University
stringclasses 19
values | Text
stringlengths 458
20.7k
|
|---|---|
Colorado School of Mines
|
used to analyze the resulting experimental intensity data[86]. As a result, both SAXS and
SANS scattering patterns suffer from the same fundamental inability to uniquely define the
shapes and interactions of particles in a sample. The analysis of small angle scattering data
requires making general assumptions about the shapes of the particles in solution and the
types of interactions expected between them to get quantitative structural information[87].
These assumptions must be made based on information from independent methods.
An independent, alternative method for gaining particle size and interaction information
is pulsed-field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy, which can be
used to measure the self-diffusion coefficients of molecular aggregates in solution. PFG-NMR
is an established method for directly measuring the average diffusion coefficients of colloidal
particles containing NMR-active nuclei[88–91]. It measures the change in the intensity of
the NMR signal of a sample with either changing applied magnetic field gradient pulse
strengthordiffusiontime. Thischangeinintensityisthenrelatedtothediffusioncoefficients
of species in the sample. The diffusion coefficient of a species is directly related to its
size and the nature of its interactions with other components in the system. Diffusion
coefficient data can be used to determine the volumes of diffusing species using models
relating the diffusion coefficient and aggregate size. The impacts of the assumptions used
in models relating the diffusion coefficient and aggregate size may be substantially less than
those used in small angle scattering data fitting. For example, Chiarizia et al., used a
non-interacting ellipsoidal model and an adhesive hard sphere model to fit scattering data
measured for samples containing TBP and zirconium[27]. The resulting model fits were
equally good. However, the aggregate volumes calculated using these two models differ by
nearly two orders of magnitude. In contrast, aggregate volumes calculated from diffusion
data may be off by as much as 12%, on average[92]. Because it provides complementary
information, diffusion NMR spectroscopy can be used as an important supplement to small
angle scattering experiments.
48
|
Colorado School of Mines
|
In this work, the use of PFG-NMR to determine the size and interparticle interactions
of metal-containing extractant aggregates is described for the first time in the literature.
The extraction systems under consideration contain TBP and either uranyl or zirconium ni-
trate. The results of PFG-NMR experiments are compared with prior small angle scattering
investigations of the same systems.
4.3 Experimental Section
4.3.1 Materials
All organic solutions were prepared using 99+% tributyl phosphate from Acros Organics
and 99+% n-dodecane from Alfa Aesar. All aqueous solutions were prepared using ACS
grade nitric acid from Macron Fine Chemicals and degassed, ultrapure (18 MΩ-cm) water.
A stock solution of zirconium nitrate (0.601 0.001 M Zr(NO ) , 6.0 0.1 M HNO )
3 4 3
± ±
was prepared from hydrous zirconium oxide as described in Chiarizia et al.[27], using reactor
grade (99.5+%) zirconium (IV) chloride (Alfa Aesar) as a starting material. A stock solution
of uranyl nitrate (1.40 0.01 M UO (NO ) , 3.0 0.1 M HNO ) was prepared using ACS
2 3 2 3
± ±
grade uranyl nitrate hexahydrate (International Bio-Analytical Industries, Inc., Boca Raton,
FL). These metal stock solutions were diluted with water and nitric acid as needed to obtain
aqueous solutions of the desired metal and acid concentrations. All reagents were used as
received, without further purification.
4.3.2 Solvent Extraction Experiments
◦
All batch solvent extractions were performed at 21 0.5 C using equal volumes of
±
aqueous and pre-equilbrated organic phases. Organic phase solutions were initially prepared
with 20 v/v% TBP in n-dodecane. This organic phase was then contacted with an equal
volume of a nitric acid solution at the same concentration as that used in the batch extrac-
tion to produce a pre-equilibrated organic phase. The aqueous phases used in the batch
extractions initially contained either 5 or 10 M HNO and 0.06 - 0.24 M Zr(NO ) or 0.4 -
3 3 4
0.51 M UO (NO ) . These systems were chosen because SANS comparison data exist for
2 3 2
49
|
Colorado School of Mines
|
them in the literature. Equal volumes of these aqueous and pre-equilibrated organic phases
were contacted for 15 minutes on a vortex mixer. Samples were centrifuged at 2000 RPM
to separate the phases. Pure organic phase samples were taken and kept neat or diluted
3:1, 1:1, or 1:3, giving samples for NMR analysis with approximately 0.2, 0.15, 0.1, and
0.05 solute fractions, respectively. The average diffusion coefficients of TBP aggregates in
these samples were measured by PFG-NMR experiments. Samples from both the organic
and aqueous phases were taken for further chemical analysis, as described below.
Zirconium concentrations in the organic and aqueous phases were found using a 95Zr
radiotracer produced by neutron irradiation of the same stock of hydrous zirconium oxide
used in the preparation of the zirconium nitrate stock solution[57]. It was assumed that the
extraction of the radiotracer would be directly proportional to that of the non-radioactive
zirconium. This assumption was verified by comparing the distribution of the 95Zr radio-
tracer to the distribution of non-radioactive zirconium, which was quantified using neutron
activation analysis. The zirconium concentrations could then be found from the specific
radioactivity of organic and aqueous phase samples from a batch extraction experiment
identical to that used in the preparation of NMR diffusion samples, to which a 10 µL spike
of the zirconium radiotracer had been added. A well-type high purity germanium detector
was used to determine the radioactivity of the samples. Uranium concentrations were found
directly by the same method, using the 235U peak at 186 keV. Organic phase water concen-
trations were found using a Mettler-Toledo DL39 coulometric Karl-Fischer titrator. Nitric
acid concentrations were determined by potentiometric titration, as described elsewhere[27].
All chemical analyses were done in triplicate. The experimental error is the average relative
standard deviation of these measurements. It was assumed that the TBP concentration in
the organic phase remained constant over the course of each batch extraction experiment.
A heavy organic phase sample containing zirconium was prepared by contacting an aque-
ous phase containing 10 M HNO and 0.24 M Zr(NO ) with a pre-equilibrated organic
3 3 4
50
|
Colorado School of Mines
|
phase consisting of 20 v/v% TBP in n-dodecane, as in previous batch extractions. The
resulting heavy organic phase was sampled, and the diffusion of the TBP species was mea-
sured by PFG-NMR. The chemical composition of the heavy organic phase sample was not
determined.
All sample compositions determined are given in Table 4.1.
4.3.3 Pulsed-Field Gradient Stimulated Echo Experiments
The average diffusion coefficients of TBP-containing species were found using a 1H NMR
pulsed-field gradient stimulated echo (STE) experiment[93] with a longitudinal eddy-current
delay (LED)[94] on a 400 MHz Bruker AVANCEIII NMR spectrometer with a 5 mm Bruker
◦
single-axis DIFF60 Z-diffusion probe. In the STE-LED experiment, an initial 90 RF pulse
rotatesthemagnetizationfromthez axistothex y plane, afterwhichamagneticfieldgra-
− −
dient pulse of strength G and duration δ is applied. This gradient pulse effectively ”marks”
the positions of 1H nuclei along the z axis of the sample by causing the magnetization of
−
nuclei in identical chemical environments to lose phase coherence depending on their location
along the z axis. A second 90◦ RF pulse stores the magnetization in the z direction, which
− −
◦
is then subject to longitudinal relaxation. A third 90 RF pulse restores the magnetization
to the x y plane with the signs of the phase angles reversed, after which a second gradient
−
pulse is applied. The magnetization is again stored in the z direction by the application
−
◦
of a fourth 90 RF pulse while eddy currents induced by high gradient pulses are allowed
to decay for a time t , after which a fifth and final 90◦ RF pulse restores the transverse
e
magnetization for measurement of the stimulated echo signal. The amplitude of this signal
can be related to the self-diffusion coefficient of a species by the Stejskal-Tanner equation:
S(G) =
S(0)e−γ2δ2G2D(∆− 3δ)
(4.1)
where S is the intensity of the NMR signal at a given magnetic field gradient strength (G), γ
is the gyromagnetic ratio of the 1H nucleus, δ is the gradient pulse length, ∆ is the diffusion
time, and D is the diffusion coefficient. The STE-LED experiment used in this work varied
52
|
Colorado School of Mines
|
the strength of the applied magnetic field gradient while keeping all other experimental
parameters constant. The resulting NMR signal intensity for the desired chemical species
was then plotted versus the magnetic field gradient strength. The self-diffusion coefficient
was calculated by fitting the Stejskal-Tanner equation (Equation 4.1) to this data. The
STE-LED pulse sequence is shown in Figure 4.3.
Figure 4.3: Schematic representation of the STE-LED pulse sequence used to measure the
diffusion coefficient of TBP aggregates.
◦
All diffusion measurements were made at 25.0 0.1 C, using a diffusion time of 20 ms,
±
a gradient pulse duration of 1 ms, a 90◦ RF pulse duration of 5 µs, and an eddy current
delay of 5 ms. Each experiment consisted of 16 gradient steps with a maximum gradient
strength between 270 and 320 G/cm, chosen to correspond to at least 95% attenuation of
the stimulated echo signal. Each gradient step consisted of 16 averaged scans collected with
a repetition time of 5000 ms. TBP diffusion was measured using the attenuation of the
1H peak at 4.3 ppm, which corresponds to the protons bound to the carbon immediately
adjacent to the butoxy oxygens of TBP[95]. Figure 4.4 shows a 1-D 1H NMR spectrum of
a sample containing only TBP and n-dodecane (no deuterated solvents) measured with the
solid-state diffusion probe used in all diffusion experiments. The spectra of the TBP samples
at different gradient strengths for a typical STE-LED experiment are shown in Figure 4.5.
A line was fit to the measured diffusion coefficients at varying solute fractions to obtain
the infinite dilution diffusion coefficient and unitless interaction parameter, α, given in Equa-
53
|
Colorado School of Mines
|
tion 4.2. Aggregate volumes were calculated from the Wilke-Chang equation (Equation 4.3)
using the infinite dilution diffusion coefficients of TBP species, a viscosity of 1.331 cP for
◦
the n-dodecane solvent at 25 C[96], and a solvent association parameter of 1. Average TBP
aggregation numbers were calculated using the sample compositions and molar volumes.
For each experimental condition, a single set of dilution samples were analyzed. Diffusion
measurements were done in duplicate, due to the low variability of this measurement. The
experimental error associated with a given system was estimated at 1.6% from the rela-
tive standard deviation of the average diffusion measurements of triplicate batch extraction
experiments under a single set of conditions.
4.4 Results and Discussion
4.4.1 Diffusion Coefficient and Inter-aggregate Interaction Models
At a given temperature, the diffusion coefficients of colloidal particles are affected by
the solvent viscosity, the sizes and shapes of the solvent molecules, the sizes and shapes
of the particles, and interparticle interactions resulting from obstruction by other diffusing
particles or electrostatic potentials[97]. The impact of interparticle interactions can be elim-
inated by measuring the diffusion coefficient of a sample at different solute fractions upon
dilution with fresh solvent, assuming a decrease in solute concentration is the only effect
of this dilution[98]. The change in the diffusion coefficient with solute fraction (ϕ) can be
approximated by a line under dilute conditions, and fit by Equation 4.2 to yield the infinite
dilution diffusion coefficient (D ) and an interaction parameter, α. The interaction param-
0
eter, α, corresponds to the second virial coefficient of the system and directly reflects the
combined effects of two-body and hydrodynamic interactions[99]. The linear approximation
for the relationship between the diffusion coefficient and solute volume fraction is accurate to
a volume fraction of approximately 0.2, after which higher order terms in the virial expansion
become relevant as three- or four-body interactions begin to increase in magnitude[100]. D
0
is only dependent on the hydrodynamic radii of the diffusing particles, while α reflects the
nature of the interparticle interactions. In the case of reversed micelles, this parameter is
55
|
Colorado School of Mines
|
usually negative due to the combination of hard sphere and attractive interactions between
micelles. Neglecting the effect of interparticle interactions in reversed micellar systems leads
to an overestimation in the size of the reversed micelles.
D = D (1+αϕ) (4.2)
0
The Stokes-Einstein equation is often used to relate diffusion coefficients of species in
dilute solution to the hydrodynamic radii of the diffusing particles[101]. However, due to the
solvent continuum assumption used in its derivation, this relationship is poor for systems
in which the solute radius is less than two to three times that of the solvent, as might be
found in solvent extraction systems[102]. The Wilke-Chang correlation was developed for
application to systems in which the solute and solvent are similar in size[92]. It is shown in
Equation 4.3:
√χM T
D = 7.4
10−8 B
(4.3)
0 × µV0.6
A
where D is the diffusion coefficient under dilute conditions, χ is the solvent association
0
parameter, M is the molar mass of the solvent, T is the temperature, µ is the solvent
B
viscosity, and V is the volume of the diffusing solute. The value for χ reflects the degree of
A
association of the solvent through intermolecular interactions like hydrogen bonding. It is
2.6 for water and 1.0 for non-associating solvents like heptane.
4.4.2 Aggregate Sizes - Comparison of NMR and SANS
The average volumes of TBP aggregates were calculated using the Wilke-Chang equa-
tion from the infinite dilution diffusion coefficients at each experimental condition. These
volumes are given in Table 4.2. An average TBP aggregation number was calculated from
the average aggregate volume, the chemical compositions of the samples, and the molecu-
lar volumes of the system components. The molecular volumes of TBP, HNO , and H O
3 2
used were 273.87, 43.26, and 18.02 cm3/mol, respectively[24, 103]. Because the molecular
volume of Zr(NO ) has not been determined, the known molecular volume of ZrCl (83.14
3 4 4
56
|
Colorado School of Mines
|
cm3/mol) was used as a reasonable estimate[27]. The molecular volume of UO (NO ) used
2 3 2
was 70.70 cm3/mol[24]. For purposes of comparison with SANS data, the hydrodynamic
radii of these aggregates were calculated from the Wilke-Chang volume by assuming the
aggregates were spherical. The corresponding hydrodynamic diameters of TBP aggregates
containing zirconium or uranium determined using NMR diffusometry are compared to the
scattering diameters determined using SANS in Figure 4.6. While the SANS diameters for
TBP aggregates containing zirconium were determined in n-octane, experimental evidence
suggests that the choice of aliphatic hydrocarbon diluent does not affect the average ag-
gregate size for a given sample composition. The distribution behavior of metals prior to
third phase formation has been observed to be independent of diluent chain length, as have
the stoichiometries of extracted species under dilute conditions.[77, 78] NMR experimental
uncertainty and SANS fitting errors have not been included as error bars in Figure 4.6 be-
cause they are smaller than the markers. It is instructive to note the differences in SANS
diameters between analyses for systems at 10 M HNO and no metal. For samples of similar
3
composition in the data set including zirconium, the average SANS diameter is less than 14
˚A, while in the uranium data set the average SANS diameter is 16 ˚A. These deviations hint
at the potential for systematic bias in aggregate size introduced in the analysis of SANS
data.
Figure 4.6 shows that the average sizes of TBP aggregates determined by NMR diffu-
sometry are comparable to those found using using SANS, suggesting that the form factor
used in the analysis of the SANS data accurately reflects the physical reality of the system.
Aggregate sizes determined using both methods should agree because both effectively relate
the size of TBP aggregates to experimental measurements defined by the farthest reach of
the butyl tails of the TBP molecules on a mass-average basis. In SANS, the calculated size
of the aggregates is primarily determined by the strongly scattering hydrogen atoms in the
butyl tails, which contrast with the deuterated solvent used in those experiments. Likewise,
NMR diffusometry relates the speed of the protons adjacent to the butoxy oxygen of TBP
57
|
Colorado School of Mines
|
Figure 4.6: The sizes of TBP aggregates found using NMR and SANS are comparable for
samples with varying zirconium, uranium, and HNO concentrations. Triangle markers are
3
samplesat5MHNO . Diamondmarkersaresamplesat10MHNO . Filledmarkersindicate
3 3
TBP aggregate diameters found by NMR spectroscopy. Unfilled markers indicate literature
values for TBP aggregate diameters found by SANS[24, 27].
molecules to the sizes of the aggregates they compose. In certain systems, diffusion-derived
aggregate sizes may be affected by association between the solvent and aggregate, similar to
the well-known phenomenon of water forming a stable solvation shell around ionic solutes in
aqueous solution. However, the strength of the interactions between the n-dodecane solvent
and TBP aggregates are low enough that a decrease in diffusion due to solvation effects is not
expected in this system. This is a common assumption in diffusion experiments involving
nonpolar solvents and surfactants[104].
Furthermore, both methods find the mass-average size of TBP aggregates in solution.
In SANS, the measured scattering intensity at a given value of the scattering vector, Q, is
directly proportional to the number of scatterers making up each aggregate. In the TBP
system, the primary scatterers are the hydrogen atoms in the TBP hydrocarbon tails, whose
total scattering cross-section is substantially larger than the other components in the system.
As a result, the contribution to the scattering signal is proportional to the number of TBP
molecules making up each aggregate, indicating a mass dependence[105]. In diffusion NMR
58
|
Colorado School of Mines
|
spectroscopy of polydisperse species with identical chemical shifts, such as polymer systems
made of a single monomer, the NMR-measured diffusion coefficient can be approximated as
the mass-average diffusion coefficient[97]. The organic phase extraction samples measured in
this work are examples of such polydisperse systems. Since diffusion can be directly related
to size, this means that diffusion NMR analysis results in mass-averaged TBP aggregate
sizes.
4.4.3 NMR Aggregate Sizes - Comparison Between Samples
The Wilke-Chang equation is a correlation based on the form of the more fundamental
Stokes-Einstein equation. Values for the parameters used in the Wilke-Chang equation were
determined through fitting diffusion data for 123 molecular solute-solvent systems[92]. As
a result, the particle volumes determined using this equation are subject to a systematic
bias that may be as high as 12% on average due to differences between the systems used in
the parameterization of the Wilke-Chang equation and the TBP solvent extraction system
explored here. However, the comparison of size trends within TBP systems is possible
because the shapes of the solutes and solvent are substantially similar between samples.
Size trends indicate an increase in the average size of TBP aggregates with increasing
metal concentration, as would be expected given the apparent saturation of the TBP ex-
tractant and the larger molecular volumes of the neutral metal salts compared to nitric acid
and water. Saturation of the extractant is relevant because it indicates that changes in the
average volumes of TBP aggregates are due to changes in the sizes of associated solutes and
are not a result of concentration-dependent self-association of TBP monomers. Saturation
of the TBP is indicated by the sample compositions, in which the combined concentrations
of the polar solutes are greater than the concentration of TBP molecules.
In the nitric acid only and zirconium systems, the average TBP aggregation number
is relatively constant at just below a value of two, while the aggregate volume increases
with increasing zirconium concentration. The concentration of zirconium that could be
reached in these samples was limited by third phase formation, which occurs at organic
59
|
Colorado School of Mines
|
phase zirconium concentrations just beyond the highest concentrations used here. Because
the concentrations of zirconium in these samples are so low (less than 4% of the total polar
solute concentration, or contained in as many as 1 in 10 TBP aggregates), this suggests that
the increase in aggregate volume is not due solely to the increased volume of the metal salt
relative the acid in identical TBP aggregates. Some TBP species formed in the presence of
zirconium appear to also have a higher TBP aggregation number. However, this effect is
difficult to quantify due to the very small contribution to the average TBP aggregate size
by zirconium-containing species.
In contrast, the concentrations of uranium are as high as 40% of the total polar solute
concentrations, corresponding to approximately 2 of every 3 TBP aggregates containing a
uranyl cation. In these samples, the average TBP aggregate size is strongly impacted by the
greater mass-average contribution of what seem to be large uranium-containing aggregates of
up to four TBP. This value is very different from the aggregation number of two determined
by traditional distribution studies under dilute uranium conditions[61], and indicates the
formation of larger TBP species at high metal and acid concentrations.
4.4.4 Diffusion in the Third Phase
Diffusion NMR spectroscopy has been used to infer the microstructure of surfactant
solutions based on the relative magnitudes of the diffusion coefficients of surfactant, oil, and
water in ternary systems[104]. For a solution of oil in which water-containing micelles are
dispersed, the diffusion coefficient of the oil is expected to be an order of magnitude higher
than that of the water, and identical to the diffusion coefficient of the surfactant. Similarly,
for a solution of water in which oil-containing micelles are dispersed, the diffusion coefficient
of the water is expected to be higher than that of the oil and surfactant. In a bicontinuous
system, where oil and water diffuse freely in surfactant liquid crystalline structures, the oil
and water diffusion coefficients are high, while the surfactant diffusion coefficient is an order
of magnitude lower.
60
|
Colorado School of Mines
|
The average diffusion coefficient of TBP-containing species in the third phase sample was
found to be 3.45 0.07 10−11 m2/s. This value is an order of magnitude smaller than the
± ×
average TBP diffusion coefficient of an n-dodecane solution containing only 20 v/v% TBP
(i.e., not pre-equilibrated with an acid solution), which was found to be 4.75 0.10
10−10
± ×
m2/s. The effects of interparticle interactions on these values are small compared to the
effects that would be expected by the participation of TBP in a liquid crystalline-like phase.
In a bicontinuous structure, like the interconnected-cylinder structure proposed by Ellis et
al.[80], for the third phase formed in a different mixed extractant system containing various
acids and TBP, it would be expected that the diffusion coefficient of TBP would be an order
of magnitude slower than the diffusion coefficient of free TBP, that is, on the order of
10−11
m2/s[104]. This is the case in an extraction system containing acid, TBP, and zirconium.
The order of magnitude decrease in the rate of TBP diffusion observed in the third phase
sample suggests that an analogy between third phase formation and the formation of liquid
crystalline phases in surfactant systems may be applicable. This observation should be
verified by measuring and comparing the n-dodecane and TBP diffusion coefficients in third
phasesamplesusingatechniquelikediffusion-orderedspectroscopy, whichisusedtoseparate
the diffusion coefficients of the components of a mixture[106].
4.4.5 Aggregate Interactions
The effects of interparticle interactions on diffusion must be eliminated to determine the
average sizes of TBP aggregates in solution from NMR diffusometry. The size and shape
of the diffusing particles, and long- and short-range attractive or repulsive interactions all
impact the change in the diffusion coefficient with solute fraction. The effects of interparticle
interactions on the measured diffusion coefficients were determined in this work by fitting a
line to a series of diffusion coefficients measured on dilution of a sample of an equilibrium
organic phase with n-dodecane. Representative data and fitted lines for diluted samples are
shown in Figure 4.7. Values of the interaction parameter, α, are given in Table 4.2. It was
assumed as part of this analysis that TBP aggregation behavior in equilibrium organic phase
61
|
Colorado School of Mines
|
samplesisunaffectedbydilution. Whilecloudingofthesampleswasinitiallyobservedonthe
addition of n-dodecane, this was found to disappear within an hour of sample preparation
and no indication of precipitation or phase separation was observed. Because the polar
solutes extracted by TBP (H O, HNO , UO (NO ) , and Zr(NO ) ) are effectively insoluble
2 3 2 3 2 3 4
inn-dodecanealone, itisreasonabletoassumethattheseextractedsolutesremainassociated
with TBP aggregates in solution on dilution with n-dodecane. Furthermore, the aggregates
breaking apart would result in a deviation from linearity of the relationship between the
diffusioncoefficientandsolutevolumefraction. RelativelymoresmallTBPaggregateswould
causetheslopetobecomesteeperatlowsolutevolumefractionsbecausetheaveragediffusion
coefficient would be disproportionately increased. Conversely, if the TBP aggregates were
coalescing to form larger aggregates on dilution, the relationship between diffusion coefficient
and solute volume fraction would flatten at low solute volume fraction. The absence of phase
separation, and the consistency of the linear relationship between solute volume fraction
and diffusion coefficient support the assumption that sample dilution does not affect TBP
aggregation in the organic phase.
Figure 4.7: Representative data showing the effect of sample dilution on TBP diffusion
coefficients. Diamond markers are for an organic phase sample in equilibrium with a 5 M
HNO only aqueous phase. Triangle markers are for an organic phase sample of 0.012 M
3
Zr(NO ) in equilibrium with a 10 M HNO aqueous phase.
3 4 3
62
|
Colorado School of Mines
|
Table 4.2: TBP aggregate infinite dilution diffusion coefficient, interaction parameter, and
size results using diffusion NMR spectroscopy.
Sample D a αb Agg. Vol.a Agg. Num.c
0
(m2/s) (˚A3)
5a 5.03
10−10
-1.3 0.1 878 1.7
Zr5b
4.85× 10−10
-1.31
±
0.09 931 1.8
Zr5c
4.74× 10−10
-1.4
±
0.2 969 1.8
10a
4.69× 10−10
-0.8
±
0.1 984 1.8
Zr10b
4.67× 10−10
-0.97
±
0.09 991 1.8
Zr10c
4.56× 10−10
-1.04
±
0.06 1031 1.9
U10b
3.32× 10−10
-1.65
±
0.07 1755 3.4
U10c
3.25× 10−10
-1.7
±
0.1 1816 3.3
× ±
aAverage uncertainty 2%; bProvided uncertainty corresponds to the fitting error;
cAverage uncertainty 3%
The α-values for all the sample compositions studied were negative, as would be expected
toresultfromthecombinedeffectsofobstructionandelectrostaticinteractions. Inacrowded
system of diffusing particles, simple obstruction by other particles decreases the observed
diffusion coefficient with increasing concentration. This effect results from the presence of
other particles along a given particle’s diffusion path, restricting the distance it can travel
in the experimental diffusion time, ∆. Simple obstruction by other particles is modeled as
a hard sphere potential. Multiple theoretical approaches for determining the concentration
dependence of the self-diffusion coefficient of uniform hard spheres in dilute solution agree on
an α-value within 10% of -2[107–109]. In the presence of attractive interparticle interactions,
the α-value would be expected to be more negative. The α-values determined for the systems
studied here are less negative, especially in the nitric acid only and zirconium systems.
The difference is great enough that it is unlikely to be solely affected by the shapes of the
particles, which may deviate from being spheres. In fact, obstruction effects are greater in
dilute solutions of hard spherocylindrical particles, resulting in α-values between -2 and -2.5
depending on their length to width ratios[110]. The α-values of approximately -1 observed
in nitric acid only and zirconium systems suggest that there are net repulsive interactions
among TBP aggregates containing these solutes.
63
|
Colorado School of Mines
|
4.4.6 Repulsive Interactions: Ramifications for Scattering Interpretations
The majority of small angle scattering studies of extractant aggregation in the presence
of polar solutes have used the Baxter model for sticky hard spheres to fit the scattering data.
In the Baxter model, particles are modeled as spheres with interparticle interactions consist-
ing of a combined hard sphere potential and an infinitely narrow attractive well potential
at the sphere’s surface[111]. In theory, the validity of the assumption of purely attractive
interactions could be determined directly from the raw scattering data by looking at the
scattering intensity at low angles corresponding to length scales similar in magnitude to the
interparticle correlation distance. The intensity would be expected to increase relative the
scattering attributable to the size and shape of the particles in systems with repulsive inter-
particles interactions, and decrease in systems with attractive interactions[112]. However,
the scattering at low angles is dominated by the size and shape of the scattering particles,
making this determination using scattering data alone difficult in these systems. The α-
values determined by NMR diffusometry suggest that an improved small angle scattering
model for systems of extracted polar solutes could include a long-range electrostatic repul-
sive potential in addition to a short-range attractive potential. Such a model has been used
in the analysis of scattering data from systems of aggregating biological molecules[113].
4.4.7 Potential Explanation for Repulsive Interactions
Long range repulsive electrostatic interactions in these systems may result from interac-
tions between charge-neutralizing nitrate anions in the polar cores of TBP aggregates. TBP
extracts electrically neutral species. For the systems explored here, these species are water,
nitric acid, zirconium nitrate, or uranyl nitrate. For each electrically neutral species there
are areas of negative charge and areas of positive charge on the surfaces of the molecules
and associated ions. The areas of negative charge are centered around the nitrate oxygen
atoms, while the areas of positive charge are centered around the proton or cation. These
areas of positive charge may interact with the negatively charged phosphoryl oxygen of the
64
|
Colorado School of Mines
|
TBP extractant, causing the TBP to remain associated with these areas of positive charge.
The placement of TBP molecules around these areas could then present a steric hindrance
to the close interaction of this positively charged surface with other charged species, and
may screen these interactions. Depending on the specific placement of the TBP extractant
around the neutral species, this may leave the areas of negative charge bare and available to
interact by repulsive interactions. The arrangement of the negatively and positively charged
areas on the surface of the neutral species, as well as the placement of the TBP molecules
around these polar solutes will differ depending on the identity of the extracted species and
may explain the origin of the observed repulsive interactions between TBP aggregates.
The apparent repulsive interactions among TBP aggregates also suggest a different driv-
ingforcebehindthirdphaseformationthanthatproposedasaresultofsmallanglescattering
studies using the Baxter model. In those, it was suggested that the appearance of a third
phase resulted from the condensation of sticky TBP aggregates in a process analogous to
sedimentation, which is observed in traditional colloidal systems of discrete particles with
surface attraction. Sedimentation is generally not observed in traditional colloidal systems
when interparticle interactions are repulsive. For a system of TBP aggregates with repulsive
interactions, the mechanism for third phase formation may be driven by the complex inter-
play among the affinity of TBP for a polar solute, the solubility of polar solute-containing
TBP aggregates in the diluent, and the repulsive interactions between these aggregates. The
first requirement for third phase formation is that solvation of the polar solute by TBP must
be competitive with its solvation by water. A third phase will not form if a polar solute is not
sufficiently extracted into the organic phase. Polar solute-containing TBP aggregates may
then become insoluble in the diluent after a reaching a certain concentration, causing forma-
tion of the third phase. This insolubility may result from diluent-aggregate interactions that
are more unfavorable than the interactions between identical species. This is similar to the
mechanism suggested by Kertes which attributes third phase formation to poor solvation
of extractant adducts by aliphatic hydrocarbon diluents[77]. These explanations contrast
65
|
Colorado School of Mines
|
with the mechanism of third phase formation suggested by the presence of attractive inter-
aggregate forces, which is defined by favorable aggregate-aggregate interactions rather than
poor diluent-aggregate interactions. Repulsive interactions between TBP aggregates in the
third phase could then result in the formation of a Wigner glass-type structure. Wigner
glasses are relatively dilute ordered phases in which repulsive interactions between particles
fix the structure of the particles making up the phase[114].
4.5 Summary and Conclusions
Diffusion NMR spectroscopy can be used to determine aggregate sizes and interactions
as a complementary method to powerful small angle scattering techniques for characterizing
the structure of the organic phase in solvent extraction systems. Small angle scattering
techniquesrelyonpriorknowledgeaboutthestructuresofsamplestoanalyzescatteringdata
and extract specific information about scattering particles. Diffusion NMR spectroscopy
is an important method for obtaining this prior knowledge, if the effects of interparticle
interactions on the diffusion coefficient can be effectively excluded. In the case of solvating
extractant systems containing metals, we have found that there appears to be a repulsive
component to interparticle interactions of TBP aggregates in solution. This suggests that
the model used in the analysis of small angle scattering data in these systems in prior work
could be improved by the inclusion of a repulsive potential. Assuming spherical aggregates,
the aggregate sizes determined by diffusion NMR spectroscopy and SANS correspond well,
indicating that these two methods are, as would be expected, measuring the same aggregate
sizes by two very different experimental means. Finally, the diffusion coefficient of TBP in
a third phase sample was found to be an order of magnitude slower than that of TBP in
solution, showing that it is possible that the third phase results from the formation of a
liquid crystalline phase.
66
|
Colorado School of Mines
|
CHAPTER 5
THE STRUCTURE OF TRIBUTYL PHOSPHATE SOLUTIONS: NITRIC ACID,
URANIUM (VI), AND ZIRCONIUM (IV)
Modified from a paper submitted to the Journal of Molecular Liquids
Anna G. Baldwin1, Michael J. Servis2, Yuan Yang3, Nicholas J. Bridges4, David T. Wu5,
Jenifer C. Shafer6
5.1 Abstract
Diffusion, rheology, and small angle neutron scattering (SANS) data for organic phase
30 v/v % tributyl phosphate (TBP) samples containing varying amounts of water, nitric
acid, and uranium or zirconium nitrate were interpreted from a colloidal perspective to give
information on the types of structures formed by TBP under different conditions. Taken as a
whole, the results of the different analyses were contradictory, suggesting that these samples
shouldbetreatedasmolecularsolutionsratherthancolloids. Thisconclusionissupportedby
molecular dynamics (MD) simulations showing the existence of small, molecular aggregates
in TBP samples containing water and nitric acid. Interpretation of TBP and nitric acid
diffusion measurements from a molecular perspective suggest that nitric acid and metal
species formed are consistent with the stoichiometric solvates that have traditionally been
considered to exist in solution.
1Primary author and experimental researcher
2Co-author and computational researcher
3Co-author, NMR research scientist
4Co-author, Savannah River National Laboratory
5Co-author
6Corresponding co-author and advisor
68
|
Colorado School of Mines
|
5.2 Introduction
The Plutonium Uranium Reduction Extraction (PUREX) process has been used for over
sixty years to recover uranium and plutonium from used nuclear fuel[3, 12], and is one of the
most important and well-characterized solvent extraction systems currently in use[33, 115].
ThePUREXprocessusesa30v/v%solutionoftheextractanttributylphosphate(TBP,Fig-
ure 5.1), dissolved in an aliphatic hydrocarbon diluent such as kerosene, to preferentially
extract tetravalent plutonium and hexavalent uranium from a 3 to 4 M nitric acid aque-
ous phase that includes fission products and other impurities[48–50]. Optimization of the
PUREX process to improve the efficiency of this separation could help reduce the volume of
radioactivewasteproduced, aswellasleadtosimplificationsintheoverallprocessdesign[47].
This requires making advancements in the molecular-scale understanding of the extraction
of inorganic species by TBP.
Figure 5.1: The molecular structure of the extractant tributyl phosphate (TBP).
Currently, anopendebateexistsoverwhetherorganicphasescontainingneutralsolvating
extractants such as TBP are best described as molecular solutions or solutions of colloidal
aggregates. Traditionally, TBPorganicphasescontaininginorganicsoluteshavebeentreated
as molecular solutions composed of free extractant and discrete stoichiometric solvates in a
diluent[19, 35, 39, 61, 116, 117]. Only extractants with long nonpolar hydrocarbon tails (8-20
methylene groups) and an ionic or highly polar head were thought to aggregate in sufficient
69
|
Colorado School of Mines
|
numberstoformcolloidal,reversedmicellarspeciesinsolution[22]. However,morerecently,it
has been suggested that TBP might also form reversed micellar species containing extracted
water, acid, and metal[31, 118]. Like traditional surfactants with much longer hydrocarbon
tails, TBP is surface-active. It is therefore possible that TBP forms structures in solution
similar to those found in ternary water, oil, and surfactant microemulsions, which are known
to form micelles and vesicles that are large enought to be considered colloidal[119–122]. This
is the premise underlying the recent use of small angle scattering experiments to understand
the structures formed by TBP in solution[118].
Since2003,smallangleX-rayandneutronscattering(SAXSandSANS)experimentshave
been used to characterize TBP species in both traditional[24–30] and nontraditional[123]
solvent extraction samples containing water, and various acids and metals. For this work,
we will only be considering the structure of TBP species in traditional samples. In order to
interpret scattering data in prior work, these samples were assumed to consist of reversed
micelles modeled as monodisperse hard spheres interacting through surface adhesion. This
simplistic interparticle interaction model, developed by Baxter in 1968[111], was used to
determinethesizesofTBPaggregatesandthestrengthoftheattractiveinteractionsbetween
them by varying the values of the aggregate diameter and stickiness parameter,
τ−1,
until
a good fit to the data by the model was achieved. The stickiness parameter is directly
proportional to the strength of the attractive interactions between adhesive hard spheres,
such that higher values of
τ−1
correspond to stronger attractive interactions. The results
for TBP aggregate sizes and interactions in SAXS and SANS investigations are consistent
for different metals and inorganic acids, suggesting that TBP aggregates consist of two
to five TBP molecules interacting through a strong attractive surface potential with
τ−1
values between approximately 6 and 12. Assuming a thin square well potential with a well
width of 10% of the hard sphere diameter, this corresponds to well depths ranging from
approximately 1.6 to 2.3 k T, with deeper well depths corresponding to samples with higher
B
metal concentrations. The source of these attractive interactions has been attributed to van
70
|
Colorado School of Mines
|
der Waals forces between polarizable aggregate cores[25, 27].
The simplicity of the Baxter fluid model means that it is easy to use and does not require
numerical methods to solve for the structure factor. The Baxter potential corresponds to
the infinitely narrow and deep limit of the square well potential, where the finite attractive
surface interactions between particles are described by the temperature-dependent stickiness
parameter,
τ−1.
The radial distribution function and osmotic equation of state for the
Baxter fluid were first calculated analytically by Baxter in 1968 using the Percus-Yevick
approximation[111]. The structure factor is calculated from the Fourier transformation of
the total correlation function, defined in terms of the radial distribution function, and can be
directly determined from these relationships. Since then, analytical and simulation results
for the phase diagram, average cluster size, and percolation threshold for the Baxter fluid
havebeenreportedintheliterature[111,124–127]. Percolationreferstoaphenomenonwhere
transient, system-spanning clusters are formed. The percolation threshold is the minimum
value of
τ−1
at which the Baxter fluid is percolated for a given solute volume fraction.
This research group recently used diffusion nuclear magnetic resonance (NMR) spec-
troscopy to corroborate the results of prior small angle scattering experiments using organic
phase TBP samples containing nitric acid and either tetravalent zirconium or hexavalent
uranium[128]. The sizes of TBP aggregates determined from diffusion coefficient measure-
ments agreed well with prior values of two to four TBP molecules per aggregate determined
by small angle scattering. The nature of the interactions between TBP aggregates was eval-
uated by assuming that the TBP aggregates could be treated as particles moving through
a continuum fluid using classical hydrodynamic theory[107–109, 129]. This analysis leads to
the conclusion of an extended repulsive component to the interaction between aggregates,
which conflicts with the strong attractive interactions found using SAXS and SANS. Given
the comparable sizes of the nonpolar diluent and TBP aggregates, the assumption of contin-
uum hydrodynamics may be suspect. The Wilke-Chang equation[92], which does not apply
in the hydrodynamic regime, was used instead of the Stokes-Einstein equation[101] to relate
71
|
Colorado School of Mines
|
the diffusion coefficient to size because of the small sizes of aggregates determined previously
by SANS. The Stokes-Einstein equation is a poor description of this relationship for small
solutes.
The diffusion of infinitely dilute particles in solution can be understood in terms of
theoretical models describing two distinguishable extremes of diffusive behavior[130]. One
extreme applies to colloidal systems, and the other applies to molecular systems. Diffusion in
colloidalsystemsisdescribedbyhydrodynamictheory,inwhichmesoscopiccolloidalparticles
are treated as macroscopic spheres moving through a continuum fluid. The continuum
approximation is valid for solutions in which the particles comprising the surrounding fluid
are very small compared to the diffusing particle. In the hydrodynamic regime, the diffusion
of a particle at infinite dilution is inversely proportional to its radius. This relationship is
given by the Stokes-Einstein equation[101], shown in Equation 5.1, where k is Boltzmann’s
B
constant, T is the temperature of the sample, η is the viscosity of the solvent at T, and r is
the hydrodynamic radius of the diffusing particle. The Stokes-Einstein equation is accurate
to about 20% for dilute solutions in which the solute size is greater than or equal to five
times the size of the solvent[101].
k T
B
D = (5.1)
0
6πηr
Incontrast, usingEnskogtheory, thediffusionofahardspherethroughafluidcomprising
hardspheresofcomparablesizecanbeshowntobeinverselyproportionaltothesquareofthe
radius[130]. In real systems, the diffusion of a molecular (non-mesoscopic) species at infinite
dilution is better described by models approaching a square dependence, such as the Wilke-
Chang correlation, given in Equation 5.2 for spherical particles, where χ is an empirical
parameter related to the self-association of the solvent and M is the solvent molecular
B
weight[92]. The Wilke-Chang correlation is accurate to about 10% for dilute solutions of
small, nondissociating solutes[131].
√χM T
D = 3.1
10−8 B
(5.2)
0 × ηr1.8
72
|
Colorado School of Mines
|
As described in our previous work, an expression for the concentration dependence of the
diffusion of colloidal particles can be derived from hydrodynamic theory[128]. The diffusion
coefficient of particles in the hydrodynamic regime increases with increasing solute volume
fraction at low concentrations according to the linear relationship[99]:
D = D (1 αϕ) (5.3)
0
−
where α is a unitless interaction parameter combining contributions from the second virial
coefficient of the particles and their hydrodynamic interactions, and ϕ is the solute volume
fraction. For a system of hard spheres, multiple theoretical approaches have determined α
to be approximately two[107–109, 129]. For a system of aggregating colloidal particles, α
is greater than two[97]. In real colloidal systems whose speciation does not change with
concentration, α is determined empirically by measuring the diffusion coefficient of particles
at different dilutions. No similarly simple diffusion coefficient/concentration relationships
exist for molecular solutes.
In this paper, we will assess the treatment of TBP aggregates as colloidal particles in
single phase organic samples under PUREX-like conditions using both experimental and
computational methods. First, the results of diffusion NMR spectroscopy, rheology, and
SANS experiments will be interpreted by treating the aggregates as colloids, and compared
with the results of molecular dynamics (MD) simulations. Each of these experimental meth-
odshasbeenusedextensivelyinthecharacterizationofcolloidalsolutionsandcomplexfluids
due to the relative ease of developing theoretical treatments for spherical particles in a con-
tinuum solvent and, in the case of SANS, radiation scattering by the correlations in positions
of spherical particles. In contrast, the development of theory to describe diffusion, viscosity,
and small angle scattering for interacting aggregates at a molecular scale in solution is more
challenging because the interactions between each type of particle in the system must be
explicitly addressed. Such complex systems often cannot be dealt with analytically, making
computational methods such as MD simulation the most effective means of theoretically
treating the dynamic and equilibrium properties of molecular solutions.
73
|
Colorado School of Mines
|
5.3 Experimental Section
5.3.1 Materials
All materials and solutions used here have been described elsewhere[128]. SANS samples
were prepared with deuterated n-dodecane, obtained from C/D/N Isotopes (98 atom % D;
Pointe-Claire, Quebec, Canada), in place of the unlabeled compound.
5.3.2 Sample Preparation and Characterization
Organic phase TBP samples containing 30 v/v % TBP dissolved in n-dodecane were
prepared and characterized as described elsewhere[128]. Briefly, all single phase organic
TBP samples were prepared using a 30% TBP organic phase (pre-equilibrated with 3 M
HNO ) contacted with an aqueous phase of equal volume containing 3 M HNO and varying
3 3
amounts of UO (NO ) or Zr(NO ) . The exceptions were a sample of the 30% TBP solution
2 3 2 3 4
that had not been contacted with any aqueous phase (TBPO), and a sample of the 30% TBP
solution contacted with pure water (TBPW). The compositions of all samples characterized
in this work are given in Table 5.1 (page 76). Metal concentrations were determined using
radiotracers, while acid and water concentrations were determined by titration. All phase
◦
contacts took place at 21 1 C.
±
5.3.3 Diffusion Coefficient Measurements
The average diffusion coefficient of TBP in each sample was measured using the same
400 MHz NMR instrument, Bruker DIFF60 Z-diffusion probe, and pulsed-field gradient
stimulated echo experiment with longitudinal eddy current delay (STE-LED) described
elsewhere[128]. The diffusion of TBP was calculated by monitoring the attenuation of the
peakcorrespondingtotheprotonon thecarbonadjacenttothebutoxyoxygen, atachemical
shift of approximately 4.3 ppm[95]. The diffusion of HNO was calculated by monitoring the
3
attenuation of the peak corresponding to the acidic proton, at a chemical shift of approxi-
◦
mately 10.5 ppm. All experiments were performed at 27.0 0.1 C.
±
74
|
Colorado School of Mines
|
The infinite dilution diffusion coefficient for each sample was determined by measuring
the diffusion coefficients of diluted samples with solute volume fractions between 0.12 and
0.3, and linearly extrapolating to a solute volume fraction of zero. This is the same approach
used previously[128], except that the organic phase samples herein were diluted 4:1, 3:2, and
2:3 with n-dodecane, giving samples with approximate solute volume fractions of 0.3, 0.24,
0.18, and 0.12 in this work.
5.3.4 Viscosity Measurements
The viscosities of samples at different solute volume fractions were determined using a
dilution procedure similar to that used for determining the infinite dilution diffusion co-
efficient. Sample Zr30 was diluted 4:1, 3:2, 2:3, and 1:4 with n-dodecane, giving samples
with approximate solute volume fractions of 0.3, 0.24, 0.18, 0.12, and 0.06. Viscosity mea-
surements of these samples were made using a ThermoScientific HAAKE Viscotester iQ
rheometer with Peltier temperature controller and cylindrical double gap measuring geom-
etry. In all experiments, a shear rate of 4000
s−1
was used. Samples were allowed to reach
◦
thermal and mechanical equilibrium at the experimental temperature, 25.1 0.1 C, after
±
which the viscosity was measured with an integration time of 10 s.
5.3.5 SANS Measurements
All SANS measurements were performed at the general purpose SANS (GP-SANS) in-
strument at Oak Ridge National Laboratory’s High Flux Isotope Reactor (HFIR). Organic
phaseTBPsamplespreparedwithdeuteratedn-dodecanewereloadedintocylindricalquartz
cuvettes with a 2 mm path length (Hellma USA) for analysis. Two instrument configura-
tions were used to cover a total scattering vector (q) range of 0.004 - 0.93 ˚A−1. The two
configurations used sample-to-detector distances of 12.8 m and 1.2 m, both with a wave-
length of 4.75 ˚A and a detector offset of 0.4 m to maximize the sampled range of q at each
setting. After azimuthal averaging of the raw 2-D scattering pattern, the data were reduced
75
|
Colorado School of Mines
|
following standard procedures using routines developed at HFIR operating in Igor Pro by
Wavemetrics. This includes corrections for detector response, background scattering by the
empty sample cell, and calibration to direct beam with a calibrated attenuator for absolute
◦
scale[132]. All SANS experiments were run at 25.0 0.1 C.
±
5.3.6 SANS Data Analysis
The SANS scattering intensity of a monodisperse system of spherical particles can be
expressed as[82, 133]:
I(q) = ϕV ∆ρ2P(q)S(q) (5.4)
p
where ϕ is the solute volume fraction, V is the volume of a scattering particle, ∆ρ is the
p
difference between the scattering length densities of the solvent and particles, P(q) is the
particle form factor, and S(q) is the structure factor. The particle form factor is related
to the shape of the scattering particle, while the structure factor reflects the nature of the
interactions between particles. Consistent with prior small angle scattering experiments on
solvent extraction systems, all samples were assumed to contain uniform particles made of
TBP and polar solute molecules in a uniform solvent made of deuterated n-dodecane. The
primary contribution to the scattering contrast is the difference in scattering probability
between hydrogen in the TBP and deuterium in the n-dodecane solvent. The scattering
length density for each type of molecule, SLD , was calculated by summing the coherent
mol,j
neutron scattering lengths, b , for each constituent atom, i, divided by the molecular volume,
i
V (Equation 5.5). The scattering length density of the particles in each sample, SLD ,
mol part
wascalculatedbymultiplyingthescatteringlengthdensityforeachmoleculetype, SLD ,
mol,j
by its volume fraction in the particles, ϕ , where j corresponds to the molecule type (Equa-
j
tion 5.6)[134, 135]. The solvent scattering length density, that of deuterated n-dodecane,
was taken as a constant for all samples.
n
b
i
SLD mol,j = X (5.5)
V
mol
i=1
77
|
Colorado School of Mines
|
n
SLD
part
= Xϕ
j
SLD
mol,j
(5.6)
×
j=1
TheexperimentalSANSdatawerefitbyEquation5.4usingtheformfactorforaspherical
particle and the structure factor for the Baxter model[24, 32, 82, 136], and including a
constant term for incoherent scattering, I , which results primarily from the hydrogen in
inc
the sample. An optimized fit of the experimental data was produced by varying the particle
diameter, interaction strength, and incoherent scattering terms to minimize the sum of the
squared errors using the generalized reduced gradient algorithm for nonlinear optimization.
For modeling purposes, the sphere diameter in the form factor function and the hard sphere
diameter in the structure factor function were assumed to be equal (the HS diameter). The
uncertainties in the measured intensities for all samples at all values of q was less than 2%.
When the scattering data for samples N3, Zr30, and U40 were modeled using the SASfit
software package, the relative standard deviations of the particle diameters and
τ−1
were
less than 1%[137]. The uncertainty in the fitted parameters for the remaining samples is
assumed to be similar in magnitude. Errors resulting from the goodness-of-fit to the data
or appropriateness of the model for the system were not addressed, which is consistent with
prior work in the literature.[24–30]
5.3.7 Molecular Dynamics Simulations
The classical molecular dynamics potentials used to simulate TBP, n-dodecane, nitric
acid and water have been previously reported[138]. Simulation compositions of the post-
contact organic phase were chosen to correspond to extraction of 5 M HNO by 20% TBP
3
and 3 M HNO by 30% TBP. Those compositions are given in Table 5.2.
3
Initial configurations were generated with the Packmol software[139]. Molecular dy-
namics simulations were performed using the GROMACS 4.5.5 software package[140]. The
isobaric isothermal NPT ensemble with periodic boundary conditions and a leap-frog Ver-
let integrator were used for all simulations. Pressure was set to 1 bar with the Berendsen
78
|
Colorado School of Mines
|
Table 5.2: The experimental conditions (first two columns) and corresponding numbers of
molecules used in simulation with a 10.5 10.5 10.5 nm box.
× ×
% TBP [HNO ] # TBP # n-dodecane # HNO # H O
3 aq,i 3 2
(mol/L)
20 5 528 2368 477 94
30 3 789 2118 398 194
barostat and temperature to 300 K with the Berendsen thermostat during equilibration and
the Nose-Hoover thermostat during sampling. Particle-Mesh Ewald summation was used for
long-range electrostatic summation with a 15 ˚A cut-off for short range electrostatic and van
derWaalsinteractions. TheLINCS algorithm wasused forconstraininghydrogen-containing
bonds to enable use of a 2 fs time step. Each system was run 10 times and values presented
hereareaveragesoverthose10runs. Eachrunconsistedofa10nsequilibrationtimefollowed
by a 50 ns production run where coordinates were recorded for analysis every 20 ps.
The hydrogen bonding definitions and cluster analysis of the hydrogen bonded species
that we have previously reported for the TBP/water/nitric acid system were implemented.
In the cluster analysis, TBP and polar solute molecules are counted as connected if at least
one hydrogen bond exists between them. Clusters are defined as a group of connected
molecules. To facilitate comparison with scattering and diffusion data, we computed the
TBP aggregation number for each cluster, defined as the number of TBP in that cluster.
The TBP aggregation number distribution is then the probability of a TBP occuring in a
cluster with a given TBP aggregation number.
5.4 Results and Discussion
5.4.1 Diffusion Data - Colloidal Interpretation
The Stokes-Einstein equation and the Wilke-Chang correlation were used to determine
the average hydrodynamic radii of TBP species in samples with different water, nitric acid,
and metal concentrations. The infinite dilution diffusion coefficients (D ) for the samples,
0
derivedfromdilutionexperiments, wereusedtocalculatetheradiiandcorrespondingparticle
79
|
Colorado School of Mines
|
volumes, given in Table 5.3. The hydrodynamic radii calculated using the Stokes-Einstein
equation substantially underestimate the sizes of the diffusing TBP species, yielding particle
volumes less than that corresponding to a single TBP molecule (455 ˚A3) in most cases. In
contrast, particle volumes calculated using the Wilke-Chang correlation are consistent with
the sizes of 2:1 TBP to metal complexes established in distribution studies[19]. These results
show that the sizes of organic phase TBP species are best described as inversely related to
the square of the radius and are in the molecular, rather than hydrodynamic, regime.
Table 5.3: The volumes of TBP species are realistic when calculated using the Wilke-Chang
(W-C)correlationratherthantheStokes-Einstein(S-E)equation. UseoftheStokes-Einstein
equation results in particle volumes less than that of a single TBP molecule (455 ˚A3) for
most samples.
Sample ID D a W-C Radiusa W-C Volumeb S-E Radiusa S-E Volumec
0
(m2/s) (˚A) (˚A3) (˚A) (˚A3)
N3 4.68
10−10
6.30 1047 3.63 200
Zr05
4.65× 10−10
6.32 1058 3.65 204
Zr10
4.65× 10−10
6.32 1056 3.65 203
Zr20
4.72× 10−10
6.27 1031 3.60 195
Zr30
4.76× 10−10
6.23 1015 3.56 189
U10
4.23× 10−10
6.66 1237 4.01 270
U20
3.83× 10−10
7.03 1458 4.43 363
U30
3.50× 10−10
7.40 1700 4.85 479
U40
3.42× 10−10
7.49 1763 4.96 511
×
aAverage uncertainty 2%; bAverage uncertainty 3%; cAverage uncertainty 6%
In the investigated TBP samples, α, the unitless interaction parameter, was determined
by measuring the diffusion coefficients of TBP species in a series of samples diluted with
n-dodecane and assuming that there were no significant changes in speciation. A line was fit
to the resulting data, and values for D and α were calculated. The α values for all samples
0
fell between 0.89 and 1.28, which in our previous work we attributed to repulsive interactions
between species[128]. An alternative explanation for this observed trend is that the results
fromhydrodynamictheorydonotapplytothissystem, andabettertreatmentwouldinvolve
explicit consideration of molecular scale solvent-solute interactions. Given the failure of the
Stokes-Einstein equation when applied to our samples, this may be a better explanation for
80
|
Colorado School of Mines
|
the observed dependence of the diffusion coefficient on solute volume fraction.
5.4.2 Viscosity Data - Colloidal Interpretation
Inclassicalhydrodynamictheory, theviscosityofcolloidalsystemsincreaseswithincreas-
ing particle concentration. This behavior is observed in water-in-oil microemulsions, where
the viscosity dependence on solute volume fraction is well-described by the hard sphere
model[141]. An empirical relationship between concentration and viscosity for concentrated
solutions of hard spheres developed by Thomas is given in Equation 5.7, where η is the
rel
viscosity of the system divided by that of the pure solvent, and ϕ is the volume fraction
of the dispersed material[142]. The higher order terms in Equation 5.7 can be disregarded
in dilute solutions (<0.02 solute volume fraction), where a linear dependence is observed.
Equation 5.7 is valid for solute volume fractions of up to 0.6 in suspensions of spherical
particles made of various materials, such as glass and polystyrene[142]. It has also been
used successfully to describe the concentration dependence of the viscosity of an oil-in-water
microemulsion[143] and a water-in-oil nanoemulsion[144]. Structures formed in TBP solvent
extraction systems containing mineral acids and metals have often been described as water-
in-oil microemulsions or reversed micelles[25, 27, 30, 31, 118, 145]. It would be expected that
if such supramolecular species were being formed, the relationship in Equation 5.7 would be
fulfilled, as is found in traditional surfactant systems.
η = 1+2.5ϕ+10.05ϕ2 +0.00273e16.6ϕ (5.7)
rel
Data for the relative viscosities of a series of dilutions of sample Zr30 with n-dodecane
◦
at 25.1 0.1 C are plotted as points in Figure 5.2, with a line corresponding to Thomas’
±
empirical expression for the viscosity of a hard sphere suspension. Again, it was assumed
that TBP speciation is not substantially affected by dilution with n-dodecane. A measured
n-dodecane viscosity of 1.35 cP was used to calculate the relative viscosities. The experi-
mentally observed increase in viscosity with increasing solute volume fraction is much less
than the exponential relationship expected for a system of hard spheres. This increase is also
81
|
Colorado School of Mines
|
less than the exponential relationship observed in any of sixteen oil-in-water and water-in-oil
emulsion systems[146]. The deviation from colloidal behavior of TBP samples is consistent
with the trends observed in the diffusion data, as would be expected given the close interre-
lationship between diffusion and viscosity in a fluid. The combined results from both data
sets give further credence to the premise that the organic phase in the PUREX process and
other TBP solvent extraction systems should be treated as a molecular solution.
Figure 5.2: The dependence of the viscosity of a TBP organic phase containing zirconium
on solute volume fraction (triangles) is not consistent with Thomas’ empirical relationship
for concentrated systems of hard spheres (line).
5.4.3 SANS Data - Colloidal Interpretation
5.4.3.1 SANS Indirect Method
There are two major ways to approach the analysis and interpretation of solution phase
small angle scattering data: the direct and indirect methods[81, 86, 147]. In the direct
method, a model describing the structure of scatterers in a sample is posited based on inde-
pendent experimental or computational work and used to calculate a theoretical scattering
pattern, which is then compared with experimental data. In the case of SANS, the scatterers
are the atomic nuclei in the sample[134]. If the solution structure is known at an atomic
level, as in the case of a trajectory calculated from an all-atom MD simulation, a theoretical
82
|
Colorado School of Mines
|
scattering pattern can be directly calculated from the known correlations between nuclei,
and nuclear scattering cross sections[148]. If explicit correlations betweens scattering nuclei
are not known, the direct method requires using a simplified model for the solution struc-
ture, e.g., assuming the existence of large scattering particles, in which the coherent neutron
scattering cross sections of the atomic nuclei in a particle are evenly distributed across its
volume. A scattering pattern, resulting from the difference in scattering probability between
the particles and the surrounding medium, can then be calculated and fit to experimental
data by varying the particle model parameters. This latter approach has been used suc-
cessfully in colloidal systems[81, 86, 149], which can be modeled as particles dispersed in a
solvent, and is less demanding than the former approach, which requires the development of
rigorously validated forcefields.
In the indirect method, an attempt is made to reverse the Fourier transformation effected
by the scattering experiment to recover the solution structure with a minimum of a priori
assumptions. For a dilute solution of scattering particles, the indirect Fourier transformation
(IFT) method can be used to recover the pair distance distribution function (PDDF) of the
scatteringparticles, fromwhichthesizesandshapesofthescatteringparticlescanbeinferred
without the need to assume an intra-particle scattering (form factor) model[150, 151]. For
concentrated solutions of scattering particles, the generalized indirect Fourier transformation
(GIFT) method can be used to recover the PDDF of the scattering particles without the
need for an intra-particle scattering model, by first assuming a particle interaction (structure
factor) model[152, 153].
Ideally, the interpretation of small angle scattering data would rely on the use of both
direct and indirect methods. An example of such an analysis is provided by Pedersen, in
which the indirect method is used to choose an appropriate simplified scattering model
for use in the direct method[82]. Consistent with this approach, the GIFT method was
initially used to interpret our SANS data for sample U40. An accurate solution function
calculated using GIFT is characterized by minimal oscillations and a small mean deviation
83
|
Colorado School of Mines
|
between the calculated and the experimental scattering patterns[151, 154]. A minimally-
oscillating PDDF and low mean deviation indicate that the calculated PDDF both describes
the experimental data well, and captures important structural information. However, we
were unable to determine an accurate, stable solution for the indirect Fourier transformation
of our SANS data using a monodisperse hard sphere structure factor. The use of a structure
factor incorporating an attractive or repulsive interparticle potential would require making
substantial assumptions about the nature of the attractive interactions between particles
to limit the accessible parameter space, effectively eliminating the model-free aspects of the
GIFTmethod. Becauseoftheseconstraints, theGIFTmethodcouldnotbeusedtointerpret
the SANS data in this work.
5.4.3.2 SANS Direct Method
Because we were unable to use an indirect method to aid in the selection of a simpli-
fied particle scattering model, it was necessary to select a model based on the shape of the
scattering data. In colloidal systems, deconvolution of the contributions from the shapes of
the particles, their polydispersity, and their interactions to the scattering intensity cannot
be accomplished without additional independent information about the system[147]. Defini-
tive independent information on the polydispersity and shapes of TBP species in solution
does not exist, so the simplest model capable of describing the system—a model assuming
monodisperse spheres interacting through the Baxter potential—was used. This model, used
previously in small angle scattering investigations of TBP structure, requires only two pa-
rameters to describe the size of the scatterers and the nature of their interactions. These
correspond to the HS diameter and
τ−1,
the stickiness parameter, respectively.
A major benefit of the Baxter model is its ability to describe the very slight rise in
the scattering intensity with decreasing q in the mid to low q range for all samples, as
shown in Figure 5.3. This rise is the result of fluctuations in the density of scatterers.
The trend at low q suggests that the hydrogen-containing TBP molecules are associated in
solution, and precludes the use of a hard sphere model for particle interactions. The low q
84
|
Colorado School of Mines
|
data also undermine our previous finding of repulsive interactions between TBP species in
solution, determined from diffusion measurements using an assumption of colloidal behavior.
An example fit of this model to the SANS data for sample U40 is given in Figure 5.3. This
figure shows that the model fits the data well at low to mid q values, but includes oscillations
at high q that are not seen in the data.
Figure 5.3: A model assuming that TBP species are monodisperse spheres interacting
through the Baxter potential (Fitted I(q): yellow line, P(q): green line, S(q): blue line)
is able to describe experimental scattering for sample U40 (red diamonds) in the low to mid
q region well. Deviations at high q result primarily from the absence of a correlation peak
in the data. Experimental error bars are smaller than the markers.
The results of fitting the Baxter model to our SANS data are given in Table 5.4. A
comparison of the diameters of TBP species determined using SANS and diffusion NMR
spectroscopy for samples containing 20% and 30% TBP is provided in Figure 5.4. The av-
erage diameters of TBP species in all samples evaluated in this work range from 16.0 to
21.0 ˚A, while the values for τ−1 range from 4.20 to 7.59. As has been found in previous
scattering work, the fitted particle diameters appear to increase with increasing uranium
concentration[24]. The particle diameters remain constant with increasing zirconium con-
centration, which is not inconsistent with past observations of slowly decreasing particle
diameter with increasing zirconium concentration[27]. Unlike in prior work, the strength of
the attractive interactions between particles does not trend upward with increasing metal
85
|
Colorado School of Mines
|
concentration, although the values for
τ−1
are similar in magnitude to those calculated pre-
viously (5-10). The
τ−1
values calculated for each sample are so great that they exceed the
percolation threshold for the Baxter fluid. The percolation threshold for each sample, given
in Table 5.4, is the minimum value of
τ−1
at which the Baxter fluid is percolated for a given
solute volume fraction[125].
Table 5.4: Parameters used to fit the Baxter model to experimental SANS data, and the
results of those fits.
Sample Solute Fraction ∆ρ2 HS Diametera τ−1,a I a Perc. Threshold
inc
cm−4 ˚A cm−1 τ−1
TBPO 0.302 4.29 1021 16.0 4.20 0.407 2.75
×
TBPW 0.308 4.31 1021 18.5 4.91 0.407 2.63
×
N3 0.339 3.95 1021 20.4 7.08 0.388 2.09
×
Zr05 0.334 3.99 1021 20.1 7.57 0.371 2.17
×
Zr10 0.336 3.97 1021 21.0 7.41 0.401 2.14
×
Zr20 0.335 3.97 1021 20.6 7.59 0.389 2.15
×
Zr30 0.337 3.95 1021 20.5 7.29 0.419 2.13
×
U10 0.336 3.88 1021 18.8 7.04 0.326 2.14
×
U20 0.337 3.78 1021 20.3 6.56 0.382 2.13
×
U30 0.338 3.68 1021 20.6 6.51 0.367 2.10
×
U40 0.339 3.61 1021 20.8 6.51 0.368 2.10
×
aEstimated uncertainty 1%
5.4.3.3 Problems with Using the Baxter Model
When used to interpret scattering data for single phase organic TBP samples, the Baxter
model yields problematic results. The
τ−1
values calculated for all samples are so large
that they exceed the threshold value beyond which the Baxter fluid has been found, both
analytically and in Monte Carlo simulations, to percolate[125, 127]. According to the Noro-
Frenkel law of corresponding states[155], this threshold holds for all systems of particles
withequivalentreducedsecondvirialcoefficientsinteractingthroughasphericallysymmetric
short-ranged attraction, regardless of its form. Similar
τ−1
values in the percolation region
of the Baxter fluid have been calculated for TBP samples in prior scattering work. These
τ−1
values were converted to the depth of an equivalent thin square well potential, which
appeared to suggest a weaker attractive interaction. However, this transformation does not
86
|
Colorado School of Mines
|
Figure 5.4: The SANS diameters for 30% TBP samples (yellow squares), found in this work,
areapproximately1.5timesgreaterthanthosedeterminedfor30%TBPsamplesbydiffusion
(blue circles), also determined here, 20% TBP samples by diffusion (red triangles)[128], and
20% TBP samples by SANS (green diamonds)[24, 27].
alter the percolated structures implied by these attractive interactions. The existence of
percolated structures is contradicted by diffusion measurements.
The fast diffusion of TBP observed in all samples demonstrates that percolated struc-
tures are not formed, independent of assumptions about whether the diffusing species are
colloidal. Diffusion coefficients of TBP species in undiluted metal and acid-containing sam-
ples (Figure Figure 5.8) are the same order of magnitude as that of a 30% TBP solution that
has not been contacted with an aqueous phase (4.3 10−10 m2/s), demonstrating that TBP
×
forms small, discrete structures in solution. Thus, the attractive interactions between TBP
species quantified using the Baxter model to interpret SANS data are likely much stronger
than the true values for the system. The Baxter model appears to be a poor description
of the weak van der Waals attractions between neutral TBP species, to which attractive
interactions between TBP species have been previously attributed.
Additionally, the SANS diameters of TBP species in 30% TBP samples are consistently
about 1.5 times larger at a given metal concentration than those determined using SANS for
20% TBP samples, and diffusion NMR spectroscopy diameters for both 20% and 30% TBP
87
|
Colorado School of Mines
|
samples. This trend is illustrated in Figure 5.4. A similar dependence of TBP aggregate
diameter on TBP concentration in SANS experiments using the Baxter model has been
observed previously in the literature[25]. Assuming spherical particles, the observed increase
in particle diameter between 20% TBP and 30% TBP samples corresponds to a more than
threefold increase in volume and, by extension, aggregation number. Such a large increase
in size would result in significant differences in the measured TBP diffusion coefficients at
different TBP concentrations, which is not observed. Specifically, the decrease in the TBP
diffusion coefficient between polar solute-containing 20% and 30% TBP samples would be
large compared to the decrease observed between uncontacted 20% and 30% TBP samples,
in which TBP is known to form only small associated species[156–158]. These observations
are also independent of assumptions about whether the diffusing species are colloidal.
Solutions of TBP in n-dodecane without any other solutes are known to contain TBP
monomers and some associated species, mostly dimers and trimers. The distribution of
TBP among these species does not change significantly between samples at 20% and 30%
TBP. Consequently, thechangeinTBPdiffusioncoefficientwithTBPconcentrationissmall,
decreasing from 4.8 10−10 m2/s to 4.3 10−10 m2/s between 20% TBP and 30% TBP solu-
× ×
tions. The diffusion coefficient of TBP in an organic phase containing 0.006 M Zr decreases
by nearly the same relative amount, from 3.8 10−10 m2/s to 3.2 10−10 m2/s, between 20%
× ×
TBP and 30% TBP solutions. Similarly small decreases are observed in zirconium sam-
ples at different concentrations, and in the uranium samples, demonstrating that substantial
changes in the average size of TBP species in 20% and 30% TBP samples do not occur. This
suggests that the changes in particle size with TBP concentration determined by fitting the
Baxter model to small angle scattering data are more likely an artifact of the model used
rather than a reflection of real changes in TBP aggregate size. These model-independent
diffusion results demonstrate that the Baxter model used to interpret SANS data in these
TBP samples yields unphysical values for aggregate size and interaction strength.
88
|
Colorado School of Mines
|
5.4.4 Structures from Molecular Dynamics Simulations
Similar conclusions can be made from MD simulations of systems containing TBP, n-
dodecane, water, and nitric acid. Figure 5.5 shows snapshots of the simulation boxes for the
20% (left) and 30% (right) TBP systems. Rather than a percolated network of spherical
particles, as implied by the choice of the Baxter potential, simulation shows formation of
small, discrete species. Figure 5.6 shows the two predominant species in solution, the 1:1
TBP:HNO adduct and a 2:1 TBP:H O “bridged” species. In the 20% TBP system, several
3 2
smallpocketsofwatersolvatedbyTBPcanbeobserved. However, thesearenotnumerousor
largeenough tosignificantlyaffecttheaverageTBPaggregation number, which isdominated
by the 1:1 TBP:HNO adduct. The absence of water pockets in the 30% system is likely
3
a reflection of the lower nitric acid concentration rather than the increased TBP volume
fraction. In the 30% system, owing to the lower initial aqueous nitric acid concentration,
the reduced ratio of acid to TBP means that there are fewer TBP-HNO hydrogen bonds
3
per TBP molecule. Therefore, more TBP are free to hydrogen bond to water, disrupting the
formation of water pockets.
Hydrogen bonded clusters were measured from simulation to quantify the distribution of
TBP among species in solution. The TBP aggregation number distributions for 30% TBP
samples and 20% TBP systems are compared to evaluate the Baxter model scattering results
indicating significant increases of up to three times the TBP aggregation number with a 50%
increase in the TBP concentration. Figure 5.7 shows TBP aggregation number distributions
for both systems. We computed the number weighted average TBP aggregation numbers,
which were found to be nearly the same for both systems at 1.84 for 20% TBP and 1.87 for
30% TBP. This is consistent with our previously reported average TBP aggregation number
of 1.7 for 20% TBP and 5 M HNO found using diffusion NMR spectroscopy[128].
3
For both TBP volume fractions, nearly all of the TBP occur in a one-TBP cluster, most
often the 1:1 TBP:HNO adduct. The 1:1 TBP:HNO species was observed 0.751 times per
3 3
TBP in the 20% TBP 5 M HNO simulation and 0.411 times per TBP in the 30% TBP
3
89
|
Colorado School of Mines
|
3 M HNO simulation. The other most probable clusters were the TBP monomer, mea-
3
sured 0.065 times per TBP in the 20% system and 0.225 times per TBP in the 30% system,
and the 2:1 TBP:H O “bridged” species, at 0.003 per TBP for 20% and 0.051 per TBP
2
for 30%. The probabilities of TBP molecules existing in larger TBP aggregation number
clusters decline rapidly with TBP aggregation number for both TBP volume fractions. Dif-
ferences in TBP aggregation number that would indicate substantially different scattering
particle volumes are not observed between the TBP volume fractions. The TBP aggregation
number distribution in a nitric acid system shows that the organic phase appears to be a
molecular solution made up of small, discrete species that occasionally associate to form
short-lived larger aggregates of variable size. The Baxter fluid model does not describe the
solution-phase structures observed in these simulations. The absence of a dependence of
TBP aggregation number on solute volume fraction in nitric acid only simulations suggests
that the dependence derived from using the Baxter model to interpret SANS data results
from inadequacies in the model. The same SANS solute volume fraction dependence found
inmetal-containingsystemsislikelytoresultfromthesameinadequaciesinthemodelrather
than an unanticipated difference in physical behavior.
Figure 5.7: The probability of TBP occuring in a cluster with a given TBP aggregation
number is plotted against the TBP aggregation number.
91
|
Colorado School of Mines
|
5.4.5 Diffusion Data - Molecular Interpretation
This section reinterprets the same set of TBP diffusion coefficients, considered earlier
from a colloidal standpoint, from a molecular point of view. In the molecular regime, the-
oretical relationships between the concentration of a solute and its diffusion coefficient are
not well-developed. Therefore, the observed relationship between diffusion coefficient and
volume fraction cannot be easily interpreted as a reflection of the nature of solute-solute
interactions, as in the hydrodynamic regime. Instead, the relationship between diffusion co-
efficient and volume fraction is impacted by solute-solute, solute-solvent, and solvent-solvent
interactions[101]. At best, it can be stated that the previously described dependence of
the diffusion coefficient on solute volume fraction is consistent with systems of associating
solutes[159, 160].
Given the assumptions required to convert TBP diffusion coefficients to an aggregation
number (no change in speciation on dilution, spherically shaped particles whose volumes are
filled completely by the partial molar volumes of TBP and extracted solutes), it is useful to
consider only the measured diffusion coefficients in undiluted samples to come to qualitative
conclusions about the nature of TBP species in solution. The diffusion coefficient can be
considered to be inversely proportional to aggregate size, assuming that changes in the
interactions between species in solution have less of an impact on the diffusion coefficient
than species size at a constant TBP concentration. This assumption is reasonable because
interactions between neutral species in a nonpolar solvent are likely the result of weak van
der Waals forces, and would not be expected to change significantly with solute composition
at a given TBP concentration. This also allows us to consider the significance of nitric acid
diffusion in these samples, which was measurable only in undiluted samples due to the low
nitric acid concentrations. While average TBP diffusion coefficients include contributions
from all possible TBP species, the average nitric acid diffusion coefficient only includes
contributions from nitric acid/TBP species. These data are presented in Figure 5.8. For
reference, the diffusion coefficient of TBP in an uncontacted 30% TBP sample is 4.3
10−10
×
92
|
Colorado School of Mines
|
m2/s.
Figure 5.8: For 30% TBP samples, the change in the diffusion of nitric acid (red circles)
with metal concentration is negligible, suggesting consistently sized aggregates. The change
in TBP diffusion with metal concentration for samples containing zirconium (blue triangles)
and uranium (green squares) is only appreciable in the uranium samples. Error bars are
smaller than the markers.
The low metal concentrations in the zirconium samples make it difficult to interpret the
diffusion data. The contribution of zirconium-containing TBP species to the average TBP
diffusion coefficient is small compared to the contribution from water or acid species. Very
generally, these data suggest that nitric acid-containing TBP species are marginally smaller
than TBP species on average and that the sizes of nitric acid-containing species are constant.
No strong conclusions can be made regarding the nature of the zirconium-containing species
in solution because of the low zirconium concentration. However, the formation of a single
nitric acid species with TBP agrees with the results of MD simulations presented previously.
In contrast, uranium concentrations are high enough that differences between nitric acid-
containing species and uranium-containing species can be clearly observed. Again, the con-
sistent nitric acid diffusion coefficients suggest that nitric acid-containing species are small
and identically sized at all uranium concentrations. The average TBP diffusion coefficient
decreases substantially with increasing uranium concentration, suggesting that uranium-
containing species are larger than, and separate from, nitric acid-containing species. These
93
|
Colorado School of Mines
|
observations are consistent with a molecular, stoichiometric understanding of TBP extrac-
tion, in which 1:1 TBP:HNO and 2:1 TBP:UO (NO ) adducts are considered to be domi-
3 2 3 2
nant in solution.
5.5 Conclusions
In this work, it was demonstrated that TBP aggregates in solution do not behave as
colloids, and that PUREX and some similar solvent extraction organic phases containing
TBP should be treated as molecular solutions. When interpreted assuming that TBP forms
colloidal species, diffusion, viscosity, and SANS data for 30% TBP samples containing nitric
acid and uranium or zirconium yield contradictory or physically unrealistic results. The
assumption that TBP forms reversed micelles interacting through surface adhesion is shown
tobeinconsistentwithdiffusionmeasurementsandtheresultsofMDsimulations. Snapshots
from these simulations illustrate what the small, molecular species formed by TBP in the
presenceofnitricacidandwaterlooklike. TBPaggregatesizedistributionsderivedfromMD
simulationsshowthatthedominanthydrogenbondedspeciesformedbywaterandnitricacid
extractedbyTBPareindependentofTBPconcentration. Thesedataalsoshowlesscommon,
larger transient clusters. Finally, the results of interpreting diffusion measurements assuming
that TBP forms simple, molecular solutions are presented. These conclusions suggest that
considering acids and metals extracted by TBP as molecular species is key to understanding
the fundamental mechanisms underlying solvent extraction in certain types of TBP solvent
extraction systems.
5.6 Acknowledgements
This material is based upon work supported by the U.S. Department of Homeland Se-
curity under Grant Award Number, 2012-DN-130-NF0001. The views and conclusions con-
tained in this document are those of the authors and should not be interpreted as represent-
ing the official policies, either expressed or implied, of the U.S. Department of Homeland
Security.
94
|
Colorado School of Mines
|
CHAPTER 6
SUMMARY AND CONCLUSIONS
In this work, solvent extraction systems containing macroscopic concentrations of met-
als were investigated to understand the molecular-scale forces driving extraction in applied
separations. Recently, it has been suggested that extraction by neutral solvating extractants
in concentrated inorganic systems is governed by extractant aggregation rather than specific
chemical interactions[31, 118]. To test this hypothesis, the extraction chemistries of solvat-
ing extractants from two different separations processes with applications in industrial-scale
metal separations were considered.
The behavior of the PUREX process extractant, TBP, was explored under various condi-
tions at high metal concentrations, including conditions similar to those found in industrial
implementations of the PUREX process. The behavior of the extractant, TODGA, which
has been considered for use in the ALSEP process, was explored in simple systems con-
taining bulk amounts of lanthanides. Distribution studies characterizing the bulk extraction
behavior of metals in these two solvent extraction systems were related to molecular-scale
processes by comparison with the extraction behavior expected to result from a traditional
solvation mechanism. Aggregation in the TBP system was characterized using diffusion
NMR spectroscopy of 20% and 30% TBP samples. The latter samples were prepared under
PUREX-like conditions. The results of diffusion, rheology, and small angle scattering exper-
iments on TBP samples were compared with MD simulations to produce a comprehensive
picture of TBP extracted species in solution. The following is a summary of this work in the
context of the objectives and hypotheses presented in the introductory chapter.
96
|
Colorado School of Mines
|
Objective 1: CollectdistributiondatainTBPandTODGAsolventextractionsystems
under concentrated conditions that have not been previously characterized in the
literature.
Hypothesis 1.1: The extraction of trace metals by TBP and lanthanides by TODGA
adhere to a traditional solvation mechanism.
Hypothesis 1.2: TheselectivityofTODGAforthelightlanthanidesresultsfromouter
coordination sphere effects.
Distribution data for the extraction of 11 trace metals by TBP in the presence of bulk
uranium under PUREX extraction and stripping conditions were collected and published.
Most metals followed the extraction behavior that would be expected based on a traditional
understanding of extraction by solvation and the known affinity of TBP for uranium. The
distribution ratios of these metals decreased with increasing uranium concentration under
both extraction and stripping conditions. However, the distribution ratios of some low-
valence transition metals were observed to increase with increasing uranium concentration,
behavior that suggests an alternative extraction mechanism for these metals. One possible
explanation for increased extraction of certain trace metals with increasing uranium concen-
tration is co-extraction occurring through the formation of TBP colloidal aggreagates.
Distribution data for the extraction of bulk amounts of lanthanides by TODGA were
collected at varying initial metal concentrations for light, middle, and heavy lanthanides. No
anomalous extraction behavior was observed in the TODGA/lanthanide extraction system.
Distribution ratios decreased exponentially with metal concentration, as is often observed in
extraction systems as the extractant approaches saturation[34]. Distribution ratios increased
across the lanthanide series as would be expected based on TODGA distribution studies of
lanthanides at low concentrations. The amount of water co-extracted with each element was
foundtofollowapatternsimilartothatfoundfortheextractionofthelanthanidesacrossthe
97
|
Colorado School of Mines
|
series. Because it has been extablished that water is not extracted in the inner coordination
sphere of these metals, the similarity between these extraction patterns suggests that outer
sphere effects may be responsible for the lanthanide selectivity of TODGA. One mechanism
for this could be through the competing effects of increased extraction with the increase in
charge density across the lanthanide series, and decreased solubility of TODGA extracted
complexes with more co-extracted water.
Objective 2: Compare the results of diffusion NMR spectroscopy and SANS studies
of organic phase TBP samples interpreted from a colloidal perspective.
Hypothesis 2.1: Like small angle scattering techniques, diffusion NMR spectroscopy
can be used to characterize the nitric acid, uranium (VI) nitrate, and zirconium
(IV) nitrate species extracted by TBP.
Diffusion NMR spectroscopy was used to measure the average diffusion coefficients of
TBP species in samples similar to ones that had been characterized previously in the lit-
erature by small angle scattering. Dilution experiments were used to find the TBP infinite
dilution diffusion coefficient for each sample, which was then related to the average volume
of TBP species using the Wilke-Chang equation. The Wilke-Change volume was then con-
verted to the diameter of an equivalent sphere for comparison to SANS results. The slope of
the line relating the average TBP diffusion coefficient and TBP concentration in dilution ex-
periments was assigned physical significance through comparison with colloidal systems. In
colloidal systems, this slope is a reflection of the nature of the interactions between colloidal
particles diffusing in a molecular solvent.
The average diameters of TBP aggregates from diffusion measurements were similar
to those found previously using SANS, with TBP aggregation numbers for all samples of
approximatelytwotofourTBPmolecules. However, theslopeofthelinerelatingtheaverage
TBP diffusion coefficient and TBP concentration in dilution experiments suggested that the
interactions between TBP species were repulsive, rather than attractive as suggested in prior
98
|
Colorado School of Mines
|
small angle scattering experiments with TBP samples.
Objective 3: Assess the use of colloidal models to describe organic phase TBP samples
by comparing the results of diffusion NMR spectroscopy, rheology, and SANS
studies of samples under concentrated (PUREX-like) conditions.
Hypothesis 3.1: Nitric acid, uranium (VI) nitrate, and zirconium (IV) nitrate are
extracted by TBP as colloidal species under PUREX-like conditions.
Identical TBP samples prepared under conditions similar to those found in the PUREX
process were characterized by diffusion NMR spectroscopy, rheology, and SANS. When the
results of these experiments were interpreted assuming that TBP forms colloidal aggregates,
contradictory conclusions were reached about the sizes and interactions between aggregates.
Diffusion measurements suggest that the average size of TBP species is not strongly im-
pacted by TBP concentration, while SANS experiments suggest that TBP species are three
times larger, by volume, in 30% TBP samples compared with 20% TBP samples. Diffusion
measurements suggest repulsive interactions bewteen aggregates, while SANS experiments
suggest attractive interactions. These contradictions are eliminated if assumptions about
the colloidal nature of TBP species are discarded and these TBP samples are treated as
molecular solutions. Such an approach is consistent with the results of MD simulations of
TBP/nitric acid systems.
6.1 Future Directions
In this work, molecular-scale details about TBP and TODGA-extracted metal species
have been eludicated, laying the groundwork for further experimental and theoretical in-
vestigations of these systems. The potential importance of outer sphere coordination to
extractant selectivity was established through TODGA distribution studies. A series of
experiments with inorganic TBP samples suggested that the treatment of TBP species as
colloidal aggregates under PUREX-like and similar conditions may be unfounded. Future
99
|
Colorado School of Mines
|
work would focus on continuing experiments to further understand molecular-scale charac-
teristics of TBP and TODGA extracted species, while extending some experimental methods
used here to investigate other solvent extraction systems.
The experimental characterization of TBP and TODGA species in solution presented in
this thesis is complicated by the complexity of the samples under investigation. Organic
phase solvent extraction samples prepared by contacting an aqeuous phase containing acid
or metal, and an organic phase containing at least one extractant and diluent are, by their
nature, at least quaternary systems. In samples prepared by solvent extraction, the contri-
bution of any single component to an experimental measurement is difficult to isolate due to
its impact on the extraction of other components. As a result, systematic investigations of
organic phase samples with, for example, a constant organic phase water concentration and
changing acid or metal concentration, are uncommon in the recent literature.
The species formed by extractants in the presence of different solutes could be more
clearly distinguished if organic phase samples were prepared by direct dissolution of the
desired solutes. Incremental changes could then be made in the compositions of such simple
binary or ternary samples to isolate the impact of each component. For example, diffusion
and small angle scattering measurements of a TBP organic phase in which anhydrous uranyl
nitrate is dissolved would not be impacted by the contributions of water and nitric acid
species. Similarly, determining the solubility limits of anhydrous lanthanide nitrates in a
TODGA organic phase would contribute to an understanding of the impact of water on the
solubility of TODGA-solvated lanthanides. Understanding the extraction of water, acids,
and metals in applied separations could be greatly bolstered by such fundamental studies of
simple organic phase samples.
In addition, other experimental and computational characterization methods could be
used to explore microscopic structures in solvent extraction systems. Sophisticated NMR
techniques such as 3-D diffusion-ordered spectroscopy (DOSY) could be used to differentiate
between species in the diffusion domain, eliminating many problems associated with sepa-
100
|
Colorado School of Mines
|
rating the diffusion coefficients of species with identical resonances in the traditional 2-D
DOSY experiment. Monte Carlo simulations could be used to understand simple behavior
in these systems, such as the rate of extractant exchange or the role that the number and
directionality of binding sites plays in the structures formed in solution.
Finally, the same methods presented in this thesis could be used to characterize other sol-
vent extraction systems. The use of theoretical relationships developed for colloidal systems
to interpret small angle scattering and other experimental data is not limited to TBP. Such
relationships have also been used in other extractant systems, with similarly limited justi-
fication. Diffusion NMR spectroscopy could corroborate the use of colloidal approaches in
these systems where appropriate, giving further validity to the physical parameters dervied
from such analyses. A series of diffusion experiments like those presented in this thesis
could be performed, in which extractant diffusion coefficients in dilutions of a solvent ex-
traction sample are measured and interpreted from a colloidal approach. These results could
then be compared with the results of small angle scattering experiments to ensure that the
assumption of colloidal behavior applies to a given solvent extraction system.
101
|
Colorado School of Mines
|
APPENDIX A
SELECTED METHODS
An overview of selected methods used in the course of this thesis is presented here.
A.1 Diffusion NMR Spectroscopy
Diffusion NMR spectroscopy is used to measure the self-diffusion (also called tracer dif-
fusion) of molecules in a liquid sample. In a basic pulsed-field gradient (PFG) diffusion
experiment, a liquid sample is placed in a gradient coil capable of generating a linear mag-
netic field gradient along the z axis of the sample, as shown in Figure A.1. A series of RF
−
and magnetic field gradient pulses is applied to the sample as shown, for example, in Fig-
ure 4.3. The strength of the applied magnetic field gradient is varied for a certain number of
steps (often 16 or 32), and at each gradient strength an NMR spectrum is acquired. The de-
cay in the NMR signal intensity of a component with increasing gradient strength is related
to the self-diffusion coefficient of that component by the Stejskal-Tanner equation[88]:
S(G) =
S(0)e−γ2δ2G2D(∆− 3δ)
(A.1)
where S is the intensity of the NMR signal at a given magnetic field gradient strength (G),
γ is the gyromagnetic ratio of the nucleus being observed, δ is the gradient pulse length,
∆ is the diffusion time, and D is the diffusion coefficient. Usually, the maximum gradient
strength is chosen to correspond to at least 95% decay of the NMR signal intensity.
The basis for the PFG diffusion experiment was first suggested by the discovery of the
spin-echo and stimulated-echo signals by Hahn in 1950[161]. Hahn discovered that the appli-
◦
cation of two 90 RF pulses to a sample in sequence resulted in a spontaneous NMR signal,
which peaked after an amount of time, τ, equal to the separation of the centers of the two
pulses (Figure A.2). This spontaneous NMR signal is referred to as the spin-echo, and re-
sults from rephasing of the tranverse magnetization by the second RF pulse. The spin-echo
116
|
Colorado School of Mines
|
Figure A.3: The stimulated-echo pulse sequence and timing of the stimulated-echo signal.
A second concept important to the PFG diffusion experiment is the relationship between
the magnetic field experienced by a nucleus and its Larmor frequency. This relationship is
given in Equation A.2, where ω is the angular (Larmor) frequency of the precession of the
magnetic moment of a nucleus with a gyromagnetic ratio of γ in the presence of a magnetic
field of strength B.
ω = γB (A.2)
When a magnetic field gradient is applied along the z axis of a sample, the Larmor fre-
−
quencies of nuclei in equivalent chemical environments are defined by their location along
the z axis of the sample.
−
The PFG diffusion experiment combines two magnetic field gradient pulses with a spin-
or stimulated-echo pulse sequence, as in the stimulated-echo pulse sequence of Figure 4.3.
The first gradient pulse effectively “marks” the location of nuclei along the z axis of the
−
sample and dephases the transverse magnetization. The second gradient pulse rephases the
transverse magnetization. Rephasing is complete only if the nuclei do not move along the
z axis in the time between the gradient pulses. In the absence of movement, the echo signal
−
amplitude is maximized. The echo signal amplitude is also maximized in the absence of a
magnetic field gradient. At a constant magnetic field gradient pulse strength, the echo signal
decreases with increasing displacement of the nuclei in the sample along the z axis, which
−
is related to their average rate of diffusion. Similarly, for nuclei moving at a constant rate,
118
|
Colorado School of Mines
|
the NMR signal intensity decreases with increasing gradient strength as shown in Figure 4.5.
These relationships are contained in the Stejskal-Tanner equation.
A.2 Small Angle X-ray and Neutron Scattering
Small angle x-ray and neutron scattering (SAXS and SANS) are used to probe nanoscale
(approximately 1 to 100 nm) structures in liquid and solid samples. X-rays are scattered by
electrons, while neutrons are scattered by atomic nuclei. The pattern of scattered radiation
in a SAXS or SANS experiment results from the distribution of scatterers in a sample.
The mathematical principles used to understand both x-ray and neutron experiments are
identical, although only liquid state SANS data are presented in this thesis. This appendix
describes the scattering of both types of radiation at small angles in liquid state samples.
In a basic small angle scattering (SAS) experiment, a beam of monoenergetic radiation
is passed through a thin liquid sample of known path length. Radiation deflected by the
sample is detected by a 2-D detector placed on the other side of the sample from the radia-
tion source, as shown in Figure A.4. The SAS experiment is run until the photon or neutron
counting statistics-derived error estimates for all pixels in the detector are small. The re-
sultant 2-D scattering pattern is then reduced by making various detector and background
corrections, and converting the counts to an absolute scattering intensity (also known as the
differential scattering cross-section) through calibration to a known source. This reduced 2-
D scattering pattern can then be azimuthally averaged to produce a 1-D scattering pattern,
where the y axis is the absolute scattering intensity and the x axis is the magnitude of the
− −
scattering vector, q. The scattering vector magnitude is related to the scattering angle by
Equation A.3, where θ is twice the scattering angle and λ is the wavelength of the radiation.
The relationship between q and the approximate length scale, d, being probed in a sample is
given by Equation A.4. The final 1-D scattering pattern can be interpreted using the direct
or indirect methods, which are described in section 5.4.3.
4πsinθ
q = (A.3)
λ
119
|
Colorado School of Mines
|
APPENDIX C
COPYRIGHT PERMISSIONS
Copyrightpermissionsfromthepublisherandco-authorsofarticlesincludedinthisthesis
as Chapter 2, Chapter 4, and Chapter 5 are reproduced here.
Title: Tributyl Phosphate Aggregation
in the Presence of Metals: An
If you're a copyright.com
Assessment Using Diffusion NMR user, you can login to
Spectroscopy RightsLink using your
copyright.com credentials.
Author: Anna G. Baldwin, Yuan Yang,
Already a RightsLink user or
Nicholas J. Bridges, et al want to learn more?
Publication:The Journal of Physical
Chemistry B
Publisher: American Chemical Society
Date: Dec 1, 2016
Copyright © 2016, American Chemical Society
PERMISSION/LICENSE IS GRANTED FOR YOUR ORDER AT NO CHARGE
This type of permission/license, instead of the standard Terms & Conditions, is sent to you because
no fee is being charged for your order. Please note the following:
Permission is granted for your request in both print and electronic formats, and translations.
If figures and/or tables were requested, they may be adapted or used in part.
Please print this page for your records and send a copy of it to your publisher/graduate
school.
Appropriate credit for the requested material should be given as follows: "Reprinted
(adapted) with permission from (COMPLETE REFERENCE CITATION). Copyright
(YEAR) American Chemical Society." Insert appropriate information in place of the
capitalized words.
One-time permission is granted only for the use specified in your request. No additional
uses are granted (such as derivative works or other editions). For any other uses, please
submit a new request.
Copyright © 2017 Copyright Clearance Center, Inc. All Rights Reserved. Privacy statement. Terms and Conditions.
Comments? We would like to hear from you. E-mail us at [email protected]
124
|
Colorado School of Mines
|
Title: Distribution of Fission Products
into Tributyl Phosphate under
If you're a copyright.com
Applied Nuclear Fuel Recycling user, you can login to
Conditions RightsLink using your
copyright.com credentials.
Author: Anna G. Baldwin, Nicholas J.
Already a RightsLink user or
Bridges, Jenifer C. Braley want to learn more?
Publication:Industrial & Engineering
Chemistry Research
Publisher: American Chemical Society
Date: Dec 1, 2016
Copyright © 2016, American Chemical Society
PERMISSION/LICENSE IS GRANTED FOR YOUR ORDER AT NO CHARGE
This type of permission/license, instead of the standard Terms & Conditions, is sent to you because
no fee is being charged for your order. Please note the following:
Permission is granted for your request in both print and electronic formats, and translations.
If figures and/or tables were requested, they may be adapted or used in part.
Please print this page for your records and send a copy of it to your publisher/graduate
school.
Appropriate credit for the requested material should be given as follows: "Reprinted
(adapted) with permission from (COMPLETE REFERENCE CITATION). Copyright
(YEAR) American Chemical Society." Insert appropriate information in place of the
capitalized words.
One-time permission is granted only for the use specified in your request. No additional
uses are granted (such as derivative works or other editions). For any other uses, please
submit a new request.
Copyright © 2017 Copyright Clearance Center, Inc. All Rights Reserved. Privacy statement. Terms and Conditions.
Comments? We would like to hear from you. E-mail us at [email protected]
125
|
Colorado School of Mines
|
Anna Baldwin <[email protected]>
Copyright Permissions for Thesis
4 messages
Anna G. Baldwin <[email protected]> Tue, Jul 11, 2017 at 9:47 AM
To: Yuan Yang <[email protected]>
Hello Yuan,
I hope your summer is going well!
In order for me to use previously published or submitted articles as chapters in my thesis, I am
required to obtain written permission from all co-authors. This may be in the form of an email.
I would greatly appreciate if you would respond to this email granting me permission to use the
following articles as chapters in my thesis:
Tributyl Phosphate Aggregation in the Presence of Metals: An Assessment Using
Diffusion NMR Spectroscopy
Anna G. Baldwin, Yuan Yang, Nicholas J. Bridges, and Jenifer C. Braley
The Journal of Physical Chemistry B 2016 120 (47), 12184-12192
DOI: 10.1021/acs.jpcb.6b09154
The Structure of Tributyl Phosphate Solutions: Nitric Acid, Uranium (VI), and Zirconium
(IV)
Anna G. Baldwin, Michael J. Servis, Yuan Yang, David T. Wu, and Jenifer C. Shafer
Thank you!
Anna G. Baldwin
Anna G. Baldwin <[email protected]> Tue, Jul 11, 2017 at 9:54 AM
To: Yuan Yang <[email protected]>
My apologies, the author list on the following article should read:
The Structure of Tributyl Phosphate Solutions: Nitric Acid, Uranium (VI), and Zirconium
(IV)
Anna G. Baldwin, Michael J. Servis, Yuan Yang, Nicholas J. Bridges, David T. Wu, and Jenifer
C. Shafer
Thank you!
Anna G. Baldwin
[Quoted text hidden]
Yuan Yang <[email protected]> Tue, Jul 11, 2017 at 3:05 PM
To: Anna Baldwin <[email protected]>
Hi Anna,
I am doing great and taking vacation right now in China.
127
|
Colorado School of Mines
|
Anna Baldwin <[email protected]>
Copyright Permission for Thesis
2 messages
Anna G. Baldwin <[email protected]> Mon, Jul 17, 2017 at 3:54 PM
To: David Wu <[email protected]>
Hello Dr. Wu,
I hope you are enjoying your summer abroad!
Thank you for your comments on the TBP paper! They really helped me to clarify some ambiguities in the
text, and fixed some important errors. Your input was invaluable, and I'm very grateful. Since I'm using it as
a chapter in my thesis, I have to obtain written permission from all co-authors. It can be granted in the form
of an email.
I would greatly appreciate if you would respond to this email granting me permission to use the following
article as a chapter in my thesis:
The Structure of Tributyl Phosphate Solutions: Nitric Acid, Uranium (VI), and Zirconium (IV)
Anna G. Baldwin, Michael J. Servis, Yuan Yang, Nicholas J. Bridges, David T. Wu, and Jenifer C. Shafer
Thank you!
Anna G. Baldwin
David Wu <[email protected]> Mon, Jul 17, 2017 at 4:03 PM
To: Anna Baldwin <[email protected]>
Hi Anna,
Glad to be helpful. Yes, I grant you permission to use the article below as a chapter in your
thesis.
Best wishes,
David Wu
[Quoted text hidden]
130
|
Colorado School of Mines
|
Anna Baldwin <[email protected]>
Copyright Permissions for Thesis
4 messages
Anna G. Baldwin <[email protected]> Tue, Jul 11, 2017 at 9:45 AM
To: [email protected]
Hello Nick,
In order for me to use previously published or submitted articles as chapters in my thesis, I am
required to obtain written permission from all co-authors. This may be in the form of an email.
I would greatly appreciate if you would respond to this email granting me permission to use the
following articles as chapters in my thesis:
Tributyl Phosphate Aggregation in the Presence of Metals: An Assessment Using
Diffusion NMR Spectroscopy
Anna G. Baldwin, Yuan Yang, Nicholas J. Bridges, and Jenifer C. Braley
The Journal of Physical Chemistry B 2016 120 (47), 12184-12192
DOI: 10.1021/acs.jpcb.6b09154
Distribution of Fission Products into Tributyl Phosphate under Applied Nuclear Fuel
Recycling Conditions
Anna G. Baldwin, Nicholas J. Bridges, and Jenifer C. Braley
Industrial & Engineering Chemistry Research 2016 55 (51), 13114-13119
DOI: 10.1021/acs.iecr.6b04056
The Structure of Tributyl Phosphate Solutions: Nitric Acid, Uranium (VI), and Zirconium
(IV)
Anna G. Baldwin, Michael J. Servis, Yuan Yang, David T. Wu, and Jenifer C. Shafer
Thank you!
Anna G. Baldwin
Anna G. Baldwin <[email protected]> Tue, Jul 11, 2017 at 9:54 AM
To: [email protected]
My apologies, the author list on the following article should read:
The Structure of Tributyl Phosphate Solutions: Nitric Acid, Uranium (VI), and Zirconium
(IV)
Anna G. Baldwin, Michael J. Servis, Yuan Yang, Nicholas J. Bridges, David T. Wu, and Jenifer
C. Shafer
Thank you!
Anna G. Baldwin
[Quoted text hidden]
131
|
Colorado School of Mines
|
ABSTRACT
Early and effective fault detection in water and wastewater treatment plants is important to
maintain water quality and prevent process disruptions. Some faults, such as spike faults, are
easily detected with traditional fault detection methods that identify extreme values, while other
faults, such as drift faults, are difficult to identify due to their slowly changing behavior. In
addition, there is the need for methods that assist operator decision making and have
straightforward interpretability. This study applies a method in functional data analysis (FDA)
for fault detection to drift faults observed in a sequencing batch membrane bioreactor and closed
circuit reverse osmosis system. FDA enables analysis of cyclic data, which are curves or
functions produced by system with repetitive behavior over a time period or process. Fault
detection in a set of curves can be accomplished through the computation of statistics describing
their shapes and magnitudes. In addition, functional plots visually supplement alarm results to
assist operators. In this study we apply an existing FDA method for retrospective outlier
detection and extend it for the non-stationary, real-time applications required for tracking water
and wastewater process data. We demonstrate its ability to identify drifts faults in early stages as
well as spike faults for three case studies analyzed.
iii
|
Colorado School of Mines
|
ACKNOWLEDGEMENTS
I would like to thank the many organizations and people who have made it possible for me to
complete this degree. Firstly, I would like to thank the National Alliance for Water Innovation
(NAWI), funded by the U.S. Department of Energy, Energy Efficiency and Renewable Energy
Office, Advanced Manufacturing Office under Funding Opportunity Announcement DE-FOA-
0001905, the National Science Foundation (NSF) Partnership for Innovation : Building
Innovation Capacity project 1632227, the NSF Engineering Research Center program under
cooperative agreement EEC-1028968 (ReNUWIt), the WateReuse Foundation, and the Edna
Bailey Sussman Foundation for their generous financial support of this study. In addition, I
would like to thank Dupont/Desalitech for their contributions of membranes for the CC-RO
system.
Great thanks to my advisors Dr. Tzahi Cath and Dr. Amanda Hering for their guidance in
helping me become a more diligent scientist and competent engineer. They have provided a
wealth of knowledge to this research, and I appreciate their thoughtful advice and feedback. In
addition, I would like to thank my committee members Dr. Douglas Nychka, Dr. Christopher
Bellona, and Dr. Kris Villez. Finally, none of these experiments could have been done without
the skill and hard work of Tani Cath who developed the control algorithms and data management
systems and Mike Veres who helped design and build the systems in the case study of this study.
Finally, I would like to thank my friends and family for their support. In particular, I want to
thank my husband Paul for his love and patience during the challenges of graduate school. In
addition, nothing I have done would be possible without the support of my parents Doug and
Michelle; I am forever leaning on their advice and wisdom.
viii
|
Colorado School of Mines
|
CHAPTER 1
INTRODUCTION
Water treatment plants (WTP) and wastewater treatment plants (WWTP) perform a vital role
in the protection of human health and the environment. In recent years, facilities have faced
pressure to meet stringent treatment standards, consider their contributions to climate change,
and update aging infrastructure, all while controlling their costs. One strategy to meet these
challenges is implementing data-driven and statistical fault detection methods (Corominas et al.,
2018; Newhart et al., 2019). In particular, statistical methods can be used for early fault detection
in treatment plants with the goal of enabling increased automation, autonomous operation, and
improved process reliability. Despite the potential benefits, adoption of fault detection tools in
full-scale applications has been slow. This is due to several factors including the cost of
implementation, limited utilities’ experience with data-driven tools, and limited reliability of
methods due to the challenging features of treatment process data. Such features include non-
normal, nonstationary, and autocorrelated characteristics (Newhart et al., 2019).
Despite these challenges, fault detection methods can play an important role in WTP and
WWTP by distinguishing normal (i.e., in-control (IC)) operating conditions from unusual (i.e.,
out-of-control (OC)) situations where operator intervention is required to maintain plant stability.
In practice, this is often achieved through the use of control charts such as Shewhart and
exponentially weighted moving average (EWMA), where high and low cutoff monitoring of
individual variables determine the alarms. These charts remain a common fault detection method
as they are easy to use and provide highly interpretable information about process changes.
However, many assumptions of such methods are not applicable for the data collected in WTP
and WWTP (Newhart et al., 2019); therefore, they often fail to identify faults reliably in the
environment of treatment plants because. As a result, many methods have been developed for
treatment plants to reduce the time to detect faults, improve reliability of alarms, and to prevent
false alarms.
One popular set of fault detection methods apply principal component analysis (PCA) to
reduce the number of variables to monitor and then apply multivariate monitoring schemes, such
as the multivariate-Shewhart and multivariate EWMA (Corominas et al., 2018). By synthesizing
1
|
Colorado School of Mines
|
relationships of highly correlated variables collected in WTP and WWTP, multivariate
monitoring methods can identify joint changes in process behavior whereas a univariate control
chart only monitors individual variables. However, multivariate fault detection combined with
PCA can lack interpretability (Qin, 2012), and when the training period is updated periodically
over time, this approach can be insensitive to long and slow drift faults (Newhart, 2020). Many
machine learning methods, such as neural networks, have similar pitfalls, where faults are
identified, but there is limited information about the location and nature of the fault (Hastie et al.,
2001). Efforts to avoid these intrinsic characteristics in data-driven models, such as isolating
variables associated with the fault through penalized regression (Klanderman et al., 2020a, b)
and integrating knowledge-based strategies such as fuzzy logic or decision trees (Hadjimichael et
al., 2016) have proven to be successful, but can result in increased cost and complexity. In
general, methods that require operator input and are straightforward for operators to use have
shown the most success in applications to real systems (Corominas et al., 2018).
Cyclical processes, such as sequencing batch reactors (SBR), filtering/backwashing in filters
and membrane systems, and chemical reactions in batch operations can be especially challenging
applications for fault detection as changes may occur at multiple time scales (Rosen and Lennox,
2001). Multi-scale PCA can be an effective fault detection method for cyclical processes because
it considers each timescale where changes occur individually (e.g., changes within a cycle vs.
changes between cycles) (Lee et al., 2005; Rosen and Lennox, 2001). While effective, multi-
scale PCA can be difficult to interpret, and the incorporation of wavelets results in a high level of
complexity for implementation. Qualitative trend analysis can also be applied for fault detection
and identification, and while it can provide additional interpretable information compared to
other methods and fault detection information , it does not consider all the features of curves and
can be complex to implement (Maurya et al., 2007; Villez and Habermacher, 2015). Thus, there
is the need for methods that are appealing to use as well as high performing for fault detection.
For variables that exhibit cyclic behavior, functional data analysis (FDA) can provide a
valuable set of tools for fault detection and can be a useful visual aid for decision-making. FDA
provides information about the characteristics of a set of curves produced by a cyclic system,
where each cycle of the system produces one function or curve. By considering data in this way,
we can improve visualization, emphasize certain characteristics of the data (such as the curvature
of the functions), and gain a better understanding of the nature of variation in a system (Ramsay
2
|
Colorado School of Mines
|
and Silverman, 1997).
Functional behavior is common in WTP and WWTP data—filters, membrane systems,
membrane bioreactors (MBRs), and SBRs all follow regular, cyclic behavior. Monitoring
functions with FDA techniques can provide an indication of system health by comparing each
new function with a sample of IC functions, allowing a direct comparison to each portion of a
new cycle to the corresponding stages of previous cycles. FDA techniques have been broadly
applied in fields such as weather (Dai and Genton, 2019), air quality (Sancho et al., 2014), and
water quality (Li et al., 2017). In addition, FDA has been used for fault detection in product
manufacturing (Woodall et al., 2004) and biosciences (Salvatore et al., 2015), but there has been
limited application of FDA in the water and wastewater field. Notable exceptions include Millan-
Roures et al. (2018) who used FDA to evaluate faults in wastewater distribution networks, and
Maere et al. (2012) and Naessens et al. (2017) applied functional PCA and fuzzy clustering to
assess the fouling behavior in an MBR and ultrafiltration system respectively. Although some
aspects of water process data, such as variable sequence lengths, can be challenging for FDA
methods, there are extensions to address these problems. In addition, FDA tools are effective at
processing noisy and missing data, both of which are often observed in water and wastewater
applications (Salvatore et al., 2016). The highly interpretable approach of FDA methods can also
provide valuable information about how key processes are changing and can act as a supplement
to dimension reduction methods such as PCA.
There is a large body of FDA literature that outlines methods for outlier identification in
cyclic data (see the review paper by Ullah and Finch, 2013). Functional data (FD) typically have
either magnitude or shape outliers. Magnitude outliers involve shifted functions with abnormally
high or low values across the entire domain of the function, and shape outliers involve unusual
curvature, but the function may still be located within the range of normal curves. Figure 1.1
provides an example of both a shape and a magnitude outlier in the transmembrane pressure
(TMP) of an MBR system. Here, the magnitude outlier is caused by excess solids causing rapid
build-up on the membrane system while the shape outlier is likely indicative of a change in
controller settings or air scouring removing solids from the membrane.
Classical methods of FD characterization involve functional depth, where functions are
ranked on a scale between 0 (least central) and 1 (most central) based on their location compared
to the overall set of curves. Such a metric inherently masks the extent of abnormality of extreme
3
|
Colorado School of Mines
|
functions by bounding the metric at 0. An alternative metric is functional directional
outlyingness, which is inversely related to depth, and where 0 indicates the most central
functions, and less central values can take negative or positive values up to infinity (Zuo and
Serfling, 2000). In addition, outlyingness metrics can be easily used to describe either univariate
or multivariate data (Mazumder and Serfling, 2013). Identification of magnitude outliers is
reliable and well-established in the FDA field, while distinguishing curves exhibiting abnormal
shapes is more challenging. Thus, several methods have been developed to distinguish between
shape and magnitude outliers (Arribas-Gil and Romo, 2014; Hyndman and Shang, 2010).
Figure 1.1 Example of typical IC functions (in blue) of trans-membrane pressure (TMP) across a
membrane in an MBR during normal filtration with shape and magnitude outliers highlighted.
This study implements a method for detection of unusual functions proposed by Dai and
Genton (2019), but we modify their method and discuss considerations for real-time application
in a sequencing batch membrane bioreactor (SB-MBR) hybrid system and in a closed circuit
reverse osmosis (CC-RO) pilot system. We choose this method for its ability to simultaneously
assess the extent of shape and magnitude outlyingness of a given function, its robustness to
outliers in the IC data, and its multivariate extensions. Figure 1.2 is an example of the resultant
shape and magnitude values calculated from the functions in Figure 1.1, exhibiting the ability to
distinguish different types of outliers. For this study, this FDA method is used to track fouling
using pressure, flows, and temperature information in cyclic membrane systems in both water
4
|
Colorado School of Mines
|
and wastewater treatment contexts. An emphasis is placed on priorities for real-time
implementation including tuning parameters, operational interpretation, and method
maintenance.
Figure 1.2 The corresponding magnitude and shape values from the functions presented in Figure
1.1, as calculated from the method proposed by Dai and Genton (2019).
Existing functional data methods, including Dai and Genton (2019), are largely designed for
retrospective analysis, where a function is identified as an outlier if it is unusual compared to a
historical reference set. Such retrospective analyses can provide valuable insight into different
phenomena impacting the process, but they do not consider how operational characteristics may
change over time. In a real-time setting, functions are considered sequentially, and functions
identified as outliers are termed faults. These faults may indicate a potential process failure that
requires rapid operator attention/intervention. Unusual functions that are considered outliers may
still arise in this context. To prevent false alarms resulting from outliers, consecutive potential
faults are required to result in a system fault classification. From this perspective, accurate
categorization of functions remains important, but special emphasis is placed on how quickly a
fault is detected, prevention of false alarms, and the quality of information provided for operator
decision-making. Thus, an extension to the Dai and Genton (2019) method is developed herein
where the training set is allowed to evolve over time. Furthermore, a solution to the challenge of
unequal sequence lengths is also presented. In three case studies, we demonstrate that the FDA
5
|
Colorado School of Mines
|
CHAPTER 2
MATERIALS AND METHODS
2.1 Smoothing
Smoothing is a key data pre-processing step for FDA required to express the discrete
observations over the domain as continuous functions. The smoothing can also be used to
remove high-frequency noise or outliers while retaining the main features of the signal. Common
smoothing methods used for FDA include kernel smoothing, b-splines, smoothing splines,
Fourier and wavelet, and regression splines (Ullah and Finch, 2013). We chose to use a cubic b-
spline for its ease of implementation, continuity, and flexibility.
The extent of smoothness achieved by any smoothing method is an important tuning
parameter for FDA applications, especially those that include shape characterization. Inadequate
smoothing can lead to a poor approximation of the shape due to over or under fitting of the data.
For cubic splines, there are two main approaches to perform smoothing; specifying a number of
knots or penalizing the smooth via an additional parameter, i.e., 𝜆 (Ramsay and Silverman,
1997). When using knots, they are placed throughout the domain of the function either at equal
or pre-defined intervals. The best cubic spline is then fit to the data for each interval, subject to
the constraint that the estimated function must be continuous where they meet at the knots.
Choosing the number of knots provides an intuitive method for obtaining a smoothed line
because by increasing the number of knots, the estimated function can become more variable.
Alternatively, the penalized smoothing approach includes a knot for each data point and then
controls the roughness of the spline directly by penalizing the total square of the function’s
roughness (i.e., the integral of the second derivative of the function squared) multiplied by 𝜆. In
this case, increasing 𝜆 leads to a smoother estimated function. Automatic methods such as
generalized and leave-one-out cross-validation (LOOCV) can be used to select the smoothness
parameter.
The smoothing approach may vary based on the characteristics of dataset. This study has
both sparse data with low sensor resolution (Figure 2.1a) and high frequency, high-resolution
data (Figure 2.1b). For the sparse, low-resolution data, the data have little noise, but there are
step changes in TMP due to sensor limitations that do not represent the continuous increase in
7
|
Colorado School of Mines
|
TMP expected in the system. In this case, smoothing is calibrated to reflect the nature of the
underlying process and for improved viewing. For high frequency data, excessive noise and
outliers should be removed. For these data, automatic methods such as LOOCV may not provide
the desired levels of smoothing, so a grid search of knot parameters can be performed based on
visual inspection of resulting curves. Examples are presented in Figure 2.1.
Figure 2.1 In (a) the raw data and smoothing results for the sparse, low-resolution SB-MBR data
are shown with different smoothing approaches. In (b), the noisy, high frequency CC-RO
smoothing data are presented with different types of smoothing applied.
2.2 FDA monitoring method
For a given dataset with n functions, we assume that each function is composed of K data
points measured at successive t values. Thus, a function is denoted as X(t) for t in the domain
i
[T , T ] and for i = 1, 2, …, n. The magnitude outlyingness (MO) and shape outlyingness, termed
1 2
variation of directional outlyingness (VO) by Dai and Genton (2019), are calculated for each
function. Prior to calculating MO and VO, the authors propose the use of the Stahel–Donoho
outlyingness metric to normalize multivariate the FD (Stahel, 1981; Donoho, 1982), but different
metrics may be applied depending on the context. This study retains the use of the robust
outlyingness metric (Eq. 1.1) for the univariate application because it is robust to outliers:
𝑜(𝑿 (𝑡)) =
𝑿!($) – ()*!+,{𝑿"($), 𝑿#($),…𝑿$($)}
, (1.1)
!
123{𝑿"($), 𝑿#($),…𝑿$($)}
8
|
Colorado School of Mines
|
where MAD is the median absolute deviation. Eq. (1.1) incorporates both the magnitude of a
given function’s outlyingness (e.g., the distance from the median function) and its direction of
outlyingness (e.g., whether the function lies above or below the median function), denoted MO.
Eq. (1.3) defines VO and is based on MO value. Eqs. (1.2) and (1.3) are discretized versions of
the continuous equations in Dai and Genton (2019). For univariate data, MO is simply the mean
of each of the normalized functions, and VO is the variance taken over each normalized function.
𝑀𝑶 (𝑋 ) = 4 ∑5 𝑜(𝑋 (𝑡 ))∗ 𝑤(𝑡) (1.2)
! ! 674 ! 6
5
𝑽𝑶 (𝑋 ) = 4 ∑5 || 𝑜(𝑋 (𝑡 )) − 𝑴𝑶 (𝑋 )||8 ∗ 𝑤(𝑡) (1.3)
! ! 674 ! 6 ! !
5
Here, the weights, w(t), can be included if needed to emphasize certain regions of the domain.
Given a set of IC functions, the (MO, VO) pairs of points (e.g., blue dots in Figure 1.2, page
5) can be provide a reference to assess whether a new function exhibits IC or OC behavior. In
particular, we are interested in the joint distribution of the MO and VO of the IC data. Assuming
an ellipsoid shape of the spread implies that MO and VO follow a multivariate normal
distribution, so Gaussian estimates of the mean vector (denoted 𝑦4) and covariance matrix
(denoted S) can be used to calculate the scatter. The MO and VO of a test function are then
compared to the IC mean and covariance to determine where the new function’s values fall in the
multivariate cloud of points. This calculation is called the Mahalanobis distance, D, of a function
(Eq. 1.4).
𝑫 = 6( 𝑦−𝑦4 ) 𝑆94 ( 𝑦−𝑦4 ) (1.4)
The y represents the vector of MO and VO values for one function. The farther a function lies
from the center of the data (i.e., 𝑦− 𝑦4 in Eq. 1.4), the larger the value of D, and the magnitude
of increase is based on the spread or covariance of the data. In this case, D provides a combined
measure of how unusual a function is with respect to both VO (shape) and MO (magnitude).
Given the assumption of normality, D will follow an F distribution, and so the threshold
p+1,m-p
for an unusual function is suggested as:
((:;4)
𝐶𝑢𝑡𝑜𝑓𝑓 = ∗ 𝐹 , (1.5)
:;4,(9:,=
<((9:)
where m is a scaling factor; c reflects the degrees of freedom for the data, which is numerically
estimated via the strategy presented in Hardin and Rocke (2005); and 𝛼 is the percentile, which
is set to 0.993 and is a standard value in the context of outlier identification in box plots. If a
9
|
Colorado School of Mines
|
function’s D value exceeds the cutoff, it is flagged as representing unusual (OC) behavior. To
account for naturally changing conditions that do not indicate fault behavior and to allow for a
local approximation of normality, a rolling window is implemented on the IC data. This window
retains a constant number of days of IC data by performing a daily update that removes the
oldest day of IC data and includes the functions identified as IC for the most recent day.
For the initial selection of IC data and when the window rolls through the data during the
fault detection process, it is possible for some OC functions to be included in the IC dataset
(Newhart, 2020). Thus, a robust estimate of the center and spread of the IC data parameters is
performed by excluding some points from the estimation of the mean and covariance of MO and
VO. To do this, an H value is specified, as presented in Dai and Genton (2019), which can take
values between 0.5 and 1. It represents the amount of expected contamination in the IC data. A
value of 0.5 means that half of the functions are expected to be contaminated with OC or unusual
data, while 1 indicates that all of the functions are expected to be a good representation of IC
conditions. The corresponding proportion of functions are included in the estimation of the
center and spread of the joint distribution of MO and VO values.
Assuming either no contamination of the IC data or even a constant level of OC
contamination in the IC dataset is not usually plausible in WTP and WWTP data. During a true
IC period, unusual functions may still arise from issues in the controller algorithm or temporary
sensor inconsistencies, and the frequency of these events may change over time as equipment
ages, sensors are calibrated, or components are replaced. In addition, drift faults can result in
high incidence of OC data being included in IC datasets because functions at the start of a drift
fault are often similar to IC functions, leading to misclassification as IC. The inclusion of these
OC functions in the IC dataset reduces the method’s sensitivity to further drift. To prevent
excessive false alarms while maintaining sensitivity to drift, we develop a method to
automatically select the H value for each new rolling window. This adaptive H allows a changing
level of estimated contamination in each new IC window.
The adaptive H selection method is outlined below, with an example of the selection process
presented in Figure 2.2. We create a grid of H values between 0.55 and 0.99, and for each H, we
calculate the sum of the variances of the MO and VO of the corresponding IC data, and this sum
is plotted in Figure 2.2a. The summed variances are fit with a cubic spline with 50 knots (i.e., the
blue line in Figure 2.2a), which is chosen for its ability to quickly identify an increase in
10
|
Colorado School of Mines
|
variance. Then, the derivative of this spline is taken, and the maximum of the derivative, where
𝑣𝑎𝑟(𝑴𝑶) + 𝑣𝑎𝑟(𝑽𝑶) changes the most, is determined. If this selected derivative is two times
higher than the average slope, and the corresponding H value is within the bounds [0.8, 0.99],
then this value of H is chosen. In the example in Figure 2.2, this is represented by the orange
line. If these criteria are not met, no H value is selected, and the contamination level is assumed
to be low, so an H value of 0.99 is used. These constraints are selected based on a reasonable
level of contamination that may be expected in the IC dataset and to ensure that the maximum
derivative value reflects a major change in the distribution of the (MO, VO) dataset and is not an
isolated spike.
Figure 2.2 (a) Results of the adaptive H selection with the total variance of MO and VO with the
smoothed curve using 50 equally spaced knots overlayed. The H value selected by the method is
indicated by the orange line and is based on (b) the derivative of the spline.
The detailed data processing and fault detection steps are outlined below:
1. Separate individual cycles via a state variable. If necessary, trim sequences to be the same
length, but this can be modified as described later. Then, smooth sequences.
2. Select the window of observations to be used for the IC training period. The length of this
window may be varied based on the appropriate time scale of changes in the system, and
the initial IC dates selected may be based on a visual inspection of the data.
3. Apply the FDA method to the window of IC data.
a. Perform a robust normalization of the set of functions by subtracting the median
function and dividing by the MAD (Eq. 1.1).
11
|
Colorado School of Mines
|
b. Compute the MO and VO of each function by taking the mean and variance of
each normalized function, respectively (Eqs. 1.2 & 1.3).
c. Select H based on the MO and VO values.
d. Calculate the robust center and scale of the (MO, VO) matrix, trimming a pre-
defined proportion, H, of the most extreme functions from the calculation.
4. Monitor each new function for faults by performing the following steps:
a. Normalize the new function (Eq. 1.1) with respect to the IC data and calculate its
MO and VO statistics.
b. Calculate the robust Mahalanobis distance of the function (Eq. 1.4) using the
center and scale from the IC data (Step 3d).
c. If D is greater than the cutoff value calculated in (Eq. 1.5), then the function is
flagged as a potential fault. If D is lower than the cutoff, then the function is
included in the IC dataset.
d. If three functions in a row are flagged, then an alarm is issued.
e. Repeat steps a-d for each new function in the monitoring period.
5. Update the IC data.
a. Remove the oldest functions in the IC set in order to maintain a consistent number
of functions in the rolling window. If there are no functions at all during the
monitoring period (i.e., the system was not running), then retain all functions from
the training window. A minimum number of sequences should be maintained to
prevent failure of the method if extended OC system behavior is observed. This
would not be an important consideration for real-time operation where repeated
alarms would lead to a remedy of the fault prior to depleting the IC dataset.
b. Calculate the new H value for the updated training period, and recalculate the
center and scale of the data.
We develop two additional extensions to (1) account for functions of different length and (2)
detect faults in long functions prior to the completion of the function. To adjust the method to
handle functions of differing lengths, the IC data are separated into subdomains of t where no
individual function starts or ends. The median and MAD of each subdomain are calculated and
concatenated together to create a discontinuous version of the median function and MAD over
12
|
Colorado School of Mines
|
the entire domain t. Then, each function is normalized by subtracting the its corresponding
subdomain’s median and dividing by its MAD (step 3a). With different sequence lengths, the
number of functions in each subdomain will vary. Subdomains with very high or low values of t
may have fewer functions available to estimate the median and MAD than central subdomains.
In particular, this can result in unreasonably small MAD values that can cause dramatic changes
in the normalized function and, consequently, excessive alarms. Thus, weights are included to
account for the reduced certainty due to fewer samples for a given subdomain. These weights are
denoted by 𝑤(𝑡) = 𝑗(𝑡)/𝑛, where j(t) is the number of functions at each point t. Thus, each
subdomain is weighted based on the number of functions in that subdomain compared to the total
number of functions in the dataset. The MO and VO values are found as usual within each
subdomain, but they are calculated in reference to a different number of functions within each
subdomain. Secondly, to account for long sequences, sequences are tested for inclusion in the IC
for each new subdomain tested, and if three subdomain are flagged as OC in a row, then an alarm
is triggered. In other words, we perform Step 4 repeatedly on intervals of the function. The
length of the subdomain chosen is dependent on the rate that process changes occur in the
system, and the time scales where faults may occur.
2.3 Case Studies
The FDA method is tested on two systems, including two drift faults in an SB-MBR’s
transmembrane pressure (TMP) caused by excess solids, and a drift fault in a CC-RO membrane
permeability resulting from CaCO scaling. Overviews of each system are presented below.
3
2.3.1 System summary: SB-MBR
The FDA fault detection method is applied to process data from a demonstration-scale SB-
MBR system located at the Mines Park dormitories (Golden, CO). A brief description is included
here and more details can be found in Vuono et al. (2013). The system operates mostly
autonomously, with data sent to a supervisory control and data acquisition (SCADA) system,
which logs key MBR variables at 5 second frequency. Designed for small-scale, decentralized
implementation, the SB-MBR consists of two parallel 4,500 gallon activated sludge (AS)
bioreactors (BR) operating in an SBR mode and two membrane tanks (MT) equipped with
PURON hollow fiber ultrafiltration membranes (Koch Separation Solutions, Willmar, MN).
13
|
Colorado School of Mines
|
Batches of 325-gallons of raw wastewater are pumped from an onsite septic tank, screened, and
alternately transferred to one of the BRs once an hour. After a new batch is transferred, the
reactor cycles through aerobic and anoxic stages for carbon nutrient removal. After one hour, the
AS starts cycling between the BR and the two MTs, which perform solid-liquid separation
(Figure 2.3). During normal operating conditions, the membranes operate in permeation mode
for an operator-specified amount of time (typically 4-5 minutes), followed by 20 seconds of
backwash. An example of the MBR’s TMP functions during 5-minute intervals is presented in
Figure 2.4 on page 16. The control system increases the flowrate of water permeating through
the membranes during a cycle if it detects that the batch could not be treated within one hour.
This state is termed f , and during f , the time between backwashes is 3 minutes. If the batch
peak peak
of water is treated before the end of the hour, water permeation through the membrane stops, and
the membranes are switched to a relaxation state for the rest of a BR cycle/hour. The f
peak
functions are not included in this study as f occurs rarely relative to the normal flux state. The
peak
system operates under constant flux, with a vacuum providing the driving force for permeation.
In order to avoid build-up of AS on the membranes, a blower provides air for regular membrane
air-scouring. Chemical cleanings with bleach are performed as needed to counter long-term
fouling, typically at a bi-weekly or monthly frequency. Even with fouling prevention in place,
process faults caused by higher total suspended solids (TSS) concentrations or air blower failure
can result in excessive membrane fouling, leading to an increase in TMP.
Methods implemented by Kazor et al. (2016), Odom et al. (2018), and Newhart et al. (2020)
found that using an adaptive, dynamic PCA with a multivariate monitoring statistic is able to
identify spike and shift faults effectively in SB-MBR systems, but it often fails to identify drift
faults in process variables. The Mines Park SB-MBR is prone to drift faults and has experienced
several TSS and TMP drift faults during its approximately 13 years of continuous operation. This
tendency for drift, in addition to the cyclic nature of the MTs, is an ideal setting for treating TMP
as functional data.
14
|
Colorado School of Mines
|
Figure 2.3 Simplified process flow diagram of the MBR tanks in the SB-MBR system with key
sensors identified.
Plots of the cycles during identified IC and OC behavior (Figure 2.4) reveals how a drift fault
alters both the shape and magnitude characteristics of MBR functions. Nearly all MBR functions
observed in the system have 3 phases: a start-up period with a steep slope as the system reaches
the set point of membrane flux, a short period with somewhat reduced slope, and then a stable
permeation period for the majority of each sequence with limited change in TMP. Maere et al.
(2012) detail the implications of the shape behavior of different stages of MBR filtration, but this
study considers each sequence as a whole. For example, in Figure 2.4b, one function has a
unique shape with a delayed start-up. This is caused by the switch to normal flux operation from
f where sequences are shorter than normal operation, but the state variable used to screen the
peak
longer sequences does not reflect this change immediately. In a few functions, the TMP begins to
decrease before the end of the sequence. This is mostly the result of controller imprecision
ending some sequences at slightly different lengths (sequence length varied by about 10
seconds), but this behavior occurs more frequently in the IC functions. Thus, it appears that
fouling may also delay the decrease in TMP. However, we note that individual, irregular cycles
including those features mentioned above do not cause an alarm because three consecutive
functions must be flagged before an alarm is issued.
15
|
Colorado School of Mines
|
The IC and OC functions presented in Figure 2.4a and 2.4b respectively each have unique
shape and magnitude characteristics. The IC functions, in particular, have a relatively flat second
phase, and the slope only increases at the end of this intermediary phase, around one minute into
the sequence (Figure 2.4a). In addition, the IC data exhibit a small amount of drift as normal
changes to TSS and temperature impact TMP, and expected, gradual fouling occurs that should
be remedied by regular membrane chemical cleanings. The OC data exhibits a slightly steeper
initial slope, a continuously increasing second phase, and a much higher slope of during the third
phase compared to the IC data. Moreover, these features become more pronounced as the fault
progresses over time. The OC data thus also exhibits a large change in magnitude, as the TMP
drifts upwards during the fault.
Figure 2.4 A selection of the MBR TMP IC functions in (a) and OC functions in panel (b) for
functions observed over five minutes.
2.3.2 System summary: CC-RO
CC-RO is a unique RO operation strategy that operates in a semi-batch mode, where the RO
concentrate stream is recycled and mixed with the feed water and is slowly concentrated in the
process while the feed pressure increases (Efraty et al., 2011; Qiu and Davies, 2012). When the
16
|
Colorado School of Mines
|
water in the closed loop reaches a pre-set brine concentration, the concentrated brine is drained,
the system is filled with new feed water, and a new sequence starts. This operational strategy
allows for a compact design, improved membrane performance, and energy savings over
traditional RO systems (Efraty et al., 2011; Warsinger et al., 2016). The cyclic behavior of CC-
RO makes it conducive for tracking with FDA.
A CC-RO pilot system was operated intermittently from June through October 2021 with
varying water recoveries (20-94%) and influent salt concentrations (500-1500 mg/L TDS). The
system was operated with one RO membrane (BW30 4040, Dupont) and synthetic brackish
water that simulated groundwater wells in the Navajo Nation. A positive displacement pump
(Hydra-Cell M03) provides pressure and influent flow to the system, while a centrifugal pump
(Grundfos MS 4000R) provides the brine recirculation flow in the CC-RO loop. The water
temperature was maintained at 20-23 °C during the experiments. To recycle process water, a tank
was used to mix the RO permeate and concentrate, which was released into a feed tank when the
feed tank reached a level set point. System components are outlined in Figure 2.5. Data were
collected at 0.25 second frequency, and state variables are used to separate each process cycle.
Figure 2.5 CC-RO pilot system process flow with relevant sensors and components.
In this small, highly interdependent system, membrane performance is a key indicator of
system health. With the high recoveries, water with scaling potential, and long-term testing,
rapid detection of scaling and fouling events is paramount. Membrane performance is tracked
using the mass transfer coefficient (MTC) (Eq. 1.6), which is a measure of membrane
permeability:
17
|
Colorado School of Mines
|
CHAPTER 3
RESULTS AND DISCUSSION
3.1. Case study: 2018 SB-MBR drift fault
An SB-MBR drift event occurred in August 2018, where excessive AS solids (i.e., higher
TSS concentrations) caused caking (severe fouling) on the membranes, eventually leading to a
TMP fault and membrane failure (Figure 3.1). The TMP of the SB-MBR is analyzed from June
2018 through September 2018, treating the observations as if they were observed in real-time.
During this period, each function had 60 points (at 5-second sampling frequency) for a total of
five minutes per filtration cycle. This produces approximately 5,000 complete functions during
the time period presented in Figure 3.1. A cubic spline with 20 equally spaced knots captures the
overall shape of the curves without including the blocky characteristics of the raw data caused by
the sampling frequency and limited sensor precision (see Figure 2.1a on page 8 and Figure 2.4
on page 16).
Regions of the time series are retrospectively shaded where a fault is reasonably expected to
have occurred and during periods that may indicate unusual behavior, but do not necessarily
require operator intervention based on a visual inspection. Alarms outsides of these regions could
be false alarms, or they could be periods when faulty behavior was not originally suspected. The
time series plot is insufficient to identify faults because some faults also occur as functional
shape changes, which are not reflected in a time series plot. However, the nature of the alarm
(e.g., whether it is truly OC or IC) can be more carefully investigated with functional plots of the
TMP. Training datasets of various lengths but all ending on July 26th are selected based on visual
inspection and because few functions occurred in f during this time. The method then cycles
peak
through the data until the end of the fault on September 6th when the membrane failed due to
excessive TMP.
20
|
Colorado School of Mines
|
Figure 3.1 The (a) TMP of the drift fault including the IC data and test data and (b) TSS
concentration in the MT of the SB-MBR system in July and August 2018. A drift in the TMP is
visible by 8/19 while the TSS drift becomes observable around 8/15.
Two primary tuning parameters are investigated in applying the FDA method: the H value
and the length of the moving window. These parameters are explored in-depth due to their strong
impact on results and lack of clear reasoning in the literature for their selection. H is first set to
0.95 to test the fault detection without varying H based on sensitivity tests with values of H
between 0.75 and 0.99 presented Figures B.1 and B.2. This H value is highly dependent on the
quality of the set of IC functions and overall characteristics of data being collected. The impact
of window length is tested by varying the window length based on reasonable time scales for the
given system. Other parameters that may influence results include the minimum number of
functions, the number of consecutive points required to identify a fault, and smoothing. The
choices for these parameters are presented in the Materials and Methods section.
Applying the FDA monitoring method to the 2018 fault with a constant H value, all four
moving window lengths tested accurately alarmed the spike fault on August 17th and the drift
fault starting on August 26th. For the drift fault, the 18-day window alarmed the drift fault the
quickest, followed by the 14- and 6-day windows (Figures 3.2b and 3.2c). The 6-day window
21
|
Colorado School of Mines
|
had consistent alarming of the drift fault, but the initial alarm was somewhat later than the 14-
day window. The 10-day window had the worst performance, and it began to alarm the fault
reliably a day later than the 6- and 14-day windows.
The 6-day window has the fewest alarms outside of the known faults, and the 10- and 18-day
windows have a similar number of alarms. The 10-day window has more alarms at the start of
the test window while the alarms for the 18-day window occur directly before the drift fault
began. The latter alarms may be the result of the method detecting changes in the functions
before the drift was easily visible or due to true inaccurate alarm behavior (see Figure 3.4 on
page 25, middle panel). Finally, the 14-day window has the most separate alarm events.
Figure 3.2 (a) A time series plot of TMP during the test window. Fault detection results for a
range of window lengths during a test period containing a drift and a spike faults are presented in
(b) with constant H value of 0.95 was used and in (c), for adaptive H selection is used.
The application of the adaptive H increased alarms before 8/02, but reduced the number of
alarms in the system outside of known faults after 8/02. The elevated number of alarms at the
beginning of the test dataset can be attributed to the shift in the IC data observed starting around
7/25 (Figure 3.1). The adaptive H removes the period after the shift from the calculations of MO
22
|
Colorado School of Mines
|
and VO because those functions are unusual compared to the rest of the IC data, but the test
period before 8/02 still exhibits the slightly elevated TMP. The adaptive H method has slightly
slower identification of the drift fault for the 14- and 18-day window, and a similar rate of alarms
for the 6- and 10-day windows.
The adaptive H selection picked lower H values (e.g., the IC data was considered more
contaminated) during the start and end of the test period for all window lengths (Figure 3.3). The
lower values at the beginning of the test window are associated with the shift observed in the IC
data. The decrease at the end of the fault is likely related to inclusion of some OC functions
during the start of the drift. The H values for the 14- and 18-day windows decrease around 8/21,
which is associated with a minor increase in TMP during that period. This decrease may have led
to the alarms between 8/22 and 8/24. Not all decreases in H are associated with visible changes
in the time series, and all windows have at least one day with a reduced H value without an
observable explanation.
The functional plots and their associated MO-VO scatterplots in Figure 3.4 provide key
insight into the progression of the fault. The columns indicate the pre-fault conditions (Figures
3.4a and b), directly before the drift (Figures 3.4c and d), and during the drift fault (Figures 3.4e
and f). A comparison of the IC data between the columns shows a small drift in the IC data, but
the shape of the IC data appears to remain consistent throughout the fault. In particular, the IC
data exhibits a steep first phase and nearly flat third phase of operation. The second phase has the
most change in shape, starting as flat, with some functions seeing a short and rapid increase in
TMP around one minute into the function, while the IC functions on 8/28 had a low and constant
upward slope during this second phase. In contrast, the characteristics of the OC data before the
drift fault (8/23) include a steeper slope of the initial phase combined with a slight upward slope
during the stable third phase rather than the flat shape observed in the IC functions. Once the
fault progressed, these characteristics are amplified, with additional increased slope in the final
two minutes of the cycle.
23
|
Colorado School of Mines
|
Figure 3.3 In (a) a time series of the 2018 TMP drift fault is provided for reference. The H values
chosen by the adaptive H selection method for the 6-day, 10-day, 14 day, and 18-day windows
are shown in (b)-(e) respectively. Reduced H values are observed at the beginning and end of the
test data for a window lengths.
It is easier to see changes in the system as plotted in Figure 3.4 compared to time-series data
(refer to Figure 3.1a). The minor drift starting at 8/22 is difficult to distinguish in the time-series
data, but it is obvious in the middle panel, with the MO-VO plot (Figure 3.4d) showing the
change most clearly. In particular, all of the functions on 8/23 have positive MO values, meaning
that they are all higher than the median function of the IC data. Therefore, the MO values of the
functions identified as IC all fall on the far right of the cloud of IC functions. The functions
identified as OC are either more unusual with respect to shape or very unusual in both shape and
magnitude. For many of the functions, the shape indicator is what primarily causes functions to
be identified as OC because the function is not unusual enough in magnitude alone to trigger a
flag.
24
|
Colorado School of Mines
|
Figure 3.4 Plots of the functional data and corresponding MO-VO scatterplots during three
selected days for the 18-day window size: two weeks prior to the start of the drift fault (a and b),
directly before the drift fault (c and d), and during the drift fault (e and f). Gray hues correspond
to functions in the IC dataset. Red hues indicate the function was flagged by the method, while
blues indicate that the function was considered to be IC and was subsequently included in the IC
training set. To compare MO-VO values, equal axis ranges are maintained, so some extreme
points are not visible.
3.2. Case study: 2021 SB-MBR drift fault
A TMP drift fault occurred in 2021 that was caused by high TSS concentration and process
disruptions. This fault exhibited different features than the 2018 drift, including a much slower
and smaller drift (Figure 3.5), and shorter sequences of 3.75 minutes rather than 5. This fault was
used to test the fault detection strategy developed for the 2018 fault. In this dataset, each function
has 45 points for a total of 3.75 minutes per cycle, resulting in approximately 12,000 sequences
during the IC and test periods presented in Figure 3.5. To account for the shorter sequences, 15
knots are used to smooth functions instead of the 20 knots used for the 2018 dataset, which is
proportional to the decrease in length compared to 2018 functions. An example of the smoothing
result is presented in Figure 2.1b on page 8. The 2021 data also exhibited several small spikes
throughout the IC and test dataset not observed in the 2018 dataset.
25
|
Colorado School of Mines
|
Figure 3.5 The 2021 SB-MBR drift fault including the IC data and test data delineated and
identified drifts marked. Note that there is a break in the data from 12/22 to 1/06 due to a
problem with the data logger. While the system was still running, no data were logged during
this period.
Alarm results presented in Figures 3.6b and 3.6c show that the 18-day window consistently
produced alarms throughout the drift. The 14-day window also alarmed during the drift at a
lower rate. Finally, the 6- and 10-day windows had the weakest alarms, with the 6-day window
primarily alarming the start of the fault and the 10-day window producing alarms more near the
end of the fault. The 18-day window likely had the strongest signal because the window had a
long history to prevent the rolling window from removing much of the true IC data after several
days of fault behavior. This observation is supported by the fact that all of the windows alarmed
the start of the fault, but only the longer 14- and 18-day windows sustained alarms throughout
the fault. During real-time implementation, alarms would help operators take corrective actions
to end the fault behavior before a sustained drift is allowed to occur. Thus, a strong initial alarm
is generally be more important to observe than a sustained alarm throughout the drift.
All windows had alarms outside of the known drift fault, but the 6-day window in particular
produced extended alarms including events on 1/16, 1/21, and 1/27. These events also caused
alarms in some of the longer window lengths but to a far lesser degree. An examination of the
time series for these periods shows a steady upper TMP value with a slight shift from previous
26
|
Colorado School of Mines
|
TMP values. These magnitude shifts are relatively minor compared to changes seen in other
portions of the domain, which did not lead to any alarms, indicating that the unusual behavior
during these periods may have been caused by shape changes in functions rather than just
magnitude changes. The reduced alarms for longer window lengths can be explained by the
increased variability incorporated into the longer IC datasets, which include a broader range of
behavior as normal.
Figure 3.6 (a) A time series plot of TMP during the test window. Fault detection results for a range
of window lengths during a test period containing a drift and spike faults are presented in (b) with
a constant H value of 0.95 was used and in (c) where the adaptive H selection is used.
The adaptive H reduced the number of alarms outside the known drift fault for the 14- and
18-day windows, and led to a different, but a similar number of alarms for the 6- and 10-day
windows. Both H selection methods lead to similar alarm results for the 6- and 18-day windows
during the drift, with a reduction in alarm intensity in some periods (e.g., 2/16 for the 6-day
window and 2/09 for the 18-day window). An examination of the H values selected for these
windows shows little pattern for the 6-day window length, while the 18-day window H values
begin to decrease on 2/08, corresponding to the start of the fault (Figure 3.7). For the 10- and 14-
27
|
Colorado School of Mines
|
day windows, the adaptive H decreased the intensity of the signal at the beginning of the drift
fault and generally increased the intensity of the signal starting around 2/10. This behavior is
reflected by the H selection results for both windows with large (0.99) H values selected up to
2/08, followed by several days with lower H values.
Figure 3.7 In (a) a time series of the 2021 TMP drift fault is provided for reference. The H values
chosen by the adaptive H selection method for the 6-day, 10-day, 14 day, and 18-day windows
are shown in (b)-(e) respectively. Reduced H values can be seen for all window lengths after the
start of the fault on 2/06.
A comparison of the 2018 and 2021 drifts shows that the method was able to adequately
detect the drift fault for most window lengths despite the different characteristics of the faults.
The 10- and 14-day windows showed similar performance between faults with more overall
alarms and a weaker signal during the drift fault than the 18-day window. Only the 6-day
window had very different results between 2018 and 2021 with the 6-day window during the
2018 fault having few alarms and a strong signal during the true faults. In contrast, the 6-day
window during the 2021 fault had multiple extended alarms and a weak signal during the true
fault behavior, especially after the initial two days of drift. This can be attributed to the weak and
longer 2021 drift that allowed more OC data into the IC dataset and the shorter moving window
28
|
Colorado School of Mines
|
removing the true IC data, masking the drift. For this slower drift fault, a window size of 10 days
or longer is advised for the best drift detection.
The functional plots of the 2021 dataset reveal unique shape and magnitude changes
compared to the 2018 drift (Figure 3.8). A similar structure of the TMP functions is observed
between faults with a start-up phase followed by a short intermediary phase and then a stable
permeation phase. The 2021 IC functions do not appear to have major shape changes between
the panels, but the spread of the IC data increases as the fault progresses and as functions
exhibiting slight drift are included in the IC dataset. The IC functions in 2018 fault exhibited
similar shape characteristics as the 2021 test period, but the spread of the functions decreased
during the 2018 test period, rather than the increase observed during the 2021 test period. The
MO-VO plot for 2/06 shows that many of the test functions are not unusual enough in MO to
trigger a flag, and only functions also unusual in terms of VO result in a flag. This is similar
behavior to the 2018 fault where the combination of MO and VO changes often leads to flags.
The functional plot on 2/06 (Figure 3.8c) reveals the nature of the shape change, as the second
phase for the functions identified as OC is a mostly continuous upward slope rather than the flat
TMP followed by an increase observed in the IC data. During the fault on 2/16, the functions
identified as OC have a steeper initial startup phase and an exaggerated second phase, with a
larger increase in slope at the end of the second phase (Figure 3.8e). Unlike the 2018 fault, the
third phase during the fault is mostly unaffected, and it remains flat for both IC and OC data.
This may be due to as less severe fault, where a chemical membrane cleaning would be sufficient
to restore the permeability, rather than leading to membrane failure.
29
|
Colorado School of Mines
|
Figure 3.8 Plots of the functional data and corresponding MO-VO scatterplots during three
selected days for the 18-day window size: before the fault (a and b), at the beginning of the drift
fault (c and d), and during the fault (e and f). Gray hues correspond to functions in the IC dataset.
Red hues indicate that the observation was flagged by the method, while blues indicate that the
method identified the function as IC. To compare MO-VO values, equal axis ranges are
maintained, so some extreme points are not visible.
3.3. Case study results: CC-RO drift
The CC-RO pilot dataset provided a different set of conditions to test the monitoring method
as the data exhibited varying sequence lengths, long sequences that required intra-sequence fault
identification, a small number of functions, intermittent operation, sensor data containing
outliers, and changing influent conditions. There IC data were insufficient to perform an
evaluation of window lengths for this dataset. Thus, approximately 4 days of identified IC data
from a separate run with the same membrane were included in addition to the 2 days of true IC
data (Figure 3.9). The time series plot of the drift fault in Figure 3.9 shows a visible drift from
10/16 to 10/19, with a change in the slope after 10/16. A membrane cleaning performed on 10/18
led to an increase in permeability that quickly began to drift downward. After 10/19, another
membrane cleaning was performed that fully restored permeability. During the period starting
10/11, a slight drift is visible in the first sequences. This is the result of stabilization after two
30
|
Colorado School of Mines
|
days of idling and is not considered fault behavior. The data values between 10/13 and 10/16
also exhibit a slight drift that should be mitigated through process changes, but it is not severe
enough to be considered fault behavior as some reduction in membrane permeability is expected
over time during normal operation and is remedied with periodic membrane cleanings.
Figure 3.9 Membrane permeability over time in the CC-RO system with faulty periods
identified; the true 2 days of IC dataset with additional IC data substituted from a different run;
and test data delineated. The break between 10/08 and 10/10 indicates a period when the system
was idle.
Unlike the SB-MBR results, longer window lengths performed poorly in the CC-RO system,
with the maximum tested window length of 6 days having numerous alarms and a weak signal at
the beginning of the fault as presented in Figures 3.10b and 3.10c. Alternatively, the 2-day
window length had only one alarm with a constant H method, and it alarmed both known faults
quickly. It did not alarm the potential faults, which may be desirable depending on the
application and sensitivity desired. For the constant H, the 2-day window also had the fastest
detection for both stages of the fault.
The 2-day window is mostly unaffected by implementing an adaptive H, with a slight
reduction in alarms outside of the drift and less sensitivity to the drift. The adaptive H made the
31
|
Colorado School of Mines
|
6-day window less sensitive at the beginning of the fault and more sensitive during the second
stage of the fault. For the 4-day window, the adaptive H selection results in fewer alarms and is
more sensitive to the known faults than the constant H. In addition, during the second stage of
the drift fault (after the membrane cleaning on 10/18), the 4-day window had the fastest detection
of all options tested. Here, window choice is dependent on the sensitivity desired. The 4-day
window with adaptive H performed best for detection of both possible and known faults, while
the 2-day window with adaptive H performed best for avoiding spurious alarms.
Figure 3.10 (a) A time series plot of MTC during the test window. Fault detection results for a
range of window lengths during a test period containing a drift fault are presented in (b) with a
constant H value of 0.95 was used and in (c) where the adaptive H selection is used.
An examination of the H selection results for the 2-day window shows high H values
throughout the test period (Figure 3.11), with reduced values at the beginning of the fault. This
selection of large H values likely resulted in the reduced sensitivity to faults observed for the
adaptive H 2-day window. The high H values selected throughout the IC period likely led to the
exclusion of the extraneous alarms and may have caused the reduced sensitivity during the
second phase of the fault. The 6-day window length had similar characteristics of H selection to
32
|
Colorado School of Mines
|
the 2-day window, with increasing H values during the first few days of the test window
followed by a period of high H and then several days of decreasing H. The lower H values at the
start may be attributed to the discontinuity of the IC data set, and the decrease in H at the end
may be attributed to the drift allowing more unusual functions into the IC dataset. Finally, the 4-
day window only observed reduced H values at the end of the test period. For the 6-day window,
H selection led to limited change in the alarming results, while it led to an improvement in the 4-
day window. This may be because the 4-day window had larger H values at the beginning of the
fault, making this window length more sensitive during the start of the fault.
Figure 3.11 In (a) a time series of the MTC drift fault is provided for reference. The H values
chosen by the adaptive H selection method for the 2-day, 4-day, and 6-day windows are shown
in (b)-(d) respectively.
The functions in the IC dataset had a strong change in magnitude and a slight change in
shape during the test period (Figure 3.12a, c, and e). Initial IC functions started with an MTC of
around 0.02 LMH/kPa with many functions at the end of the fault starting with an MTC around
0.16 LMH/kPa. This reflects the slight reduction in MTC observed in the IC data. Regarding
shape, initial IC functions appear to have a stable period around 5-10 mS/cm followed by a
slowing curving downward slope. In contrast, the IC functions at the end of the fault have a
33
|
Colorado School of Mines
|
similar startup behavior followed by straight (rather than curving) downward slope. In addition,
there is a larger spread in the functions at the beginning of the test period compared to the end of
the fault.
The variation in function lengths and intra-sequence alarming changes how and when alarms
occur. For example, in the pre-fault plot (Figure 3.12a and b), there is a very long sequence in
dark blue that corresponds to the first potential alarm of the dataset in Figure 3.9. The start of the
sequence is similar to the IC data and other test functions during the day, but after 20 mS/cm, it
is compared to fewer, earlier functions that have much higher MTC values. Even so, this section
is not alarmed. The MO-VO scatterplot (Figure 3.12b) provides a justification of this result as the
overall function (located at approximately (-2.0, 1.5)) does not have the most unusual MO score
or VO scores. Thus, the high variability of the shape of the function combined with the down
weighting of the period with fewer functions leaves this function within the range of what can be
considered normal for the dataset. A similar situation is observed in Figure 3.12c and d that
includes some alarms on 10/13. Despite the large spread of the data after 20 mS/cm and a smaller
number of functions on this portion on the domain, several test functions are alarmed. For these
functions, the operator would receive the warning of an unusual function around 22 mS/cm, after
the sequence is identified as unusual in three consecutive checks occurring every five minutes.
These early warnings are especially helpful in the CC-RO system where the system is prone to
scaling near the end of the sequences when the highest TDS levels in the brine occur. The MO-
VO scatterplot of alarmed functions on 10/13 (Figure 3.12d) indicates that the shape
characteristics were more abnormal than the magnitude score. This makes sense as the
corresponding normalized function would see a rapid decrease compared to the median function
starting at 20 mS/cm. This results in a large variance of the normalized function (VO). Finally,
by 10/19, the fault has progressed enough that alarms occur in all portions of the domain, and
this is reflected in the MO-VO plot where all of the test functions are far from the spread of the
IC data (Figure 3.12e and f). For many of these functions, an alarm would be issued after 15
minutes after the start of the sequence, when three consecutive sub-sequence checks identify the
sequence as OC. For context, the typical functions range from 60-120 minutes long.
34
|
Colorado School of Mines
|
Figure 3.12 Plots of the functional data and corresponding MO-VO scatterplots during three
selected days for the 4-day window size: before the fault (a and b), during a period of alarms
occurring outside of the known drift (c and d), and during the fault (e and f). Gray hues
correspond to functions in the IC dataset. Orange indicates the point or portion of the function
was flagged by the method, while blues indicate the method identified the function as normal to
be subsequently included in the IC dataset. To compare MO-VO values, equal axis ranges are
maintained, so some extreme points are not visible.
3.4. Window length selection
Window length is an important tuning parameter as there can be competing considerations
for the choice of window length. Long windows can include a greater range of expected variation
in the IC dataset, thereby reducing false alarms. In addition, long window lengths can detect long
drifts when there is enough historical IC data such that any initial faulty drifted data incorporated
into the IC dataset does not substantially change the characteristics of the IC data. This behavior
was observed for the longest (18-day) window length in the SB-MBR faults where there were
few alarms outside of the known faults and quick alarming at the start of the drift faults. There is
also the potential for long windows to reduce sensitivity to drifts in some situations, with
increased variability in IC dataset accepting more functions as normal. This occurred in the 6-
day window for the CC-RO fault, where there is a delay in the initial identification of the fault.
The rate of natural change in the system should also be considered when selecting window
35
|
Colorado School of Mines
|
length, with windows sized such that natural change in the system does not lead to unnecessary
alarms. In the CC-RO system, a slow drift in membrane permeability is expected with changes
occurring on the timescale of weeks. A very long moving window could identify this expected
drift as a fault. In addition, practical considerations such as start-up time and achieving enough
time in IC operation to get an initial complete IC dataset should be considered when selecting the
window length. The IC datasets in this study were imperfect, with potential OC behavior in the
2018 SB-MBR and CC-RO IC periods, but the FDA monitoring method still provides
meaningful results because the H value trims unusual functions out of the IC set. Initial testing
with multiple window lengths (as done in this study) is recommended to determine the
appropriate length for a given application.
3.5. H selection
Unlike window length, adjusting the H value has a more straightforward impact than
changing the window size has. In particular, higher H values result in fewer alarms due to the
inclusion of more variability in the calculations of center and spread of the (MO, VO) statistics.
Thus, H is a useful parameter to adjust the levels of false alarms tolerated, with the
understanding that increasing the H value could result in reduced sensitivity to true faults,
especially drift faults. In this study, high values of H (greater than 0.8) were appropriate as there
were acceptable number of functions in the IC dataset, and there was enough consistency in
incoming functions to prevent excessive levels of contamination of the IC dataset. In general, H
values greater than 0.95 provided good results in both systems, but a lower H value may be
needed when there is a highly contaminated IC dataset. The adaptive H generally improved the
performance of the method by reducing the number of alarms outside the known drifts and
maintaining consistent alarms during faults. Given that, the adaptive H selection only helps after
OC data have contaminated the IC dataset. It cannot be used as a substitute for effective fault
detection, but it can help prevent continued contamination of the IC training set. This is
especially useful for drift faults where changes occur over long periods of time. This
characteristic of the adaptive H is observed in the 2021 SB-MBR drift fault during the 10- and
14-day windows where the initial fault response is muted compared to the constant H, but
alarmed more consistently in subsequent days. The adaptive H also delayed initial alarms for
longer window lengths in the 2018 fault. In contrast, the adaptive H both reduced alarms outside
36
|
Colorado School of Mines
|
of the main drift fault and increased sensitivity to the fault for the 4-day window length in the
CC-RO system. Thus, there is the potential for improved alarm response in some cases,
especially during continuous slow drifts as observed in the CC-RO system where OC functions
may be marginally included in the IC dataset and are easily identified and removed by the
adaptive H. The adaptive H values selected generally reflect the operational characteristics of the
system with reduced H values during initial days of drift and elevated H values during known IC
behavior, although several windows had isolated reductions in H value that were unassociated
with visible system changes. In addition, the adaptive H impacted different window lengths
differently. While the adaptive H is designed to be easily applied to different situations without
additional tuning, if a dataset is highly contaminated, the lower bound on H can be adjusted as
appropriate. Overall, the constant H provides more control over alarming by providing a
straightforward setpoint to adjust, while the adaptive H provides an automatic option for
balancing false alarms and fault sensitivity.
37
|
Colorado School of Mines
|
CHAPTER 4
CONCLUSION
Existing fault detection methods such as PCA combined with Hotelling’s T2 or similar
extensions are hard to interpret and may fail to detect some types of faults. Thus, there is the
need for effective fault detection and identification methods that aid operators in decision-
making to identify and remedy faults, and especially drift faults. This study demonstrates the
value of viewing cyclic variables as functions for fault detection and analysis in diverse systems.
FDA fault detection monitoring provides straightforward information about key system
behaviors with functional and MO-VO plots that provide information about how functions
change during a fault. Meanwhile, the alarming method provides timely warnings, especially for
drift and spike faults. Special attention should be paid to the selection of the H value and window
length as the method can be sensitive to these parameters. The inclusion of the adaptive H
selection method reduces the number of alarms, while maintaining a strong signal during known
faulty periods. This FDA fault detection method can be extended to multivariate monitoring, and
future work applying the method to multivariate scenarios while maintaining interpretability
could increase the type of faults that can be detected. In addition, pairing the FDA fault detection
method with clustering or categorization techniques such as those presented in Maere et al
(2012) for real-time fault analysis to supplement the current fault detection is a promising
extension. Further extensions may consider applying FDA fault detection for data exhibiting
multiple states (such as f for the SB-MBR data) or selecting non-parametric thresholds to
peak
reduce false alarms. By prioritizing visual representation of fault information, the FDA fault
detection method presented in this study can help operators make decisions and easily observe
system changes in systems with cyclic variables.
38
|
Colorado School of Mines
|
ABSTRACT
Iron is a common contaminant encountered in most metal recovery operations, and particularly
hydrometallurgical processes. For example, the Hematite Process uses autoclaves to precipitate
iron oxide out of the leaching solution, while other metals are solubilized for further
hydrometallurgical processing. In some cases, Basic Iron Sulfate (BIS) forms in place of
hematite. The presence of BIS is unwanted in the autoclave discharge because it diminishes
recovery and causes environmental matters. The focus of this master thesis is on the various iron
phases forming during the pressure oxidation of sulfates. Artificial leaching solutions were
produced from CuSO , FeSO and H SO in an attempt to recreate the matrix composition and
4 4 2 4
conditions used for copper sulfides autoclaving. The following factors were investigated in order
to determine which conditions hinder the formation of BIS: initial free acidity (5 – 98 g/L),
initial copper concentration (12.7 – 63.5 g/L), initial iron concentration (16.7 - 30.7 g/L) and
initial iron oxidation state.
There were three solid species formed in the autoclave: hematite, BIS and hydronium jarosite.
The results show that free acid is the main factor influencing the composition of the residue. At
an initial concentration of 22.3 g/L iron and no copper added, the upper limit for iron oxide
formation is 41 g/L H SO . The increase of BIS content in the residue is not gradual and occurs
2 4
over a change of a few grams per liter around the aforementioned limit. Increasing copper sulfate
concentration in the solution hinders the formation of BIS. At 63.5g/L copper, the upper free
acidity limit is increased to 61g/L. This effect seems to be related to the buffering action of
copper sulfate, decreasing the overall acid concentration and thus extending the stability range of
hematite. The effect of varying iron concentration on the precipitate chemistry is unclear. At high
iron levels, the only noticeable effect was the inhibition of jarosite. The results were reported
within a Cu-Fe-S ternary system and modeled. The modeling confirmed the experimental
observations with the exception that increasing iron concentrations seem to promote BIS
stability.
iii
|
Colorado School of Mines
|
CHAPTER 1 INTRODUCTION
Iron is a common contaminant in hydrometallurgy. This first chapter presents general facts about
iron contamination during extraction processes. The motivation for this thesis is also detailed.
1.1 Background
Iron is the 4th most abundant element in Earth‘s crust (5% by weight) and is present in
many minerals forming the ores exploited for mining activities. Iron sulfides, especially, are a
common component of base and precious metals deposits. Iron is readily solubilized and
oxidized by most acid leach solutions. It interferes with the extraction process on many levels,
thus it is paramount to achieve separation as early as possible in the metallurgical circuit.
Among the metallurgical processes used to treat sulfide ores, leaching methods are widely
used to concentrate and recover metals. The last decades have witnessed an increasing
complexity to efficiently process ore bodies. Because most high grade ore bodies have already
been found, the mining industry has turned to lesser grade and more complex deposits. New
leaching processes had to be developed to efficiently extract metals. For base and precious
metals, the challenge consists in selectively solubilizing the wanted values, leaving as many
contaminants as possible in the residue. It relies on the use of high pressure over a wide range of
temperature to break down complex minerals, as well as overstep kinetic and thermodynamic
barriers.
1.2 Motivation
The Hematite Process is used to precipitate iron from leach liquors as an oxide, hematite.
The residues are washed and filtered while the leach solutions are further processed for metal
recovery. Within some gold and/or copper pressure leaching operations, iron hydroxysulfates or
Basic Iron Sulfate (BIS) appear to precipitate along with hematite. They are highly unwanted
products in the autoclave discharge. BIS have been proven to form even when operating at
conditions which would normally yield hematite. Because they are only forming under high
pressure and very corrosive environments, BIS stability is not fully understood. By quantifying
1
|
Colorado School of Mines
|
CHAPTER 2 LITERATURE REVIEW
The second chapter presents pressure leaching and how it is used to process complex ores
and selectively precipitate iron.
2.1 Historical overview and development of high pressure leaching
Pressure leaching describes the use of high pressure to enhance the chemical break down
of mineral particles. Because pressurization is coupled with heat, pressure leaching is often
associated with higher temperatures than regular hydrometallurgical processes. This branch of
metallurgy has been used for about 150 years but most advances were made over the last 30
years. Pressure metallurgy is a great application for ―difficult‖ ores which cannot be treated by
traditional techniques. As a result, it also represents a technical challenge.
2.1.1 Early work
The very first pressure hydrometallurgy experimentation was conducted in 1859 by
Nikolai Nikolayevitch Beketoff, a Russian chemist [1]. He managed to precipitate silver by using
overpressure of hydrogen gas in a sealed glass tube. The first major application was found by
Karl Josef Bayer in 1885, in Saint Petersburg. Bayer used a pressurized autoclave operating at
170°C to enhance the crystallization process of aluminum hydroxide, known for its gelatinous
structure. This was the beginnings of the Bayer Process for aluminum production from bauxite.
2.1.2 Developments made in the 20th century
The applications of pressure leaching for base metals such as copper, nickel and cobalt
were discovered in 1903 when Malzac leached sulfides with ammonia [1]. This specific patent
recommended the use of high pressure and temperature in pressure vessels. Leaching of zinc
sulfide was later achieved by Fredrick A. Heinglein (1927), using pure oxygen at 290 psi and
180°C. He demonstrated that galena (which was normally insoluble even at very high
temperatures) could be completely converted as lead sulfate in six hours (Equation 2.1).
MS + 2O 2 + nNH 3 [M(NH 3) n]2+ + SO 42- (Equation 2.1)
3
|
Colorado School of Mines
|
About 40 years later, nickel sulfide leaching by ammonia in oxidative conditions prior
reduction to nickel was developed by Sherritt Gordon Limited and the Chemical Construction
Corporation. Next, Vladimir N. Mackiw discovered that copper could be taken out of the
solution as a sulfide prior to reducing nickel, just by boiling treatment in presence of thiosulfate
ions. Consecutively, all existing patents on ammonia leaching were used to obtain an efficient
method for precipitating pure nickel in 1956 in Ottawa[1].
In the meantime, a Canadian team (Kenneth W. Downes and R.W. Bruce) succeeded in
solubilizing nickel out of a pyrrhotite-pentlandite concentrate while hematite and sulfur remained
in the residue. In 1953, the leaching of a Ni-Cu-Co concentrate started in Fort Saskatchewan,
Canada, at the Sherritt-Gordon Plant which is still active today. The development of this process
was the most important advance made in pressure leaching technology in the 20th century.
As presented above, most of the early significant developments at industrial scale were
made for the aluminum and nickel industries. Pressure leaching is nowadays used for uranium,
copper, gold, tungsten, zinc and titanium (Figure 2.1). Common leaching agents are ammonia,
chloric or sulfuric acid, sodium hydroxide.
Figure 2.1: Summary of hydrometallurgical processes related to pressure leaching [1]
2.2 Recent advances in pressure leaching
Three applications have driven recent developments in high pressure technology: oxidation
of refractory gold ores, leaching of base metals sulfide concentrates and leaching of aluminum-
4
|
Colorado School of Mines
|
rich laterites [2]. One of the reasons for development of high pressure leaching is the increasing
complexity of the extracted ores, requiring stronger treatments for acceptable separation [3].
2.2.1 High pressure acid leaching for gold recovery
One of the methods used in gold recovery circuits is cyanidation followed by solid-liquid
separation. The solution is then treated to extract the gold (Equation 2.2). This method becomes
problematic when the ore has low-grade or a complex composition, referred as ―refractory‖. The
diversity and refractoriness of ores is explained by mineralogical, metallurgical and chemical
properties. From a definition standpoint, refractoriness is due to:
- Physical encapsulation in an inert gangue preventing the precious metals to be leached
and/or,
- Contamination by a constituent which interfere with the chemicals used.
Common gangue minerals are arsenopyrite, pyrite, pyrrhotite and realgar. Gold is usually found
finely disseminated in these minerals [4].
4Au + 8[X]CN + H O + O = 4NaOH + 4[X]KAu(CN) [X]= K or Na (Equation 2.2)
2 2 2
To liberate the gold, sulfides are oxidized prior to cyanidation. It can be achieved by roasting,
pressure oxidation or bacterial leaching [5]. Up to 25 years ago, roasting with air was the main
process used for oxidation. The switch to pressure leaching from roasting was made because of:
- environmental regulations on sulfur dioxide and arsenic trioxide release in the air
- higher gold recovery was achieved by pressure leaching
Autoclaving achieves better results because of the concentrate dissolution in the vessel,
allowing the oxidation of all particles, even the finest, fully encapsulated in the gangue. Roasting
products are porous, but not enough to ensure an optimum complexation of the gold with cyanide
[4]. Bacterial leaching is a recent and promising technique, which development has been slowed
down by technical issues. As of 2010, only 10 plants in the world were operating using bacterial
leaching.
As an alternative, pressure leaching was developed in order to break down the sulfide
matrix and convert sulfides to sulfates reporting to the aqueous phase (Figure 2.2). After
leaching, the pregnant leach solution is neutralized and pumped to cyanidation tanks [3].
5
|
Colorado School of Mines
|
Figure 2.2: Gold extraction flowsheet by cyanidation including pressure oxidation [6]
When refractoriness is associated with contaminants, there are two common difficulties
encountered to treat the ore:
- consumption of the leaching agent or oxygen by sulfides which react readily with cyanide
(in this case, increasing the concentrations is not always economically viable)
- carbonaceous material in the ore responsible for the preg-robbing phenomenon: after
being solubilized in cyanide, gold is readsorbed onto the carbon particles. Several options
have been considered to overcome this issue: deactivate carbonaceous materials with
chlorine or organic compounds, mineral processing, roasting or using Carbon In Leach
(CIL) rather than Carbon In Pulp (CIP) with specific activated carbon. There is no
universal solution to the carbonaceous matter problem and each of the previous
techniques cited has its own disadvantages (kinetics, cost…). Pressure leaching in this
specific case is not always adapted because it potentially activates the particles of
carbonaceous material [4].
As aforementioned, refractory ores represent most of the new deposits found over the last
decades. Besides ore diversity which prevents the use of a single process for all of them,
refractoriness requires the development of new extraction schemes. As a result, it is more and
more difficult to extract the precious values economically. When the contamination by
carbonaceous material is minor, pressure leaching is extremely relevant and has been widely
used for refractory ore treatment.
6
|
Colorado School of Mines
|
2.2.2 Extraction of zinc and copper from sulfide ores
Development of high pressure oxidation (HPOX) processes was also promoted by the
necessity of finding alternatives to roasting of copper and zinc sulfide ores.
2.2.2.1 Pressure leaching of zinc sulfides
The Cominco Process developed in 1981 in British Columbia was the first zinc treatment
plant by pressure leaching [1]. Sphalerite concentrates are oxidized in acidic environment at
150°C and 700kPa oxygen overpressure (Equation 2.3). After oxidation, the PLS is purified and
zinc is recovered by electrolysis (Figure 2.3). In this specific process, sulfides are only oxidized
to elemental sulfur because of the process temperature.
ZnS + 2H+ + ½O 2 Zn2+ + S + H 2O (Equation 2.3)
When it was first introduced, this process helped solving two major problems related to
hydrometallurgical treatment of roasted ores. First, no sulfur dioxide was produced, thus
reducing emissions or necessity for recycling as fertilizer. Then, this method prevented ferrites
formation, increasing the ratio of zinc effectively recovered in solution.
Figure 2.3: Flowsheet for the oxidation of sulfide concentrates in acid medium [7]
7
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.