modeling adsorption of cane sugar colorant in packed-bed
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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
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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
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
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
v
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
viii
ABSTRACT
The removal of cane sugar solution colorant by packed-bed ion exchangers
was modeled using a linear driving force (LDF) adsorption model. Adsorption of
colorant is of interest to the developers of the White Sugar Mill (WSM) process as it
is a complex subject.
The problem is that color is an indiscrete mixture of many components
making it difficult to measure and even more challenging to model. Colorant
formation was investigated using gel permeation chromatography (GPC) with the
objective of developing a method to define pseudo-components representative of
cane sugar solution colorants.
WSM is a process for producing white sugar directly from sugarcane in the
raw sugar mill by using ultrafiltration and continuous ion exchange technology.
The ion exchange resins employed were a strong acid cation (SAC) resin in the
hydrogen form, a weak base anion (WBA) resin in the hydroxide form and a
decolorizing resin in the chloride form. Decolorization using the three resins was
then analyzed using the GPC pseudo-component technique.
Batch testing of the resin allowed the development of equilibrium isotherms
that could be substituted into a standard LDF model. Column testing was then
performed to investigate the dynamics of adsorption of colorant in packed-beds.
Linear isotherms were measured for each of the three resins, indicating that
the colorant is dilute. Results indicated that a plug-flow model with a constant
linear isotherm was sufficient in all cases except the SAC resin. The SAC
adsorption parameter decreased sharply as the pH increased, causing colorant to be
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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.
CHAPTER 1. INTRODUCTION
1.1 The White Sugar Mill Process
1.1.1 The Production of White Cane Sugar
The production of white cane sugar is currently a two-step operation. Raw
sugar is light brown in color and is produced in sugar mills. Mills are located close
to the cane growers to minimize cane degradation and transportation costs. The raw
sugar is subsequently transported to a refinery where the remaining impurities are
removed. Figure 1.1 shows the basic steps in the production of raw sugar from
sugarcane. Sucrose is first extracted from sugar cane with water, by counter-current
milling or cane diffusion. The juice is screened, heated to its boiling point, and then
flashed. Suspended solids and colloidal materials are then precipitated with milk of
lime (calcium hydroxide solution) and settled in a clarifier. The resulting clear juice
is evaporated to approximately 65% dissolved solids in a multiple effect evaporator
train. Sugar is then crystallized from the syrup in a three-stage crystallization
process. After each crystallization step, sugar crystals are separated from the
mother liquor in centrifuges. The raw sugar is then transported to the refinery
where it is dissolved, purified and re-crystallized to white sugar.
Cane
Extraction DJ
Heating MJ
Clarification CJ
Evaporation
Sy. 3 Stage Crystallization
Ma. Centrifugation
RS
Mol
Key: DJ = Draught juice; MJ = Mixed Juice; CJ = Clear Juice; Sy. = Syrup; Ma. = Massecuite
RS = Raw sugar; Mol. = Final Molasses
Figure 1.1: Raw sugar mill flowsheet
1
1.1.2 The White Sugar Mill
There are three main areas in which the profitability of the raw sugar mill
may be increased (Fechter et al., 2001):
1. Improve the quality of the sugar produced
2. Increase overall recovery of sugar
3. Make use of products in the molasses
The sugar refinery is a simple and relatively low cost operation except for the
significant costs in transporting raw sugar from the mill and sugar losses in the
refining process. These costs could be removed by producing white sugar at the raw
sugar mill.
Recent advances in membrane and continuous ion exchange technology
have been utilized by Tongaat-Hulett Sugar Limited and S.A. Bioproducts Limited
in the development of a process to produce white sugar directly in the raw sugar
mill (Rossiter, 2002). The process design may be incorporated into an existing raw
sugar mill (see Figure 1.2).
Cane Extraction Juice Heating 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
2
Juice from the existing first evaporation effect at 20 to 25% brix is first
ultrafiltered. This removes high molecular weight material from the syrup that
would otherwise irreversibly foul the ion exchange resins. The retentate (the
material rejected by the membrane) may be used as a feedstock to a neighboring
distillery or may be recycled to the clarifiers. Impurities leave the system in the
clarifier mud. The permeate from the membrane unit must be refrigerated to 10oC
as in the subsequent ion exchange separations low pH conditions are experienced.
Under acidic conditions, sucrose breaks down to fructose and glucose. This reaction
is termed inversion in the sugar industry.
The heart of the process is the continuous ion-exchange demineralization
using Calgon Carbon 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
3
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
4
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
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
6
under almost all conditions, as reducing sugars and amines or amino acids are
always present except in the purest of solutions. Iron also plays an important role,
particularly in plant-derived colorants (Godshall, 1996). Many polyphenolic
compounds found in cane juice are able to produce highly colored iron complexes.
It must be noted that just as important as the colorants themselves are the
compounds that are color precursors. These, often colorless, compounds can react
to form highly colored species. Table 2.1 summarizes the general types of colorant
found in a cane sugar mill (adapted from Godshall, 2000). Cane sugar colorant is a
difficult issue as it is so difficult to define.
Table 2.1: Types of sugar colorants
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.
7
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
8
stream of a buffer solution that flows into a column packed with a gel of precisely
controlled pore size. The gel pores are arranged in such a size distribution that
small molecules are able to diffuse into the pores whereas larger molecules are
excluded. A detector is used at the end of the column to measure the concentration
of the material exiting the column. Typically, a refractive-index (RI) or an
ultraviolet-visible (UV-VIS) detector is used.
The analysis may be calibrated by injecting standards of precise molecular
weight into the column. If the samples to be analyzed are of the same molecular
size and shape as the standards, their weights may be read off the calibration curve.
The buffer solution masks the gel from any ionic behavior of the sample, as no
interaction is wanted between the analyte and the stationary phase.
Many authors have made use of GPC to analyze sugar solutions, including
Shore et al (1984), Godshall et al (1988, 1992a, 2000), Bento et al (1997) and Saska
& Oubrahim (1987). Of particular interest is the work of Godshall (1992a). The
removal of high molecular weight colorants in batch experiments was measured
using GPC. The resulting chromatograms all had three distinct peaks. Each peak
was treated as a single pseudo-component to investigate the decolorizing ability of a
number of different adsorbents. Saska & Oubrahim (1987) report that GPC is a
reliable method to investigate the molecular weight effects of decolorization
mechanisms. The WSM process has been investigated using this principle except
that it was applied to the dynamics of the process and not just the overall
decolorization.
9
2.2.3 Advanced Techniques
The fluorescent nature of sugar colorant has been extensively studied
(Carpenter & Wall, 1972). Recently using advanced equipment and techniques
researchers have been able to use this property to provide more information about
sugar colorants (Bro, 1999, Baunsgaard, 2000 & Godshall & Baunsgaard, 2000).
This research is still in its beginnings and is outside the scope of this investigation.
Gas chromatography with mass selective detection (GC-MS) has also been
used in the identification of colorants and other impurities (Letcher & Whitehead,
1996, Godshall, 1996 & Papageorgiou, 1999). The biggest downfall of this method
is that most of the highly colored compounds have a molecular weight greater than
1,000 (Godshall, 1996), which is the operating limit of most gas chromatographs.
2.3 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
10
important, as the membrane must be able to withstand the harsh cleaning chemicals
used to remove buildup of foulants in the pores.
In many industrial separation processes membrane filtration has been used
effectively. This unit operation has, however, only been incorporated into one sugar
production facility (in Hawaii, using the New Applexion Process), despite
considerable interest by many researchers (Steindl, 2001). The Sugar Research
Institute in Australia has been researching ultrafiltration since 1975. Membrane
filtration can drastically increase sugar quality, and give rise to higher crystal
growth rates (Crees, 1986) but it was concluded that capital and operating costs
were excessive.
Suspended solids, colloidal particles and soluble high molecular weight
material can be removed using membrane filtration. Average performance data
(Steindl, 2001) show the effectiveness of this unit operation in removing impurities
from clarified juice:
• Purity rise 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,
11
1991) unless the pore size is reduced to below 20,000MW. Use of the lowest
MWCO is not practical as the sugar produced is not of significantly less color than
of sugar produced from membranes of higher MWCO (Cartier et al, 1997).
Membranes may be sized primarily on minimizing the membrane area (capital cost)
and maximizing the permeate flux (Fechter et al, 2001).
One of the problems associated with membrane separation is that the
retentate stream contains sucrose. It is not economic to simply dispose of this
stream and so a number of researchers have proposed methods to recycle the
retentate or use it for some other purpose. Proposals include:
• Dilution of the retentate stream followed by a secondary filtration
(Steindl, 2001)
• Clarification of the retentate using a flotation clarifier (Steindl,
2001)
• Recycling the retentate to the existing settling clarifiers (Rossiter
et al, 2002)
• Using the retentate as a feed to an attached ethanol facility
(Rossiter et al, 2002)
Membrane technology may be applied to raw cane sugar mills after the lime
defecation and clarification stage. Steindl (2001) reports that raw juice clarification
removes the insoluble solids and some soluble material. The lower impurity
concentration found in clarified juice allows higher filtration fluxes and reduces the
risk of erosion on the membrane surface.
12
Urquhart et al, (2000) report that filtering clarified juice with a membrane
unit allows the production of high pol, low color sugar to satisfy the Australian QHP
(Queensland High Pol) standard. Another installation allowed the production of a
super VLC (very low color) sugar (Kwok, 1996). High quality sugar produced
using this technique allowed the Crockett refinery in California to eliminate both the
affination and the remelt stations. Balakrishnan et al (2000) investigated the use of
ultrafiltration to produce a plantation white sugar with a color of approximately 150
ICUMSA units.
Ultrafiltration has also been suggested as a pretreatment since it generally
cannot produce a syrup of high enough quality to directly crystallize white sugar
(Steindl, 2001). Ion exchange and chromatography require a very clean feed, to
protect the resin from fouling. Membrane filtration has proved to be a very
effective pretreatment (Fechter et al, 2001), allowing the use of a single set of resin
for a period longer than the length of an average South African season (about 9
months). Saska et al (1995) proposed the use of nanofiltration following
ultrafiltration to produce an upgraded syrup from which white sugar could be
crystallized. Monclin and Willett (1996) proposed using adsorptive decolorization
of ultrafiltered juice. Amalgamated Research Inc. has developed and patented a
direct white sugar production process using ultrafiltration followed with
chromatography (Kearny, 1999a). Lancrenon et al (1998) propose the use of
microfiltration in the sugar refining process.
Despite the numerous investigations into membrane separations in the cane
sugar industry there has been no widespread adoption of the unit operation (Steindl,
13
2001). It is likely that the next major installation of a membrane unit will be as a
pretreatment to either ion exchange or chromatography. The use of ultrafiltration in
the sugar industry is limited by economics. This unit operation will not make an
appearance in the sugar industry until a process with proven economics is
developed. It is likely that ultrafiltration will be used in series with another
separation process.
2.3.2 Decolorization with Ion Exchange Resins
Since the 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%
14
Caramels are least retained by the resin, as they are relatively uncharged whereas
the other colorants are anionic in alkaline medium.
Morley (1988) made a detailed study of fixed-bed decolorizing ion
exchangers. Color was measured by the ICUMSA color method. An analytic
mathematical model was derived assuming no axial dispersion and constant linear
isotherms. Model parameters were estimated from experimental data giving an
average correlation coefficient of 0.91. Batch tests were also performed to measure
the equilibrium properties of the resin, expressed as an isotherm. A Langmuir
isotherm was measured but in the concentration (color) range used, a linear fit was
deemed acceptable. This model was used to improve the Tongaat-Hulett refinery in
Durban, South Africa. The model does however, display the shortcomings of the
ICUMSA color method on which it is based. An early breakthrough of a
component that is strongly transferred to the crystal on crystallization could easily
go unnoticed.
2.3.3 Chromatography
Sugar solutions may also be purified using chromatography. This is a
technique where a pulse of sugar solution is injected into a mobile phase that passes
through a media, typically an ion exchange resin. In a favorable case different
components in solution have differing affinities for the resin. If a pulse of material
is introduced at the top of a packed-bed, into the mobile phase, the components will
move down the columns at differing speeds causing separation. For an industrial
operation, a simulated moving bed (SMB) design is often used, as it simulates a
counter-current separation process, reducing the amount of resin required. The
15
French process engineering company, Applexion, have designed a process to give a
column efficiency increase of 100% (Paananen & Rousset, 2001).
There are numerous possibilities in applying chromatographic separation
techniques to the cane sugar industry (Paillat & Cotillon, 2000; Kearney, 2002).
Desugarization of final molasses is possible providing that the feed material is free
of suspended solids. This is a significant problem for cane final molasses
desugarization as the pretreatment to remove the suspended solids is difficult
(Kearney & Kochergin, 2001). This process is more effective in the beet sugar
industry as higher final molasses purities are experienced helping the process
economics. Kearney & Kochergin (2001) report that the process economics are
marginal for cane sugar operations. One of the problems associated with sucrose
recovery from final molasses is the inhibiting effect of divalent cations, particularly
calcium. Softening is also required as a pretreatment. A similar process is
described by Lancrenon et al (1998) for the chromatographic separation of refinery
molasses.
Another option is the removal of non-sucrose products from molasses.
Glycerin and other products can be recovered from cane molasses stillage after the
production of ethanol (Kampen & Saska, 1999). Peacock (1999) showed that syrup
rich in invert sugars could be separated from final molasses. Unlike, sucrose
recovery, the above-mentioned processes were not affected by divalent cations in
laboratory and pilot scale studies. The economics of these processes is determined
by the product prices (Kearney & Kochergin, 2001).
16
Chromatography of refinery syrup is also possible. Kearney (1999b)
showed that refinery syrup at 84% purity could be upgraded to 90% with 90% color
removal and 96% invert sugar removal.
Extensive testing has been performed on the chromatography of evaporator
syrup prior to crystallization in the raw sugar mill (Kearney, 1997). The syrup must
be filtered and softened (removal of calcium) prior to chromatography. The
chromatography upgrades the syrup to 98% purity and removes enough color to
allow the direct crystallization of white sugar (Kochergin et al, 2000, 2001).
2.4 Color Transfer in Crystallization
A colorant (or impurity) can be transferred to the sucrose crystal on
crystallization in three mechanisms (Godshall & Baunsgaard, 2000):
• Adsorption onto the crystal surface
• Co-crystallization into the crystal matrix (occlusion)
• Trapped by liquid inclusions inside the crystal
Godshall & Baunsgaard (2000) focused on occlusion (co-crystallization) of
colorants into the crystal matrix. Carbohydrate-type material was found to have a
greater tendency to be occluded in the crystal. In addition, the higher the molecular
weight the greater the occlusion. As a whole, color transferred 10-20% into the
crystal, but color is not one entity, and different types of colors will have a greater
or lesser affinity for the crystal. One of the greatest problems are polysaccharides as
these species are indigenous in the cane and complex with color molecules,
“pulling” them into the sugar crystal as the polysaccharide material is occluded.
17
Lionnet (1998) extensively studied the incorporation of impurities into the
sucrose crystal on crystallization. It was concluded that color (and other impurities)
were not transferred exclusively by liquid inclusions. Two mechanisms for transfer
were investigated: adsorption isotherms and partition coefficients. Impurities can be
adsorbed into crystals by an equilibrium process, governed by an isotherm
(Donovan & Williams, 1992; Grimsey & Herrington, 1994). Witcamp and von
Rosmalen (1990) and Zumstein et al (1990) proposed the use of a partition
coefficient to measure transfer of impurities into a crystal. The partition coefficient
method was found to be applicable to the case of sugar crystallization. The partition
coefficient of a particular species i is defined as:
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
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.
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
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
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
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
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
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
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
( ) 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
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
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
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
=Γ
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.
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
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
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
removed by vacuum filtration using a Buchner funnel and Whatman No. 4
qualitative filter paper. The dried material is then added to the beaker and a timer
started.
Samples are taken at five-minute intervals, starting with the initial material,
using an Eppendorf® adjustable-volume pipettor. Care must be exercised when
sampling so that no resin is removed. It is advisable to turn off the stirrer 5-10
seconds before the sample time so that the resin in the top layer of liquid can settle.
After all the samples have been taken, the exact resin is volume is measured in a
measuring cylinder.
4.1.3 Void Fraction Measurement
An important parameter in all the resin experiments is the resin packed-bed
void fraction, or the resin voidage. This is simply measured by drying
approximately 5ml of resin in a vacuum oven. The dry resin is placed into a 10ml
measuring-cylinder and 5ml of water is added by pipette. The cylinder is then
plugged and inverted a number of times to ensure complete mixing of the water and
resin. Extra water may be added to wash down any beads from the cylinder walls
above the liquid level by pipette. The resin packed-bed volume, volume of water
added, and the total volume may be used to calculate the voidage.
4.1.4 Column Loading
Three resins were investigated in the column loading experiments (Table
4.1), with three runs performed on each resin at different flow rates. Jacketed
25mm OD glass columns of 600mm length were connected to a Neslab circulating
refrigerated water-bath set to 10oC. FMI piston pumps were used to control the
34
liquid flow rates in and of the column. Two pumps were used on the column as it
allowed simpler control of the liquid level above the column (Figure 4.3). The
pump at the column exit was set and not adjusted during an entire run. The level of
liquid above the resin bed was controlled by setting the flow-rate of the inlet pump.
An Oakton pH meter was placed after the column to continuously monitor the
product pH.
Table 4.1: Ion-exchange resins investigated
Resin 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
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
Materials: Evaporator syrup was obtained from the Cinclaire mill for the
caramelization and alkaline degradation tests. Molasses was obtained from stock at
the Audubon Sugar Institute for investigation of the Maillard reactions. Cane juice
was produced by disintegrating cane with water in a stainless steel environment
using a Jeffco disintegrator.
Caramelization and Alkaline Degradation: Syrup was boiled under constant reflux
in an atmospheric laboratory still for 30 minutes. In the case of alkaline
degradation, the syrup pH was increased with sodium hydroxide to pH 8.8.
Maillard Reactions: Conditions favoring the Maillard reactions (Newell, 1979)
were used: high temperature and brix but low purity. Molasses was maintained at
75oC in a constant temperature bath for 24 hours.
The Effect of Iron on Cane Juice: Cane juice was heated at 50oC in a water bath
for one hour. The effect of iron on cane juice was investigated by placing rusty and
acid cleaned coiled wire of equal lengths into the heating tubes. Non-enzymatic
effects were investigated by autoclaving (at 110oC for 10 minutes) the juice prior to
exposure to iron and also by the addition of one part mercuric chloride to 5,000
parts juice to denature any enzymes (Meade, 1963). For each treatment, a control
experiment was performed to check the effects without any iron in contact with the
juice.
4.1.7 Color Transfer in Crystallization
A batch pilot-plant crystallizer and centrifuge were used to produce raw
sugar from ultrafiltered syrup. Syrup form the St James mill was used in place of
the normal syrup as supplies had run out. The feed syrup, sugar and final molasses
37
were analyzed with GPC and ICUMSA color to measure the color transfer
experienced. The color transfer data will be useful in investigating “good” and
“bad” color. A detailed description of the crystallization equipment is given by
Saska (2002).
4.2 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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
( ) ( )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
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
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
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
60
occurring in Figure 5.17. In addition, it is interesting to note that the effect appears
to occur in parallel to the change in the pH and conductivity of the product.
Changing the pH of a colorant solution drastically affects it color, indicating
a pH sensitivity of the colorant molecule. It appears, in this case, that either or both
the resin and the colorant display a change in affinity for each other as the pH
increases. Essentially the equilibrium constant becomes a function of pH (as
mentioned in section 3.2.1). It will be assumed that this dependence will be similar
to the Arrhenius equation (5.2) that applies to the dependency most rate constants on
temperature (Fogler, 1999).
( ) 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
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
62
successful as most cases displayed a coefficient of correlation (R2) above 0.9. The
Regressed Stanton numbers were similar to those calculated using correlations from
the literature (see section 3.2.5).
Components A and B have not been reported here as component A was too
close to the detection limit of the detector to produce reliable results and component
B displayed different dynamics. Component B (Figures F.11, F.20 & F.29) appears
to have a much larger affinity for the resin than the other components; this
corresponds to the batch data (Table 5.3). A pH effect is viewed as in the other
components.
In Table 5.4, the Stanton number remains relatively constant with changes in
velocity over the region investigated. This is interesting as it means that the mass
transfer coefficient, , 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
63
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
Figure 5.21 shows some resemblance to this proportionality. Another check on the
Stanton number is to compare it to a correlation as in section 3.2.5. The correlation
indicates that the measured data is in the correct range.
There is some variation in the equilibrium expression parameters (Table
5.5). Ideally, this equilibrium expression should remain constant as only the flow
rate is changing in each case. There are a number of possible explanations for this.
Despite appropriate measures taken, the resin may not have been returned to the
same initial condition at the start of each run. Another likely possibility is that since
the model does not perfectly emulate the dynamics measured, the regression
package alters the equilibrium parameters unnecessarily in searching for a best fit.
For design purposes, a constant equilibrium should be used. It would be
useful to measure this expression experimentally. This could be done by spiking the
solution with a inorganic salt (e.g. NaCl) to force more hydrogen ions into solution,
lowering the pH. For high pH values, it becomes more complicated.
Two possibilities would be:
• Adding a pH buffer
• Making the feed material basic prior to resin addition
It is also interesting to compare the values of the adsorption parameter
obtained in the column tests (Table 5.5) to the value obtained in the batch tests
(Table 5.3). The batch test adsorption parameters were significantly higher than the
values measured in the column test. There is a clear need for further investigation
into this resin. The dynamics of the process have been identified but data is
required over a wider range of flows to find optimum operating conditions.
65
5.4 Weak-Base Anion Resin
5.4.1 WBA Batch Tests
The WBA resin showed results slightly different from the SAC in the batch
tests (Appendix C.1, Graph 5.22). Components B through D have an adsorption
isotherm that does not pass through the origin.
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
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
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
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
69
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
70
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
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
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
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
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
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
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
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
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
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,→
80
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
81
close to those in literature. The resin was shown to have particularly strong affinity
for the high molecular weight component B. Components E,D and F were severely
affected by the pH change causing major drops in decolorization.
If the resin is to be operated making use of its full decolorizing power the pH
must not be allowed to increase in the column. The conductivity of the product
appeared to be a good indicator of the state of the resin. A falling conductivity gave
some advanced warning of the impeding color problem. Operating in the low
conductivity, “softening”, region allows the removal of divalent cations (e.g.
calcium, magnesium) increasing the ash capacity of the resin. This becomes less
attractive when the decolorizing ability of the resin is considered.
The use of a methanol wash was effective in quickly removing a large
portion of color from the SAC resin that was not removed in regeneration. Ethanol
washing become particularly attractive when operating a distillery on the WSM
retentate and molasses. Despite not being investigated here, the drop in
decolorizing ability of the SAC resin over many loading/regeneration cycles may be
attributed to incomplete regeneration. A more thorough investigation into the use of
methanol or ethanol washes is recommended.
6.4 WBA Resin
The weak-base anion exchange resin showed much simpler dynamics than
the SAC resin. Unlike the SAC resin, pH did not influence the adsorption parameter
strongly. Constant 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
82
stronger mass transfer limitations than the SAC resin, causing the WBA resin to
take longer to reach equilibrium.
Higher affinities for colorant were observed for the WBA resin, particularly
for the low molecular weight material. The lack of a pH effect makes the resin
simple to design as only the deashing conditions need be considered. The resin is a
good follow up to the SAC resin, as the SAC resin has a higher affinity for the large
material, whereas the WBA material has higher capacities for the low molecular
weight material.
6.5 Decolorizing Resin
The affinity of the decolorizing resin for colored bodies is far higher than
any of the other resins. The constant linear isotherm model was found to be
sufficient, except that the feed concentration (unmodeled color removal) was used
as a variable in the regression. The decolorizing resin also showed far higher mass
transfer coefficients than the SAC and WBA resins. Further experimentation is
required to investigate the unmodeled color removal as scatter was observed in the
regressed data.
6.6 WSM Process Design
The model data may be used to size a WSM ion exchange process in
conjunction with the current design techniques. 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;
83
otherwise, the decolorization capacity of the resin will be greatly
reduced.
ii. Since the WBA resin displays constant adsorption parameters, this
resin may be sized only on deashing considerations.
iii. The models for the resins must then be employed to calculated the
WBA product. First, the SAC model used on the UF syrup feed, and
subsequently the WBA model on the SAC product.
iv. The model for the decolorizing resin is then used to calculate the
required volume of resin.
6.7 Future Research Directions
More advance GPC detectors have been used in studying colorant. Bento et
al (1997) used Evaporative Light Scattering (ELS) detection in place of the RI
detector and a Diode Array Detection (DAD) instead of the absorbance detector.
DAD allows the absorbance measurement over a large range of wavelengths instead
of just one. Colorants show absorbance in the UV region and so this gives a lot
more information about the colorant. Analysis of DAD chromatograms is complex
as they are three dimensional, having retention, response and wavelength axes. It
may be more practical to analyze colorants at a single UV wavelength making use
of the higher absorbances in this region.
There is a clear need for more experimental data. More column tests would
allow a complete picture to be developed over a range of fluid velocities. This
would give the designer a better ability to optimize the process. The foundation has
been laid for the measurement to be made.
84
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.
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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.
89
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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.
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
91
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
92
i.) Each Gaussian curve (Graph A.2) is integrated to determine the peak
area.
j.) The sum of the peaks is compared with the original curve to determine
the correlation coefficient R2. (Graph A.3)
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
93
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.
94
-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)
95
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.
96
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
97
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
98
minimizes the sum-of-squares by varying the model parameters using the Sequential
Quadratic Programming (SLP) technique.
A.5.1 Regression Algorithm
a.) Define input vectors:
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)
99
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)
100
ii. The highly nonlinear problem option must be checked as this
reduces the damping parameters used in the solver.
h.) From this data the breakthrough curve, ( )jpHKKStF φλ ,,,,, 10 , is then
extracted as the function return.
( ) ( )φηφλ ,1,,,,, 10 ==CpHKKStF j (A.7)
101
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
102
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
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
104
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
105
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
106
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
107
0
20
40
60
80
100
120
140
160
180
200
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
C C (calculated) C (feed) pH Conductivity
Figure B.12: SAC 6 Product Color Component C
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 (calculated) D (feed) pH Conductivity
Figure B.13: SAC 6 Product Color Component D
108
0
20
40
60
80
100
120
140
160
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
E E (calculated) E (feed) pH Conductivity
Figure B.14: SAC 6 Product Color Component E
0
20
40
60
80
100
120
140
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
F F (calc) F (feed) pH Conductivity
Figure B.15: SAC 6 Product Color Component F
109
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
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.16: SAC 8 Product pH
110
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35
BV
Con
duct
ivity
(mS/
cm)
SAC Product Feed
Figure B.17: SAC 8 Product Conductivity
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 5 10 15 20 25 30 35
BV
IU
SAC Product SAC Feed
Figure B.18: SAC 8 Product ICUMSA Color
111
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70 80 90 100
φ
C
A A (feed)
Figure B.19: SAC 8 Product Color Component A
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90 100
φ
C
0
2
4
6
8
10
12
14
Con
duct
ivity
(mS/
cm) o
r pH
B B (calculated) B (feed) pH Conductivity
Figure B.20: SAC 8 Product Color Component B
112
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70 80 90 100
φ
C
0
2
4
6
8
10
12
14
Con
duct
ivity
(mS/
cm) o
r pH
C C (calculated) C (feed) pH Conductivity
Figure B.21: SAC 8 Product Color Component C
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70 80 90 100
φ
C
0
2
4
6
8
10
12
14
Con
duct
ivity
(mS/
cm) o
r pH
D D (calculated) D (feed) pH Conductivity
Figure B.22: SAC 8 Product Color Component D
113
0
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140
0 10 20 30 40 50 60 70 80 90 100
φ
C
0
2
4
6
8
10
12
14
Con
duct
ivity
(mS/
cm) o
r pH
E E (calculated) E (feed) pH Conductivity
Figure B.23: SAC 8 Product Color Component E
0
20
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80
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120
140
0 10 20 30 40 50 60 70 80 90 100
φ
C
0
2
4
6
8
10
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Con
duct
ivity
(mS/
cm) o
r pH
F F (calc) F (feed) pH Conductivity
Figure B.24: SAC 8 Product Color Component F
114
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
0
1
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7
8
0 5 10 15 20 25 30 35 40 45
BV
pH
Feed pH Product pH
Figure B.25: SAC 9 Product pH
115
0
2
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6
8
10
12
14
0 5 10 15 20 25 30 35 40 45
BV
Con
duct
ivity
(mS/
cm)
SAC Product SAC Feed
Figure B.26: SAC 9 Product Conductivity
0
2000
4000
6000
8000
10000
12000
0 5 10 15 20 25 30 35 40
BV
IU
SAC Product SAC Feed
Figure B.27: SAC 9 Product ICUMSA Color
116
0
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14
0 20 40 60 80 100
φ
C
120
A A (feed)
Figure B.28: SAC 9 Product Color Component A
0
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160
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0 20 40 60 80 100 120
φ
C
0
2
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14
Con
duct
ivity
(mS/
cm) o
r pH
B B (calculated) B (feed) pH Conductivity
Figure B.29: SAC 9 Product Color Component B
117
0
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250
0 20 40 60 80 100 120
φ
C
0
2
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6
8
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14
Con
duct
ivity
(mS/
cm) o
r pH
C C (calculated) C (feed) pH Conductivity
Figure B.30: SAC 9 Product Color Component C
0
20
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180
0 20 40 60 80 100 120
φ
C
0
2
4
6
8
10
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14
Con
duct
ivity
(mS/
cm) o
r pH
D D (calculated) D (feed) pH Conductivity
Figure B.31: SAC 9 Product Color Component D
118
0
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160
0 20 40 60 80 100 120
φ
C
0
2
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8
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14
Con
duct
ivity
(mS/
cm) o
r pH
E E (calculated) E (feed) pH Conductivity
Figure B.32: SAC 9 Product Color Component E
0
20
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140
0 20 40 60 80 100 120
φ
C
0
2
4
6
8
10
12
14
Con
duct
ivity
(mS/
cm) o
r pH
F F (calc) F (feed) pH Conductivity
Figure B.33: SAC 9 Product Color Component F
119
APPENDIX C. WBA RESIN RESULTS
C.1 WBA Resin Isotherms
-20
-10
0
10
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30
40
50
60
70
0 1 2 3 4 5 6 7 8 9
Initial Color in Solution
Col
or in
Res
in
5 10 15 20 25 30
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
0
200
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800
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1200
0 10 20 30 40 50 60 70 8
Initial Color in Solution
Col
or in
Res
in
0
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
120
0
500
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1500
2000
2500
3000
0 20 40 60 80 100 120 140 160 180 200
Initial Color in Solution
Col
or in
Res
in
5 10 15 20 25 30
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
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100 120 140 160 180 200
Initial Color in Solution
Col
or in
Res
in
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
121
0
500
1000
1500
2000
2500
0 20 40 60 80 100 120 140 160 180
Initial Color in Solution
Col
or in
Res
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
0
500
1000
1500
2000
2500
0 20 40 60 80 100 120 140 16
Initial Color in Solution
Col
or in
Res
in
0
5 10 15 20 25 30
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
122
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
2
4
6
8
10
12
0 2 4 6 8 10
BV
pH
12
Product pH
Figure C.7: WBA 5 Product pH
123
0
2
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6
8
10
12
0 2 4 6 8 10
BV
Con
duct
ivity
( µS/
cm)
12
WBA Product Feed
Figure C.8: WBA 5 Product Conductivity
0
1000
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6000
7000
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9000
0 2 4 6 8 10
BV
IU
12
WBA Product Feed
Figure C.9: WBA 5 Product ICUMSA Color
124
0
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6
7
8
9
0 2 4 6 8 10 12 14 16 18 20
φ
C
A A (feed)
Figure C.10: WBA 5 Product Color Component A
0
5
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40
45
50
0 2 4 6 8 10 12 14 16 18 20
φ
C
0
2
4
6
8
10
12
pH
B B (calculated) B (feed) pH
Figure C.11: WBA 5 Product Color Component B
125
0
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0 2 4 6 8 10 12 14 16 18 20
φ
C
0
2
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6
8
10
12
pH
C C (calculated) C (feed) pH
Figure C.12: WBA 5 Product Color Component C
0
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0 2 4 6 8 10 12 14 16 18 20
φ
C
0
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12
pH
D D (calculated) D (feed) pH
Figure C.13: WBA 5 Product Color Component D
126
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0 2 4 6 8 10 12 14 16 18 20
φ
C
0
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pH
E E (calculated) E (feed) pH
Figure C.14: WBA 5 Product Color Component E
0
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0 2 4 6 8 10 12 14 16 18 20
φ
C
0
2
4
6
8
10
12
pH
F F (calc) F (feed) pH
Figure C.15: WBA 5 Product Color Component F
127
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
0
2
4
6
8
10
12
0 2 4 6 8 10 12 14 1
BV
pH
6
Feed pH Product pH
Figure C.16: WBA 6 Product pH
128
0
100
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0 2 4 6 8 10 12 14 16 18
BV
Con
duct
ivity
( µS/
cm)
WBA Product
Figure C.17: WBA 6 Product Conductivity
0
1000
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5000
6000
7000
8000
0 2 4 6 8 10 12 14 1
BV
IU
6
WBA Product Feed
Figure C.18: WBA 6 Product ICUMSA Color
129
0
1
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3
4
5
6
7
8
9
0 5 10 15 20 25 30 35
φ
C
A A (feed)
Figure C.19: WBA 6 Product Color Component A
0
10
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80
90
0 5 10 15 20 25 30 35
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
B B (calculated) B (feed) pH Conductivity
Figure C.20: WBA 6 Product Color Component B
130
0
20
40
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100
120
140
0 5 10 15 20 25 30 35
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
C C (calculated) C (feed) pH Conductivity
Figure C.21: WBA 6 Product Color Component C
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
D D (calculated) D (feed) pH Conductivity
Figure C.22: WBA 6 Product Color Component D
131
0
10
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30
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90
0 5 10 15 20 25 30 35
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
E E (calculated) E (feed) pH Conductivity
Figure C.23: WBA 6 Product Color Component E
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
F F (calc) F (feed) pH Conductivity
Figure C.24: WBA 6 Product Color Component F
132
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
0
2
4
6
8
10
12
0 2 4 6 8 10 12 14
BV
pH
Feed pH Product pH
Figure C.25: WBA 7 Product pH
133
0
100
200
300
400
500
600
0 2 4 6 8 10 12
BV
Con
duct
ivity
( µS/
cm)
14
SAC Product
Figure C.26: WBA 7 Product Conductivity
0
1000
2000
3000
4000
5000
6000
7000
0 2 4 6 8 10 12
BV
IU
14
WBA Product Feed
Figure C.27: WBA 7 Product ICUMSA Color
134
0
1
2
3
4
5
6
7
0 5 10 15 20 25
φ
C
A A (feed)
Figure C.28: WBA 7 Product Color Component A
0
10
20
30
40
50
60
70
0 5 10 15 20 25
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
B B (calculated) B (feed) pH Conductivity
Figure C.29: WBA 7 Product Color Component B
135
-20
0
20
40
60
80
100
120
0 5 10 15 20 25
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
C C (calculated) C (feed) pH Conductivity
Figure C.30: WBA 7 Product Color Component C
0
20
40
60
80
100
120
0 5 10 15 20 25
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
D D (calculated) D (feed) pH Conductivity
Figure C.31: WBA 7 Product Color Component D
136
0
10
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30
40
50
60
70
80
90
0 5 10 15 20 25
φ
C
0
2
4
6
8
10
12
Con
duct
ivity
(10
x m
S/cm
) or p
H
E E (calculated) E (feed) pH Conductivity
Figure C.32: WBA 7 Product Color Component E
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25
φ
C
0
2
4
6
8
10
12
F F (calc) F (feed) pH Conductivity
Figure C.33: WBA 7 Product Color Component F
137
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
7.5
8
8.5
9
9.5
10
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
138
0
2000
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6000
8000
10000
12000
0 5 10 15 20 25 30 35 40 45
BV
IU
Decol.Product Decol. Feed
Figure D.2: DECOL 7 Product ICUMSA Color
-2
0
2
4
6
8
10
12
14
16
18
0 50 100 150 200 250
φ
C
A A (feed)
Figure D.3: DECOL 7 Product Color Component A
139
0
20
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100
120
140
160
180
200
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
B B (calculated) B (feed) pH Conductivity
Figure D.4: DECOL 7 Product Color Component B
0
50
100
150
200
250
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
C C (calculated) C (feed) pH Conductivity
Figure D.5: DECOL 7 Product Color Component C
140
0
20
40
60
80
100
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140
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
D D (calculated) D (feed) pH Conductivity
Figure D.6: DECOL 7 Product Color Component D
0
20
40
60
80
100
120
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
E E (calculated) E (feed) pH Conductivity
Figure D.7: DECOL 7 Product Color Component E
141
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
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
7.5
8
8.5
9
9.5
10
10.5
0 5 10 15 20 25 30 35 40 45
BV
pH
Feed pH Product pH
Figure D.8: DECOL 8 Product pH
142
0
2000
4000
6000
8000
10000
12000
0 5 10 15 20 25 30 35 40 45
BV
IU
Decol.Product Decol. Feed
Figure D.9: DECOL 8 Product ICUMSA Color
-5
0
5
10
15
20
0 50 100 150 200 250
φ
C
A A (feed)
Figure D.10: DECOL 8 Product Color Component A
143
0
50
100
150
200
250
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
B B (calculated) B (feed) pH
Figure D.11: DECOL 8 Product Color Component B
0
50
100
150
200
250
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
C C (calculated) C (feed) pH Conductivity
Figure D.12: DECOL 8 Product Color Component C
144
0
20
40
60
80
100
120
140
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
D D (calculated) D (feed) pH
Figure D.13: DECOL 8 Product Color Component D
0
20
40
60
80
100
120
0 50 100 150 200 250
φ
C
0
2
4
6
8
10
12
pH
E E (calculated) E (feed) pH
Figure D.14: DECOL 8 Product Color Component E
145
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
F F (calc) F (feed) pH
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
146
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
0 10 20 30 40 50 6
BV
pH
0
Feed pH Product pH
Figure D.16: DECOL 9 Product pH
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 10 20 30 40 50 6
BV
IU
0
Decol.Product Decol. Feed
Figure D.17: DECOL 9 Product ICUMSA Color
147
-5
0
5
10
15
20
0 50 100 150 200 250 300
φ
C
A A (feed)
Figure D.18: DECOL 9 Product Color Component A
0
50
100
150
200
250
0 50 100 150 200 250 300
φ
C
0
2
4
6
8
10
12
pH
B B (calculated) B (feed) pH
Figure D.19: DECOL 9 Product Color Component B
148
0
50
100
150
200
250
0 50 100 150 200 250 300
φ
C
0
2
4
6
8
10
12
pH
C C (calculated) C (feed) pH Conductivity
Figure D.20: DECOL 9 Product Color Component C
0
20
40
60
80
100
120
140
0 50 100 150 200 250 300
φ
C
0
2
4
6
8
10
12
pH
D D (calculated) D (feed) pH
Figure D.21: DECOL 9 Product Color Component D
149
0
20
40
60
80
100
120
0 50 100 150 200 250 300
φ
C
0
2
4
6
8
10
12
pH
E E (calculated) E (feed) pH
Figure D.22: DECOL 9 Product Color Component E
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300
φ
C
0
2
4
6
8
10
12
pH
F F (calc) F (feed) pH
Figure D.23: DECOL 9 Product Color Component F
150
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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% 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,:);
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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