# Selective recovery of critical materials in supercritical water desalination

Tae Jun Yoon  Erica P. Craddock  Jeremy C. Lewis  John A. Matteson  Jong Geun
Seong  Rajinder P. Singh  Katie A. Maerzke  Robert P. Currier  Alp T.
Findikoglu  Los Alamos National Laboratory, Los Alamos, NM 87545, United
States

###### Abstract

Supercritical water desalination (SCWD) is an alternative zero-liquid
discharge desalination technique that can overcome many technical and
environmental challenges in common desalination processes. Our recent techno-
economic analyses on the process integration and intensification of an SCWD
process suggest that SCWD can be an economically competitive zero-liquid
discharge desalination technique for highly concentrated brines. In addition
to these attractive features, this work explores the possibility of utilizing
the SCWD process for the selective recovery of industrially essential
materials as co-products. Model brines containing sodium chloride, neodymium
chloride, and other sodium-containing salts, are examined as model feeds from
25 to 450 ∘C at 25 MPa. The sodium contents in the effluent were not sensitive
to the presence other salts, but that of neodymium was. When sodium acetate
was added, water-insoluble precipitates were obtained. The characterization of
these deposits using gas pycnometer, FT-IR, SEM/EDS, and XRD indicates that
the precipitates mainly contain neodymium hydroxide and some low-concentration
impurities. These results suggest that an SCWD process has the potential to
recover critical materials while producing freshwater.

###### keywords:

Supercritical Water; Desalination; Critical materials; Selective recovery; Ion
speciation

##  1 Introduction

Desalination, a physical/chemical process for removing salts from brine, is a
feasible route for addressing water scarcity. The ever-increasing need for
drinkable water has led to the advancement of many desalination technologies
[1, 2] such as reverse osmosis [3], multi-stage flash [4], multiple-effect
distillation [2], mechanical vapor compression [5], and electrodialysis [6].
These techniques are relatively mature and show good performance for potable
water production, but one of their major drawbacks is that a highly
concentrated brine is discharged from the plant. Since the concentrated brine
can harm the environment [7], an additional discharge step (e.g., surface
discharge, deep well injection, and evaporation pond) or process (e.g., brine
concentrator and crystallizer) is required [8, 9, 10]. To avoid this expense,
zero-liquid discharge techniques that do not produce any liquid wastes are
being explored [11, 12].

Supercritical water desalination (SCWD) is one option for realizing zero-
liquid discharge desalination [13, 14, 15, 16, 12, 17]. In this process, a
salt-containing aqueous mixture is pressurized and heated above the critical
point of pure water ($T_{\mathrm{c}}=374\ ^{\circ}$C and $p_{\mathrm{c}}=22.1$
MPa). The typical operating condition in the SCWD process is, in fact, not
beyond the critical point of the brine; the critical temperature and pressure
in concentrated salt solutions are much higher than that of pure water. Above
a threshold temperature, the compressed brine is split into a distillate and
bottoms fraction. The salt concentration in the distillate is usually less
than the potable water limit ($<1,200$ ppm), and the remaining salts are
concentrated in the bottoms fraction. The bottom stream is usually rapidly
depressurized to obtain additional clean water as a superheated vapor and
precipitate the salts.

The SCWD process offers other advantages compared to commercial desalination
processes. Above all, it accommodates a variety of feeds consisting of highly
concentrated brines (well above the seawater levels) and wastewater containing
organic pollutants. Common organic substances can be quickly decomposed into
CO2 and H2O at high temperatures via exothermic oxidation reactions [18, 19,
20].

On the other hand, the high thermal energy input required to reach operating
conditions is a significant obstacle impeding the widespread commercialization
of SCWD processes. This disadvantage can be partially avoided by using waste
heat from power plants or by process integration. Our recent techno-economic
analyses demonstrated that the energy use and the water cost could be
significantly reduced by integrating SCWD with other processes [17]. For
example, the heat generated by the oxidation of organic pollutants or
hydrocarbons can even generate energy beyond that necessary to operate the
process [16, 21, 22, 23].

This work explores another potential advantage of SCWD. Specifically, the
possibility of selective recovery of critical materials that are commercially
or strategically important is explored. Industrial wastewater [24], acid mine
drainage [25, 26, 27], groundwater in the vicinity of mine sites [28], and
produced water [29] are known to contain critical materials that are
indispensable in high-tech industries, such as lithium, nickel, copper,
scandium, yttrium, and lanthanides (rare earth elements, or REEs). Since both
the feed composition and operating conditions control the solubility of salts
in near-critical and supercritical water [30], an SCWD process might work
synergetically for recovering such precious elements while producing drinkable
water.

We designed, built, and executed a series of experiments involving
supercritical desalination of model solutions in a continuous flow unit. The
operating temperature varied from 20 to 450 ∘ C along an isobar (25 MPa). The
model feed solutions consisted of neodymium chloride (NdCl3), sodium chloride
(NaCl), different sodium salts, and distilled water. By analyzing the
distillate compositions and precipitates and combining them with theoretical
calculations, we demonstrate that SCWD shows considerable promise for the
selective recovery of critical materials while producing potable water.

##  2 Methods

###  2.1 Materials

Distilled water (H2O, Kroger®) was locally purchased. The specific conductance
of the distilled water was determined as $<1\mathrm{\mu S/cm}$ using a
handheld conductometer (EW-19601-03, Cole-Parmer®). All salts, including
sodium chloride (Sigma Aldrich, NaCl, $\geq 99.0\ \%$), sodium sulfate (Sigma
Aldrich, Na2SO4, $\geq 99.0\ \%$), sodium acetate (Sigma Aldrich, CH3COONa or
Na(Ac), $\geq 99.0\ \%$), and neodymium chloride hexahydrate (Sigma Aldrich,
$\mathrm{NdCl\textsubscript{3}\cdot(H_{2}O)_{6}}$, $\geq 99.0\ \%$), were
purchased from Sigma Aldrich. No additional purification was performed on the
substances.

###  2.2 SCWD apparatus

Before each experiment, feed solutions were prepared by weighing the salts
(Model MS 204S/03, Mettler Toledo®) and adding them to 2 L of distilled water
(see Table 1 for the feed compositions). The concentration of neodymium in
solutions was selected to be approximately 200 ppm (based on Nd3+),
considering the lowest detection limit of the ultraviolet-visible
spectrophotometer.

Table 1: Model feed compositions studied in this work. Each run was named as $b$ (binary), $c$ (chloride), $s$ (sulfate), and $a$ (acetate). Run | Anion (A) |  $c_{\mathrm{NaCl}}^{0}$ (ppm) |  $c_{\mathrm{NdCl_{3}}}^{0}$ (ppm) |  $c_{\mathrm{Na_{x}A_{y}}}^{0}$ (ppm)
---|---|---|---|---
$\mathrm{b1}$ | None | 10,168 | 0 | 0
$\mathrm{b2}$ | None | 0 | 344 | 0
$\mathrm{c1}$ | None | 1,067 | 347 | 0
$\mathrm{c2}$ | None | 10,168 | 332 | 0
$\mathrm{c3}$ | None | 104,547 | 334 | 0
$\mathrm{s1}$ | $\mathrm{SO_{4}^{2-}}$ | 9,924 | 334 | 590
$\mathrm{s2}$ | $\mathrm{SO_{4}^{2-}}$ | 9,681 | 349 | 1,181
$\mathrm{s3}$ | $\mathrm{SO_{4}^{2-}}$ | 8,952 | 347 | 2,954
$\mathrm{a1}$ | $\mathrm{CH_{3}COO^{-}}$ | 9,679 | 347 | 685
$\mathrm{a2}$ | $\mathrm{CH_{3}COO^{-}}$ | 9,190 | 343 | 1,371
$\mathrm{a3}$ | $\mathrm{CH_{3}COO^{-}}$ | 7,737 | 400 | 3,412
Figure 1: Schematic of the supercritical water desalination (SCWD) unit
designed and operated in this work: 1, model brine (feed); 2, high-pressure
liquid chromatography (HPLC) pump; 3, in-line check valve; 4, purge gas; 5,
ball valve; 6, vessel; 7, electrical heater; 8, pressure relief device; 9,
single-pass heat exchanger; 10, dome-type back pressure regulator (BPR)
connected to a forward pressure regulator; 11, distillate (effluent); 12,
needle valve; 13, 6000 psi argon cylinder.

Figure 1 shows the process flow diagram of the continuous desalination unit.
The unit is identical to the in-situ conductometric device described in our
earlier work [31]. In this work, the in-situ electrochemical sensor was
removed since the precipitates generated in concentrated brine feeds could
contaminate the electrodes.

In this unit, two high-pressure LS Class pumps (LS- Class Pump 903034 REV L,
Teledyne SSI) supply brine solution(s) from the bottom into a tubular vessel.
A split-type heater (A3653HC20EE, ThermCraft®) can heat the vessel to 500 ∘C.
Two thermocouples are used to measure and control the system temperature; one
of the thermocouples measures the solution temperature, and the other is
located outside the vessel and measures the vessel surface temperature. After
passing through the vessel, the solution is cooled by a single-pass heat
exchanger that uses water as a coolant (RTE-111, Neslab®). The operating
pressure is regulated by a back pressure regulator (BPR, A93VB, Parr
Instrument Company®) connected to a 40 MPa (6,000 psi) Argon cylinder ($\geq$
99.999 %, Matheson Tri-Gas®). The pressure of the BPR dome was regulated by a
spring-loaded forward pressure regulator (FPR, 44-1166-24, Tescom®).
Additional details are described elsewhere [31].

The basic operating procedure was as follows. Before every experiment, the
vessel was flushed with distilled water at 300 ∘C and 10 MPa for 3 hours.
Then, distilled water was continuously flowed for 3 hours to remove any
impurities or corrosion products. The vessel was dried at 120 ∘C overnight.
Then, the desalination vessel (c.a. 420 mL) was filled with the sample by
supplying feed solution at 20 mL/min. One liter of the feed solution was
supplied to the vessel to remove any remaining water or impurities within the
unit. Then, the feed flow rate was decreased to 3 mL/min, and the system
pressure was increased to 25 MPa. When the system reached the target pressure,
the temperature increased from 25 ∘C to 450 ∘C. Approximately 10 mL of the
effluent was collected when the system reached the target temperature for
compositional analysis.

Figure 2: (a) Bulk solution densities as a function of temperature and feed
concentration calculated from the Driesner correlation. (b) NaCl (aq)
concentrations in vapor and liquid phases above the phase separation
temperature ($T_{\mathrm{s}}$). Open circles and squares denote the vapor and
liquid branches, respectively. The colored open symbols are the distillate
concentrations obtained in this work (see Table and main text for the detailed
description of the feed composition in each run). The total concentration of
sodium in the distillates ($c_{\mathrm{Na}}^{\mathrm{D}}$) was slightly higher
than those from the Driesner model below 420 ∘C. This discrepancy mainly
occurs through either carryovers or some remaining salt solutions in the
cooling section.

Figure 2 (a) shows the bulk densities of NaCl (aq) at 25 MPa as a function of
temperature and NaCl concentrations calculated based on the Driesner
correlation [32, 33]. The densities of pure water were calculated from the
Wagner-Pruß Equation of State (EoS) [34]. All NaCl solutions studied in this
work ($w_{\mathrm{NaCl}}<10$ wt% where $w$ is the weight fraction) exist as
homogeneous compressed liquids below the vapor-liquid separation temperature
($T_{\mathrm{s}}=386.74\ ^{\circ}$C). Figure 2 (b) shows the NaCl partition
between vapor and liquid above $T_{\mathrm{s}}$. The phase coexistence lines
were also calculated from the Driesner correlation.

After the experiment was completed, the vessel was cooled and depressurized.
The cooled vessel was then disassembled and examined. When insoluble
precipitates were observed inside the vessel, they were collected by washing
the inner parts with distilled water and scraping the vessel’s bottom head and
wall. The collected precipitates were filtered, washed and sonicated in
distilled water, and dried overnight in an oven at 125 ∘C.

###  2.3 Analytical procedures

A sodium-selective electrode (LAQUAtwin Na-11 ion meter, Horiba®) was used to
measure the total concentration of sodium in the distillate (effluent). The
sodium-selective electrode was calibrated with standard solutions (150 ppm and
2,000 ppm) every day. The electrode resolution was 1 ppm ($0-99$ ppm), 10 ppm
($100-990$ ppm), and 100 ppm ($1,000-9,900$ ppm), and its accuracy level was
$\pm 10$ %, according to the manufacturer. For each sample, the measurements
were performed in triplicate.

An ultraviolet-visible spectrophotometer (Evolution 201, Thermo Scientific,
Inc.) was used to determine the total neodymium concentration in the effluent
($c_{\mathrm{Nd}}^{\mathrm{D}}$). When neodymium was added to the sample, a
strong absorption was observed at wavelengths around 574 nm. Thus, the
calibration curve was constructed by subtracting the minimum absorbance
strength (baseline) from the maximum absorbance around 574 nm (see the
ultraviolet spectra and calibration curve in the Supplementary Material). The
resultant calibration curve showed good linearity in the concentration range
from 20 to 4,000 ppm (based on the Nd3+ concentration). Below 20 ppm, the
height of the absorption peak became indistinguishable from the background
noise. The calibration curve was also tested against various samples that
contain other organic/inorganic species to check the interference effect. No
significant change was observed in the prominent peak of the ultraviolet
spectra and the readings from the sodium ion meter.

In order to characterize the precipitates obtained in the SCWD process,
skeletal density measurements, optical and scanning electron microscopy (SEM),
energy-dispersive X-ray spectroscopy (EDS), Fourier transform infrared
spectroscopy (FT-IR), and X-ray diffraction analysis (XRD) were conducted.
Skeletal density measurements were conducted on precipitates with a gas
pycnometer (AccuPyc II 1345, Micromeritics®) using helium as the analysis gas.
The densities were measured repeatedly, since some impurities (e.g., grahite
gasket) from the reactors were mixed with the samples. All samples were held
in a $0.1\ \mathrm{cm^{3}}$ sample cell.

Field-emission scanning electron microscopy (FE-SEM, FEI InspectTM) and
energy-dispersive X-ray spectroscopy (EDS) techniques were employed to observe
the morphology of the precipitates and confirm the presence of neodymium. The
samples were prepared by dispersing the precipitates on a carbon tape adhered
to an aluminum stub. Precipitates were coated with gold (c.a. 5 nm) using a
sputter coater (Q150R, Quorum Technologies, Ltd.) to maximize X-ray counts
during EDS and minimize charging effects. A roughly 5 min. EDS scan at low
resolution was adequate to show the presence of neodymium in the precipitates
with a high degree of certainty. The precipitate color was demonstrated by
imaging the crystals with a digital optical microscope (VHX-7000, Keyence).
The precipitate was imaged on a reflective stage using white, combined ring
and confocal lighting at $300\times$ zoom. A digital image was taken through
the microscope lens with the fully integrated head (VHX-7100, Keyence).

ATR-FTIR analysis was performed with a PIKE Technologies VeeMAX III ATR
accessory on a Thermo Fisher Nicolet 6700 FTIR spectrometer (resolution: $2\
\mathrm{cm}^{-1}$, 64 scans). The single bounce Zn/Se crystal temperature was
maintained at 35 ∘C with a temperature controller (GladiATRTM, PIKE
Technologies). The samples were clamped with $0.2\ \mathrm{N{\cdot}m}$ of
torque to ensure contact with the crystal. Since some parts of the graphite
gaskets detached from the desalination unit were mixed with the precipitates,
the baseline slope had to be corrected. The baseline correction and the
signal-to-noise ratio enhancement were performed based on the correction
algorithm by Zhang et al. [35] and the Savitzky-Golay filter [36].

Wide angle X-ray diffraction (XRD) analysis was performed to investigate
crystal structure of the precipitates. A diffractometer with a graphite
diffracted beam monochromator (Siemens D5000) was used for the investigation
and Cu K$\alpha$ (1.54 Å) was a source for the radiation. The XRD spectra were
obtained at 2$\theta$ angle range from 5∘ to 60∘ with a scanning speed of
0.4∘/ min. The detailed experimental procedure was also presented in the
previous report by Zhao et al. [37]. The measured spectra were analyzed by
comparing them with theoretical spectra calculated from the unit cell
structures. The unit cell structures were obtained from Crystallography Open
Database (COD) [38] and Inorganic Crystal Structure Database (ICSD) [39].

###  2.4 Theoretical analysis

To elucidate the behavior of electrolyte solutions at elevated temperatures
and pressures, we performed ion speciation calculations at different
temperatures along the 25 MPa isobar. When cation(s) $\mathrm{C}$ and anion(s)
$\mathrm{A}$ form an ion pair $\mathrm{P}$, the chemical equilibrium between
these species is represented as:

$\nu_{\mathrm{C}}\mathrm{C}+\nu_{\mathrm{A}}\mathrm{A}\rightleftharpoons\mathrm{P}$
(1)

where $\nu_{\mathrm{i}}$ denotes the stoichiometric coefficients of the
species $i$ forming the ion pair $\mathrm{P}$. The ion association constant of
this reaction $K_{\mathrm{a,c}}$ in molarity scale is given as:

$K_{\mathrm{a,c}}=\frac{a_{\mathrm{P}}}{a_{\mathrm{A}}^{\mathrm{\nu_{A}}}a_{\mathrm{B}}^{\mathrm{\nu_{B}}}}=\frac{c_{\mathrm{P}}}{c_{\mathrm{A}}^{\mathrm{\nu_{A}}}c_{\mathrm{B}}^{\mathrm{\nu_{B}}}}f_{\mathrm{P}}^{-1}$
(2)

where $a_{\mathrm{i}}$ is the activity of the species $i$, a product of the
concentration $c_{\mathrm{i}}$ and the activity coefficient $y_{\mathrm{i}}$.
The activity coefficient ratio is denoted as $f_{\mathrm{P}}$. The molarity-
based association constant was obtained by converting the molality-based
constant ($K_{\mathrm{a,m}}$) following the formula given by Robinson and
Stokes [40]. In the conversion from molality to molarity, solution density is
required. Since the feed concentration of sodium chloride was much higher than
the other salts, we assumed that the density of the mixed electrolyte solution
was essentially equal to the density of NaCl (aq) calculated from the Driesner
model.

Figure 3: Chemical speciation algorithm designed in this work. The DEWPython
library was connected to the mean spherical approximation (MSA) algorithm to
obtain the association constants and activity coefficients. Chemical
equilibria together with the mass and charge balance equations were solved by
using the Newton-Krylov method. For the detailed description, see the
Supplementary Material. $\Gamma$ denotes the screening parameter, a key
parameter in the MSA calculation.

Figure 3 shows the ion speciation calculation procedure used in this work. In
this procedure, ion association constants and activity coefficients are first
calculated. Most ion association constant data were obtained from the modified
Helgeson-Kirkham-Flowers (HKF) model, also known as the Deep Earth Water (DEW)
model [41, 42, 43, 44, 45, 46, 47]. The DEWPython module [48], a python-based
software to calculate the thermodynamic properties in high-temperature brines,
was connected to the activity coefficient calculation algorithm. DEW model
provides a general thermodynamic framework to predict a wide range of
geophysical properties. However, the predicted properties disagree with
experimental measurements in some substances. For instance, the first and the
second ion association constants between neodymium and chloride ions from
experiments and MD simulations [49, 50, 51, 52] are considerably different
from those predicted by the DEW parameters proposed by Haas et al. [53]. Thus,
when the discrepancy is considerable, or no HKF parameter is available (e.g.,
$\mathrm{Nd(SO_{4})_{2}}^{-1}$ [54, 55] and $\mathrm{(Na_{2}SO_{4})}^{0}$
[56]), empirical results were chosen by comparing literature (See the
Supplementary Material for the detailed description).

A variety of activity coefficient models have been proposed, including Debye-
Hückel equation, Helgeson equation [57], Bromley equation [58], Pitzer
equation [59], and mean spherical approximation (MSA) [60]. We used the MSA
model to calculate the activity coefficients since it will also be used to
estimate thermophysical properties from conductance measurements [61] in our
future work. The MSA model dissects the activity coefficient into hard-sphere
($y_{\mathrm{i}}^{\mathrm{hs}}$) and electrostatic contributions
($y_{\mathrm{i}}^{\mathrm{el}}$) as
$\ln{y_{\mathrm{i}}}=\ln{y_{\mathrm{i}}^{\mathrm{hs}}}+\ln{y_{\mathrm{i}}^{\mathrm{el}}}$.
Each contribution was calculated based on hard-sphere radii, charge, and
number density of ionic species (see the Supplementary Material for the
detailed calculation procedure for the activity coefficients).
Crystallographic radii taken from Marcus [62] were used as the hard-sphere
radii. In calculating the electrostatic part, the Bjerrum radius (instead of
the hard-sphere radius) was used, following the suggestion by Sharygin et al.
[63]. Since the activity coefficients in the MSA framework depend on the
concentration of charged species in a system, an iterative procedure was
required.

After determining the activity coefficients and the association constant, the
ion speciation calculation was conducted by solving the mass balance and the
electroneutrality condition (charge balance). For instance, the concentration
of each species in Eq. (2) can be obtained by solving the following set of
equations.

$c_{\mathrm{C}}^{0}=c_{\mathrm{C}}+\nu_{\mathrm{C}}c_{\mathrm{P}}$ (3a)
$c_{\mathrm{A}}^{0}=c_{\mathrm{A}}+\nu_{\mathrm{C}}c_{\mathrm{P}}$ (3b)
$c_{\mathrm{P}}=K_{\mathrm{a}}f_{\mathrm{P}}c_{\mathrm{C}}^{\mathrm{\nu_{C}}}c_{\mathrm{A}}^{\mathrm{\nu_{A}}}$
(3c)

Although this simple example is analytically solvable, the ion speciation
procedure in our system is much more complex since (1) neodymium ion shifts
the pH by making hydroxide complexes, and (2) it makes multiple ion pairs. For
instance, in “simple” NdCl3 (aq), at least nine chemical equilibria should be
considered.

$\mathrm{Nd^{3+}}+n\mathrm{Cl^{-}}\rightleftharpoons{(\mathrm{NdCl}_{n})^{3-n}}$
(4a)
$\mathrm{Nd^{3+}}+n\mathrm{(OH)^{-}}\rightleftharpoons{[\mathrm{Nd(OH)}_{n}]^{3-n}}$
(4b) $\mathrm{H^{+}}+\mathrm{(OH)^{-}}\rightleftharpoons\mathrm{H_{2}O}$ (4c)

where the stoichiometric coefficient $n$ varies from one to four. Note that we
neglected the formation of mixed ion pairs (e.g.,
${\mathrm{Nd(OH)}_{m}\mathrm{(Cl)}_{n}}$) due to the absence of ion
association constants. Nevertheless, the concentration of twelve ionic species
should be solved simultaneously. The conjugated direction method proposed by
Powell [64] was adopted to solve this set of equations. Since the solution
does not converge easily [65], different initial estimates were attempted for
each system. When a stable solution was obtained, the calculation was repeated
until the concentrations of all species converged. Considering that a
description of the calculation details and all relevant assumptions is quite
lengthy, all procedures are described in detail in the Supplementary Material.

##  3 Results and Discussion

Figure 4: (a) Sodium ($c_{\mathrm{Na}}^{\mathrm{D}}$) and (b) neodymium
($c_{\mathrm{Nd}}^{\mathrm{D}}$) concentrations in the effluents (distillates)
as a function of the operating temperature in binary systems. The onset
temperatures ($T_{\mathrm{on}}$) were obtained as 381.6 (Run $\mathrm{b1}$)
and 329.4 ∘C (Run $\mathrm{b2}$), respectively. The onset temperature in Run
$\mathrm{b1}$ is close to the phase separation temperature $T_{\mathrm{s}}$,
suggesting that the decrease in $c_{\mathrm{Na}}^{\mathrm{D}}$ mainly
originates from the phase separation. Ion speciation in these systems [(c) and
(d)] demonstrates that the temperature dependence of the ion association
behaviors in these systems is also completely different.

Figure 4 shows the sodium and neodymium concentrations in effluents
($c_{\mathrm{Na}}^{\mathrm{D}}$ and $c_{\mathrm{Nd}}^{\mathrm{D}}$) as a
function of temperature in the Runs $\mathrm{b1}$ and $\mathrm{b2}$. In both
runs, only a single salt was dissolved in the distilled water. No appreciable
decrease in $c_{\mathrm{Na}}^{\mathrm{D}}$ was observed in the sodium chloride
solution ($c_{\mathrm{Na}}^{0}=4,000$ ppm) until the system temperature
reached 385 ∘C. When the operating temperature was beyond that threshold
temperature, the volumetric flow rate of the effluent increased significantly,
and the $c_{\mathrm{Na}}^{\mathrm{D}}$ profile showed a sharp decrease. This
behavior suggests that the $c_{\mathrm{Na}}^{\mathrm{D}}$ profile change is
almost purely attributed to vapor/liquid separation in the solution. According
to the Driesner correlation, the phase separation in NaCl (aq) systems at 25
MPa occurs at 386.74 °C (Figure 2). The effluent concentrations obtained from
different experiments (Runs $\mathrm{b1}$, $\mathrm{c1}$, $\mathrm{c2}$, and
$\mathrm{c3}$) agree well with the vapor composition line calculated from the
Driesner correlation, except for data very near the threshold temperature.
These results suggest that the operating conditions with the desalination unit
are close to equilibrium. The discrepancies observed near the phase separation
temperature likely arise from liquid remaining in the single-pass heat
exchanger and/or back-pressure regulator or possibly carry-over of the
concentrated brine from the vessel.

The temperature dependence of the concentration profiles along the isobar is
well described by a generalized logistic equation (Richards equation [66]),
which is expressed as:

$\frac{c_{\mathrm{i}}-c_{\mathrm{i}}^{\mathrm{min}}}{c_{\mathrm{i}}^{0}-c_{\mathrm{i}}^{\mathrm{min}}}=\frac{1}{\left[1+\exp\left[a(T-T_{\mathrm{thr}})\right]\right]^{b}}$
(5)

where $c_{\mathrm{i}}$ is the concentration of the species $i$ in ppm, and
$c_{\mathrm{i}}^{0}$ is the feed concentration. Other quantities
$c_{\mathrm{i}}^{\mathrm{min}}$, $a$, $b$, and $T_{\mathrm{thr}}$ are
adjustable parameters. The onset temperature $T_{\mathrm{on}}$ where the
concentration profile starts to decrease steeply was calculated from Eq. 5.
From tedious but straightforward algebra, it is obtained as:

$T_{\mathrm{on}}=T_{\mathrm{thr}}+\frac{2}{ab}(1-2^{b})$ (6)

where $a$ and $b$ are the adjustable parameters in Eq. 5. In Run $\mathrm{b1}$
(NaCl), $T_{\mathrm{on}}$ was obtained as 381.6 ∘C, close to the phase
separation temperature. Thus, NaCl separation should be driven only by phase
separation. On the other hand, the onset temperature in Run $\mathrm{b2}$
(NdCl3) was calculated as 329.4 ∘C. Although the onset temperature for
neodymium chloride is significantly lower than that of sodium chloride, it
should be noted that a considerable amount of neodymium
($c_{\mathrm{Nd}}^{\mathrm{D}}=59.3$ ppm) still exists in the effluent at 385
∘C.

Ion speciation analysis on these binary systems suggests that their ion
association behaviors are entirely different. In Run $\mathrm{b1}$, no
appreciable ion pair formation occurs up to 243 ∘C; thermal/kinetic energy can
easily overcome the ion aggregation induced by the decrement in the dielectric
constant. Above 243 ∘C, a decrease in the dielectric constant of water
stabilizes ion pairs. The temperature where the free ion concentration starts
to decrease is close to the threshold temperature found using molecular
dynamics (MD) simulations and separate experimental measurements [67, 31]. On
the other hand, the free ion concentration in Run $\mathrm{b2}$ showed an
almost sigmoidal dependence on temperature. It starts to decrease near 150 ∘C.
Interestingly, neodymium hydroxide [$\mathrm{Nd(OH)}^{2+}$] and neodymium
monochloride [$\mathrm{NdCl}^{2+}$] are formed as dominating species below 300
∘C. The formation of neodymium hydroxide complex suggests that multiple ion
aggregation (e.g., ${\mathrm{Nd}^{3+}+x\mathrm{Cl}^{-}+y\mathrm{(OH)}^{-}}$),
which could not be considered in the theoretical calculation due to the lack
of the association constants, would play an important role in decreasing
$c_{\mathrm{Nd}}^{\mathrm{D}}$; the decrease in $c_{\mathrm{Nd}}^{\mathrm{D}}$
observed in the experiment is significantly affected by the pH level [68].

Figure 5: The concentration of (a) sodium ($c_{\mathrm{Na}}^{\mathrm{D}}$) and
(b) neodymium ($c_{\mathrm{Nd}}^{\mathrm{D}}$) in the distillate as a function
of the NaCl feed concentration and temperature in the NaCl/NdCl3 mixtures (25
MPa). Despite the significant change in the NaCl feed concentration, the
normalized sodium concentration in the effluent
($c_{\mathrm{Na}}^{\mathrm{D}}/c_{\mathrm{Na}}^{0}$) shows an almost identical
dependence on temperature. This result suggests that the separation of sodium
ions would be driven by the phase change. On the contrary,
$c_{\mathrm{Nd}}^{\mathrm{D}}$ shows a complex temperature/concentration
dependence. Ion speciation analyses in (c) and (d) demonstrate that ion pair
formation between $\mathrm{Nd}^{3+}$ and $\mathrm{Cl^{-}}$ is facilitated as
$c_{\mathrm{Na}}^{0}$ increases. The presence of $\mathrm{Nd^{3+}}$ does not
have a significant influence on the formation of $\mathrm{(NaCl)^{0}}$.

Next, we examine the influence of NaCl concentration in the feed solution
(Figure 5 (a) and (b), Runs $\mathrm{c1-c3}$). Although
$c_{\mathrm{Na}}^{\mathrm{0}}$ was changed one hundredfold (from 420 to 41,128
ppm) and neodymium chloride was added in the feed,
$c_{\mathrm{Na}}^{\mathrm{D}}$ did not show a significant change. This result
again confirms that sodium chloride precipitation is mainly driven by the
vapor-liquid separation at 386.74 ∘C. On the contrary,
$c_{\mathrm{Nd}}^{\mathrm{D}}$ profile was notably affected by
$c_{\mathrm{Na}}^{0}$. As $c_{\mathrm{Na}}^{0}$ increased, the onset
temperature of $\mathrm{Nd}^{3+}$ decreased from 277.5 (Run $\mathrm{c1}$) to
255.7 (Run $\mathrm{c2}$) to 191.8 ∘C (Run $\mathrm{c3}$). Moreover,
$c_{\mathrm{Nd}}^{\mathrm{D}}$ showed a double-sigmoidal behavior in Run
$\mathrm{c3}$. It decreased sharply at the first onset temperature, decreased
slowly between 191.8 to 310 ∘C, and then decreased sharply again. Ion
speciation analysis results [Figure 5 (c) and (d)] explain the decrease in
$T_{\mathrm{on}}$. As the chloride ion concentration increases, the chemical
equilibrium between $\mathrm{Nd^{3+}}$ and $\mathrm{Cl^{-}}$ is shifted,
facilitating the formation of ion pairs. As a result, $\mathrm{NdCl_{2}^{+}}$
becomes a dominating species among Nd-containing ion aggregates.

There are two possible contributions to the double-sigmoidal behavior in
$c_{\mathrm{Nd}}^{\mathrm{D}}$ profile (Run $\mathrm{c3}$) at high
temperatures. First, as given in Figure 2 (a), the solution density in Run
$\mathrm{c3}$ is much higher that in other Runs. High solution density results
in the solubility increase of neutral species not considered in the numerical
calculation (e.g., ${\mathrm{Nd(OH)}_{n}\mathrm{Cl}_{(3-n)}}$). Second, it
should be noted that the dielectric constant of pure water was only used in
this work. Indeed, the presence of NaCl in aqueous media can increase the
dielectric constant in high-temperature brines. In a highly polar medium like
ambient water, the addition of salts typically decreases the dielectric
constant, which arises from kinetic depolarization [69]. In a low-dielectric
medium, the formation of multiple ion aggregates enhances the mean dipole
moment in a system [70]. Our recent MD simulations on high-temperature NaCl
solutions modeled with several different molecular models also support the
idea that the dielectric constant of high-temperature brine is increased as
the brine concentration increases at simulated pressures of 20 MPa
(approximately 30 MPa in reduced units) [71]. According to the MD simulations,
a dielectric constant increment is observed when the temperature is above the
critical temperature of pure water. This dielectric enhancement will also
increase the solubility of free neodymium ions and charged ion pairs. The
overall results suggest that the presence of NaCl can alter the precipitation
behavior of NdCl3. This phenomenon has great potential to be utilized in
controlling the selective recovery of neodymium from highly concentrated
brines.

Figure 6: Concentration of neodymium ions in (a) NaCl/NdCl3/Na2SO4 systems
(Runs $\mathrm{s1-s3}$) and (b) NaCl/NdCl3/NaAc systems (Runs
$\mathrm{a1-a3}$). In the sulfate systems, the onset temperature of neodymium
slightly increased as the sodium sulfate concentration in the feed solution
increased. This behavior reflects the retrograde solubility of sulfate salts
in the system. On the contrary, the onset temperature in the acetate systems
decreased as the sodium acetate concentration increased. Ion speciation
analyses given in (c) and (d) show that the ion aggregation tendency in water
is $\mathrm{Cl^{-}<Ac^{-}\ll{SO_{4}^{2-}}}$ below the onset temperatures, as
demonstrated in room temperature experiments [72, 68]. Note that the fraction
of hydroxide complex $\mathrm{Nd(OH)^{2+}}$ is very high in acetate systems,
which explains the formation of water-insoluble precipitates in these Runs.
For other species, see the Supplementary Material.

Next, we examined the influence of different anions on neodymium ion
concentration in the effluent. Figure 6 (a) and (b) shows the concentration of
neodymium ions in NaCl/NdCl3/Na2SO4 systems (Runs $\mathrm{s1-s3}$) and in
NaCl/NdCl3/NaAc systems (Runs $\mathrm{a1-a3}$). Consistent with the previous
operations, sodium concentrations in the effluent were not affected by the
presence of neodymium or other anions (see the numerical data in the
Supplementary Material). On the other hand, the onset temperature of neodymium
in sulfate-containing systems was altered significantly.
$T_{\mathrm{on}}^{\mathrm{sulfate}}$ was obtained as 131.0, 141.2, and 162.6,
∘C as the sodium sulfate concentration in the feed increased. That is, the
addition of sulfate increased the onset temperature slightly. This behavior
could come from the retrograde solubility of neodymium sulfate, which is
commonly observed in sulfate systems [55, 73]. Even though the sulfate salts
show retrograde behavior, the average onset temperature in NaCl/NdCl3/Na2SO4
systems was quite a bit lower (145 ∘C) compared to non-sulfate systems. It is
even lower than that obtained from Run c3
($T_{\mathrm{on}}^{\mathrm{c3}}=191.8\ ^{\circ}$C).

These results can also be understood from the ion speciation analyses [Figure
6 (c)]. When sulfate exists, $c_{\mathrm{Nd}}$ shows a steep decrease with
increasing temperature, and $\mathrm{(NdSO_{4})^{+}}$ becomes a dominating
species below the onset temperatures. The concentrations of chloride and
hydroxide complexes were much lower than those in NaCl/NdCl3 systems.

When sodium acetate (NaAc) was added, the onset temperature changed from 169.1
(Run $\mathrm{a1}$) to 161.0 (Run $\mathrm{a2}$) to 143.2 ∘C (Run
$\mathrm{a3}$). The onset temperature was decreased as the sodium acetate
concentration increased, and no retrograde behavior was observed. The average
onset temperature was higher than that of the sulfate systems. In the ion
speciation analysis, the fractions of free neodymium ions in the acetate
systems were higher than those in the sulfate systems but lower than those in
the chloride systems below the onset temperatures. Similar to the sulfate
systems, only a small amount of neodymium chloride complexes (see Figure S4)
were observed. However, the dominating species near the onset temperatures
were not neodymium acetate but neodymium hydroxide complexes. The fraction of
hydroxide complexes is significantly increased due to the pH shift induced by
sodium acetate. Since acetic acid is an associating acid, hydrogen ions in
water make $\mathrm{(HAc)^{0}}$ complexes while increasing the pH level. The
overall results suggest that the ion aggregation tendency is
$\mathrm{Cl^{-}<Ac^{-}\ll{SO_{4}^{2-}}}$, which agrees with earlier studies at
ambient conditions [72, 68].

Although the neodymium-acetate ion pair formation is not as prevalent as
neodymium-sulfate ion association, we did observe that insoluble precipitates
were obtained after all acetate runs (Runs $\mathrm{a1-a3}$), whereas no
insoluble precipitates were obtained in the other experiments. Three types of
reactions are likely responsible for the generation of water-insoluble
precipitates. First, thermal decarboxylation of sodium acetate yields methane
and carbon dioxide in hydrothermal environments according to:

$\mathrm{2CH\textsubscript{3}COONa+H\textsubscript{2}O\rightarrow
2CH\textsubscript{4}+Na\textsubscript{2}CO\textsubscript{3}+CO\textsubscript{2}}$
(7)

Carbon dioxide generated in this reaction can make ion pairs with the
dissolved neodymium ions. The decarboxylation/oxidation mechanism and role of
experimental factors, including reactor surface, catalyst, temperature,
pressure, pH, and feed concentration, have been studied extensively [74, 75,
76, 77, 78, 79]. There are some variations in the threshold temperature for
this reaction, but it is generally accepted that the decomposition readily
occurs above 400 ∘C. In this route, double carbonate salt
($\mathrm{NaNd(CO_{3})_{2}}$) (instead of neodymium carbonate
$\mathrm{Nd_{2}(CO_{3})_{3}}$) is known to be preferred [80, 81, 82].
Considering that $c_{\mathrm{Nd}}^{\mathrm{D}}$ decreased significantly below
250 ∘C, this reaction mechanism would not significantly contribute to the
formation of insoluble precipitates. Another possible mechanism is the thermal
degradation of neodymium acetate. When exposed to high temperatures, neodymium
acetate [Nd(Ac)3] is degraded to neodymium monohydroxide acetate
(Nd(OH)(Ac3)2), $334-345\ ^{\circ}$C), neodymium monoxide carbonate
(Nd2O(CO3)2), $359-370\ ^{\circ}$C), neodymium dioxide carbonate (Nd2O2CO3),
$371-410\ ^{\circ}$C) and neodymium oxide (Nd2O3, $684-700\ ^{\circ}$C) [83,
84]. Lastly, hydrothermal synthesis of neodymium hydroxide [Nd(OH)3] or
hydroxide-containing crystals (e.g., Nd(OH)2.45(Ac)0.55 [84] or Nd(OH)2Cl [85,
86]) would be feasible, depending on the reaction environment.

Together with the ion speciation analyses above [Figure 6 (d)], we
characterized the precipitate to elucidate what types of water-insoluble
precipitates were obtained in Runs $\mathrm{a1-a3}$. The skeletal densities of
our samples were obtained as $\rho_{\mathrm{sk}}=4.674\pm 0.084\
\mathrm{g/cm^{3}}$ (Run $\mathrm{a1}$), $\rho_{\mathrm{sk}}=4.398\pm 0.364$
$\mathrm{g/cm^{3}}$ (Run $\mathrm{a2}$), and $\rho_{\mathrm{sk}}=4.892\pm
0.344$ $\mathrm{g/cm^{3}}$ (Run $\mathrm{a3}$). Theoretical skeletal densities
of some neodymium crystals were obtained either directly from literature or by
calculating the X-ray densities from the unit cell structures. They are given
as $\rho_{\mathrm{sk}}^{\mathrm{Nd(Ac)_{3}}}$=2.179 $\mathrm{g/cm^{3}}$ [87],
$\rho_{\mathrm{sk}}^{\mathrm{Nd(OH)_{2}(Cl)}}$=4.730 $\mathrm{g/cm^{3}}$ [85],
$\rho_{\mathrm{sk}}^{\mathrm{Nd(OH)_{3}}}$=4.777 $\mathrm{g/cm^{3}}$ [88],
$\rho_{\mathrm{sk}}^{\mathrm{Nd(OH)CO_{3}}}$=4.510 $\mathrm{g/cm^{3}}$ [89],
$\rho_{\mathrm{sk}}^{\mathrm{Nd_{2}O_{2}(CO)_{3}}}$=6.331 $\mathrm{g/cm^{3}}$
[90], and $\rho_{\mathrm{sk}}^{\mathrm{Nd_{2}O_{3}}}$=7.24
$\mathrm{g/cm^{3}}$. Assuming that adsorbed water molecules do not
significantly influence the measurement results, the density of the obtained
precipitates is close to hydroxide-containing crystals.

Figure 7: Characterization of the precipitates obtained in Run
$\mathrm{a1-a3}$. (a) Optical spectroscopy image of the precipitate from Run
$\mathrm{a1}$. The precipitate color is pinkish. (b) SEM-EDS analyses on the
samples obtained in Run $\mathrm{a2}$. The energy-dispersive X-ray
spectroscopy reveals that the water-insoluble precipitates contain neodymium.
(c) Infrared (IR) spectra of the neodymium-bearing precipiates from Run
$\mathrm{a3}$. The IR spectrum suggests that the precipitate contains
hydroxide group and neodymium. (d) X-ray diffraction spectrum of the
precipitate obtained in Run $\mathrm{a3}$ (top) and the theoretical XRD
spectrum calculated from the unit cell structure of Nd(OH)3 (bottom). The
consistency between the spectra suggests that the precipitate mainly consists
of neodymium and hydroxide (with some impurities).

Figure 7 (a) and (b) shows the appearance of the obtained precipitates. The
precipitates were pinkish to the naked eye and under white light, which is a
general color observed in neodymium salts. SEM/EDS analysis revealed that the
obtained crystals definitely do contain neodymium and have a rod-like shape.
Figure 7 (c) shows the FT-IR spectra of the precipitates. They suggest that
the precipitate contains the hydroxide group ($\mathrm{OH}$), which shows a
sharp absorption peak at 3610 $\mathrm{cm}^{-1}$. A strong peak around 680
$\mathrm{cm}^{-1}$ corresponds to the Nd-OH interaction, which is observed in
oxygen-containing neodymium salts such as neodymium acetate [84]. Many weak
signals were observed within 950-1600 $\mathrm{cm^{-1}}$, which might be
relevant to the carboxyl group (1560 $\mathrm{cm^{-1}}$) and the methyl group
(1153 $\mathrm{cm^{-1}}$) observed in $\mathrm{Nd(Ac)_{3}}$ crystals [83].
However, they could not be clearly distinguished since the signal strength was
relatively weak. Figure 7 (d) shows the X-ray diffraction spectrum of the
precipitates from Run $\mathrm{a3}$. In all samples, the prominent peaks in
the spectrum match with those observed in the neodymium hydroxide (see the
Supplementary Material). The X-ray diffraction spectra of other potential
substances (e.g., Nd2CO3 and Nd2O3) did not show a complete match with that of
the precipitate. Similar to the FT-IR spectra, the diffraction spectra in
other samples were similar except that there were some shifts in peak
positions and non-identifiable peaks. Considering all characterization
results, the obtained precipitates would mainly consist of neodymium hydroxide
with some low-concentration anions such as acetate, carbonate, and chloride.
Kȩpiński, Zawadzki and Mis̀ta, for instance, obtained
Nd(OH)2.45(Ac)0.55$\cdot$0.45H2O crystals by a hydrothermal reaction of
neodymium acetate [84]. Overall, this result suggests that the selective
recovery of neodymium from concentrated brine solutions in a water-insoluble
precipitate form would be feasible by adding acetate.

##  4 Conclusions

In this work, a series of supercritical water desalination experiments were
conducted on model brines that consist of water, sodium chloride, neodymium
chloride, sodium acetate, and sodium sulfate from 20 to 450 ∘C along an isobar
of 25 MPa.

The distillate concentration of sodium chloride, one of the most common salts
in nature, shows a drastic decrease when vapor-liquid separation occurs at 387
∘C. NaCl distribution between the distillate and bottoms was not affected
significantly by other salts or their feed concentration. This result suggests
that vapor-liquid separation is primarily responsible for the sodium chloride
separation in the SCWD process.

In contrast, neodymium (one of the most sought-after rare earth elements)
shows a noticeable dependence on the brine composition. The onset temperature
where the neodymium concentration in the effluent decreases is reduced
dramatically when the sodium chloride concentration is high or small amounts
of sulfate or acetate salts exist in the feed. Ion speciation analysis
suggests that ion pair formation of the neodymium with anions is responsible
for this change.

When sodium acetate is added to the brine, a water-insoluble precipitate is
obtained. Characterization of the precipitates suggest that this insoluble
precipitate is predominantly neodymium hydroxide with some impurities such as
acetate, chloride, and carbonate.

This work examined whether supercritical water desalination can be utilized
for selective recovery of critical materials while simultaneously producing
potable water. The experimental and theoretical calculations suggest that it
has a considerable potential to retrieve critical materials by way of either
liquid adducts (concentrate) or water-insoluble salts. Taking into account
that (1) supercritical water desalination is insensitive to organic impurities
in the feed and (2) the concentration of critical materials in wastewater or
some natural water sources can be relatively high (ppm levels), it is expected
that the supercritical desalination with co-product production may prove to be
an attractive option for economically viable and environmentally benign zero-
liquid discharge desalination. It will be interesting to study feed solutions
containing other naturally common salts or industrially essential elements to
further test the applicability of the supercritical water desalination process
with selective recovery of valuable components.

## Acknowledgement

This work was supported by the Director’s Postdoctoral Fellow Program
(20190653PRD4) and the Laboratory Directed Research and Development Program
(20190057DR) at Los Alamos National Laboratory.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or
personal relationships that could have influenced the work reported in this
paper.

## CRediT authorship contribution statement

Tae Jun Yoon: Conceptualization; Methodology; Software; Validation; Formal
analysis; Investigation; Data Curation; Writing - Original Draft; Writing -
Review & Editing; Visualization; Funding acquisition Erica P. Craddock: Formal
analysis; Writing - Review & Editing Jeremy C. Lewis: Formal analysis; Writing
- Review & Editing John A. Matteson: Formal analysis; Writing - Review &
Editing Jong Geun Seong: Formal analysis; Writing - Review & Editing Rajinder
P. Singh: Resources; Writing - Review & Editing Katie A. Maerzke: Writing -
Review & Editing; Funding acquisition Robert P. Currier: Writing - Review &
Editing; Supervision; Project administration; Funding acquisition Alp T.
Findikoglu: Writing - Review & Editing; Supervision; Funding acquisition

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