

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 one-

dimensional 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:

Ftuda =Γ⋅∇+∂∂ in (3.34) Ω

The above equation is the general system of PDE’s in the domain Ω . The solution

vector of the dependent variables is u. The time derivative is preceded by the

coefficient matrix and Γ represents the vector of partial derivatives with respect

to the independent distance variable. Any remaining terms are placed into the

vector F.

ad

29

Page 41: Modeling adsorption of cane sugar colorant in packed-bed

The boundary conditions of the domain, on ∂ , are represented for the

Neumann (constant derivative) case as:

Ω

0=Γ⋅− n on ∂ (3.35) Ω

In the above equation n is the outward normal, and Γ as in equation 3.34. For the

simpler Dirichlet conditions (dependent variable equal to a constant),

30

0 on ∂ (3.36) =R Ω

is used. The expression is substituted into the vector R. Expanding the above PDE

to the derived case yields:

=

ΓΓ

⋅∇+

∂∂

2

1

2

1

2

1

22,21,

12,11,

FF

uu

tdddd

aa

aa in (3.37) Ω

3.3.3 FEMLAB Parameters

Converting the governing PDE’s (3.28 and 3.29) and associated boundary

conditions to this general form yields the parameters to enter into FEMLAB.

=

qC

u

=

1000

ad

0C

( )

( )

−−

=

pHKqCSt

pHKqCSt

F (3.38)

The boundary conditions are all of the Dirichlet form:

−+−

=qCC

R 0 (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.

Page 42: Modeling adsorption of cane sugar colorant in packed-bed

CHAPTER 4. MATERIALS AND METHODS

4.1 Experiments

4.1.1 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. The feed was prepared by

ultrafiltration through a 0.45µm membrane. 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

Page 43: Modeling adsorption of cane sugar colorant in packed-bed

Permeate

Retentate

Steam

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.) Heat to approximately 65oC with steam

c.) Open feed valve and start pump

d.) Set cross membrane pressure to 100psi by adjusting flow control valve

e.) Start oscillating motor and set vibration to recommended amplitude

f.) Alter motor setting throughout run to maintain constant amplitude

throughout concentration

g.) When feed runs low turn-off oscillating motor and feed pump

h.) Washout feed tank and fill with water

i.) Heat to scalding and add a small amount of bleach

j.) Start pump and motor and clean membrane for 10 to 15min

k.) Empty tank and refill with water

l.) 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

Page 44: Modeling adsorption of cane sugar colorant in packed-bed

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

investigated by altering the concentration of the feed. Volumes of resin are

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

Page 45: Modeling adsorption of cane sugar colorant in packed-bed

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

Page 46: Modeling adsorption of cane sugar colorant in packed-bed

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 Type Form Feed

Rohm & Haas Amberlite 252 RF Strong acid cation (SAC) H+ 20%brix UF syrup

Rohm & Haas Amberlite IRA 92 RF Weak base anion (WBA) OH- Cation product

Rohm & Haas Amberlite IRA 958 Strong base anion (decolorizing) Cl- 10%brix UF syrup

Figure 4.3: Column loading apparatus

Water- Bath

10oC

Feed

Resevoir

pH

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

Page 47: Modeling adsorption of cane sugar colorant in packed-bed

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. The ICUMSA color of a number of samples is also

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 Regenerant Temperature

SAC 6% HCl 25oC

WBA 10% NaOH 60 oC

Decol. 10% NaCl; 0.2% NaOH 60 oC

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

Page 48: Modeling adsorption of cane sugar colorant in packed-bed

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

Page 49: Modeling adsorption of cane sugar colorant in packed-bed

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 Sample Analysis

4.2.1 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 7±0.1 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

0.45µm 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:

( ) ( )mmlength Cell(g/ml)ion Concentrat

000,10420nmAbs Color 420nmICUMSA ⋅×

= (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.

( ) Brix9978.0Brix10021.4g/100mlion Concentrat 22 +×= − (4.2)

38

Page 50: Modeling adsorption of cane sugar colorant in packed-bed

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 pH’s (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 Cell constant

10µS/cm – 1mS/cm 1cm-1

>1mS/cm 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

Page 51: Modeling adsorption of cane sugar colorant in packed-bed

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 100µl 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.

Pump

Colum

n H

eater ABS 420nm Detector

Autosampler

RI Detector

Fraction Collector

Computer Interface

Signal Liquid flows

Drain

Solvent Resevoir

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

(Version 4). Dextran standards, sucrose and water were used to generate a

molecular weight calibration curve (Figure 4.5). The detectors can be calibrated to

40

Page 52: Modeling adsorption of cane sugar colorant in packed-bed

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.

10

100

1000

10000

100000

1000000

10000000

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Retention Time (min)

MW

Figure 4.5: GPC Molecular Weight Calibration

Samples were prepared by diluting to 7-10 %brix and filtering through a

5.0µm syringe filter. Godshall et al (1988) show that a 0.45µm filter removes very

high molecular weight material. This was confirmed by GPC analysis. A 5.0µm

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

4.2.4.1 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

Page 53: Modeling adsorption of cane sugar colorant in packed-bed

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):

( )( )

20

2max

σtt

extx−

−= (4.3)

where is the maximum concentration attained, t is the retention time at the

peak and 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.

maxx

σ

0

2

0 1 2 3 4 5 6 7 8

t

x

Single species

0 1 2 3 4 5 6 7 8

t

x

Two Species (No deconvolution required)

xmax

t0 σ2

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

Page 54: Modeling adsorption of cane sugar colorant in packed-bed

0 2 4 6 8 10

t

X

12

x1 x2 X

Figure 4.8: Two Gaussian distributions deconvoluting a chromatogram

For N components the recorded signal X is:

( ) ( ) ( ) ( )

( )

∑=

−−

=

+++=

N

i

tt

i

N

i

i

ex

txtxtxtX

1max,

21

2,0

....

σ (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.

4.2.4.2 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

Page 55: Modeling adsorption of cane sugar colorant in packed-bed

44

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.

Page 56: Modeling adsorption of cane sugar colorant in packed-bed

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).

0

5000

10000

15000

20000

25000

30000

Syrup Caramel ADP

ICU

MC

SA C

olor

Uni

ts (I

U)

Figure 5.1: ICUMSA Color of Caramelization and Alkaline Degradation

45

Page 57: Modeling adsorption of cane sugar colorant in packed-bed

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.

0 5.00 10.00 15.00 20.00 25.00 30.00Retention Time (min)

2-2.00x10

0

22.00x10

24.00x10

26.00x10

28.00x10

31.00x10

31.20x10

31.40x10

RI R

espo

nse

(mV)

ADP

Caramel

Syrup

Sugar Peak

Figure 5.2(a): RI GPC chromatograms for Caramelization and Alkaline Degradation

8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00Retention Time (min)

-40

-20

0

20

40

60

80

100

120

RI R

espo

nse

(mV)

ADP

Caramel

Syrup

Figure 5.2(b): Region of interest in GPC chromatograms

46

Page 58: Modeling adsorption of cane sugar colorant in packed-bed

0

100

200

300

400

500

600

700

>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

RI a

rea

resp

onse

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 ADP’s show more highly colored than the caramel products. Figure 5.4 shows

that ADP’s 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

Page 59: Modeling adsorption of cane sugar colorant in packed-bed

0

2000

4000

6000

8000

10000

12000

14000

16000

>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

Abs

orba

nce

(420

nm) a

rea

resp

onse

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

Sample Acetic Aconitic Citric Formic Lactic Malic Oxalic Propionic

Syrup 1040 2999 310 220 1418 413 33 43

Caramel 687 1141 186 153 937 234 19 n/d

ADP 2058 3243 365 437 2392 492 108 82

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

Page 60: Modeling adsorption of cane sugar colorant in packed-bed

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).

0

20000

40000

60000

80000

100000

120000

140000

160000

Molasses Maillard

Figure 5.5: Increase in ICUMSA Color from the Maillard Reactions

0

500

1000

1500

2000

2500

3000

3500

>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

RI D

etec

tor -

Are

a re

spon

se

Molasses Maillard

Figure 5.6: Maillard Reactions – RI Areas

49

Page 61: Modeling adsorption of cane sugar colorant in packed-bed

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 absorbance’s (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.

0

20000

40000

60000

80000

100000

120000

>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

Abs

orba

nce

(420

nm) -

Are

a re

spon

se

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

Page 62: Modeling adsorption of cane sugar colorant in packed-bed

ferrous iron (Fe2+) can form complexes with phenolics and caramels to form darker

products. To investigate these effects three experiments were performed.

i. Untreated cane juice was exposed to iron – enzymes still active

ii. 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). For the

remainder of this analysis the RI changes will not be included.

0

5

10

15

20

25

30

35

40

45

50

>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

RI D

etec

tor -

Are

a re

spon

se

Juice Control Clean Fe Rusty Fe

Figure 5.8: The effect of iron on untreated cane juice – RI Area Response

51

Page 63: Modeling adsorption of cane sugar colorant in packed-bed

0

50

100

150

200

250

>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

AB

S (4

20nm

) - A

rea

resp

onse

Juice Control Clean Fe Rusty Fe

Figure 5.9: The effect of iron on untreated cane juice – ABS (420nm) Area Response

0

50

100

150

200

250

>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

AB

S (4

20nm

) - A

rea

resp

onse

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

Page 64: Modeling adsorption of cane sugar colorant in packed-bed

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.

0

50

100

150

200

250

>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

AB

S (4

20nm

) - A

rea

resp

onse

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

Page 65: Modeling adsorption of cane sugar colorant in packed-bed

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

Pseudo-Component A B C D E F

Retention time (min) 14.4 16.6 18 19.2 20.4 21.2

Molecular weight 10,000 6,000 3,000 1,800 1,200 800

5.2 Ultrafiltration

The removal of dissolved solids and color by ultrafiltration may be analyzed

with GPC. Figure 5.12 shows that the 0.45µm 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

Page 66: Modeling adsorption of cane sugar colorant in packed-bed

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.

0

20

40

60

80

100

120

140

160

180

200

0 5 10 15 20 25

Retention time (min)

RI S

igna

l

Feed Syrup Permeate

Figure 5.12: Effect of ultrafiltration: GPC-RI

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25

Retention time (min)

AB

S 42

0nm

Sig

nal

Feed Syrup Permeate

Figure 5.13: Effect of ultrafiltration: GPC-ABS 420nm

55

Page 67: Modeling adsorption of cane sugar colorant in packed-bed

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).

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250

C*(t)

q(t)

A B C D E FLinear (A) Linear (B) Linear (C) Linear (D) Linear (E) 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), , the final equilibrium value may be calculated (see Appendix

C.4, Equation 5.1). This relationship is plotted in Figure 5.15.

( )tKC0

56

Page 68: Modeling adsorption of cane sugar colorant in packed-bed

( ) ( )teq eKtK β−−= 1 (5.1)

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35

Time (min)

KC

0(t)

A B C D E FA (calc) B (calc) C (calc) D (calc) E (calc) 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 A B C D E F

Keq 56.11 67.67 31.62 22.00 17.38 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

Page 69: Modeling adsorption of cane sugar colorant in packed-bed

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.

18.6

18.8

19

19.2

19.4

19.6

19.8

20

20.2

20.4

20.6

20.8

0 5 10 15 20 25 30 35

Time (min)

GPC

Ret

entio

n tim

e (m

in)

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, φ , (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

. During this period hydrogen ions ( ) attached to the resin exchange for

cations ( etc.) in the syrup feed, lowering the pH (see

equation 5.2).

30=φ +H

++++ 22 Mg& Ca ,K ,Na

[ ]+−= HpH 10log (5.2)

58

Page 70: Modeling adsorption of cane sugar colorant in packed-bed

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

φ

C

0

2

4

6

8

10

12

14

16

Con

duct

ivity

(mS/

cm) o

r pH

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 resin’s supply of hydrogen ions is exhausted, the

conductivity begins to drop. It is interesting that at φ 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 φ , 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).

46=

35=

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

Page 71: Modeling adsorption of cane sugar colorant in packed-bed

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

force term,

KqCSt , tending to zero. This is shown graphically in Figure 5.18.

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.

0 20 40 60 80 100 1200

20

40

60

80

100

120

140

160

180

200

φ

C

S t = 1; K = 18; C0 = 180

CC0

Figure 5.18: Constant linear isotherm model solution

If the resins affinity for the solute species (the colorant) were somehow

decreased during the run it would drastically alter the dynamics. Going back to the

linear isotherm, if decreases, then is forced to decrease, releasing material

already absorbed to the resin. This effect appears to explain the phenomena

K q

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Page 72: Modeling adsorption of cane sugar colorant in packed-bed

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).

( ) RTE

r ekTk−

= 0 (5.3)

Since the pH is defined as a logarithmic function, this equation will be

adapted slightly so that is high at low pH conditions and decreases

exponentially to a constant value at low pH conditions (Figure 5.19; Equation 5.4).

(pHK )

( ) 10 KeKpHK pH += −λ (5.4)

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7

pH

K(p

H)

Figure 5.19: Proposed functionality of K with pH

61

Page 73: Modeling adsorption of cane sugar colorant in packed-bed

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 is not perfect (pHK )

• Similar mass transfer effects i.e. ( )pHSt

0 10 20 30 40 50 60 70 80 90 100 1100

20

40

60

80

100

120

140

160

180

200

220

C

φ

St = 1; K0 = 18; K1 = 7; λ = 1

CC0

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

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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, , is proportional to the superficial velocity. The increase in

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.

k ′

k ′

Table 5.4: SAC Stanton number

′=

iuLkSt

as a function of superficial

velocity

SAC 6 8 9

u0 (m/h) 3.75 4.89 6.21

C 0.96211 0.90784 0.8535

D 1.0308 0.91952 1.0431

E 1.0415 1.1358 1.0079

F 1.0799 1.4159 0.9710

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Table 5.5: Regressed SAC column isotherm parameters as a function of superficial velocity

K0 K1 λ

SAC 6 8 9 6 8 9 6 8 9

u0 (m/h) 3.75 4.89 6.21 3.75 4.89 6.21 3.75 4.89 6.21

C 25.73 29.51 16.80 18.57 21.22 10.23 1.034 1.798 0.807

D 19.70 30.88 18.82 6.18 11.98 4.17 1.097 2.009 1.163

E 19.94 22.31 17.90 4.65 5.37 3.94 1.016 1.388 1.130

F 20.11 22.36 17.51 4.50 3.20 3.73 0.960 1.152 1.062

0

5

10

15

20

25

30

35

40

3 3.5 4 4.5 5 5.5 6 6

u0 (m/h)

k' (

1/h)

.5

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.

( ) 31

iuk ∝′ (5.5)

64

Page 76: Modeling adsorption of cane sugar colorant in packed-bed

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

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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.

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30 35 40 45

C*(t)

q(t)

A B C D E F

Linear (B) Linear (C) Linear (D) Linear (E) Linear (F)

Figure 5.22: WBA Isotherms after 30 minutes

Morley (1988) reports an isotherm of form,

0* qKCq += (5.6)

The parameter q 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

0

( ) 00, qq ==φη (5.7)

Fortunately by defining a dimensionless concentration parameter

0qqq −= (5.8)

66

Page 78: Modeling adsorption of cane sugar colorant in packed-bed

The initial condition is returned to zero and can be ignored in the governing

equations. This is particularly convenient as the actual values of are not as

important as the values of C .

0q

q

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).

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30 35 40

Time (min)

KC

0(t)

B C D E F

B (calc) C (calc) D (calc) E (calc) 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 , to take into

account not passing through the origin.

0

( )tK

( ) ( )( )01 tteq eKtK −−−= β (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

Page 79: Modeling adsorption of cane sugar colorant in packed-bed

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 B C D E F

Keq 45.35 47.29 47.82 40.62 50.99

b 205.20 461.97 424.75 360.51 219.33

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 ( ) are released from the resin. As the resin’s 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 resin’s hydroxide ion supply runs out.

−OH

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

φ

C

0

2

4

6

8

10

12

10xC

ondu

ctiv

ity (m

S/cm

) or p

H

D D (feed) pH Conductivity

Figure 5.24: A typical WBA breakthrough curve (WBA6-D)

68

Page 80: Modeling adsorption of cane sugar colorant in packed-bed

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 5 6 7

u0 (m/h) 3.10 3.76 4.28

B 0.54166 0.91915 1.1748

C 1.6502 1.8763 2.5726

D 1.9882 2.1675 3.4093

E 1.9848 2.0009 2.8938

F 2.0038 1.9517 2.8066

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Page 81: Modeling adsorption of cane sugar colorant in packed-bed

0

5

10

15

20

25

30

35

40

3 3.2 3.4 3.6 3.8 4 4.2 4.4

u0 (m/h)

k' (1

/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 5 6 7

u0 (m/h) 3.10 3.76 4.28

B 4.60 13.15 10.38

C 18.46 12.12 12.56

D 22.72 13.99 12.43

E 22.53 14.51 13.96

F 22.93 15.61 14.36

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0

5

10

15

20

25

3 3.2 3.4 3.6 3.8 4 4.2 4.4

u0 (m/h)

K

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 Morley’s 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

Page 83: Modeling adsorption of cane sugar colorant in packed-bed

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250

φ

C

0

2

4

6

8

10

12

pH o

r Con

duct

ivity

(mS/

cm)

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. Morley’s 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

Page 84: Modeling adsorption of cane sugar colorant in packed-bed

Table 5.9: DECOL Stanton number as a function of superficial velocity

DECOL 7 8 9

u0 (m/h) 3.68 5.50 6.36

B 9.092 13.269 14.335

C 5.710 7.766 8.418

D 3.939 3.654 4.596

E 3.383 3.242 4.213

F 3.310 2.685 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 pseudo-

components.

Table 5.10: DECOL column isotherm parameter as a function of superficial velocity

DECOL 7 8 9

u0 (m/h) 3.68 5.50 6.36

B 142.50 152.65 148.98

C 113.47 119.50 119.38

D 104.16 152.53 140.08

E 110.32 164.04 137.18

F 97.94 161.28 114.97

73

Page 85: Modeling adsorption of cane sugar colorant in packed-bed

0

20

40

60

80

100

120

140

160

3 3.5 4 4.5 5 5.5 6 6.5 7

u0 (m/h)

k' (1

/h)

B C D E F

Figure 5.28: DECOL mass transfer coefficient versus superficial velocity

0

20

40

60

80

100

120

140

160

180

3 3.5 4 4.5 5 5.5 6 6.5 7

u0 (m/h)

K

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

Page 86: Modeling adsorption of cane sugar colorant in packed-bed

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 7 8 9

u0 (m/h) 3.68 5.50 6.36

B 20.3% 37.3% 32.6%

C 2.5% 21.1% 18.9%

D 6.0% 0.0% 7.6%

E 3.4% 0.0% 11.9%

F 9.7% 4.5% 38.2%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

3 3.5 4 4.5 5 5.5 6 6.5 7

u0 (m/h)

% U

nmod

eled

col

or re

mov

al

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

Page 87: Modeling adsorption of cane sugar colorant in packed-bed

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

0

100

200

300

0 5 10 15 20 25 30

Retention time (min)

Res

pons

e

RI ABS 420nm

Figure 5.31: GPC analysis of SAC methanol wash effluent 1 Rolf Reiman, Personal communication

76

Page 88: Modeling adsorption of cane sugar colorant in packed-bed

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

Page 89: Modeling adsorption of cane sugar colorant in packed-bed

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

Retention Time (min)

GPC

-RI S

igna

l / B

rix

Raw Sugar UF Syrup Affinated Sugar

Dextran formation

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. This

78

Page 90: Modeling adsorption of cane sugar colorant in packed-bed

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.

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

Retention Time (min)

GPC

-AB

S Si

gnal

/ B

rix

Raw Sugar UF Syrup Affinated Sugar

Figure 5.33: Sugar Crystallization: GPC-ABS chromatograms

0%

5%

10%

15%

20%

25%

30%

A B C D E

Pseudo-Component

Tran

sfer

Fac

tor,

P i

Pi,raw Pi,affinated

Figure 5.34: Sugar Crystallization: Pseudo-component transfer

79

Page 91: Modeling adsorption of cane sugar colorant in packed-bed

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. Consider the multi-

component Langmuir isotherm:

ii

iiii CK

CKqq

+=

1max, (6.1)

As , . Clearly if our colorant components are dilute enough,

the equilibrium expressions can be considered independently. In our case

0→iC iiii CKqq max,→

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Page 92: Modeling adsorption of cane sugar colorant in packed-bed

iiKqmax, was grouped as a single parameter 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.

K

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

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Page 93: Modeling adsorption of cane sugar colorant in packed-bed

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 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

K

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Page 94: Modeling adsorption of cane sugar colorant in packed-bed

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. Designing for optimal

decolorization would follow these steps:

i. Set the SAC resin volume by deashing requirements. The operating

condition must be constrained to the high conductivity region;

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Page 95: Modeling adsorption of cane sugar colorant in packed-bed

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. This

would give the designer a better ability to optimize the process. The foundation has

been laid for the measurement to be made.

84

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85

Another useful task would be applying the column model to the ISEP. This

is primarily a bookkeeping task, tracking the conditions of the resin. The SAC

model would be more difficult to model, as a numeric solution is required. The

heart of the process is however is the column loading performed in this research and

from it the ISEP operation becomes relatively predictable.

Page 97: Modeling adsorption of cane sugar colorant in packed-bed

REFERENCES

Baker & Pepper (1991). Finite Elements 1-2-3, McGraw-Hill Ryerson, Limited, Whitby, ON, Canada. Balakrishnan, M., Dua, M. & Bhagat, J.J. (2000). Ultrafiltration for juice purification in plantation white sugar manufacture, Int. Sugar J., 102 (1213): 21-25. Baunsgaard, D., Nørgaard, L. & Godshall, M.A. (2000). Fluorescence of raw cane sugars evaluated by chemometrics, 48: 4955-4962. Bento, L.S.M., Guimarães, C. & Mota, M. (1996). A study of colorants through ion exchange and salt regeneration, Int. Sugar. J., 98(1175): 584-587. Bento L.S.M., Pereira, M.E. & Sá S. (1997). Improved analysis of sugar colorants by gel chromatography with UV and ELS, Int. Sugar J., Vol. 99, No. 1187: 555-562. Bro, R. (1999). Exploratory study of sugar production using fluorescence spectroscopy and multi-way analysis, Chemom. Intell. Lab. Syst., 46: 133-147. Broadhurst, H.A. & Rein, P.W. (2002). The characterization of cane sugar colorant, Proc. Sug. Processing Res. Conf. (in press). Bubnik, Z., Kadlec, P., Urban, D. & Bruhns, M. (1995). Sugar Technologists Manual. Chemical and Physical data for sugar manufacturers and users, Albert Bartens KG, Berlin, Germany. Carberry, J.J. & Wendel, A computer model of the fixed bed catalytic reactor: the adiabatic and quasi-adiabatic cases, M. (1963) AIChE J., 9(132): 129-133. Cartier, S., Theoleyre, M.-A., & Decloux M. (1997). Treatment of affination syrup by micro/ultrafiltration: Impact on crystallization process, Proc. Sugar Industry Technol., 56: 133-145. Chern J.-M. & Chien, Y.-W. (2001). Adsorption isotherms of benzoic acid onto activated carbon and breakthrough curves in fixed-bed columns, Ind. Eng. Chem. Res., 40: 3775-3780. Coombs J. and Baldry, C.W. (1978). Formation of color in cane juice by enzyme catalyzed reactions: Part 1. Mechanism and chemical inhibition. Int. Sug. J., 80: 291-294. Crees, O.L. (1986). Pilot scale ultrafiltration of clarified juice, Proc. Aust. Soc. Sugar Cane Technol., 8: 209-213.

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Donovan, M. & Williams, J.C. (1992). The factors influencing the transfer of color to sugar crystals, Proc. Sug. Processing Res. Conf.: 75–93. Fechter, W.L., Kitching, S.M., Rajh, M., Reimann, R.H., Ahmed, F.E., Jensen, C.R.C., Schorn, P.M., & Walthew, D.C. (2001). Direct production of white sugar and whitestrap molasses by applying membrane and ion exchange technology in a cane sugar mill, Proc. Int. Soc. Sugar Cane Technol., 24: 100-107. Fogler, F.H. (1999). Elements of chemical reaction engineering, 3rd Edition, Prentice-Hall PTR, New Jersey. Froment, G.F. & Bischoff, K.B. (1990). Chemical reactor analysis and design, 2nd Edition, John Wiley & Sonss Inc., New York. Glueckauf, E. & Coates, J.J. (1947). Theory of Chromatography. Part IV. The influence of incomplete equilibrium on the front boundary of chromatograms and on the effectiveness of separation, J. Che. Soc.: 1315. Godshall, M.A., Clarke, M.A., Dooley, C.D. and Roberts, E.J. (1988). High molecular weight color in refineries, Proc. Sug. Processing Res. Conf.: 75–93. Godshall, M.A., Clarke, M.A., Xavier, M.M., Blanco, R.S. (1992a). Comparison of refinery decolorization systems, Proc. Sug. Processing Res. Conf.: 281–305. Godshall, M.A. (1992b). Isolation of a high molecular weight colorant from white beet sugar, Proc. Sug. Processing Res. Conf. 312–319. Godshall, M.A. (1996). Recent progress in sugar colorants: GC-MS studies and extraction techniques. Proc. S. Afr. Sug. Technol. Assoc., 70: 153-161. Godshall, M.A. & Baunsgaard, D. (2000). The nature of colorant, Proc. Sug. Processing Res. Conf.: 122–137. Grimsey, I.M. & Herrington, T.M. (1994). The formation of inclusions in sucrose crystals, Int. Sugar J., 96: 504-514. Guibal, E., Saucedo, I., Roussy, J. & Le Cloirec, P. (1994). Uptake of uranyl ions by new sorbing polymers: Discussion of adsorption isotherms and pH effect, React. Polym., 23: 147-156. Kampen, W.H. & Saska, M. (1999). Value added products from stillage of ethanol-form-molasses and corn-to-ethanol plants, Proc. Sugar Industry Technol., 58: 195-208. Katz, E., Eksteen, R., Schoenmakers, P. & Miller, N. (1998). Handbook of HPLC, Marcel Dekker Inc., New York.

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Kearney, M. (1997). The amalgamated beet/cane raw juice chromatographic separator, Sugar y Azucar, 92: 38-43. Kearney, M., Kochergin, V.N., Petersen, K. & Velasquez, L. (1999a). Sugar juice purification process, U.S. Patent 5,466,294 (1995). Ref# 36361. Kearney, M. (1999b). Advances in the ARi coupled loop chromatographic separation process, Proceedings of the Symposium on Advanced Technology for Raw Sugar and Cane and Beet Refined Sugar Production, SPRI Inc.: 163-172. Kearney, M. & Kochergin, V.N. (2001). Chromatographic applications in the cane sugar industry, Proc. Int. Soc. Sugar Cane Technol., 24: 11-15. Kearney, M. (2002). Chromatographic applications in the cane sugar industry, Int. Sugar J., 104(1241): 194-203. Kochergin V.N. (1997). Membrane filtration of various sugar solutions, Proc. Amer. Soc. Sugar Beet Technol., 29: 359-373. Kochergin, V., Kearney, M., Jacob, W., Velasquez, L., Alvarez, J. & Baez-Smith, C. (2000). Chromatographic desugarization of syrups in cane mills, Int. Sugar J., 102(1223): 568-578. Kochergin, V., Kearney, M. & Alvarez, J. (2001). Direct production of white sugar in cane mills: Technical and economic aspects, Proc. Int. Soc. Sug. Cane Technol., 24: 108-111. Kwok, R.J. (1996). Ultrafiltration/softening of clarified juice – The door to direct refining and molasses desugarization in the cane sugar industry, Proc. S. Afr. Sug. Technol. Assoc., 70: 166-170. Lancrenon, X., Herve, D. & Rousset, F. (1998). A new generation of cane sugar refineries?, Int. Sugar J., 100(1198): 490-498. Letcher, T.M. & Whitehead, P.G. (1996). Separation and identification of sugar colorant, Proc. S. Afr. Sug. Technol. Assoc., 70: 162-165. Lin C.-C. & Liu, H.-S. (2000). Adsorption in a centrifugal field: Basic dye adsorption by activated carbon, Ind. Emg. Chem. Res., 39: 161-167. Lionnet, G.R.E (1998). The incorporation of impurities into sucrose crystals during the crystallization process, Ph.D. Thesis, Department of Chemistry and Applied Chemistry, University of Natal, Durban, South Africa.

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Meade, G.P. (1963). Cane Sugar Handbook. 9th Ed., John Wiley & Sons Inc., USA. 532. Monclin, J.-P. & Willett, S.C. (1996). The ‘A.B.C. Process’ for the direct production of refined sugar from cane mixed juice, Proceedings of SPRI Inc. Workshop on Separation Processes in the Sugar Industry: 16-28. Morley, J.P. (1988). Mathematical model of an ion exchange column, Proc. S. Afr. Sug. Technol. Assoc., 62: 56-64. Newell, G.M. (1979). A preliminary investigation into factors affecting gas formation in massecuite and molasses. Proc. S. Afr. Sug. Technol. Assoc., 53: 62-65. Paananen H. & Rousset, F. (2001). New generation of chromatographic separators using the FAST technology, Zuckerindustrie, 126(8): 601-604. Paillat D. & Cotillon, M. (2000). Different industrial applications of continuous chromatography both in the sugar industry and for the production of byproducts, Zuckerindustrie, 125(1): 47-51. Papageorgiou, J., Doherty, W.O.S., Walker, B., Edye, L.A., Analysis of organic impurities in raw sugar by a HPLC-UV-mass spectrometer, Zuckerindustrie, 124, Nr. 2: 133-138. Patel, M.N. (1991). The potential application of membrane processes in the cane sugar industry, Proc. S. Afr. Sug. Technol. Assoc., 65: 161-168. Peacock, S., Davis, S., Walford, S. & Bernhardt, H. (1999). Invert form South African cane molasses using chromatographic techniques, Proceedings of the Symposium on Advanced Technology for Raw Sugar and Cane and Beet Refined Sugar Production, SPRI Inc.: 205-228. Polson, A.. (1950). Some aspects of diffusion in solution and a definition of a colloidal particle, J. Phys. Colloid Chem., 54: 649-652. Rice, R.G. (1982). Approximate solutions for batch, packed tube, and radial flow adsorbers – Comparison with experiments, Chem. Eng. Sci. 37: 83-97. Rice, R.G. & Do, D.D. (1995). Applied mathematics and modeling for chemical engineers, John Wiley & Sons Inc., New York. Rossiter, G., Jensen, C. & Fecter, W. (2002). White sugar from cane at the factory: The impact of WSM, Proc. Sug. Processing Res. Conf. Ruckenstein, W., Vaidyanathan, A.S. & Youngquist, G.R. (1971). Sorption by solids with bidisperse pore structures, Chem. Eng. Sci., 26: 1305-1318.

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90

Saska, M. & Oubrahim, Y. (1987). Gel permeation chromatography of sugarcane products, Sugar J., June 1987: 22-25. Saska, M., Deckherr, A.-S. & Le Renard, C.E. (1995). Direct production of white cane sugar with clarification and decolorization membranes, Sugar J., 58(6): 19-21. Saska, M. (2002). Boiling point elevation of technical sugarcane solution, Int. Sugar. J., In Press. Seader, J.D. & Henley, E.J. (1998). Separation process principles, John Wiley & Sons Inc., New York. Shore, M., Broughton N.W., Dutton, J.V. & Sissons, A. (1984). Factors affecting white sugar color, Sug. Tech. Rev., 12 (1984). 1-99. South African Sugar Technologists’ Association (1985). Laboratory Manual for South African sugar factories: 262. Skoog, D.A., West, M.W. & Holler, F.J. (1996). Fundamentals of analytical chemistry, 7th Edition, Saunders College Publishing, Orlando. Steindl, R.J. (2001). Membrane filtration technology in the cane sugar industry, Proc. Int. Soc. Cane Technol., 24: 3-10. Urquhart, P.C., Atkins, P.C. & Metcalfe, G.M. (2000). Meeting the marketing challenge, Proc. Aust. Soc. Sugar Cane Technol., 22: 46-50. Van der Poel, P.W., Schiweck, H. and Schwartz T. (1998). Sugar technology: Beet and cane sugar manufacture, Albert Bartens KG, Berlin, Germany. Wilson, E.J. & Geankoplis, C.J. (1966). Liquid mass transfer at very low Reynolds number in packed beds, Ind. Eng. Chem. Fund., 5(1): 9-14. 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.

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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

( )

mlgmlg

/0694.0100/94.6

6.779978.06.7710021.4g/100mlion Concentrat 22

==

+×= −

Calculate ICUMSA color (round to nearest hundred)

8100100694.0562.0000,10

000,10420ICUMSA

×=

⋅=

lcA

A.2 GPC Chromatogram Analysis

A.2.1 Refractive Index Deconvolution Algorithm

a.) Obtain initial guess

b.) Load chromatogram

c.) Set baseline (user input) – see Figure A.1

d.) 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

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e.) Using the initial guesses, a set number of Gaussian distributions are

added together to fit the chromatogram.

12 14 16 18 20 22 24

0

200

400

600

800

1000

Zoom to best view for sugar peak detection (Press enter when done)

Baseline

Sugar Peak

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.) The second regression is on the retention times using the first derivative.

h.) The third regression is on standard deviation and maximum value on the

original chromatogram

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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)

12 14 16 18 20 22

0

20

40

60

80

100

120

Retention time (min)

RI

Figure A.2: Regression of RI Chromatograms with seven Gaussian profiles

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10 12 14 16 18 20 22

-40

-20

0

20

40

60

80

100

120

140

Retention time (min)

RI

MeasuredCalculated

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). A baseline correction is also performed in this

analysis.

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-50

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Retention time (min)

Abs

orba

nce F

E

D

C

B

A

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 A B C D E F

Retention time (min) 14.4 16.6 18 19.2 20.4 21.2

Molecular weight 10,000 6,000 3,000 1,800 1,200 800

Absorbance signal 10.64 142.66 177.87 150.79 105.61 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.

( )( )3

3

m volumebedm volumevoid

=ε (A.1)

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The following values are measured:

waterV - Volume of water added (ml)

TV - Total volume in measuring cylinder (ml)

bedV - Volume of resin bed (ml)

The voidage can be derived in terms of the measured variables:

bed

waterT

bed

rebrd

bed

void

VVV

VVV

VV −

−=−

== 1sinε (A.2)

For the cation resin,

mlVmlVmlV

bed

T

water

8.538.7

5.5

===

Calculating the voidage as in A.2:

676.08.5

5.538..71 =−

−=ε

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.

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From the experiment the following is obtained:

- Resin volume (ml) – measuring cylinder packed-bed sinreV

- Liquid volume (ml) liquidV

- Absorbance responses for pseudo-components form GPC

analysis

( )tCi

At time, , the absorbance (analogous to concentration) on the resin may be

calculated after correcting for the dilution factor used in the analysis.

t

( ) ( ) ( )[ ]sin1

0

re

liquidiii V

VtCtCtqε−−=

= (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)

t (min) 0 5 10 15 20 25 30

CC(t) 355.4 264.8 235.0 233.7 230.3 219.2 219.0

qC(t) 0 3636.2 4831.6 4885.246 5023.2 5465.6 5473.9

This is repeated over all initial concentrations and plotted as on the

horizontal axis and on the vertical axis. For each time an isotherm may be

regressed (Table A.3). In this case a straight-line with slope, , is used. Using

the complete set of C versus q data, the data is determined

(Table A.3) using Microsoft Excel Solver.

( 0=tCi )

)

( )tqi

C

( )tKi

)t( 0=t ( )tC (KC

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The data may then be fitted to determine the final equilibrium value using the

following equation:

( )tKi

( ) ( )teqii eKtK β−−= 1, (A.4)

Least-squares regression using this equation yields

37.16, =eqCK

Table A.3: Calculation of adsorption constants as a function of time from data (SAC) ( )tqC

t ( )0=tCC

0 46.7 106.7 129.6 216.5 220.6 355.4 425.3 ( )tKC

5 613.3 1321.9 1612.1 2200.9 1896.6 3636.1 5384.8 11.21

10 641.9 1676.7 1949.2 2984.6 2620.4 4831.6 6372.2 14.11

15 685.2 1661.1 2200.1 3284.2 2933.4 4885.2 6966.6 15.126

20 683.6 1696.0 2301.0 3503.4 3064.5 5023.2 7355.3 15.83

25 622.4 1824.2 2392.8 3495.4 3312.3 5465.6 7725.0 16.73

30 722.7 1952.9 2593.4 3678.8 3357.2 5473.9 7549.5 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

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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:

φ - Dimensionless relative time (3.25)

( )φmeasiC , - Measured component concentration

( )φpH - Measured pH

b.) Define feed concentration and first guess of model parameters:

0C - Measured feed concentration

St - First guess of Stanton number

0K , , - Equilibrium parameter 1K λ

c.) The minimization may be described mathematically as

( )[ ]2,10,,,

,,,,,21min

10

∑ −j

jmeasijKKSt

CpHKKStF φφλλ

( ) (A.5)

d.) As mentioned above the function ( )jpHKKStF φλ ,,,,, 10 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 FEMLAB Algorithm

a.) Create Geometry

b.) Define mesh on which to solve the solution

c.) Define PDE coefficients (3.37)

d.) Define Boundary coefficients (3.38)

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e.) Create user defined expression for : ( )φ,pHK

( ) ( )10, KeKpHK pH += − φλφ (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 in its calculations. The

expression is calculated symbolically by FEMLAB. The derivative of

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 using the Hermite polynomials. This

greatly decreases the time to generate a solution.

( φ,pHK )

( )φpH

( )φpH

g.) The model solution may then be calculated:

( )φη,C - Fluid concentration for all positions and times

( )φη,q - 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)

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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, ( )jpHKKStF φλ ,,,,, 10 , is then

extracted as the function return.

( ) ( )φηφλ ,1,,,,, 10 ==CpHKKStF j (A.7)

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APPENDIX B. SAC RESIN RESULTS

B.1 SAC Resin Isotherms

0

100

200

300

400

500

600

700

0 5 10 15 20 25

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure B.1: Color component A - SAC isotherm as a function of time

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250 300 350 400

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure B.2: Color component B - SAC isotherm as a function of time

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0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150 200 250 300 350 400 450 500

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure B.3: Color component C - SAC isotherm as a function of time

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 50 100 150 200 250 300 350

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure B.4: Color component D - SAC isotherm as a function of time

103

Page 115: Modeling adsorption of cane sugar colorant in packed-bed

0

500

1000

1500

2000

2500

3000

3500

4000

0 50 100 150 200 250

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure B.5: Color component E - SAC isotherm as a function of time

0

500

1000

1500

2000

2500

3000

3500

0 50 100 150 200 250

Initial Color in Solution

Col

or in

Res

in

5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linearr (20) Linear (25) Linear (30)

Figure B.6: Color component F - SAC isotherm as a function of time

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B.2 SAC Resin Column Tests

Table B.1: Summary of Tests Performed

Test Resin Volume Flow (BV/h) Section

SAC 6 160.0 11.5 B.2.1

SAC 8 147.5 16.3 B.2.2

SAC 9 147.5 20.7 B.2.3

SAC void fraction: 676.0=ε

B.2.1 SAC 6

Table B.2: SAC 6 Regression Summary

Component C D E F

St 0.9621 1.0308 1.0415 1.0799

K0 25.7301 19.6975 19.9381 20.1055

K1 18.5667 6.1811 4.6464 4.4968

λ 1.0344 1.0973 1.0164 0.9598

R2 0.94 0.97 0.94 0.94

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

BV

pH

Feed pH Product pH

Figure B.7: SAC 6 Product pH

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0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30 35

BV

Con

duct

ivity

(mS/

cm)

SAC Product Feed

Figure B.8: SAC 6 Product Conductivity

0

2000

4000

6000

8000

10000

12000

0 5 10 15 20 25 30 35

BV

IU

SAC Product SAC Feed

Figure B.9: SAC 6 Product ICUMSA Color

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0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60 70 80 90 100

φ

C

A A (feed)

Figure B.10: SAC 6 Product Color Component A

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

φ

C

0

2

4

6

8

10

12

14

16

Con

duct

ivity

(mS/

cm) o

r pH

B B (calculated) B (feed) pH Conductivity

Figure B.11: SAC 6 Product Color Component B

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Figure B.12: SAC 6 Product Color Component C

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Figure B.13: SAC 6 Product Color Component D

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Figure B.14: SAC 6 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure B.15: SAC 6 Product Color Component F

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B.2.2 SAC 8 Table B.3: SAC 8 Regression Summary

Component C D E F

St 0.9078 0.91952 1.1358 1.4159

K0 1.7983 2.0085 1.3879 1.1520

K1 29.5050 30.881 22.3090 22.3620

λ 21.2240 11.979 5.3744 3.1999

R2 0.91 0.92 0.90 0.94

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Figure B.16: SAC 8 Product pH

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0

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Figure B.17: SAC 8 Product Conductivity

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Figure B.18: SAC 8 Product ICUMSA Color

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Figure B.19: SAC 8 Product Color Component A

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Figure B.20: SAC 8 Product Color Component B

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Figure B.21: SAC 8 Product Color Component C

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D D (calculated) D (feed) pH Conductivity

Figure B.22: SAC 8 Product Color Component D

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E E (calculated) E (feed) pH Conductivity

Figure B.23: SAC 8 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure B.24: SAC 8 Product Color Component F

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B.2.3 SAC 9 Table B.4: SAC 9 Regression Summary

Component C D E F

St 0.8535 1.0431 1.0079 0.9710

K0 0.8075 1.1627 1.1299 1.0616

K1 16.8020 18.818 17.9010 17.5060

λ 10.2340 4.1669 3.9439 3.7276

R2 0.98 0.92 0.88 0.87

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Figure B.25: SAC 9 Product pH

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Figure B.26: SAC 9 Product Conductivity

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SAC Product SAC Feed

Figure B.27: SAC 9 Product ICUMSA Color

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A A (feed)

Figure B.28: SAC 9 Product Color Component A

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B B (calculated) B (feed) pH Conductivity

Figure B.29: SAC 9 Product Color Component B

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Figure B.30: SAC 9 Product Color Component C

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D D (calculated) D (feed) pH Conductivity

Figure B.31: SAC 9 Product Color Component D

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E E (calculated) E (feed) pH Conductivity

Figure B.32: SAC 9 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure B.33: SAC 9 Product Color Component F

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APPENDIX C. WBA RESIN RESULTS

C.1 WBA Resin Isotherms

-20

-10

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Initial Color in Solution

Col

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Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.1: Color component A - WBA isotherm as a function of time

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Initial Color in Solution

Col

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5 10 15 20 25 30Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.2: Color component B - WBA isotherm as a function of time

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Initial Color in Solution

Col

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in

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Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.3: Color component C - WBA isotherm as a function of time

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Initial Color in Solution

Col

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5 10 15 20 25 30

Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.4: Color component D - WBA isotherm as a function of time

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Initial Color in Solution

Col

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in

5 10 15 20 25 30

Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.5: Color component E - WBA isotherm as a function of time

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Initial Color in Solution

Col

or in

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in

0

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Linear (5) Linear (10) Linear (15) Linear (20) Linear (25) Linear (30)

Figure C.6: Color component F - WBA isotherm as a function of time

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C.2 WBA Resin Column Tests

Table C.1: Summary of WBA tests performed

Test Resin Volume Flow (BV/h) Section

WBA 5 363.5 4.2 C.2.1

WBA 6 363.5 5.1 C.2.2

WBA 7 363.5 5.8 C.2.3

WBA Void Fraction: 517.0=ε

C.2.1 WBA 5

Table D.2: WBA 5 Regression Summary

Component B C D E F

St 0.542 1.650 1.988 1.985 2.004

K 4.60 18.46 22.72 22.53 22.93

R2 0.82 0.91 0.97 0.97 0.97

0

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Product pH

Figure C.7: WBA 5 Product pH

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Con

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WBA Product Feed

Figure C.8: WBA 5 Product Conductivity

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WBA Product Feed

Figure C.9: WBA 5 Product ICUMSA Color

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Figure C.10: WBA 5 Product Color Component A

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B B (calculated) B (feed) pH

Figure C.11: WBA 5 Product Color Component B

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Figure C.12: WBA 5 Product Color Component C

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D D (calculated) D (feed) pH

Figure C.13: WBA 5 Product Color Component D

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E E (calculated) E (feed) pH

Figure C.14: WBA 5 Product Color Component E

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F F (calc) F (feed) pH

Figure C.15: WBA 5 Product Color Component F

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C.2.1 WBA 6

Table E.3: WBA 6 Regression Summary

Component B C D E F

St 0.919 1.876 2.168 2.001 1.952

K 13.15 12.12 13.99 14.51 15.61

R2 0.89 0.96 0.95 0.97 0.97

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pH

6

Feed pH Product pH

Figure C.16: WBA 6 Product pH

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Con

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WBA Product

Figure C.17: WBA 6 Product Conductivity

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IU

6

WBA Product Feed

Figure C.18: WBA 6 Product ICUMSA Color

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Figure C.19: WBA 6 Product Color Component A

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B B (calculated) B (feed) pH Conductivity

Figure C.20: WBA 6 Product Color Component B

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Figure C.21: WBA 6 Product Color Component C

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D D (calculated) D (feed) pH Conductivity

Figure C.22: WBA 6 Product Color Component D

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E E (calculated) E (feed) pH Conductivity

Figure C.23: WBA 6 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure C.24: WBA 6 Product Color Component F

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C.2.1 WBA 7

Table C.3: WBA 7 Regression Summary

Component B C D E F

St 1.175 2.573 3.409 2.894 2.807

K 10.38 12.56 12.43 13.96 14.36

R2 0.95 0.98 0.99 0.99 0.98

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Feed pH Product pH

Figure C.25: WBA 7 Product pH

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Con

duct

ivity

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14

SAC Product

Figure C.26: WBA 7 Product Conductivity

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WBA Product Feed

Figure C.27: WBA 7 Product ICUMSA Color

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Figure C.28: WBA 7 Product Color Component A

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B B (calculated) B (feed) pH Conductivity

Figure C.29: WBA 7 Product Color Component B

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Figure C.30: WBA 7 Product Color Component C

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D D (calculated) D (feed) pH Conductivity

Figure C.31: WBA 7 Product Color Component D

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E E (calculated) E (feed) pH Conductivity

Figure C.32: WBA 7 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure C.33: WBA 7 Product Color Component F

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APPENDIX D. DECOLORIZING RESIN RESULTS

D.1 Decolorization Column Tests

Table D.1: Summary of DECOL tests performed

Test Resin Volume Flow (BV/h) Section

DECOL 7 138 19.6 D.1.1

DECOL 8 152 11.9 D.1.2

DECOL 9 152 20.5 D.1.3

WBA Void Fraction: 822.0=ε

D.1.1 DECOL7

Table D.2: DECOL 7 Regression Summary

Component B C D E F

St 9.092 5.710 3.939 3.383 3.310

K 142.50 113.47 104.16 110.32 97.94

Unmodeled Removal 20.3% 2.5% 6.0% 3.4% 9.7%

R2 0.998 0.997 0.991 0.987 0.984

6

6.5

7

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10.5

0 5 10 15 20 25 30 35 40 45

BV

pH

Feed pH Product pH

Figure D.1: DECOL 7 Product pH

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Decol.Product Decol. Feed

Figure D.2: DECOL 7 Product ICUMSA Color

-2

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A A (feed)

Figure D.3: DECOL 7 Product Color Component A

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Figure D.4: DECOL 7 Product Color Component B

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C C (calculated) C (feed) pH Conductivity

Figure D.5: DECOL 7 Product Color Component C

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Figure D.6: DECOL 7 Product Color Component D

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E E (calculated) E (feed) pH Conductivity

Figure D.7: DECOL 7 Product Color Component E

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F F (calc) F (feed) pH Conductivity

Figure D.7: DECOL 7 Product Color Component F

D.1.2 DECOL8

Table D.3: DECOL 8 Regression Summary

Component B C D E F

St 13.269 7.766 3.654 3.242 2.685

K 152.65 119.50 152.53 164.04 161.28

Unmodeled Removal 37.3% 21.1% 0.0% 0.0% 4.5%

R2 0.996 0.990 0.978 0.974 0.963

6

6.5

7

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8

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9

9.5

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0 5 10 15 20 25 30 35 40 45

BV

pH

Feed pH Product pH

Figure D.8: DECOL 8 Product pH

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BV

IU

Decol.Product Decol. Feed

Figure D.9: DECOL 8 Product ICUMSA Color

-5

0

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φ

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A A (feed)

Figure D.10: DECOL 8 Product Color Component A

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pH

B B (calculated) B (feed) pH

Figure D.11: DECOL 8 Product Color Component B

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C C (calculated) C (feed) pH Conductivity

Figure D.12: DECOL 8 Product Color Component C

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Figure D.13: DECOL 8 Product Color Component D

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Figure D.14: DECOL 8 Product Color Component E

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0

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Figure D.15: DECOL 8 Product Color Component F

D.1.3 DECOL 9

Table D.4: DECOL 9 Regression Summary

Component B C D E F

St 14.335 8.418 4.596 4.213 4.093

K 148.98 119.38 140.08 137.18 114.97

Unmodeled Removal 32.6% 18.9% 7.6% 11.9% 38.2%

R2 0.996 0.991 0.994 0.988 0.965

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6

6.5

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Figure D.16: DECOL 9 Product pH

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Decol.Product Decol. Feed

Figure D.17: DECOL 9 Product ICUMSA Color

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-5

0

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Figure D.18: DECOL 9 Product Color Component A

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Figure D.19: DECOL 9 Product Color Component B

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Figure D.20: DECOL 9 Product Color Component C

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Figure D.21: DECOL 9 Product Color Component D

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Figure D.22: DECOL 9 Product Color Component E

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Figure D.23: DECOL 9 Product Color Component F

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APPENDIX E. MATLAB CODE

E.1 GPC-RI Deconvolution

% GPC - Refractive Index % HA Broadhurst % Audubon Sugar Institute clear all close all % File Allocation P = questdlg('Do you want to print the chromatograms and save the integrated areas?'... ,'Print','Yes','No ','No '); Date = '4/27/2002'; samples = [1]; NoF = length(samples); count = 0; t_peak = [12.5818 13.8967 16.9690 18.0356 19.0589 20.2360 21.2585]; s_peak = [0.3679 1.3366 0.2998 0.2845 0.3733 0.4359 0.2513]; m_peak = [1.2005 1.2774 1.7842 29.2396 12.8829 59.2378 46.9782]; for file = samples % Load Data name = strcat('C:\Hugh\IX\SAC Isotherms\20Brix\20brix-',num2str(file),'-RI.txt'); data = load(strcat(name),'-ascii'); N = max(size(data)); OK = 1; count = count + 1; while isempty(OK)==0 t = data(1:N,1); r = data(1:N,2); delta = mean(diff(t))/2; clear tb yb tr nr ns smax stdev r_calc close all figure(1) set(1,'Position',[5 5 1015 695]) plot(t,r) grid on title('Zoom to best view for setting the baseline (Press enter when done)') zoom on pause zoom off title('Set baseline') [tb,yb] = ginput(2); n1 = find(t>tb(1)-delta & t<tb(1)+delta); n2 = find(t>tb(2)-delta & t<tb(2)+delta); m = mean(r(n1:n2)); r = r-m; plot(t,r); grid on % Sugar Peak title('Zoom to best view for sugar peak detection (Press enter when done)') zoom on pause zoom off title('Click on portion of sugar peak to regress (2 points)')

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[tr_sug,y_sug]=ginput(2); for i=1:length(tr_sug) ns(i) = find(t>tr_sug(i)-delta & t<tr_sug(i)+delta); end t_sug = vertcat(t(ns(1):ns(2))); r_sug = vertcat(r(ns(1):ns(2))); x0 = [22.5,0.5,6000]; lb(3) = 0; options = optimset('lsqcurvefit'); optnew = optimset(options,... 'Display','off',... 'LargeScale','on'); [x_sug,resnorm] = lsqcurvefit(@normal,x0,t_sug,r_sug,lb,[],optnew); % Peak Detection N_peak = length(t_peak); for i = 1:N_peak r_peak(:,i) = normal([t_peak(i),s_peak(i),m_peak(i)],t); end %for i = 1:N_peak % n_p(i) = find(t>t_peak(i)-delta & t<t_peak(i)+delta); %end figure(1) set(1,'Position',[5 5 1015 695]) %plot(t,normal(x_sug,t),'k:',t,r,'b-',t_peak,r(n_p),'rx') plot(t,normal(x_sug,t),'k:',t,r,'b-',t,r_peak,':') grid on title('Zoom to best view for peak detection (Press enter when done)') zoom on pause zoom off title('Click on maxima - press enter when done') [tr,yr] = ginput; Np = length(tr); for i=1:Np nr(i) = find(t>tr(i)-delta & t<tr(i)+delta); end r = r(1:ns(2)); t = t(1:ns(2)); dt = t(1:length(t)-1)+delta; dr = diff(r); plot(t,r) nr = nr(1:Np); tr = tr(1:Np); smax = r(nr)'; stdev = ones(1,Np).*0.2; % Set Regression Options options = optimset('lsqcurvefit'); optnew = optimset(options,... 'Display','iter',... 'LargeScale','on'); close all lb = zeros(1,Np); tr = tr'; % Least squares non-linear regression - Standard Deviation x0 = stdev; lb(Np) = 0; [x,resnorm] = lsqcurvefit(@normals6,x0,dt,dr,lb,[],optnew,tr,smax,x_sug,delta); stdev = x; % First derivative for times x0 = tr; lb = ones(1,Np).*10; ub = ones(1,Np).*25; [x,resnorm] = lsqcurvefit(@normals4,x0,dt,dr,lb,ub,optnew,x_sug,stdev,smax,delta);

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tr = x; % Time Domain x0 = horzcat(stdev,smax); lb = zeros(1,Np*2); [x,resnorm] = lsqcurvefit(@normals3a,x0,t,r,lb,[],optnew,tr,x_sug); stdev = x(1:Np); smax = x(Np+1:2*Np); % Derivative - standard and times %x0 = horzcat(stdev,tr); %[x,resnorm] = lsqcurvefit(@normals7,x0,dt,dr,lb,[],optnew,x_sug,smax,delta); %stdev = x(1:Np); %tr = x(Np+1:2*Np); stds = horzcat(stdev,x_sug(2)); smax = horzcat(smax,x_sug(3)); tr = horzcat(tr,x_sug(1)); figure(1) set(1,'Position',[5 5 1015 695]) R_calc = 0; for i = 1:Np+1 r_calc(:,i) = normal([tr(i),stds(i),smax(i)],t); R_calc = R_calc + r_calc(:,i); end E = num2str(trapz(abs(R_calc(601:length(r))-r(601:length(r))))/... trapz(r(601:length(r)))*100); plot(t,r,t,r_calc,t,r-R_calc) axis([10 23 -20 100]) title(strcat('GPC DRI detector - Sample ',name,' - ',Date,... ' - Percent Deconvolution Area Error = ',E)) grid on %zoom on %pause response = questdlg('Are you happy with the deconvolution',... 'Integration','Yes','No','Yes'); if strcmp(response,'Yes') OK = []; end end for i=length(stdev)+1:10 stdev(i) = 0; tr(i) = 0; smax(i) = 0; end standard(count,:) = horzcat(file,stdev); RT(count,:) = horzcat(file,tr); Maximum(count,:) = horzcat(file,smax); if P=='Yes' orient landscape print end end function dist = normals6(par,xdata,tr,smax,x_sug,delta) N = length(par); stdev = par; xdata = xdata-delta; n = length(xdata); xdata(n+1)=xdata(n)+2*delta; f = 0; for i=1:N f = f+normal([tr(i),stdev(i),smax(i)],xdata); end

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dist = diff(f+normal(x_sug,xdata)); function dist = normals4(par,xdata,x_sug,stdev,smax,delta) N = length(par); tr = par; xdata = xdata-delta; n = length(xdata); xdata(n+1)=xdata(n)+2*delta; f = 0; for i=1:N f = f+normal([tr(i),stdev(i),smax(i)],xdata); end dist = diff(f+normal(x_sug,xdata)); function dist = normals3a(par,xdata,tr,x_sug) % Maximum and deviation N = (length(par))/2; stdev = par(1:N); smax = par(N+1:2*N); f = 0; for i=1:N f = f+normal([tr(i),stdev(i),smax(i)],xdata); end dist = f+normal(x_sug,xdata); function dist = normals(stdev,xdata,tr,smax,x_sug) % Standard f = 0; N = length(stdev); for i=1:N f = f+normal([tr(i),stdev(i),smax(i)],xdata); end dist = f+normal(x_sug,xdata); function dist = normal(pars,x) x0 = pars(1); stdev = pars(2); s_max = pars(3); dist = s_max.*exp(-0.5*((x-x0)/stdev).^2);

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E.2 GPC-ABS % GPC - Color Measurements % HA Broadhurst % Audubon Sugar Institute clear all close all samples = [47]; NoF = length(samples); t_peak = [14.4, 16.6, 18, 19.4, 20.4, 21.2]; abs = horzcat(0,t_peak); count = 0; for file = samples % Load Data name = strcat('C:\Hugh\IX\Cycle5\Decol5a\gpcData\D5-',num2str(file),'-ABS.txt'); data = load(strcat(name),'-ascii'); N = max(size(data)); count = count +1; t = data(1:N,1); r = data(1:N,2); delta = mean(diff(t))/2; clear tb yb tr close all figure(1) set(1,'Position',[5 5 1015 695]) plot(t,r) grid on title('Set baseline') [tb,yb] = ginput(2); n1 = find(t>tb(1)-delta & t<tb(1)+delta); n2 = find(t>tb(2)-delta & t<tb(2)+delta); m = mean(r(n1:n2)); r = r-m; Np = length(t_peak); for i=1:Np np(i) = find(t>t_peak(i)-delta & t<t_peak(i)+delta); end abs = vertcat(abs,horzcat(file,r(np)')); end close all

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E.3 Model Parameter Regression % Model Parameter Regression % Hugh Broadhurst % 11/11/2001 clear all % Input data xdata = [ 2.165019834 6.415146051 10.66527227 14.91539849 19.1655247 23.41565092 27.66577714 31.91590335 36.16602957 40.41615579 44.66628201 48.91640822 53.16653444 57.41666066 61.66678687 65.91691309 70.16703931 74.41716552 78.66729174 82.91741796 87.16754418 91.41767039 95.66779661]; ydata = [ 50.876896 52.870447 65.818711 68.419808 82.806857 83.851026 93.597647 107.19704 107.38002 115.24227 110.76467 104.89539 108.76371 106.51 106.96975 100.95747 103.82812 94.491724 100.95951 94.15874 94.971836 90.789237 95.78847]; pH = [1.7 1.54 1.49 1.45 1.45 1.44 1.44 1.47 1.61 2.82 4.52 5.09 5.35 5.53 5.67 5.77 5.87 5.95 6.03 6.11 6.17 6.25 6.3]; phi = xdata; %xdata = horzcat(xdata(1:5),xdata(9:length(xdata))); %ydata = horzcat(ydata(1:5),ydata(9:length(ydata))); % Knowns c_eq0,K,qmax,c0,e Ke = 13.32628959; c0 = 90.8787; St = 1; lambda = 1; K0 = 18; K1 = 4; % Starting guess for Pe,St,C_eq0,K,qmax x0 = [St,lambda,K0,K1]; % Set Options options = optimset('lsqcurvefit'); optnew = optimset(options,... 'MaxFunEvals',200,... 'Display','Iter',... 'LargeScale','on'); % Set bounds lb = [0,0,0,0]; % Least squares non-linear regression [x,resnorm] = lsqcurvefit(@ldfreg_linear,x0,xdata,ydata,lb,[],optnew,Ke,c0,pH,phi); % Plot results t = sort(horzcat(xdata,[0:0.5:35])); [t1,c] = FlinearPlugA(x(1),x(2),x(3),x(4),Ke,c0,phi,pH,t); plot(t1,c,'b-',xdata,ydata,'ro') legend('Calculated','Measured') xlabel('\phi') ylabel('C') % Determine correlation coefficent for i = 1:length(xdata) j = find(t1==xdata(i)); y(i) = c(j); end r2 = prod(prod(corrcoef(ydata,y))); title(strcat('St = ',num2str(x(1)),'; \lambda = ',num2str(x(2)),'; K_0 = ',num2str(x(3)),'; K_1 = ',num2str(x(4)),'; R^2 =',num2str(r2)))

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orient landscape %print function F = ldfreg_linear(x,tdata,Ke,c0,pH,phi) disp(x) n = length(tdata); t(1) = 0; for i = 1:n t(2*i) = 0.5*(t(2*i-1)+tdata(i)); t(2*i+1) = tdata(i); end [tlist,data] = FlinearPlugA(x(1),x(2),x(3),x(4),Ke,c0,phi,pH,t); for i = 1:n j = find(tlist==tdata(i)); y(i) = data(j); end F = y; E.4 FEMLAB Solution function [t,c] = FlinearPlugA(St,lambda,K0,K1,Ke,c0,phi,pH,t) % FEMLAB Model M-file % Generated 31-May-2002 10:24:55 by FEMLAB 2.2.0.181. %flclear fem % FEMLAB Version clear vrsn; vrsn.name='FEMLAB 2.2'; vrsn.major=0; vrsn.build=181; fem.version=vrsn; % Recorded command sequence % New geometry 1 fem.sdim='z'; % Geometry clear s c p Column=solid1([0 20],[1 0;0 1]); objs=Column; names='Column'; s.objs=objs; s.name=names; objs=; names=; c.objs=objs; c.name=names; objs=; names=; p.objs=objs; p.name=names; drawstruct=struct('s',s,'c',c,'p',p); fem.draw=drawstruct; fem.geom=geomcsg(fem); clear appl % Application mode 1 appl1.mode=flpdeg1d(2,'dim','c','q','c_t','q_t','sdim','z','submode', ...

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'std','tdiff','on'); appl1.dim='c','q','c_t','q_t'; appl1.form='general'; appl1.border='off'; appl1.name='g1'; appl1.var=; appl1.assign=; appl1.elemdefault='Lag2'; appl1.shape='shlag(2,''c'')','shlag(2,''q'')'; appl1.sshape=2; appl1.equ.da='1','0';'0','1'; appl1.equ.ga='-cz';'-qz'; appl1.equ.f='1';'1'; appl1.equ.weak='0';'0'; appl1.equ.dweak='0';'0'; appl1.equ.constr='0';'0'; appl1.equ.gporder=4;4; appl1.equ.cporder=2;2; appl1.equ.shape=[1 2]; appl1.equ.init='0';'0'; appl1.equ.usage=1; appl1.equ.ind=1; appl1.bnd.g='0';'0'; appl1.bnd.r='-c';'-q'; appl1.bnd.type='dir'; appl1.bnd.weak='0';'0'; appl1.bnd.dweak='0';'0'; appl1.bnd.constr='0';'0'; appl1.bnd.shape=0; appl1.bnd.ind=[1 1]; fem.appl=appl; % Initialize mesh fem.mesh=meshinit(fem,... 'Out', 'mesh',... 'Hgrad', 1.3); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular'); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [1 2 3 4 5 6 7 8 16 17 18 19 20 21 22;1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [16 17 18 19 24 25 26 31 32 33 34 39 40 41;1 1 1 1 1 1 1 1 1 1 1 ... 1 1 1]); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [32 33 34 36 37 39 40 43 44 46 47 48 50 51 53 54 57 58;1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1 1 1 1]); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [42 43 45 47 48 49 51 52 54 56 57 58 60 61 63 65 66 67 69 70 72 ... 74 75 76;1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]);

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% Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [54 55 56 57 59 60 62 63 65 66 67 68 69 71 72 74 75 77 78 79 80 ... 81 83 84 86 87 89 90 91 92 93 95 96 98 99 101;1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]); % Refine mesh fem.mesh=meshrefine(fem,... 'out', 'mesh',... 'rmethod','regular',... 'tri', [66 68 69 70 71 72 73 74 75 77 78 79 80 81 82 84 86 87 88 89 90 ... 91 93 95 96 97 98 99 100 102 104 105 106 107 108 109 110 111 113 114 115 ... 116 117 118 120 122 123 124 125 126 127 129 131 132 133 134 135 136;1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]); % Problem form fem.outform='general'; % Differentiation fem.diff='ga','g','f','r','var','expr'; % Differentiation simplification fem.simplify='on'; % Boundary conditions clear bnd bnd.g='0';'0','0';'0'; bnd.r='-c+c0';'-q+c0.*Ke','-c';'-q'; bnd.type='dir','dir'; bnd.weak='0';'0','0';'0'; bnd.dweak='0';'0','0';'0'; bnd.constr='0';'0','0';'0'; bnd.shape=0,0; bnd.ind=[1 2]; fem.appl1.bnd=bnd; % PDE coefficients clear equ equ.da='0','0';'0','1'; equ.ga='c';'0'; equ.f='-St.*(c-q./K)';'St.*(c-q./K)'; equ.weak='0';'0'; equ.dweak='0';'0'; equ.constr='0';'0'; equ.gporder=4;4; equ.cporder=2;2; equ.shape=[1 2]; equ.init='0';'0'; equ.usage=1; equ.ind=1; fem.appl1.equ=equ; % Internal borders fem.appl1.border='off'; % Shape functions fem.appl1.shape='shlag(2,''c'')','shlag(2,''q'')'; % Geometry element order fem.appl1.sshape=2; % Expressions at equ level clear equ equ.expr='K','K0.*exp(-lambda.*flinterp1(phi,pH,t,4))+K1'; equ.ind=1; fem.equ=equ;

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160

% Differentiation rules fem.rules='flinterp1(a,b,c,d)','0,0,flinter p1(a,b,c,4,1),0'; % Define variables fem.variables=... 'St', St,... 'c0', c0,... 'phi', phi,... 'pH', pH,... 'Ke', Ke,... 'lambda', lambda,... 'K0', K0,... 'K1', K1; % Multiphysics fem=multiphysics(fem); % Extend the mesh fem.xmesh=meshextend(fem,'context','local','cplbndeq','on','cplbndsh','on'); % Evaluate initial condition init=asseminit(fem,... 'context','local',... 'init', fem.xmesh.eleminit); % Solve dynamic problem fem.sol=femtime(fem,... 'tlist', t,... 'atol', 0.001,... 'rtol', 0.01,... 'jacobian','equ',... 'mass', 'full',... 'ode', 'ode15s',... 'odeopt', struct('InitialStep',[],'MaxOrder',5,'MaxStep',[]),... 'out', 'sol',... 'stop', 'on',... 'init', init,... 'report', 'off',... 'timeind','auto',... 'context','local',... 'sd', 1,... 'nullfun','flnullorth',... 'blocksize',5000,... 'solcomp','c','q',... 'linsolver','matlab'); t = fem.sol.tlist; c = fem.sol.u(40,:);

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VITA

Hugh Anthony Broadhurst was born in Cambridge, England, on November

21 1978. He spent the next 22 years in the Republic of South Africa. After

graduating from high school, at Hilton College in 1996, he went on to the University

of Natal in Durban, South Africa. Here he obtained a Bachelor of Science degree in

Chemical Engineering, graduating in December 2000. Tongaat-Hulett Sugar

Limited (Durban, South Africa) and Calgon Carbon Corporation (Pittsburgh, United

States of America) sponsored him to study for his Master of Science degree in

Chemical Engineering at the Audubon Sugar Institute, Louisiana State University.

On completion of his degree, he will assume a position at Rohm & Haas Company

in Louisville, Kentucky.

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