International Sugar Journal, 2002, 104, 1247, pp 500-507
Boiling point elevation of technical sugarcane solutions and its use in
automatic pan boiling
Michael Saska
Audubon Sugar Institute
Louisiana State University Agricultural Center
Baton Rouge, LA 70803
Introduction
Despite the advances in recent years in developing new sensors1,2,3,4 for control of sugar
crystallization, boiling point elevation (BPE) remains a simple, robust and inexpensive means for
monitoring supersaturation over the full range of massecuite purity, from refinery white sugar to
low grade massecuites in the raw sugar mills. In the framework of a general program at ASI on
optimization and automation of sucrose crystallization, it was deemed of interest to review the
commonly used BPE data found in the sugar literature, and, if warranted, perform additional
measurements over the pertinent range of purities, concentrations and temperatures.
A considerable body of literature has accumulated since the early work of Claassen in the
1900’s, and yet, on closer inspection, original data, particularly for industrial (low purity)
sugarcane solutions are surprisingly limited. Of the major sugar technology texts in use today,
Honig5 and VanDerPoel6 rely on the sugarbeet-based data of Spengler7, the Cane Sugar
Handbook8 presents Holven’s interpretation of Thieme’s data9, and Hugot10 gives the data of
Thieme and a nomograph of Othmer and Silvis11 based on Spengler. Thus the historical, and
rather sparse data of Thieme from the 1920’s and the fairly recent equilibrium (non-boiling)
measurements of Batterham and Norgate12 that appear to have been so far disregarded by the
handbooks but are reportedly used in Australia13 are the only data of note derived from impure
sugarcane solutions. The scarcity of the original data is contrasted by the profusion in the
literature of interpretations, correlations, smoothing and other manipulations of the few limited
experimental points11,14-24
Of the two pilot sized vacuum pans at ASI, the larger, all-stainless steel, one (Table I and
Figure 1) is fully instrumented and well suited for measuring the relevant parameters of the
crystallization process. Forced circulation is provided by two impellers, one located at the top of,
the other at the bottom of the central downtake. Calandria is made of two concentric rings,
supplied by pressure-regulated steam, and provided with condensate and incondensible gas
outlets. A Honeywell UMC 800 controller in conjunction with a PC-based Honeywell
PlantScape®, Version 400.0 package, with an in-house developed automatic sugar boiling
software provides the parameter control, automation and data collection and display.
Table I: Design parameters of the 200 liter ASI pilot vacuum pan.
Pan Design
Pan I.D. at Calandria, mm
Downtake I.D., mm
Dished End Volume, L
Graining Volume, L
Strike Volume, L
Total Volume, L
450
216
20
123
200
661
Calandria Details
Circulation System
Impeller Diameter, mm
Pitch, mm
Power installed, kW
Stirrer Speed, rpm
Tip Speed, m/s
Heating Elements
Large Ring, OD/ID/Height, mm
Small Ring, OD/ID/Height, mm
Heating Surface, Large Ring/Small
Ring, mm2
Heating Surface/Volume, 1/m
Signal
Absolute pressure
Steam pressure
Temperature 1 (below calandria)
Temperature 2 (above calandria)
Level
Conductivity
RF- capacitance/resistance
Microwave density
Agitator load
Agitator speed
Feed flow rate
Steam condensate flow rate
178
76
0.37
233 (at 8 Hz)
2.2 (at 8 Hz)
381/330/216
273/216/210
499,000/342,000
4.1
Instrument type
Barksdale, 0-15PSIA
ABB TEPI11Ex
Flow-temp, PT100 , 3-wire, accuracy 0.01% FS
Flow-temp, PT100 , 3-wire, accuracy 0.01% FS
Foxboro IDP10 differential pressure
Dynamic Systems, Model CTX/AC
Fletcher Smith, Digital Duotrac
pro-M-tec Theisen GmbH, Model uWA-2.5
Load Control, Inc. PH-3A Power Transducer
Teco-Westinghouse FM100
Yokogawa AM-105AG magnetic flowmeter
Yokogawa AM-110AG magnetic flowmeter
Generation of experimental data.
The temperatures of the boiling liquors, at various absolute pressures and purities, were
measured during slow concentration over 1 to 3 hours from some 65 to about 80 % refractometric
dry solids (WDS) with periodic sampling and WDS determination off-line with a standard Abbe
refractometer. The absolute pressure, steam pressure, level and agitator speed were automatically
maintained at constant levels, while all signals (Table I) - some unused in this work - were
recorded at a frequency of some 3 samples per minute on the 3-1/2” disk drive of the UMC 800
controller (Fig. 2 and 3). Care was taken to assure synchronicity of the off-line WDS measurements
with the on-line recordings, as both were later imported in Excel for evaluation and graphing (Fig.
5-7). In order to account for and eliminate or minimize the effect of possible minor systematic
errors in measuring either the liquor temperatures or absolute pressure (Figure 4), and in order to
at least partially compensate for the theoretical effects on the boiling point of the hydrostatic head
and any solution superheat, temperature of the boiling water was recorded as with sugar liquors in
separate “water tests” (Figure 3) lasting some 1 to 2 hours each, and interspersed between the
sugar liquor tests. Again, the data were recorded and averaged, and a correlation (Figure 4) of the
averaged data, viz. temperature v. absolute pressure was then used in the BPE evaluations, rather
than the literature data. The difficulties with location of the temperature sensors, particularly in
large pans, and the effects of superheat at the heating surface are well recognized and documented
in the literature. The temperature of the boiling liquid was therefore measured and recorded at two
locations, one under the calandria (tb1), and the other just above it (tb2). A small but rather
systematic difference (tb1 – tb2) of about 0.2 to 0.8oC was found between the two, and nearly
identical, on average, in the water tests (Figure 3) as well as measurements with sugar liquors
(Figure 2). As this difference does not appear related to concentration (viscosity) of the boiling
liquid or the heat flux (change of steam pressure from 5 to 3 psi in Figure 3), and therefore to any
possible liquid superheat at the heating surface, it comes most likely from an offset of one of the
two temperature sensors and is not expected therefore to effect BPE evaluation. The average of
the two readings was used throughout this work in evaluation and reporting of the data. The
average values from the six water tests were correlated (Figure 2) to obtain
tbW = 3.3374Pabs + 40.746
(1)
where tbW is the water boiling temperature (oC) and Pabs, the absolute pressure (in Hg). From tbW,
and the boiling temperature of sugar liquor (tb), the boiling point elevation is calculated as
∆tb= tb- tbW
(2)
where tbW comes from equation 1 taking into account the actual Pabs for each recorded data point.
The experimental correlation is nearly parallel to and offset by some 0.2 to 0.4oC off the points
taken from the literature10 (Figure 4).
Three levels of (HPLC) purity (100 WS/ WDS) were included in the measurements, viz. a
refined sugar liquor (Q=100), a mill (Louisiana) syrup (Q=85) and, for the lowest level (Q=58), a
blend of blackstrap molasses and raw sugar.
Data Analysis and Presentation
Comparison of experimental data with literature
Four equations from the literature were chosen for comparison with the experimental data.
An extensive, but limited to pure sucrose solutions, set of literature data was fitted by Starzak and
Peacock23 with a five-parameter equation
t bW + C SP
Q


2
2
1 − RB X S 1 + a SP X S + bSP X S t + 273.15 
SP
bW
∆t b = 
− 1 (t bW + C SP )
t
+
C


bW
SP
1+
Ln(1 − X S )


BSP


(
)
(3)
with aSP = -1.0038 ; bSP = -0.24653 ; BSP = 3797.06 oC ; CSP = 226.28 oC ; Q = -17638 J/mole
and R (8.3143 J/mole K), the universal gas constant. The scatter of the data at the very high solids
contents and temperatures (up to 99 % sucrose concentration!) is very large and was expected to
affect the applicability of the equation in the narrow range (7< ∆t b <13oC) of ∆t b encountered in
sugar crystallization. The sucrose concentration in equation 3 is expressed as a mole fraction,
XS =
WS / MWS
WS / MWS + (100 − WS ) / MWW
(4)
Batterham and Norgate12 measured BPE of cane solutions at purities 100, 70 and 41 using
the equilibrium (non-boiling) technique of Dunning. Theirs appear to be the only data of note for
cane solutions besides the limited set of Thieme from the 1920’s. A correlation
∆tb = ABN tbW + BBN + CBN
(5)
with
ABN = 0.3604 - 2.5681 x 10-2WDS + 6.8488 x 10-4WDS2 – 8.0158 x 10-6WDS 3 + 3.5601 x 10-8WDS 4
BBN = 50.84 - 3.516WDS + 9.122 x 10-2WDS 2 – 1.0492 x 10-3WDS 3 + 4.611 x 10-6WDS 4
CBN = -0.272 - 2.27(Q/100) + 2.542(Q/100)2 + 0.05311WDS(1 - Q/100)
was developed over the concentration range of WDS 47 to 84% and tbW range 40 to 75 oC. The
absence of boiling avoids complications with superheat and hydrostatic head, but a closer
inspection of the presented data reveals significant and systematic deviations between the
experimental points and the correlation lines, particularly at high concentrations and low purities,
but even in pure sucrose liquors at WDS > 70 %, viz. the only regions that matter in sucrose
crystallization. This reliance on the more numerous data for dilute solutions and the Duhring rule
in fitting of data, and disregard for the experimental points for concentrated liquors introduced
some uncertainty as to its applicability. Nevertheless, the comparison offered by Batterham with
Thieme’s data is significant and shows much smaller effect on BPE of purity than thought
previously.
Hoekstra20 fitted the data taken from Honig5, Batterham and Norgate12, Hugot10 and Lyle24
with the integrated form of the Clausius-Clapeyron equation
 W DS
∆t b = AH 
 100 − W DS



BH
 273 + t bW 


 100 
CH
 Q 


 100 
DH
(6)
with the coefficients AH = 0.1379, BH = 0.808,
CH = 2.327 and DH = -0.42 , Although no
comments on the fit with or deviations from the literature were offered, and an apparent omission
in the reported equation of a factor of
nd
rd
( 273 + t bw ) 2
2
2
∆t b = a B * W DS
bB (W DS − 60) + c B 100 in the 2 and 3 terms of the right0.38
(374 .3 − t bw )
hand side of the equation, and some
uncertainty about the absolute values of
25
some of the coefficients , it was nevertheless deemed of interest to compare this correlation as it
has apparently found some use within the South African sugar industry.
[
]
Bubnik etal22 developed a nine-parameter equation
(7)
aB = a0+a1Q+a2 Q 2
bB = b0+b1Q+b2Q2
cB = c0+c1Q+c2Q2
and a0 = 1.67525*10-4, a1 = -1.85299*10-6, a2 = 7.92284*10-9, b0 = 2.87764*10-6,
b1 = -2.77263*10-8, b2 = 1.44306*10-10, c0 = 1.06668*10-3, c1 = 2.10304*10-6 and c2 = 4.28274*10-8, with the mean difference between calculated and experimental data reported to be
only 0.15oC. Despite the claim of multiple sources, the underlying data appear limited to the sugar
beet set of Spengler.
Fitting of the experimental data
The NLIN routine (Table II) of SAS26 version 8.2 was used to find new parameters (Ax,
Bx, Cx, Dx) of equation 6. The Hoekstra parameters AH, BH, CH and DH were used as the starting
points for the iterative fitting.
Table II: SAS code for, and output of fitting of the experimental points.
SAS code:
data one; infile cards;
input WDS ∆t b p tbW Q;cards;
70.60 5.14 5.39 58.73 100
72.60 5.92 5.39 58.73 100
74.80 6.44 5.40 58.77 100
..
proc nlin;
parameters A = 0.1379 B = 0.808 C = 2.237 D = -0.42;
model
∆t b = AX * (WDS / (100 - WDS))**BX * ((273 + tbW) / 100)**CX *(Q/
100)**DX; run;
The SAS output is in the following table:
Parameter
AX
BX
CX
DX
Estimate
Approx Std Error
0.1660
1.1394
1.9735
0.1237
 W DS
∆t b = AX 
 100 − W DS



BX
Approximate 95% Confidence Limits
0.0556
0.0172
0.2750
0.0137
 273 + t bW 


 100 
CX
0.0568
1.1056
1.4331
0.0967
 Q 


 100 
0.2752
1.1732
2.5138
0.1507
DX
AX = 0.1660 BX = 1.1394 CX = 1.9735 DX = 0.1237
(8)
Graph of the boiling point elevation v. liquid temperature.
QWDS
100(100 − WDS )
Equation. 8 with the new parameters was used over a range of
the variables (purity, supersaturation and temperature) and their
increments that were chosen such as to be directly comparable with the
frequently used older graphs of Holven carried unchanged from the 8th to the 12th edition of the
Cane Sugar Handbook8.
qS /W =
For each set of the variables tb, Q and y, and taking into account the definitions
(9)
q S / W (100 − Wsat , p )
WS / WW
y=
=
(WS / WW ) sat
Wsat , p q sat
QWDS
100
=
100 − WDS
WDS −
q NS / W
(10)
q sat =
WS , sat / WW , sat
Wsat , p / WW , sat , p
= 1 − 0.088q NS / W
(12)
(11)
the dry solids concentration WDS in solution was calculated as
100 / WDS = 1.088 +
q (100 − Wsat , p )
100 yWsat , p
−
0.088Q
100
(13)
where the solubility (g/100 g solution) of pure sucrose was taken27 as
Wsat,p = 64.407 + 0.0725tb + 0.002057tb2 – 0.00000935tb3
(14)
and the solubility coefficient (equation 11), applicable to cane liquors is simplified from Steindl
etal28. The boiling point of water tbW is then calculated from the equation
t bW
 W DS
= t b − AX 
 100 − W DS
BX
  273 + t bW 
 

  100 
CX
 Q 


 100 
DX
(15)
where AX, BX, CX and DX are the new coefficients (equation 8 and Table II). To solve the nonlinear equation, the Maple Version 6 software29 was used to obtain a tbW for every set of Q , tb
and y. As the solution was unstable with CX = -1.9735 or -1.97, an approximation CX=-2 had to
be introduced, with an negligible effect on the results. From tbW,, BPE is obtained using equation
(2). The procedure was then repeated for all combinations of Q, tb and y, and plotted (Figure 8) in
the form comparable to the existing literature graphs8.
Graphs of BPE v. supersaturation.
The data generated in the previous section was replotted (points in Figures 10) at different
temperature 55, 60, 65, 70 and 75oC, supersaturation from 1.0 to 1.3, and at five purity levels , 60,
70, 80, 90, and 100.
The NLIN procedure of SAS26 was again used to develop a general correlation between
BPE, temperature, supersaturation and purity, and, of the several models tested, the fourparameter equation
∆t b /y = aX tbQbX - cXQdX
(16)
with aX = 0.4702, bX = - 0.2586, cX = 0.0688 and dX = 0.7875
was found to fit the points reasonably well over the full range of purities and temperatures and is
represented by lines in the graphs in Figure 10.
The threshold or critical supersaturation limit (nucleation limit) was calculated30 as
y crit = 1.129 − 0.284(1 − Q / 100) + [2.333 − 0.0709(t b − 60)](1 − Q / 100) 2
(17)
Discussion of the results
For pure sucrose solutions our data and the correlation, equation 8, labeled “ASI” in
Figures 5 - 7 – lie some 0.5 to 1oC above the other lines, with Batterham and Norgate’s and
Starzak’s nearly identical, and Bubnik’s some 0.3oC below them . At all purities, Hoekstra’s has a
distinctly lower slope than any of the other correlations or the experimental data. At 85 purity
(Figure 6), the ASI and Bubnik’s correlations nearly coincide, and Baterham’s lies some 0.5 to
0.7oC below. At the lowest purity (Figure 7), the equation of Bubnik far overpredicts BPE as
does, to a smaller degree that of Hoekstra. This, of course, is reflected in the small and opposite
effect of purity, (DX > 0 in Table II) on BPE found here in comparison with previous works. The
apparently smaller BPE of sugarcane solutions than that of sugarbeet liquors at the same purity
was already noted by Thieme. Later, Baterham and Norgate found even smaller effect than
Thieme of purity for cane sugar liquors. Hardly any detail of the experimental procedures is given
in the historical publications, so the reasons for the deviations are hard to ascertain. Differences in
analytical techniques and possibly of non-sugar composition may also be responsible for at least
some of the discrepancies. The fact that our data, at the lowest purity lie slightly below, and
nearly coincide at the 85 purity with, the non-boiling data of Batterham is a strong indication of
absence of any measurable superheat or hydrostatic head effects in our experiments. Although our
data and our (ASI) correlation for pure sucrose exceed the other lines by some 0.5 to 1oC, they
agree quite well with the curves compiled by Holven14 in his Figure 1. A few points in Figures 5 –
6 were extracted from Holven’s lines and document the agreement. The fit and scatter of the
experimental data with and around the ASI equation is reasonable, with the exception of a few
tests that may have been affected by poorer than usual control of absolute pressure.
In order to make the data useful for control of sugar boiling, the solubility and
supersaturation concepts were introduced as described in the preceding sections, and the graphs
(Figure 8) constructed as in the often used nomograph in the Cane Sugar Handbook8. A
comparison of the two (Figure 9) reveals a relatively good agreement in the middle of the
temperature range at high purities, but an increasingly large overprediction of BPE at lower
purities by the Cane Sugar Handbook8 data. The straight lines in Figure 10, calculated from the
new (ASI) equation 16 fit reasonable well the points in Figure 10, which in turn were calculated
from the equation 8, and represent a general correlation in the form that is suited for control of
sugar boiling. The equation 16 was incorporated into the UMC 800 controller and the initial tests
of automatic boiling at ASI indicate that it is appropriate to accurately indicate the seeding point
and control the seed addition. A literature equation30 for the critical supersaturation (dotted lines
in Figure 10) is given as a guide for sugar boiling to delineate the “danger” zone for false grain,
and its validity is subject of ongoing tests.
Summary
A series of boiling point elevation measurements was made with sugarcane liquors at three purity
levels and three absolute pressures, and an equation
 W DS
∆t b = AX 
 100 − W DS



BX
 273 + t bW 


 100 
CX
 Q 


 100 
DX
(AX = 0.1660 BX = 1.1394 CX = 1.9735 DX = 0.1237)
developed that fits well the experimental data. Through an introduction of the solubility and
supersaturation concepts a general equation
∆t b /y = aX tbQbX - cXQdX
(aX = 0.4702, bX = - 0.2586, cX = 0.0688 and dX = 0.7875)
and a series of graphs were produced that are suitable for use in, or direct incorporation into the
software of, automatic control of sugar boiling in the sugarcane industry.
Acknowledgments
A partial funding from the American Sugar Cane League (ASCL) and the Sugar
Processing Research Institute, Inc (SPRI) are gratefully acknowledged, as are useful input from
prof. P. W. Rein and technical assistance of Lenn Goudeau, Scott Barrow, Joe Bell and Ms.
LiFeng.
Symbols
A, B, C ,D,a,b,c,d
MW
P
Q
Q
qsat
qS/W
qNS/W
R
t
∆t b
W
X
y
coefficients in equations 3,5,6,7,8,15,16.
molecular weight, g/mole
pressure
constant (17638 J/mole)
purity (%)
solubility coefficient
sucrose/water mass ratio in the solution
impurity/water mass ratio in the solution
8.3143 J/(mole K), the universal gas constant
temperature
boiling point elevation
mass concentration (g/100 g solution)
mole fraction
supersaturation
Index
Abs
B
b
absolute
Bubnik etal
boiling point
BN
Crit
DS
H
I
NS
p
SP
S
sat
W
X
Batterham and Norgate
critical
(refractometric) dry solids
Hoekstra
impure (WNS > 0)
non sucrose
pure solution (WNS = 0)
Starzak and Peacock
sucrose
saturated (y = 1)
water
this work (equations 8,16)
References
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Legends to the Figures
Figure 1: The 200 L ASI vacuum pan and a view of the calandria.
Figure 2: Some of the trends recorded during the BPE measurement tests. Purity 85, Pabs = 5.4 in
Hg (Test 2-27-02). Only the absolute pressure, and liquor temperatures were used for the BPE
calculations.
Figure 3: Some of the trends recorded in the course of the “water tests” Note the steam pressure
set point change at 10:53 AM. Pabs 5.4 inHg (Test 3-01-02).
Figure 4: Correlation of the boiling point of water measurements used in the BPE calculations.
Figure 5: Measured BPE points (diamonds), their correlation (ASI) and literature correlations. A
few points (round symbols) were read off Holven’s compilation of pure sucrose data (Figure 1 in
ref 14). Purity 100.
Figure 6: Measured BPE points (diamonds), their correlation (ASI) and three literature
correlations. Purity 85.
Figure 7: Measured BPE points (diamonds), their correlation (ASI) and three literature
correlations. Purity 58.
Figure 8: BPE (at various liquor purities) vs. liquor (massecuite) temperature, calculated from
equation 8.
Figure 9: Difference of BPE (at various liquor purities) calculated from equation 8 and BPE
given in ref.8, p.238, respectively, vs. liquor (massecuite) temperature, supersaturation 1.00. At
higher supersaturations, the differences become proportionately higher.
Figure 10: BPE (at various liquor or massecuite temperatures) vs. supersaturation, calculated
from equation 16. Dotted lines: spontaneous nucleation limit calculated from equation 17.